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3 years ago

Prove that angle W is congruent to angle Y with a two column proof.

Mathematics

1 answer:

iren2701 [21]3 years ago

4 0

Statement 1: WXYZ is a kite

Reason 1: Given

Statement 2: WX = XY and WZ = YZ

Reason 2: Definition of a kite

Statement 3: XZ = XZ

Reason 3: Reflexive property

Statement 4: Triangle WXZ = Triangle YXZ

Reason 4: SSS Congruence

Statement 5: Angle W = Angle Y

Reason 5: CPCTC

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Extra notes:

* A kite is a quadrilateral that has two pairs of adjacent congruent sides. In this case, WX and XY is one pair of congruent sides that are adjacent (ie next to each other). So that's why WX = XY. Similarly, WZ = YZ is the second pair of adjacent congruent sides.

* Draw in a segment from point X to point Z to help form two triangles. The two triangles are congruent as proven in statement 4. One triangle is a reflection over the line XZ to get the other triangle.

* Due to this reflection, angle W reflects over line XZ to get angle Y. Proving that angle W = angle Y

* SSS means "side side side", basically saying "you use three pairs of congruent sides to prove two triangles congruent".

* The acronym CPCTC stands for "corresponding parts of congruent triangles are congruent"

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Step-by-step explanation:

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3 years ago

When using the given diagram to determine the area of the pentagon by decomposition, which statements are correct?:

pogonyaev

Answer:

Options (B) and (E)

Step-by-step explanation:

Area of ΔABC = $\frac{1}{2}(\text{Base})(\text{Height})$

= $\frac{1}{2}(14)(6)$

= 42 in²

Area of trapezoid ADEC = $\frac{1}{2}(b_1+b_2)h$

[Here, $b_1$ and $b_2$ are the parallel sides and 'h' is the height of the isosceles trapezoid given]

= $\frac{1}{2}(10+14)(8)$

= 96 in²

Area of the pentagon = Area of triangle ABC + Area of trapezoid ADEC

= 42 + 96

= 138 in²

Therefore, Options (B) and (E) are the correct options.

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3 years ago

Find the particular solution of the differential equation that satisfies the initial condition(s). f ''(x) = x−3/2, f '(4) = 1,

sweet [91]

Answer:

Hence, the particular solution of the differential equation is $y = \frac{1}{6} \cdot x^{3} - \frac{3}{4}\cdot x^{2} - x$ .

Step-by-step explanation:

This differential equation has separable variable and can be solved by integration. First derivative is now obtained:

$f'' = x - \frac{3}{2}$

$f' = \int {\left(x-\frac{3}{2}\right) } \, dx$

$f' = \int {x} \, dx -\frac{3}{2}\int \, dx$

$f' = \frac{1}{2}\cdot x^{2} - \frac{3}{2}\cdot x + C$ , where C is the integration constant.

The integration constant can be found by using the initial condition for the first derivative ( $f'(4) = 1$ ):

$1 = \frac{1}{2}\cdot 4^{2} - \frac{3}{2}\cdot (4) + C$

$C = 1 - \frac{1}{2}\cdot 4^{2} + \frac{3}{2}\cdot (4)$

$C = -1$

The first derivative is $y' = \frac{1}{2}\cdot x^{2}- \frac{3}{2}\cdot x - 1$ , and the particular solution is found by integrating one more time and using the initial condition ( $f(0) = 0$ ):

$y = \int {\left(\frac{1}{2}\cdot x^{2}-\frac{3}{2}\cdot x -1 \right)} \, dx$

$y = \frac{1}{2}\int {x^{2}} \, dx - \frac{3}{2}\int {x} \, dx - \int \, dx$

$y = \frac{1}{6} \cdot x^{3} - \frac{3}{4}\cdot x^{2} - x + C$

$C = 0 - \frac{1}{6}\cdot 0^{3} + \frac{3}{4}\cdot 0^{2} + 0$

$C = 0$

Hence, the particular solution of the differential equation is $y = \frac{1}{6} \cdot x^{3} - \frac{3}{4}\cdot x^{2} - x$ .

5 0

3 years ago

In assessing the validity of any test of hypotheses, it is good practice to a. examine the probability model that serves as a ba

ehidna [41]

Answer:

The Correct option is - d. all of the above.

Step-by-step explanation:

To find - In assessing the validity of any test of hypotheses, it is good practice to

a. examine the probability model that serves as a basis for the test by using exploratory data analysis on the data.

b. determine exactly how the study was conducted.

c. determine what assumptions the researchers made.

d. all of the above.

Proof -

All the Given options are correct to study the validity of a hypothesis test.

So,

The Correct option is - d. all of the above.

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3 years ago

Which algebraic expression is equivalent to the expression below? 10(5x - 3/5) + 50

Kamila [148]

Hello!

You can distribute the 10

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Combine like terms

50x = 44

Divide both sides by 50

x = 44/50

Simplify

x = 22/25 = 0.88

The answer is x = 0.88

Hope this helps!

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3 years ago