Mathematics High School


An expression is shown below:
3x3y + 15xy − 9x2y − 45y

Part A: Rewrite the expression so that the GCF is factored completely. Show the steps of your work. (4 points)

Part B: Rewrite the expression completely factored. Show the steps of your work.

Answers

Answer 1
A]
3x^3y+15xy-9x^2y-45y
=3x^3y+3*5x*y-3*3x^2*y-3*15y
factoring 3y we get:
3y(x^3+5x-3x^2-15)

B]
Factoring the expression we get:
3x^3y+15xy-9x^2y-45y
=3xy(x^2+5)-9y(x^2+5)
=(3xy-9y)(x^2+5)

Related Questions

The original value of a car is 18000, and it depreciates (loses value) by 15% each year. What is the value of the car after three years?

Answers

At the end of each year, the value is 100% -15% = 85% = 0.85 what it was at the beginning of the year. After 3 years, the value is
.. 18,000*0.85^3 = 11,054.25

Find the volume for the regular pyramid.

4 cu. units
6 cu. units
12 cu. units

Answers

4 cu units
Formula is V = lwh/3
v=volume
I=base length
w=base length
h=base height

Answer:

[tex]4\ cu.\ units[/tex]

Step-by-step explanation:

we know that

The volume of the pyramid is equal to

[tex]V=\frac{1}{3}Bh[/tex]

where

B is the area of the base of the pyramid

h is the height of the pyramid

Find the area of the base

[tex]B=2^{2}=4\ units^{2}[/tex]

[tex]h=3\ units[/tex]

Find the volume

[tex]V=\frac{1}{3}(4)(3)=4\ units^{3}[/tex]

Find the ratio of the longest side to the perimeter of the​ right-triangular-shaped billboard. 20 feet 21 feet 29 feet

Answers

29:70

29/70

29 to 70

the ratio is 29 ft. to 70 ft.

Solution:

we have been asked to find the ratio of the longest side to the perimeter of the​ right-triangular-shaped billboard.

Sides of the right-triangular-shaped billboard are 20 feet 21 feet 29 feet.

As we know perimeter is just the sum of all the sides.

Perimeter[tex]=20+21+29=70\\[/tex]

And the longest side is 29 feet.

Hence the required ratio  [tex]=\frac{29}{70}=29:70[/tex]

Soon you will determine the right triangle connection the pythagorean theorem

Answers

I don't know I just need the points Lol sorry

Somebody help. I can’t figure this question out. thanks

Answers

The large triangle and the smaller one are similar. Comparing long sides to short ones, we get
.. (30 mm)/(21 mm) = (14 mm +x)/(14 mm)
.. (14 mm)*10/7 = 14 mm +x
.. (14 mm)*(10/7 -1) = x
.. (14 mm)*(3/7) = x = 6 mm

The value of x is 6 mm.

[tex]21 \div 30 = 14 \div 14 + x[/tex]
[tex]30 \times 14 = 420[/tex]
[tex]21 \times 14 + x = 294 + 21x[/tex]
[tex]420 = 294 + 21x[/tex]
[tex]420 - 294 = 126[/tex]
[tex]126 = 21x[/tex]
[tex]126 \div 21 = 6[/tex]
[tex]x = 6[/tex]

If arc XV = 68° and ∠YUV = 36°, what is the measure of arc VY?

Answers

the complete question in the attached figure

we have
arc XV = 68°
∠YUV = 36°
 
we know that
The measure of the external angle is the semidifference of the arcs that it covers.
therefore
∠YUV =[arc VY-arc XV]/2
arc VY=[2*∠YUV]+arc XV----------> [2*36]+68---------> 140°

the answer is
the measure of arc VY is 140°

how fast is the water level rising in a rectangular fish tank whose base is 20 ft^2 if the tank is being filled at a rate of 0.5ft^3/min

Answers

V = Bh
0.5 ft^3 = (20 ft^2)h
h = (0.5 ft^3)/(20 ft^2) = 0.025 ft

The rate of change of water depth is 0.025 ft/min.

The water level is rising at a rate of 0.025 ft/min.

