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Svetllana [295]
3 years ago
11

Kim ran 5 miles more than Jake last week. Kim ran 13 miles. How many miles did Jake run?

Mathematics
1 answer:
ANEK [815]3 years ago
8 0

Answer:

Jake ran 8 miles.

Step-by-step explanation:

Subtract 5 from 13.

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Find the area of the figure.EXPlAIN THE STEPS!!!!
hichkok12 [17]

Answer:

30.56 yd²

Step-by-step explanation:

To determine the area of the composite shape, we need to:

  1. Divide the shape into two smaller "known" shapes (Refer to image).
  2. Determine the area of those "known" shapes.
  3. Add the area of the known shapes to obtain the area of the figure.

<u>Determining the area of shape 1 (Rectangle 1):</u>

⇒ Area of rectangle = Lenght × Breadth

⇒                               = 2.1 × 4.8

⇒                               = 10.08 yd²

<u>Determining the area of shape 2 (Rectangle 2):</u>

⇒ Area of rectangle = Lenght × Breadth

⇒                               = 6.4 × 3.2

⇒                               = 20.48 yd²

<u>Determining the area of the figure:</u>

⇒ Area of figure = Area of rectangle 1 + Area of rectangle 2

⇒                         = 10.08 + 20.48

⇒                         = 30.56 yd²

6 0
2 years ago
Need help with these following questions
vagabundo [1.1K]

Answer:

there are 13 of them brother from another mother

5 0
3 years ago
Solve for x<br> 6/x^2+2x-15 +7/x+5 =2/x-3
timama [110]

Answer:

x = ((-5)^(1/3) (2140 - 9 sqrt(56235))^(2/3) - 17 (-5)^(2/3))/(15 (2140 - 9 sqrt(56235))^(1/3)) - 1/3 or x = 1/15 (17 5^(2/3) (-1/(2140 - 9 sqrt(56235)))^(1/3) - (-5)^(1/3) (9 sqrt(56235) - 2140)^(1/3)) - 1/3 or x = -1/3 - 17/(3 (10700 - 45 sqrt(56235))^(1/3)) - (2140 - 9 sqrt(56235))^(1/3)/(3 5^(2/3))

Step-by-step explanation:

Solve for x:

6/x^2 + (2 x - 8)/(x + 5) = 2/x - 3

Bring 6/x^2 + (2 x - 8)/(x + 5) together using the common denominator x^2 (x + 5). Bring 2/x - 3 together using the common denominator x:

(2 (x^3 - 4 x^2 + 3 x + 15))/(x^2 (x + 5)) = (2 - 3 x)/x

Cross multiply:

2 x (x^3 - 4 x^2 + 3 x + 15) = x^2 (2 - 3 x) (x + 5)

Expand out terms of the left hand side:

2 x^4 - 8 x^3 + 6 x^2 + 30 x = x^2 (2 - 3 x) (x + 5)

Expand out terms of the right hand side:

2 x^4 - 8 x^3 + 6 x^2 + 30 x = -3 x^4 - 13 x^3 + 10 x^2

Subtract -3 x^4 - 13 x^3 + 10 x^2 from both sides:

5 x^4 + 5 x^3 - 4 x^2 + 30 x = 0

Factor x from the left hand side:

x (5 x^3 + 5 x^2 - 4 x + 30) = 0

Split into two equations:

x = 0 or 5 x^3 + 5 x^2 - 4 x + 30 = 0

Eliminate the quadratic term by substituting y = x + 1/3:

x = 0 or 30 - 4 (y - 1/3) + 5 (y - 1/3)^2 + 5 (y - 1/3)^3 = 0

Expand out terms of the left hand side:

x = 0 or 5 y^3 - (17 y)/3 + 856/27 = 0

Divide both sides by 5:

x = 0 or y^3 - (17 y)/15 + 856/135 = 0

Change coordinates by substituting y = z + λ/z, where λ is a constant value that will be determined later:

x = 0 or 856/135 - 17/15 (z + λ/z) + (z + λ/z)^3 = 0

Multiply both sides by z^3 and collect in terms of z:

x = 0 or z^6 + z^4 (3 λ - 17/15) + (856 z^3)/135 + z^2 (3 λ^2 - (17 λ)/15) + λ^3 = 0

Substitute λ = 17/45 and then u = z^3, yielding a quadratic equation in the variable u:

x = 0 or u^2 + (856 u)/135 + 4913/91125 = 0

Find the positive solution to the quadratic equation:

x = 0 or u = 1/675 (9 sqrt(56235) - 2140)

Substitute back for u = z^3:

x = 0 or z^3 = 1/675 (9 sqrt(56235) - 2140)

Taking cube roots gives (9 sqrt(56235) - 2140)^(1/3)/(3 5^(2/3)) times the third roots of unity:

x = 0 or z = (9 sqrt(56235) - 2140)^(1/3)/(3 5^(2/3)) or z = -((-1)^(1/3) (9 sqrt(56235) - 2140)^(1/3))/(3 5^(2/3)) or z = ((-1)^(2/3) (9 sqrt(56235) - 2140)^(1/3))/(3 5^(2/3))

Substitute each value of z into y = z + 17/(45 z):

x = 0 or y = (9 sqrt(56235) - 2140)^(1/3)/(3 5^(2/3)) - (17 (-1)^(2/3))/(3 (5 (2140 - 9 sqrt(56235)))^(1/3)) or y = 17/3 ((-1)/(5 (2140 - 9 sqrt(56235))))^(1/3) - ((-1)^(1/3) (9 sqrt(56235) - 2140)^(1/3))/(3 5^(2/3)) or y = ((-1)^(2/3) (9 sqrt(56235) - 2140)^(1/3))/(3 5^(2/3)) - 17/(3 (5 (2140 - 9 sqrt(56235)))^(1/3))

Bring each solution to a common denominator and simplify:

x = 0 or y = ((-5)^(1/3) (2140 - 9 sqrt(56235))^(2/3) - 17 (-5)^(2/3))/(15 (2140 - 9 sqrt(56235))^(1/3)) or y = 1/15 (17 5^(2/3) ((-1)/(2140 - 9 sqrt(56235)))^(1/3) - (-5)^(1/3) (9 sqrt(56235) - 2140)^(1/3)) or y = -(2140 - 9 sqrt(56235))^(1/3)/(3 5^(2/3)) - 17/(3 (5 (2140 - 9 sqrt(56235)))^(1/3))

Substitute back for x = y - 1/3:

x = 0 or x = 1/15 (2140 - 9 sqrt(56235))^(-1/3) ((-5)^(1/3) (2140 - 9 sqrt(56235))^(2/3) - 17 (-5)^(2/3)) - 1/3 or x = 1/15 (17 5^(2/3) (-1/(2140 - 9 sqrt(56235)))^(1/3) - (-5)^(1/3) (9 sqrt(56235) - 2140)^(1/3)) - 1/3 or x = -1/3 - 1/3 5^(-2/3) (2140 - 9 sqrt(56235))^(1/3) - 17/3 (5 (2140 - 9 sqrt(56235)))^(-1/3)

5 (2140 - 9 sqrt(56235)) = 10700 - 45 sqrt(56235):

x = 0 or x = ((-5)^(1/3) (2140 - 9 sqrt(56235))^(2/3) - 17 (-5)^(2/3))/(15 (2140 - 9 sqrt(56235))^(1/3)) - 1/3 or x = 1/15 (17 5^(2/3) (-1/(2140 - 9 sqrt(56235)))^(1/3) - (-5)^(1/3) (9 sqrt(56235) - 2140)^(1/3)) - 1/3 or x = -1/3 - (2140 - 9 sqrt(56235))^(1/3)/(3 5^(2/3)) - 17/(3 (10700 - 45 sqrt(56235))^(1/3))

6/x^2 + (2 x - 8)/(x + 5) ⇒ 6/0^2 + (2 0 - 8)/(5 + 0) = ∞^~

2/x - 3 ⇒ 2/0 - 3 = ∞^~:

So this solution is incorrect

6/x^2 + (2 x - 8)/(x + 5) ≈ -3.83766

2/x - 3 ≈ -3.83766:

So this solution is correct

6/x^2 + (2 x - 8)/(x + 5) ≈ -2.44783 + 1.13439 i

2/x - 3 ≈ -2.44783 + 1.13439 i:

So this solution is correct

6/x^2 + (2 x - 8)/(x + 5) ≈ -2.44783 - 1.13439 i

2/x - 3 ≈ -2.44783 - 1.13439 i:

So this solution is correct

The solutions are:

Answer:  x = ((-5)^(1/3) (2140 - 9 sqrt(56235))^(2/3) - 17 (-5)^(2/3))/(15 (2140 - 9 sqrt(56235))^(1/3)) - 1/3 or x = 1/15 (17 5^(2/3) (-1/(2140 - 9 sqrt(56235)))^(1/3) - (-5)^(1/3) (9 sqrt(56235) - 2140)^(1/3)) - 1/3 or x = -1/3 - 17/(3 (10700 - 45 sqrt(56235))^(1/3)) - (2140 - 9 sqrt(56235))^(1/3)/(3 5^(2/3))

4 0
3 years ago
What is the slope of the line that connects the points (0,7) and (4,15)
vladimir2022 [97]

Answer:

m=2

General Formulas and Concepts:

<u>Pre-Alg</u>

  • Order of Operations: BPEMDAS

<u>Alg I</u>

  • Slope Formula: m=\frac{y_2-y_1}{x_2-x_1}

Step-by-step explanation:

<u>Step 1: Define</u>

Point (0, 7)

Point (4, 15)

<u>Step 2: Find slope </u><em><u>m</u></em>

  1. Substitute:                    m=\frac{15-7}{4-0}
  2. Subtract:                       m=\frac{8}{4}
  3. Divide:                           m=2
3 0
2 years ago
I need help with number 18
horrorfan [7]

40 degrees, because ΔABC is isoceles, so angles B and C are equal.

7 0
3 years ago
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