Find the greatest common factor : 32a^3b^2, 44ab^3 and 40a^2b
Find the greatest common factor : 25^2q^3, 15p^2q^2 and 35pq^4
Answers
1) 4ab
2) 5pq²
Explanation
Greatest common factor is sometimes known as GCD (greatest common divisor). It means the greatest number that can divide a set of numbers.
For example, the GCD of 12 and 18 is 6.
Question 1
Find the GCF of 32a^3 b^3,44ab^3,and 40a^2 b. To do this you can factor out the common term.
32a^3 b^3,44ab^3,and 40a^2 b
Dividing every term by ab we shall have,
ab(32a^2 b^2,44b^2,and 40a)
Dividing again by 4,
4ab(8a^2 b^2,11b^2,and 10a)
Have no other common factor, the GCF = 4ab
Question 2
Find the GCF of 25p²q³,15p² q² and 35pq^4 . To do this you can factor out the common term.
25p²q³,15p² q² and 35pq^4
Dividing each term by 5,
5(5p²q^3, 3p²q² and 7pq^4)
Dividing again by pq2,
5pq² (5pq, 3p and 7q² )
There no been any other common divisor, the GCF = 5pq²
Answer:
Part A. 4ab
Part B. 5pq²
Step-by-step explanation:
Part A). In this part the given expressions are 32a³b², 44ab³, 40a²b
We have to find the greatest common factor of these expressions.
Factors of 32a³b² = 2×2×2×2×2×a×a×a×b×b
Factors of 44ab³ = 2×2×11×a×b×b×b
Factors of 40a²b = 2×2×2×5×a×a×b
So for the the greatest common factor we will choose the common factors (bold letters) of three expressions
GCF = 2×2×a×b = 4ab
Part B). The given expressions are 25p²q³, 15p²q² and [tex]35pq^{4}[/tex]
Factors of 25p²q³ = 5×5×p×p×q×q×q
Factors of 15p²q² = 3×5×p×p×q×q
Factors of [tex]35pq^{4}[/tex] = 5×7×p×q×q×q×q
Therefore greatest common factor will be = 5pq²
Related Questions
What is the correct definition of the third quartile of a data set?
A. The third quartile is all the numbers of the data set added together and divided by 3. B. The third quartile is the difference between the maximum and median. C. The third quartile is the median of the upper half of data in the data set. D. The third quartile is the mode of the upper half of data in the data set.
Answers
The third quartile (also called the upper quartile) has 75 percent of the data below it and the top 25 percent of the data above it. The third quartile is the same as the median of the part of the data which is greater than the median.
therefore
the answer is the option
C.) The third quartile is the median of the upper half of data in the data set.
Option: C is the correct answer.
C. The third quartile is the median of the upper half of data in the data set.
Step-by-step explanation:We know that our data is divided into three quartiles:
1)
First quartile or lower quartile--
It is the median of the lower set of the data.
2)
Middle quartile or Median--
Median is the central tendency of the data and it always exist in the middle of the data set.
3)
Third quartile or upper quartile--
It is obtained by finding the median of the upper set of the data.
Hence, the answer is: Option: C
which reason justifies the last step in a proof that ΔEDG≌ΔADC?
Answers
fd is congruet to db
ed is congruent to da
and vertical angles theorem
Rotate this image 90 clockwise around the point (-1 1 )
Answers
In this case given the point (-1, 1), the image will be (1, -(-1)) or (1, 1)
Answer: You didn't put options A, B, C, OR D
no picture either
Step-by-step explanation:
There are seven black marbles and nine white marbles in a bag what is the aprroximate probability of drawing two black marbles and then a white marble without replacement
Answers
There is a probability of 43.75% to pick a black marble in the bag with 16 marbles.
If you do , there will be 6 black marbles and 9 white marbles left in the bag. The probability to pick anpther black marble is 6/15 or 40%.
If you do pick another black marble , there will be 5 black marbles and 9 white marbles left in the bag , which means the probability of you getting a white marble next is 9/14 or 64.28%.
Now we just have to multiply the probability of you picking the marbles in the right order :
0.4375 × 0.4 × 0.6428 = 0.11249
Which is approximately 11.25%
There is a probability of 11.25% of you getting two black marbles and one white marble in a bag with 7 black marbles and nine white marbles .
I hope you understood my brief explanation. And please consider marking this awnser as Branliest if you think it deserves it. Thank you :)
The approximate probability of drawing two black marbles and then a white marble without replacement is 9/80.
What is probability?Probability deals with the occurrence of a random event. The chance that a given event will occur. It is the measure of the likelihood of an event to occur.The value is expressed from zero to one.
For the given situation,
Number of black marbles = 7
Number of white marbles = 9
The event of drawing two black marbles from seven black marbles is
⇒ [tex]\frac{7C_{2} }{16C_{2} }[/tex]
[tex]7C_{2} =\frac{(7)(6)}{(1)(2)}[/tex]
⇒ 21
[tex]16C_{2}=\frac{(16)(15)}{(1)(2)}[/tex]
⇒ 120
Now, [tex]\frac{7C_{2} }{16C_{2} }=\frac{21}{120}[/tex]
Total number of balls, after drawing 2 black balls without replacement is
⇒ 16 - 2 = 14
The event of drawing a white marble without replacement from nine white marbles is
[tex]\frac{9C_{1} }{14C_{1} } = \frac{9}{14}[/tex]
Thus, the approximate probability of drawing two black marbles and then a white marble without replacement is
P(E) = [tex](\frac{21}{120}) (\frac{9}{14} )[/tex]
⇒ 9/80
Hence we can conclude that the approximate probability of drawing two black marbles and then a white marble without replacement is 9/80.
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The table below shows the data collected on the number of car washes, y, each day since the Auto Spa opened, x.
Days Since Auto Spa Opened 0 20 40 60 80 100
Number of Car Washes 29 35 18 31 28 14
The owner of the new Auto Spa created a line of best fit for the data that can be modeled by the following equation.
y = -0.12x + 31.76
Match the slope and y-intercept with the correct description for the given situation.
titles
the number of cars washes on the day the Auto Spa opened
the ratio of car washes to the number of days since the Auto Spa opened
the number of car washes
the total number of days since the Auto Spa opened
the ratio in the number of days since the Auto Spa opened to the total profit
pair
y-intercept
slope
Answers
Explanation:
This line of best fit is in slope intercept form: y=mx+b, where m is the slope and b is the y-intercept.
In this equation, m corresponds with -0.12 and b corresponds with 31.76.
The slope is the ratio of change in y to change in x. The y-coordinate of each point represents the number of car washes and the x-coordinate represents the number of days since Auto Spa opened; the ratio of change in y to change in x is then the ratio of the number of car washes to the number of days since Auto Spa opened.
The y-intercept is the point where the data crosses the y-axis; at this point, and all on the y-axis, the x-coordinate is 0. In this problem, the x is the number of days since Auto Spa opened; if it is 0, this means 0 days since it opened, which would be its opening day. Thus the y-intercept is the number of car washes on opening day.
Answer:
The slope is the ratio of car washes to the number of days since Auto Spa opened; and the y-intercept is the number of car washes on the day the Auto Spa opened.
Step-by-step explanation:
What is the measure of ∠EGF?
What is the measure of ∠CGF?
Answers
= 1/2(130)
= 65
the measure of ∠CGF = 180 - 65
= 115
This is an isosceles triangle, which means its base angles are congruent. Interior angles of triangle add to equal 180 degrees, so you can make an equation to solve for the measure of the base angles. I'll call the base angles x.
180 = 50 + 2x
130 = 2x
65 = x
That gives you m∠EGF and m∠FGE (65°).
To find m∠CGF, you must know that it and ∠EGF are supplementary (they add to equal 180 degrees). Make another equation setting them to equal 180 using m∠EGF (65°):
180 = 65 + x
115 = x
Answer:
m∠EGF = 65°
m∠CGF = 115°
PLEASE HELP ASAAAAPPPPPP
Answers
A lake has the capacity to support 10,000 trout. Suppose that the conditions are such that the current population of trout will grow logistically up until it stabilizes at the amount that the lake can support. Currently there are 1,500 trout in the lake. Which of the following is a possible model for P(t), the trout population in t years?
Answers
Answer:
P(t) = 10,000/ (1+9e^-0.48t)
Step-by-step explanation:
i think because it starts at around 1500 for t=1 and then when t=2 and so on it grows exponentially.
(x 2 + 2x - 1)(x 2 + 2x + 5) Please help asap!
Answers
To solve this equation, we can use distributive property.
I listed the terms you have to multiply :
x² × x² = x^4
x² × 2x = 2x³
x² × 5 = 5x²
2x × x² = 2x³
2x × 2x = 4x²
2x × 5 = 10x
-1 × x² = -x²
-1 × 2x = -2x
-1 × 5 = -5
Add all of them....
x^4 + 2x³ + 5x² +2x³ + 4x² + 10x - x² - 2x - 5
add up the like terms to simplify
x^4 + 4x³ + 8x² + 8x - 5
Hope this helped! :)
If GH = 3 and HJ = 5, then G ___ J.
Choose the relationship symbol that would make a true statement.
Answers
Step-by-step explanation:
The given equation is as follows.
GH = 3 and HJ = 5
Therefore, simplify for H from both the equations as follows.
H = [tex]\frac{3}{G}[/tex] .......... (1)
and, H = [tex]\frac{5}{J}[/tex] .......... (2)
Equating both equation s(1) and (2), we get the following.
[tex]\frac{3}{G}[/tex] = [tex]\frac{5}{J}[/tex]
G = [tex]\frac{3J}{5}[/tex]
or, G = 0.6J
This means that J will be 0.6 times greater than G.
Thus, we can conclude that G < J.
The mean of the data set is 18 what’s the missing number 21,11,blank,27,22,13,16
Answers
9514 1404 393
Answer:
16
Step-by-step explanation:
The sum of the 7 numbers needs to be 7·18 = 126.
Then the missing number is ...
126 -21 -11 -27 -22 -13 -16 = 16
Write the polynomial in standard form. Then name the polynomial based on it's degree and number of terms.
3 - 10x^2 - 7x + 3x^2
Answers
-7x^2 - 7x + 3
This is a trinomial because it has 3 terms.
The degree of this polynomial is 2.
For which data representation is the median the better measure of center
Answers
In all but the 3 graphs, the data is perfectly symmetrical. This means that the mean and the median would be the same.
However, in the second graph the data is skewed to the right. This means that the mean would also be skewed to the right due to the larger scores there. Using the median in this case would give a clearer picture of the data.
Compare the values of the underlined digits.
34,258 and 47,163
- -
The value of 4 in _________ is______ times the value of 4 in ________
PLEASE ANSWER ASAP IT'S FOR MY SISTER
Answers
In the second number, the "4" is in the ten thousands place - meaning it's
40,000 + 7,163.
40,000/4,000 = 10
The value of 40,000 in the second value is 10x greater than the value of 4,000 in the first value.
Galileo wanted to release a wooden ball and an iron ball from a height of 100 meters and measure the duration of their fall. He found a plane with an incline of 12 degrees that he could climb until he could get to an altitude of 100 m. How far should Galileo walk up the inclined plane? Round your final answer to the nearest hundredth.
Answers
We have to find the value of the hypotenuse.
For this we use the following trigonometric relationship:
senx = C.O / h
Where
x: angle
C.O: opposite leg
h: hypotenuse.
Substituting the values we have:
sen (12) = 100 / h
We cleared h:
h = 100 / sin (12)
h = 480.97 m
Answer:
Galileo should walk 480.97 m up the inclined plane
Galileo walk 480.97 meters up the inclined plane if Galileo wanted to release a wooden ball and an iron ball from a height of 100 meters and measure the duration of their fall.
What is the trigonometric ratio?The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.
We have:
Galileo wanted to release a wooden ball and an iron ball from a height of 100 meters.
Let's suppose Galileo walked x meters up the inclined plane.
The plane with an inclined a 12°
As we can see in the right angle triangle the sin ratio:
[tex]\rm sin24\° = \frac{100}{x}[/tex]
[tex]\rm x = \frac{100}{sin24\°}[/tex]
x = 480.97 meters (Sin12° = 0.20791)
Thus, Galileo walk 480.97 meters up the inclined plane if Galileo wanted to release a wooden ball and an iron ball from a height of 100 meters and measure the duration of their fall.
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Your school drama club is putting on a play and hopes to raise $600 from ticket sales. They sell adult tickets for $8 each and student tickets for $5 each. Let x represent the number of adult tickets and y represent the number of student tickets. The equation to represent the number of tickets sold to reach their goal, 8x+ 5y = 600, is graphed below. If 40 adult tickets are sold, how many student tickets must be sold to reach their goal?
Diagram can be shown here:
https://static.k12.com/eli/bb/343/3_23939/2_15013_4_23943/d7066d09bfa7bf4e8df2b2c0b508a3e8ba21c76d/media/b1cd8381087979f1dffbcd6f3efef158a61fbd57/mediaasset_649354_1.gif
Answers
15. The following statements concerning the location of an extreme value of a twice-differentiable function, f, are all true. Which statement also includes the correct justification?
(A) The function has a maximum at x=5 because f'(5)=0.
(B) The function has a maximum at x=5 because f'(x)<0 for x<5 and f'(x)>0 for x>5.
(C) The function has a minimum at x=3 because the tangent line at x=3 is horizontal.
(D) The function has a minimum at x=3 because f'(x)<0 for x<3 and f'(x)>0 for x>3.
(E) The function has a minimum at x=3 because f"(3)<0.,
Answers
What is the maximum number of real zeros that a function with degree 5?
Answers
y = (x - 22)(x - 1)(x + 1)(x - 2)(x+2)
Can someone please help me out on this?
Answers
Find the inverse of the following function. f(x) 8√ x for x > 0
Answers
The inverse of the function f(x) = 8√x for x > 0 is g(x) = x^2/64.
To find the inverse of the function f(x) = 8√x for x > 0, we need to interchange the roles of x and y and solve for y.
Let's start by rewriting the function using y instead of f(x):
y = 8√x
Next, we'll swap x and y:
x = 8√y
To isolate y, we can square both sides:
[tex]x^2 = (8\sqrt y)^2\\\\x^2 = 64y[/tex]
Now, divide both sides by 64:
[tex]x^2/64 = y[/tex]
Simplifying further:
[tex]y = x^2/64[/tex]
Therefore, the inverse of the function f(x) = 8√x for x > 0 is given by [tex]g(x) = x^2/64.[/tex]
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I'll give you brainliest answer!! Help me. This diagram shows a smaller square inscribed within a larger square.
Answer with supporting work:
Answers
hypotenuse^2 = 3^2 + 4^2
hypotenuse^2 = 9 + 16
hypotenuse^2 = 25
hypotenuse = 5
Therefore, the area of the smaller square is 5 * 5 = 25
Instructions:Select the correct answer from each drop-down menu. The sum of the squares of two consecutive positive even numbers is 340. Find the numbers. The consecutive even numbers are
Answers
[tex] x^{2} + (x + 2)^{2} = 340[/tex]
If we expand the second term:
[tex] x^{2} + x^{2} + 4x + 4 = 340[/tex]
Combine like terms:
[tex]2 x^{2} + 4x + 4 = 340[/tex]
You can reduce this by dividing both sides of the equation by two:
[tex] x^{2} + 2x + 2 = 170[/tex]
And we transpose 170 to get a standard quadratic form that the right side will be zero:
[tex] x^{2} + 2x - 168 = 0[/tex]
Then factor the left side:
[tex](x +14)(x-12) = 0[/tex]
Find out the values of x that makes each factor = 0
x + 14 = 0
x = -14
We can eliminate the negative symbol because the problem is asking for positive even integers.
and;
x - 12 = 0
x = 12
Now we can say that the first positive integer is 12 and the second one is 14
the sum of the squares of these 2 numbers are 340
x² + (x+2)² = 340
x² + x² + 4x + 4 = 340
2x² + 4x - 336 = 0
we are left with a quadratic equation
coefficient of x is 2 therefore divide each number by 2
x² + 2x - 168 = 0
to solve the quadratic equation , the 2 factors whose product is 168x² and sum is 2x is -12x and 14x
x² + 14x -12x -168 = 0
x (x + 14) - 12(x + 14)=0
(x+14)(x-12) = 0
we have 2 possible values for x
x + 14 = 0 x-12 = 0
x = -14 x = 12
from the 2 answers the correct answer is x = 12 as it should be a positive integer
one integer is 12 and consecutive even integer is 14
to check the product of the squared numbers
= 14² + 12²
= 196 + 144
= 340
Rules that govern the ways that logarithms are simplified and combined are going to be very similar to simplifying and combining rules for what other family of functions?
Exponential
Linear
Rational
Polynomial
Answers
Rules that govern the ways that logarithms are simplified and combined are going to be very similar to simplifying and combining rules for the exponential family of function.
This comes from the definition of logarithm itself which says that a logarithm is a quantity representing the power to which a fixed number (the base) must be raised to produce a given number.
Let us illustrate this by way of an example. We know that 100 can be represented as [tex] 10^2 [/tex]. Here 10 is the base, 2 is the power and 100 is the given number. Therefore,
[tex] 10^2=100 [/tex]
Likewise, we can represent 1000 as [tex] 1000=10^3 [/tex]
Now, if we multiply [tex] 10^2 [/tex] and [tex] 10^3 [/tex] we will get: [tex] 10^2\times 10^3=10^{2+3}=10^5 [/tex]. We added the powers. Therefore, the logarithm of [tex] 10^5 [/tex] to the base 10 is 5.
Let us see if we will get the same result by using the rules of logarithms.
[tex] log(10^2\times 10^3)=log(10^2)+log(10^3)=2log(10)+3log(10)=2+3=5 [/tex]
As we can see we got the same result by using the logarithm and the exponential rule, thus, verifying our answer. Similar results can be obtained for other operations of the logarithmic rule.
The measure of a minor arc is equal to the measure of __________
Answers
The point nearest to the origin on a line is at (4, -4). Find the standard form of the equation of the line.
Answers
.. y = (x -4) -4
or, in standard form
.. x - y = 8
AC is tangent to circle O at A. If mBY =24, what is m
Answers
we know that
the inscribed angle measures half of the arc it comprises.
then
m∠YAB=(1/2)*m∠BY-------------> m∠YAB=(1/2)*24°=12°
m∠YAC=90°-m∠YAB=90°-12°=78°
the answer is the option C) 78°
Factor completely x2 - 8x + 16
A. (x+4)(x+4)
B. (x-4)(x-4)
C. (x+4)(x-4)
D. (x-2)(x-8)
Answers
When you take -4+-4, you will get -8 and when you multiply -4 x -4, you will get 16
Suppose the dial on the spinner is spun 2 times in a row.
X is the number of times the dial lands on region A.
Which table represents the probability distribution for the variable X?
Answers
1) Dial does not land in the region A
2) Dial lands once in the region A
3) Dial lands twice in the region A
The combined probability of these three events has to be 1.
Let's calculate probabilities of each event:
[tex]1) P=P(1,1)=\frac{2}{3}\cdot\frac{2}{3}=\frac{4}{9}\\ 2)P=P(1,2)+P(2,1)=2\cdot \frac{2}{3}\cdot \frac{1}{3}=\frac{4}{9}\\ 3)P=P(3,3)=\frac{1}{3}\cdot\frac{1}{3}=\frac{1}{9}[/tex]
If we summ all those probabilities we get 1.
The answer would table C (lower left corner).
if this is your spinner the answer is
the answer is
X P
0 1/9
1 4/9
2 4/9
You bought a coat at $78.50 and two shirts at $21.99 each. if the sales tax rate is 7%, how much is the total purchase?
Answers
Answer:
The answer is going to be $131.05
Step-by-step explanation:
I just took the test
Convert the fraction to decimal and decimal into the fraction 10.222
Answers
I'm not sure if that's what you were looking for but I hope this helps!
Answer:
10 and 222/1000
Step-by-step explanation: