An expression is shown below:
3x3y + 12xy − 9x2y − 36y
First Rewrite the expression so that the GCF is factored completely. Show the steps of your work.
Then Rewrite the expression completely factored. Show the steps of your work.
Answer:
Part A: so the GCF is 3y,
We need to rewrite the equation such as:
-36 as -12 · 3, -9 as -3 · 3, 12 as 4 · 3
It will look like this:
3x^3 y +4 · 3xy + 3 · 3x^2 y + 4 · 3 · 3y
We then need to factor out 3y:
3y(x^3 + 4x - 3x^2 - 12)
Part b: factor out completely
3y(x^3 + 4x - 3x^2 - 12)
So, we need to do the following:
3y{x^2(x-3) + 4 (x-3)}
we then get the final factor: 3y(x - 3) (x^2 + 4)
Step-by-step explanation:
The factored expression is:
[tex]3y(x^3 + 4x - 3x^2 - 12)[/tex]
------------------------
To factor the expression:
First, we need to find the greatest common factor of the numeric and symbolic coefficients.Then, we divide each term of the expression by it's gcf.------------------------
The expression is:
[tex]3x^3y + 12xy - 9x^2y - 36y[/tex]
------------------------
The numeric coefficients are: 3, 12, 9, 36
The gcf of the numeric coefficients is:
3 - 12 - 9 - 36|3
1 - 4 - 3 - 12
The gcf of the numeric coefficients is 3, as 3 is the only number by which 3, 12, 9 and 36 are all divisible.
------------------------
The symbolic coefficients are: [tex]x^3y, xy, x^2y, y[/tex]
The only common term is y, so y is the gcf of the symbolic coefficients.
------------------------
The gcf of the entire expression is the multiplication of the gcfs of the numeric and of the symbolic coefficients, so it is 3y.
Now, to factore the expression:
[tex]3x^3y + 12xy - 9x^2y - 36y = 3y(\frac{3x^3y}{3y} + \frac{12xy}{3y} - \frac{9x^2y}{3y} - \frac{36y}{3y}) = 3y(x^3 + 4x - 3x^2 - 12)[/tex]
The factored expression is:
[tex]3y(x^3 + 4x - 3x^2 - 12)[/tex]
A similar problem is given at https://brainly.com/question/20691631
solve the system by substitution.......
Answer:
x=3
y=15
Step-by-step explanation:
y=5x
y=-4x+27
5x=-4x+27
+4x +4x
9x=27
/9 /9
x=3
y=5x
y=5(3)
y=15
The homecoming dance committee plans to conduct a survey to determine
the student body's opinion on a theme for the dance. Which sampling method
would be most likely to result in nonresponse bias?
A. Handing a survey to all the students who attended the previous
year's homecoming dance
B. Entering a second-period math class and surveying all the
students in that class
C. Standing at the school entrance and surveying every 5th student
that walks in
D. Emailing a survey to all students, but only freshman girls respond
Answer: It's D
Step-by-step explanation:
Answer:
Step-by-step explanation:
Entering a second-period math class and surveying all the students in that class
How many solutions does y=3x+1 and y=x+1 have?
46764need photo ryyiouttgg
A bicycle is originally priced at $80 the store owner gives a discount in the bicycle is know priced at $60 enter the percent markdown for the cost of the bicycle
Answer:
25%
Step-by-step explanation:
Since we know that the markdown is $20 by subtracting 80-60 , we find out what percent of 20 is 80. To do that you do 20/80, which is 0.25, or 25 percent.
Two people share proceeds of a business venture in the ratio 2:3 If the proceeds came to GHS 2,350,000 how much does each get?
Answer:
GHS 940,000 and GHS 1,410,000
Step-by-step explanation:
Total Ratio, thus 2+3 = 5 = 2,350,000
2/5 × 2,350,000 = 940,000
3/5 × 2,350,000 = 1,410,000
In conclusion, the money was shared at GHS 940,000 and GHS 1,410,000 among the two.
13.50 x 8.5????????
help
Answer:
[tex]13.50 \times 8.5 \\ = 13.5 \times 8.5 \\ = 114.75[/tex]
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I
Alex jogged round a 400-m track. He took a total of 16 min to jog 3 rounds of
the same track.
(a)
(b)
Find the total distance that Alex had jogged.
Find Alex's average speed in m/min.
19
Answer: [tex]1200 m[/tex]
[tex]75\ m/min[/tex]
Step-by-step explanation:
Given
Alex Jogged 3 rounds of 400 m track
It took 16 min to Jog 3 rounds
(a) Total distance Alex had Jogged
[tex]\Rightarrow 3\times 400=1200\ m[/tex]
(b) Average speed is the total distance by the total time
[tex]\Rightarrow \dfrac{1200}{16}=75\ m/min[/tex]
If a ball is dropped on the ground from a height of h meters, then the ball reaches the ground with the velocity 4.43h m/sec.
Find the velocity with which a ball reaches the ground when it is dropped from a height of 32 m.
Answer:
v = 141.76 m/s
Step-by-step explanation:
Given that,
The ball reaches the ground with a velocity of 4.43h m/sec.
We need to find the velocity of the ball at a height of 32 m.
Since, v = 4.43h
Put h = 32 m in the above expression.
v = 4.43(32)
v = 141.76 m/s
So, the velocity of the ball is equal to 141.76 m/s.
What is the slope of the line perpendicular to 2x-3y=8
Answer:
y = - [tex]\frac{3}{2}[/tex]x - [tex]\frac{8}{3}[/tex]
Step-by-step explanation:
2x-3y=8
rewrite, solve for y
3y = 2x - 8
divide by 3
y = [tex]\frac{2}{3}[/tex]x - [tex]\frac{8}{3}[/tex]
perpendicular = negative reciprocal slope = - [tex]\frac{3}{2}[/tex]
125 a la octava potencia?
please lo necesito
I need help what do I put in this blank what is the last number
Answer:
8 in
Step-by-step explanation:
? = a
a² + b² = c²
a² + 15² = 17²
a² + 225 = 289
a² = 289 - 225
a² = 64
[tex]\sqrt{a^2} =\sqrt{64}[/tex]
a = 8
It takes 3 hour 15 minutes to fly from city a to city b at constant speed. Find how long the journey takes if
A) the speed is 1×1÷2 times of the original speed and
B) if the speed is three-quarters of the original speed.
Answer:
a) t= 2hours and 10 minutes
b) t=4hours and 20 minutes
v1t1=v2t2
Answer:
Step-by-step explanation:
rate = distance / time distance is constant (a-b) so call it D
time = distance / rate rate = speed (ie miles per hour = mph)
time = distance / speed
A) if the new speed is 1.5 of the original speed
original time = 3.25 hours or 195 minutes
3.25 = D / 1 new time = D/1.5 find new time
3.25 is to D as new time is to D/1.5
3.25/D = new time / D/1.5 multiple D/1.5 on both sides
(3.25/D) ( D/1.5) = new time the distance D cancels
3.25 (D / D) / 1.5 = new time
3.25 / 1.5 = 2.167 hours or 2 hours and 10 minutes
B) if the speed is 3/4 the original speed
original time = 3.25 hours or 195 minutes
3.25 = D / 1 new time = D/(3/4) find new time
3.25 is to D as new time is to D/0.75
3.25/D = new time / D/0.75 multiple D/0.75 on both sides
(3.25/D) ( D/0.75) = new time
3.25 (D / D) / 0.75 = new time
3.25 / 0.75 = 4.333 hours or 4 hours and 20 minutes
A Ferris wheel has a radius
of 72 feet. What is the
distance a passenger will
travel one time around the
Ferris wheel?
Answer:
144
Step-by-step explanation:
radius is half of a diameter so that means you need to multiply 72 times 2
What percent of Miss Colwell's day does she spend watching Netflix if she
watches 4 hours a night?
a) 25%
b) 6%
c) 16.7%
d) 33.33%
A day is 24 hours.
She watches tv 4 out of 24 hours.
4/24 = 1/6 = 0.167 x 100 = 16.7 %
The answer is C. 16.7 %
Please i need help :(
Answer:
Step-by-step explanation:
7 is 1
8 is 2
Heather invested $25,800 in an account that pays 4% simple interest. If she invests the money for 10 years, how much will she have?
Answer:
First, converting R percent to r a decimal
r = R/100 = 4%/100 = 0.04 per year.
Solving our equation:
A = 25800(1 + (0.04 × 10)) = 36120
A = $36,120.00
The total amount accrued, principal plus interest, from simple interest on a principal of $25,800.00 at a rate of 4% per year for 10 years is $36,120.00.
NEED HELP FOR HOMEWORK: Quadrilateral FGHJ was dilated with the origin as the center of dilation to create quadrilateral F' G′ H′ J′.
Which rule best represents the dilation that was applied to quadrilateral FGHJ to create quadrilateral F' G′ H′ J′?
A. (x, y) à (x - 2, y + 1)
B. (x, y) à (1.4x , 1.4y)
C. (x, y) à (x + 1, y + 2)
D. (x, y) à (5/7x, 5/7y)
Answer:
B
Step-by-step explanation:
Without even trying to figure out the solution you can tell it is b, because adding and subtracting to the x's and y's results in a translation. D is wrong because it would result in a smaller figure, so it is B
A fudge recipe calls for 1/2 cup of cocoa if only 1/2 of the recipe is made how much cocoa should be used
Answer:
1/4
Step-by-step explanation:
Answer:
1/4 cup
Step-by-step explanation:
What is the volume of the sphere below?
1.5
O A.
I units3
O B.
17 units 3
units3
500
3
RE
I units3
Answer:
ans is (D)500/3 π unit^3
Explanation :
Formula for volume of sphere is 4/3 π r^3 .
The volume of the sphere below is 500π/3 units³, the correct option is D.
What is the volume of sphere?
If the given sphere is of radius r units, then its volume is given as:
[tex]V= \dfrac{4}{3} \pi r^3 \: \rm unit^3[/tex]
Suppose that radius of the considered sphere is of 'r' units.
Then, its surface area S would be:
[tex]S = 4\pi r^2 \: \rm unit^2[/tex]
We are given that;
The radius = 5
Now,
The volume of a sphere is given by the formula V = ⁴⁄₃πr³, where r is the radius of the sphere1. To find the volume of a sphere whose radius is 5 units, you need to plug in r = 5 into the formula and simplify it using arithmetic operations.
V = ⁴⁄₃πr³
V = ⁴⁄₃π(5)³
V = ⁴⁄₃π(125)
V = (4)(125)π/3
V = 500π/3
Therefore, by the volume of sphere formula the answer will be V = 500π/3 units³.
Learn more about volume of a sphere here:
https://brainly.com/question/381274
#SPJ7
6/7 - 1/3
Your answer
11/21
b/t/w you con go on this website called calculator soup and it has fraction calculators
and the website it self has nothing to download im pretty sure it doesnt
20 POINTS please help
Which ratio represents the probability of taking a red apple from a bag containing 8 red apples, 4 yellow apples, and 3 green apples?
A) 1:15
B) 3.15
C.4:15
D) 8:15
Answer:
D) 8:15
The first thing you do is add up all the apples which equals 15. And then you see how many red apples there are which is 8. Then you write your ratio which is 8:15.
Your answer is D) 8:15
1. Select all the letters below that have a line of symmetry?
A. M
B. V
C. L
D. G
E. D
Answer:
A,M,V
Step-by-step explanation:
Find the value of x.
Answer:
x = 113
Step-by-step explanation:
Since the shape is a quadrilateral, the angles add up to 360 so:
x + 87 + 113 + 47 = 360
x + 247 = 360
x = 360 - 247
x = 113
A fashion designer wants to know how many new dresses women buy each year. A sample of 208 women was taken to study their purchasing habits. Construct the 85% confidence interval for the mean number of dresses purchased each year if the sample mean was found to be 6.2. Assume that the population standard deviation is 1.1.
Answer:
The 85% confidence interval for the mean number of dresses purchased each year is (6.1, 6.3).
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.85}{2} = 0.075[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.075 = 0.925[/tex], so Z = 1.44.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.44\frac{1.1}{\sqrt{208}} = 0.1[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 6.2 - 0.1 = 6.1
The upper end of the interval is the sample mean added to M. So it is 6.2 + 0.1 = 6.3
The 85% confidence interval for the mean number of dresses purchased each year is (6.1, 6.3).
Help please include explanation screenshot attached and brainliest to correct answer
Answer:
x>-8 (Or option D)
Step-by-step explanation:
-2x+7<23 Subtract 7 from both sides
-2x<16 Now divide by -2. You also have to flip the < sign because you are dividing by a negative number
x>-8
The reasoning for D over C is because D is an open circle meaning that it is only less than or greater than. When it is a closed circle, it means less than or equal to or greater than or equal to. :)
Kathryn is 1.6 meters tall. Convert her height to feet. Round to the nearest tenth.
Answer:
1.6 m = 5.3 ft
Help me plz thank you
Answer:
[tex]\text{Axis of symmetry: }x=-2\\\text{Vertex: }x=-2,\ y=10[/tex]
Step-by-step explanation:
[tex]y=-2x^2-8x+2\\\\\text{Solving }y=0:\\-2x^2-8x+2=0\\x=-2\pm\sqrt{5}\text{ (Using the quadratic formula)}\\\\\text{Finding mid-point (x-coordinate):}\\\frac{-2+\sqrt{5}-2-\sqrt{5}}{2}=-2\\\\\therefore\text{Vertex: }x=-2,\ y=10\\\text{Axis of symmetry: }x=-2[/tex]
how many 3/5 are in 5
Answer: the answer is 1.6 or 0.6.
Answer:
8⅓
Step-by-step explanation:
divide 5 by (3/5). To divide by a fraction, flip the fraction and multiply. Make the 5 into a fraction by putting a '1' underneath:
(5/1)(5/3) = 5x5/1x3 = 25/3 = 8⅓
You can take 3/5 away from 5, 8⅓times
Can someone help me find the answer and write a step by step explanation?
Answer: I got 144cm I'm not sure if its right though
Step-by-step explanation:
I did 12x6=72 then I did 72+72=144