For a collection of numbers to be considered a sequence, it is essential that they have a law of formation, are ordered in a specific manner, and can be either finite or infinite.
B: They have a law of formation:
A sequence is a set of numbers arranged in a specific order according to a rule or pattern. The numbers in a sequence are not random but follow a specific law of formation.
This law can be a mathematical formula, a recursive relationship, or any other systematic pattern that determines the values of the sequence. Without a well-defined law of formation, a collection of numbers cannot be considered a sequence.
C: They are ordered:
In a sequence, the numbers are arranged in a specific order or sequence. The order of the numbers is crucial and defines the pattern and structure of the sequence.
Each number in the sequence has a unique position or index that determines its place in the sequence. The order of the numbers allows us to identify the next number or predict the pattern of the sequence. Without the concept of order, the numbers would simply be a set of unrelated elements and not a sequence.
A: They may or may not be infinite:
Sequences can be finite or infinite. A finite sequence has a specific number of terms, and once the pattern or rule is established, the sequence ends.
On the other hand, an infinite sequence continues indefinitely, and its terms extend infinitely in one direction or both directions. Whether a sequence is finite or infinite depends on the context and the specific rule or pattern that governs its formation.
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Note: the translated question is:
To have a sequence it is essential that the numbers that form it:
A: be infinite
B: they have a law of formation C: they are ordered
The midpoint of AB is M(-4,2). If the coordinates of A are (-7,3), what are the
coordinates of B?
The midpoint of AB is M(-4,2). If the coordinates of A are (-7,3), and the coordinates of B is (-1, 1).
To find the coordinates of point B, we can use the midpoint formula, which states that the coordinates of the midpoint between two points (A and B) can be found by averaging the corresponding coordinates.
Let's denote the coordinates of point A as (x1, y1) and the coordinates of point B as (x2, y2). The midpoint M is given as (-4, 2).
Using the midpoint formula, we can set up the following equations:
(x1 + x2) / 2 = -4
(y1 + y2) / 2 = 2
Substituting the coordinates of point A (-7, 3), we have:
(-7 + x2) / 2 = -4
(3 + y2) / 2 = 2
Simplifying the equations:
-7 + x2 = -8
3 + y2 = 4
Solving for x2 and y2:
x2 = -8 + 7 = -1
y2 = 4 - 3 = 1
Therefore, the coordinates of point B are (-1, 1).
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Un chavo mide 3 pulgadas + un 1/4 de pulgada y otro mide 9.045 cm que diferencia de tamaño hay entre ellos
The difference in size between the two guys is approximately -0.3108 inches, which implies that the first guy is bigger than the second guy.
To calculate the difference in size between two people, one measuring in inches and the other measuring in centimeters, we must first convert all measurements to a common unit.
Guy measures 3 inches + 1/4 inch. We can convert 1/4 inch to a decimal fraction by dividing 1 by 4, which gives us 0.25 inches. So your measurement in inches would be 3 + 0.25 = 3.25 inches.
The other guy measures 9.045 cm. To convert centimeters to inches, we use the following relationship: 1 cm = 0.3937 inches. Multiplying the measurement in centimeters by 0.3937, we get the measurement in inches: 9.045 cm * 0.3937 = 3.5608 inches (approximately).
Now we can calculate the size difference between them. We subtract the measurement of the second chavo (3.5608 inches) from the measurement of the first chavo (3.25 inches):
3.25 inches - 3.5608 inches = -0.3108 inches.
The resulting difference is -0.3108 inches. This means that the second chavo is smaller in size than the first. Since the difference is negative, it indicates that the first chavo is bigger than the second.
In summary, the difference in size between the two guys is approximately -0.3108 inches, which implies that the first guy is bigger than the second guy.
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What is the volume of this
figure?
A 774 cm³
B 3,546 cm³
C 843 cm3
D 2,250 cm³
Hello!
V
= (18cm * 15cm * 6cm) + ((13cm - 6cm) * 15cm * 6cm)
= 1,620cm³ + 630cm³
= 2,250cm³
Which expression is equivalent to 10f - 5f + 8 +6g +4?
The given expression, 10f - 5f + 8 + 6g + 4, simplifies to 5f + 12 + 6g when like terms are combined.
To simplify the expression 10f - 5f + 8 + 6g + 4, we can combine like terms by adding or subtracting coefficients that have the same variables:
10f - 5f + 8 + 6g + 4
Combining the terms with 'f', we have:
(10f - 5f) + 8 + 6g + 4
This simplifies to:
5f + 8 + 6g + 4
Next, we can combine the constant terms:
8 + 4 = 12
Thus, the simplified expression is:
5f + 12 + 6g
This expression is equivalent to 10f - 5f + 8 + 6g + 4.
In summary, the expression 10f - 5f + 8 + 6g + 4 simplifies to 5f + 12 + 6g after combining like terms.
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Write a linear equation for the following table.
x = number
y = cost
0
15
35
55
75
95
y =
4
8
12
16
X +
Answer:
[tex]m = \frac{35 - 15}{4 - 0} = \frac{20}{4} = 5[/tex]
[tex]y = 5x + 15[/tex]
02.05 MC)
What additional information would you need to prove that ΔABC ≅ ΔDEF by SAS?
Triangle ABC is drawn with a single hash mark between A and B and triangle DEF is marked with a single hash mark between D and
(4 points)
Group of answer choices
segment AC≅segment EF
segment BC ≅ segment FE
segment AC ≅ segment FE
segment BC ≅ segment EF
Having the information that segment AC ≅ segment EF, angle B ≅ angle E, and segment BC ≅ segment FE is sufficient to prove that triangles ΔABC and ΔDEF are congruent by the Side-Angle-Side (SAS) criterion.
To prove that triangles ΔABC and ΔDEF are congruent using the Side-Angle-Side (SAS) criterion, we need the following additional information:
The length of segment AC is equal to the length of segment EF: This establishes that one pair of corresponding sides is congruent.
The measure of angle B is equal to the measure of angle E: This provides the congruent angle between the corresponding sides.
The length of segment BC is equal to the length of segment FE: This establishes that the other pair of corresponding sides are congruent.
By having this information, we can apply the SAS congruence criterion. The SAS criterion states that if two triangles have a pair of corresponding sides that are congruent, and the included angles are congruent, then the triangles are congruent.
In this case, having segments AC ≅ EF, angle B ≅ angle E, and segment BC ≅ FE would be sufficient to prove that ΔABC ≅ ΔDEF by SAS.
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1) (20) The temperature on a mountain forms a linear relationship with
the altitude at any given point of the mountain.
The temperature at 4800 feet is 79 degrees while the temperature at
6400 feet is 67 degrees.
=Find a linear model T(x) = mx + b Where x is the altitude.
a) Find the linear model. Show work!
b) What are the units of m, the slope of the line? Hint: Look at the units
of the x values and y values.
c) Find T(5800)
By analyzing the temperature-altitude relationship on a mountain, we can establish a linear model that describes how temperature changes with varying altitudes.
Step-by-step explanation:
a) Knowing the altitude and temperature data, we can use the formula for the slope of a line:
m = (y2 - y1) / (x2 - x1),
where (x1, y1) and (x2, y2) are two points on the line.
Using the altitude and temperature values provided:
(x1, y1) = (4800, 79) and (x2, y2) = (6400, 67),
we can calculate the slope:
m = (67 - 79) / (6400 - 4800)
= -12 / 1600
= -0.0075.
Now, to find the y-intercept (b), we can substitute one of the points (4800, 79) into the equation:
79 = (-0.0075)(4800) + b.
Solving for b, we have:
b = 79 + 0.0075(4800)
= 79 + 36
= 115.
Therefore, the linear model is T(x) = -0.0075x + 115.
b) The units of the slope (m) can be determined by looking at the units of the y values (temperature) and x values (altitude). In this case, the units of temperature are degrees, and the units of altitude are feet. Therefore, the units of the slope (m) are degrees per foot.
c) To find T(5800), we can substitute x = 5800 into the linear model:
T(5800) = -0.0075(5800) + 115
= -43.5 + 115
= 71.5.
