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3 years ago

Given: ZDEF is a right angle. Using a paragraph proof, prove 41 is acute.

Mathematics

1 answer:

Slav-nsk [51]3 years ago

4 0

Let G be some point on the diagonal line away from point E.

Angle DEG represents angle 1.

We're given that angle DEF is a right angle which means it's 90 degrees. Angle DEG is some angle smaller than 90 degrees. By definition, that must mean angle 1 is acute. Any acute angle is smaller than 90 degrees. There's not much else to say other than this is just a definition problem.

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Extra side notes:

If angle 1 was a right angle, then that would mean angle GEF would have to be 0 degrees; however the diagram shows this isn't the case.

If angle 1 was obtuse, then there's no way we'd be able to fit it into angle DEF. In other words, there's no way to have an angle larger than 90 fit in a 90 degree angle.

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Completely factorize (2x+3)^-2 + 2x(2x+3)^-3

Alexxx [7]

Hello,

$\dfrac{1}{(2x+3)^2} + \dfrac{2x}{(2x+3)^3} \\

= \dfrac{(2x+3)+2x}{(2x+3)^3}\\

= \dfrac{4x+3}{(2x+3)^3}$

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3 years ago

Chase is building a birdhouse in the shape of a regular polygon. He knows that the measure of the interior angle is twice the me

mel-nik [20]

Answer:

The perimeter of the base of the birdhouse is 36 units

Step-by-step explanation:

<u><em>The complete question is</em></u>

Chase is building a birdhouse in the shape of a regular polygon. He knows that the measure of the interior angle is twice the measure of the exterior angle and the length of a diagonal that passes through the center is 12. What is the perimeter of the base of the birdhouse?

step 1

Find the measure of the interior angle

Let

x ---> the measure of the interior angle

y ---> the measure of the exterior angle

Remember that

the sum of the interior and exterior angle in any polygon is equal to 180 degrees

$x+y=180^o$ ----> equation A

we have that

the measure of the interior angle is twice the measure of the exterior angle

$x=2y$ ----> equation B

substitute equation B in equation A

$2y+y=180$

$y=60^o$

$x=120^o$

That means-----> The figure is a regular hexagon

step 2

Remember that

The length of the diagonal that passes through the center of the hexagon is equal to two times the length of the regular hexagon

Let

b ----> the length side of the hexagon

$b=12/2=6\ units$

The perimeter of the hexagon is given by the formula

$P=6b$

substitute

$P=6(6)=36\ units$

3 0

3 years ago

What is mathematical equation?

Talja [164]

Answer:

A statement asserting the equality of two expressions, usually written as a linear array of symbols that are separated into left and right sides and joined by an equal sign.

Step-by-step explanation:

A statement asserting the equality of two expressions, usually written as a linear array of symbols that are separated into left and right sides and joined by an equal sign.

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2 years ago

Read 2 more answers

What is the simplified form of (1/x)-(2/x^2+x)

julsineya [31]

The answer would be C)3-x/x(x-1)

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3 years ago

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in 1991, a gallup poll reported this percent to be 79%. using the data from this poll, test the claim that the percent of driver

snow_lady [41]

We reject our null hypothesis, H₀, at a level of significance of =0.01 since the P-value is less than that threshold. There is compelling statistical data to indicate that since 1991, the proportion of drivers who love driving has decreased.

Given,

The Pew Research Center recently polled n=1048 U.S. drivers and found that 69% enjoyed driving their automobiles.

In 1991, a Gallup poll reported this percentage to be 79%. using the data from this poll, test the claim that the percentage of drivers who enjoy driving their cars has declined since 1991.

To report the large-sample z statistic and its p-value,

Null hypothesis,

H₀ : p = 0.79

Alternative hypothesis,

Ha : p < 0.79

Level of significance, α = 0.01

Under H₀

Test statistic,

$Z_0= \frac{\hat p - p}{\sqrt{\frac{p(1-p)}{n} } }$

Z₀ = -7.948

The alternative hypothesis(Ha) is left-tailed, so the P-value of the test is given by

P-value = P(z <-7.945)

= 0.000 (from z-table)

Since the P-value is smaller than given level of significance, α=0.01 we reject our null hypothesis, H₀, at α=0.0.1 level Strong statistical evidence to conclude that the percentage of drivers who enjoy driving their cars has declined since 1991.

To learn more about hypothesis click here:

brainly.com/question/17173491

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1 year ago