Answer:
[tex]x^2[/tex]
Step-by-step explanation:
Hello!
The HCF or the highest common factor (sometimes also known as the greatest common factor, GCF), is the greatest factor between terms.
First, let's expand both terms:
[tex]x^3y^2 = x*x*x*y*y[/tex][tex]x^2 = x*x[/tex]If we keep them on top of another, we can see that the overlapping variables are [tex]x*x[/tex], meaning that the greatest common factor between them is [tex]x^2[/tex].
if 75 percent is 66 pounds what is the full cost
Zarko and Manchu are two ctas that like to catch fish in the pond in their backyard. Zarko can catch 5 fish evry hour, while manchu can catch 2 fish every half an hour. How long did it take them to catch 27 fish in all,
It takes 3 hours for the cats to catch 27 fish in the pond.
How long did it take them to catch 27 fish in all?Zarko can catch 5 fish per hour.
Manchu can catch 2 fish every 0.5 of an hour, so in an hour, the cat would catch 2 times that, which is 4 fish.
When working together, the cats can catch 4 + 5 = 9 fish per hour
If the cats work for x hours, then they catch 9*x fish.
To get the time that takes them to catch 27 fish we just need to solve the linear equation:
9x = 27
Solving for x:
x = 27/9 = 3
It takes 3 hours for the cats to catch 27 fish in the pond.
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Whats the correct answer answer asap for brainlist
Find the missing angle in the diagram.
Help asap (Ty!)
Jared has one pizza that has 12 slices. He wants to share his pizza with his two brothers. How many slices will each boy have if they each have an equal amount?
Answer:
4 slices for all the brothers
Step-by-step explanation:
please solve for both parts
(a) The differential equation
[tex]y' + \dfrac14 y = 3 + 2 \cos(2x)[/tex]
is linear, so we can use the integrating factor method. We have I.F.
[tex]\mu = \displaystyle \exp\left(\int \frac{dx}4\right) = e^{x/4}[/tex]
so that multiplying both sides by [tex]\mu[/tex] gives
[tex]e^{x/4} y' + \dfrac14 e^{x/4} y = 3e^{x/4} + 2 e^{x/4} \cos(2x)[/tex]
[tex]\left(e^{x/4} y\right)' = 3e^{x/4} + 2 e^{x/4} \cos(2x)[/tex]
Integrate both sides. (Integrate by parts twice on the right side; I'll omit the details.)
[tex]e^{x/4} y = 12 e^{x/4} + \dfrac8{65} e^{x/4} (8\sin(2x) + \cos(2x)) + C[/tex]
Solve for [tex]y[/tex].
[tex]y = 12 + \dfrac8{65} (\sin(2x) + \cos(2x)) + Ce^{-x/4}[/tex]
Given that [tex]y(0)=0[/tex], we find
[tex]0 = 12 + \dfrac8{65} (\sin(0) + \cos(0)) + Ce^0 \implies C = -\dfrac{788}{65}[/tex]
and the particular solution to the initial value problem is
[tex]\boxed{y = 12 + \dfrac8{65} (\sin(2x) + \cos(2x)) - \dfrac{788}{65} e^{-x/4}}[/tex]
As [tex]x[/tex] gets large, the exponential term will converge to 0. We have
[tex]\sin(2x) + \cos(2x) = \sqrt2 \sin\left(2x + \dfrac\pi4\right)[/tex]
which means the trigonometric terms will oscillate between [tex]\pm\sqrt2[/tex]. So overall, the solution will oscillate between [tex]12\pm\sqrt2[/tex] for large [tex]x[/tex].
(b) We want the smallest [tex]x[/tex] such that [tex]y=12[/tex], i.e.
[tex]0 = \dfrac8{65} (\sin(2x) + \cos(2x)) - \dfrac{788}{65} e^{-x/4}[/tex]
[tex]\dfrac{788}{65} e^{-x/4} = \dfrac{8\sqrt2}{65} \sin\left(2x + \dfrac\pi4\right)[/tex]
[tex]\dfrac{197}{\sqrt2} e^{-x/4} = \sin\left(2x + \dfrac\pi4\right)[/tex]
Using a calculator, the smallest solution seems to be around [tex]\boxed{x\approx21.909}[/tex]
The length of one side of a triangle is 2 feet less than three times the length of its second side. The length of the third side is 3/4 of the sum of the lengths of the first two sides. Find the lengths of all three sides if the perimeter of the triangle is 17.5 feet.
