Question:
Which of the equivalent expressions for P(x) reveals the profit when the price is
zero without changing the form of the expression? P(x) = -3x² + 432x - 1680
a) P(x) = -3(x - 4)(x - 140)
b) P(x) = -3(x - 72)² + 13872
Find the profit when the price is zero
Answer:
- P(x) = -3(x - 140)(x - 4).
- P(0) = -1680
Step-by-step explanation:
Given
P(x) = -3x² + 432x - 1680
Required
- Find equivalent of P(x)
- Find P(x) when x = 0
To find the equivalent of P(x), we simply factorize P(x) = -3x² + 432x - 1680.
This is done as follows
P(x) = -3x² + 432x - 1680
P(x) = -3x² + 12x + 420x - 1680
P(x) = -3x(x - 4) + 420(x - 4)
P(x) = (-3x + 420)(x - 4)
Further expand -3x + 420
P(x) = -3(x - 140)(x - 4).
Hence, the equivalent of
P(x) = -3x² + 432x - 1680
without changing its form is
P(x) = -3(x - 140)(x - 4).
When price is 0, then x = 0.
Substitute 0 for P(x) in P(x) = -3(x - 140)(x - 4).
P(0) = -3(0 - 140)(0 - 4).
P(0) = -3(-140)(-4)
P(0) = -1680
Hence, the profit when price is 0 is -1680
Oil is leaking from an oil tanker, and an expanding circle of oil is spreading on the ocean. The radius, r, of the circle measured in inches is modeled by the function r(s)=3 sqrt s, where s is time in seconds. The area of the spill when s=5 seconds is ___ pi square inches.
Answer:
[tex]Area=45\pi$ square inches[/tex]
Step-by-step explanation:
The radius, r of the expanding circle of oil is modeled by the function:
[tex]r(s)=3\sqrt{s}[/tex], where s is time in seconds.
When s=5
Radius, [tex]r(5)=3\sqrt{5}$ inches[/tex]Area of a circle[tex]=\pi r^2[/tex]
Therefore, area of the oil spill when s=5 seconds is:
[tex]Area=\pi (3\sqrt{5})^2\\=\pi *3^2*(\sqrt{5})^2\\=\pi *9*5\\$Area=45\pi$ square inches[/tex]
The area of the spill when s=5 seconds is 45pi square inches.
Translate the statement into an equation. Then solve the equation.
The sum of 8 and 3 times a number is 23.
3x - 8 = 23; 5
8+ 3x = 23,5
3x = 8+23; 10
(8 + 3)x = 23; 2
A fast food chain surveyed a random sample of students to determine what pizza they prefer. Cheese pizza was preferred by 40 students. Pepperoni pizza was preferred by 28 students. Based on the results, how many of the 340 students can be expected to prefer cheese pizza?
Answer:
11.76
Step-by-step explanation:
We are given that,
Total number of students = 340
Students that prefer cheese pizza = 40
Students that prefer pepperoni pizza = 28
Thus, we get that,
The proportion of students that prefers cheese pizza =
i.e. The proportion of the students preferring cheese pizza = 0.1176 = 11.76%
Hence, 11.76% of the students prefer cheese pizza.
Anthony has a combination of 104 nickels and quarters totaling $22. Which system of linear equations can be used to find the number of nickels?
Answer:
The answer is c and we'll use c to get the actual answers.
A) n + q = 104
B) .05n + .25q = 22 we'll multiply B) by -4
B) -.2n -1q = -88 then we add A)
A) n + q = 104 which equals
.8n = 16
n = 20 nickels
q = 84 quarters
20 nickels = $1
84 quarters = $21
Successful!!!
Step-by-step explanation:
An equilateral triangle has perimeter 57cm, what is the length of one of the sides?
Answer:
19 cm
Step-by-step explanation:
An equilateral triangle has all 3 sides the same length
P = 3s where s is the side length
57 = 3s
Divide each side by 3
57/3 = 3s/3
19 =s
Jack wants to buy 30 chocolate chip cookies that are $1.25 each. If sales tax is 7.5%. What will Jack’s total bill be?
Answer:
which will be about $2.81
Step-by-step explanation:
30 times 1.25 = 37.50
then multiply that by 7.5%
i may be wrong. i am sorry if i am worong
Answer:
$318.75
Step-by-step explanation:
30 cookies x $1.25 = $37.5
37.5 x 7.5% tax = 281.25
37.5 + 281.25 = 318.75
what are the solutions to the system of equations graphed below?
Answer:
(-3,-3) and at (0,6)
Step-by-step explanation:
The solution to the system of equations is where the graphs intersect
The graphs intersect at (-3,-3) and at (0,6)
simplify x^2+(y-9)^2=
Answer: Simplify each term.
x^2+y^2−18y+81
Step-by-step explanation:
Three of the bedrooms in Lana’s house are rectangular, each 101/2 feet by 111/4 feet, What is the least amount of carpeting needed to completely cover the three floors?
