The greatest common factor of [tex]20x^{6} y+40x^{4} y^{2} -10x^{5} y^{5}[/tex] is [tex]10x^{4} y[/tex] .
The greatest common factor of a set of numbers is defined as the largest number that divides all the numbers in that given set and leaves 0 as remainder in each case.
In the given expression
[tex]20x^{6} y+40x^{4} y^{2} -10x^{5} y^{5}[/tex]
Applying Prime Factorization and Writing all the terms in the above expression as
[tex]20x^{6} y=10x^{4}y *2x^{2}[/tex]
[tex]40x^{4} y^{2} =10x^{4} y*4y[/tex]
[tex]10x^{5} y^{5} =10x^{4}y*xy^{4}[/tex]
As we can see that [tex]10x^{4} y[/tex] is common and greatest in all the terms .
Hence [tex]10x^{4} y[/tex] is the Greatest common factor.
Therefore , the greatest common factor of [tex]20x^{6} y+40x^{4} y^{2} -10x^{5} y^{5}[/tex] is [tex]10x^{4} y[/tex] , the correct option is (a)[tex]10x^{4} y[/tex].
The given question is incomplete , the complete question is
What is the greatest common factor of [tex]20x^{6} y+40x^{4} y^{2} -10x^{5} y^{5}[/tex]
(a)[tex]10x^{4} y[/tex]
(b)[tex]5x^{2} y^{5}[/tex]
(c)[tex]5x^{4} y[/tex]
(d)[tex]20x^{6} y[/tex]
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In a book store,60 books of the same kind occupy 1.4m of shelf length . how much shelf length is required for 300 such books ? if a shelf is 84cm long,how many books are needed to fill the shelf?
7m shelf length is required for 300 such books, and 36 books are needed to fill the 84cm long shelf. So option (a). 7m,36 books is the correct option.
here in the question we need to apply concept of division.
what is division ?
Division is kind of mathematical operation where we find out equals parts of a number, by applying it a number can cut into many equal parts. It is opposite to multiplication.
As 60 books occupy 1.4 m of shelf ,
S0, 1 books occupies = 1.4/60 m of shelf
Then, 300 books occupy {(1.4/60)×300} m of shelf=
7m of shelf
Now, 7m=700cm is occupied by 300 books,
So,1cm is occupied by (300/700) books
Then, 84cm is occupied by (300/700)×84 books=36 books.
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The question was incomplete.
Check below the full question.
In a book store,60 books of the same kind occupy 1.4m of shelf length . how much shelf length is required for 300 such books ? if a shelf is 84cm long, how many books are needed to fill the shelf?
a. 7m,36 books
b. 5m,32 books
c. 10m,16 books
d. 3m,9 books
A ball is thrown upward and outward from a height of 5 feet. The height of the ball, y, in feet, can be modeled by y=-0.4x^2+1.6x+5 where x is the ball's horizontal distance, in feet, from where it was thrown.
a. What is the maximum height of the ball and how far from where it was thrown does this occur?
b. How far does the ball travel horizontally before hitting the ground?
c. Graph the equation that models the ball's parabolic path.
The maximum height of the ball is 9.8 feet.
The distance the ball travels horizontally before hitting the ground is 2.
The graph that model the parabolic path is given below.
What is a parabolic path?Parabolic path is defined as the angle of trajectory of a projectile.
We have,
y = 0.4x² + 1.6x + 5 _____(1)
Where,
x = balls horizontal distance
y = height of the ball
To find the maximum height we need to differentiate y and set y = 0.
y' = 0
0.4 x (2x) + 1.6 + 0 = 0
0.8x + 1.6 = 0
-0.8x = -1.6
x = 1.6 / 0.8
x = 2
Now the maximum height of the ball is:
Put x = 2 in (1)
y = -0.4 x (2)² + 1.6 x (2) + 5
y = 0.4 x 4 + 3.2 + 5
y = 1.6 + 3.2 + 5
y = 9.8
The distance the ball travels horizontally before hitting the ground:
x = 2
The equation that models the ball's parabolic path is given below:
Thus,
The maximum height of the ball is 9.8 feet.
The distance the ball travels horizontally before hitting the ground is 2.
