Answers
Answer:
a) x = 14
b) The perimeter of △QRS is 77 units.
Step-by-step explanation:
a) Due to the question asking for a solution using the Triangle Proportionality Theorem, it is assumed that △RQS is similar to the smaller triangle inside it.
Let us define the point at which the line inside △RQS meets line RQ as T, and the point at which that same line meets line RS as V.
Hence, △RTV ~ △RQS.
According to the Triangle Proportionality Theorem:
[tex]\frac{RT}{RQ} = \frac{TV}{QS} = \frac{VR}{SR}[/tex]
Hence, we can substitute all values that we know from the diagram:
[tex]\frac{2x - 2}{2x - 2 + 13} = \frac{TV}{17} = \frac{21 - 7}{21}[/tex]
After getting this information, all we have to do is simplify and solve the equation:
[tex]\frac{2x - 2}{2x - 2 + 13} = \frac{21 - 7}{21}[/tex]
[tex]\frac{2x - 2}{2x + 11} = \frac{14}{21}[/tex]
[tex]\frac{2x - 2}{2x + 11} = \frac{2}{3}[/tex]
[tex]3(2x - 2) = 2(2x + 11)[/tex]
[tex]6x - 6 = 4x + 22[/tex]
[tex]6x - 4x = 22 + 6[/tex]
[tex]2x = 28[/tex]
[tex]x = 14[/tex]
To verify this answer, we can plug in the value of x into the equation:
[tex]\frac{2(14) - 2}{2(14) - 2 + 13} = \frac{2}{3}[/tex]
[tex]\frac{26}{39} = \frac{2}{3}[/tex]
[tex]\frac{2}{3} = \frac{2}{3}[/tex]
Hence, after verification, we can get the answer: x = 14.
--------------------------------------------------------------------------------------------------------------
b) To find the perimeter of △QRS, all we have to do is to add all the lengths of the sides of △QRS together.
Hence, 2(14) - 2 + 13 + 17 + 21
= 28 - 2 + 13 + 17 + 21
= 77 units
Therefore, the perimeter of △QRS is 77 units.
Hope this helped!
Related Questions
find the sum of (2c+6)+3(c+8) pls help me for 15 points and a brainiest!!!
Answers
Answer:
(2c+6)+3(c+8)
=2c+6+3c+24
=5c+30
x - 2y =0
3x + y = 0
solve using the substitution method
to solve the linear system
Answers
Answer:
x=0, y=0
Step-by-step explanation:
① Label the 2 given equations.
x -2y= 0 -----(1)
3x +y= 0 -----(2)
② Make x the subject of formula in equation (1).
From (1): x= 2y -----(3)
③ Substitute equation (3) into (2):
3(2y) +y= 0
Expand:
6y +y= 0
Simplify:
7y= 0
y= 0
④ Find x.
Subst. y=0 into (3):
x= 2(0)
x= 0
Box 1:
Dimensions: x by 3x by x
Area of base =x(3) = 3r?
Dimensions: x by 4x-1 by x
Area of base = x(4x-1) = 41²-x
Answers
Answer:
1. monomial
2. binomial
Step-by-step explanation:
Box 1's volume will be a monomial
Box 's volume will be a binomial
Can you please answer number 23. And number 24.
Please please show me how to do it and tell me the answers
Answers
Answer:24 is 34miles per hour
Step-by-step explanation:
Answer:
1st
A pound is defined as exactly 0.45359237 kilograms.
so 50 x 0.45359237 = 22.679619 Kilograms
2. 55km to miles = 34.16
for an approximate result, divide the length value by 1.609
Step-by-step explanation:
Basic Computation: Testing M1 2 M2 A random sample of 49 measurements from a population with population standard deviation 3 had a sample mean of 10. An independent random sample of 64 measurements from a second population with population standard deviation 4 had a sample mean of 12. Test the claim that the population means are different. Use level of significance 0.01. (a) Check Requirements What distribution does the sample test statistic follow
Answers
Answer:
The sample statistics follows a standard normal distribution since the sample size are large enough.