Answer:
The answer is D, or 354 3/8 ft^2
PLEASE HELP FAST
Find the volume of a rectangular prism. Iength measures 16 ft, width measures 3 ft, and height measures 2 1/2 feet
Answer:
120 ft ^2
Step-by-step explanation:
Volume= lwh
Volume= 16(3)(2 1/2)
Volume= 120 ft^2
Answer: 120
Step-by-step explanation: 16 x 3 x 2.5 = 120
please help me with this it is the last quastion i need help with
Answer:
$92.92
Step-by-step explanation:
$72.60 * 20% = 14.53
$72.60 + 8%= $78.40
$78.40 + $14.52 = $92.93
David correctly factored the expression m^2-12m - 64.
Which expression did he write?
(1) (m - 8)(m - 8) (3) (m - 16)(m +4)
(2) (m - 8)(m + 8) (4) (m +16)(m - 4)
Explain why
Answer:
(m-16)(m+4)
Step-by-step explanation:
To factor a quadratic expression
First write the variable in each parentheses, then put negative/ positive, after that ask yourself what numbers have the product of the coefficient of x^0 and the sum of x^1.
David correctly factored the expression m^2 - 12m - 64 and got (m - 16)(m + 4).
How to factor an equation?An equation can be factored into its factors by splitting the middle term of the equation.
The given expression can be factored as shown below:m^2 - 12m - 64 = 0
⇒ m^2 - 16m +4m - 64 = 0
⇒ m(m - 16) + 4(m - 16) = 0
⇒ (m + 4)(m - 16) = 0
The factors of the equation m^2 - 12m - 64 = 0 are (m - 16)(m + 4).
Therefore, we have found that David correctly factored the expression m^2 - 12m - 64 and got (m - 16)(m + 4). The correct answer is option C or (3).
Learn more about factorization here: https://brainly.com/question/25829061
#SPJ2
Help me please............
Answer:
Step-by-step explanation:
16*[tex]x^{2}[/tex]
Answer:
16* x^2
Step-by-step explanation:
k* x^n
First simplify the expression:
4^2*x^2
So:
16* x^2
Take 2 y2 - 3 y - 5 from y3 - 6 y2 + 5 y . Select the correct answer.
A) y3 - 2 y2 + 3 y + 5
B) y3 - 4 y2 + 2 y - 5
C) y3 - 4 y2 + 2 y + 5
D) y3 - 8 y2 + 8 y + 5
Answer:
b
Step-by-step explanation:
Hope this helpsss :)
Answer:
your answer will be: B. y3 - 4 y2 + 2 y - 5
Step-by-step explanation:
Multiply (x - 2)(3x + 4) using the distributive property. Select the answer
choice showing the correct distribution.
Answer:
(x-2)(3x)+(x-2)(4)
When distributing you just break up the second parentheses and put the first parentheses infront of both of them, as it is shown in this answer.
Stan guessed on all 10 questions of a multiple-choice quiz. Each question has 4 answer choices. What is the probability that he got at least 2 questions correct? Round the answer to the nearest thousandth.
P (k successes) = Subscript n Baseline C Subscript k Baseline p Superscript k Baseline (1 minus p) Superscript n minus k. Subscript n Baseline C Subscript k Baseline = StartFraction n factorial Over (n minus k) factorial times k factorial EndFraction
0.211
0.244
0.756
0.944
Answer:
The answer is C.) 0.756
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
just did the test on edge 2020
Find the greatest common factor of 6w^3 and 8w.
Answer:2w
Step-by-step explanation: Find the prime factors of each term in order to find the greatest common factor (GCF).
2w
5x+2y = 10
Identify the y-intercept of the
following equation.
Answer:
y intercept = 10
hope this answer helped
Brett is comparing the graphs of y = 2X and y = 5x. Which statement is true?
The correct question is:
Brett is comparing the graphs of y = 2^x and y = 5^x. Which statement is true?
(1) The y-intercept of y = 2^x is (0,2), and the y-intercept of y = 5^x
is (0,5). [
(2) Both graphs have a y-intercept of (0,1), and y = 2^x is steeper.
(3) Both graphs have a y-intercept of (0,1), and y = 5^x is steeper.
(4) Neither graph has a y-intercept.
Answer:
(2) and (3) are true.
Step-by-step explanation:
The correct options are:
(2) Both graphs have a y-intercept of (0,1), and y = 2^x is steeper. Since X < 0
(3) Both graphs have a y-intercept of (0,1), and y = 5^x is steeper. Since X > 0
Which phrase represents this expression?
