Answer:
[tex](x^2-4y)(x^4+4x^2y+16y^2)[/tex]
Step-by-step explanation:
Factoring
We need to recall the following polynomial identity:
[tex](a^3-b^3)(a-b)(a^2+ab+b^2)[/tex]
The given expression is:
[tex]x^6- 64y^3[/tex]
To factor the above expression, we need to find a and b, knowing a^3 and b^3. a is the cubic root of a^3, and b is the cubic root of b^3:
[tex]a=\sqrt[3]{x^6}=x^2[/tex]
[tex]b=\sqrt[3]{64y^3}=4y[/tex]
Now we apply the identity:
[tex]x^6– 64y^3=(x^2-4y)[(x^2)^2+(x^2)*(4y)+(4y)^2][/tex]
Operating:
[tex]x^6– 64y^3=(x^2-4y)[x^4+4x^2y+16y^2][/tex]
The remaining factors cannot be factored in anymore. Thus the completely factored form is:
[tex]\boxed{(x^2-4y)(x^4+4x^2y+16y^2)}[/tex]
1) The Boateng family has a sickening house whose layout is shown
above. They would like to renovate just bedrooms #2 and 3. Because you
are a contractor, you receive 20% off from Home Depot whenever you
make any purchases. If Home Depot sells your client's ideal wool carpet
for $8.99 per square foot, how much will it cost to carpet both
bedrooms? (Keep in mind that 10'8" would be written as a decimal
approximation of 10.67 ft. Think about why this is.)
a) How many total square feet of carpeting will you need?
Answer:
The cost will be $1662.136
The total square ft of carpeting will be 231.1122ft^2
Step-by-step explanation:
For the bedrooms, the dimension from the image is shown as(see attahced)
Bedroom #2= 10"8' x10"4'
Bedroom #3= 10"8' x11"4'
let us convert all dimension to feet and solve for the area of the bedrooms
Bedroom #2= 10"8' x10"4'
Bedroom #2=10.67x10.33feet
Area of Bedroom #2= 110.2211ft^2
Bedroom #3 = 10"8' x11"4'
Bedroom #3 =10.67x11.33feet
Area of Bedroom #3= 120.8911ft^2
The total area of both rooms is
Total area=110.2211+120.8911
Total area=231.1122ft^2
now the cost of one square floor s $8.99
hence the cost of 231.1122ft^2 will be
Cost of carpet = 231.1122*8.99
Cost of carpet = $2,077.67
Given that, because you are a contractor, you will receive 20% off
therefore it will cost
= (20/100)*2,077.67
=0.2*2,077.67
=$415.534
The cost will now be $2,077.67-$415.534
= $1662.136
Jordan has a garden that is enclosed by a rectangular fence. The perimeter of the garden is 84 feet. The length of one side of fencing is 8 yards. What is the area of Jordan's garden?
Answer: 432 ft^2
Step-by-step explanation:
See attached picture
Solve the inequality. c + 5 ≥ 10
Answer:
c≥5
Step-by-step explanation:
hope that helps :)
4x-5x+7-9y+2x+34
(Simply)
Answer:
Hi there!
Your answer is:
x-9y +41
Step-by-step explanation:
4x-5x+7-9y+2x+34
COMBINE LIKE TERMS!
First, X
4x-5x+2x
-1x+2x
x
x+7-9y+34
Next, whole numbers
7+34
41
x-9y +41
I don't know how to explain it
Answer:
Sam's thinking was incorrect.
On number first we have to move 10 units from 0 in positive direction after that negative sign means move in left direction.
But we have 2 negative signs so we need to move 6 units more on positive or right direct as shown below.
Step-by-step explanation:
Answer:
No, Sam was thinking was incorrect
Step-by-step explanation:
Sam's thinkin was incorrect when every time you add and negative to a negative it always become a positive number.
10 - (-6)
10 + 6 = 16
A plane ticket to New York costs 120 the tax is 9.5 what is the cost of the flight
Whats the value of x? 2−(3x−4)=2x−9
Answer:
x=3
Step-by-step explanation:
Use pemdas!
First use distributive property to get rid of the parenthesis, by multiplying 2 by 3x and -4. Then combine like terms and use inverse operations to simplify each side until you get it down to just x! Hope this helped! :)
Consider the function. find f(5)
Answer:
f(5) = -1
Step-by-step explanation:
f(5) is x = 5.
When x = 5, y = -1.
Therefore, f(5) = -1
What is 3/4 times 1/8=
Answer:
The answer should be 3/22.
Step-by-step explanation:
To multiply the fractions, multiply the numerators and denominators separately.
3 times 1 over 4 times 8,
Multiply straight across,
Answer should be 3/22
The 3/4 times 1/8 equals 3/32.
