The maximum power is 4A.
What is Function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
The given function
P(x) = - 15x (x-8)
P(x) = - 15x² + 120x
The standard form of a quadratic function is:
y = ax² + bx + c
For which x is the maximum of the parabola
x = - b/2a
So, a = -15 and b = 120.
Then, x = - 120/(2 · (-15))
x = - 120/ (-30)
x = 4A
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The Johnson family is going to build a new home. They need to have working drawings of their house plans created by a design firm. They will choose between Rock the House Digital Designs and Elegant Home Architects. Rock the House Digital Designs charges $500.00 for the initial consultation with the Johnson family, plus $50.00 for every additional hour of work for the house plans. Elegant Home Architects charge $75.00 per hour for the house plans. Let ℎ represent the number of hours for which the Johnson family hires the design firm. Which of the following statements are true? Select all that apply.
Answer:
Statements B, D, E are TRUE
Step-by-step explanation:
A. The expression 50ℎ represents the total charge for Rock the House Digital Designs.
NOT TRUE
The expression 500 + 50h represent total charge for Rock the house digital design
B. The expression 75ℎ represents the total charge for Elegance Home Architects.
TRUE
Elegance Home Architects
75h
C. The cost for using Rock the House Digital Designs for an initial consultation only is $550.
NOT TRUE
The cost for using Rock the House Digital Designs for an initial consultation only is $500
D. If the Johnson family hires the design firm for 15 hours, then Elegance Home Architects will be cheaper.
TRUE
Rock the house digital designs
$500 + $50h
= 500 + 50(15)
= 500 + 750
=$1,250
Elegant home architect
$75h
= 75(15)
= $1,125
Elegant home architect is cheaper
E. If the Johnson family hires the design firm for 40 hours, then Rock the House Digital Designs will be cheaper.
TRUE
Rock the house digital designs
$500 + $50h
= 500 + 50(40)
= 500 + 2,000
= $2,500
Elegant home architect
$75h
= 75(40)
= $3,000
Rock the House Digital Designs will be cheaper.
Write an expression with a negative exponent that has a value between 0 and 1/2. Please answer ASAP, thank you!
Answer:
4^-2
Step-by-step explanation:
Answer:
[tex] 2^{-2} [/tex]
Step-by-step explanation:
1/4 is between 0 and 1/2.
[tex] \dfrac{1}{4} = \dfrac{1}{2^2} = 2^{-2} [/tex]
The square of a number minus twice the number is 48. What is the number? (An explanation would be appreciated)
Step-by-step explanation:
The square of a number minus TWICE the number is 48
let the number be" X "
X^2-2X-48 = 0
(X - 8)(X + 6) = 0
x = 8 ᴏʀ X = -6
mark brainliest
someone help me
i will give u 5 star..
Answer:
Step-by-step explanation:
what quadrant is -2 (radians) in?
Answer:
From unit Symbol Equals Result To unit Symbol
1 quadrant quad. = 1.57 radians rad
Step-by-step explanation:
URGENT! find the smallest whole number when divided by 4 gives a remainder of 3, when divided by 3 gives remainder of 2, when divided by 2 gives a remainder of 1
Answer:
11 is the smallest whole number when divided by 4 gives a remainder of 3, when divided by 3 gives remainder of 2, when divided by 2 gives a remainder of 1
. Answer:1.when divide by 4 and gives a remainder of 3 = 12
2 .when divided by 3 gives a remainder of 2 = 6
3. when divided by 2 and gives a remainder of 1 = 2
Step-by-step explanation:
1. 12 ÷ 4 = 3
2. 6 ÷ 3 = 2
3.2 ÷ 2 = 1
Which statement is true Every real number is an integer Every integer is a counting number Every integer is a rational number Every terminating decimal number is an irrational number
Answer:
C. Every integer is a rational number
Step-by-step explanation:
Integers are whole numbers which could be positive or negative and zero. Examples of integers are 330, 21, 10,052, 0, -425, -879, etc. Fractions are not integers. Rational numbers are numbers that are expressed as the ratio of two integers. So numbers that have integers as their numerators and denominators can be rightly said to be rational numbers. Examples are, 5/7, 10,111/880, -365/15.
