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3 years ago

Write a simplified polynomial expression in standard form to represent the area of the rectangle below.

Mathematics

2 answers:

Margarita [4]3 years ago

4 0

Answer:

The correct option is C.

Step-by-step explanation:

Given information: One side of the rectangle is (5x+2) and another sides of rectangle is (x-4).

The area of rectangle is

$A=length \times width$

Substitute length = (5x+2) and width = (x-4) in the above formula, to find the simplified polynomial expression in standard form to represent the area of the rectangle.

$A=(5x+2)\times (x-4)$

Using distributive property,

$A=5x(x-4)+2(x-4)$

$A=5x(x)+5x(-4)+2(x)+2(-4)$

On simplification we get

$A=5x^2-20x+2x-8$

On combining like terms we get

$A=5x^2+(-20x+2x)-8$

$A=5x^2+(-18x)-8$

$A=5x^2-18x-8$

Therefore the correct option is C.

motikmotik3 years ago

3 0

(5x+2)(x-4
5x (x)+2(x)+5x (-4)+2 (-4)
5x^2+2x-20x-8
5x^2-18x-8
C. 5x^2-18x-8

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An automobile company wants to determine the average amount of time it takes a machine to assemble a car. A sample of 40 times y

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Answer:

A 98% confidence interval for the mean assembly time is [21.34, 26.49] .

Step-by-step explanation:

We are given that a sample of 40 times yielded an average time of 23.92 minutes, with a sample standard deviation of 6.72 minutes.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample average time = 23.92 minutes

s = sample standard deviation = 6.72 minutes

n = sample of times = 40

$\mu$ = population mean assembly time

Here for constructing a 98% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.

So, a 98% confidence interval for the population mean, $\mu$ is;

P(-2.426 < $t_3_9$ < 2.426) = 0.98 {As the critical value of z at 1% level