Answers
Answer:
\(\sqrt{72a^8b^5} = 6a^4b^2 \sqrt{2b}\)
Step-by-step explanation:
Given
\(\sqrt{72a^8b^5\)
Required
Simplify
Express 72 as 36 * 2
\(\sqrt{72a^8b^5} = \sqrt{36 * 2*a^8b^5}\)
Express \(b^5\) as \(b^4*b\)
\(\sqrt{72a^8b^5} = \sqrt{36 * 2*a^8*b^4*b}\)
Reorder
\(\sqrt{72a^8b^5} = \sqrt{36 *a^8*b^4* 2*b}\)
Split:
\(\sqrt{72a^8b^5} = \sqrt{36} *\sqrt{a^8} *\sqrt{b^4} * \sqrt{2*b}\)
Simplify each term
\(\sqrt{72a^8b^5} = 6 * a^{\frac{8}{2}} * b^{\frac{4}{2}} * \sqrt{2*b}\)
\(\sqrt{72a^8b^5} = 6 * a^4 * b^2 * \sqrt{2*b}\)
\(\sqrt{72a^8b^5} = 6a^4b^2 * \sqrt{2*b}\)
\(\sqrt{72a^8b^5} = 6a^4b^2 \sqrt{2b}\)
Related Questions
I need help, what are the step by step math problem to -20/2+2x-10?
Answers
2x-20
Step-by-step explanation:
-20/2+2x-10
-10+2x-10
-20+2x
2x-20
Answer:
2x - 20
Step-by-step explanation:
\( - \frac{20}{2} + 2x - 10 \\ - 10 + 2x - 10 \\ - 20 + 2x \\ 2x - 20 \\ \)
a cone has the diameter of 3 inches. the cone holds 12 cubic inches of water. to the nearest inch, what is the height of the cone?
Answers
Answer:
The height is about 5 inches.
Step-by-step explanation:
The volume for a cone is \(\frac{1}{3}\) × π × r² × h
The radius of the cone is 1.5
12= \(\frac{1}{3}\) × π × 1.5² × h
12= \(\frac{1}{3}\) × π × 2.25 × h
12=0.75×π×h
Divide both sides by 0.75
16=π×h
Divide both sides by π
5≈h
The height is about 5 inches.
All the angles in the diagram are measured to the nearest degree. Work out the upper bound and lower bound of angle x 59 degree 108 degree 81 degree X degree ??????
Answers
Answer: lower bound, x = 110.5°
upper bound, x = 113.5°
Step-by-step explanation:
There is no diagram but I am going to assume it is a quadrilateral since it has 4 angles. The sum of the angles of a quadrilateral is 360°.
Upper Lower
59° 58.5° ≤ a < 59.5
108° 107.5° ≤ b < 108.5°
81° 80.5° ≤ c < 81.5°
Total: 246.6° ≤ x < 249.5°
Subtract the lower and upper bound totals from 360° :
360.0 360.0
- 246.5 - 249.5
x = 1 1 3.5 1 1 0.5
↓ ↓
upper lower
bound bound
Convert 0.0001 to a power of ten.
Answers
All the numbers written in scientific notation are between 1 and 10 multiplied with powers of 10.
On average, Nathaniel drinks
4/5 of a 10-ounce glass of water in
2 2/5
hours. How many glasses of water does he drink in one hour? Enter your answer as a whole number, proper fraction, or mixed number in simplest form.
Answers
Nathaniel drinks 3 glasses of water in one hour.
To find out how many glasses of water Nathaniel drinks in one hour, we need to calculate his drinking rate per hour.
In 2 2/5 hours, Nathaniel drinks 4/5 of a 10-ounce glass of water.
Let's convert the mixed number of hours to an improper fraction:
\(2\frac{2}{5} = \frac{(5 \times2 + 2)}{5}\)
\(=\frac{12}{5}\)
Now, we can set up a proportion to find his drinking rate per hour.
We know that \(\frac{12}{5}\) hours corresponds to \(\frac{4}{5}\) of a glass of water.
Let's assign "x" as the number of glasses he drinks in one hour.
The proportion is then
\(\frac{(\frac{12}{5} hours) }{(x glasses) } =\frac{(\frac{4}{5} glass)}{(1 hour)}\)
Cross-multiplying gives us
\((\frac{12}{5} )\times1=\frac{4}{5}\times(x)\)
Simplifying, we get
\(\frac{12}{5} =\frac{4}{5}\times x\)
Dividing both sides by \(\frac{4}{5}\), we find x:
\(x=\frac{(\frac{12}{5} )}{\frac{4}{5} }\)
\(x=\frac{12}{4}\)
\(x = 3.\)
Therefore, Nathaniel drinks 3 glasses of water in one hour.