Answers:
a) T(x) = -0.0075x + 115.
b) The units of the slope (m) can be determined by looking at the units of the y values (temperature) and x values (altitude). In this case, the units of temperature are degrees, and the units of altitude are feet. Therefore, the units of the slope (m) are degrees per foot.
c) 71.5 degrees.
3. Your family is planning a road trip stretching from coast to coast for this summer. The route and the time frame are nearly set; now you need to plan out the finances. Your parents have decided that rental of an RV will be cheaper than staying in hotels, but they would like an estimate on the total cost. Can you help them?
a. To rent an RV, the following costs apply: $125 per day, plus 32 cents per mile. Additionally, to drop off the RV on the other side of the country, there is an extra fee of $2,500. Write an equation to describe the total cost of RV rental.
b. Your parents have two options for their road trip plans. The first option stretches over 3500 miles and includes fewer stops but more beautiful scenery. It will take about a week and a half (11 days). The second option stretches over just 3000 miles, but it includes more overnight stops and will therefore take two weeks (14 days). Which of these two options is cheaper?
c. Your little sister really wants to take the two-week trip, but your parents really want to keep the RV rental cost under $5,000. You can compromise by either taking a more direct route (lessening the miles) or by stopping for less overnight stays (lessening the days of the rental). What would the domains be for these two compromises? Justify why you think your domains are correct.
d. Write and solve equations to find how many miles or how many days you would have to eliminate in order to stay under the $5,000 budget. Explain each step as you solve your equations. Finally, make a recommendation to your parents about which compromise you think is best.
Answer:
Step-by-step explanation:
a. To write an equation describing the total cost of RV rental, we can use the given information:
Let x be the number of days of rental.
Let y be the number of miles driven.
The total cost of RV rental can be calculated as follows:
Total cost = (125 * x) + (0.32 * y) + 2500
b. To compare the cost of the two options, we need to calculate the total cost for each option.
Option 1:
x = 11 days
y = 3500 miles
Total cost = (125 * 11) + (0.32 * 3500) + 2500
Option 2:
x = 14 days
y = 3000 miles
Total cost = (125 * 14) + (0.32 * 3000) + 2500
Compare the total costs of both options to determine which one is cheaper.
c. To compromise and keep the rental cost under $5,000, we can adjust either the number of miles driven or the number of days of rental.
For the first compromise (lessening the miles), let's assume the new number of miles driven is y1.
The domain for the compromise in miles would be 0 ≤ y1 ≤ 3500, as you cannot drive more miles than the original option or negative miles.
For the second compromise (lessening the days of rental), let's assume the new number of days of rental is x1.
The domain for the compromise in days would be 0 ≤ x1 ≤ 14, as you cannot have more days of rental than the original option or negative days.
The justification for these domains is that they restrict the values within the range of the original options while allowing for adjustments in the desired direction.
d. To find out how many miles or how many days need to be eliminated to stay under the $5,000 budget, we can set up and solve equations.
For the compromise in miles (y1):
(125 * x) + (0.32 * y1) + 2500 ≤ 5000
For the compromise in days (x1):
(125 * x1) + (0.32 * y) + 2500 ≤ 5000
Solve each equation by isolating the variable to determine the maximum allowed value for y1 or x1, respectively.
Finally, after solving the equations, compare the maximum allowed values for y1 and x1 and consider other factors like practicality, time constraints, and preferences to make a recommendation to your parents about which compromise is best.
The crew from Disneyland Entertainment launches fireworks at an angle. The height of the firework can be modeled by h(t) = -2t^2+ 8t + 300 where height, h, is measured in feet and the
time, t, in seconds. What is the greatest height the fireworks reach?
Answer:
The function given here is a quadratic function of the form f(t) = at^2 + bt + c, where a is -2, b is 8, and c is 300. The maximum value of a quadratic function occurs at its vertex. For a function in the form f(t) = at^2 + bt + c, the t-coordinate of the vertex is given by -b/(2a). We can use this to find the time at which the firework reaches its maximum height.
Given a = -2 and b = 8, we can calculate t = -b/(2a):
t = -8/(2*-2) = 2
We can then substitute this value back into the height equation to find the maximum height:
h(2) = -2(2)^2 + 8*2 + 300
h(2) = -8 + 16 + 300
h(2) = 308
So, the greatest height the fireworks reach is 308 feet.
