Help please!!.Use estimation to check the answer to this story problem.

Find the equation of a line, in slope-intercept form of a line that passes through the point (9, 2) and is perpendicular to the

11Alexandr11 [23.1K]

Answer:

The equation of the line would be y = -1/2x + 13/2

Step-by-step explanation:

In order to get the slope of the line, you need to first find the slope of the original line. You do this by solving for y.

2x - y = 8

-y = -2x + 8

y = 2x - 8

Now that you have the slope, we take the opposite and reciprocal slope to be the perpendicular (based on the definition of perpendicular lines). This means we take the opposite of 2 (which is -2) and then we flip the term (which means -2 becomes -1/2).

To find the slope-intercept form, we'll use our new slope of -1/2 and a point in point-slope form and solve for y.

y - y1 = m(x - x1)

y - 2 = -1/2(x - 9)

y - 2 = -1/2x + 9/2

y = -1/2x + 13/2

4 0

3 years ago

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The combined area of two squares is 80 square centimeters. Each side of one square is twice as long as a side of the other squar

olganol [36]

Answer:

The length of each side of the larger square is 8 centimeter.

Step-by-step explanation:

Given:

The combined area of two squares is 80 square centimeters. Each side of one square is twice as long as a side of the other square.

Now, to find the length of each side of the larger square.

Let $s$ be the length of the smaller square.

So, the length of the larger square = $2s.$

Now, we find the areas of the square by putting formula:

The area of smaller square = length² $=s^2.$

The area of larger square = (length)² $=(2s)^2=4s^2.$

As, given:

The combined area of two squares is 80 square centimeters.

According to question:

$s^2+4s^2=80\\5s^2=80$

So, dividing both sides by 5 we get:

$s^2=16$

Using square root on both sides we get:

$s=4\ centimeter.$

And, to get the length of each side of the larger square we substitute the value of $s$ :

$2s=2\times 4=8\ centimeter.$

The length of larger square = 8 centimeter

Therefore, the length of each side of the larger square is 8 centimeter.

8 0

3 years ago

If the discriminant of a quadratic equation is -4, how many solutions does the equation have?

SCORPION-xisa [38]

No real solutions....................

5 0

3 years ago

Suppose that the amount of time T a customer spends in a bank is exponentially distributed with an average of 10 minutes. What i

Bad White [126]

Answer:

The probability that a customer will spend more than 15 minutes total in the bank, given that the customer has already waited over 10 minutes is 0.6065.

Step-by-step explanation:

The random variable T is defined as the amount of time a customer spends in a bank.

The random variable T is exponentially distributed.

The probability density function of a an exponential random variable is:

$f(x)=\lambda e^{-\lambda x};\ x>0$

The average time a customer spends in a bank is β = 10 minutes.

Then the parameter of the distribution is:

$\lambda=\frac{1}{\beta}=\frac{1}{10}=0.10$

An exponential distribution has a memory-less property, i.e the future probabilities are not affected by any past data.

That is, P (X > s + x | X > s) = P (X > x)

So the probability that a customer will spend more than 15 minutes total in the bank, given that the customer has already waited over 10 minutes is:

P (X > 15 | X > 10) = P (X > 5)

$\int\limits^{\infty}_{5} {f(x)} \, dx =\int\limits^{\infty}_{5} {\lambda e^{-\lambda x}} \, dx\\=\int\limits^{\infty}_{5} {0.10 e^{-0.10 x}} \, dx\\=0.10\int\limits^{\infty}_{5} {e^{-0.10 x}} \, dx\\=0.10|\frac{e^{-0.10 x}}{-0.10}|^{\infty}_{5}\\=[-e^{-0.10 \times \infty}+e^{-0.10 \times 5}]\\=0.6065$

Thus, the probability that a customer will spend more than 15 minutes total in the bank, given that the customer has already waited over 10 minutes is 0.6065.

8 0

3 years ago

How do I show work for this?

romanna [79]

Answer:

you don't because its not relivant

Step-by-step explanation:

4 0

3 years ago

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