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2 years ago

Slope = 4, passing through (-6, 8)

Mathematics

1 answer:

Mademuasel [1]2 years ago

7 0

The point slope form is y - 8 = 4(x + 6) and the slope intercept form would be y = 4x + 32.

In order to find this, we'll start with the base form of point-slope form.

y - y1 = m(x - x1) ----> Plug in the numbers

y - 8 = 4(x - -6) ----> Simplify

y - 8 = 4(x + 6)

Now to find slope intercept form, solve for y.

y - 8 = 4(x + 6) ----> distribute the 4

y - 8 = 4x + 24 -----> add 8 to both sides

y = 4x + 32

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2 years ago

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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1 year ago

What is the y value of the solution to the system of equations given? y=5x-3 3x-2y=27

nignag [31]

Answer:

y = -18

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS
Equality Properties

Algebra I

Solving systems of equations using substitution/elimination

Step-by-step explanation:

Step 1: Define systems

y = 5x - 3

3x - 2y = 27

Step 2: Rewrite systems

Define: 3x - 2y = 27
Add 2y on both sides: 3x = 2y + 27
Divide 3 on both sides: x = 2/3y + 9

Step 3: Redefine

y = 5x - 3

x = 2/3y + 9

Step 4: Solve for y

Substitute in x: y = 5(2/3y + 9) - 3
Distribute 5: y = 10/3y + 45 - 3
Combine like terms: y = 10/3y + 42
Subtract 10/3y on both sides: -7/3y = 42
Divide -7/3 on both sides: y = -18

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2 years ago