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3 years ago

The interior angle measures of a convex pentagon are consecutive multiples of 4. find the measure of each interior angle.

Mathematics

1 answer:

lawyer [7]3 years ago

3 0

Answer:

100°, 104°, 108°, 112°,116°

Step-by-step explanation:

Let the smallest angle be $4x$ . Since, the interior angles are consecutive, the other angles are $4(x+1)$ , $4(x+2)$ , $4(x+3)$ and $4(x+4)$ .

Sum of interior angles = 540°

$4x+4(x+1)+4(x+2)+4(x+3)+4(x+4)=540$ °

$20x+40=540$ °

$20x=(540-40)$ °

$20x=500$ °

$x=(500/20)$ °

$x=25$

Using the value of x to calculate the angles:

$4x=4*25=100$ °

$4(x+1)=4*26=104$ °

$4(x+2)=4*27=108$ °

$4(x+3)=4*28=112$ °

$4(x+4)=4*29=116$ °

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Rewrite the radical expression as an expression with a rational exponent. the seventh root of x to the third power

kherson [118]

The expression with a rational exponent of the seventh root of x to the third power is x to the three sevenths power ⇒ answer A

Step-by-step explanation:

Let us explain how to change the radical expression as an expression

with a rational exponent

1. Find the number of the root and make it the denominator of the

fraction exponent

2. Find the power of the term under the radical and make it the

numerator of the fraction exponent

Examples:

$\sqrt{x^{n}}=x^{\frac{n}{2}}$

$\sqrt[3]{x^{n}}=x^{\frac{n}{3}}$

$\sqrt[5]{x^{n}}=x^{\frac{n}{5}}$

So $\sqrt[m]{x^{n}}=x^{\frac{n}{m}}$

∵ the radical expression is the seventh root of x to the third power

∵ seventh root = $\sqrt[7]{}$

∵ x to the third power = x³

∴ seventh root of x to the third power = $\sqrt[7]{x^{3}}$

Let us change it to the rational exponent

∵ $\sqrt[m]{x^{n}}=x^{\frac{n}{m}}$

∵ $\sqrt[7]{x^{3}}$

∴ m = 7 and n = 3

∴ $\sqrt[7]{x^{3}}$ = $x^{\frac{3}{7}}$

∵ $x^{\frac{3}{7}}$ is x to the three sevenths power

∴ $\sqrt[7]{x^{3}}$ is x to the three sevenths power

The expression with a rational exponent of the seventh root of x to the third power is x to the three sevenths power

Learn more:

You can learn more about radical equation is brainly.com/question/7153188

#LearnwithBrainly

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4 years ago

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Jobisdone [24]

Answer:

235

Step-by-step explanation:

Add the labeled angles

23+40+92+80

235

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soldi70 [24.7K]

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3 years ago

The Scottsdale fire department aims to respond to fire calls in 4 minutes or less, on average. Response times are normally distr

IgorC [24]

<h2><u>Answer with explanation</u>:</h2>

Let $\mu$ be the population mean.

As per given , we have

$H_0:\mu \leq4\\\\ H_a: \mu >4$

Since the alternative hypothesis is right-tailed , so the test is a right-tailed test.

Also, population standard deviation is given $\sigma=1$ , so we perform one-tailed z-test.

Test statistic : $z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

, where $\mu$ = Population mean

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For n= 18 , $\overline{x}=4.50$ , $\sigma=1$ , $\mu =4$ , we have

$z=\dfrac{4.5-4}{\dfrac{1}{\sqrt{18}}}\approx2.12$

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Decision : Since P-value(0.9660) > Significance level (0.01), it means we are failed to reject the null hypothesis.

[We reject null hypothesis if p-value is larger than the significance level . ]

Conclusion : We do not have sufficient evidence to show that the goal is not being met at α = .01 .

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