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3 years ago

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Given the figure below is a special type of trapezoid and WX || YZ, which angle pairs can be proven supplementary by the given i

nformation? Select all that apply.
∠W and ∠Z
∠W and ∠Y
∠X and ∠Y
∠X and ∠Z
∠W and ∠X

2 answers:

RSB [31]3 years ago

8 0

Answer:

The answer:

<W and <Z

<X and <Y

<W and <X

Step-by-step explanation:

svetlana [45]3 years ago

6 0

Answer: The correct options are

(A) ∠W and ∠Z

(C) ∠X and ∠Y.

Step-by-step explanation: Given that the figure is a special type of trapezoid and WX || YZ.

We are to select all the angle pairs that can be proven supplementary by the given information.

We know that

if two parallel lines are cut by a transversal, then the sum of the measures of interior angles on the same side of the transversal is 180°.

In the given trapezoid, we have

WX || YZ and WZ is a transversal, so ∠W and ∠Z are interior angles on the same side of the transversal WZ.

So,

m∠W + m∠Z = 180°.

This implies that ∠W and ∠Z are supplementary.

Similarly,

WX || YZ and XY is a transversal, so ∠X and ∠Y are interior angles on the same side of the transversal XY.

So,

m∠X + m∠Y = 180°.

This implies that ∠X and ∠Y are supplementary.

Therefore, the pairs of angles that can be proven supplementary with the given information are

∠W and ∠Z ; ∠X and ∠Y.

Thus, (A) and (C) are correct options.

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natali 33 [55]

Answer:

The tangent line to the given curve at the given point is $y=9x-26$ .

Step-by-step explanation:

To find the slope of the tangent line we to compute the derivative of $y=2x^2-7x+6$ and then evaluate it for $x=4$ .

$(y=2x^2-7x+6)'$ Differentiate the equation.

$(y)'=(2x^2-7x+6)'$ Differentiate both sides.

$y'=(2x^2)'-(7x)'+(6)'$ Sum/Difference rule applied: $(f(x)\pmg(x))'=f'(x)\pm g'(x)$

$y'=2(x^2)'-7(x)'+(6)'$ Constant multiple rule applied: $(cf)'=c(f)'$

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$y'=4x-7+0$ Simplifying and apply constant rule: $(c)'=0$

$y'=4x-7$ Simplify.

Evaluate y' for x=4:

$y'=4(4)-7$

$y'=16-7$

$y'=9$ is the slope of the tangent line.

Point slope form of a line is:

$y-y_1=m(x-x_1)$

where $m$ is the slope and $(x_1,y_1)$ is a point on the line.

Insert 9 for $m$ and (4,10) for $(x_1,y_1)$ :

$y-10=9(x-4)$

The intended form is $y=mx+b$ which means we are going need to distribute and solve for $y$ .

Distribute:

$y-10=9x-36$

Add 10 on both sides:

$y=9x-26$

The tangent line to the given curve at the given point is $y=9x-26$ .

------------Formal Definition of Derivative----------------

The following limit will give us the derivative of the function $f(x)=2x^2-7x+6$ at $x=4$ (the slope of the tangent line at $x=4$ ):

$\lim_{x \rightarrow 4}\frac{f(x)-f(4)}{x-4}$

$\lim_{x \rightarrow 4}\frac{2x^2-7x+6-10}{x-4}$ We are given f(4)=10.

$\lim_{x \rightarrow 4}\frac{2x^2-7x-4}{x-4}$

Let's see if we can factor the top so we can cancel a pair of common factors from top and bottom to get rid of the x-4 on bottom:

$2x^2-7x-4=(x-4)(2x+1)$

Let's check this with FOIL:

First: $x(2x)=2x^2$

Outer: $x(1)=x$

Inner: $(-4)(2x)=-8x$

Last: $-4(1)=-4$

---------------------------------Add!

$2x^2-7x-4$

So the numerator and the denominator do contain a common factor.

This means we have this so far in the simplifying of the above limit:

$\lim_{x \rightarrow 4}\frac{2x^2-7x-4}{x-4}$

$\lim_{x \rightarrow 4}\frac{(x-4)(2x+1)}{x-4}$

$\lim_{x \rightarrow 4}(2x+1)$

Now we get to replace x with 4 since we have no division by 0 to worry about:

2(4)+1=8+1=9.

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3 years ago

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svetoff [14.1K]

Answer:

C, E

Step-by-step explanation:

A. INCORRECT

A is wrong because a reflection across the x-axis DOES move the position of the figure (as it is flipped, so the position changes), but it DOES NOT change the angle (since a shift in position doesn't equal to a change in angle measure)

B. INCORRECT

Although a reflection across the x-axis does change the position of the angle, it DOES NOT change the measure of the angle.

C. CORRECT

A reflection across the x-axis does in fact move the position of the figure and does not change the angle measure. Reflections only deal with flipping a figure, not changing it's shape/distorting it so that the angle will change.

D. INCORRECT

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E. CORRECT

Yes, a translation right WILL change the position of the figure but will NOT change the measure of the angle. This is because a translation is simply moving a figure up and down; it has nothing to do with changing the shape of the figure/distorting it so that the angle is different.

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g100num [7]

Answer:

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Step-by-step explanation:

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step 1

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