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spayn [35]
2 years ago
13

Dad is 4 times as old as his son Jim. In 10 years, Dad's age will be 20 years more than twice Jim's age. How old is Jim? 10 year

s old 15 years old 30 years old
Mathematics
1 answer:
mezya [45]2 years ago
8 0
Jim is currently 15 years old!!
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The table includes points on a quadratic function used to model the shape of a hole for one support beam at a new building site.
erastovalidia [21]

The hole is 8 feet deep at ground level ⇒ 3rd answer

Step-by-step explanation:

The form of the quadratic function is y = ax² + bx + c, where

  • a is the coefficient of x²
  • b is the coefficient of x
  • c is the y-intercept (at x = 0)

The vertex point of the quadratic is (h , k), where h=\frac{-b}{2a}

and k is the value of y when x = h

The table:

→  x  :  -2   ,  0  ,  2

→  y  :  -6   , -8  ,  -6

∵ x represents distance from hole's center in feet

∵ y represents the depth from level ground

∴ The quadratic function is y = ax² + bx + c

∵ c is the value of y at x = 0 ⇒ y-intercept

- From the table at x = 0 ⇒ y = -8

∴ c = -8

- Substitute its value in the function model

∴ y = ax² + bx - 8

- To find the values of a and b substitute x and y in the model by

   the coordinates of the point in the table

∵ x = -2 and y = -6

∴ -6 = a(-2)² + b(-2) - 8

∴ -6 = 4a - 2b - 8

- Add 8 to both sides

∴ 2 = 4a - 2b

- Switch the two sides

∴ 4a - 2b = 2 ⇒ (1)

∵ x = 2 and y = -6

∴ -6 = a(2)² + b(2) - 8

∴ -6 = 4a + 2b - 8

- Add 8 to both sides

∴ 2 = 4a + 2b

- Switch the two sides

∴ 4a + 2b = 2 ⇒ (2)

Now we have a system of equation to solve it

Add equations(1) and (2) to eliminate b

∵ 8a = 4

- Divide both sides by 8

∴ a = 0.5

- Substitute value of a in equation (1) or to to find b

∵ 4(0.5) + 2b = 2

∴ 2 + 2b = 2

- Subtract 2 from both sides

∴ 2b = 0

- Divide both sides by 2

∴ b = 0

Substitute the values of a and b in the function model

∴ y = 0.5x² + (0)x - 8

∴ y = 0.5x² - 8

∵ y represents the depth from level ground

∵ The vertex of the function model is (h , k)

∴ The deep of the hole at ground level is the value of k

∵ h=\frac{-b}{2a}

∴ h=\frac{-(0)}{2(0.5)}

∴ h = 0

∵ k is the value of y when x = h

- From the table at x = 0 ⇒ y = -8

∴ k = -8

- Ignore the sign (-) because the k represents the depth of the

  hole in feet

∴ The deep of the hole at ground level is 8 feet

The hole is 8 feet deep at ground level

Learn more:

You can learn more about the quadratic function in brainly.com/question/1332667

#LearnwithBrainly

4 0
3 years ago
What is the least common denominator of the rational expressions below?
Lyrx [107]

Answer:

B.(x-6)

Step-by-step explanation:

12/(x^2 - 11x+30) - 43/(x^2-6x)

12/((x - 5) (x - 6)) - 43/x(x-6) [Factoring the denominator]

Both have x-6 common in the denominator,

4 0
2 years ago
2x+3y=6 what is the Solution
serg [7]

Answer:

x = 3- 3y/2

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
2 to the fourth power subtracted by 8 multiplied by 2 divided by 4 simpified
Korvikt [17]

2^4-8x2/4  (PEMDAS) Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction

first you want to do exponents.. so 2x2x2x2 = 16

then you want to do multiplication so.. -8x2 = -16

now you have.. 16-16/4 .. then you want to do division so divide -16 by 4 and get -4

then you're left with 16-4 which is 12

THE ANSWER IS 12

6 0
3 years ago
Please help me!! 45 points!! Find the values of the variables in the figure. Thank you I really need this!!
Mice21 [21]

Answer:

x=2x, y=5y

Step-by-step explanation:

180-108=72+120=192,360-192=168

5 0
2 years ago
Read 2 more answers
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