Answer:
7 feet, 3 feet, 7.5 feetStep-by-step explanation:
Let the sides be a, b and c.
GivenThe length of one side of a triangle is 2 feet less than three times the length of its second side
a = 3b - 2The length of the third side is 3/4 of the sum of the lengths of the first two sides:
c = (3/4)(a + b)The perimeter of the triangle is 17.5 feet:
a + b + c = 17.5SolutionSubstitute a with b in the second equation:
c = (3/4)(3b - 2 + b) = (3/4)(4b - 2) = (3/4)(4b) - (3/4)(2) = 3b - 1.5Now substitute a and c with b in the third equation and solve for b:
a + b + c = 17.53b - 2 + b + 3b - 1.5 = 17.57b - 3.5 = 17.57b = 17.5 + 3.57b = 21b = 3Find the value of a:
a = 3b - 2 = 3*3 - 2 = 9 - 2 = 7Find the value of c:
c = 3b - 1.5 = 3*3 - 1.5 = 9 - 1.5 = 7.5The sides of the triangle are:
a = 7 feet, b = 3 feet, c = 7.5 feetIf Mia works for 9 hours daily for 5 days in a week at a pay rate of $20.50per hour. Based on 8 hours a day rule what will be her gross income for that week?
Answer:
just multiply 20.50 by 8 and how many days she work in a week
Select the correct answer. Absolute value functions coordinate plane parabola graphs. Parabola passes through points at (minus 2, 0), (minus 1.5, minus 2.5), (0, 5), (1, 0), (1.5, 2.5) and (2, 0) Which of the given functions could this graph represent? A. B. C. D.
The equation of parabola passing through coordinates A (-2,0), B (-1.5,-2.5), C (0,5), D (1, 0), E (1.5, 2.5), and F (2, 0) is y = -2.5(2x+4)², and the graph is attached.
What is a function?Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.
Given:
The coordinates of the point of parabola A (-2,0), B (-1.5,-2.5), C (0,5), D (1, 0), E (1.5, 2.5), and F (2, 0).
Calculate the equation of parabola by the formula given below,
[tex]y=a(x-h)^2+k[/tex]
Here (h, k) are the coordinates,
Put A (-2,0)
y = a[x- (-2)] ² + 0
y = a(2x + 4)²
Put B (-1.5,-2.5)
y = a[x- (-1.5)]² + (-2.5)
y = a(x + 1.5)² - 2.5
y = 2ax + 3a -2.5
Solve the above equation
a = -2.5
Thus, the equation of the parabola is,
y = -2.5(2x+4)²
Therefore, the equation of parabola passing through coordinates A (-2,0), B (-1.5,-2.5), C (0,5), D (1, 0), E (1.5, 2.5), and F (2, 0) is y = -2.5(2x+4)², and the graph is attached.
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Craig ran 4 days last week. His distances were
3.25, 6.5, 7.25, and 10.5 kilometers. What was
his average distance per day for the 4 days?
Which of the relations given by the following sets of ordered pairs is a function? {(−5,−4),(−4,−3),(−3,−2),(−4,−5),(−2,−1)} {(0,3),(−6,8),(−3,5),(0,−3),(7,11)} {(2,4),(2,6),(2,8),(2,10),(2,12)} {(8,1),(−4,1),(3,5),(0,4),(−1,2)}
The relations from the following sets of ordered pairs which is a function is; {(8,1),(−4,1),(3,5),(0,4),(−1,2)}
Which of the relations given by the following sets of ordered pairs is a function?It follows from the definition of a function that a function from an array of X-values to a set Y-values assigns only one Y-value to each X-value.
Hence, it follows from the definition above that the relation; {(8,1),(−4,1),(3,5),(0,4),(−1,2)} is that which is a function.
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find the domain and range of the exponential function h(x) = 125x. explain your findings. as x decreases, does h increase or decrease? explain. as x increases, does h increase or decrease? explain.
We have an exponential growth. The domain is the set of all real numbers and the range is R: (0, ∞).
What can we say about the exponential function?Here we have the exponential function:
[tex]h(x) = 125^x[/tex]
Notice that the base, 125, is larger than 1, which means that we have an exponential growth.
