Answer:
D
Step-by-step explanation:
The income is given by:
[tex]y=-0.5x^2+6x+90[/tex]
And the costs are given by:
[tex]y=2.5x+30[/tex]
Where x is the number of units sold, in hundreds, and y is the total dollar amount, in thousands.
We want to find a viable solution for the number of units sold that would cause the income and cost to be the same.
So, we can set the two equations equal to each other and solve for x. Therefore:
[tex]-0.5x^2+6x+90=2.5x+30[/tex]
Subtract 2.5x and 30 from both sides:
[tex]-0.5x^2+3.5x+60=0[/tex]
Remove the decimals and the negative of the leading coefficient by multiply both sides by -2:
[tex]x^2-7x-120=0[/tex]
Factor. We can use -15 and 8. So:
[tex](x-15)(x+8)=0[/tex]
Zero Product Property:
[tex]x=15 \text{ or } x=-8[/tex]
The answer must be positive since we cannot sell negative units.
So, the value of x is:
[tex]x=15\text{ or } 1,500 \text{ units}[/tex]
Then using either equation, the value will be:
[tex]2.5(15)+30=67.5=\$67,500[/tex]
Our answer is D.
Answer:
d. 1,500 units sold and a value of $67,500
Step-by-step explanation:
The value of 2^0 ??
Answer:
1
Step-by-step explanation:
. It is read as 2 raised to zero. Now let see how to solve such problem For example 3^5 then it means 3×3×3×3×3 = 243 Now back to question Anything raised to zero is always 1 Hence 2^0= 1
ansition Mrs. Tucker had taught school 24 years. Mr. Tucker realized that her number of years teaching was a multiple of Mr Glover's number of years teaching. Find all the number of years that Mr. Tucker could have taught
Answer:
Your question isn't full ?ansition?
Step-by-step explanation:
Here is a diagram of a person standing next to a tree.
The diagram shows two centimeter rulers.
The tree and the person are drawn to the same scale.
The person is approximately 1.75 m tall.
Using the scale diagram, estimate the height of the tree in meters.
15 points + Brainiest + Heart
The estimated height of the tree is approximately 5 meters.
To estimate the height of the tree using the scale diagram, we need to compare the height of the person on the diagram to the height of the tree.
Given that the person's height is approximately 1.75 meters, we can use the scale of the diagram to make the estimation.
Let's assume that the scale on the diagram is such that each centimeter on the ruler corresponds to 1.75 meters in real life.
By measuring the height of the person on the diagram using the ruler, let's say it corresponds to 2 centimeters.
Now, using the scale of 1.75 meters per centimeter, we can calculate the estimated height of the tree:
2 centimeters * 1.75 meters/centimeter = 5 meters
Therefore, based on the scale diagram, the estimated height of the tree is approximately 5 meters.
To know more about height click here :
https://brainly.com/question/21690792
#SPJ2
A book has 244 pages. Theo has read 81 pages so far. About what percent
of the book has Theo read?
A. 82%
B. 66%
C. 50%
D. 33%
Answer:
33%
Step-by-step explanation:
81 pages ÷244 pages ×100=33%
Answer:
D. 33% (rounded)
What is 54/100 as a percentage
Answer:
54%
Step-by-step explanation:
Sorry, I don't really know how to explain this.
Hope this helps!
Maybe braniliest?
Answer: 54%
Explanation: A percent is a ratio that compares a number to 100.
So we can write 54/100 as 54%.
You and classmate have volunteered to contact everyembervof your class by phone to inform them of an upcoming event you can complete the calls in 6 days od you woek alonw id u work togehwr you can complwte the calls in 2.4 days how long would it takw your classmate to make call alon
Answer:
what
Step-by-step explanation:
did you have a stroke?
Suppose that G(x) = F(x + 9). Which statement best compares the graph of G(x) with the graph of F(x)?
A. The graph of G(x) is the graph of F(x) shifted 9 units up.
B. The graph of G(x) is the graph of F(x) shifted 9 units to the right.
C. The graph of G(x) is the graph of F(x) shifted 9 units down.
D. The graph of G(x) is the graph of F(x) shifted 9 units to the left.
Answer:
Option D
Step-by-step explanation:
The graph of G(x) is the graph of F(x) shifted 9 units to the left.
The positive 9 in the parenthesis let's us know that the transformation should be 9 units to the left.
What is the distance from J to K?
Answer:
A. 13 units is the answer
pls subscribe my channel
https://youtu.be/RTFkRTT0EUY
Answer:
13 Units
Step-by-step explanation:
Find the slope of the following graphs ?
Answer:
slope=2
Step-by-step explanation:
the line is negative since it's downwards, and the slope goes 2 down and 1 right to meet the next point. -2/1=-2
The slope of the given graph is -2.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
Points from the graph (1, 0) and (0, 2).
So, the slope of line
= ( 2- 0) / (0 -1)
= 2 / (-1)
= -2/1
= -2
Hence, the slope of graph is -2.