The graph that model the parabolic path is given below.
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Rewrite the expression as the sum of two numbers. 7(2 + 6)
Answer: First you used distribute property
7(2+6) bring 7 into the parentheses
14+42 Then you just add
56 that’s the sum
Step-by-step explanation: hope this helps
Explain how you can tell if y=ab x represents exponential growth or exponential decay.
In the form y = ab^x, if b is a number between 0 and 1, the function represents exponential decay.
The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time. It can be written as y=a(1-b)x, where x is the amount of time that has passed, an is the initial amount, b is the decay factor, and y is the final amount.
Radioactive decay and population decline are two examples of exponential decay. The data collected can be used to forecast future population trends for cities and colonies as well as the half-life of radioactive materials.
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Use the properties of exponential and logarithmic functions to solve each system. Check your answers.
log (2 x-y)=1
log (x+y)=3 log 2
The solved logarithmic function is 2x - y = e and x + y = 8 for log (2x - y) = 1 and log (x + y) = 3 log 2 respectively.
What is a logarithmic and exponential function?
Logarithmic functions and exponential functions are inverses of each other. The logarithmic function is denoted by using the word log while exponential by using the alphabet, e. For example log 10 = 1 and e^2.
Solving the given expressions: log (2x - y) = 1 and log (x + y) = 3 log 2
Applying given properties of logarithmic and exponential function;
log a + log b = log (ab)
4 log x = log x⁴
e^(log x) = 1
e^(x + y) = (e^x) × (e^y)
Take expression, log (2x - y) = 1
Applying exponential on both sides, we get,
e^(log 2x - y) = e^1
2x - y = e
To Check Results,
Taking logarithm both sides,
log (2x - y) = log e
log (2x - y) = 1
Thus, the answer is verified.
Take expression, log (x + y) = 3 log 2
Applying exponential on both sides, we get,
e^(log (x + y) = e^(3 log 2)
x + y = e^(log 8)
x + y = 8
To Check Results,
Taking logarithm both sides,
log (x + y) = log 8
log (x + y) = 3 log 2
Thus, the answer is verified.
Hence, the solved expression is 2x - y = e and x + y = 8 for log (2x - y) = 1 and log (x + y) = 3 log 2 respectively.
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If x=10, find m∠WYZ
Will choose brainliest
Answer:
23˚
Step-by-step explanation:
If x = 10, then angle VYZ = 157 by basic algebra. Knowing that VYZ and WYZ are supplementary angles, we can do 180-157 to find angle WYZ. 180-157 = 23˚
Estimate each value to the nearest whole number.
5.4²
Hey there!
(5.4)^2
= 5.4^2
= 5.4 * 5.4
= 29.16
Therefore, your answer should be:
29.16
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Can someone help me with this please? I need the answers and the work shown please... thank you!
Answer:
Below
Step-by-step explanation:
Ok, there is a few ways to slove this problem. You could just try to plug in both xs and see which is true, or you could actually do the math. I will do the math.
Alright, the first question is a corrseponding angle, so they are equal to each other. Set it up like this:
3x-1=x+5
Now, you need to get the variable by itself, so do that.
3x-1=x+5
+1 +1
3x=x+6
-x -x
2x=6
/2 /2
x=3
The arrow will go to the right.
Now, you have a same side exterior angle. When you add these together, they will equal 180 degrees, so set up the equation like this.
8x+10+6x+2=180
Now, solve
8x+10+6x+2=180
Combine like terms (8x+6x)+(10+2)
14x+12=180
-12 -12
14x=168
/14 /14
x=12
Your arrow will go down.
Same side interior angles is your next problem, and it is like same side exterior angles as it equal 180. Set up your equation accordingly
10x-8+5x+8=180
Combine like terms (10x+5x)+(8-8)
15x=180
/15 /15
x=12
Your arrow will go down.
These are opposite side exterior angles, so they will equal each other. Set up the equation accordingly.
9x+18=10x-8
Get the variable on one side and by themselves
9x+18=10x-8
+8 +8
9x+26=10x
-9x -9x
26=x
Your arrow will go upper corner right
This problem is opposite side exterior angles, so they will equal each other. Set up the equation accordingly.