To calculate the product of fractions, you multiply the numerators together to get the numerator of the result, and multiply the denominators together to get the denominator of the result.
For 3/4 times 1/8:
Numerator: 3 × 1 = 3
Denominator: 4 × 8 = 32
To know more about equals here
https://brainly.com/question/33293967
#SPJ6
HELPP PLS I BEG PLSSSS I BEG AHHH
Answer:
1. correct (3+2) x 5 is 5 squared
2. 125 5 cubed is 125
3. 50 10 squared and divided by 2 is 50
Step-by-step explanation:
1. is correct
2. 5x5x5
=25x5
=125
3. 10x10=100
100/2
=50
Hope this helps :)
Answer:
(3+2)*5 ---------> 5 squared
5 cubed --------> 125
10 squared divided by 2 ---------> 50
Step-by-step explanation:
First of all, you don't need to beg. It's all right. You got this!
This question is asking us to simplify what is on the left and match it to the right.
(3+2)*5
5*5= 25
5 squared is 5*5 which is equal to 25
5 cubed is 5*5*5 which is equal to 125
10 squared divided by 2
10*10= 100
100/2= 50
Hope this helps!
Does anyone know the differences and similarities between theorems and conjectures?
I searched on google but I didn’t understand! So in easy words please.. I’m sorry I’m dumb (;´༎ຶٹ༎ຶ`)
The difference between a theorem and a conjecture :-
Theorem :- Something which is true and can be proved .
I am giving a very simple example here .
Angle sum theorem :- sum of all angles in a triangle will be equal to 180° .
This is a theorem because every interior angle of a triangle will add up to 180° . It cannot change .
So , something that is definitely true and can be proved is a theorem .
Conjecture :- Something that is supposed to be true , but still hasn't been proved to be true .
Example :-
1a = 10
2a = 20
3a = 30
With this you can guess that 4a must be equal to 40 , but it can't be proved without using algebra .
Therefore , something which is likely to be true is a conjecture ( in maths ) .
factorise the following by grouping pairs (1) a2_9a+3a_27
Answer:
13a_29
Step-by-step explanation:
group like terms
Bruce wants to make 50 ml of an alcohol solution with a 12% concentration. He has a 10% alcohol solution and a 15% alcohol solution.
Which equation can Bruce use to determine how much of the 10% alcohol solution he should use?
ingredients summed = final product
.10 * x ml + .15 (50ml - x) = .12 (50 ml) solve for x the amount of 10 %
.1x + 7.5 - .15x = 6 - .05x = -1.5
x = 30 ml of 10%
50-30 = 20 ml of 15%
the sum of three numbers is 78. the third number is 2 times the second. the first number is 6 less than the second. what are the numbers
Simplify to a single power of 4:
4^7/4^6
Step-by-step explanation:
[tex] \frac{ {4}^{7} }{ {4}^{6} } [/tex]
= 4
.......
The formula for the density of a bacteria population is \dfrac NA A N start fraction, N, divided by, A, end fraction where there's an average of NNN bacteria in an area size AAA. Guang and Orion are doing an experiment in school for which they need to measure the density of a bacteria population after a certain solution has been introduced. Guang reports a density of 450045004500 bacteria per square centimeter and Orion reports a density of 505050 bacteria per square millimeter. Which one reports a higher density? Choose 1 answer:
Answer:
Guang reports a higher density of 4.5 × 10⁷ bacteria/m²
Step-by-step explanation:
Since Guang reports a density of 4500 bacteria per square centimeter and Orion reports a density of 50 bacteria per square millimeter, we convert both densities into bacteria per square meter to compare their values.
So, for Guang 4500 bacteria/cm² = 4500 bacteria/cm² × 10⁴ cm²/1 m² = 4500 × 10⁴ bacteria/m² = 4.5 × 10⁷ bacteria/m²
For Orion 50 bacteria/cm² = 50 bacteria/cm² × 10⁴ cm²/1 m² = 50 × 10⁴ bacteria/m² = 5 × 10⁵ bacteria/m²
Since 4.5 × 10⁷ bacteria/m² > 5 × 10⁵ bacteria/m², Guang reports a higher density of 4.5 × 10⁷ bacteria/m²
Answer:
B.) orion reports a higher desity than guang
Step-by-step explanation:
We found that Guang's reported density is 45 bacteria/ millimeter^2, while orion's reported density is 50 bacteria/ millimeter^2.
9. you work a part time job and got your first paycheck from $210. your hourly wage is $8.25. Write and equation that models this situation
a. 8.75 = 210x
b. 210 = 8.75 + x
c. 210 = 8.75 - x
d. 210 = 8.75x
10. you work a part time job and got your first paycheck from $210. your hourly wage is $8.75. how many hours did you work?
a. 3.5
b. 8
c. 4
d. 1
Answer:
9.= D
10.= 3.5
Step-by-step explanation:
STAY UP LATE TONIGHT!!!
