Given:
Height of box = (x-2)
Volume of box = [tex](x^3-8)[/tex]
To find:
The expression for the base area.
Solution:
We know that,
Volume of a box(V) = Base area(B) × Height(h)
[tex]V=Bh[/tex]
[tex]\dfrac{V}{h}=B[/tex]
On substituting the given values, we get
[tex]B=\dfrac{x^3-8}{x-2}[/tex]
[tex]B=\dfrac{x^3-2^3}{x-2}[/tex]
[tex]B=\dfrac{(x-2)(x^2+2x+2^2)}{x-2}[/tex] [tex][\because a^3-b^3=(a-b)(a^2+ab+b^2)][/tex]
[tex]B=x^2+2x+4[/tex]
So, the base area is [tex]x^2+2x+4[/tex].
Therefore, the correct option is B.
help me please , the question is in the picture .
Answer: 4.2x10^5=420000
Step-by-step explanation: its a positive five so you go in the positive direction from the decimal but if it was a negative you could go the other way (hope this helps)
Daniel bought 8 pairs of socks and a tshirt. The t-shirt cost $15.
Write an equation for the Total Cost Let x = the price of socks. How much was each pair of
socks if the Total Cost was $31? Show all calculations/work.
write an equivalent expression by distributing the "_" sign outside the parenthesis
1.6n-(4p-3)
9514 1404 393
Answer:
1.6n -4p +3
Step-by-step explanation:
Distributing the minus sign changes the signs of all the terms inside parentheses.
-(4p-3) = -4p +3
When that is added to 1.6n, the entire expression is ...
1.6n -4p +3
the sum of 2 numbers is 35 and their difference is 15
Answer:
x = 25,
y = 10
Step-by-step explanation:
Call the larger number "x", and the smaller one "y".
Set up a system, based on the given infomration
x + y = 35
x - y = 15
Solve the system by elimination, in this case, one can just add the two systems to eliminate a variable.
x + y = 35
x - y = 15
x + y + x - y = 15 + 35
Simplify,
2x = 50
Inverse operations,
2x = 50
/2 /2
x = 25
Substitute back in to find y,
x + y = 35
x = 25
25 + y = 35
Inverse operations,
25 + y = 35
-25 -25
y = 10
Simplify the expression 7(3+2p+7).
Answer: 14p +70
Step-by-step explanation:
Answer:
84p
Step-by-step explanation:
3+2=5 +7=12x7+84
Given f(x) = 2x^3 + ax^2 - 7a^2x - 6a^3, determine whether or not x-a and x+a are factors of f(x). Hence, find, in terms of a, the roots of f(x) = 0.
thankyou so much
Answer:
Step-by-step explanation:
f(x) = 2x³ + ax² - 7a²x - 6a³
= 2x³ - 2a²x + ax² - a³ - 5a²x - 5a³
= 2x(x² - a²) + a(x² - a²) - 5a²(x+a)
= (2x+a)(x - a)(x + a) - 5a²(x + a)
= (x + a)[(2x + a)(x - a) - 5a²]
= (x + a)(2x² - ax - 6a²)
= (x + a)(2x + 3a)(x - 2a)
x-a is the factor of the equation and x + a is not a factor of the equation,
All the roots of the equation are x + a, 2x+3a, x-2a.
What is a cubic equation ?"In algebra, a cubic equation in one variable is an equation of the form
ax^3+bx^2+cx+d=0
in which a is nonzero.
The solutions of this equation are called roots of the cubic function defined by the left-hand side of the equation. If all of the coefficients a, b, c, and d of the cubic equation are real numbers, then it has at least one real root (this is true for all odd-degree polynomial functions). "
Given equation is [tex]f(x) = 2x^3 + ax^2 - 7a^2x - 6a^3[/tex]
Now,
[tex]f(x) = 2x^3 + ax^2 - 7a^2x - 6a^3\\\\= 2x^3 - 2a^2x + ax^2 - a^3 - 5a^2x - 5a^3\\\\= 2x(x^2 - a^2) + a(x^2 - a^2) - 5a^2(x+a)\\\\= (2x+a)(x - a)(x + a) - 5a^2(x + a)\\\\= (x + a)[(2x + a)(x - a) - 5a^2]\\\\= (x + a)(2x^2 - ax - 6a^2)\\\\= (x + a)(2x + 3a)(x - 2a)[/tex]
Hence, the roots of the equation are x + a, 2x +3a, x - 2a.
To know more about cubic equation here
https://brainly.com/question/13730904
#SPJ2
The perimeter of a rectangular parking lot is 312m .
If the length of the parking lot is 95 m, what is its width?
Answer:
61 meters
Step-by-step explanation:
The perimeter of a rectangle is 2l + 2w, l being the length and w being the width. Substitute the known value into the equation and solve:
312 = 2(95) + 2w
312 = 190 + 2w
122 = 2w
w = 61
Okay yes I know it's messy it was a long stressful day lol so just check the last two, are they written right? are they even right? Thanks so much love you guys!!!!!!
Answer:
Yes
Step-by-step explanation:
Yes it is
No 1 is correct
No 2 is correct
No 3 is correct
No 4 is correct
and what i mean by correct is you answered it correct
I hope this helps you :)
Answer:
yes
Step-by-step explanation:
yes it is
it is all correct
A pie recipe calls for u to use 3/8 cup of milk, 1/8 cup of oil, and 3/8 cup of water. How many liquid do you need to make the pie
Problem 3: Serena is the manager of the coffee shop. The amount of money she earns is represented by the equation m=21h, where h is the number of hours Serena works, and m is the amount of money she earns. How much more money does Serena make an hour than Gabe? Explain your thinking.
Answer:
Serena earns $7.50 per hour more than Gabe
Step-by-step explanation:
Given
Serena:
[tex]m = 21h[/tex]
Gabe
Earnings: $13.50 per hour ----- Missing Part of equation
Required
How much more does Serena earn per hour
For Serena
[tex]m = 21h[/tex] implies that She earns $21 per hour
So, to determine how much more She earns, we simply calculate the difference.
[tex]Difference = \$21 - \$13.50[/tex] (per hour)
[tex]Difference = \$7.50[/tex] (per hour)
The difference implies that Serena earns $7.50 per hour more than Gabe
common difference for 7,15,23,31,29
Answer: it’s 8 if that 29 is supposed to be a 39 otherwise i don’t know
Step-by-step explanation:
2x + y = -8
3x - 5y = -25
It’s substitution
Answer:
x = -5 , y = 2
Step-by-step explanation:
Solve the following system:
{y + 2 x = -8
-5 y + 3 x = -25
Hint: | Choose an equation and a variable to solve for.
In the first equation, look to solve for y:
{y + 2 x = -8
-5 y + 3 x = -25
Hint: | Solve for y.
Subtract 2 x from both sides:
{y = -2 x - 8
-5 y + 3 x = -25
Hint: | Perform a substitution.
Substitute y = -2 x - 8 into the second equation:
{y = -2 x - 8
3 x - 5 (-2 x - 8) = -25
Hint: | Expand the left hand side of the equation 3 x - 5 (-2 x - 8) = -25.
3 x - 5 (-2 x - 8) = (10 x + 40) + 3 x = 13 x + 40:
{y = -2 x - 8
13 x + 40 = -25
Hint: | Choose an equation and a variable to solve for.
In the second equation, look to solve for x:
{y = -2 x - 8
13 x + 40 = -25
Hint: | Isolate terms with x to the left hand side.
Subtract 40 from both sides:
{y = -2 x - 8
13 x = -65
Hint: | Solve for x.
Divide both sides by 13:
{y = -2 x - 8
x = -5
Hint: | Perform a back substitution.
Substitute x = -5 into the first equation:
{y = 2
x = -5
Hint: | Sort results.
Collect results in alphabetical order:
Answer: {x = -5 , y = 2
About how many $40 shirts could you buy with $290?
Answer:
7 shirts
Step-by-step explanation:
290/40 = 7.25
But since you can't have 7.25 shirts, it's just 7.
.In a factory all employees work a basic week of 38 hours. Any overtime worked during weekdays is paid for at time-and-a-half. Overtime worked on Saturday is paid for at double-time, whilst on Sunday it is paid for at triple time. If the basic rate is $8.96 per hour, find the gross wage of a man who worked 15 hours overtime from Monday to Friday, 3 hours overtime on Saturday and 2 hours overtime on Sunday
Answer:
1. reg pay: 8.96,week days: 1.5 overtime pay, sat: double pay, sun: triple pay
38 hrs regular pay : 38 * 8.96 = 340.48
15 hrs overtime during week : 15 * 1.5(8.96) = 15 * 13.44 = 201.60
3 hrs overtime on saturday: 3 * 2(8.96) = 3 * 17.92 = 53.76
2 hrs overtime on sunday: 2 * 3(8.96) = 2 * 26.88 = 53.76
Gross wage = (340.48 + 201.60 + 2(53.76) = 649.60 <====
Hope this helps!
URGENT Find the base angles of the figure below.
Answer:
25°
Step-by-step explanation:
Since AB = AC then the triangle is isosceles.
Thus the 2 base angles are congruent, that is
base angle = [tex]\frac{180-130}{2}[/tex] = [tex]\frac{50}{2}[/tex] = 25°
Answer:
D. 25° hope this helps
Step-by-step explanation:
The graph of a function f is shown. Use the graph to estimate the average rate of change from x=-2 to x=0
Answer:
2
Step-by-step explanation:
Given:
The interval, x = -2 to x = 0.
Required:
Average rate of change from x = -2 to x = 0.
SOLUTION:
From the graph,
If x = -2, f(-2) = 0.
If x = 0, f(0) = 4
Average rate of change = [tex] \frac{f(b) - f(a)}{b - a} [/tex]
Where,
[tex] a = -2, f(a) = 0 [/tex]
[tex] b = 0, f(b) = 4 [/tex]
Plug in the values into the formula:
[tex] = \frac{4 - 0}{0 -(-2)} [/tex]
[tex] = \frac{4}{2} = 2 [/tex]
Average rate of change from x = -2 to x = 0 is 2.
pls help me with this
Error: She did not fully simplify [tex]\sqrt{12x^{3}}[/tex]
Correct simplification:
[tex]5x\sqrt{48x^{5}}\\\\=5x\sqrt{16x^{4}}\sqrt{3x}\\\\=5x(4x^{2})\sqrt{3x}\\\\=20x^{3}\sqrt{3x}[/tex]
A student makes paper airplanes. She can make 3 airplanes from each sheet of paper.
She wants to have 105 paper airplanes ready for her birthday party. She has 9 paper
airplanes in her paper airplane hanger left over from last year. What is considered the
independent variable in this situation?
A. 3 airplanes from each sheet
B. 105 paper airplanes
O
C. 9 paper airplanes in the hanger
D. 32 sheets of paper
Answer:
3 airplanes from each sheet
Answer:
3 airplanes from each sheet Hope it helps :)
Step-by-step explanation:
find the rate 3\4 of a page in 1\3 of an hour
Answer:
2.5 pages an hour
Step-by-step explanation:
3 times 3 is 9 9 divided by 4 is 2.5
please complete the chart with the correct angle measures
Answer:
10. X= 11
11. X= 5
Step-by-step explanation:
5x-8+43=90
x= 11
--------------------
3x+3+72=90
x= 5
give brainliest pls
4.A 5 ft. by 20 ft room has a circular rug. If the rug has a dlameter of 10 ft., how much of the floor
is not covered by the rug?
Answer:
option 4
Step-by-step explanation:
At the time that a 55 foot tall tree casts a shadow that is 32 feet long, a nearby woman is 5.5 feet tall. Which measure is the closest to the length of the shadow she will cast?