So, as x increases, also does h(x).As x decreases, also does h(x).Now, the domain of any exponential equation is the set of all real numbers.
For the range, as x tends to negative infinity, the function will tend to zero.
And as x tends to infinity, h(x) also tends to infinity.
So the range is R: (0, ∞).
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Problem
(a) Expand and simplify [tex](x^2+2)^2[/tex]
(b) Hence fully factorise [tex]x^4+4x+3[/tex]
Please do not give me irrelevant answers.
Answer:
a)
[tex](x^{2} + 2)(x^{2} + 2)\\x^{4} + 2x^{2} + 2x^{2} + 4\\= x^{4} + 4x^{2} + 4\\[/tex]
b)
[tex](x +1)(x + 1)(x^{2} -2x +3) = (x + 1)^{2} (x^{2} -2x +3)[/tex]
Several students made comments about this image.
D
Which comment is true?
56:
"If I know the measures of A and B, I can subtract those measures from 180 to find the measures of the othe
two angles."
"If I know the measure of C, I can find the measure of angle A because they are the same."
"If I know the measures of angles C and B, I can find the measures of A and D."
"If I know the measure of angle A, I can find the measure of angle D by subtracting from 180."
Answer:
"If I know the measures of A and B, I can subtract those measures from 180 to find the measures of the other
two angles."
Step-by-step explanation:
i did it
Early in 2022, Pina Company switched to a just-in-time inventory system. Its sales revenue, cost of goods sold, and inventory amounts for 2021 and 2022 are shown below.
The Inventory Turnover for 2021 is 5.9 times and for 2022 is 10 times.
Inventory turnover2021
Inventory Turnover = Cost of Goods sold / Average Inventory
Cost of Goods sold = $1,165,250/[($170,000+$225,000)/2]
Cost of Goods sold = $1,165,250/($395,000/2)
Cost of Goods sold = $1,165,250/197,500
Cost of Goods sold = 5.9 times
2022
Inventory Turnover = Cost of Goods sold / Average Inventory
Cost of Goods sold = $1,525,000/[($225,000+$80,000)/2]
Cost of Goods sold = $1,525,000/($305,000/2)
Cost of Goods sold = $1,525,000/152,500
Cost of Goods sold = 10 times
Therefore the Inventory Turnover for 2021 is 5.9 times and for 2022 is 10 times.
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The complete question is:
Pina Colada Corp. switched to a just-in-time inventory system. Its sales and Inventory amounts for 2021 and 2022 are shown below.
2021 2022
Sales revenue $3,360,000 $3,900,000
Cost of goods sold 1,165,250 1,525,000
Beginning inventory 170,000 225,000
Ending inventory 225,000 80,000
Determine the inventory turnover for 2021 and 2022.
A spring supporting a mass of 30 kg compresses 0.6 m. how far does the spring compress when it supports a mass of 10 kg? 0.1 m 0.2 m 1.2 m 1.8 m
The spring .2m far when it is compressed on being supported by a mass of 10kg.
Given: Mass of 30 kg which compresses spring by 0.6m
To find: The compression of the spring when it is supported by a mass of 10 kg
Concept: Compression springs are coiled springs that hold mechanical energy in a compressed state. When these springs are subjected to compressive loads, they compress and shorten, capturing and storing significant potential force.
The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
By using unitary method,
10 is 3 times less than 30.
so, 30/3=10
Also applying the same proportion over the lengths compressed,
we get, 0.6/3=.2
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Maria just got a raise at work. She was making $9 per hour, but now she makes 150% of that amount.
Explain how you would find the amount of money Maria now makes per hour.
It takes 96 pounds of seed to plant a 10 acre field how many acres can be planted per pound of seed
Answer:
9.6 lbs per acre
Step-by-step explanation:
96lbs for 10acres
96 divided by 10= 9.6 lbs per acre.
I ate 8/15 of the total amount of soup, then 140 ml of it remained in the bowl. how many milliliters of soup were there in the bowl originally?
What is the domain of the function on the graph
Answer:
Domain [-3 , ∞ ]Step-by-step explanation:
Domain is the set of all inputs for which the given function is defined.
graphically it represents the shadow of the graph taken on the x axis from above and below the x axis
Here is the shadow will be formed from -3 till +∞, hence we have our domain as [-3 , ∞ ]
Hi, need help please to get my HS diploma...did not graduate :(
Which of the following equations is written in standard form?