What is the value of the rational expression below when x is equal to 4?
x-12
X-8
O A. -2
о B. 8
о C. 2
OD. -8
The value of the rational expression when x is equal to 4 is 2. The correct answer is option C: 2.
To find the value of the rational expression (x - 12)/(x - 8) when x is equal to 4, we substitute x = 4 into the expression:
[(4) - 12]/[(4) - 8]
Simplifying the numerator and denominator:
(4 - 12)/(-4)
Further simplifying the numerator:
(-8)/(-4)
Now, we can divide -8 by -4:
(-8)/(-4) = 2
So, when x is equal to 4, the value of the rational expression is 2.
Therefore, C is the right response.
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You were assigned to make souvenirs. You have 4m
20cm of ribbon which you plan to use. You want to
cut the ribbon equally into 70cm long pieces. How
many smaller ribbons can you make?
First, we need to convert the length of the ribbon to centimeters to match the length of the ribbon pieces we plan to cut:
4m 20cm = (4 x 100)cm + 20cm = 420cm
Next, we can divide the total length of the ribbon by the length of each piece to find how many pieces we can cut:
420cm ÷ 70cm = 6
Therefore, we can cut 6 smaller ribbons, each 70cm long, from the 4m 20cm length of ribbon we have.
Find the value of the combination. 10C0 0 1 10
The formula to find the value of a combination is
[tex]C(n, r) = n! / (r!(n-r)!),[/tex]
where n represents the total number of items and r represents the number of items being chosen at a time. 10C0 is 1
In the combination,
n = 10 and r = 0,
so the formula becomes:
C(10,0) = 10! / (0! (10-0)!) = 10! / (1 x 10!) = 1 / 1 = 1
This means that out of the 10 items, when choosing 0 at a time, there is only 1 way to do so. In other words, choosing 0 items from a set of 10 items will always result in a single set. This is because the empty set (which has 0 items) is the only possible set when no items are chosen from a set of items. Therefore, the value of the combination 10C0 is 1.
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Let (1=1,2,3, 4, 5, 6, 7, 8, 9, 10
The list of elements in the sets are as follows:
A. A ∩ B = {2, 9}
B. B ∩ C = {2, 3}
C. A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}
D. B ∪ C = {2, 3, 5, 7, 9, 10}
How to find the elements in a set?Set are defined as the collection of objects whose elements are fixed and can not be changed.
Therefore,
universal set = U = {1,2,3, 4, 5, 6, 7, 8, 9, 10}
A = {1, 2, 7, 8, 9}
B = {2, 3, 5, 9}
C = {2, 3, 7, 10}
Therefore,
A.
A ∩ B = {2, 9}
B.
B ∩ C = {2, 3}
C.
A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}
D.
B ∪ C = {2, 3, 5, 7, 9, 10}
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I need help!! f(x)=-2(x-3)
Answer:
Step-by-step explanation:
Certainly! I'm here to assist you.
The given function is f(x) = -2(x - 3).
To simplify this expression, we can distribute the -2 to the terms inside the parentheses:
f(x) = -2 * x - (-2) * 3
Simplifying further:
f(x) = -2x + 6
Therefore, the simplified form of the function f(x) = -2(x - 3) is f(x) = -2x + 6.
SOMEONE PLEASE HELP WITH THIS EQUATION
The composite functions for this problem are given as follows:
a) (f ∘ g)(x) = 4x² + 24x + 32.
b) (g ∘ f)(x) = 2x² - 8x
How to define the composite function of f(x) and g(x)?The composite function of f(x) and g(x) is defined by the function presented as follows:
(f ∘ g)(x) = f(g(x)).
For the composition of two functions, we have that the output of the inner function, which in this example is given by g(x), serves as the input of the outer function, which in this example is given by f(x).
The functions for this problem are given as follows:
f(x) = x² - 4x.g(x) = 2x + 8.Hence the function for item a is given as follows:
(f ∘ g)(x) = f(2x + 8)
(f ∘ g)(x) = (2x + 8)² - 4(2x + 8)
(f ∘ g)(x) = 4x² + 32x + 64 - 8x - 32
(f ∘ g)(x) = 4x² + 24x + 32.