To determine how fast the water level is rising in the rectangular fish tank, you can use the formula for the volume of a rectangular prism:

V = base area × height

Given that the base area is 20 [tex]ft^2[/tex] and the tank is being filled at a rate of

0.5 cube ft/min, you want to find the rate at which the height (h) is changing  [tex](\frac{dh}{dt} )[/tex].

V = base area × height

[tex]\frac{d V}{d t}=\text { base area } \times \frac{d h}{d t}[/tex]

Substitute the known values:

0.5 = 20 x [tex](\frac{dh}{dt} )[/tex]

Now, solve for [tex](\frac{dh}{dt} )[/tex]

[tex]\frac{d h}{d t}=\frac{0.5}{20}[/tex] = 0.025 ft/min

Thus, the required answer is 0.025 ft/min.

Circle 1: center (8, 5) and radius 6
Circle 2: center (−2, 1) and radius 2
What transformations can be applied to Circle 1 to prove that the circles are similar?
What scale factor does the dilation from Circle 1 to Circle 2 have?
Show your work.

Answers

we have that
Circle 1: center (8, 5) and radius 6
Circle 2: center (−2, 1) and radius 2

we know that
the equation of a circle is
(x-h)²+(y-k)²=r²
for the circle 1---------> (x-8)²+(y-5)²=36
for the circle 2---------> (x+2)²+(y-1)²=4

using a graph tool 
see the attached figure

Part A)What transformations can be applied to Circle 1 to prove that the circles are similar?

we know that
r1/r2---------> 6/2------> 3

to prove that the circle 1 and circle 2 are similar, the radius of circle 1 must be divided by 3 and  translate the center of the circle 1  (10) units to the left and (4) units down  

 the answer part A) is
the radius of circle 1 must be divided by 3 and  translate the center of the circle 1  (10) units to the left and (4) units down  


Part B) What scale factor does the dilation from Circle 1 to Circle 2 have?

the answer Part B) is 
the scale factor is (3/1)

Factor completely: 9ab + 12ax - 6b - 8x (1 point)
1. Prime
2. (3b - 4x)(3a - 2)
3. (3b + 4x)(3a - 2)
4. (3b + 4x)(3a + 2)

Answers

3. (3b + 4x)(3a - 2) is correct.
Use FOIL to expand each factored form, only #3 will result in 9ab + 12ax - 6b - 8x
the correct answer would be C or #3

PLS HELP ME ASAP ON THIS!! THANK YOU SO MUCH!!

BRAINLIEST WILL BE GIVEN



(RANDOM ANSWERS GETS MODERATED.)

Answers

Your picture shows 3 combinations that are sufficient to tell you the price of each item.

The other two are
.. 0 fries + 1 shake + 1 burger = 4.20
.. 1 fries + 1 shake + 0 burger = 2.80

_____
Add any two orders and subtract the third to find the cost of one of the items.
For example add the two orders written above and subtract the one shown in the picture.
.. (1 fries + 2 shakes + 1 burger) - (1 fries + 1 burger) = (4.20 +2.80) -(3.40)
.. 2 shakes = 3.60
.. 1 shake = 1.80
Then the last equation tells you
.. 1 fries = 2.80 - 1 shake = 1.00
and the first equation tells you
.. 1 burger = 3.40 - 1 fries = 2.40

1 fries = $1.00
1 shake = $1.80
1 burger = $2.40

trevor needs to let his puppy outside every quarter (1 fourth) hour to potty train him. draw and label a number line from 0 hours to 1 hour to show every 1 fourth hour.

Answers

make a number line and make it into four parts that shows that needs to let his puppy outside every 25 min.

Given that the points (-3, 8), (2, 8), (2, -2), and (-3, -2) are vertices of a rectangle, what is the ratio of the rectangle's length to its width?

Answers

let
A ---> (-3, 8)
B ---> (2, 8) 
C----> (2, -2) 
D----> (-3, -2)

step 1
find the distance AB
d=√[(y2-y1)²+(x2-x1)²]-----> d=√[(8-8)²+(2+3)²]----> d=√25-----> d=5 units

step 2
find the distance BC
d=√[(y2-y1)²+(x2-x1)²]-----> d=√[(-2-8)²+(2-2)²]----> d=√100-----> d=10 units

step 3
find the ratio of the rectangle's length to its width
ratio=rectangle's length/rectangle's width
length=10 units
width=5 units
ratio=10/5-----> ratio=2

the answer is 
 the ratio of the rectangle's length to its width is 2

see the attached figure

Answer:

2:1

Step-by-step explanation:

Regard triangleTRI and the following facts:
Segment IR || Segment NA
TA= 12 cm, RA= 3 cm, NT= 18 cm, AN= 22

(a)What theorem or postulate proves Triangle ANT similar to RIT?(b)Solve for NI by using the Side-Splitting Theorem.Show all work.(c)What is the scale factor for similar triangles ANT and RIT?
(d)Calculate RI. Show your work.
(e)What is the ratio of the areas of the two triangles? Show your work.

