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3 years ago

12

Figure ABCDE is the result of a 180 °rotation of figure LMNOP about the point.

1 answer:

Blababa [14]3 years ago

5 0

Angle O in the pre-image corresponds to angle D in the image.

Step-by-step explanation:

Step 1; Shape LMNOP is rotated through 180° about point F to create the shape ABCDE. The highest point on LMNOP will be the lowest point on ABCDE and the lowest point on LMNOP will be the highest point on ABCDE. The highest point and the lowest point on LMNOP are P and N respectively. The highest and the lowest point on ABCDE are C and E. So Angle P equals angle E and angle N equals angle C.

Step 2; We measure the sides and assign the corresponding values from the first shape to the second shape.

Angle E = Angle P,

Angle D = Angle O,

Angle C = Angle N,

Angle B = Angle M,

Angle A = Angle L.

So angle D in the shape ABCDE corresponds to angle O in the shape LMNOP.

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Help with Algebra 2: 1. <img src="https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B7%5D%7Bx%5E5%7D%20%7D%7B%5Csqrt%5B4%5D%7Bx%5E2%7D%

Mars2501 [29]

Answer:

See explanation

Step-by-step explanation:

1. Given the expression

$\dfrac{\sqrt[7]{x^5} }{\sqrt[4]{x^2} }$

Note that

$\sqrt[7]{x^5}=x^{\frac{5}{7}} \\ \\\sqrt[4]{x^2}=x^{\frac{2}{4}}=x^{\frac{1}{2}}$

When dividing $\sqrt[7]{x^5}$ by $\sqrt[4]{x^2},$ we have to subtract powers (we cannot subtract 4 from 7, because then we get another expression), so

$\dfrac{5}{7}-\dfrac{2}{4}=\dfrac{5}{7}-\dfrac{1}{2}=\dfrac{5\cdot 2-1\cdot 7}{14}=\dfrac{3}{14}$

and the result is $x^{\frac{3}{14}}=\sqrt[14]{x^3}$

2. Given equation $3\sqrt[4]{(x-2)^3} -4=20$

Add 4:

$3\sqrt[4]{(x-2)^3} -4+4=20+4\\ \\3\sqrt[4]{(x-2)^3}=24$

Divide by 3:

$\sqrt[4]{(x-2)^3} =8$

Rewrite the equation as:

$(x-2)^{\frac{3}{4}}=8\\ \\(x-2)^{\frac{3}{4}}=2^3$

Hence,

$\left((x-2)^{\frac{3}{4}}\right)^{\frac{4}{3}}=(2^3)^{\frac{4}{3}}\\ \\x-2=2^{3\cdot \frac{4}{3}}\\ \\x-2=2^4\\ \\x-2=16\\ \\x-2+2=16+2\\ \\x=18$

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3 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

A business reports a net income of −$2,730−$2,730 over a 3-month period.

bearhunter [10]

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3 years ago

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A package of twelve cans of black beans cost $6.84. What is the cost of 5 can of black

elena-s [515]

Answer:

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Step-by-step explanation:

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3 years ago

The mean maximum aerobic power (VO2MAX) score for women ages 20 to 29 is 36 ml/min/kg with a standard deviation of 7 ml/min/kg.

Scrat [10]

Answer:

0.099 is the probability of a woman between the ages of 20 to 29 having a VO2MAX score of greater than 45 ml/min/kg.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 36 ml/min/kg

Standard Deviation, σ = 7 ml/min/kg

We assume that the distribution of aerobic power is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) P(woman between the ages of 20 to 29 having a VO2MAX score of greater than 45 ml/min/kg.)

P(x > 45)

$P( x > 45) = P( z > \displaystyle\frac{45 - 36}{7}) = P(z > 1.285)$

$= 1 - P(z \leq 1.285)$

Calculation the value from standard normal z table, we have,

$P(x > 45) = 1 - 0.901 =0.099 = 9.9\%$

0.099 is the probability of a woman between the ages of 20 to 29 having a VO2MAX score of greater than 45 ml/min/kg.

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3 years ago