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.
Writing explain how you know when a linear system in three variables has infinitely many solutions.
A linear system in three variables has infinitely many solutions when the equations are dependent on each other and represent the same line or plane. To determine if a system has infinitely many solutions, we can solve the system and check if any of the equations can be derived from the others or if they represent the same line or plane.
Explanation:When a linear system in three variables has infinitely many solutions, it means that the three equations are dependent on each other and represent the same line or plane. This happens when the coefficients of the variables in the equations are proportional to each other. To determine if a system has infinitely many solutions, we can solve the system and check if any of the equations can be derived from the others or if they represent the same line or plane.
Let's take the system of equations given in the question:
7y = 6x + 84y = 8y + 7 = 3xWe can start by solving equations (1) and (2) for y:
7y = 6x + 8 (equation 1)4y = 8 (equation 2)Simplifying equation (2), we get:
y = 2
Substituting y = 2 into equation (1), we have:
7(2) = 6x + 8
14 = 6x + 8
6x = 14 - 8
6x = 6
x = 1
Now, let's substitute the values of x and y into equation (3):
y + 7 = 3x
2 + 7 = 3(1)
9 = 3
This equation is not true. Therefore, the system of equations is inconsistent and does not have infinitely many solutions. The system does not represent the same line or plane.
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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
What is the measurement of JKM
will mark brainliest pls help asap
What is the inter-quartile range of the given data set?
a.2
b.3
c.6
Please help asap! Ignore the answer selected
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.
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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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.
Factoring pattern for x squared plus bx plus c
Final answer:
To factor a quadratic expression in the form of x² + bx + c, find two numbers whose sum is equal to b and whose product is equal to c.
Explanation:
To factor a quadratic expression in the form of x² + bx + c, we look for two numbers whose sum is equal to b and whose product is equal to c. Let's illustrate with an example:
For the expression x² + 5x + 6, we need to find two numbers whose sum is 5 and whose product is 6. In this case, the numbers are 2 and 3.
Therefore, we can factor the expression as (x + 2)(x + 3).
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
Which exponential function is represented by the table? f(x) = 2(2x) f(x) = 0.8(0.8x) f(x) = 2(0.8x) f(x) = 0.8(2x)
table
-2 0.2
-1 0.4
0 0.8
1 1.6
2 3.2
Given G (1,2) and K(8,12) Part A what does it mean to find the point ponline gk such that 3(GP)=2(PK)?
Answer:
To find point [tex]\( P \)[/tex] on line segment [tex]\( GK \)[/tex] such that [tex]\( 3(GP) = 2(PK) \)[/tex], we're seeking a point dividing [tex]\( GK \)[/tex] into segments at a \( 3:2 \) ratio.
Explanation:
To find the point [tex]\( P \)[/tex] on the line segment [tex]\( GK \)[/tex] such that [tex]\( 3(GP) = 2(PK) \)[/tex], we're essentially looking for a point [tex]\( P \)[/tex] that divides the line segment [tex]\( GK \)[/tex] into two segments, where the ratio of the length of the segment from [tex]\( G \) to \( P \)[/tex] to the length of the segment from [tex]\( P \) to \( K \) is \( 3:2 \).[/tex]
Here's how to approach it:
1. Calculate the distances [tex]\( GP \) and \( PK \)[/tex] using the distance formula (or Pythagorean theorem if it's a 2D coordinate plane).
2. Let [tex]\( x \)[/tex] be the distance from [tex]\( G \) to \( P \)[/tex] and [tex]\( y \)[/tex] be the distance from [tex]\( P \)[/tex] to [tex]\( K \).[/tex]
3. Set up the equation [tex]\( 3x = 2y \),[/tex] representing the ratio of the lengths.
4. Solve for [tex]\( x \) and \( y \)[/tex] to find the coordinates of point [tex]\( P \).[/tex]
This process ensures that the point [tex]\( P \)[/tex] divides the line segment [tex]\( GK \)[/tex] into two segments according to the given ratio.
What's a fraction for 77/200
Determine if the ordered pair is a solution to the equation. Y = -x - 2; (2,-4)
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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Simplify y 5 • y 3 ÷ y 2
∠C and ∠D are vertical angles with m∠C=−2x+90 and m∠D=x−30 . What is m∠D ?
The measure of m∠D is 10 degrees
In line geometry, vertical angles are always equal.
Given the following vertical angles
m∠C=−2x+90 and m∠D=x−30
Since m∠C= m∠, hence;
-2x + 90 = x - 30
-2x - x = -30 - 90
-3x = -120
x = 40
Get the measure of m∠D
m∠D = x - 30
m∠D = 40 - 30
m∠D = 10degree
Hence the measure of m∠D is 10 degrees
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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
What’s 2ax2b simplified?
What is the measure of angle S?
132 + 56 + 79 = 267
360 - 267 = 93
answer is 93 degrees
∠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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-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.
While solving an equation, Lenny wrote the following steps on the board.
(2x + 1) + 5 = 9
2x + (1+5) = 9
What property of real numbers guarantees that the second equation is equivalent to the first?
A. Associative property of addition
B. Additive inverse property
C. Commutative property of addition
D. Distributive property
Lenny used the Associative property of addition to show that rearranging the grouping of numbers being added does not change the outcome of the equation.
While solving an equation, Lenny used the Associative property of addition which guarantees that the second equation (2x + (1+5) = 9) is equivalent to the first ((2x + 1) + 5 = 9). This property states that the grouping of numbers being added does not change the sum, as shown:
(A + B) + C = A + (B + C).
In the context of the provided equations, Lenny grouped the 1 and 5 together without changing the sum, illustrating that it doesn't matter how the numbers are grouped in addition.
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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Determine whether the inequality is always, sometimes, or never true. 4x - 8 > 1 + 4(x+3)
Answer:
Never true
Step-by-step explanation:
Given inequality,
[tex]4x - 8 > 1 + 4(x+3)[/tex]
[tex]4x-8 > 1 + 4x + 12[/tex]
[tex]4x-8 > 4x + 13[/tex]
[tex]-8 > 13[/tex] ( false )
Since, when after solving an equation or inequality we get a true statement then the equation or inequality has infinitely many solution or true for all numbers while if we get a false statement then the equation of inequality has no solution or not true.
Hence, the given inequality is never true.
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:
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
What is the greatest perfect square that is a factor of 756?