Answer:
3.2ft long shadow
Step-by-step explanation:
In this problem we are given a ratio between the tree/shadow and woman/shadow therefore we are given 3 values and 1 unknown then we can use the Rule of Three to calculate the length of the shadow which we will refer to as x. The Rule of Three simply multiplies the diagonal values and divides by the third value in order to get the missing unknown like so...
55ft tall <======> 32ft long shadow
5.5ft tall <======> x ft long shadow
(5.5 * 32) / 55 = 3.2ft long shadow
Finally, we can see that the woman's shadow would be a 3.2ft long shadow
Aubrey bought 5 packs of stickers each with 30 stickers. Izzy bought 4 packs,
each with 40 stickers. How many stickers do they have total
They have 310 stickers in total
PLZ HELP QUICK Which property explains why these two expressions are equal - the commutative, the associative, or distributive property of addition?
1 + (2 + 3) = (1 + 2) + 3
Answer:
I think it's commutative. ;-;
Step-by-step explanation:
D is f(x)=3(x+2)^2-2 it wasn’t able to fit on the screen HELP ME THOUGH PLZ
Answer:
The answer is B (filler)
A biker cycles 9 miles in 2 3 of an hour.
a
Make a chart and fill it in to show how far he will bike if he maintains the same pace for 2 hours, 3 hours, 3.5 hours
Answer:
2 hours: 27 miles, 3 hours: 40.5 miles, 3.5 hours: 47.25 miles
Step-by-step explanation:
1.) If a hiker hikes 9 miles in 2/3 of an hour, he will hike 4.5 (Half of 2/3 is 1/3 and half of 9 is 4.5) miles in 1/3 of an hour and 13.5 miles per hour. (1/3 times 3 gives us a whole and 4.5 times 3 is 13.5)
2.) 2 hours: 13.5 * 2 = 27 miles
3.) 3 hours: 13.5 * 3 = 40.5 miles
4.) 3.5 hours: 13.5 * 3.5 = 47.25 miles
2 hours: 27 miles, 3 hours: 40.5 miles, 3.5 hours: 47.25 miles
Step-by-step explanation:
1.) If a hiker hikes 9 miles in 2/3 of an hour, he will hike 4.5 (Half of 2/3 is 1/3 and half of 9 is 4.5) miles in 1/3 of an hour and 13.5 miles per hour. (1/3 times 3 gives us a whole and 4.5 times 3 is 13.5)
2.) 2 hours: 13.5 * 2 = 27 miles
3.) 3 hours: 13.5 * 3 = 40.5 miles
4.) 3.5 hours: 13.5 * 3.5 = 47.25 miles
this is the guys above i just need points
Jaxon invested $58,000 in an account paying an interest rate of 2.7% compounded
quarterly. Assuming no deposits or withdrawals are made, how much money, to the
nearest dollar, would be in the account after 14 years?
Answer:
A≈84536
Step-by-step explanation:
After 14 year span, the money in the account would be $84,535.62.
Given that,
Jaxon invested $58,000 in an account paying an interest rate of 2.7% compounded quarterly.
Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.
Here,
principal(P) = 85000
rate(r) = 2.7% = 0.027
Time(a) = 14 years,
n = 4
Apply compound interest identity,
Amount = principal[1 + r/n]ⁿᵃ
Amount = 58000[ 1 + 0.027/4]⁴ˣ¹⁴
Amount = 84,535.62
Thus, After a 14-year span, the money in the account would be $84,535.62.
Learn more about compound interest here:
https://brainly.com/question/14295570
#SPJ2
PLS HELP ITS DUE IN AN HOUR!
WILL GIVE BRAINLIEST!
Answer:
Step-by-step explanation:
Unfortunately other people have promised to give Brainliest before and they never did. However, I'll answer the third question and tell you that it's 8 sides.
Ricky and Sam each bought a remote control car for $80. A few months later they both sold it. Ricky sold his car for 25% less than the original price and Sam sold his car for 30% less than the original price. How much more did Ricky get than Sam?
Answer:
Ricky get $4 than Sam.
Step-by-step explanation:
.25x80=20
80-20=60
.30×80=24
80-24=56
please help! algebra 1
