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ale4655 [162]
2 years ago
12

A variable needs to be eliminated to solve

Mathematics
1 answer:
lesya692 [45]2 years ago
6 0

Answer:

(7, - 7 )

Step-by-step explanation:

- 4x + y = - 35 → (1)

- 2x - y = - 7 → (2)

adding the 2 equations term by term will eliminate the y- term

(- 4x - 2x) + (y - y) = - 35 - 7

- 6x + 0 = - 42

- 6x = - 42 ( divide both sides by - 6 )

x = 7

substitute x = 7 into either of the 2 equations and solve for y

substituting into (1)

- 4(7) + y = - 35

- 28 + y = - 35 ( add 28 to both sides )

y = - 7

solution is (7, - 7 )

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For Greta's birthday party, her parents ordered 6 pizzas. If they cut the pizzas into sixths, how many pieces will there be? Cho
saw5 [17]

Options aren't avaible

Answer:

(1 ÷ 1/6) * 6

36 pieces of pizza

Step-by-step explanation:

Given that :

Number of pizzas ordered = 6

Divisions per pizza = 1/6 ;

Hence, 1 full pizza is divided into 1 ÷ 1/6 = 1 * 6/1 = 6 pieces

6 * 1/6(1)

The total pieces of pizzas equals :

6 pieces per pizza * number of pizzas

6 * 6

= 36 pieces of pizza

4 0
3 years ago
Solve by factoring.<br><br> m^2+6m+5=0
alina1380 [7]

Answer:

<u>-1 and -5</u>

Step-by-step explanation:

m^2 + 6m + 5 = 0 is factored to: (m + 1)(m + 5) = 0.

The zero product property states that one of the represented parenthesis must equal zero to satisfy the right side of the equation.

(m + 1) = 0

(-1 + 1) = 0

This means that one of the values for m is -1.

(m + 5) = 0

(-5 + 5) = 0

This means that one of the values for m is -5.

<u>Moreover, the value of m by factoring is -1 and -5</u>

3 0
2 years ago
PLEASE HELP QUICK!!! A bowl has 85 pieces of candy. Nineteen children empty the bowl of candy. Some children take 3 pieces, some
Mekhanik [1.2K]

Answer: 3 kids take 3 pieces of candy each

Step-by-step explanation:

Let the number of children that took 3 pieces is x ( total take 3*x pieces of candy)

Number of children that took 5 pieces is y ( total take 5*y pieces of candy)

1 child took 1 piece that actually means that x+y=18 and 3*x+5*y=84.

( Because total number of all kids is 19. We just deduct one kid (Let his name is John) who took only 1 candy.  So we have 19-1 =18 kids without John. The similar is with the candies. Total number is 85. We deduct 1 piece which John has taken. )

So we have 2 equations or the system of 2 equations:

1).  x+y=18

2). 3*x +5*y=84

Multuply both sides of equation 1) by 3

We have   3*x+3*y=18*3

Deduct 3*y from both sides of this equation

3*x+3*y-3*y=54-3*y

3*x=54-3*y

Substitute 3*x in equation  2).  by 54-3*y

2) 54-3*y+5*y=84

2*y=30

y=15  ( kids take 5 pieces of candy each)

Using equation 1) find x

x+15=18

x=3 (kids take 3 pieces of candy each)

5 0
3 years ago
The inverse of this equation
In-s [12.5K]

Answer:

{f}^{ - 1}(x)  =  \frac{x + 11}{ - 5}

Step-by-step explanation:

f(x) =  - 5x - 11 \\  - 5x - 11 =x \\  - 5x = x + 11 \\  {f}^{ - 1}(x)  =  \frac{x + 11}{ - 5}

7 0
3 years ago
A portrait has dimensions of 30“ x 60“ and is surrounded by a frame of uniform width. If the total area (Portrait plus frame) is
Law Incorporation [45]

Answer:

The width of the is 4 inches

Step-by-step explanation:

Assume that the width of the frame is x

∵ The width of the fame is x inches

→ That means each dimension will increase by 2x ⇒ x from each side

∵ The portrait has dimensions of 30“ x 60“

∴ Its dimensions including the frame = (30 + 2x) × (60 + 2x)

∴ The total area of the portrait plus frame = (30 + 2x)(60 + 2x)

→ Multiply the brackets

∵ (30 + 2x)(60 + 2x) = 30(60) + 30(2x) + 2x(60) + (2x)(2x)

∴ (30 + 2x)(60 + 2x) = 1800 + 60x + 120x + 4x²

→ Add the like terms

∴ (30 + 2x)(60 + 2x) = 1800 + 180x + 4x²

∴ The total area of the portrait plus frame = 4x² + 180x + 1800

∵ The total area of the portrait plus frame = 2584 square inches

→ Equate the two right sides of the area

∴ 4x² + 180x + 1800 = 2584

→ Subtract 2584 from both sides

∴ 4x² + 180x + 1800 - 2584 = 0

→ Add the like terms in the left side

∴ 4x² + 180x - 784 = 0

→ Divide all terms by 4 to simplify

∴ x² + 45x - 196 = 0

→ Factorize it to find the value of x

∵ x² + 45x - 196 = (x - 4)(x + 49)

→ Equate the right side by 0

∴ (x - 4)(x + 49) = 0

→ Equate each factor by 0

∵ x - 4 = 0  

→ Add 4 to both sides to find x

∴ x = 4

∵ x + 49 = 0

→ Subtract 49 from both sides to find x

∴ x = -49 ⇒ refused it x can not be -ve (no negative dimensions)

∴ The width of the is 4 inches

7 0
2 years ago
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