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2 years ago

Look at this graph:

Mathematics

2 answers:

skelet666 [1.2K]2 years ago

7 0

Answer:

Slope = 3/2

Step-by-step explanation:

Slope = rise/over or change in x/change in y

To find the slope, use two points and the slope formula

Slope formula: (y₂ - y₁)/(x₂ - x₁)

Points (any point): (20, 40) & (40, 70)

Step 1. Plug the two points into the formula (where the first point indicates the firsts x and y coordinates and the second point indicates the seconds x and y coordinates)

(70 - 40)/(40 - 20)

Step 2. Subtract

30/20

Step 3. Simplify

3/2

Sergeu [11.5K]2 years ago

4 0

Y= mx+b, y=3/2+10
30/20=3/2
b=10

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Write the equation of the ellipse with foci at (-2,2) and (4,2) and major axis of length 10 *

Luda [366]

Answer:

The answer to your question is $\frac{(x - 1)^{2}}{25} + \frac{(y - 2)^{2}}{16} = 1$

Step-by-step explanation:

Data

Foci (-2, 2) (4, 2)

Major axis = 10

Process

1.- Plot the foci to determine if the ellipse is vertical or horizontal. See the picture below.

From the graph we conclude that it is a horizontal ellipse.

2.- Determine the foci axis (distance between the foci)

2c = 6

c = 6/2

c = 3

3.- Determine a

2a = 10

a = 10/2

a = 5

4.- Determine b using the Pythagorean theorem

a² = b² + c²

-Solve for b

b² = a² - c²

b² = 5² - 3²

b² = 25 - 9

b² = 16

b = 4

5.- Find the center (1, 2) From the graph, it is in the middle of the foci

6.- Find the equation of the ellipse

$\frac{(x - 1)^{2}}{5^{2}} + \frac{(y - 2)^{2}}{4^{2}} = 1$

$\frac{(x - 1)^{2}}{25} + \frac{(y - 2)^{2}}{16} = 1$

3 0

2 years ago

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Andre45 [30]

Answer:

$\frac{1}{3} \sqrt{2}$ or 0.471405

Step-by-step explanation:

$\frac{(2)(2)}{\sqrt{72} }$

8 0

3 years ago

a prism with a base area of 5ft2 and a height of 10 ft is dilated by a factor of 6/5. what is the volume of the dilated prism

Volgvan

I guess 52inches as volume of a prism=Base area x Height

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2 years ago

The longest side of a triangle is 3 in. longer than the shortest side. The medium side is 2 in. longer than the shortest side. I

Olenka [21]

s = length of the shortest side of the triangle

m = length of the medium side of the triangle

l = length of the longest side of the triangle

(you can use different variables like l, w, h, x, y.......)

Perimeter(P) of a triangle is the total sum of the sides, in this case:

P = s + m + l

You know:

P = 26in

l = s + 3 [longest side is 3in longer/more than(addition) the shortest side]

m = s + 2 [medium side is 2in longer than the shortest side]

To find the lengths of the three sides, you can do this:

P = s + m + l Substitute/plug in what you know. So plug in 26 into "P" since P = 26, plug in (s + 3) into "l" since l = s + 3, and plug in (s + 2) into "m" since m = s + 2

26 = s + (s + 2) + (s + 3) Combine like terms (like terms have the same variable and power/exponent)

26 = 3s + 5 To find "s", isolate/get the variable "s" by itself. Subtract 5 on both sides

21 = 3s Divide 3 on both sides to get "s" by itself

7 = s

Now that you found s, you can use it to find the other sides

m = s + 2 Substitute/plug in 7 into "s" since s = 7

m = 7 + 2

m = 9

l = s + 3 Plug in 7 into "s"

l = 7 + 3

l = 10

The longest side is 10 inches, the medium side is 9 inches, the shortest side is 7 inches

PROOF

P = s + m + l

P = 7 + 9 + 10

P = 26 inches

7 0

3 years ago

Read 2 more answers

10 gallons of gas = 200 miles How many gallons per 20 miles?

kolbaska11 [484]

Answer:

One gallon for 20 miles.

Step-by-step explanation:

200 / 10 = 20

1 gallon = 20 miles

Plz mark as brainliest if correct! Have a nice day!!!

-Lil G

7 0

2 years ago

Read 2 more answers