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2 years ago

Write an equation in point-slope form for the line through the given point with the given slope

Mathematics

1 answer:

Neko [114]2 years ago

3 0

Point-slope form:

y - y₁ = m(x - x₁) "m" is the slope

Since you know:

m = -2/5

(x₁ , y₁) = (-3, -5)

Plug it into the equation:

y - y₁ = m(x - x₁)

y - (-5) = -2/5(x - (-3))

y + 5 = -2/5(x + 3)

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Which system of equation is represented

olga nikolaevna [1]

Answer:

Step-by-step explanation:

First, let us figure out what is graphed and then manipulate each answer to try to match it.

The one with a positive slope is

$y\leq x-2$

The one with the negative slope is

$y\geq 3-2x$

Now that we have our graphed system of inequalities, we can try to match them to an answer.

A. while the x-2 is the same, the other does not have an x, so it cannot match.

B. The second inequality has the wrong sign, so it is impossible for this to be our answer.

C. When each of these are solved for y, you get $y\leq 2x-3\\\\y\leq 2-x$ . Neither of these match so this cannot be correct.

D. When the first inequality is solved you get $y\geq 3-2x$

When the second inequality is solved you get $y\leq x-2$

As both of these answers match our graphed inequalities, D is the correct answer.

4 0

3 years ago

Graph and label the image of the figure below after a dilation by a factor of 1/2.

neonofarm [45]

Answer:

M' (1.5, -1), F' (2, -1), L' (0.5 -2.5), W' (2.5, -2.5)

see graph below

Explanation:

Given:

The image of a quadrilateral on a coordinate plane

To find:

The coordinates of the new image after dilation of 1/2 have been applied to the original image.

Then graph the coordinates

First, we need to state the coordinates of the original image:

M = (3, -2)

F = (4, -2)

L = (1, -5)

W = (5, -5)

Next, we will apply a scale factor of 1/2:

$\begin{gathered} Dilation\text{ rule:} \\ (x,\text{ y\rparen}\rightarrow(kx,\text{ ky\rparen} \\ where\text{ k = scale factor} \\ \\ scale\text{ factor = 1/2} \\ M^{\prime}\text{ = \lparen}\frac{1}{2}(3),\text{ }\frac{1}{2}(-2)) \\ M^{\prime}\text{ = \lparen}\frac{3}{2},\text{ -1\rparen} \\ \\ F\text{ = \lparen}\frac{1}{2}(4),\text{ }\frac{1}{2}(-2)) \\ F^{\prime}\text{ = \lparen2, -1\rparen} \end{gathered}$ $\begin{gathered} L\text{ = \lparen}\frac{1}{2}(1),\text{ }\frac{1}{2}(-5)) \\ L^{\prime}\text{ = \lparen}\frac{1}{2},\text{ }\frac{-5}{2}) \\ \\ W\text{ = \lparen}\frac{1}{2}(5),\text{ }\frac{1}{2}(-5)) \\ W^{\prime}\text{ = \lparen}\frac{5}{2},\text{ }\frac{-5}{2}) \end{gathered}$

The new coordinates:

M' (3/2, -1), F' (2, -1), L' (1/2, -5/2), W' (5/2, -5/2)

M' (1.5, -1), F' (2, -1), L' (0.5 -2.5), W' (2.5, -2.5)

Plotting the coordinates:

3 0

8 months ago

dale has a square garden. He adds a 2-foot-wide walkway around his garden. If the total area of the walkway and garden is 196 sq

dem82 [27]

Let the side of the garden alone (without walkway) be x.
Then the area of the garden alone is x^2.
The walkway is made up as follows:

1) four rectangles of width 2 feet and length x, and
2) four squares, each of area 2^2 square feet.

The total walkway area is thus x^2 + 4(2^2) + 4(x*2).

We want to find the dimensions of the garden. To do this, we need to find the value of x.

Let's sum up the garden dimensions and the walkway dimensions:

x^2 + 4(2^2) + 4(x*2) = 196 sq ft

x^2 + 16 + 8x = 196 sq ft

x^2 + 8x - 180 = 0

(x-10(x+18) = 0

x=10 or x=-18. We must discard x=-18, since the side length can't be negative. We are left with x = 10 feet.

The garden dimensions are (10 feet)^2, or 100 square feet.

4 0

3 years ago

More math sorry. But I honestly don’t know any of these

DIA [1.3K]

Answer: A

Step-by-step explanation:

The main parent functions are x, and x raised to the power of something (examples: $x^2, x^3, x^4$ , etc)

8 0

2 years ago

Greg had $17 more than Fred, and together they had just enough money to by their mom a present that costs $85. How much money di

babunello [35]

Define x:

Let Fred had x dollar.

Fred = x
Greg = x + 17

Solve x :

x + x + 17 = 85
2x + 17 = 85
2x = 68
x = 34

Find the amount each of them had:

Fred = x = $34
Greg = x + 17 = 34 + 17 = $51

Answer: Greg had $51

3 0

3 years ago

Read 2 more answers