(47−17)×4
A. 4 times the difference of 47 and 17
B. 4 times the difference of 17 and 47
C. the difference of the product of 4 times 17 and 47
D. the difference of 47 and the product of 4 times 17
A cylinder has a height of 19 inches and a radius of 18 inches. What is its volu
3.14 and round your answer to the nearest hundredth.
Answer:
19339.64 in³
Step-by-step explanation:
Volume of a cylinder: V = π · r² · h
V = π · 18² · 19
V = π · 6156
V = 19339.64 cubic inches
Please help me with this
Answer:
no
Step-by-step explanation:
a 13% discount on an item that costs $1150 will cost u $1000.50
tell me if u want work i assumed u wanted a quick answer since its a quiz
Answer: No, you would still need $0.50
Step-by-step explanation:
1150 x 0.13= 149.5
1150-149.5= 1000.5
Can you help me please
Answer:
372.6
3Step-by-step explanation:
There are six slices of cake left at the end of a party. If that was 2/9 of the total of the cake that the party began with, how many slices were in the cake to begin with? (enter you answer as a number only, no words) *
Answer:
27
Step-by-step explanation:
6 divided by 2/9=27
write the equation of circle b with center B(-2,3) that passes through (1,2)
Answer:
[tex](x+2)^2 + (y-3)^2 = 10[/tex]
Step-by-step explanation:
The standard equation for circle is
[tex](x-a)^2 + (y-b)^2 = r^2[/tex]
where point (a,b) is coordinate of center of circle and r is the radius.
______________________________________________________
Given
center of circle =((-2,3)
let r be the radius of circle
Plugging in this value of center in standard equation for circle given above we have
[tex](x-a)^2 + (y-b)^2 = r^2 \ substitute (a,b) \ with (-2,3) \\=>(x-(-2))^2 + (y-3)^2 = r^2 \\=>(x+2)^2 + (y-3)^2 = r^2 (1)[/tex]
Given that point (1,2 ) passes through circle. Hence this point will satisfy the above equation of circle.
Plugging in the point (1,2 ) in equation 1 we have
[tex]\\=>(x+2)^2 + (y-3)^2 = r^2 \\=> (1+2)^2 + (2-3)^2 = r^2\\=> 3^2 + (-1)^2 = r^2\\=> 9 + 1 = r^2\\=> 10 = r^2\\=> r^2 = 10\\[/tex]
now we have value of r^2 = 10, substituting this in equation 1 we have
Thus complete equation of circle is [tex]=>(x+2)^2 + (y-3)^2 = r^2\\=>(x+2)^2 + (y-3)^2 = 10[/tex]
Montel needs to determine the distance from -3 to zero. Which statement best desribes the process Montel should use?
F. Find the absolute value of negative three.
G. Find the opposite of positive three.
H. Find the absolute vaule of positive three.
J. Find the opposite of negative three.
Answer:
F
Step-by-step explanation:
Absolute value finds the distance between a number and 0, which is what the question is asking for -- the distance between -3 and 0.
please help i don't get it
Answer:
97 cm
Step-by-step explanation:
The perimeter of a shape is the length of the whole shape so the perimeter of this shape would be
3 + 10 + 3 + 33 + 33 + 15 = 97 cm
The value of an antique can be predicted by the expression 250 * (1.12) ^ t where is the number of years since 2014. What does the value 250 represent?
Answer:
mark brainlyest and I will
The value 250 represents the predicted value of antique in year 2014.
Given Expression,
[tex]250\times(1.12)^{t}[/tex]
Here [tex]t[/tex] represents the no. of years since 2014.
Now clearly 250 shows here the predicted price of the antique in year 2014 and [tex](1.12)^t[/tex] shows how much percent the product is increasing over the year.
Hence the value 250 represents the predicted value of antique in year 2014.
For more details on Decay rate problems follow the link:
https://brainly.com/question/8725872
Find the hypotenuse of each Isosceles right triangle when the legs are of the given measure.
Given = 6squareroot2
Answer:
12
Step-by-step explanation:
We can use the pythagorean theorem giving us:
a^2+b^2=c^2
(6sqr2)^2 + (6sqr2)^2 = c^2
72+72=c^2
144=c^2
12=c
A snack company makes three batches of a nut mix using the recipe shown.
Each batch contains a different total amount of mix.
Drag numbers to show how much of each type of nut should be used in each batch.
1 of the mix is pistachios.
of the mix is almonds
of the mix is cashews
PLEASE HELP!!!
Answer:
batch 1
3 cups cashews
batch 2
2/6 or 1/3 cups (simplified) of pistachios
batch 3
1 1/3 cups of almonds
2 cups of cashews
