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IrinaK [193]
2 years ago
9

Please help Will mark Brainliest

Mathematics
1 answer:
Alchen [17]2 years ago
3 0

Answer:

I'm pretty sure it's the last one !

Step-by-step explanation:

Good luck on your quiz!!

Hope you have a good day

:)

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Write an equation of a parabola that passes through (3,-30) and has x-intercepts of -2 and 18. Then find the average rate of cha
Nookie1986 [14]

Answer:

The equation of the parabola is y = \frac{2}{5}\cdot x^{2}-\frac{32}{5}\cdot x -\frac{72}{5}.  The average rate of change of the parabola is -4.

Step-by-step explanation:

We must remember that a parabola is represented by a quadratic function, which can be formed by knowing three different points. A quadratic function is standard form is represented by:

y = a\cdot x^{2}+b\cdot x + c

Where:

x - Independent variable, dimensionless.

y - Dependent variable, dimensionless.

a, b, c - Coefficients, dimensionless.

If we know that (3, -30), (-2, 0) and (18, 0) are part of the parabola, the following linear system of equations is formed:

9\cdot a +3\cdot b + c = -30

4\cdot a -2\cdot b +c = 0

324\cdot a +18\cdot b + c = 0

This system can be solved both by algebraic means (substitution, elimination, equalization, determinant) and by numerical methods. The solution of the linear system is:

a = \frac{2}{5}, b = -\frac{32}{5}, c = -\frac{72}{5}.

The equation of the parabola is y = \frac{2}{5}\cdot x^{2}-\frac{32}{5}\cdot x -\frac{72}{5}.

Now, we calculate the average rate of change (r), dimensionless, between x = -2 and x = 8 by using the formula of secant line slope:

r = \frac{y(8)-y(-2)}{8-(-2)}

r = \frac{y(8)-y(-2)}{10}

x = -2

y = \frac{2}{5}\cdot (-2)^{2}-\frac{32}{5}\cdot (-2)-\frac{72}{5}

y(-2) = 0

x = 8

y = \frac{2}{5}\cdot (8)^{2}-\frac{32}{5}\cdot (8)-\frac{72}{5}

y(8) = -40

r = \frac{-40-0}{10}

r = -4

The average rate of change of the parabola is -4.

3 0
3 years ago
Which number line represents the solution set for the inequality 4(x + 3) 5 2 2X?
tatuchka [14]

Answer:

-2

Step-by-step explanation:

6 0
3 years ago
James bought a cake that weighs 3 and 1 over 4 pounds. How many ounces does the cake weigh? Show your work. (5 points)
kolezko [41]

The weight of James cake in ounces is 52 ounces and the Pint of water dispensed in 20 seconds is 24 pints

<h3>Weight</h3>

  • Weight of cake = 3 1/4 pounds

1 pound = 16 ounces

Number of ounces the cake weigh = 3 1/4 pounds × 16 ounces

= 13/4 × 16

= (208) / 4

= 52 ounces

  • Water dispensed per second = 0.15 gallons
  • Number of seconds = 20 seconds

1 gallon = 4 quarts

0.15 gallon = 0.6 quarts

1 quart = 2 pints

0.6 quart = 1.2 pints

Pint of water dispensed in 20 seconds = 1.2 × 20

= 24 pints of water

Learn more about weight:

brainly.com/question/229459

#SPJ1

8 0
2 years ago
Mr. Falco baked blueberry muffins several times in May using the recipe shown. He used 3 3/4 cups of milk in all. How many times
const2013 [10]

Answer:

use fraction caculator

Step-by-step explanation:

srry for wrong answer just need points for this question ineed only one more answer for so again i am so srry pls dont get amd or just dont pay any attention to this

3 0
3 years ago
Read 2 more answers
Lisa used 1/4 cups of milk per batch using her muffin recipes. How many cups of Milan will she use when she made 6 batches of mu
marin [14]

Answer:

1 1/2

Step-by-step explanation:

1/4 cups * 6 batches = 1/4 * 6 = 6/4 = 1 2/4 = 1 1/2

7 0
3 years ago
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