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lawyer [7]
3 years ago
11

Solve the system of linear equations by substitution.

Mathematics
1 answer:
dem82 [27]3 years ago
7 0
Don't stress so much! I use to find these difficult as well! Everyone needs help sometime in their life!

<span>2x + 3y = 0:
</span>
1. Subtract 3y from both sides

2x = -3y

2. Divide both sides by 2

x = -3y over 2

****

1. Subtract 2x from both sides

3y = -2x

2. Divide both sides by 3

y = -2x over 3

-------------------------------------------------

8x + 9y = 18:

1. Subtract 9y from both sides

8x = 18 - 9y

2. Divide both sides by 8

x = 18 - 9y over 8

3. Factor out the common term 9

x = 9(2 - y) over 8

****

1. Subtract 8x from both sides

9y = 18 - 8x

2. Divide both sides by 9

y = 18 - 8x over 9

3. Factor out the common term 2

y = 2(9-4x) over 9
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William and his puppy Rover are out for a morning jog at a comfortable pace of 10 minutes per mile. If they keep up this pace fo
mojhsa [17]

Answer:

12 miles

Step-by-step explanation:

60 min in 1 hr and 10 min = 1 mile..... so 6, 10 min intervals..... and so 6 time 2 is 12

8 0
3 years ago
What is the scale factor of ABC to A DEF?
vampirchik [111]

Answer:

6

Step-by-step explanation:

All sides of triangle EFD have x6 of BAC.

E.g.: BA = 2. ED = 2 x 6 = 12

8 0
3 years ago
Now there is a square city of unknown size with a gate at the center of each side. There is a tree 20 b from the north gate. Tha
Brums [2.3K]

Answer:

The length of each side of the city is 250b

Step-by-step explanation:

Given

a = 20 --- tree distance from north gate

b =14 --- movement from south gate

c = 1775 --- movement in west direction from (b)

See attachment for illustration

Required

Find x

To do this, we have:

\triangle ADE \sim \triangle ACB --- similar triangles

So, we have the following equivalent ratios

AE:DE = AB:CB

Where:

AE = 20\\ DE = x/2 \\ AB = 20 + x + 14 \\ CB = 1775

Substitute these in the above equation

20:x/2 = 20 + x + 14: 1775

20:x/2 = x + 34: 1775

Express as fraction

\frac{20}{x/2} = \frac{x + 34}{1775}

\frac{40}{x} = \frac{x + 34}{1775}

Cross multiply

x *(x + 34) = 1775 * 40

Open bracket

x^2 + 34x = 71000

Rewrite as:

x^2 + 34x - 71000 = 0

Expand

x^2 + 284x -250x - 71000 = 0

Factorize

x(x + 284) -250(x + 284)= 0

Factor out x + 284

(x - 250)(x + 284)= 0

Split

x - 250 = 0 \ or\ x + 284= 0

Solve for x

x = 250 \ or\ x =- 284

x can't be negative;

So:

x = 250

6 0
3 years ago
The graph of f(x)=√x Is shifted four units up and five units to the right. What is the equation of the resulting graph?
RoseWind [281]

A vertical shift adds/subtracts a constant to/from every y-coordinate while leaving the x-coordinate unchanged. A horizontal shift adds/subtracts a constant to/from every x-coordinate while leaving the y-coordinate unchanged. Vertical and horizontal shifts can be combined into one expression.

Shifting up or to the right means add

Shifting down or to the left means subtract

the 3rd option is the correct one

7 0
2 years ago
Factor this trinomial completely.
kifflom [539]

Answer:

2 ( x+3) (x+1)

Step-by-step explanation:

2x^2+8x+6

Factor out a 2

2(x^2 +4x+3)

Factor in side the parentheses

What multiply to 3 and adds to 4  (3(1=3  3+1 =4)

2 ( x+3) (x+1)

8 0
3 years ago
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