Answers

A) Using the side-splitter theorem we know that the sides that are intersected by the parallel lines are proportional.  It can also be shown that the angles are congruent due to the parallel segments cut by a transversal.
B) NI = 4.5
C) 4:5
D) RI = 27.5
E) 16:25

Explanation
We will set up a proportion for b:
AT/RT = NI/TI
12/15 = 18/x

Cross multiply:
12*x = 18*15
12x = 270

Divide both sides by 12:
12x/12 = 270/12
x = 22.5

Since TI = TN + NI, we have
22.5 = 18 + NI
-18       -18
4.5 = NI

C) The ratio of the sides of the smaller triangle to the larger rectangle are given by the ratio AT/RT, or 12/15 = 4/5.

D)  Setting up a proportion we have
AN/RI = AT/RT
22/RI = 12/15

Cross multiply:
22*15 = RI*12
330 = 12RI

Divide both sides by 12:
330/12 = 12RI/12
RI = 27.5

E)  The ratio of the areas will be the square of the ratio of the side lengths, since area is a square measurement:
(4/5)² = 4²/5² = 16/25

Is the mean always a more accurate measure of center than the median

Answers

I want to say yes it is but it's been a little while since I have learned this

find the exact value of cos285 using the fact that 285=330-45

Answers

[tex]\bf \textit{Sum and Difference Identities} \\\\ cos(\alpha - \beta)= cos(\alpha)cos(\beta) + sin(\alpha)sin(\beta)\\\\ -------------------------------\\\\ cos(285^o) \\\\\\ cos(330^o-45^o)=cos(330^o)cos(45^o)+sin(330^o)sin(45^o) \\\\\\ cos(330^o-45^o)=\left( \frac{\sqrt{3}}{2} \right)\left( \frac{\sqrt{2}}{2} \right)~~+~~\left( \frac{1}{2} \right)\left( \frac{\sqrt{2}}{2} \right) \\\\\\ cos(330^o-45^o)=\cfrac{\sqrt{6}}{4}+\cfrac{\sqrt{2}}{4}\implies cos(330^o-45^o)=\cfrac{\sqrt{6}+\sqrt{2}}{4}[/tex]

can someone help me with this?

Answers

It's C.

I did it by plugging the functions into a graphing calculator and seeing which one matched, but you could also plug in 2 or 3 values into each x position and see which one's results matched with the shown function.

please help me thank you.

Answers

The length of an arc (s) is given in terms of the circle radius (r) and the central angle (θ) by
.. s = rθ . . . . . . . . . . . θ in radians

Your arc length is
.. s = (5 m)*(2π/3)
.. = 10π/3
.. ≈ 10.47 m

The 3rd selection is appropriate.

Where is the centroid of any given triangle?
A. the point of concurrency of the altitudes of the triangle.
B. the point of concurrency of the medians of the triangle.
C. the point of concurrency of the perpendicular bisectors of the triangle.
D. the point of concurrency of the angle bisectors of the triangle.
Which of the following best describes the altitude of a triangle?
A. a segment perpendicular to a side of the triangle.
B. a segment that passes through the midpoint and is perpendicular to a side of a triangle.
C. a segment drawn from the ve

Answers

 The answers are the following:

1. The centroid of any given triangle is at B. the point of concurrency of the medians of the triangle. It is a point is where the three points of the medians of the triangle meet.

2. B. a segment that passes through the midpoint and is perpendicular to a side of a triangle. It is line segment that is perpendicular to a line containing the base 

Cheryl volunteers to mow the lawn at a retirement home.She can mow 1/4 of the lawn in 3/4 of an hour .At what rate ,how many hours will it take Cheryl to mow the entire lawn

Answers

It will take three hours to mow the grass.
Hey there!