Since both the numerators and denominators are whole numbers, the entire figures can be said to be rational numbers. So, fractions are rational numbers.
Please show all work and not just the answers.
Answer:
(-1, 6)
Step-by-step explanation:
Midpoint formula:
xm = (x1 +x2)/2ym = (y1+y2)/2For G(-7, 3) and H(5, 9) the midpoint:
((-7+5)/2, (3+9)/2) = (-1, 6)Answer:
(-1,6)
Step-by-step explanation
use the midpoint formula:
(x 1 + x2 /2 , y1 + y2/2)
(-7+ 5 /2, 3+ 9 /2)
after simplfying
(-1,6)
Ray KN is the angle bisector of angle JKL.
Explain how you could find m angle JKN
if you know m angle JKL.
Answer:
See Explanation
Step-by-step explanation:
Given
Angle: JKL
Bisector: KN
Required
How to determine JKN if JKN is known
When a line bisects an angle into two, the angle are divided into two equal parts.
In this case, JKL is bisected by KN;
The resulting angles are JKN and NKL
So:
[tex]JKL = JKN + NKL[/tex] --------- (1)
From the explanation, we can understand that JKN and NKL hold the same value.
i.e. [tex]JKN = NKL[/tex]
So, (1) becomes
[tex]JKL = JKN + JKN[/tex]
[tex]JKL = 2JKN[/tex]
Divide by 2
[tex]JKN = \frac{JKL}{2}[/tex]
Take for instance; JKL =8
[tex]JKN = \frac{8}{2} = 4[/tex]
Andre and Morgan are both headed to Florida for vacation. Andre will drive 70 miles per hour. Morgan will drive 55 miles per hour but will leave 3 hours earlier than Andre. How many hours will Morgan have been driving before Andre catches up with her?
Answer:
The number of hours Moran wold have driven before Andre catches up with him is 14 hours
Step-by-step explanation:
The given information are;
The speed with which Andre will drive = 70 miles per hour
The speed with which Morgan will drive = 55 miles per hour
The time of departure of Morgan = 3 hours before Andre departs
Let the time at which Andre catches up with Morgan be, t
We have, from the definition of distance traveled;
Distance traveled =Speed × Time
The distance Morgan would have driven in t hours = 55 × t
Given that to catch up with Morgan, Andre has to travel the same distance, and that Andre starts 3 hours late, we have;
The distance Andre would drive when Morgan has driven for t hours = 70 × (t - 3)
Therefore, since the distance at the point they meet is the same distance for them both, we have;
55 × t = 70 × (t - 3)
55 × t = 70 × t - 210
210 = 70 × t - 55 × t = 15 × t
t = 210/15 = 14 hours
Therefore, Morgan would have driven for 14 hours before Andre catches uo with him.
Answer:
Morgan walks 2 miles per hour.
Step-by-step explanation:
took the test. ;)
Identify the real number that corresponds to the point plotted on the real number line.
Math problem giving brainlist and points!
Answer:
2c + 15 = 25
Step-by-step explanation:
The total he wants to earn is $25, so we know the equation must be an expression that equals 25.
____ = 25
He earns a fixed $15. He also earns $2 per customer.
The total he earns is the sum of the fixed amount ($15) and the amount he earns per customer. Let the number of customers be c. The amount he earns from the number of customers is 2c.
fixed amount + amount per customer = 25
15 + 2c = 25
2c + 15 = 25
Answer: 2c + 15 = 25
One root of f(x)=x^3-4x^2-20x+48 is x = 6. What are all the factors of the function? Use the Remainder Theorem.
A. (x + 6)(x + 8)
B. (x – 6)(x – 8)
C. (x – 2)(x + 4)(x – 6)
D. (x + 2)(x – 4)(x + 6)
Answer:
(x - 6)(x + 4)(x - 2)
Step-by-step explanation:
since x = 6 is a root then (x - 6) is a factor
x³ - 4x² - 20x + 48 ÷ (x - 6)
= (x - 6)(x² + 2x - 8)
= (x - 6)(x + 4)(x - 2) ← factors of f(x)
By using the Remainder Theorem, all the factors of the function are,
⇒ (x - 6) (x + 2) (x - 4)
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
One root of function f (x) = x³ -4x² -20x + 48 is, x = 6.
