how do you simplify the square root of 27a?
The simplified form of the square root of 27a is [tex]3\sqrt{3a}[/tex]. In other words, the required answer is [tex]3\sqrt{3a}[/tex]
To simplify the square root of 27a, we can break it down into its prime factors.
Step 1: Prime factorize the number inside the square root:
27 = 3 * 3 * 3
a = a (since 'a' is already in its simplest form)
Step 2: Rewrite the square root using the prime factors:
[tex]\sqrt{27a} = \sqrt{(3 * 3 * 3 * a)}[/tex]
Step 3: Group the prime factors into pairs:
[tex]\sqrt{(3 * 3 * 3 * a)} = \sqrt{(3^2 * 3 * a)}[/tex]
Step 4: Simplify the square root:
[tex]\sqrt{(3^2 * 3 * a) }= 3 * \sqrt{(3 * a)}[/tex]
Therefore, the simplified form of the square root of 27a is [tex]3\sqrt{3a}[/tex]. In other words, the required answer is [tex]3\sqrt{3a}[/tex].
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Determine if the ordered pair is a solution to the equation. Y = -x - 2; (2,-4)
an ice cream factory makes 260 quarts of ice cream in 10 hours. How many quarts could be made in 36 hours? What was that rate per day?
Final answer:
The ice cream factory can make 936 quarts in 36 hours and the rate per day is 624 quarts.
Explanation:
To find out how many quarts of ice cream can be made in 36 hours, we can set up a proportion based on the rate of production. The rate of production is 260 quarts of ice cream in 10 hours. We can set up the proportion:
260 quarts / 10 hours = x quarts / 36 hours
Cross-multiplying, we get:
10x = 260 * 36
Simplifying, we find:
x = (260 * 36) / 10 = 936
Therefore, 936 quarts of ice cream can be made in 36 hours.
To find the rate per day, we need to calculate how many quarts can be made in 24 hours. We can set up the proportion:
260 quarts / 10 hours = y quarts / 24 hours
Cross-multiplying, we get:
10y = 260 * 24
Simplifying, we find:
y = (260 * 24) / 10 = 624
Therefore, the rate per day is 624 quarts of ice cream.
Simplify y 5 • y 3 ÷ y 2
you have $85 in your bank account. Each week you plan to deposit $8 from your allowance and $15 from your paycheck. The equation b=85+(15+8)w gives the amount b in your bank account after w weeks. How many weeks from now will you have $175 in your bank account??
Final answer:
To have $175 in your bank account, starting with $85 and depositing $23 weekly, solve the equation 175 = 85 + 23w. It takes approximately 3.913 weeks, so you will need to round up to 4 weeks to reach at least $175.
Explanation:
To find out how many weeks it will take to have $175 in your bank account, we can use the equation given: b = 85 + (15 + 8)w. We know the initial amount b is the goal of $175, and from the equation, we understand that every week you add $23 to your account ($8 from the allowance and $15 from the paycheck). Now, we set up the equation with the known values: 175 = 85 + 23w.
To solve for w, which represents the number of weeks, we follow these steps:
Subtract 85 from both sides, which gives us 175 - 85 = 23w or 90 = 23w.Divide both sides by 23 to find w, resulting in 90 / 23 = w which simplifies to approximately 3.913.Since we cannot have a fraction of a week, we'll round up to the next whole number, which means it takes 4 weeks to have at least $175 in your bank account.
Therefore, it will take 4 weeks to reach or surpass the goal of $175 in your bank account.
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What is the inter-quartile range of the given data set?
a.2
b.3
c.6
What's a fraction for 77/200
What is the product? (X-3)(2x^2-5x+1)
Answer:
C. 2x^3-11x^2+16x-3
Find the value of y for a given value of x, if y varies directly with x.
If y = -252 when x = 84, what is y when x = 74?
Please explain with steps, thank you!