Since she mows 1/4 in 3/4 hours, you can multiply 4 and 3/4 . . .

4 = 4/1

3/4 = 3/4

4 x 3 = 12

1 x 4 = 4

Simplifying 12/4 . . .

12/4 = 3  <---------

It will take 3 hours for Cheryl to mow the entire lawn.

Hope this helps you.
Have a great day!

A cell phone weighs about 2.8X10^n pounds. Which value of n is most reasonable? A)-3 b)-1 c)0 d)1
please help im stuckk

Answers

The average cell phone weighs about 4 ounces, or 0.25 pounds... 0.28 is closest to this number.

2.8 * 10^-3 = 0.0028 - Much too light

2.8 * 10^-1 = 0.28 - Reasonable weight

2.8 * 10^0 = 2.8 - Too heavy

2.8 * 10^1 = Much too heavy
Just plug in every value and see if it's a reasonable weight for a cell phone.

[tex]\sf 10^{-3}=0.001[/tex]
[tex]\sf 10^{-1}=0.1[/tex]
[tex]\sf 10^0=1[/tex]
[tex]\sf 10^1=10[/tex]

[tex]\sf 2.8\times 0.001=0.0028[/tex]
[tex]\sf 2.8\times 0.1=0.28[/tex]
[tex]\sf 2.8\times 1=2.8[/tex]
[tex]\sf 2.8\times 10=28[/tex]

So what is the most reasonable weight for a cell phone? 0.0028 pounds, 0.28 pounds, 2.8 pounds, or 28 pounds? I would definitely say 0.28 pounds.

4) A mountain climber climbed up a cliff 1/4 mile at a time. he did this 5 times in one day. How many miles did he climb up? *

Answers

He climbes 1 1/4 miles.
1/4+1/4+1/4+1/4+1/4= 1 1/4.

Explain what needs to happen to the inequities sign when dividing or multiplying by a negative number

Answers

Inequality symbols need to be reversed when multiplying or dividing by a negative number, because that reverses the ordering of values.
2 > 1
-2 < -1 . . . . . multiplied or divided by -1

___
A more "interesting" case is when a function is applied that has a negative slope.
0 < a < b < π
cos(0) > cos(a) > cos(b) > cos(π)

Laila is having shirts made with a logo printed on them to promote her band. The total cost consists of a one-time fee of $75 to have the logo designed, plus $8 per shirt to print the logo. Write an equation that Laila can use to determine the total cost c, in dollars, to make x shirts

Answers

c=8x+75 c is equal to cost and x is equal to the amount of shirts

A die is tossed. Find the odds against rolling a number greater than 4.
*the probability of rolling a # greater than 4 is 1/3.
*the probability that the event doesn't occur is 2/3.

What is the ratio?

Answers

The chance of rolling a number greater than 4 (a 5 and 6) is 2/6 = 1/3 after simplification. The probability it WON'T happen is 1 - 1/3 = 2/3. 
 The ratio of against to for is 2/3:1/3
 You can further simplify this ratio by multiplying each side by 3 and yielding
 2:1.
 The chance of it not happening is twice as likely as it is to roll a number greater than 4

What is the simplified form of (x – 2)(2x +3)? Use the Distributive Property. (1 point)
2x2 – x – 6
2x2 – 6
2x2 – 7x – 6
2x2 + x – 6
2. What is the simplified form of (3x + 2)(4x – 3)? Use a table. (1 point)
12x2 + 18x + 6
12x2 + x – 6
12x2 + 18x – 6
12x2 – x – 6
3. What is the simplified form of (4p – 2)(p – 4)? (1 point)
4p2 + 6p – 16
4p2 – 18p + 8
4p2 – 14p – 6
4p2 – 6p + 16
4. The radius of a cylinder is 3x – 2 cm. The height of the cylinder is x + 3 cm. What is the surface area of the cylinder? Use the formula A = 2r2 + 2rh.,

Answers

1. 2x2 – x – 6
2. 12x2 – x –6
3. 4p2 – 18p + 8

A rectangle is 7 feet long by 2 feet wide. If 2 feet are added to the length of the rectangle, what would be the area, in square feet, of the new rectangle?

