Here are two rectangles.
Complete this sentence:
The two rectangles are similar and the scale factor is __
Answer:
It is
Scale Factor = Ratio of Side Lengths
= 12/8 = 9/6 = 1.5.
Step-by-step explanation:
Hope this helped have an amazing day!
The two rectangles are similar and the scale factor is 3/2.
Given data:
The first rectangle is represented as ABCD
The second rectangle is represented as PQRS
Now, the dimensions of ABCD is 8 cm x 6 cm
The dimensions of PQRS is 12 cm x 9 cm
So, the scale factor is represented as k and the value of k is :
k = length of PQRS / length of ABCD
So, k = 12 / 8
k = 3/2
Hence , the similar rectangles have a scale factor of 3/2
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What is an equation of the line that passes through the points (1, 2) and (2, -1)?
Put your answer in fully reduced form.
Answer:
y = -x + 3
Step-by-step explanation:
The equation of a straight line is generally written as;
y = mx + b
where m is the slope and b is the intercept
To get the slope we use the slope formula
Mathematically, that is;
m = (y2-y1)/(x2-x1) = (-1-2)/2-1 = -3/1 = -1
To get the intercept we equate any of the points to the partial equation that we have;
From;
y = -x + b
2 = -1 + b
b = 1 + 2 = 3
So the equation is;
y = -x + 3
A ball is thrown upward at an angle of 30° to the horizontal and lands on the top edge of a building that is 20 m away. The top edge is 5.0 m above the throwing point. How fast was the ball thrown? Use: sin30°=0.5 and cos30°=0.9
a. 20 m/s
b. 11 m/s
c. 52.3 m/s
d. 16 m/s
Answer:
The correct option is;
a. 20 m/s
Step-by-step explanation:
The given parameters are;
The angle at which the ball is thrown, θ = 30° to the horizontal
The horizontal distance of the top edge of the building where the ball lands from where the ball is thrown, x = 20 m
The height of the top edge of the building above the throwing point = 5 meters
Let "v" represent the speed with which the ball is thrown
We have;
The vertical component of the speed with which the ball is thrown, [tex]v_y[/tex] = v × sin(θ) = v × sin(30°) = v × 0.5 = 0.5·v
[tex]v_y[/tex] = 0.5·v
The horizontal component of the speed with which the ball is thrown, vₓ = v × cos(θ) = v × cos(30°) = v × 0.9 = 0.9·v
vₓ = 0.9·v
The kinematic equation of the motion is y = [tex]v_y[/tex]·t - (1/2)·g·t², where;
y = The vertical height reached = 5 metes
t = The time taken to reach the specified 5 m, height
g = The acceleration due to gravity = 9.8 m/s², we have;
Therefore, we have;
5 = 0.5·v·t - (1/2)·9.8·t²...(1)
Also, from the horizontal motion of the ball, we have the following kinematic equation of motion;
x = vₓ × t
Therefore, by substituting the known values, we have;
20 = 0.9·v × t
∴ v = 20/(0.9·t) = 200/(9·t)...(2)
Substituting the value of t in equation (1) gives;
5 = 0.5·v·t - (1/2)·9.8·t² = 0.5·(200/(9·t))·t - (1/2)·9.8·t²
∴ 5 = 0.5·(200/(9·t))·t - (1/2)·9.8·t² = 100/9 - 4.9·t²
4.9·t² = 100/9 - 5 = 55/9
t = √(55/(9 × 4.9)) ≈ 1.116766
The time taken to reach the specified 5 m height = t ≈ 1.116766 seconds
From equation (2), we have, v = 200/(9·t) = 200/(9 × 1.116766) ≈ 19.8987 m/s
The speed with which the ball is thrown = v ≈ 19.8987 m/s ≈ 20 m/s. to the nearest whole number.
The speed with which the ball is thrown is approximately 20 m/s
Answer:
The answer is:
a) 20 m/s
Hope it helps:D
3/7 to its decimal form and rounded to the nearest thousandth
Answer:
Decimal form: 0.4286
Step-by-step explanation:
The value of 3/7 in decimal form up to nearest thousands will be 0.4285.
A fraction 3/7 is given in the question.
We have to find it's decimal form and round-off it to nearest thousands.
What will be the value of 1/2 in decimal form rounded to units place ?
The value will be 0.5
To find the decimal form let's divide 3 by 7.
3 ÷ 7 = 0.428572
We have to round it to nearest thousands i.e., up to 4 places Right to decimal point.
The rounded value will be 0.4285.
thus , the decimal form of 3/7 will be 0.4285 rounded off to nearest thousands.
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|-4/5-1/10| + |-3/4+5/2|
A.) 9/10
B.) 53/20
C.) 7/4
D.) 17/10
Answer:
B.) 53/20
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
|Absolute Value| makes any negative number positiveStep-by-step explanation:
Step 1: Define
|-4/5 - 1/10| + |-3/4 + 5/2|
Step 2: Evaluate
Subtract: |-9/10| + |-3/4 + 5/2|Add: |-9/10| + |7/4|Absolute Value: 9/10 + 7/4Add: 53/20TRAVEL It is about 350 miles from Ruidoso, New Mexico, to Abilene, Texas. Haruko has already driven 75 miles and made it to Roswell, New Mexico. She hopes to finish the rest of her trip, including stops, in 5 hours. Write an equation to find the average speed Haruko needs to drive to finish the rest of her trip in 5 hours.
Answer:
55 mph
Step-by-step explanation:
Given that:
Total miles of journey = 350 miles
Miles already driven = 75 miles
To cover the rest of the journey in 5 hours, the average speed of travel. Will be:
Recall:
Speed = (Distance left to cover ÷ budgeted travel time)
Distance left to cover : (total miles - distance already driven)
Average speed required = (350 - 75) / 5
= 275 / 5
= 55 mph
A contractor needs to buy nails to build a house. The nails come in small boxes and large boxes. Each small box has 150 nails and each large box has 450 nails. The contractor bought twice as many large boxes as small boxes, which altogether had 4200 nails. Write a system of equations that could be used to determine the number of small boxes purchased and the number of large boxes purchased. Define the variables that you use to write the system.
Step-by-step explanation:
Let s represent the number of small boxes and l represent the number of large boxes.
We have 2s = l and 150s + 450l = 4200.
Therefore 150s + 450(2s) = 4200,
150s + 900s = 4200, 1050s = 4200, s = 4.
l = 2s = 2(4) = 8.
Hence there are 4 small boxes and 8 large boxes.
Help me on this math problem please! I’ve been stuck on it for 15 mins now
Answer:
Step-by-step explanation:
P = perimeter = 114
P =2 * length +2* width
P = 2(2x - 3) + 2(x)
114 = 4x-6 + 2x
114 = 6x -6
19 = x -1
20 = x
check it
2( 2x -3)+2x = ?
4x -6 +2x=?
6x -6 = ?
6(20)-6 =?
120-6 = 114
yep this is correct
Use the graph that shows the solution to f(x) = g(x).
f(x) = 27* - 4
g(x) = 2x² - 4
f(x)
-2
What is the solution to f (x) = g(x)?
Select each correct answer
9(X)
x = -1
x = 0
X = 1
913
-3 -2
x=2
13
f(x)
3
4
5
7
8
Finish
Answer:(9X+3Y
Step-by-step explanation:
MULTIPLY BY 4
agenthammerx please help What is BPEMDAS
Answer:
BPEMDAS is the order of operations that every mathematician must follow.
General Formulas and Concepts:
Order of Operations: BPEMDAS
1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction
- Left to Right
Step-by-step explanation:
When we are given an evaluative expression, we must follow Order of Operations: BPEMDAS to evaluate the given expression. Here’s an example:
[2 + (4 / 2)] * 10
Evaluating this:
1. [Brackets] (Parenthesis) Divide: [2 + 2] * 10
2. [Brackets] Add: 4 * 10
3. Multiply: 40
Here we see that we use Order of Operations: BPEMDAS to evaluate a given expression.
the diagram shows two parallel lines cut by a transversal. If the measure of < 3 = ( 7y + 15) and the measure of < 5 = ( 110 - 2y) , what is the measure of <4
Step-by-step explanation:
Angle 3 + Angle 5 = 180° (C-angles)
Therefore 7y + 15 + 110 - 2y = 180, 5y = 55, y = 11.
Angle 4 = Angle 5 (Z-angles)
Hence Angle 4 = 110 - 2y = 110 - 2(11) = 88°.
Express 0.000000000936 in
scientific notation.
9.36x10
Enter
Answer:
9.36 x 10^(-10)
Step-by-step explanation:
Which equation describes the line with slope 5 that contains the point (-2,4)?
(Question 20)
Answer:
4x-3
Step-by-step explanation:
Bc i said so
Thomas and Audrey ordered 1 salad for $8, 2 pizzas for x dollars each, and 2 glasses of juice for $3 each. Their total cost in dollars can be represented by the expression 8 + 2 ( x + 3) . Which expression is equivalent to 8 + 2 ( x + 3)?
Solve.
y= 2x - 6
4x – 2y = 14
Use the substitution method.
Answer:
y=2x-6. ---------(1)
4x-2y=14. --------(2)
substituting equation 2 in 1
4x-2(2x-6)=14
4x-4x+12=14
so it has no solution
Step-by-step explanation:
As you can see in the image below, the answer is no solution.
BC = 17.89
DC = 16
with reference to the figure sin x=?
a.0.250
b. 0.447
c.0.894
d. 1
Answer:
c
Step-by-step explanation:
The value of sin x in the given right triangle is 0.894.
What sine of an angle?The sine of an angle is a trigonometric function that is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle.
Given is right triangle ABC, we need to find the value of sin x,
So, we see that the figure is divided into three similar triangles,
Namely,
Δ CDB ~ Δ BDA ~ Δ CBA,
Therefore, according to the definition of similarity,
We have,
CD / CB = BD / BA = 16/17.89
Therefore, BD / BA = 0.894
Also,
sin x = BD / BA
Therefore,
sin x = 0.894
Hence the value of sin x in the given right triangle is 0.894.
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PLEASE HELPP
What is the solution to the following system of equations?
x − 3y = 6
2x + 2y = 4
(-1, 3)
(3, -1)
(1, -3)
(-3, 1)
Answer:
The solution to the system of equations be:
[tex]x=3,\:y=-1[/tex]
Hece, option B is correct.
Step-by-step explanation:
Given the system of equations
[tex]\begin{bmatrix}x-3y=6\\ 2x+2y=4\end{bmatrix}[/tex]
Multiply x − 3y = 6 by 2: 2x-6y=12
[tex]\begin{bmatrix}2x-6y=12\\ 2x+2y=4\end{bmatrix}[/tex]
so
[tex]2x+2y=4[/tex]
[tex]-[/tex]
[tex]\underline{2x-6y=12}[/tex]
[tex]8y=-8[/tex]
so the system of equations becomes
[tex]\begin{bmatrix}2x-6y=12\\ 8y=-8\end{bmatrix}[/tex]
Solve 8y = -8 for y
[tex]8y=-8[/tex]
Divide both sides by 8
[tex]\frac{8y}{8}=\frac{-8}{8}[/tex]
[tex]y=-1[/tex]
[tex]\mathrm{For\:}2x-6y=12\mathrm{\:plug\:in\:}y=-1[/tex]
[tex]2x-6\left(-1\right)=12[/tex]
[tex]2x+6=12[/tex]
subtract 6 from both sides
[tex]2x+6-6=12-6[/tex]
[tex]2x=6[/tex]
Divide both sides by 2
[tex]\frac{2x}{2}=\frac{6}{2}[/tex]
[tex]x=3[/tex]
Therefore, the solution to the system of equations be:
[tex]x=3,\:y=-1[/tex]
Hence, option B is correct.
