Subject offered monthly charges Duration
(Subjects) (monthly charges) (duration)
Mathematics R280
Consumer Studies R350
8 hours Per month
3 hours per Saturday.
write down (in Simplified form) the ratio of the
amount charged in mathematics to consumer
studies

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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The area of the segment is 9( π-2) units²

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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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.

The two roots of the quadratic function f(b) = b² - 75 are:

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

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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The best measure of center of the data is (a) mean; because the data are close together

From 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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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.

Answer:

Therefore, the cost of a pen is $2.30.

Step-by-step explanation:

Let's assign variables to represent the cost of a calculator and the cost of a pen.

Let c represent the cost of a calculator.

Let p represent the cost of a pen.

Based on the given information, we can form the following pair of simultaneous equations:

Equation 1: 4c + 2p = 20.60   (Mia buys 4 calculators and 2 pens for $20.60)

Equation 2: 5c + 3p = 26.90   (Heidi buys 5 calculators and 3 pens for $26.90)

To solve for the cost of a pen, we'll eliminate the variable c by multiplying Equation 1 by 5 and Equation 2 by 4. Then we'll subtract Equation 1 from Equation 2:

5 * (4c + 2p) = 5 * 20.60

4 * (5c + 3p) = 4 * 26.90

20c + 10p = 103.00

20c + 12p = 107.60

Subtracting Equation 1 from Equation 2:

(20c + 12p) - (20c + 10p) = 107.60 - 103.00

20c - 20c + 12p - 10p = 4.60

2p = 4.60

p = 4.60 / 2

p = 2.30

Therefore, the cost of a pen is $2.30.

Answer:

Let's assume that the cost of a calculator is x and the cost of a pen is y. Then we can write the following pair of equations:

4x + 2y = 20.60    (equation 1)

5x + 3y = 26.90    (equation 2)

To solve for the cost of a pen, we need to eliminate x from the equations. We can do this by multiplying equation 1 by 5 and equation 2 by -4, and then adding them:

(5)(4x + 2y = 20.60)  becomes  20x + 10y = 103    (equation 3)

(-4)(5x + 3y = 26.90) becomes -20x - 12y = -107.60    (equation 4)

Adding Equation 3 and Equation 4 gives:

-2y = -4.60

Divide both sides by -2:

y = 2.30

Therefore, the cost of a pen is $2.30.

Step-by-step explanation:

MARK ME BRAINLIST

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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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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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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The area of the shaded part is 640.56 m²

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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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.

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.

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

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

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

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 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}

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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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.

Hello!

V

= (18cm * 15cm * 6cm) + ((13cm - 6cm) * 15cm * 6cm)

= 1,620cm³ + 630cm³

= 2,250cm³

Answer:

y > Two-thirds x + 1     /c

Answer:

(-4,4)

Step-by-step explanation:

You rewrite the terms:

(x + 4)^2 => [x - (-4)]^2

(y - 4)^2 => [y - (4)]^2

so h = -4 and k = 4

so center of ellipse is (h,k) or (-4,4)

Answer:

Center = (-4, 4)

Step-by-step explanation:

The standard form of the equation of an ellipse with center (h, k) is:

[tex]\boxed{\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1}[/tex]

The given equation is:

[tex]\dfrac{(x+4)^2}{25}+\dfrac{(y-4)^2}{9}=1[/tex]

Comparing the given equation with the standard form, we can see that h = -4 and k = 4. Therefore, the center (h, k) of the ellipse is (-4, 4).

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 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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The composite functions for this problem are given as follows:

a) (f ∘ g)(x) = 4x² + 24x + 32.

b) (g ∘ f)(x) = 2x² - 8x

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:

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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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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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.

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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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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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).

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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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.

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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