Step-by-step explanation:
Given that:
First population:
Sample size [tex]n_1[/tex] = 49
Population standard deviation [tex]\sigma_1[/tex] = 3
Sample mean [tex]\overline x _1[/tex]= 10
Second population:
Sample size [tex]n_2[/tex] = 64
Population standard deviation [tex]\sigma_2[/tex]= 4
Sample mean [tex]\overline x_2[/tex]= 12
The sample statistics follows a standard normal distribution since the sample size are large enough.
The null and alternative hypotheses can be computed as:
[tex]\mathbf{H_o:\mu_1=\mu_2}[/tex]
[tex]\mathbf{H_1:\mu_1\ne\mu_2}[/tex]
Level of significance = 0.01
Using the Z-test statistics;
[tex]Z = \dfrac{\overline x_1 - \overline x_2}{\sqrt{\dfrac{\sigma_1^2}{n_1} + \dfrac{\sigma_2^2}{n_2}}}[/tex]
[tex]Z = \dfrac{10- 12}{\sqrt{\dfrac{3^2}{49} + \dfrac{4^2}{64}}}[/tex]
[tex]Z = \dfrac{-2}{\sqrt{\dfrac{9}{49} + \dfrac{16}{64}}}[/tex]
[tex]Z = \dfrac{-2}{\sqrt{0.18367 +0.25}}[/tex]
[tex]Z = \dfrac{-2}{\sqrt{0.43367}}[/tex]
[tex]Z = \dfrac{-2}{0.658536}[/tex]
Z = - 3.037
Z [tex]\simeq[/tex] - 3.04
The P-value = 2P (z < -3.04)
From the z tables
= 2 × (0.00118)
= 0.00236
Thus, since P-value is less than the level of significance, we fail to reject the null hypotheses [tex]H_o[/tex]
Select all graphs that represent functions
Answers
Answer:
where is the functions
Step-by-step explanation:
Brian borrows $7,400 from Ed, who charges him 12% simple interest each year. How much will Brian pay Ed, if he repays after 5 years?
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Answer:
$11,840
Step-by-step explanation:
Answer:
$11,840
Step-by-step explanation:
TRUST ME
A right triangle has an area of 36 square units.
If you draw scaled copies of this triangle using the scale factors in the table, what will the areas of these scaled copies be?
Answers
If you draw scaled copies of this triangle using the scale factors in the table, what will the areas of these scaled copies be?
Answer:
the answer is 4
ANSWER ASAP AS MANY AS YOU CAN ITS FOR FINALS
Name the relationship complementary,
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2. Alternate exterior
3. Linear pair
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can you understand ........
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Answer:
Step-by-step explanation:
is the first choice, no other terms have anything in common with the number
399 or variable w
PLEASE HELP if you help you like to play among us
Subtracting a number is the same as adding its opposite.
Use this understanding to complete each of the equations below.
CLEAR CHECK
Answers
Answer:
-5 - (-7) = -5 + -7
= 2
-5 - 7 = -5 + -7
= -12
A polygon is graphed on a coordinate plane, with a vertex located at
a point represented by (x,y).
The polygon is dilated with a scale factor, a , with the origin as the
center of dilation. The dilated image of the polygon is larger than
the polygon.
Which statement is true?
Answers
Answer:
a is greater than 1
Step-by-step explanation:
Let the two polygons be represented as A and B.
Where A is the original polygon and B is the image of A
Such that
Polygon A has vertex (x,y) and scale factor = a
From the question, we understand that polygon B is bigger than A
When the dilated image (polygon B) is bigger than the original image (polygon A), then the scale factor is greater than 1.
Take for instance.
One of the coordinate point of polygon A is (2,4)
The corresponding coordinate point of polygon B will be greater than (2,4) because a is greater than 1.
Take a as 2:
The corresponding point on Polygon B would be 2 * (2,4) = (4,8)
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Answers
Answer:
The Answer is 12 feet
Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
Plug in 60 for t and calculate
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Answers
Answer:
a. 73 percent
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Step-by-step explanation:
What is the present value of ₱30,000 due in 27 months at 3% compounded annually?
Answers
Answer:
32,063.06
Step-by-step explanation:
the formula for compound interest: [tex]A = P(1+\frac{r}{n})^{nt\\}[/tex]
so to use this you are essentially solving for a.
p is the principle (or initial) amount deposited.
r is the rate (in percent)
n is the number of time periods compounded (like annually, monthly, weekly, or daily)
t is the time period (in years)
In this instance the formula looks like: [tex]A = 30,000(1+\frac{0.03}{1})^{1*2.25}[/tex]
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Answers
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Step-by-step explanation:
2 1/2 --> 5/2
2 2/3 --> 8/3
5/2 / 8/3
15/6 / 16/6
15. 16
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6*15 ÷ 16*6
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What is the result of 60-15? Use the model to find the answer. A 4 B 5 C 12 D 20
Answers
Answer:
its a).4
Step-by-step explanation: 60 divided by 15= 4 you can use a calculator to check if im right if you dont trust me
The answer would be 4 if the number expression is 60 ÷ 15 after using the arithmetic operation, option (A) 4 is correct.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that is +, -, ×, and ÷.
It is given that:
The number expression is:
60 ÷ 15
Using model:
= (15 + 15 + 15 + 15) ÷ 15
= 1 + 1 + 1 + 1
= 4
Thus, the answer would be 4 if the number expression is 60 ÷ 15 after using the arithmetic operation, option (A) 4 is correct.
Learn more about the arithmetic operation here:
brainly.com/question/20595275
#SPJ6
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Answer:
A.
Step-by-step explanation:
It has both in it, so its correct
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Answer:
9.9 months not counting mortgage or any other factors
Step-by-step explanation:
Determine the total surface area of each right triangle-based prism
Answers
Answer:
small prism: 630 m²large prism: 2520 m²Step-by-step explanation:
The total surface area of the prism is the sum of the base area and the lateral area. The base area is made up of two right triangles, so will be the product of the triangle leg dimensions. The lateral area is made up of three rectangles whose width is that of the prism and whose equivalent length is the perimeter of the triangle base.
For the smaller prism, the area is ...
(20 m)(21 m) +(3 m)(20 m + 21 m + 29 m) = 420 m² +210 m² = 630 m²
The larger prism is similar, with a scale factor of 2, so its area will be 2² = 4 times that of the smaller prism:
4×630 m² = 2520 m²
__
In summary, the total surface area of each prism is ...
small prism: 630 m²large prism: 2520 m²Representative: “I am planning to attend a company-paid conference. My charges will include $412.00 for airfare, $378.00 for conference registration, and $210.00 for food.” Supervisor: “Please submit an expense form for a total of __________ when you return.”
Answers
When he returns, the total will be "$1,000".
Given charges are:
For airfare,
= $412.00
For conference registration,
= $378.00
For food,
= $210.00
The total charges will be:
= [tex]Airfare+Conference \ registration+Food[/tex]
= [tex]412+378+210[/tex]
= [tex]1,000[/tex] ($)
Thus $1,000 is the right answer.
Learn more:
https://brainly.com/question/18057159
time. weight
8. 0.04
9. 0.07
10. 0.14
11. 0.25
12. 0.49
what is the average rate of change in weight of the plankton from week 8 to week 12?
A) 0.0265
B)0.0375
C)0.055
D)0.1125
Answers
Answer:D
Because 0.49/12 -0.04/8 = 0.1125
A store manager purchases a DVD for $15. He marks it up to $21.75 in order to make a profit. What is the percent of increase?
Answers
(21.75-15)/15 = 0.45 * 100
There is a 45% increase
0.25 of 40 plz plz help
Answers
Find the value of x.
Group of answer choices
77
34
69
146
Answers
Answer:
69
Step-by-step explanation:
Use the 3x-2 and take it out
I need help with this
Answers
Answer:
A
Step-by-step explanation:
process of elimination... :D
A Polynomial, p(x), has zeros when x = -2, x = 1/3, X = 3. What could be the equation of p(x)?
Answers
Answer:
(x+2)(x-1/3)(x-3)
Step-by-step explanation:
This could be a possible equation, the signs of the of the roots are always the opposite in the equation form.
What is the equation in slope-intercept form of the line that passes through the point (6, 1) and is parallel to the line represented by
y = -3x + 2?
Enter your answer by filling in the boxes.