Learn more about slope here:
https://brainly.com/question/3605446
#SPJ2
y = 4sin(1/2x-6)
What is the graph for this equation and is there a reflection?
Whoever answers this for me gets brainliest!! I need answers ASAP
Answer: 60
Step-by-step explanation:
Use proportions
Answer:
C.) 60
Step-by-step explanation:
435/12 = 60
12 x 5 = 60
The width of a rectangle is 9 feet less than the length. The area is 580 square feet. Find the length and width of the rectangle.
Answer:
5220
Step-by-step explanation:
A=580, A=LW, W=L-9
580=L(L-9)
L^2-9L-580=0
(L-29)(L+20)=0, L>0 so L=29, W=29-9=20
if tantheta -cottheta =a and costheta +sintheta =b then 4b^2(2-b^2)
Answer:
= 4(1+sin2theta)²
Step-by-step explanation:
Given the equations
tantheta -cottheta =a... 1
costheta +sintheta =b .... 2
We are to find 4b^2(2-b^2)
Squaring both sides of equation 2
(costheta +sintheta)^2 = b^2
cos^2theta + 2costheta sintheta + sin^2 theta = b^2
(cos^2theta+ sin^2 theta) + 2costheta sintheta = b^2
1 + 2costheta sintheta = b^2
1 + sin2theta = b^2
substitute
4b^2(2-b^2)
= 4(1+sin2theta)(2-1+sin2theta)
4(1+sin2theta)(1+sin2theta)
= 4(1+sin2theta)²
In a brochure about an outdoor wilderness camp, the yearly attendance is rounded to 28,000 students.
Which could be the number of students who attended the camp if the attendance was rounded to the
nearest thousand?
Choose all answers that apply:
А
28,620
B
27.500
28.350
Answer:
B) 27,500
Looks like the decimal points in your question are a typo and should be commas... ;) If so, the answer is B
1.
Directions:
Factor each expression.
Then find the roots of each equation.
I found all the factors, but not sure the roots of each equation.
Answer:
a. – 4 or –3
b. –4 or –2
c. 4 or –3
d. 7 or 4
Step-by-step explanation:
To factorize the above expression, multiply the first and last term together, then find two factors of the result such that their sum will result to the middle term of the expression.
Now, we shall give the answers to the question.
a. x² + 7x + 12 = 0
x² + 3x + 4x + 12 = 0
Factorise
x(x + 3) + 4(x + 3) = 0
(x + 4)(x + 3) = 0
x + 4 = 0 or x + 3 = 0
x = 0 – 4 or x = 0 – 3
x = – 4 or –3
Therefore, the roots of the equation are – 4 or –3
b. t² + 6t + 8 = 0
t² + 2t + 4t + 8 = 0
Factorise
t(t + 2) + 4(t + 2) = 0
(t + 4)(t + 2) = 0
t + 4 = 0 or t + 2 = 0
t = 0 – 4 or t = 0 – 2
t = –4 or –2
Therefore, the roots of the equation are –4 or –2
c. 2n² – 2n – 24 = 0
Divide through by 2
n² – n – 12 = 0
n² + 3n – 4n – 12 = 0
Factorise
n(n + 3) – 4(n + 3) = 0
(n – 4)(n + 3) = 0
n – 4 = 0 or n + 3 = 0
n = 0 + 4 or n = 0 – 3
n = 4 or n = –3
Therefore, the roots of the equation are 4 or –3
d. y² – 11y + 28 = 0
y² – 4y – 7y + 28 = 0
Factorise
y(y – 4) – 7(y – 4) = 0
(y – 7)(y – 4) = 0
y – 7 = 0 or y – 4 = 0
y = 0 + 7 or y = 0 + 4
y = 7 or 4
Therefore, the roots of the equation are 7 or 4.
a person walks 1/3 mile in 1/24 hour what is the persons speed in miles per hour?
Answer:
8mph
Step-by-step explanation:
Distance= 1/3 mile
time= 1/24 hour
Speed= distance/time
speed = 1/3 divided by 1/24
= 8mph
Answer:
8 im pretty sure
Step-by-step explanation:
Prove that the value of the expression: 731^2−631^2 is divisible by 100
Answer:
Step-by-step explanation:
731² - 631² is the difference of squares.
731² - 631² = (731+631)(731-631) = 1362×100
therefore, 731² - 631² is divisible by 100
Complete the equation describing how c and y are related
Describe how you would evaluate this algebraic
expression: 7-2m when m=2
Answer:
Step-by-step explanation:
Just plug in
7 - 2(2) = 3
Answer:
3
Step-by-step explanation:
By substituting m for 2, you would get:
7 - 2(2) =
7 - 4 = 3
Consider f(x) = 1.8x – 10 and g(x) = −4.
A 2 column table with 6 rows. The first column, x, has the entries, negative 4, 0, 2, 4. The second column, f(x) has the entries, negative 17.2, negative 13.6, negative 10, negative 6.4, negative 2.8. A 2 column table with 6 rows. The first column, x, has the entries, negative 4, 0, 2, 4. The second column, fgx) has the entries, negative 17.2, negative 4, negative 4, negative 4, negative 4.
