Answer: $35 is the selling price and $1225 is the maximum revenue.
Step-by-step explanation:
Since we have given that
[tex]R(x)=-x^2+70x[/tex]
We need to find the maximum revenue.
So, We will first derivative it w.r.t. x.
So, it becomes,
[tex]R'(x)=-2x+70[/tex]
Now, we will find critical points.
So, R'(x) = 0
So, it becomes,
[tex]-2x+70=0\\\\-2x=-70\\\\x=\dfrac{70}{2}=35[/tex]
Now, to check whether it yields maximum revenue or not.
So, second derivative w.r.t. x, we get that
R''(x) = -2<0
So, At $35, it yields maximum revenue.
Amount of maximum revenue would be
[tex]R(35)=-(35)^2+70\times 35=-1225+2450=\$1225[/tex]
Hence, $35 is the selling price and $1225 is the maximum revenue.
What is the cube root of 27a^l2?
-3a4
-3a
3a
3a*
Answer:
[tex]3a^4[/tex]
Step-by-step explanation:
What is the cube root of [tex]27a^{12}[/tex]? This is the question.
We can write:
[tex]\sqrt[3]{27a^{12}}[/tex]
We will use the below property to simplify:
[tex]\sqrt[n]{a*b}=\sqrt[n]{a} \sqrt[n]{b}[/tex]
So, we have:
[tex]\sqrt[3]{27a^{12}} =\sqrt[3]{27} \sqrt[3]{a^{12}}[/tex]
We will now use below property to further simplify:
[tex]\sqrt[n]{x} =x^{\frac{1}{n}}[/tex]
Thus, we have:
[tex]\sqrt[3]{27} \sqrt[3]{a^{12}} =3*(a^{12})^{\frac{1}{3}}[/tex]
We know power to the power rule: [tex](a^z)^b=a^{zb}[/tex]
Now, we have:
[tex]3*(a^{12})^{\frac{1}{3}}\\=3*a^{\frac{12}{3}}\\=3a^4[/tex]
This is the correct answer: [tex]3a^4[/tex]
Please help asap!! Explain too!
Answer:
x = 31°
Step-by-step explanation:
Since, CB ║ FG and AB is a transverse, so ∠ BAG = ∠ ABC = 28° {Alternate angles}
Now, ∠ CAG = 90° = ∠ CAD + ∠ BAG
⇒ ∠ CAD = 90° - 28° = 62°
From, Δ ADE, ∠ ADE + ∠ DEA + ∠ EAD = 180°
⇒ ∠ ADE = 180° - 62° - 3x = 118° - 3x.
Now, ADB being a straight line, so ∠ ADE + ∠ EDC + ∠ CDB = 180°
⇒ 118 - 3x + x + 4x = 180
⇒ 2x = 62
⇒ x = 31° (Answer)
30 points pls help image included
how to do this?? give me a solution its confusing me?!!
Answer:
t = 3h
Step-by-step explanation:
Given
h = [tex]\frac{1}{3}[/tex] t
Multiply both sides by 3 to clear the fraction
3h = t
BRAINLIEST!!!
18. Point p is chosen at random on EH. Find the probability that p is on FG.
Answer:
[tex]\frac{2}{5}[/tex]
Step-by-step explanation:
The total length of this line is 15 units. FG is 6 units long.
This means that the probability of p being on FG would be [tex]\frac{6}{15}[/tex] which can be simplified to [tex]\frac{2}{5}[/tex]
Answer:
2/5
Step-by-step explanation:
Line EH has three line segments:
EF which measure 4
FG which measures 6
GH which measures 5
The total measure of the line (EH) = 4 + 6 + 5 = 15
So if we are calculating the probability of landing on FG,
6 / 15
Reduce the fraction to make,
2 / 5
Determine the type and number of solutions of 4x2 − 3x + 1 = 0. A two imaginary solutions B two real solutions C one real solution
Option A
The equation [tex]4x^2 - 3x + 1 = 0[/tex] has two imaginary solutions
Solution:
Given that we have to determine the type and number of solutions of given quadratic equation
[tex]4x^2 - 3x + 1 = 0[/tex]
[tex]\text {For a quadratic equation } a x^{2}+b x+c=0, \text { where } a \neq 0\\\\x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]
In a quadratic equation, the discriminant helps tell you the number of real solutions to a quadratic equation
In the case of a quadratic equation [tex]ax^2 + bx + c = 0[/tex], the discriminant is [tex]b^2 -4ac[/tex]
[tex]\text{If } b^{2}-4 a c=0 ;$ then the given quadratic equation has one real root\\\\If b^{2}-4 a c>0,$ then the given quadratic equation has two real roots[/tex]
If [tex]b^2-4ac<0[/tex], then the given quadratic equation has two imaginal roots which are complex conjugates
Given quadratic equation is:
[tex]4x^2 - 3x + 1 = 0[/tex]
Here a = 4 and b = -3 and c = 1
The discriminant is given as:
[tex]b^2 - 4ac = (-3)^2 - 4(4)(1) = 9 - 16 = -7\\\\b^2 - 4ac = -7\\\\b^2-4ac < 0[/tex]
Therefore the given equation has two imaginary solutions
Answer:
two imaginary solutions
Step-by-step explanation:
How can the distributive property be used to write equivalent expressions
with an expression like 3x6 you can separate parts of the expression using parentheses like: 3(2+4)
you can find ways to separate a variable (like 6) into a sum of two addends
ex 1+5
0+6
3+3
so a distributive version of 3x6 is 3(2+4) = (3x2) + (3x4)
Christian reads 14 book every 23 week.
How many books does Christian read per week?
16
38
223
6 ///////What percent is equivalent to 45 ?
20%
40%
60%
80% /////// Blueberries are on sale for $2.80 per pint. The regular price is $3.50 per pint.
What is the percent of decrease?
Select from the drop-down menu to correctly complete the statement.
The percent of decrease is
Picture 1: The amount of tax for Veena's meal is $1.02
Picture 2: Christian reads [tex]\frac{3}{8}[/tex] books per week.
Picture 3: 80% is equal to [tex]\frac{4}{5}[/tex].
Step-by-step explanation:
Picture 1: Veena ate lunch at a deli. She ordered turkey sandwich for $9.25 and a salad for $4.35. The tax was 7.5%. What is the amount of tax for Veena's meal.
Given,
Price of turkey sandwich = $9.25
Price of salad = $4.35
Total amount = 9.25+4.35 = $13.60
Tax = 7.5%
Amount of tax = 7.5% of total cost
Amount of tax = [tex]\frac{7.5}{100}*13.60[/tex]
Amount of tax = [tex]\frac{102}{100} = \$1.02[/tex]
The amount of tax for Veena's meal is $1.02
Picture 2: Christian reads 1/4 book every 2/3 week. How many books does Christian read per week?
Given,
Books read every 2/3 weeks = 1/4 books
[tex]\frac{2}{3}\ weeks=\frac{1}{4}\ books\\[/tex]
For determining the number of books read per week, we will multiply both sides by [tex]\frac{3}{2}[/tex]
[tex]\frac{3}{2}*\frac{2}{3}\ week=\frac{1}{4}*\frac{3}{2}\ books\\\\1\ week = \frac{3}{8}\ books\\\\[/tex]
Christian reads [tex]\frac{3}{8}[/tex] books per week.
Picture 3: What percent is equivalent to [tex]\frac{4}{5}[/tex]?
We will multiply the given fraction with hundred for calculating the percentage.
[tex]\frac{4}{5}*100\\\\\frac{400}{5}\\\\80\%[/tex]
Therefore,
80% is equal to [tex]\frac{4}{5}[/tex].
Keywords: percentage, division
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A truck carries apples, grapes, and blackberries in the ratio of 4:3:4 if the apple weighs 160 pounds how much does the truckload of fruit weigh in total
Answer:
440 pounds
Step-by-step explanation:
Ratio is basically "parts".
We have ratio of 4:3:4, that is a total of 4 + 3 + 4 = 11 parts
The apple is 4 parts and total amount is 160 pounds. So each "part" is:
160/4 = 40 pounds
The total pounds of all 3 fruits is 11 parts * 40 pounds per part = 11 * 40 = 440 pounds
hence,
Truckload of fruits weigh at 440 pounds
Simplify this expression:
16 + 28 ÷ 2 – 6
______________
10 – 4 x 2
-2.4
-4.8
8
12
20
Answer:
12
Step-by-step explanation:
28/2=14
16+14=30
30-6=24
-----------------
4*2=8
10-8=2
---------------
24/2=12
Orlando worked $6/h one week and $7/h the next week. He worked 5 more hours the second week than the first and earned $347 for the 2 weeks of work. How many hours did he work each week?
Answer:
24 hours in first week and 29 hours in second week.
Step-by-step explanation:
Given: Orlando work at $6/h in first week and at $7/h in second week.
Total earning is $347 in both weeks.
Let the number of hours Orlando work in first week be`x` hours
∴ working hours in second week is (x+5) hours
Now, solving to find the number of working hours.
⇒ Total earning= earning in first week+earning in second week.
⇒ [tex]\$ 347= x\times 6+(x+5)\times 7[/tex]
Opening the parenthesis and solving it.
⇒ [tex]\$ 347= 6x+7x+35[/tex]
Subtracting both side by 35
⇒ [tex]312= 13x[/tex]
∴ x= [tex]\frac{312}{13} = 24\ h[/tex]
∴ Working hours in first week is 24 hours
Working hours in second week is [tex]24+5= 29\ h[/tex]
Can you please help me solve questions 1 and 2
Answer:
see explanation
Step-by-step explanation:
(1)
Given the perimeter then the third side is the perimeter subtract the sum of the 2 given sides, that is
third side
= 4x + 3y - (x - y + x + y)
= 4x + 3y - 2x ← collect like terms
= 2x + 3y
(2)
The area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
Here b = 2x + 6 and h = x - 2, thus
A = [tex]\frac{1}{2}[/tex](2x + 6)(x - 2) ← expand factors using FOIL
= [tex]\frac{1}{2}[/tex](2x² + 2x - 12) ← distribute
= x² + x - 6 ← in standard form
What is the value of f(x) = 9x when x = -2?
Answer:-18
Step-by-step explanation: if f(x)= -9x
And x =2
-9(2)
= -18
Answer:
f(-2)=-18
Step-by-step explanation:
given f(x)=9x...........(1)
put x=-2 in equation (1)
f(-2)=[tex]9\times(-2)[/tex]
f(-2)=-18 answer
For the open-ended question below, be sure to show your work and/or explain your reasoning.
Scott has $15.00, and he earns $6.00 an hour babysitting.
a) Write an equation for the amount of money (m) Scott has after a number of hours babysitting (h).
b) After how many hours of babysitting will Scott have $51.00?
(a) m=6h+15 can be used to find the total amount of money for h hours of babysitting.
(b) After 6 hours of babysitting, Scott will have $51.00
Step-by-step explanation:
Given,
Amount Scott has = $15.00
Per hour amount of babysitting = $6.00
a) Write an equation for the amount of money (m) Scott has after a number of hours babysitting (h).
Total amount of money = m
Number of hours babysitting = h
Total amount of money = Per hour earning from babysitting*Number of hours + Amount Scott has
[tex]m=6h+15[/tex]
m=6h+15 can be used to find the total amount of money for h hours of babysitting.
b) After how many hours of babysitting will Scott have $51.00?
Putting m = 51
[tex]51=6h+15\\51-15=6h\\36=6h\\6h=36[/tex]
Dividing both sides by 6
[tex]\frac{6h}{6}=\frac{36}{6}\\h=6[/tex]
After 6 hours of babysitting, Scott will have $51.00
Keywords: linear equation, division
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SOMEONE HELP‼️THE WORK IS FINISHED ONT THAT SIDE BUT HELP ON THE OTHER SIDE ‼️
Answer:
e) Shamika= 224 balloon, Crystal= 112 balloon, Aliya= 114 Balloon.
f) We know,Crystal sold "b" balloon
Aliya sold (b+2) balloon
Shamika sold 2b balloon.
As per data given in question part c that each balloon cost $2 and Total cost of balloon is $900.
Now, solving to find how much each student sold balloon at school´s winter dance.
As we know total cost is $900 and each balloon cost is $2.
∴ Total cost= [tex]Total\ quantity \times cost\ of\ each\ unit[/tex]
Total quantity= [tex]{b+(2+b)+2b}[/tex]
∴ [tex]\$ 900= {b+(2+b)+2b}\times \$ 2[/tex]
Once we solve, we will get the value of b as 112 balloon, which is the number of balloon sold by Crystal.
Substituting the value of b in the equation of Aliya and Shamika, we will get the number of balloon sold by them.
Which is 114 and 224 respectively.
Step-by-step explanation:
Given: Crystal sold "b" balloon
Aliya sold (b+2) balloon
Shamika sold 2b balloon.
As per data given in question part c that each balloon cost $2 and Total cost of balloon is $900.
Now, solving to find how much each student sold balloon at school´s winter dance.
As we know total cost is $900 and each balloon cost is $2.
∴ Total cost= [tex]Total\ quantity \times cost\ of\ each\ unit[/tex]
Total quantity= [tex]{b+(2+b)+2b}[/tex]
∴ [tex]\$ 900= {b+(2+b)+2b}\times \$ 2[/tex]
Opening the parenthesis.
⇒[tex]\$ 900= (b+2+b+2b)\times \$ 2[/tex]
⇒[tex]\$ 900= 2+4b \times 2[/tex]
Dividing both side by 2
⇒ [tex]\$ 450= 2+4b[/tex]
Subtracting both side by 2
⇒ [tex]\$ 448= 4b[/tex]
Cross multiplying
∴[tex]b= \frac{448}{4} = 112[/tex]
∴ b= 112.
Hence, we can say Crystal have sold 112 balloons.
Next subtituting the value of "b" in the equation for Aliya and Shamika to get number of balloon they have sold.
We know, Aliya sold b+2 balloons
∴ Aliya sold= [tex]112+2= 114\ balloon[/tex]
Aliya sold 114 balloon.
We know, Shamika sold 2b balloons
∴[tex]2\times 112= 224 balloon.[/tex]
Shamika sold 224 balloon.
What is the value of -9 r - 7 when r = 2?
Answer:
I thinks its r = 11
Step-by-step explanation:
So you just need to take the number to the r and multipliy it by r So,
9x2=18
then minus it by the other number which would Be 7 so.
18-7=11
Answer:
11
Step-by-step explanation:
(-9 times 2) - 7
18 - 7
11
What is the value of the expression |x + y| when x = –7 and y = 18? –25 25 –11 11
Answer:
11
Step-by-step explanation:
- 7 + 8 = 11 and the absolute value of 11 is 11
Italy’s time zone is GMT + 1, so if it is 1 PM GMT, it is what time in Italy?
Answer:
Italy Time is in the Central European Time Zone . Central European Standard Time ( CET ) is 1 hours ahead of Greenwich Mean Time ( GMT+1 ).
Step-by-step explanation:
Central European Time Zone
Italy's time zone is one hour ahead of GMT (Greenwich Mean Time), so if it is 1 PM GMT, it would be 2 PM in Italy. This reflects the Time Zone Difference concept.
Explanation:If Italy's time zone is GMT + 1, and it is currently 1 PM GMT, then the time in Italy would be 2 PM. This is due to the fact that Italy is one hour ahead of GMT (Greenwich Mean Time). Therefore, to convert from GMT to Italy's time zone, one simply needs to add one hour. For example, if it was 5 PM in GMT, it would be 6 PM in Italy, and so on. This concept is referred to as Time Zone Difference.
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Can anyone help me with math? Struggling !
Will Mark brainiest
Answer:
yes
what grade
Step-by-step explanation:
If Q is half way between 0 and -1 what is Q
Answer:
it's -1/2
Step-by-step explanation:
you need to go half way between 0 and -1 and that's -1/2
Answer:
-0.5 or -1/2
Step-by-step explanation:
You can solve using operations or with a number line.
To find the value halfway between two numbers, add the two numbers and divide the sum by 2.
Q = (0 + -1)/2
Q = (0 - 1)/2
Q = -1/2
Q = -0.5
Number line:
<- (-1) --------- (-0.5) ---------- 0 ----------- (0.5) --------- (1) ->
Find halfway between 0 and 1.
Q = -0.5
t rectangular prism has a length of 2 1/2 feet, a width of 3 feet, and a height of
1 1/2 feet. Unit cubes with side lengths of 1/2 foot are added to completely
fill the prism with no space remaining. What is the volume, in cubic feet, of the right rectangular
prism?
Show your work.
Answer:
Volume of the rectangular prism is [tex]11\frac{1}{4}[/tex] cubic feet.
The number of small cubes required is 90.
Step-by-step explanation:
The rectangular prism has a length of [tex]2\frac{1}{2}[/tex] feet, a width of 3 feet, and a height of [tex]1\frac{1}{2}[/tex] feet.
Now, the volume of the rectangular prism will be [tex](2\frac{1}{2} \times 3 \times 1\frac{1}{2}) = (\frac{5}{2} \times 3 \times \frac{3}{2}) = \frac{45}{4}[/tex] cubic feet i.e. [tex]11\frac{1}{4}[/tex] cubic feet. (Answer)
Now, the volume of the small unit cubes of side lengths of [tex]\frac{1}{2}[/tex] feet will be [tex](\frac{1}{2})^{3} = \frac{1}{8}[/tex] cubic feet.
So, the number of small cubes required to fill the large cube will be [tex](\frac{45}{4} \div \frac{1}{8}) = 90[/tex]. (Answer)
What is 7(x-3)=56 and how do you solve the problem step by step?
Answer:
x=11
Step-by-step explanation:
7(x)-7(3)=56
7x-21=56
7x-21+21=56+21
7x=77
7x/7=77/7
x=11
complete the equation of the lines whose slope is 5 and y-intercept is (0,4)
y = ?
Answer:
y = 5x + 4
Step-by-step explanation:
y - 4 = 5(x - 0)
That is point-slope form. I'm not sure if you want it in slope intercept form, but slope intercept form of the equation is -
y = 5x + 4
Answer:
Step-by-step explanation:
thx i needed this
Solve for the value of z: 14/5 = z/25
Answer: z = 70
Explanation: To solve this proportion for z, we can use cross products.
*Image provided.*
When we get the equation 5z = 350, we can get z by itself on the left side of the equation by dividing both sides of the equation by 5. On the left, the 5's cancel each other out and we have z. On the right, 350 divided by 5 simplifies to 70 so we have z = 70.
Answer:
z = 75
Step-by-step explanation:
Please can someone help I try it hard but I don’t understand it
He could have scored 7, 14, 21, 28, 35, or 42 points (all multiples of 7 less than 45).
answer: B
Eric and his wife are each starting a saving plan. Eric will initially set aside $50 and then add $30.65 every week to the savings. The amount A (in dollars) saved this way is given by the function A=50+30.65N, where N is the number of weeks he has been saving.
His wife will not set an initial amount aside but will add $55.85 to the savings every week. The amount B (in dollars) saved using this plan is given by the function B= 55.85N.
Let T be the total amount in dollars saved using both plans combined. Write and equation relation T to N. Simplify your answer as much as possible
Answer:
T=50+86.49N
Step-by-step explanation:
you just have to combine A and B.
Total (T)=A(50+30.65N)+B(55.85N) thank just open the prentices and add 30.65N and 55.85N=86.49N. so total is initial savings+ weekly savings by both.
Which is a factor of 144 − 49x2?
12 - 7x2
72 – 7x2
12 – 7x
72 + 7x
Answer:
(12-7x)
Step-by-step explanation:
144 − 49x²
by observation, we can see that 144 = 12² and 49 = 7²
hence we can rewrite the equation
144 − 49x²
= 12² - 7²x²
= 12² - (7x)²
recall that the expression x² - y² = (x+y)(x-y)
hence,
12² - (7x)²
= (12 + 7x)(12-7x)
(12-7x) appears in the expression above, hence 12 -7x is a factor
Answer:
Answer is C
Step-by-step explanation:
on the first day of their 2598-mile trip, the kalsbeeks drove 683 miles. How many more miles do they have to drive to complete their trip?
Answer:
1915 miles more to drive to complete their trip.
Step-by-step explanation:
Given:-
Total distance to travel (D) = 2598 miles.
Distance travelled (d) = 683 miles.
To calculate = remaining distance (r) to complete trip.
Remaining distance = Total distance minus Distance travelled
i.e. [tex]r=D-d[/tex]
[tex]r=2598-683[/tex]
[tex]r=1915\ miles[/tex]
Therefore kalsbeeks have to travel 1915 miles more to complete their trip.
Which of the following statements is needed in order to prove these triangles are congruent using SSS?
A
∠BCA≅∠EFD
B
AC¯¯¯¯¯≅ED¯¯¯¯¯
C
DE¯¯¯¯¯≅BC¯¯¯¯¯
D
AB¯¯¯¯¯≅DE¯¯¯¯¯
To prove congruence by SSS, two statements are needed about equal sides: AC―――― ≅ ED―――― and DE―――― ≅ BC――――. A third unlisted statement equating the other sides is also required.
Explanation:To prove two triangles are congruent using the Side-Side-Side (SSS) Postulate, we need to establish that all three corresponding sides of the triangles are equal in length. Statement B indicates that AC―――― ≅ ED――――, which provides one pair of corresponding sides. Statement C suggests that DE―――― ≅ BC――――, providing a second pair of corresponding sides. Lastly, if we had information that AB―――― = DF――――, not provided in the options but necessary to complete the SSS congruence, then we could establish the congruence of the two triangles. Therefore, the statements needed for SSS congruence proof are options B and C, along with an unlisted statement that equates the third pair of corresponding sides.
Amanda has a shipping box in the shape of a triangular prism. It is 9 inches tall with a triangular base that is 3 inches by 2 inches. What is the volume of this shipping box?
Answer:
The volume of the shipping box is [tex]V=27\ in^3[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
The volume of the triangular prism is equal to
[tex]V=BH[/tex]
where
B is the area of the triangular base
H is the height of the prism
In this problem we have
[tex]H=9\ in[/tex]
Find the area of the triangular base B
[tex]B=\frac{1}{2}bh[/tex]
we have
[tex]b=3\ in\\h=2\ in[/tex]
substitute
[tex]B=\frac{1}{2}(3)(2)=3\ in^2[/tex]
Find the volume of the triangular prism
[tex]V=BH[/tex]
we have
[tex]B=3\ in^2[/tex]
[tex]H=9\ in[/tex]
substitute
[tex]V=(3)(9)=27\ in^3[/tex]