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Pavel [41]
3 years ago
15

Need to solve this problem in steps 5(2x+6)=-4(-5-2x)+3x

Mathematics
1 answer:
Dovator [93]3 years ago
5 0

Answer:

Simplifying

5(2x + 6) = -4(-5 + -2x) + 3x

Reorder the terms:

5(6 + 2x) = -4(-5 + -2x) + 3x

(6 * 5 + 2x * 5) = -4(-5 + -2x) + 3x

(30 + 10x) = -4(-5 + -2x) + 3x

30 + 10x = (-5 * -4 + -2x * -4) + 3x

30 + 10x = (20 + 8x) + 3x

Combine like terms: 8x + 3x = 11x

30 + 10x = 20 + 11x

Solving

30 + 10x = 20 + 11x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-11x' to each side of the equation.

30 + 10x + -11x = 20 + 11x + -11x

Combine like terms: 10x + -11x = -1x

30 + -1x = 20 + 11x + -11x

Combine like terms: 11x + -11x = 0

30 + -1x = 20 + 0

30 + -1x = 20

Add '-30' to each side of the equation.

30 + -30 + -1x = 20 + -30

Combine like terms: 30 + -30 = 0

0 + -1x = 20 + -30

-1x = 20 + -30

Combine like terms: 20 + -30 = -10

-1x = -10

Divide each side by '-1'.

x = 10

Simplifying

x = 10

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The answer to this is 8

7 0
2 years ago
For his troops' popcorn fundraiser sale, Mike sold caramel corn for $10, buttered microwave popcorn for $8, and lightly buttered
Bad White [126]
\bf \begin{cases}
c=\textit{caramel corn}\\
b=\textit{buttered microwave popcorn}\\
p=\textit{lightly buttered popcorn}
\end{cases}

so... he sold 400 items, that means, whatever those quantities of c,b,p are, they add up to 400, thus

c+b+p = 400

now, the "c" sold for $10
the "b" sold for $8
and the "p" sold for $7

so, the amount of revenue on the "c" is 10 * c, or 10c
the revenue on "b" is 8*b or 8b
and the revenue on "p" is 7*p or 7p

whatever those amounts are, they ended up in $3,272
thus
10c + 8b + 7p = 3,272

now, he sold more lightly buttered, or "p", than just buttered corn or "b"
he actually sold twice as much, so whatever "b" is, "p" is twice that much
or 
p = 2b

thus      \bf \begin{cases}
c+b+\boxed{p}=400\\\\
\boxed{p}=2b\qquad thus\\\\
c+b+\boxed{2b}=400\qquad or\\\\
c+3b=400\implies c=\underline{400-3b}\\
--------------\\
10c+8b+7p=3272\qquad or\\\\
10(\underline{400-3b})+8b+7(\boxed{2b})=3272
\end{cases}

solve for "b", to see how many buttered microwave popcorn Mike sold

how many lightly buttered?  well, p = 2b
how many caramel ones?   well  c = 400 - 3b
5 0
3 years ago
Fill in the blank with a constant, so that the resulting quadratic expression is the square of a binomial. $\[x^2 + 22x + \under
saw5 [17]

Answer:

$\[x^2 + 22x + 121\]$

Step-by-step explanation:

Given

$\[x^2 + 22x + \underline{~~~~}.\]$

Required

Fill in the gap

Represent the blank with k

$\[x^2 + 22x + k\]$

Solving for k...

To do this, we start by getting the coefficient of x

Coefficient of x = 22

<em />

Divide the coefficient by 2

Result = 22/2

Result = 11

Take the square of this result, to give k

k= 11^2

k= 121

Substitute 121 for k

$\[x^2 + 22x + 121\]$

The expression can be factorized as follows;

x^2 + 11x + 11x + 121

x(x + 11)+11(x+11)

(x+11)(x+11)

(x+11)^2

<em>Hence, the quadratic expression is </em>$\[x^2 + 22x + 121\]$<em></em>

8 0
3 years ago
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Lorico [155]

Answer:

Greatest common factor of 280 and 168 is 56

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