For item b, the function is given as follows:
(g ∘ f)(x) = g(x² - 4x)
(g ∘ f)(x) = 2(x² - 4x)
(g ∘ f)(x) = 2x² - 8x
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Pls help me asap I’m stuck in this
Answer:
Step-by-step explanation:
[tex]\angle x=\angle y=\angle z=90\deg\ \text{(angle in a semi-circle is a right angle)}[/tex]
All 3 angles are examples of the theorem which states that any angle coming off the diameter of a circle going to the edge of the circle will form a right angle.
calculate the area of the following shapes
The area of the shaded part is 640.56 m²
What is area of shape?The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.
The figure is a concentric circle, i.e a circle Ina circle. Therefore to calculate the area of the shaded part,
Area of shaded part = area of big circle - area of small circle
area of big circle = 3.14 × 20²
= 1256
area of small circle = 3.14 × 14²
= 615.44
Area of shaded part = 1256 - 615.44
= 640.56m²
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What is the area of
the segment? Express
the answer in terms
of pi.
The area of the segment is 9( π-2) units²
What is area of segment?The area of a figure is the number of unit squares that cover the surface of a closed figure.
A segment is the area occupied by a chord and an arc. A segment can be a major segment or minor segment.
Area of segment = area of sector - area of triangle
area of sector = 90/360 × πr²
= 1/4 × π × 36
= 9π
area of triangle = 1/2bh
= 1/2 × 6²
= 18
area of segment = 9π -18
= 9( π -2) units²
therefore the area of the segment is 9(π-2) units²
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CD is perpendicular to AB and passes through point C(5, 12).
If the coordinates of A and B are (-10, -3) and (7, 14), respectively, the x-intercept of CD is {blank A}. The point {blank B} lies on CD.
Options:
Blank A:
(12,0)
(15,0)
(17,0)
(19,0)
Blank B:
(-5,24)
(-2,19)
(7,-10)
(8,11)
Answer:
Blank A: (17, 0)
Blank B: (-2, 19)
Step-by-step explanation:
Blank A:
Step 1: Find the slope of AB:
Before we can find the equation of CD, we'll first need to find the slope of AB
We can do this using the slope formula, which is given by:
m = (y2 - y1) / (x2 - x1), where
m is the slope,(x1, y1) is one point,and (x2, y2) is another point.Thus, we can plug in (-10, -3) for (x1, y1) and (7, 14) for (x2, y2) in the slope formula to find m, the slope of AB:
m = (14 - (-3)) / (7 - (-10))
m = (14 + 3) / (7 + 10)
m = 17 / 17
m = 1
Thus, the slope of AB is 1.
Step 2: Find the slope of CD:
The slope of perpendicular lines are negative reciprocals of each other as shown by the following formula:
m2 = -1 / m1, where
m2 is the slope of the line we're trying to find, and m1 is the slope of the line we know.Thus, we can plug in 1 for m1 in the perpendicular slope formula to find m2, the slope of CD:
m2 = -1 / 1
m2 = -1
Thus, the slope of CD is -1.
Step 3: Find the y-intercept of CD:
One of the equations we can use when looking for intercepts is the slope-intercept form of a line, whose general equation is given by:
y = mx + b, where
(x, y) is any point on the line,m is the slope,and b is the y-intercept.Thus, we can plug in (5, 12) for (x, y) and -1 for m to find b, the y-intercept of the line, allowing us to have the full equation in slope-intercept of CD:
12 = -1(5) + b
12 = -5 + b
17 = b
Thus, the equation of CD is y = -x + 17
For any x-intercept, the y-coordinate will always be 0 since the line is intersecting the x-axis.
Thus, we can find the x-coordinate of the x-intercept by plugging in 0 for y in y = -x + 17 and solving for x:
0 = -x + 17
-17 = -x
17 = x
Thus, the x-coordinate of the x-intercept of CD is 17.
