If f(x)=x^2 and g(x)=x+3, which of the following statements is true?

Can i get help? Don’t really understand.

Rufina [12.5K]

First option: correct. This is because angles WOX and XOZ are supplementary, so

$m\angle WOX=180^\circ-104^\circ=76^\circ$

Second option: correct. By the inscribed angles theorem, we have

$m\angle XWZ=m\angle XYZ=\dfrac{113^\circ}2=56.5^\circ$

Angles WOX and YOZ are congruent because they form a vertical pair; they both have measure 76 degrees. This means angles WXY and WZY are also congruent, since the interior angles of any triangle sum to 180 degrees in measure. Therefore triangles WXO and YZO form a side-side-side pair, and all SSS triangles are similar.

Third option: not correct. There is a theorem (not sure what the name is) regarding intersecting chords that asserts the average of the measures of arcs WY and XZ is the same as the measure of angle XOZ. This means

$\dfrac{m\widehat{WY}+113^\circ}2=104^\circ\implies m\widehat{WY}=95^\circ$

Fourth option: not correct. This is because arcs WX and XZ are not "supplementary" in the sense that they do not form a semicircle and their measures do not add to 180 degrees. We know this because it's clear that point O is not the center of the circle. If it was, then angle XOZ would be a central angle and its measure would be the same as the arc XZ it subtends.

Fifth option: correct. The theorem mentioned in the assessment of the third option makes itself useful here. We have

$\dfrac{m\widehat{WX}+m\widehat{YZ}}2=m\angle WOX\implies m\widehat{WX}+m\widehat{YZ}=2\cdot76^\circ=152^\circ$

4 0

3 years ago

Sears sells a sweater for $ 69 and has a 60% markup on the selling price what is the cost of the sweater to sears

Jobisdone [24]

$110.40 because 60% of $69 is $41.40. Then add $69 and $41.40.

8 0

3 years ago

Select the equation of the line that passes through the point (−2, 3) and is perpendicular to the line on the graph.

valentinak56 [21]

Y = 3
It passes through the point and is perpendicular to x = 4

4 0

3 years ago

Read 2 more answers

Which statement represents 8 more than 6 times a number is 5 less than 3 times that number

riadik2000 [5.3K]

6n+8+3n-5 because you have to flip the numbers when a question says less than or more than

3 0

3 years ago

Mr. Clark claims that he has a coin that is weighted so that the probability of heads is 40%. To test this, his students flip th

Hunter-Best [27]

While I'm not sure what the answer choices were, his claim is likely to be true.
Since he claims the probability of heads is 40%, that should be what we see in an experiment. 0.38 is very close to 0.40, or 40%, so this is true. Therefore his claim is likely to be true, and the probability of tails should be about 60%.

6 0

4 years ago