Answer:
The first answer
4x-2y=0
Select the correct answer.
Which equation represents the line that is perpendicular to y = 1/4 and passes through (-6,-9)?
A. x = -9
B. X=-6
C. y=-9
D. y=-4
Answer:
B. x = -6
Step-by-step explanation:
Use a graphing calculator such as desmos and enter each equation, you'll find the only one that falls on (-6, -9) and is perpendicular is B.
Answer:
B. x = -6
Step-by-step explanation:
A family has two cars. The first car has a fuel efficiency of 20 miles per gallon of gas and the second has a fuel efficiency of 30 miles per gallon of gas. During one particular week, the two cars went a combined total of 1300 miles, for a total gas consumption of 50 gallons. How many gallons were consumed by each of the two cars that week?
20 gallons of gas was consumed by the car that has efficiency of 20 miles per gallon and 30 gallons of gas was consumed by the car that has efficiency of 30 miles per gallon .
How to find the consumption of gallons using equation?The first car has a fuel efficiency of 20 miles per gallon of gas and the second has a fuel efficiency of 30 miles per gallon of gas.
Therefore,
let
x = number of gallons for car that consume 20 miles per gallon of gas
y = number of gallons for car that consume 30 miles per gallon of gas
Hence,
x + y = 50
20x + 30y = 1300
20x + 20y = 1000
20x + 30y = 1300
10y = 300
y = 300 / 10
y = 30
Therefore,
x = 50 - 30
x = 20
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(-2, 1), (-1, 4), (0, 4), (1, 6), (2, 7)
find domain and range
Answer:
(-2,-1,0,1,2)
(1,4,6,7)
Using the following information about the family’s assets and liabilities, calculate the debt ratio:
Based on the various assets and liabilities that the family has, the debt ratio can be calculated to be D. 54.1%.
How is the debt ratio calculated?the debt ratio can be found as:
= Total debt / Total assets
Solving:
= (5,500 + 210,000 + 180,000+ 25,000) / (3,000 + 13,000 + 320,000 + 25,000 + 15,000 + 64,000 + 39,000)
= 258,500 / 479,000
= 54.1%
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sally has a pet snail that fell into a well.The well is 16 feet deep. Each day the snail climbs up 5 feet, but each night slides down 4 feet. How many days will it take Sallys snail to get to the top of the well
Answer:
16 days
Step-by-step explanation:
OK, The pet snail only moves a foot per day because at night it falls again, SO ima going with 16 days.
[<Answer>] (2):
Hello! I'm Avery. And I'm here to help! :)
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[<The Explanation>}:
Sally has pet snail that fell into a well.
(Depth of the well = 16 feet)
Snail climbs up 5 feet but each night it slides back down 4 feet.
So the snail climbs up per day = 5 feet - 4 feet = 1 feet.
Number of days snail took to reach at 11 feet = 11 × 1 = 11 feet
Remaining distance to cover by the snail = 16 - 11 = 5 feet
Number of days to cover remaining 5 feet to reach the top of the well = 1 day
Therefore, snail will take 12 days to reach the top of the well.
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[<Ending>] <3
Hope this helps and if it's wrong, you can't sue me! :D
Bye! Hope this works for you :)
Have a nice day! - Avery <3
MATH: FINDING HALF LIFE PT 2..HELP!
The half life of the radioactive Rutherford-265 is;
13.1 hours.
What is the half-life of the radioactive Rutherford-265?It follows from the task content that the given function represents the decay function of the radioactive material. Since half-life corresponds to the point at which only half of the starting material remains, hence we have;
(1/2) = e ^(-0.053t)
By taking the natural log of both sides, we have;
-0.6931 = -0.053t
Hence, t = -0.6931/ -0.053 = 13.1 hours.
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suppose that 18 inches of wire costs 90 cents. At the same rate, how many inches of wire can be bought for 55 cents?
Answer:
11 inches
Step-by-step explanation:
90 divided by 18 is 5 so each inch is worth 5 cents so 55 cents would give you 11 inches of wire because 55/5 is 11
pls solve...I will mark as BRAINLIST........
Answer:
Step-by-step explanation:
X
What is the volume of the following rectangular prism?
Volume
Area of base×Height9/5×2/33/5×26/5units³1 1/5units³Volume
Ah9/5×2/36/5units³1-1/5 units ³