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
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)
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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:
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y= 0
④ Find x.
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x= 2(0)
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Answer:
A.
Step-by-step explanation:
It has both in it, so its correct
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Subtracting a number is the same as adding its opposite.
Use this understanding to complete each of the equations below.
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Answers
Answer:
-5 - (-7) = -5 + -7
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Representative: “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.
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Answer:
A
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A right triangle has an area of 36 square units.
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Answer:
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Answer:
where is the functions
Step-by-step explanation:
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Answers
Answer:
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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
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In summary, the total surface area of each prism is ...
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Answer:
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Step-by-step explanation:
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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.
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Answer:
(2c+6)+3(c+8)
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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:
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[tex]\mathbf{H_1:\mu_1\ne\mu_2}[/tex]
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It is given that:
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60 ÷ 15
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Step-by-step explanation:
Answer:
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Enter your answer by filling in the boxes.