Thus, the coordinates of the x-intercept of CD are (17, 0)
Blank B:
We can see that (-2, 19) lies on CD when we plug in (-2, 19) for (x, y) in y = -x + 17, as we get 19 on both sides of the equation when simplifying:
19 = -(-2) + 17
19 = 2 + 17
19 = 19
Thus, (-2, 19) lies on CD.
The vertices of $\triangle ABC$ represent the buoy markers that form the legs of the course for a swim race. What is the distance from marker $A$ to marker $B$ ? Round your answer to the nearest tenth of a meter.
Rounding to the nearest tenth of a meter, the distance from marker A to marker B (side AB) is approximately 5.7 meters.
To find the distance from marker A to marker B in triangle ABC, we need to calculate the length of side AB.
The distance between two points (x1, y1) and (x2, y2) can be found using the distance formula:
d = √[tex]((x2 - x1)^2 + (y2 - y1)^2)[/tex]
In this case, let's assume that the coordinates of marker A are (x1, y1) and the coordinates of marker B are (x2, y2).
Given that the coordinates of marker A are not provided in the question, we would need the coordinates of both marker A and marker B to calculate the distance between them accurately.
Once we have the coordinates of marker A and marker B, we can substitute them into the distance formula to calculate the distance AB.
For example, if the coordinates of marker A are (x1, y1) = (3, 4) and the coordinates of marker B are (x2, y2) = (7, 8), we can calculate the distance as follows:
d = [tex]\sqrt{((7 - 3)^2 + (8 - 4)^2)}[/tex]
= √[tex](4^2 + 4^2)[/tex]
= √(16 + 16)
= √32
≈ 5.66
Rounding to the nearest tenth of a meter, the distance from marker A to marker B (side AB) is approximately 5.7 meters.
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Which order pair? Explain.
A function can't have more than one value for an argument. Therefore, it's either (1,1) or (1,3), but since there's not (1,3) among the possible answers, it must be (1,1).
8.4.4. Define sets. How many kinds of sets Also list the operation of sets. Give the short activites for teaching Learning Union of sets. 2+2+2+4=10)
In mathematics, a set is a well-defined collection of distinct objects, called elements or members of the set. These objects can be anything: numbers, letters, people, or even other sets.
he concept of sets is fundamental in various branches of mathematics, including set theory, algebra, and statistics.There are different kinds of sets based on their properties:
Finite set: A set with a specific number of elements, which can be counted.Infinite set: A set with an endless number of elements.Empty set: A set with no elements. It is denoted by the symbol Ø or {}.
Singleton set: A set with only one element.Subset: A set whose elements are all contained within another set.Universal set: A set that includes all the possible elements of interest in a particular context.Operations on sets involve various ways of combining or manipulating sets:
Union: The union of two sets A and B is the set that contains all the elements from both sets. It is denoted by A ∪ B.Intersection: The intersection of two sets A and B is the set of elements that are common to both sets. It is denoted by A ∩ B.
Complement: The complement of a set A, denoted by A', is the set of all elements that are not in A but are in the universal set.Difference: The difference between two sets A and B is the set of elements that are in A but not in B. It is denoted by A - B.
Cartesian Product: The Cartesian product of two sets A and B is the set of all possible ordered pairs, where the first element is from set A and the second element is from set B. It is denoted by A × B.
For teaching the concept of the union of sets, you can use the following activity:
Activity: Venn Diagrams
Draw two overlapping circles on the board or use physical cut-out circles.Label one circle as Set A and the other as Set B.
Ask the students to suggest elements for each set and write them inside the circles.Discuss the elements that are common to both sets and write them in the overlapping region.Explain that the union of sets A and B represents all the elements in both sets.
Combine the elements from sets A and B, including the elements in the overlapping region, and write them in a new circle labeled as A ∪ B.Emphasize that the union includes all the distinct elements from both sets without repetition.
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Which are the roots of the quadratic function f(b) = b² - 75? Select two options.
Ob=5√3
Ob=-5√3
Ob=3√5
Ob=-3√5
Ob=25√3
The two roots of the quadratic function f(b) = b² - 75 are:
b = 5√3 and b = -5√3What is the quadratic function?A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two. Since the highest degree term in a quadratic function is of the second degree, therefore it is also called the polynomial of degree 2. A quadratic function has a minimum of one term which is of the second degree.
We have
[tex]f(b) = b^2 - 75[/tex]Remember that the root of a function is the value of x when the value of the function is equal to zero.
In this problem
The roots are the values of b when the function f(b) is equal to zero.
So,
For f(b)=0
[tex]b^2-75=0[/tex]
[tex]b^2=75[/tex]
Square root both sides
[tex]b=(+/-)\sqrt{75}[/tex]
Simplify
[tex]b=(+/-)5\sqrt{3}[/tex]
[tex]b=5\sqrt{3}[/tex] and [tex]b=-5\sqrt{3}[/tex]
Therefore
[tex]\rightarrow\bold{b = 5\sqrt{3}}[/tex]
[tex]\rightarrow\bold{b=-5\sqrt{3}}[/tex]
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On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 3) and (3, 1). Everything below and to the right of the line is shaded.
Which linear inequality is represented by the graph?
y > Two-thirdsx – 2
y < Two-thirdsx + 2
y > Two-thirdsx + 1
y < Two-thirdsx – 1
Answer:
y > Two-thirds x + 1 /c
Ms. Florinda is a kindergarten teacher. She buys 100 pencils and wants to give 2 pencils to each of her students. She has 2 classes, a class with 22 students and a class with 19 students.
Part A
Write an expression for how many pencils she has left after giving them out to her students.
A.
100
−
2
×
(
22
−
19
)
B.
100
−
2
×
22
−
19
C.
100
−
2
×
22
−
2
×
19
D.
100
−
22
−
19
Part B
Does she have enough pencils to give each of her students 2?
Yes or no
, she has
15,18,37,59
More or fewer
than she needs.
Answer:
Part A:
The correct expression for how many pencils Ms. Florinda has left after giving them out to her students is:
A. 100 - 2 × (22 - 19)
Part B:
To determine whether Ms. Florinda has enough pencils to give each of her students 2, we can calculate the total number of pencils needed. The total number of students is the sum of the students in both classes, which is 22 + 19 = 41.
If each student needs 2 pencils, then the total number of pencils needed is 2 × 41 = 82.
Comparing this with the initial number of pencils Ms. Florinda bought (100), we can see that she has more than enough pencils to give each of her students 2.
Yes, she has enough pencils to give each of her students 2.
She has 18 more than she needs.
Solve using inverse (matrix) method
5x - 4y + z = 12
x + 7y-z = -9
2x+3y + 3z = 8
The solution to the system of equations using the inverse matrix method is x = -1, y = 2, z = 3.
To solve the system of equations using the inverse matrix method, we need to represent the system in matrix form.
The given system of equations can be written as:
| 5 -4 1 | | x | = | 12 |
| 1 7 -1 | [tex]\times[/tex]| y | = | -9 |
| 2 3 3 | | z | | 8 |
Let's denote the coefficient matrix on the left side as A, the variable matrix as X, and the constant matrix as B.
Then the equation can be written as AX = B.
Now, to solve for X, we need to find the inverse of matrix A.
If A is invertible, we can calculate X as [tex]X = A^{(-1)} \times B.[/tex]
To find the inverse of matrix A, we can use the formula:
[tex]A^{(-1)} = (1 / det(A)) \times adj(A)[/tex]
Where det(A) is the determinant of A and adj(A) is the adjugate of A.
Calculating the determinant of A:
[tex]det(A) = 5 \times (7 \times 3 - (-1) \times 3) - (-4) \times (1 \times 3 - (-1) \times 2) + 1 \times (1 \times (-1) - 7\times 2)[/tex]
= 15 + 10 + (-13)
= 12.
Next, we need to find the adjugate of A, which is obtained by taking the transpose of the cofactor matrix of A.
Cofactor matrix of A:
| (73-(-1)3) -(13-(-1)2) (1(-1)-72) |
| (-(53-(-1)2) (53-12) (5[tex]\times[/tex] (-1)-(-1)2) |
| ((5(-1)-72) (-(5(-1)-12) (57-(-1)[tex]\times[/tex](-1)) |
Transpose of the cofactor matrix:
| 20 -7 -19 |
| 13 13 -3 |
| -19 13 36 |
Finally, we can calculate the inverse of A:
A^(-1) = (1 / det(A)) [tex]\times[/tex] adj(A)
= (1 / 12) [tex]\times[/tex] | 20 -7 -19 |
| 13 13 -3 |
| -19 13 36 |
Multiplying[tex]A^{(-1)[/tex] with B, we can solve for X:
[tex]X = A^{(-1)}\times B[/tex]
= | 20 -7 -19 | | 12 |
| 13 13 -3 | [tex]\times[/tex] | -9 |
| -19 13 36 | | 8 |
Performing the matrix multiplication, we can find the values of x, y, and z.
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how to write a decimal as a mixed number
Answer:
Here's an example:
convert 2.5 into a mixed number.
Make the denominator less than the original.
The easy way for this is to do 25/10
when you put it through a calculator it ends up being 2.5
(essentially the mixed number and the decimal are the SAME numbers.)
Hope this clarified. :)
To convert a decimal to a mixed number, follow these steps:
Step 1: Identify the whole number part of the decimal. This is the part of the decimal before the decimal point.
Step 2: Identify the decimal part. This is the part of the decimal after the decimal point.
Step 3: Express the decimal part as a fraction by using the place value of the last digit.
Step 4: Simplify the fraction, if possible, by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it.
Step 5: Combine the whole number part, the fraction, and simplify if necessary.
Here's an example:
Let's say we have the decimal 2.75.
Step 1: The whole number part is 2.
Step 2: The decimal part is 0.75.
Step 3: To express 0.75 as a fraction, we write it as 75/100. Since 75 and 100 have a common factor of 25, we can simplify it to 3/4.
Step 4: The fraction 3/4 is already in its simplest form.
Step 5: Combining the whole number part and the fraction, we have 2 3/4.
So, the decimal 2.75 can be written as the mixed number 2 3/4.
Remember to always simplify the fraction part if possible.
A person leaves home and walks 5 miles west, then 6 miles southwest.
How far from home is she?
The person is approximately 7.73 miles from home.
To solve this problem, we can use the Pythagorean theorem and trigonometry. Let us assume that the person starts from the origin (0, 0) and walks 5 miles west, which takes her to the point (-5, 0) on the x-axis.
If we assume that the starting point is (0, 0) and we assign a coordinate system, then the point reached after walking 5 miles west can be represented as (-5, 0). Similarly, the point reached after walking 6 miles southwest can be represented as (-3, -6).Then, she walks 6 miles southwest, which forms a 45-degree angle with the x-axis. We can represent this vector as (6 cos 45°, -6 sin 45°) = (3√2, -3√2).
To find the total distance from home, we need to add the magnitude of these two vectors using the Pythagorean theorem:
d =[tex]\sqrt((-5)^2 + (-3\sqrt2)^2)[/tex]≈ 7.73 miles
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What is the mean and median reasoning, As the last one is incorrect
The best measure of center of the data is (a) mean; because the data are close together
How to determine the best measure of center of the dataFrom the question, we have the following parameters that can be used in our computation:
The dataset of 10 values
Where we can see that there are no outliers present in the dataset
By definition, outliers are extreme values.
Since there are no outliers, it means that the mean is the best measure of center
This is because the mean is affected by the presence of outliers and since no outlier is present, we use the mean
From the list of options, we have the mean value to be 42.536
Hence, the true statement is (a)
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Which ordered pair makes both inequalities true?
y < –x + 1
y > x
On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 1) and (1, 0). Everything below and to the left of the line is shaded. The second dashed line has a positive slope and goes through (negative 1, negative 1) and (1, 1). Everything above and to the left of the line is shaded.
(–3, 5)
(–2, 2)
(–1, –3)
(0, –1)
Answer:
(-2, 2)
Step-by-step explanation:
We will start by just plugging in the numbers to see if they work.
(-3, 5)
5<-(-3)+1
5<4
This is not possible, so the answer is not (-3, 5).
(-2, 2)
2<-(-2)+1
2<3
2>-2
The point (-2, 2) works for both equations, so that is the answer.