From the question given above, we were told that y varies directly with x. This can be expressed mathematically as:
y ∝ x
Replacing the proportionality sign (∝), we have
y = Kx
K => constant of proportionality
Next, we shall determine the value of K. This can be obtained as follow:
y = –252
x = 84
K =?y = Kx
–252 = K * 84
Divide both side by 84
[tex]K = \frac{-252 }{84}[/tex]
K = –3Finally, we shall determine the value of y when x = 74. This can be obtained as follow:
x = 74
K = –3
y =?y = Kx
[tex]y = - 3 * 74[/tex]
y = –222Therefore, the value of y when x = 74 is –222
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What is the greatest perfect square that is a factor of 756?
would you produce an item if the cost of producing and distributing the item was more than 100% of its value? Explain.
It is not advisable to produce an item due to high production costs compared to its value.
This situation is known as allocative inefficiency, where the costs outweigh the benefits to society.
For instance, if the cost of producing gold eyeglass frames is more than what customers are willing to pay for them due to their high production costs, it would not make economic sense to produce them.
In such cases, producers would opt to reduce production or not produce the item at all to avoid incurring losses.
-38d-57 greater than or equal to -19d+76
Final answer:
To solve the inequality -38d-57 ≥ -19d+76, we isolate d, resulting in d ≤ -7, meaning d is any number less than or equal to -7.
Explanation:
The question asks us to solve an inequality: -38d - 57 ≥ -19d + 76. This requires us to isolate the variable d on one side of the inequality.
Add 19d to both sides: -38d + 19d - 57 ≥ 76.
Simplify: -19d - 57 ≥ 76.
Add 57 to both sides: -19d - 57 + 57 ≥ 76 + 57.
Simplify: -19d ≥ 133.
Divide both sides by -19, and remember to reverse the inequality sign when dividing by a negative number: d ≤ -7.
The solution to the inequality is d ≤ -7. This means that d can be any number less than or equal to -7.
Lisa and Mike are partners in a business. The income that the business earns is divided between Lisa and Mike in a 2:3 ratio respectively. Their business earned an income of $250,000 this year. How much will Lisa receive?
Answer : Lisa earns $100,000 and
Mike earns $150,000
Explanation :
Let the share of income Lisa earns be 2x
Let the share of income Mike earns be 3x
According to question,
[tex]2x+3x= \$ 250,000\\\\5x=\$250,000\\\\x=\frac{250000}{5}\\\\x=\$50,000[/tex]
So,
[tex]\text{Lisa's share} = 2\times 50000=\$100000\\\\\text{Mike's share }= 3\times 50000=\$150000[/tex]
Hence, Lisa earns $100,000adn
Mike earns $150,000
Final answer:
Lisa will receive $100,000 of the business income, which is her part of the 2:3 ratio they share from the $250,000 total income.
Explanation:
To calculate Lisa's share of the $250,000 income from the business she runs with Mike, which is divided between them in a 2:3 ratio, we need to find the total parts they share the income into and then assign the monetary values accordingly to each part.
The total parts of the ratio = 2 parts (for Lisa) + 3 parts (for Mike) = 5 parts.Each part is worth = Total income ÷ Total parts = $250,000 ÷ 5 = $50,000.Lisa's share = 2 parts × value of each part = 2 × $50,000 = $100,000.Thus, Lisa will receive $100,000 of the business income.
If 15 workers can paint 18 houses in 24 days how many days will 40 workers take to paint 22 house
If h(x)= (f o g)(x) and h(x)= 4 √x+7, find g(x) if f(x) = 4 √x+1
The equation of a line is x + 4y = 15.
What is the y-intercept of the line?
415
15
−15
154
Danny's truck has a fuel tank with a capacity of 20 gallons of gas. The truck averages 17 miles per gallon of gas. The function M(g) = 17g represents the number of miles that Danny's truck travels on g gallons of gas. What domain and range are reasonable for the function? D: 0 ≤ g ≤ 340 R: 0 ≤ M(g) ≤ 20 D: 0 ≤ g ≤ 20 R: 17 ≤ M(g) ≤ 340 D: 17 ≤ g ≤ 20 R: 20 ≤ M(g) ≤ 340 D: 0 ≤ g ≤ 20 R: 0 ≤ M(g) ≤ 340 NextReset
The domain and range of the function will be D: 0 ≤ g ≤ 20 R: 17 ≤ M(g) ≤ 340 option second is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
M(g) = 17g
g = amount of gas.
M(g) = number of miles that Danny's truck travels on g gallons of gas
Maximum fuel capacity = 20 gallons
So the domain D will be:
D: 0 ≤ g ≤ 20
If g = 0, M(g) = 0
If g = 20, M(g) = 340
So the range:
R: 17 ≤ M(g) ≤ 340
Thus, the domain and range of the function will be D: 0 ≤ g ≤ 20 R: 17 ≤ M(g) ≤ 340 option second is correct.
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Answer:
0 ≤ g ≤ 20 R: 17 ≤ M(g) ≤ 340 option
Step-by-step explanation:
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The domain and range of the function will be D: 0 ≤ g ≤ 20 R: 17 ≤ M(g) ≤ 340 option second is correct.
What is a function?
It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
M(g) = 17g
g = amount of gas.
M(g) = number of miles that Danny's truck travels on g gallons of gas
Maximum fuel capacity = 20 gallons
So the domain D will be:
D: 0 ≤ g ≤ 20
If g = 0, M(g) = 0
If g = 20, M(g) = 340
So the range:
R: 17 ≤ M(g) ≤ 340
Factor the polynomial given a common factor.
A scatterplot is produced to compare the number of hours that students study to their test scores. There are 25 data points, each representing a different student. The scatterplot shows a grouping of points rising from left to right. Which statement could be true?
a.)There is no relationship between the number of hours that students study and their test scores because the scatterplot does not have a cluster.
b.)As the number of hours of studying increases, test scores decrease because the scatterplot has a cluster that increases from left to right.
c.)As the number of hours of studying increases, test scores increase because the scatterplot has a cluster that increases from left to right.
d.)The number of hours that students study is equal to the test scores because the scatterplot does not show a cluster.
Answer:
c
Step-by-step explanation:
4. Your Turn: Find the measure of angle B. Enter only the number as your answer. *
What is the measure of angle S?
132 + 56 + 79 = 267
360 - 267 = 93
answer is 93 degrees
Major help with this!
What is the volume of a right circular cylinder with a radius of 5 cm and a height of 12 cm?
60π cm³
120π cm³
300π cm³
1200π cm³
The volume of a cylinder is 225π cm³ and its height is 9 cm.
What is the length of the cylinder's radius?
Enter your answer in the box.
What is the volume of a right circular cylinder with a base diameter of 6 m and a height of 5 m?
Enter your answer in the box. Express your answer using π .
What is the volume of a right circular cylinder with a base diameter of 17.5 ft and a height of 24.5 ft?
Enter your answer in the box. Use 3.14 for pi and round only your final answer to the nearest hundredth.
A right circular cylinder has a height of 20 1/2 ft and a diameter 115 times its height.
What is the volume of the cylinder?
Enter your answer in the box. Use 3.14 for pi and round only your final answer to the nearest hundredth.
Answer
300
Step-by-step explanation:
The volume of the first cylinder is 300π cm³. The height of the second cylinder is 5 cm. The volume of the third cylinder is [tex]45\pi \rm\; m^3[/tex]. The volume of the fourth cylinder is 5889.95 cubic feet. The volume of the fifth cylinder is 89438997.08 cubic feet.
We have a right circular cylinder with a radius of 5 cm and a height of 12 cm.
It is required to calculate the volume of the cylinder.
So, the volume of the cylinder will be,
[tex]V=\pi r^2h\\V=\pi\times 5^2\times 12\\V=300\pi \rm\; cm^3[/tex]
The volume of a cylinder is 225π cm³ and its height is 9 cm. It is required to calculate the radius of the cylinder.
So, the radius of the cylinder will be,
[tex]V=\pi r^2h\\225\pi=\pi\times r^2\times 9\\r^2=\dfrac{225}{9}\\r=\dfrac{15}{3}=5\rm\;cm[/tex]
We have a right circular cylinder with a diameter of 6 m and a height of 5 m.
It is required to calculate the volume of the cylinder.
