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1 year ago

What is an equation of the line that passes through the points (4,-2) and (-1,3)

2 answers:

6 0

The answer would be y=-x-4

3-(-2)/-1-4 is the slope
Simplified, the slope is -1
So far, we have y=-1x+b.
We know that 4,-2 is a point on this line, so we plug it in.
-2=-1(-2)+b which is the same as -2=2+b
Therefore b=-4
Then plug b back in. We get
y=-x-4 which is the answer

Paraphin [41]1 year ago

4 0

Answer:

<h3>The slope is -1.</h3>

Step-by-step explanation:

To find an equation of the line that passes through the points, you have to use the slope formula.

Slope:

$\Rightarrow \sf{\dfrac{y_2-y_1}{x_2-x_1} }$

y2=3

y1=(-2)

x2=(-1)

x1=4

Solve.

3--2/-1-4=5/-5=-1

The slope is -1.

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How is this proportional?

Alja [10]

Answer:

you are subtracting 1.40 everytime to get the number at the bottom

Step-by-step explanation:

2 - 1.40 = 1.40

3 - 1.40 = 2.40

6 - 1.40 = 5.40

7 - 1.40 = 6.40

4 0

3 years ago

Hayden has $20 to spend at the county fair. Admission to the fair is $5.00 per person, and tickets for food and games are $1.25

Kamila [148]

Answer:

prices of food and games and tickets

6 0

2 years ago

Jose earned 5h + 5 dollars for h hours and Alex earned 8h – 10 for h hours mowing lawns. If they earned the same amount

AlekseyPX

Answer:

5 hours

Step-by-step explanation:

This is a classic pre-algebra question.

$5h+5=8h-10\\5=3h-10\\15=3h\\h=5$

3 0

3 years ago

jenna's rectangular garden borders a wall. she buys 80 ft of fencing. what are the dimensions of the garden that will maximize i

FrozenT [24]

Answer:

The dimensions are x =20 and y=20 of the garden that will maximize its area is 400

Step-by-step explanation:

Step 1:-

let 'x' be the length and the 'y' be the width of the rectangle

given Jenna's buys 80ft of fencing of rectangle so the perimeter of the rectangle is 2(x +y) = 80

x + y =40

y = 40 -x

now the area of the rectangle A = length X width

A = x y

substitute 'y' value in above A = x (40 - x)

A = 40 x - x^2 .....(1)

Step :2

now differentiating equation (1) with respective to 'x'

$\frac{dA}{dx} = 40 -2x$ ........(2)

Find the dimensions

$\frac{dA}{dx} = 0$

40 - 2x =0

40 = 2x

x = 20

and y = 40 - x = 40 -20 =20

The dimensions are x =20 and y=20

length = 20 and breadth = 20

Step 3:-

we have to find maximum area

Again differentiating equation (2) with respective to 'x' we get

$\frac{d^2A}{dx^2} = -2$

Now the maximum area A = x y at x =20 and y=20

A = 20 X 20 = 400

Conclusion:-

The dimensions are x =20 and y=20 of the garden that will maximize its area is 400

verification:-

The perimeter = 2(x +y) =80

2(20 +20) =80

2(40) =80

80 =80

8 0

3 years ago

How does the graph of g(x) = <img src="https://tex.z-dn.net/?f=%28x%2B12%29%5E%7B2%7D" id="TexFormula1" title="(x+12)^{2}" alt="

Law Incorporation [45]

Answer:

Horizontal translation of the parent graph

Step-by-step explanation:

<h2>Definitions:</h2>

In the vertex form of a quadratic function, f(x) = a(x - h)² + k, where:

(h, k) = vertex of the graph

a = determines the width and direction of the graph's opening.

A horizonal translation to the parent graph is given by, y = f(x - h), where:

h > 0 ⇒ Horizontal translation of h units to the right

h < 0 ⇒ Horizontal translation of |h | units to the left

In the graph of g(x) = (x + 12)², the vertex occurs at point (-12, 0).

While the vertex of the parent graph, f(x) = x² occurs at point, (0, 0).

<h2>Answers:</h2>

Since the vertex of g(x) occurs at point, (-12, 0), substituting the value of (h, k ) into the vertex form will result into:

g(x) = a(x - h)² + k

g(x) = [x - (-12)]² + 0

g(x) = (x + 12)² + 0

g(x) = (x + 12)²

Therefore, the graph of g(x) = (x + 12)² represents the horizontal translation of the parent graph, f(x) = x², where the graph of g(x) is horizontally translated 12 units to the left.

3 0

2 years ago