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3 years ago

ALGEBRA 2!!!!!!!HELP

Mathematics

1 answer:

Inessa [10]3 years ago

8 0

Answer:

x = - 1, x = - 11

Step-by-step explanation:

Given

2| x + 6 | - 4 = 6 ( add 4 to both sides )

2|x + 6 | = 10 ( divide both sides by 2 )

| x + 6 | = 5

The absolute value function always gives a positive result, but the expression inside can be positive or negative, that is

x + 6 = 5 or - (x + 6) = 5

solve both

x + 6 = 5 ( subtract 6 from both sides )

x = - 1

- (x + 6) = 5 , that is

- x - 6 = 5 ( add 6 to both sides )

- x = 11 ( multiply both sides by - 1 )

x = - 11

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3 years ago

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Step-by-step explanation:

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Please help

Alekssandra [29.7K]

Answer:

25 in x 15 in

Step-by-step explanation:

Given:

Length = 3/5 the width
Area = 375 in²

Let width = $x$

Therefore, length = 3/5 $x$

First create an equation for the area of the picture based on the given information for its width and length:

$\begin{aligned} \implies \textsf{Area of original picture} & = \sf width \times length\\& = x\left(\dfrac{3}{5}x\right)\\& = \dfrac{3}{5}x^2\end{aligned}$

We are told the area of the enlarged picture is 375 in². Therefore, substitute this into the equation and solve for $x$ to find the width of the enlarged picture:

$\begin{aligned}\textsf{Area} & = 375\\ \implies \dfrac{3}{5}x^2 & = 375\\ x^2 & =375 \cdot \dfrac{5}{3}\\ x^2 & =625\\ x & = \sqrt{625}\\ x& = 25\end{aligned}$

Therefore, the width of the enlarged picture is 25 in.

Substitute the found value of $x$ into the expression for length to find the length of the enlarged picture:

$\begin{aligned}\sf Length & = \dfrac{3}{5}x\\\\\implies \sf Length & = \dfrac{3}{5}(25)\\\\& = 15\: \sf in\end{aligned}$

Therefore, the dimensions of the enlarged picture are 25 in x 15 in. The width is 25 in and the length is 15 in, as the length is 3/5 of the width.

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