2x+5=3x-7
+7 +7
2x+12=3x
-2x -2x
12=x
Your arrow will go up
Now, you have a same side exterior angle. When you add these together, they will equal 180 degrees, so set up the equation like this.
8x+5+2x-15=180
Combine like terms (8x+2x)+(5-15)
10x-10=180
+10 +10
10x=190
/10 /10
x=19
Arrow goes diagonal right down
The angles are opposite side interior angles, so they are equal to each other. Set up your equation like this:
4x-4=-3x+52
+4 +4
4x=-3x+56
+3x +3x
7x=56
/7 /7
x=8
That is your finish!
Bentley drove 329 miles in 7 hours. On average, how fast did he drive, in miles
hour?
per
Answer:
47mph
Step-by-step explanation:
329/7=47
There are 75 men at a party and 60 women. How many more percent more men are there then women?
Need help, had a brain fart
There are 11.2% more men than women
How to calculate the percentage ?The First step is to calculate the percentage of men in attendance
There are 75 men and 60 women
Total number of people in attendance= 75 +60
= 135
75/135 × 100
= 0.556 × 100
= 55.6
The percentage of women in attendance
= 60/135 × 100
= 0.444 × 100
= 44.4
Next step is to subtract both percentages
= 55.6 - 44.4
= 11.2
Hence there are 11.2% more men that women
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Ms. Moya has received 13 Starbucks cards from students and generally gets 2 more
each year she teaches. Ms. Powers has only ever been given 1 Starbucks gift card but
plans to get 5 more each year she teaches. Which equation models the situation to find
the number of years before they have the same number of Starbucks cards?
Answer:
13+2=15+2=17+2=19+2=21
1+5=6+5=11+5=16+21
(The Pink Answer)
help please i dont know
Denote by x the number of miles traveled.
Denote by p(x) the price paid
[tex]p(x) = 2 + 0.75x[/tex]
B.[tex]p(12) = 2 + 0.75(12) \\ p(12) = 2 + 9 \\ p(12) = 11 \: dollars[/tex]
C.No he is not, since they stated that the price is equal to two more than the product of 0.75 and the distance traveled, in this case represented by the variable m
If y varies directly as x and y= 64 when x=4 find x when y=48
Answer:
If y varies directly as x and y= 64 when x=4 find x when y=48
x=3
The function g is defined as follows.
g(x)=3x² +5
If the graph of g is translated vertically downward by 6 units, it becomes the graph of a function f.
Find the expression for f(x).
Answer: graph the function defined by the formula g(x) = f(x)+2. To graph y = f(x) - k, shift the graph of y = f(x) down k units by subtracting k from.
Step-by-step explanation:
Two financial institutions offer different deals to new customers. The first bank offers an interest rate of 3 % for the first year and 2 % for the next two years. The second bank offers an interest rate of 2.49 % for three years. You decide to invest the same amount of principal in each bank. To answer the following, assume you make no withdrawal or deposits during the three-year period.
c. Write a function that represents the total amount of money in both accounts at the end of three years.
The function that represents the total amount of money in both accounts at the end of three years as
First Bank - 107 P / 100
Second Bank - 10747 P / 10000
Simple interest :
Simple interest can be calculated as follows
S.I = PRT / 100
Let the amount invested in two banks be 'P'
First Bank :
Given the first bank offers an interest rate of 3% for the first year and 2% for the next two years as
R₁ = 3%, R₂ = 2% T₁ = 1, T₂ = 2
Now the simple interest for the first bank is
S. I = PR₁T₁ / 100 + PR₂T₂ / 100
= P(3*1 / 100 + 2*2 / 100)
= P(3 / 100 + 4 / 100)
= 7P/100
The total amount of money in the first bank at the end of three years is
= S.I + P
= 7P / 100 + P
= 107 P / 100
Second Bank:
Given the second bank offers an interest rate of 2.49% for the three years as
R = 2.49, T = 3
Now the simple interest for the second bank is
S. I = PRT / 100
= P(2.49 * 3 / 100 )
= P(7.47 / 100)
= 7.47P/100
The total amount of money in the second bank at the end of three years is
= S.I + P
= 7.47P / 100 + P
= 107.47 P / 100
= 10747 P / 10000
Therefore, the function that represents the total amount of money in both accounts at the end of three years as
First - 107 P / 100
Second - 10747 P / 10000
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Solve each equation.
2⁵x⁺¹=32
After solving the equation, x = 4/5 is the value of x in [tex]2^{5x+1} = 32[/tex]
⇒ [tex]2^{5x+1} = 32[/tex]
⇒ [tex]2^{5x+1} = 2^5[/tex]
⇒ 5x + 1 = 5
⇒ 5x = 5 - 1
⇒ 5x = 4
⇒ x = 4/5
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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a_1=4 and an=a_{n-1}+6
The value of the fifth term based on the expression a + (n - 1) + 6 is 14.
How to calculate the value?From the information, it should be noted that the first term has been given and the nth series has been given.
It should be noted that the fifth term will be:
= a + (n - 1) + 6
where
a = 4
n = 5
Therefore, a + (n - 1) + 6
= 4 + (5 - 1) + 6
= 4 + 4 + 6
= 14
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a_1=4 and an=a + {n-1}+6. Find the fifth term
if f(x) is the height in cm of a sunflower plant that is x days old which of the following statements best describes the meaning of f(60) = 210
Ifa box of apples is distributed among 28 children , each gets 3 . iF 7 children were not present , their share would also ne distriibuted among the others How many apples would each children get
Answer:
First subtract 28 by 7.
28 - 7 = 21
Then multiply 28 times 3
28 times 3 is 84
Then finally divide 84 by 21
84/21 = 4
Each of the children would get 4 apples
Step-by-step explanation:
0.6r = 4.5
giving brainlest n a lot of points
to determine the number of cashiers needed when a grocery store opens each
morning, the manager of the store wanted to estimate the typical number of items each
customer purchased. the manager took all the receipts from the first 30 minutes the
store was open on a particular day and recorded the number of items purchased by
each customer. the manager constructed the following boxplot from the information
on the receipts.
From the box-and-whisker plot of the distribution, we have that:
The center of the distribution is the median of 32.The range of the distribution is described by two measures, the IQR of 35 - 22 = 13 and the range of 62 - 17 = 45.The distribution is left skewed.What is the missing information?The plot of the distribution is missing, as is given at the end of the answer.
It asks to describe:
The center of the distribution.The variability of the distribution.The shape of the distribution.What does a box-and-whisker plot shows?A box and whisker plot shows five things:
The minimum value.The 25th percentile, which is the median of the bottom 50%.The median, which splits the entire data-set into two halfs, the bottom 50% and the upper 50%.The 75th percentile, which is the median of the upper 50%.The maximum value.For the plot in this problem, we have that:
Minimum: 17.Q1: 22.Median: 32.Q3: 35.Maximum: 62.Hence:
The center of the distribution is the median of 32.The range of the distribution is described by two measures, the IQR of 35 - 22 = 13 and the range of 62 - 17 = 45.The distribution is left skewed, as Q3 - Q2 < Q2 - Q1.More can be learned about box-and-whisker plots at https://brainly.com/question/12343132
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What is the longest side of a right triangle
A right angle
B leg B
C leg A
Hypotenuse
Answer:
Hypotenuse
Step-by-step explanation:
The longest side of a triangle is opposite the largest angle, which is the right angle in a right triangle.
Answer:
Hypotenuse.
Step-by-step explanation:
Discussion
A: says it is a right angle. It can't be the answer to the longest side.
B: Usually B and A might be the hypotenuse, but that is generally not the way they are displayed.
C: Neither B nor A can be chosen.
D: Answer:
Simplify each expression.
[tex](y-3)(y^2+9)(y+3) - (2y^2 -y)^2 - 19[/tex]
The simplified expression of the expression given as (y - 3)(y^2 + 9)(y + 3) - (2y^2 - y)^2 - 19 is (y^4 - 81) - (2y^2 - y)^2 - 19
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to simplify the expression?The expression is given as
(y - 3)(y^2 + 9)(y + 3) - (2y^2 - y)^2 - 19
Rewrite the above expression as
(y + 3)(y - 3)(y^2 + 9) - (2y^2 - y)^2 - 19
Apply the difference of two squares formula
So, we have
(y^2 - 9)(y^2 + 9) - (2y^2 - y)^2 - 19
Evaluate the product
So, we have
(y^4 - 81) - (2y^2 - y)^2 - 19
Hence, the simplified expression of the expression given as (y - 3)(y^2 + 9)(y + 3) - (2y^2 - y)^2 - 19 is (y^4 - 81) - (2y^2 - y)^2 - 19
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Write the phrase as an expression. Twice a number w
Answer: w2
Step-by-step explanation:
It is just w2, or w*2, or w x 2. You just have the number w twice.
5. Table Item The table shows the time and
distance Hector walked in a 5-kilometer-long
walk for charity. The distance is proportional
to the time walked. Complete the table to
show the times of his last three walks.
(Lesson 3)
Distance (km) Time (min)
1.5
13.5
2010
4.5
5
The distance being proportional to the time Hector walked 2 km in 18 minutes.
Two variables are proportional if they can be written in the form ak=b where k is the proportionality constant.
Here the proportionality constant is speed.
Speed is defined as the distance covered in unit time. The unit of speed can be written as kilometer per hour, miles per hour or meters per second.
The distance is proportional to the time walked therefore:
1.5/2=13.5/T₁
or, T₁=18
Similarly:
1.5/4.5=13.5/T₂
or, T₂=40.5 minutes
again,
1.5/5=13.5/T₃
or, T₃=45 minutes.
Hence the total time taken to complete the distances 2,4.5 and 5 is given by 18,40.5 and 45 minutes.
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Which table shows a constant of proportionality of 2 for the ratio of string instruments to percussion instruments?
Table with proportionality 2 is table 3
Percussion string
1 2
2 4
3 6
What is proportionality?A proportion is an equation in which two ratios are set equal to each other.
from first table
2/3
4/6=3/2
6/9=3/2
from second table
2/5
4/10=5/2
6/15=5/2
From the third table
2/1=2
4/2=2
6/3=2
and from fourth table
2/4=1/2
4/8=1/2
6/12=1/2
hence, the table with proportionality 2 is table 3.
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Scott is making pizzas for everyone at a party.
He has 644 pepperonis. How many pizzas can
Scott make with 9 pepperonis on each?
Answer:
71.5556 but since you cant have half a pizza its only 71
Step-by-step explanation:
butterfly population at Glen Arbor farms was 250 last year. this year there are 100 butterflies. what is the percent increase or decrease.
Answer:
250% decrease
Step-by-step explanation:
How many times does 100 go into 250. 2.5 times. Thus it is 250%
For a result to be considered _____, the chances of its occurring as a result of random error are often less than 5 percent.
For a result to be considered significant, the chances of its occurring as a result of random error are often less than 5 percent.
What is Random error?A coincidental discrepancy between the observed and true values of anything is known as a random error (e.g., a researcher misreading a weighing scale records an incorrect measurement).
It's not always a mistake when there is random error; rather, it happens when measurements are made. Even when you measure the same item repeatedly, there will always be some variation in your results because to changes in the environment, the instrument, or your own perceptions.
Your measurements are equally likely to be greater or lower than the genuine values due to random error, which has unexpected effects.
According to the given data,
For a result to be considered significant, the chances of its occurring as a result of random error are often less than 5 percent.
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On a slow weekend, you spend at least two hours on homework. on a busyweekend, you spend as much as five hours on homework. write an ablosue value inequality that repersents the number of hours you spend doing homework on a typical week day. math problem
The absolute value inequality that represents the number of hours spent on doing homework is 2 ≤ x ≤ 5
Let us assume that one spends x hours doing homework on a typical weekday. Then we can write
The inequality expression for a slow weekend is given as;
X ≥ 2
In the same vein, the inequality expression for a busy weekend is given as;
X ≤ 5
Pooling the two inequalities expression we have;
2 ≤ x ≤ 5
Two inequality expression could be written simultaneously if they can be expressed individually. They are commonly referred to as a “double” inequality and is often written in the form a ≤ f (x) ≤ b
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