Select the equation that can be used to find the input value at which f (x ) = g (x ), and then use that equation to find the input, or x -value.
1.8x – 10 = –4; x = 1.8 x minus 10 equals negative 4; x equals StartFraction 10 Over 2 EndFraction.
1.8x = –4; x = 1.8 x equals negative 4; x equals negative StartFraction 20 over 9 EndFraction.
1.8x – 10 = –4; x = A 2 column table with 6 rows. The first column, x, has the entries, negative 4, 0, 2, 4. The second column, f(x) has the entries, negative 17.2, negative 4, negative 4, negative 4, negative 4.
–4 = x
Answer:
I got you
Step-by-step explanation:
A
Answer:
A. 1.8x – 10 = -4x = 10/3
Step-by-step explanation:
I did the assignment
Solve.
sec 315 degrees
Answer:
1.41
Step-by-step explanation:
Which of the following is an equivalent expression to the expression
Answer:
a. [tex]a^{\frac{1}{12} }[/tex]
Step-by-step explanation:
[tex]\frac{a^{\frac{1}{3} } }{a^{\frac{1}{4} } }[/tex] = [tex]a^{\frac{1}{3}-\frac{1}{4} }[/tex] = [tex]a^{\frac{1}{12} }[/tex]
A homeowner is building a flower bed in the backyard. He plans to put a layer of fertilizer over the entire flower bed.The diagram shows the flower bed and its dimensions in feet.
4w2 + 3w - 1
5w - 2.
Which expression represents the area in square feet that the homeowner will cover with fertilizer?
Answer:
The answer is 4w^2 + 8w - 3
Step-by-step explanation:
Umm I hope it's right
Find the difference.
4-(-8)=
Answer:
4
Step-by-step explanation:
subtract negative 4 by negative 8
What is the slope of this graph
Answer: positive I think
Step-by-step explanation:
This is very urgent!!!!!!!! URGENT URGENT!!!!!!!!!!!!!!!!!!!
Answer:
234
Step-by-step explanation:
Answer:
234
!
Step-by-step explanation:
A cylinder has a height h, and a radius (3h-2)
The area of the base is pi (3h-2)^2
The volume of the clinder is V= pi(3h-2)^2h
10. Multiply the polynomials to simplify the expression for the volume:
V=pi(3h-2)^2h by
Answer:
[tex]V= 4\pi (9h^2 -12h + 4)[/tex]
Step-by-step explanation:
Given
Shape: Cylinder
[tex]Radius = 3h - 2[/tex]
[tex]Height = h[/tex]
[tex]Base\ Area = \pi (3h - 2)^2[/tex]
Required
Simplify the volume
The volume is calculated as:
[tex]Volume = Base\ Area * Height[/tex]
Substitute values for Base Area and Height
[tex]V= \pi(3h-2)^2*h[/tex]
Expand the bracket
[tex]V= \pi(3h-2)(3h-2)*h[/tex]
Open brackets
[tex]V= \pi (9h^2 -6h - 6h + 4) *h[/tex]
[tex]V= \pi (9h^2 -12h + 4) *h[/tex]
[tex]V= 4\pi (9h^2 -12h + 4)[/tex]
The Crews family went on a day trip to Nashville. For lunch they paid $7.50 for each adult meal and $5 for each child meal for a total of $65. For dinner the family paid $10.50 for each adult meal and $5 for each child meal for a total of $77. How many adults and how many children were on the trip?
Answer:
Number of adult were on the trip = 4
Number of child were on the trip = 7
Step-by-step explanation:
Let the Number of adult were on the trip = x
Let the Number of child were on the trip = y
As given,
For lunch they paid $7.50 for each adult meal and $5 for each child meal for a total of $65.
⇒7.50x + 5y = 65 ...........(1)
Also,
For dinner the family paid $10.50 for each adult meal and $5 for each child meal for a total of $77.
⇒10.50x + 5y = 77 ...........(2)
Now,
Subtract equation (2) from equation (1) , we get
10.50x + 5y - ( 7.50x + 5y ) = 77 - 65
⇒10.50x + 5y - 7.50x - 5y = 12
⇒10.50x - 7.50x = 12
⇒3x = 12
⇒x = [tex]\frac{12}{3}[/tex] = 4
⇒x = 4
Now,
Put the value of x in equation (2) , we get
10.50(4) + 5y = 77
⇒42 + 5y = 77
⇒5y = 77 - 42
⇒5y = 35
⇒y = [tex]\frac{35}{5}[/tex] = 7
⇒y = 7
∴ we get
Number of adult were on the trip = x = 4
Number of child were on the trip = y = 7
what are the first 4 multiples of 9
9,18,27,36,45
Step-by-step explanation:
A tree cast a shadow 21 meters long. The angle of elevation of the sun is 51 degrees. What is the height of the tree?
Answer:
64feet
Step-by-step explanation: