Use substitution to solve the system. x=3y+7 and 3x-4y=16

x=
y=

Answers

Answer 1

Answer: First we already know x, so we can put it into the other equation like so:

3(3y+7)-4y=16

Then we can solve it.

9y+21-4y=16

5y=-5

y=-1

Then we can find x.

x=3y+7

x=3(-1)+7

x=-3+7

x=4

Hope I helped!

Answer 2

Answer: x = 3y + 7
3x - 4y = 16

Substituting the value of x,

3(3y + 7) - 4y = 16

9y + 21 - 4y = 16

5y + 21 = 16

5y = -5

Thus, y = -1.

Substituting the value of y,

x = 3y + 7

x = -3 + 7

Thus, x = 4.

Thus, x = 4, and y = -1

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A juice stand uses 11 cups of strawberries to make 6 pitchers of juice. What is true about the number of cups of strawberries in each pitcher?

Answers

use ratio and proportion 11/6=x/1 cross multiply x= 15/6 which is approximately 2 cups

There is less than one cup of strawberries in one pitcher of juice.

What is the distance between points (3,8) and (-9,-8)5
10
15
20

what is the distance between points (2,6) and (5,2)
3
4
5

what is the distance between points (21,16) and (9,11)
13
12
22
24

Answers

It is better to graph these points, to easily understand that the distance of the two points form the hypotenuse of the right triangle. We need to use the Pythagorean theorem to solve for the distance of the two points.

a² + b² = c² ; a = x value ; b = y value

1) (3,8) and (-9,-8)
a = 3 - (-9) = 3 + 9 = 12 ⇒ 12² = 144
b = 8 - (-8) = 8 + 8 = 16 ⇒ 16² = 256 ⇒⇒ 144 + 256 = 400 ; c = √400 = 20

2) (2,6) and (5,2)
a = 2 - 5 = 3 ⇒ 3² = 9
b = 6 - 2 = 4 ⇒ 4² = 16 ⇒⇒ 9 + 16 = 25 ; c = √25 = 5

3) (21,16) and (9,11)
a = 21 - 9 = 12 ⇒ 12² = 144
b = 16 - 11 = 5 ⇒ 5² = 25 ⇒⇒ 144 + 25 = 169 ; c = √169 = 13

Write this equation: 8.75×10−4 in standard notation

Answers

To write in standard notation means writing the equation "normally", solving it and then writing the resulting number in its extensive form with all explicit digits. 10^-4 is 0,0001, so: 8,75x0,0001=0,000875

Given x varies inversely with y and xy = 2, what is the value of x when y = 1?a) -1

b) 1/2

c)1

d) 2

Answers

Answer is (d).

Let's take the constant as K.
x=K. (1/y)----(1)'
K= xy
so; according to the data given above K=2.

Let's substitute K=2 & y=1 to ----(1)'

x=2x (1/1)
x= 2×1
so x = 2... :)

Determine which relation is a function. A.{(–4, 3), (–2, 3), (–1, 2), (2, 5), (3, 2)}

B.{(–4, 1), (–2, 3), (–2, 1), (–1, 5), (3, 2)}

C.{(–4, 1), (–2, 3), (–1, 2), (3, 5), (3, 2)}

D.{(–4, 1), (–2, 3), (–1, 1), (–1, 5), (3, 2)}

Answers

The A is a function, because all the values of the independent variable (the first value of the ordered pairs) are related to only one value, i.e. have only one image.

In B - 2 has two different images: 3 and 1. That makes that this is not a function.

In C, 3 has two different images: 5 and 2. That makes that this is not a function.

In D, - 1 has two different images: 1 and 5. That makes that this is not a function.

Which shows one way to determine the factors of x3 – 9x2 + 5x – 45 by grouping?x2(x – 9) – 5(x – 9)
x2(x + 9) – 5(x + 9)
x(x2 + 5) – 9(x2 + 5)
x(x2 – 5) – 9(x2 – 5)

Answers

x³ - 9x² + 5x - 45

x²(x - 9) - 5(x - 9) ⇒ x³ - 9x² - 5x + 45 INCORRECT
x²(x + 9) - 5(x + 9) ⇒ x³ + 9x² - 5x - 45 INCORRECT

x(x² + 5) - 9(x² + 5) ⇒ x³ + 5x - 9x² - 45 CORRECT
It just needs to be rearranged.

x(x² - 5) - 9(x² - 5) ⇒ x³ - 5x - 9x² + 45 INCORRECT

The answer choice which shows a way to determine the factors by grouping is; x(x² + 5)–9(x² + 5).