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2 years ago

What is the slope of the line? y + 1 = 3(x- 4)

Mathematics

2 answers:

user100 [1]2 years ago

8 0

Answer:

Step-by-step explanation:

What is the slope of the line?

y + 1 = 3(x- 4)

y + 1 = 3x - 12

y = 3x - 13

the number next to the x is the slope which is 3

answer : 3

NARA [144]2 years ago

5 0

Answer: 3

Step-by-step explanation:

Let's start by converting this equation to slope intercept form

First Simplify

$y + 1 = 3(x- 4)\\y+1=3x-12$

Then isolate y

$y+1-1=3x-12-1\\\\y=3x-13$

In slope intercept form, y=mx+b, the slope is m

In this equation the slope would be 3

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A building in a city has a rectangular base. the length of the base measures 65 ft less than twice the width. the perimeter of t

dybincka [34]

By solving a system of equations, we will see that the width is 170ft and the length 275 ft.

<h3>How to get the dimensions of the base?</h3>

For a rectangle of length x and width y, the perimeter is:

P = 2*(x + y).

Here we know that:

x = 2y - 65ft

p = 890ft = 2(x + y)

So we have a system of equations.

To solve this, we need to replace the first equation into the second one:

890ft = 2(x + y)

890ft = 2(( 2y - 65ft) + y)

Now we can solve this for y.

890ft = 4y - 130ft + 2y

890ft + 130ft = 6y

1020ft/6 = y = 170ft

So the width is 170ft, and we know that:

x = 2y - 65ft = 2*(170ft) - 65ft = 275ft

So the length is 275 ft.

If you want to learn more about systems of equations:

brainly.com/question/13729904

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5 0

2 years ago

Suppose that the probability that any particle emitted by a radioactive material will penetrate a certain shield is 0.01. If 10

AnnyKZ [126]

Answer:

a)P=0.42

b) $n\geq 297$

Step-by-step explanation:

We have a binomial distribution, since the result of each experiment admits only two categories (success and failure) and the value of both possibilities is constant in all experiments. The probability of getting k successes in n trials is given by:

$P=\begin{pmatrix}n\\ k\end{pmatrix} p^k(1-p)^{n-k}=\frac{n!}{k!(n!-k!)}p^k(1-p)^{n-k}$

a) we have k=2, n=10 and p=0.01:

$P=\frac{10!}{2!(10!-2!)}0.01^2(1-0.01)^{10-2}\\P=\frac{10!}{2!*8!}0.01^2(0.99)^{8}\\P=45*0.01^2(0.99)^8=0.42$

b) We have, $1-(1-p)^n=P$ , Here P is the probability that at least one particle will penetrate the shield, this probabity has to be equal or greater than 0.95. Therefore, this will be equal to subtract from the total probability, the probability that the particles do not penetrate raised to the total number of particles.