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Can someone please help me figure out the answer to the question in the picture?
Answers
g=12-1/25(100)
g=12-4
g=8, d=100
d=200:
g =12-1/25(200)
g=12-8
g=4, d=200
d=300:
g =12-1/25(300)
g=12- 12
g=0, d=300
TRAVEL Marion is travelling 500 miles by car. She drives 250 miles at an average rate of x miles per hour the first day and the remaining 250 miles at an average rate of x−5
miles per hour. Select the expression that represents the amount of time Marion spent traveling the 500 miles. (Hint: Write out the units to determine how to solve the problem.)
Multiple choice question.
A)
x(x−5)/500x−1250
B)
62,500/x(x−5)
C)
500x−1250/x(x−5)
D)
500/2x−5
Answers
Answer:
C) (500x - 1250)/x(x - 5)----------------------------------
We know that the equation for the time is:
time = distance / speedFind the time at travel in the first day:
250/xFind the time at travel in the second day:
250/(x - 5)To find the total time add app the two expressions we got above:
250/x + 250/(x - 5) = 250[1/x + 1/(x - 5)] = 250(x - 5 + x)/x(x - 5) = 250(2x - 5)/x(x - 5) = (500x - 1250)/x(x - 5)There matching choice is C.
Here is the question that is hard for me
Answers
Answer:
It says that angle ABD all together equal 116 degrees so the angle CBD equals 48 degrees so to find out what x is just subtract angles ABD and CBD which is
116-48 = 68
C. 68
Best way to solve this type of equation Ax+by=c
Answers
The best way to solve an equation of the form Ax+by=c could be either substitution, completing the squares or graphical method depending on the type of equation given.
Quadratic equation
The equation in the form Ax+by=c is a quadratic problem which could be approached in different ways depending on the specific equation given and the information provided.
The methods of approach are substitution, completing the squares or graphical method which all have proven to be suitable ways to arrive at the solution.
Hence, either of the three methods are good ways to solve such equation.
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What is angle
Enter your answer in the box
Answers
Answer:
CAB is 37 degrees
Step-by-step explanation:
90 + 53 = 143
180 - 143 = 37
You lease a car at $23,495 for 3 years at $429.95 a month with a $500 down payment. The interest is 30% of the payments and $4,643.46 in interest is paid over 3 years. What is the remaining balance when the lease ends? How did you arrive at $12,160.26?
Answers
Answer:
Step-by-step explanation:
total interest paid is given as $4,643.46.
total payments = $429.95 x 36 months = $15,478.20
total lease payments = total payments - total interest
total lease payments = $15,478.20 - $4,643.46 = $10,834.74
Remaining balance = Total cost of the lease - Total lease payments
$23,495 - $10,834.74 = $12,660.26
Help please i dont know how to do it
Answers
Answer:
14 is D but I don't 15 question answer
Find the value of x.
Answers
Answer:
x=13
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
(2*x+14)-((3*x+1))=0
1.1 Solve : -x+13 = 0
Subtract 13 from both sides of the equation :
-x = -13
Multiply both sides of the equation by (-1) : x = 13
The sum of two numbers is 37 and the difference is 13. What are the numbers
Answers
Answer:
25 and 12
Step-by-step explanation:
1) x+y=37
x-y=13 or x=13+y
Put x=13+y into equation 1:
13+y+y=37
y+y=24
y=12
x=25
2. The diagram above shows a wooden structure in the form of a cone mounted on hemispherical base. The vertical height of the cone is 24cm and the base 7cm. Calculate correct to 3 significant figures the surface area of the structure. (Take π= 22/7)
Answers
The surface area of the wooden structure is approximately 1012 cm².
To calculate the surface area of the wooden structure, we need to find the surface area of the cone and the surface area of the hemispherical base, and then add them together.
Surface Area of the Cone:
The surface area of a cone is given by the formula:
A_{cone = \(\pi \times r_{cone} \times (r_{cone} + s_{cone})\), \(r_{cone\) is the radius of the base of the cone and \(s_{cone\) is the slant height of the cone.