So, the volume of the cylinder will be,
[tex]V=\pi r^2h\\V=\pi\times 3^2\times 5\\V=45\pi \rm\; m^3[/tex]
We have a right circular cylinder with a diameter of 17.5 ft and a height of 24.5 ft.
It is required to calculate the volume of the cylinder.
So, the volume of the cylinder will be,
[tex]V=\pi r^2h\\V=3.14\times (\dfrac{17.5}{2})^2\times 24.5\\V=5889.95 \rm\; ft^3[/tex]
A right circular cylinder has a height of [tex]20 \dfrac{1}{2}[/tex] ft and a diameter 115 times its height.
The diameter of the cylinder will be,
[tex]d=115\times 20\dfrac{1}{2}\\d=2357.5\\r=1178.75\rm\; ft[/tex]
It is required to calculate the volume of the cylinder.
So, the volume of the cylinder will be,
[tex]V=\pi r^2h\\V=3.14\times (1178.75)^2\times 20.5\\V=89438997.08 \rm\; ft^3[/tex]
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the first term of a arithmetic sequence is 2 and the 4th term is 11, how do I find the sum of the first 50 terms
∠A and ∠B are vertical angles with m∠A=x and m∠B=5x−80 .
What is m∠A ?
The measure of two vertical angles is same. So , the measure of angle A and angle B will be each equal to 20°.
What are the vertical angles ?
Vertical angles are the angles which are opposite to each other. A pair of vertically opposite angles are always equal to each other.
It is given that there are two vertical angles , which are ∠A and ∠B, The measure of the angles is given which is : m ∠A = x° and m ∠B = (5x - 80)°.
We know that the property of vertical angles states that two angles if they are vertical and opposite to each other then they have equal measures.
So , solving for the value of x :
x° = (5x - 80)°
Reordering the like terms :
5x - x = 80°
4x = 80°
or
x = 20°
or
The measure of angle A i.e., m ∠A is 20°.
And the measure of angle B will be :
= (5 × 20°) - 80°
= 20°
Therefore , the measure of two vertical angles is same. So , the measure of angle A and angle B will be each equal to 20°.
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What is the measure of an exterior angle of a regular 11-sided polygon? enter your answer as a decimal in the box. round to the nearest tenth of a degree?
A 90-inch board is cut into two pieces. one piece is two times the length of the other. find the lengths of the two pieces
Final answer:
To find the lengths of the two pieces, set up an equation using the given information. Solve for x and find the lengths of the two pieces.
Explanation:
To solve this problem, let's assume the length of one piece is x inches. Since the other piece is two times the length of the first piece, its length is 2x inches. According to the given information, the total length of the board is 90 inches. Therefore, setting up the equation x + 2x = 90, we can solve for x and find the lengths of the two pieces.
Combining like terms, we have 3x = 90. Dividing both sides of the equation by 3, we get x = 30. Therefore, the length of one piece is 30 inches, and the length of the other piece is 2(30) = 60 inches.
Angles L and M are supplementary. What is the sum of their measures? The sum of the measures of angles L and M is
Please help asap! Ignore the answer selected
Mr.Frost typed for 12 minutes at a constant rate of 50 words per minute. Mrs. Grey typed the same number of words at a constant rate of 60 words per minute.
How many minutes did it take Mrs. Grey to type the same amount as Mr. Frost?
Drag the steps in the correct order to solve the problem.
Strategize. Let x = Mrs. Grey's time.
Solve for x. x=10.
Identify. Mrs. Grey's time is the unknown.
Set up. 12(50)= x(60)
Check. 12(50) = 10(60)
Identify
strategize
set up
solve
check
1) Identify ------> Mrs. Grey's time is the unknown
2) Strategize
Let
x--------> Mrs. Grey's time in minutes
3) set up
we know that
[tex]12*50=x*60[/tex]
4) solve
[tex]12*50=x*60\\ x=(12*50)/60\\x=10\ minutes[/tex]
5) check
[tex]12*50=10*60\\600=600[/tex]
therefore
the answer is
-Identify
-strategize
-set up
-solve
-check
How do you work out a quadratic equation with a maximum value?