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2 years ago

10

What is the simplified result of following the steps below in order?

1 answer:

Keith_Richards [23]2 years ago

3 0

(5y+2x)*3+(x+y)=15y+6x-x-y=5x+14y

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Given the following three points, find by the hand the quadratic function they represent (0,6, (2,16, (3,33)

Lisa [10]

Answer:

$f(x) = 4x^2 - 3x + 6$

Step-by-step explanation:

Quadratic function is given as $f(x) = ax^2 + bx + c$

Let's find a, b and c:

Substituting (0, 6):

$6 = a(0)^2 + b(0) + c$

$6 = 0 + 0 + c$

$c = 6$

Now that we know the value of c, let's derive 2 system of equations we would use to solve for a and b simultaneously as follows.

Substituting (2, 16), and c = 6

$f(x) = ax^2 + bx + c$

$16 = a(2)^2 + b(2) + 6$

$16 = 4a + 2b + 6$

$16 - 6 = 4a + 2b + 6 - 6$

$10 = 4a + 2b$

$10 = 2(2a + b)$

$\frac{10}{2} = \frac{2(2a + b)}{2}$

$5 = 2a + b$

$2a + b = 5$ => (Equation 1)

Substituting (3, 33), and c = 6

$f(x) = ax^2 + bx + x$

$33 = a(3)^2 + b(3) + 6$

$33 = 9a + 3b + 6$

$33 - 6 = 9a + 3b + 6 - 6$

$27 = 9a + 3b$

$27 = 3(3a + b)$

$\frac{27}{3} = \frac{3(3a + b)}{3}$

$9 = 3a + b$

$3a + b = 9$ => (Equation 2)

Subtract equation 1 from equation 2 to solve simultaneously for a and b.

$3a + b = 9$

$2a + b = 5$

$a = 4$

Replace a with 4 in equation 2.

$2a + b = 5$

$2(4) + b = 5$

$8 + b = 5$

$8 + b - 8 = 5 - 8$

$b = -3$

The quadratic function that represents the given 3 points would be as follows:

$f(x) = ax^2 + bx + c$

$f(x) = (4)x^2 + (-3)x + 6$

$f(x) = 4x^2 - 3x + 6$

6 0

3 years ago

What is the sum of (8b+7)+(6x-4)+(5c+8)?????

34kurt

Answer:

8b + 6x + 5x + 18

Step-by-step explanation:

8b + 7 + 6x + 4 + 5c + 8

8b + 6x + 5x + 18

Answer: 8b + 6x + 5x + 18

8 0

3 years ago

Read 2 more answers

When Anna was born 16 years ago, her small town of Lewisville had a population of 15,000. The population has increased 11% each

Alex17521 [72]

15.000 ÷ 100

150 = 1%

1650 = 11%

1650 x 16 = 26.400

26.400 + 15.000 = 41.400

So 41.400 is the population number now.

7 0

3 years ago

What is the difference?<br> x2 - 2x-15<br> x2+2x-35

omeli [17]

Answer:

<h3>x^2+3x-12/(x+3)(x-5)(x+7) </h3>

Step-by-step explanation:

<h3>D</h3>

3 0

3 years ago

Compare the linear functions expressed below by data in a table and by an equation.

kondor19780726 [428]

Answer:

b,c,e

Step-by-step explanation:

7 0

2 years ago