MARS WILL BE VISIBLE FROM EARTH!!!
IT WON'T BE LIKE THIS AGAIN, UNTIL 15 YEARS!!!
Answer:
You sure this true
Step-by-step explanation:
How you know
Answer:
OOOOOOOO THANK YOU!!!!!!
-(y + 2) + 8 = 3
I’m so confused on this, please send help
Don't be worried friend :)
-(y + 2) + 8 = 3
=> -(y + 2) = -5
=> y + 2 = 5
=> y = 3
Help me out thankkk you
This is my last question for the day please help
Answer:
B: billie's solution is incorrect since she didnt
subtract 36 from both sides
Step-by-step explanation:
on the second step, she added 36 on the right.
This is incorrect because when changing one
side on an equation you must change the side
in the same way.
Answer:
B. Billie's solution is right
What is the solution for x in the inequality 4−2x>8
Answer:
X<-2
Step-by-step explanation:
Answer:
x<-2
Step-by-step explanation:
1. Write equation
4-2x>8
2. Combine like terms
-2x>4
3. Divide(and switch ineqaulity sign because the coefficent is negative)
-2x<4
x<-2
A new amusement-park ride that lasts 1 minute can have up to 1200 riders per hour. How many riders can ride per minute?
Answer:
20 riders can ride per minute.
Step-by-step explanation:
The picture says to divide to find the number of riders. If we apply this here, we can see that 1200 ÷ 60 is 20.
The reasoning behind this is:
There are 60 minutes in an hour.
If the park ride lasts a minute, then the ride can have 60 rides per hour.
The question states that the ride can have up to 1200 riders per hour, so you need to divide 1200 by 60.
1200 ÷ 60 = 20.
Calculate Social Security taxes, Medicare taxes, and FIT for Jordon Barrett. He earns a monthly salary of $13,400. He is single and claims 1 deduction. Before this payroll, Barrett’s cumulative earnings were $128,120. (Social Security maximum is 6.2% on $128,400 and Medicare is 1.45%.) Calculate FIT by the percentage method.
Answer:
Step-by-step explanation:
From the given information:
Social security taxes can be calculated as:
$128,400 - $128,120
= $280
Also, we know that the current monthly salary = $13, 400
So, social security tax is withheld by $280
This implies that:
Social security taxes = 280 × 0.062
= $17.36
The medical care taxes will now be:
= $13,400 × 1.45%
= $194.30
Using the percentage method to calculate the federal income tax; we have:
Use the tax bracket from 2017, marginal tax rate = 28%
∴
federal income tax = $13400 × 0.028
federal income tax = $3752
Problem 4:
The hypotenuse of a right angled triangle is 20 cm. The difference between its other two sides is 4 cm. Find the length of the sides.
Answer:
12cm and 16cm
Step-by-step explanation:
The hypotenuse of the right angle triangle = 20cm
let the other two sides be x and y;
The difference;
x = y - 4
Problem:
Find x and y;
Solution:
According to the pythagoras theorem;
x² + y² = 20² ------ i
x² + y² = 400 ----- i
and x - y = 4 ---- ii
So; x = 4 + y
Now input the value into equation (i);
(y + 4)² + y² = 400
(y+4)(y+4) + y² = 400
y² + y² + 4y + 4y + 16 = 400
2y² + 8y + 16 = 400
2y² + 8y + 16 -400 = 0
2y² + 8y - 384 = 0;
y² + 4y - 192 = 0
Factorize the equation;
y² + 16y - 12y - 192 = 0
y(y + 16) - 12(y + 16) = 0
(y-12)(y + 16) = 0
y -12 = 0 or y+ 16 = 0
y = 12 or -16
It is not realistic for the length of a body to be a negative value, so y= 12;
since;
x - y = 4,
x = 4 + 12
x = 16
What is the volume of the prism below
Answer:
D
Step-by-step explanation:
Volume= 1/2 (b*h*l)
((5*3*10)/2 = 75 Units^3
HELP WITH GEOMETRY PLSSS
2.8 x 10^3=
What is the answer
Answer:
9.24
Step-by-step explanation:
Last Friday Mary had $28 over the weekend she received some money for washing the dog she now has $42 how much money does she receive
Answer:
14
Step-by-step explanation:
42-28
Solve the following compound inequality 4<_x+4<_12
Answer:
0 ≤ x ≤ 8
Step-by-step explanation:
Given
4 ≤ x + 4 ≤ 12 ( subtract 4 from each of the 3 intervals
0 ≤ x ≤ 8