The vertical height of the cone is 24 cm, and the base radius is 7 cm, we can calculate the slant height using the Pythagorean theorem:
\(s_{cone\) = \(\sqrt{(r_{cone}^2 + h_{cone}^2).\)
Using the given measurements:
\(s_{cone\) = √(7² + 24²) cm
\(s_{cone\) ≈ √(49 + 576) cm
\(s_{cone\) ≈ √625 cm
\(s_{cone\) ≈ 25 cm
Now, we can calculate the surface area of the cone:
\(A_{cone\) = π × 7 cm × (7 cm + 25 cm)
\(A_{cone\) = (22/7) × 7 cm × 32 cm
\(A_{cone\) = 704 cm²
Surface Area of the Hemispherical Base:
The surface area of a hemisphere is given by the formula:
\(A_{hemisphere\) = \(2 \times \pi \times r_{base}^2\), \(r_{base\) is the radius of the base of the hemisphere.
Given that the base radius is 7 cm, we can calculate the surface area of the hemispherical base:
\(A_{hemisphere\) = 2 × (22/7) × (7 cm)²
\(A_{hemisphere\) = (22/7) × 2 × 49 cm²
\(A_{hemisphere\) = 308 cm²
Total Surface Area:
To calculate the total surface area, we add the surface area of the cone and the surface area of the hemispherical base:
Total Surface Area = \(A_{cone} + A_{hemisphere}\)
Total Surface Area = 704 cm² + 308 cm²
Total Surface Area = 1012 cm²
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How many different sums of money can be made from 4coins of different denomination
Answers
Answer:
15 different sums----------------------
There are various combinations of coins.
1 coin:4 options2 coins:4C2 = 4!/(2!2!) = 6 options3 coins:4C3 = 4!/(3!1!) = 4 options4 coins: 1 optionIn total there are:
4 + 6 + 4 + 1 = 15 different sumsLisa will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $55 and costs an additional $0.13 per mile driven. The second plan has an initial fee of $48 and costs an additional $0.15 per mile driven.
For what amount of driving do the two plans cost the same?
What is the cost when the two planes cost the same?
Answers
Answer:
Step-by-step explanation:
To find the point at which the two plans cost the same, we can set their total costs equal to each other:
55 + 0.13x = 48 + 0.15x
Simplifying and solving for x, we get:
0.02x = 7
x = 350
Therefore, the plans will cost the same when Lisa drives 350 miles.
To find the cost at this point, we can substitute x=350 into either equation. Let's use the first plan:
Total cost = 55 + 0.13(350) = $97.50
Therefore, if Lisa drives 350 miles, the cost for either plan will be $97.50.
Supposed the length of a rectangle is three times the width and the area is 300 ft.² then what is the width of the rectangle in feet
Answers
Step-by-step explanation:
the area is
A = length × width.
length = 3 × width
=>
A = 3 × width × width = 3 × width²
300 = 3 × width²
100 = width²
width = 10 ft
Which of the expressions are equivalent to the one below check all that apply
Answers
Answer:
A , B and C
Step-by-step explanation:
evaluate the expressions following the order of operations as set out in PEMDAS
initial expression
note that • indicates multiplication
3 (2 + 6) + 4 × 5 ← evaluate parenthesis
= 3(8) + 20 = 24 + 20 = 44
A
5 × 4 + 3 × (6 + 2) ← evaluate parenthesis
= 5 × 4 + 3 × 8 ← perform multiplication
= 20 + 24 ← perform addition
= 44
B
(6 + 2) × 3 + 4 × 5 ← evaluate parenthesis
= 8 × 3 + 4 × 5 ← perform multiplication
= 24 + 20 ← perform addition
= 44
C
3 × 2 + 3 × 6 + 4 × 5 ← perform multiplications
= 6 + 18 + 20 ← perform addition
= 44
D
3 × 2 + (6 + 4) × 5 ← evaluate parenthesis
= 3 × 2 + 10 × 5 ← perform multiplication
= 6 + 50 ← perform addition
= 56
the expressions equivalent to the initial expression are A , B and C
Red beads come in packages of 10. Blue beads come in packages of 12. Lee wants to buy an equal number of red and blue beads. He thinks he has to buy 10 packages of blue beads and 12 packages of red beads to have the least equal number of each. Is lee correct?
(Needs answer asap)
Answers
What is the product of 8 times 4 minus the sum of 12 and 7?
Answers
Answer:
13
Step-by-step explanation:
8 × 4 = 32
12 + 7 = 19
32 - 19 =13
Diego is buying shrimp and rice to make dinner. Shrimp
costs $6.20 per pound and rice costs $1.25 per pound.
Diego spent $10.55 buying shrimp and rice.
The relationship between pounds of shrimp s, pounds
of rice r, and the total cost is represented by the
equation 6.20s + 1.25r= 10.55.