⚽ From Equation (i) we get :
x = 6 + 3y......[Equation (iii)]⚽ Now, Substitute the equation (iii) in equation (ii) we get :
→ 2(6 + 3y) + 2y = 4
→ 12 + 6y + 2y = 4
→ 8y = 4 - 12
→ 8y = -8
→ y = -8 ÷ 8
→ y = -1
⚽ Now Substituting value of y = -1 in equation (iii) we get :
→ x = 6 + 3y
→ x = 6 + 3(-1)
→ x = 6 + (-3)
→ x = 6 - 3
→ x = 3
Hence,the value of x = 3 and value of y = -1.Kira is on her way home in her car. Her drive is 30 miles long. She has finished one-third of the drive so far. How far has she driven?
Answer:
10 miles
Step-by-step explanation:
1/3 × 30 miles = 10 miles
Answer:
Step-by-step explanation:
30 * 1/3 = 10 :)
Solve the equation. −2+j=−22
Answer:
j = - 20
Step-by-step explanation:
-2 + j = -22
-2 + 2 + j = -22 + 2
j = - 20
j= -20 hope that helped
help!!
Find the solution of the system of equations
shown on the graph.
Answer:
(0,6)
Step-by-step explanation:
When a system of equations is graphed, the point at which the lines intersect is a solution to the system. Looking at the graph, we can see that the lines intersect at (0,6). Therefore, (0,6) is a solution to the system of equations.
SOMEONE HELP I WILL KISS U!!!!! NEED THIS EXTRA CREDIT DONE BY MIDNIGHT!!
Answer:
A, C, D, F, G
Explanation:
A rational number is any integer, fraction, terminating decimal, or repeating decimal. :D
Naveen is a video game designer creating a new video game in the racing genre. Outline the elements of the game that Naveen will focus on in his design.
Answer:
Hi
Step-by-step explanation:
it will be C
Explain how to create an equation with infinity many solutions.
you need both sides of the equation to be equal to each other.
ex: 1 = 1
x = x
10 - x = -x + 10
this may not be what you're looking for and if it isn't just let me know
What is 5 billion times 0
Answer:
0
Step-by-step explanation:
Anything multiplied by 0 is 0
Work out the Value of the missing fraction 1/7+ ?=1/3
Step-by-step explanation:
1/7 + ? = 1/3
? = 1/3 - 1/7 = 7/21 - 3/21 = 4/21.
The missing fraction is 4/21.
Suppose you know that the volume of the following prism is represent by V(x) = -2x^3 + 14x^2 + 120x.
Step-by-step explanation:
-2x³ + 14x² + 120x
= -2x(x² - 7x - 60)
= -2x(x - 12)(x + 5).
The other 2 dimensions are -2x and (x + 5).
When using a graphing calculator to maximise the volume of the prism, we get x = 7.378. However this value is not reasonable as it makes -2x and (x - 12) negative, which are the sides of the prism.
(77) – 32
a. - 2
b. 16
C. 52
d. - 16
Answer:
b. 16 not sure its correct just trying to help out. :)
Step-by-step explanation:
a carpenter sands 1/2 of a dresser in 3/4 of an hour. At this rate, how long does it take the carpenter to sand 1 dresser
Answer:
hour and a half
Step-by-step explanation:
20)
The perimeter of a triangle is given by the formula P= a + b + c Solved for b, this formula becomes b =
A
P+ a + c
B)
Р-а - с
P-a-c
р- а - с
Answer:
sin B sin C. When this equation is combined with the previous equation, we obtain the Law of. Sines. ... ас. B. FIGURE 4.5 Solving an. ASA triangle. Keep in mind that we must be given one of the three ratios to apply the ...
How many solutions exist for the given equation?
1/2(x+12) = 4x - 1
Zero
One
Two
Infinitely many
Answer:
1
Step-by-step explanation:
Answer:
One
Step-by-step explanation:
[tex] \frac{1}{2} (x +12) = 4x - 1 \\ \\ \frac{1}{2} x + \frac{1}{2} \times 12 = 4x - 1 \\ \\ \frac{1}{2} x + 6 = 4x - 1 \\ \\ 6 + 1 = 4x - \frac{1}{2} x \\ \\ 7 = \frac{8x - x}{2} \\ \\ 7 = \frac{7}{2} x \\ \\ 7 \times 2 = 7x \\ \\ x = \frac{7 \times 2}{7} \\ \\ x = 2[/tex]
So, there exist only one solution for the given equation.