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3 years ago

Given: Quadrilateral PQRS is a rectangle. Prove: PR = QS

Mathematics

1 answer:

lord [1]3 years ago

6 0

Answer:

Given: Quadrilateral P QR S is a rectangle.

To prove :PR= Q S

Construction : Join PR and Q S.

Proof: In Rectangle PQRS, and

→ taking two triangles PSR and Δ QRS

1. PS = Q R

2. ∠ PS R = ∠ Q RS [Each being 90°]

3. S R is common.

→ ΔP SR ≅ Δ Q RS → [Side-Angle-Side Congruency]

∴ PR =Q S [ corresponding part of congruent triangles ]

Hence proved.

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Please can someone do this for me? thanks alot x

Nimfa-mama [501]

Answer:

Learning Objective: Use the mean and range to compare the spread and averages.

a) Sarah Mean = 70.9, Katie Mean = 78.9

b) Sarah Range = 15, Katie Range = 25

c) Sentences

- The mean shows, on average, Sarah was 8 seconds quicker than Katie.

- The range shows that Sarah was more consistent with her times. Katie had a larger spread of times which shows she was less consistent.

Step-by-step explanation:

Given:

Sarah's Data Set:

79, 70, 68, 75, 69, 64, 69, 75, 64, 76

Katie's Data Set:

79, 79, 76, 81, 89, 76, 64, 85, 82, 78

To Find:

The mean and range of both data sets separately.

Work:

The mean of a data set is commonly known as the average. You find the mean by taking the sum of all the data values and dividing that sum by the total number of data values. The formula for the mean of a population is $\mu = \frac{{\sum}x}{N}$ .

The formula for the mean of a sample is $\bar{x} = \frac{{\sum}x}{n}$ .

Both of these formulas use the same mathematical process: find the sum of the data values and divide by the total. For the data values given above, the solution is: $\frac{709}{10} = 70.9$

Therefore, the mean of Sarah's data set is 70.9.

For Katie's Data Set, $\frac{789}{10} = 78.9$ .

Therefore, the mean of Katie's data set is 78.9.

To fill in the summary, we have to use the data we just calculated.

That summary can be found in the answer section.

4 0

2 years ago

Read 2 more answers

Find the value of x. B 6 8 А х D x = [?]

Keith_Richards [23]

Answer:

What's the question is that a good thing

5 0

3 years ago

Suppose P(A)=0.9, P(B)=0.4 and P(B|A)=0.2. What is P(A|B)?

Leokris [45]

The answer is 0.45

------------------------------------

Work Shown:

P(B|A) = P(B and A)/P(A)
0.2 = P(B and A)/0.9
0.2*0.9 = P(B and A)
0.18 = P(B and A)
P(B and A) = 0.18
P(A and B) = 0.18

P(A|B) = P(A and B)/P(B)
P(A|B) = 0.18/0.4
P(A|B) = 0.45

3 0

3 years ago

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A net is a two-dimensional pattern that can be folded to form a three-dimensional surface. T/F

Nitella [24]

Answer: True

Explanation:

Consider a 3D cardboard box that you can unfold. It would unfold into a 2D net that you can then re-fold back into its 3D form. The 2D net is useful to help visualize and calculate the surface area. The surface area is simply the total area of all the external faces.

4 0

3 years ago

Given the function f(x) = the quantity of 5x minus 3, divided by 4, which of the below expressions is correct?. f−1(x) = The qua

Sophie [7]

F(x) = [5x - 3] / 4

f[-1] (x) = {4 [f(x)] + 3 } / 5

Answer: f−1(x) = The quantity of 4x plus 3, divided by 5

6 0

3 years ago

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