Write an equation that makes it easy to find the number
of pounds of rice if we know the number of pounds of
shrimp purchased.
Answers
Answer:
r= (10.55−6.20s)
--------------------------
1.25
Step-by-step explanation:
Using the principle of subject of formula, we make number of pounds of rice, r the subject of the given equation. Hence, the equation would be r = (10.55 - 6.20s)/1.25
Given the expression :
6.20s + 1.25r = 10.55
Isolate 1.25r
1.25r = 10.55 - 6.20s
Divide both sides by 1.25 to isolate r
r = (10.55 - 6.20s)/1.25
Therefore, the required expression would be
r = (10.55 - 6.20s)/1.25
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What is the answer?
2/5 + 3/4
Answers
Take LCM
5×4=20Now
2/5+3/48+15/2023/20Answer:
23/20
Step-by-step explanation:
2/5 + 3/4
LCM = 5 * 4 = 20
=》2/5 * 4/4 = 8/20
=》3/4 * 5/5 = 15/20
So,
2/5 + 3/4
= 8/20 + 15/20
= 23/20
_________
Hope it helps ⚜
Create an example of a difference of
polynomials and explain how to simplify
your expression.
Answers
(9x² + 8x) - (2x²+ 3x) = 7x² + 5x .
By simplifying we get x( 7x + 5) .
What is polynomial ?Polynomials are algebraic expressions with variables and coefficients. Variables are also known as indeterminates. For polynomial expressions, we can perform arithmetic operations such as addition, subtraction, multiplication, and positive integer exponents, but not division by variable.The variables and exponents of polynomials do not change when they are subtracted. Only their coefficients are subject to change. This ensures that the difference has variables and exponents that are already classified as polynomials. As a result, the difference is always a polynomial.Consider two polynomials,
(9x² + 8x) and (2x² + 3x)
The difference of polynomials is,
(9x² + 8x) - (2x²+ 3x)
9x² + 8x - 2x²+ 3x
= 7x² + 8x - 3x
= 7x² + 5x
Simplifying we get ,
taking x common,
= x( 7x + 5) .
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Name the four basic steps to take when solving a word problem.
Answers
Answer:
Step 1: Identify the important information.
Step 2: Make a plan.
Step 3: Solve the problem using your plan.
Step 4: Check your work using a different strategy.
Step-by-step explanation:
Step 1: Identify the important information.
Step 2: Make a plan.
Step 3: Solve the problem using your plan.
Step 4: Check your work using a different strategy.
What is the arithmetic mean (average) of all the positive two-digit multiples of 4?
Answers
Answer:
54
Step-by-step explanation:
You want the mean of the positive 2-digit multiples of 4.
MeanThe 2-digit multiples of 4 form an arithmetic sequence whose first term is 12, and whose last term is 96. The arithmetic mean of the numbers in the sequence will be the average of the first and last numbers:
(12 +96)/2 = 108/2 = 54
The average of the 2-digit multiples of 4 is 54.
Merrisa is booking a holiday costing £660.
She needs to pay a deposit of of the total cost of the booking
How much does she pay?
Answers
The amount of money she will have to pay for booking of the holidays would be = £220
How to calculate the amount ofr deposit?The total amount of money that will cost Merrisa for booking of holidays = £660
The fraction of the total cost that she needs to deposit = 1/3
Therefore, the actual amount that she needs to deposit = 1/3 of £660
= 1/3× 660
= £220
Therefore, in conclusion, Merrisa would have to pay a total of £220 for booking of the holidays. This total amount is ⅓ of total cost of booking.
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y and x have a proportional relationship, and y = 8 when x = -16.
What is the value of y when x = 4?
• y = -8
• y = -2
• y = 2
• y= 8
Answers
Explanation: if x=4 now it divide the -16 by -4 so you divide 8 by -4 which now equals -2
HELP PLEASE NEED IT THANKS
Answers
Answer:
<
Step-by-step explanation:
1) Substitute 5 into the question
\(\frac{4(5)}{4}\)\(2(5)-3\)2) Work out the sides
\(\frac{4(5)}{4} =5\)\(2(5)-3=7\)3) Put it into an inequality
5 < 7
Hope this helps, have a great day!
Tina's Treats charges a $4.35 fee for each delivery. Which table best represents the relationship between f, the amount made from the delivery fee, and d, the number of deliveries made in a day?
Answers
Answer:
Is there any answer choices? If not I would think its 5$
5$
4$
Step-by-step explanation: