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3 years ago

Write the point -slope form of the equation of each line given the slope and y-intercept. Slope=(2/3), y-intercept =0

Mathematics

1 answer:

MakcuM [25]3 years ago

6 0

Answer:

$\large\boxed{y-0=\dfrac{2}{3}(x-0)\to y=\dfrac{2}{3}x}$

Step-by-step explanation:

The point-slope form of ane equation of a line:

$y-y_1=m(x-x_1)$

m - slope

(x₁, y₁) - point on a line

We have:

$m=\dfrac{2}{3}$

y-intercept is for x = 0.

Therefore, if y-intercept = 0, then we have the point (0, 0).

$y-intercept=0\to(0,\ 0)$

Substitute:

$y-0=\dfrac{2}{3}(x-0)\to y=\dfrac{2}{3}x$

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2) 2(8r + 5) = 24 + 9r

Anna35 [415]

Answer:

r = 2

Step-by-step explanation:

2(8r + 5) = 24 + 9r

16r + 10 = 24 + 9r

16r - 9r = 24 - 10

7r = 14

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3 years ago

Read 2 more answers

The sum of two consecutive integers is one less than three times the smaller integer. Find the two integers.

Minchanka [31]

The small number is 2.

The large number is 3.

Step-by-step explanation:

Let the two consecutive numbers be x and x+1.

x be the small integer.
x+1 be the large integer.

The sum of these two consecutive integers = small integer + large integer

The sum of these two consecutive integers is x+x+1 = (2x+1)

It is given that,

The sum of two consecutive integers is one less than three times the smaller integer.
This means that, (2x+1) is one less than three times the smaller integer.
Here, the small integer is represented as x.

Therefore, it can determined that :

(2x+1) = 3x-1

Keeping x term on one side and constants on other side,

3x-2x = 1+1

x = 2

Therefore, the small number is 2 and the large number is x+1 = 3.

3 0

3 years ago

A. One player places 1 red, 5 green and 3 blue tiles in Bag A, and 6 red, 4 green, and 2 blue in Bag B. What is the probability

cupoosta [38]

Answer:

$\frac{8}{27}$ is the probability that a player draws out two tiles of the same color assuming they are drawing one tile from each bag.

Step-by-step explanation:

In each bag there are red, green, and blue tiles, meaning that no matter which color is pulled out first there is always some probability that the second tile will be the same color. So, we can set up three possible outcomes:

Red: The player pulls out a red tile first. This has a $\frac{1}{9}$ probability of happening. Then in order to succeed for the problem, the next tile also needs to be red which has a $\frac{6}{12}$ probability attached to it. $\frac{1}{9}$ × $\frac{6}{12}$ = $\frac{1}{18}$ probability of happening.

Green: There is a $\frac{5}{9}$ probability of the player pulling out a green tile first. In this case we want to calculate the probability of the second tile being green, which would be $\frac{4}{12}$ . $\frac{5}{9}$ × $\frac{4}{12}$ = $\frac{5}{27}$ .

Blue: There is a $\frac{3}{9}$ probability of the first tile being blue in which case we are hoping for the second tile to be blue as well. The probability of the second tile being blue is $\frac{2}{12}$ on its own, and them both being blue is $\frac{3}{9}$ × $\frac{2}{12}$ = $\frac{1}{18}$

Adding $\frac{1}{18}$ + $\frac{1}{18}$ + $\frac{5}{27}$ we get the answer $\frac{8}{27}$ .

4 0

3 years ago