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!
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Answer:
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Step-by-step explanation:
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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.
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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:
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;
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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]
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
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It is given that:
The number expression is:
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Step-by-step explanation:
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Answers
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Answers
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Step-by-step explanation:
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Answers
Answer:
x=0, y=0
Step-by-step explanation:
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3x +y= 0 -----(2)
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y= 0
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x= 2(0)
x= 0