Answers

it would be 9 x 2 so the area would be 18 sq ft

If a rectangle is 7 feet long by 2 feet wide and  2 feet are added to the length of the rectangle then the area of rectangle is 18 square feet.

What is Area of Rectangle?

The area of Rectangle is length times of width.

Given that a rectangle has a length of 7 feet.

The width of rectangle is 2 feet.

We have to find the area of rectangle when 2 feet is added to the length of rectangle

Initial length is 7 feet

When 2 feet is added the length will be 7+2, 9 feet.

Area of rectangle = Length × width

=9×2

Nine times two is eighteen.

=18 square feet.

Hence, if a rectangle is 7 feet long by 2 feet wide and  2 feet are added to the length of the rectangle then the area of rectangle is 18 square feet.

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A horizontal line goes through the point (–7,10). Which statements are true about this line? Check all that apply. The slope of the line is zero. Another point on the line is (3,10). The y-intercept of the line is –7. The equation of the line is y = 10.

Answers

A. The slope of the line is zero. True
All horizontal lines have a slope of 0

B. Another point on this line is (3,10). True
All points on this line have a y coordinate of 10

C. The y intercept of the line is -7. False
The y intercept is 10 which is at the point (0,10)

D. The equation of the line is y = 10. True
The equation y = 10 indicates all y coordinates are 10 while the x coordinate is anything you want.

------------------------------------------------------------------------

Answers are: A, B, and D

The statement 1,2, and 4 are true and 3 is not true below given the reason behind it.

What is a graph?

The link between lines and points is described by a graph, which is a diagrammatic representation of a network.

A graph is made up of some points and the distance between two It doesn't matter how much time the lines are or where the points are located. A node is a name for each constituent in a graph.

The given statement is a line passing through ( -7, 10 ) so

Option 1 ⇒ the slope of that line will be zero because it is a horizontal line so it will be true.

Option 2 ⇒another point on this line will be (3,10) since it is a horizontal line so the y coordinate is the same and the x coordinate can vary so it is also true.

Option 3 ⇒ the y-intercept of this line will be 10 which is not true and can be confirmed by options 1 and 2.

Option 4 ⇒ the equation of the line will be y =10 which is true hence it is a horizontal line.

For more details about the graph

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Which ordered pair is a solution for this system of inequalities?
2x + 3y > 1 and y < 5/4 x - 1

A.(3, 9)
B.(-4, 2)
C.(8, -1)
D.(-2, -5),

Answers

C. (8, -1)

For this problem, the easiest method is to simply try each of the 4 possible answers and see which one fits. So
A. (3, 9)
2x + 3y > 1
2*3 + 3*9 > 1 ; Obviously true, not going to finish calculation.

y < 5/4 x - 1
9 < 5/4 3 - 1
9 < 15/4 - 1 ; Obviously false, not going to finish calculation.

B. (-4, 2)
2x + 3y > 1
2*(-4) + 3*2 > 1
-8 + 6 > 1 ; Obviously false, not going to finish calculation.
No need to bother with 2nd inequality.


C. (8, -1)
2x + 3y > 1
2*8 + 3*(-1) > 1
16 - 3 > 1 ; Obviously true, not going to finish calculation.


y < 5/4 x - 1
-1 < 5/4 * 8 - 1
-1 < 40/4 - 1
-1 < 10 - 1 ; Obviously true, not going to finish calculation.
Both inequalities satisfied, this is the correct choice.

D. (-2, -5)
2x + 3y > 1
2*(-2) + 3*(-5) > 1; Left hand side is obviously negative, so obviously false,
not going to finish calculation.
No need to bother with 2nd inequality.

A circular piece of glass has a radius of 2.1 meters. The glass sells for $1.70 per square meter. What is the total cost of the circular piece of glass?

$23.54


$94.16


$3.57


$11.21

Answers

the answer is $3.57 because $1.70x 2.1 is $3.57 

Jose owns 40 shares of stock A whose price increased by $0.75 per share. He also owns 100 shares of stock B whose price decreased by $0.20 per share. What is the total change in the value of Paul’s stock (A and B together)?


PLEASE HELP!

Answers

it will increase the current value.
40*$0.75 +100*(-$0.20) = $30 -20 = $10

Paul's portfolio increased in value by $10.
Other Questions
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