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3 years ago

Y=6x-11 -2x-3y=-7 solve each system of equation by substitution

Mathematics

1 answer:

Anit [1.1K]3 years ago

5 0

Answer:

(2, 1 )

Step-by-step explanation:

Given the 2 equations

y = 6x - 11 → (1)

- 2x - 3y = - 7 → (2)

Substitute y = 6x - 11 into (2)

- 2x - 3(6x - 11) = - 7 ← distribute and simplify left side

- 2x - 18x + 33 = - 7

- 20x + 33 = - 7 ( subtract 33 from both sides )

- 20x = - 40 ( divide both sides by - 20 )

x = 2

Substitute x = 2 into (1) for corresponding value of y

y = 6(2) - 11 = 12 - 11 = 1

Solution is (2, 1 )

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Given a bag of 5 blue, 3 green, and 8 red marbles.. What is the probability of picking a blue

Anvisha [2.4K]

$b = 5, \: g = 3, \: r = 8$

$total = 5 + 3 + 8 = 16$

$p(b) = \frac{5}{16}$

$p(g |without \: replacement|) = \frac{3}{16 - 1} = \frac{3}{15} = \frac{1}{5} \\$

$p(b \: and \: g) = \frac{5}{16} \times \frac{1}{5} = \frac{1}{16}$

6 0

3 years ago

Factor by grouping. 9c^3-12c^2+18c-24

xeze [42]

Answer:

$9c^3 - 12c^2 - 18c - 24= [3c^2 - 6][3c - 4]$

Step-by-step explanation:

Given

$9c^3 - 12c^2 - 18c - 24$

Required

Factor

Group into 2

$[9c^3 - 12c^2] - [18c + 24]$

Factorize each group

$3c^2[3c - 4] - 6[3c - 4]$

Factor out 3c - 4

$[3c^2 - 6][3c - 4]$

Hence:

$9c^3 - 12c^2 - 18c - 24= [3c^2 - 6][3c - 4]$

8 0

2 years ago

What number will the function return if the input is 15.4?

wlad13 [49]

The rule of the function is to multiply the input by 3, since one yard is equal in length to three feet.

So, if the input is 15.4, the output will be

$f(x)=3x \implies f(15.4)=3\cdot 15.4 = 46.2$

4 0

3 years ago

The sum of two numbers is -10.5.

grandymaker [24]

Answer:

-5 and -5.5;

-12.5 and 2

Step-by-step explanation:

Two negative addends, can be added together to give -10.5.

For example:

(-5) + (-5.5) = -5 - 5.5 = -10.5

Also, it is possible for one of the addends to be negative while the other is positive, and their sum will give us -10.5.

For example:

The sum of -12.5 and 2 will give us -10.5.

We are adding a positive and a negative number here. As usual, we will subtract the smaller number from the bigger number, while the result will carry the sign of the bigger number, which in this case is negative sign.

Thus:

(-12.5) + (2) = -10.5

4 0

3 years ago

Nick wrote the function p(x) = 17 + 42x – 7x2 in vertex form. His work is below.

Finger [1]

Answer:

step 3

Step-by-step explanation:

he should have subtracted 9 to the outside.

whatever you do to the inside you must do to the opposite to the outside

so your final form must be -7(x-3)^2 + 8

8 0

2 years ago