1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
marusya05 [52]
2 years ago
15

For what value of x will the function f(x) = -3(x - 10)(x - 4) have a maximum value? Find the maximum value.

Mathematics
2 answers:
gayaneshka [121]2 years ago
4 0

Hello!

To find the maximum value of the function f(x) = -3(x - 10)(x - 4), the easiest way is to find the vertex using the formula: x = -b/2a.

Firstly, we need to simplify f(x).

f(x) = -3(x - 10)(x - 4)

f(x) = -3(x² - 14x + 40)

f(x) = -3x² + 42x + -120

Since the equation f(x) is now simplified to standard form, we can find the vertex.

a = -3, b = 42, and c = -120

x = -(42)/2(-3) = -42/-6 = 7

Then, we substitute 7 into the the function f(x) = -3(x - 10)(x - 4), or

f(x) = -3x² + 42x + -120, to find the y-value of the vertex.

f(x) = -3(7 - 10)(7 - 4)

f(x) = -3(-3)(4)

f(x) = 27

The vertex of f(x) is (7, 27).

Therefore, the maximum x-value for the function f(x) is 7.

il63 [147K]2 years ago
3 0

Maximum point occurs at the line of symmetry

<u>Step 1: Find the x-intercept. [ x- intercept = when f(x) = 0 ]</u>

f(x) = -3(x - 10)(x - 4)

-3(x - 10)(x - 4) = 0

x - 10 = 0 or x - 4 = 0

x = 10 or x = 4

-

<u>Step 2 : Find the line of symmetry [ Midpoint of x ]</u>

midpoint of x = (10 + 4) ÷ 2 = 7

Line of symmetry : x = 7

-

Answer: Maximum value occurs when x = 7

You might be interested in
chris bought a cup of hot chocolate does his cup probably hold 400 liters or 400 milliliters of hot chocolate
vivado [14]

Answer:

Millileters

Step-by-step explanation:

If it held 400 liters, it would be a pretty gigantic cup

8 0
3 years ago
Read 2 more answers
Simplify. 5 - 2(x - 3)
V125BC [204]
To solve this, we simply need to remember our rules about order of operations. They tell us that first, we should distribute the 2 with the rest of the parentheses.

5-2(x-3)
5-2x+6

Next, we should combine our like-terms.

5-2x+6
11-2x

Seeing as we do not know the value of the variable, the simplest form of the expression is 11-2x.
3 0
3 years ago
Identify the coefficient of 17xy3z12
expeople1 [14]

Answer: Coeffcient is 17

Explaination:-

Given expression is :

17xy³z¹²

To find the coefficient of given expression

In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or any expression; it is usually a number, but may be any expression.

For example : In 2x⁵

Coeffcient is 2

Now come to the question:

Coeffcient is 17.

8 0
3 years ago
(-3,2), (0, 3), (6,5)
Leni [432]

Answer: (3,8)  and 2-,10)  or  the slope will be 3/2x

7 0
2 years ago
Can someone help pls!!
kari74 [83]

Answer:

C) 42.14 cm²

Step-by-step explanation:

<u>Recall the area formulas for a square and circle:</u>

Area of square: A=s²

Area of circle: A=πr²

<u>Given:</u>

π=3.14

s=14

r=s/2=14/2=7

Therefore, the area of the square is A=14²=196 cm²

The area of the two semicircles is A=3.14(7)²=3.14(49)=153.86 cm²

Find the difference between the two areas to get the shaded area:

196 - 153.86 = 42.14

Therefore, the shaded area is 42.14 cm², making C the correct choice.

5 0
3 years ago
Read 2 more answers
Other questions:
  • Am I correct? It's important that I get the right answer, so if I'm wrong please tell me what I did wrong
    13·1 answer
  • 29) PLEASE HELP WITH QUESTION.<br><br> MARKING BRAINLIEST + POINTS GIVEN.
    14·1 answer
  • What is the greatest common factor of 35y4, 14y4, and 63y4?
    7·1 answer
  • What are the length and width of the terracr
    15·2 answers
  • How do I solve this
    9·2 answers
  • A lorry weighs 4.65 tonnes. It carries a load of 748 kg. What is the total weight of the lorry and its load?
    12·2 answers
  • <img src="https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B216%5C%5C%7D" id="TexFormula1" title="\sqrt[3]{216\\}" alt="\sqrt[3]{216\\}"
    9·1 answer
  • How long does it take $6,000 to quadruple if it is invested at 9.1% interest compounded annually?
    14·1 answer
  • Plz someone help me I just guessed but what's the real answer, I need this asap​
    9·1 answer
  • -2
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!