Hence, (x - 6) is divide the function f (x) = x³ -4x² -20x + 48 as;
(x - 6) ) x³ -4x² -20x + 48 ( x² + 2x - 8
x³ - 6x²
--------------
2x² - 20x
2x² - 12x
-----------------
- 8x + 48
- 8x + 48
----------------
0
Hence, We get;
f (x) = x³ -4x² -20x + 48
f (x) = (x - 6) (x² + 2x - 8)
⇒ f (x) = (x - 6) (x² - 4x + 2x - 8)
⇒ f (x) = (x - 6) (x(x - 4) + 2(x - 4))
⇒ f (x) = (x - 6) (x + 2) (x - 4)
Thus., By using the Remainder Theorem, all the factors of the function are,
⇒ (x - 6) (x + 2) (x - 4)
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If x2 + ax + b = (x – 9)(x + 9), what is the value of
ab?
A) -81
B)
0
C)
81
D) 1458
Step-by-step explanation:
X2+ax+b=(x-9)(x+9)
X2+ax+b=x2-9x+9x-81
X2+ax+b=x2-81
therefore,a=0,b=(-81)
Then , ab = 0×-81 = 0
Answer:
B) 0Step-by-step explanation:
x² + ax + b = (x – 9)(x + 9)
x² + ax + b = x² – 9x + 9x – 81
x² + ax + b = x² + 0x – 81
x²=x² +ax = +0x +b = -81
a = 0 b = -81
ab = 0(-81) = 0
What is the answer. What is the unknown length
Answer:
9 cm
Step-by-step explanation:
Solve the literal equation −cy+2=3d+7y for y.
Answer:
y = (2-3d)/(7+c)
Step-by-step explanation:
-cy + 2 = 3d + 7y
To solve this equation in terms of y, we must first move all of the terms containing a y to one side of the equation and move all of the other terms to the other side.
Our first step is going to be to add cy to both sides of the equation.
- cy + cy + 2 = 3d + 7y + cy
2 = 3d + 7y + cy
Next, we can subtract 3d from both sides of the equation.
2 - 3d = 7y + cy
Next, we can factor out a y from the right side of the equation.
2 - 3d = y (7 + c)
Finally, we can divide both sides by the quantity (7+c) to get the y alone on the right side of the equation.
(2-3d)/(7+c) = y
Therefore, your answer is y = (2-3d)/(7+c).
Hope this helps!
Which statement about the number −3 is true? Select all that apply.
A. It is a natural number.
B. It is a whole number.
C. It is an integer.
D. It is a rational number.
E. It is an irrational number.
Answer:
I'm pretty sure it's c and d
Susan will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $70 and costs an additional $0.40 per mile driven. The second plan has no initial fee but costs $0.60 per mile driven. How many miles would Susan need to drive for the two plans to cost the same?
Answer:
350 miles
Step-by-step explanation:
Let x represent the miles driven
The cost with the first plan will be represented by 0.40x + 70
The second plan will be represented by 0.60x
Set these 2 expressions equal to each other and solve for x:
0.40x + 70 = 0.60x
70 = 0.20x
350 = x
So, Susan will have to drive 350 miles for the cost to be the same
How to find midpoint
Answer:
Midpoint of a Line Segment
Step-by-step explanation:
Add both "x" coordinates, divide by 2.
Add both "y" coordinates, divide by 2.
Simplify (-2V7)(3V28)
Answer:
v^2 -4v-21
Step-by-step explanation:
Simplify. 3(2a+4b+7) +6a *Plz explain your answer*
Answer:
3(2a+4b+7)+6a = 12a+12b+21
m−4=2m What would M=
Answer:
m = -4
Step-by-step explanation:
m - 4 = 2m
Switch sides.
2m = m - 4
Subtract m from both sides.
m = -4
Answer:
-4
Step-by-step explanation:
cause mafs
(X+9)(x-2)-9x-6 equivalen to
Answer:
hrheje
Step-by-step explanation:
bdhsjsiskskdkdhdhennsjss
What would c need to be for this equation to be no solutions? l x+8 l = c
Answer:
Basically , anything negative number.
The absolute value can not be less than 0
Step-by-step explanation:
Example
[tex]\left|x+8\right|=-8\\\\\mathrm{Absolute\:value\:cannot\:be\:less\:than\:0}\\\mathrm{No\:Solution\:for}\:x\in \mathbb{R}\\[/tex]
PLS answer will mark brainliest⦁ The average age of a family of 5 is 30 years. The average of the 3 children in the family is 12 years. If the mother is 4 years as young as the father, calculate the age of the father.
Answer:
20
Step-by-step explanation:
I can explain in 2 - 3 sentences why the interger -2 has a greater value than the integer -5. In order to solve 2 - 3 you __________________. The reason -2 has a greater value than -5 is because ________________________________________________.
Answer:
I can explain in 2 - 3 sentences why the interge,r -2, has a greater value than the integer, -5. In order to solve, 2 - 3, you SUBTRACT. The reason, -2, has a greater value than, -5, is because, -2, is a negative so, -2 is bigger number than -5.
what is the average speed of a train that covers 80 km in 1 hour, 200 km in 2 hours and 420 kn in 4 hours
Answer:
95
Step-by-step explanation:
80+(200 divided by 2)+(420 divided by 4)=285
285 divided by 3=95
HELP 25 POINTS!!! MARK THE BRAINIEST!
Answer:
first option
Step-by-step explanation:
To find the product, that is
(4x + 1)(x² - 5)
Each term in the second factor is multiplied by each term in the first factor, that is
4x(x² - 5) + 1(x² - 5) ← distribute both parenthesis
= 4x³ - 20x + x² - 5
= 4x³ + x² - 20x - 5
You own a fish store with 478 fishes. You put the same number of fish into 17 tanks, but there are 2 fishes left over. How many fishes are in each tank?
Answer:
10
Step-by-step explanation:
478-2=476
476÷17= 10
therefore you put 10 fish in each tank.
Let me know if this helps:)
Answer:
10
Step-by-step explanation:
An experienced carpenter can frame a house twice as fast as an apprentice. Working together, it takes the carpenters 2 days. How long would it take the apprentice working alone?
Answer:
6 days
Step-by-step explanation:
Let the time taken by Carpenter working alone = [tex]C[/tex] days
Then time taken by apprentice alone = Twice as that of taken by Carpenter = 2[tex]C[/tex] days
Time taken working together = 2 days
Work done in one day working together = [tex]\frac{1}{2}[/tex]
Work done in one day by Carpenter working alone = [tex]\frac{1}{C}[/tex]
Work done in one day by apprentice working alone = [tex]\frac{1}{2C}[/tex]
Work done in one day by Carpenter working alone + Work done in one day by Carpenter working alone = [tex]\frac{1}{C}[/tex]+[tex]\frac{1}{2C}[/tex] = Work done in one day working together = [tex]\frac{1}{2}[/tex]
[tex]\dfrac{1}{C}+\dfrac{1}{2C}=\dfrac{1}{2}\\\Rightarrow \dfrac{2+1}{2C}=\dfrac{1}{2}\\\Rightarrow C = 3\ days[/tex]
Time taken by Carpenter alone to complete the work = 3 days
Time taken by Apprentice alone to complete the work = 3 [tex]\times[/tex] 2= 6 days
We are required to calculate the number of days it would take the apprentice working alone
The number of days it takes the apprentice working alone is 6 days
let
Number of days taken for the carpenter to work alone = x
Number of days taken by the apprentice to work alone = 2x
Number of days taken to work together = 2 days
Work done per day Carpenter = 1/x
work done per day apprentice = 1/2x
work done per day together = 1/2
So,
work done per day together = Work done per day Carpenter + work done per day apprentice
1/2 = 1/x + 1/2x
1/2 = (2 + 1) / 2x
1/2 = 3/2x
cross product
1(2x) = 2(3)
2x = 6
x = 6/2
x = 3 days
Therefore,
Number of days taken by the apprentice to work alone = 2x
= 2(3)
= 6 days
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