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3 years ago

15

The length of a rectangular garden is 9 feet longer than its width. If the garden’s perimeter is 182 feet, what is the area of t

he garden in square feet? (please show all work)

1 answer:

Ivanshal [37]3 years ago

8 0

Answer:

1660.75 square feet

Step-by-step explanation.

Width=<em>x</em>

Length =<em>x</em>+9

(<em>(</em><em>x</em><em>)</em><em>+</em><em>(</em><em>x</em><em>+</em><em>9</em><em>)</em>)×2=182 feet

(2x+9)×2=182

18+4x=164

x=36.5

Width=36.5 feet

Length=45.5 feet

Area=36.5×45.5

=1660.75 square feet

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What all is equivalent to 7:5

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A, B, and C are all equal to the ratio 7:5

If you simplify each of the numbers in A, B, and C, you will find that they will come to equal 7:5

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3 years ago

What are the coordinates of the image of the point (1-, 2) under a dilation of 3 with the origin

Gemiola [76]

Answer:

The image of the point (1, -2) under a dilation of 3 is (3, -6).

Step-by-step explanation:

Correct statement is:

<em>What are the coordinates of the image of the point (1, -2) under a dilation of 3 with the origin.</em>

From Linear Algebra we get that dilation of a point with respect to another point is represented by:

$\vec P' = \vec R + r\cdot (\vec P-\vec R)$ (Eq. 1)

Where:

$\vec R$ - Reference point with respect to origin, dimensionless.

$\vec P$ - Original point with respect to origin, dimensionless.

$r$ - Dilation factor, dimensionless.

If we know that $\vec R = (0,0)$ , $\vec P = (1, -2)$ and $r = 3$ , then the coordinates of the image of the original point is:

$\vec P' = (0,0) +3\cdot [(1,-2)-(0,0)]$

$\vec P' = (0,0) + 3\cdot (1,-2)$

$\vec P' = (3,-6)$

The image of the point (1, -2) under a dilation of 3 is (3, -6).

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2 years ago

The sum of 55+66 as the product of their gcf and another sum

marusya05 [52]

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3 years ago

Read 2 more answers

Question:Find the area of he trapezoid by decomposing it into other shapes.

Ad libitum [116K]

Answer:

D) 171 cm²

Step-by-step explanation:

You don’t actually need to decompose it. You could just do it as a trapezoid:

(15+23)/2=19

19x9=171

If you want to decompose it into 2 triangles and a rectangle:

10=15x9=135

1/2(3)(9)=13.5

1/2(5)(9)=22.5

135+13.5+22.5=171 also

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2 years ago

The temperature of coffee served at a restaurant is normally distributed with an average temperature of 160 degrees Fahrenheit a

posledela

Answer:

The 20th percentile of coffee temperature is 155.4532 degrees Fahrenheit.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 160 degrees

Standard Deviation, σ = 5.4 degrees

We are given that the distribution of temperature of coffee is a bell shaped distribution that is a normal distribution.

Formula:

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

We have to find the value of x such that the probability is 0.2

$P( X < x) = P( z < \displaystyle\frac{x - 160}{5.4})=0.2$

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

$\displaystyle\frac{x - 160}{5.4} = -0.842\\\\x = 155.4532$

Thus,

$P_{20}=155.4532$

The 20th percentile of coffee temperature is 155.4532 degrees Fahrenheit.

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2 years ago