Part A: The area of a square is (4x2 − 12x + 9) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work. (5 points)

Part B: The area of a rectangle is (16x2 − 9y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work. (5 points)

Answers

Answer 1

Answer:

Step-by-step explanation:

4x² - 12x + 9 = ?

4x² - 12x + 9 = 4x²- 6x - 6x + 9 = 2x

2x(2x - 3) - 3(2x - 3)

(2x - 3)(2x - 3)

(2x - 3)²

Welcome Brazil!!!!

Answer 2

Answer:

Part B: The dimensions are (4x + 3y) and (4x - 3y)

Step-by-step explanation:

our equation is: (16x^2 - 9y^2)

With this equation, we must plug it into the formula: (a + b)(a - b) = a^2 - b^2

so,

a^2 = 16x^2

b^2 = 9y^2

then,

a = sqrt(16x^2) = 4x

b = sqrt(9y^2) = 3y

(these are the correct variables because 3*3 = 9, and 4*4 = 16)

now, we plug this information back into the formula again;

(a + b)(a - b) = (4x + 3y)(4x - 3y)

therefore, (4x + 3y)(4x - 3y) is the answer!

I hope this helps, have a wonderful day!


Related Questions

If three circular metal discs of equal thickness whose radii are 5cm, 20cm and 40cm are melted down to form one circular disc of the same thickness, find its radius.

Answers

Answer: 45 (cm)

Step-by-step explanation:

Since the discs have the same thickness, we will think about the areas.

Let say x the new radius:

[tex]\pi*5^2+\pi*20^2+\pi*40^2=\pi*x^2\\\Longrightarrow\ 5^2+20^2+40^2=x^2\\\\\Longrightarrow\ 2025=x^2\\\\\Longrightarrow\ x=\sqrt{2025} =45[/tex]

6 to the power of 3 times w divided by 6 to the 2nd power

Answers

Answer:

The equation needed to solve your problem is below,...!

Step-by-step explanation:

[tex]6^{3}*\frac{w}{6}^{2}[/tex]

Chow,...!

PLEASE HELP ME WITH THIS QUESTION!!! WILL MARK BRAINLIEST

Answers

Answer:

non-linear, y = -6, x = 2 & x = 6, y = 2 & x = 4, above.

Step-by-step explanation:

The graph is not a straight line so that means that it is linear.

The y-intercept is the point at which the function touches the y-axis, which is at the coordinate point (0, -6), so y = -6.

The x-intercepts are the points at which the function touches the x-axis, which is at x = 2 and x = 6.

The highest y value is y = 2, and it happens when x =4.

Between x = 2 and x = 6, the function is above the x-axis line, so that means it must be above 0.

What least number should be subtracted from 45,632 so that the number is divisible by 100 (plzz answer)

Answers

Answer:

32

Step-by-step explanation:

I don't know if I am correct but if you subtract 32 from 45632 then you will get 45600 which is easily divisible by 100, so your answer is 32

-6+7s-4r-2 use s=7 and r=-7

Simplified

Answers

Answer:

[tex] - 6 + 7s - 4r - 2 \\ \\ - 6 + 7(7) - 4( - 7) - 2 \\ \\ - 6 + 49 + 28 - 2 \\ \\ = 6 9[/tex]

I hope I helped you^_^

IV - SOLVING 1. Find the 7th term in the arithmetic sequence 6, 10, 16, ... Show your solution.​

Answers

Step-by-step explanation:

the distance between 6 and 10 is 4, same distance between 10 to 16 is 6 by the way:

16+8=24

24+10=34

34+12=46

46+14=58 and 58 is 7th term in arithmetic sequence.

I hope it will help you.

Simplify the expression: 63(13−18)+24÷6

Answers

Answer:

-311

Step-by-step explanation:

A farmer plowed 9/10 of a acre in the morning and 1/2 of an acre in the afternoon. How many acres did the farmer plow in all?

Answers

Answer:

7/5

Step-by-step explanation:

Answer:

1[tex]\frac{2}{5}[/tex] of an acre or 1.4 acres.

Step-by-step explanation:

The least common multiple of 10 and 2 is 10.

Convert [tex]\frac{9}{10}[/tex] and [tex]\frac{1}{2}[/tex] to fractions with a denominator of 10.

[tex]\frac{9}{10}[/tex]+[tex]\frac{5}{10}[/tex]

Since these fractions now have the same denominator, add them by adding the numerators.

[tex]\frac{9+5}{10}[/tex]

Add 9 and 5 to get 14.

[tex]\frac{14}{10}[/tex]

Reduce the fraction to the lowest terms by extracting and canceling out 2.

[tex]\frac{7}{5}[/tex]= [tex]1\frac{2}{5}[/tex] =1.4

hope this helps!

8b-4x+5 use b=-2 and x=-9

Simplified is?

Answers

Answer:

[tex]8b - 4x + 5 \\ \\ 8( - 2) - 4( - 9) + 5 \\ \\ - 16 + 36 + 5 \\ \\ = 25[/tex]

I hope I helped you^_^

Answer:

25

Explanation:

Evaluate  [tex]8(-2)-4(-9)+5[/tex]

Determine if the two triangles shown are similar. If so, write the similarity statement.

Options:
A) The triangles are not similar.
B) ΔVML ∼ ΔUTM
C) ΔVML ∼ ΔUMT
D) Impossible to determine.

Answers

Based on the SAS similarity theorem, the right option is: C) ΔVML ∼ ΔUMT.

How to Determine if Two Triangles are Similar?

In order to determine if two triangles are similar, find out if the ratio fo their corresponding side lengths are equal, that is, their lengths must be proportional to each other if they are similar triangles.

What is the SAS Similarity Theorem?

The SAS states that if two pairs of sides of two triangles are proportional to each other, and they have a pair of corresponding congruent included angles, then they are similar triangles.

Given the image showing the two triangles, we have the following measures:

VM = 14, which is corresponding to UM = 49

LM = 8, which is corresponding to TM = 28

VM/UM = 14/49 = 2/7

LM/TM = 8/28 = 2/7

This means the two sides are proportional.

Also, angles VML and UMT are congruent to each other based on the vertical angles theorem.

Therefore, we can state that the ΔVML ∼ ΔUMT by SAS. The right option is C.

Learn more about similar triangles on:

https://brainly.com/question/14285697

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give 2/2 examples of finite,infiniteand empty sets​

Answers

Answer:

[tex]finite \: set \: \\ 1) set \: of \: one \: digit \: whole \: number \\2) set \: of \: number \: of \: players \: in \: a \: cricket \: team \\ infinite \: set \\ 1)set \: of \: all \: whole \: numbers \\ 2) \: set \: o f \: all \: ponts \: in \: a \: line \\ empty \: set \\ 1)set \: of \: whole \: numbers \: between \: 1 \: and \: 2 \\ 2)set \: of \: prime \: numbers \: between \: 3\: and \: 5 \\ thank \: you[/tex]

Dana recorded a temperature drop of 2º and a second temperature drop of 3º. What is the total change in temperature?

Answers

Answer:

1° or 5° i think one of those answer

The total change in temperature is a decrease of 5 degrees Celsius (ºC).

To find the total change in temperature, you simply add the individual temperature drops together.

1. First Temperature Drop: -2º (negative because it's a drop)

2. Second Temperature Drop: -3º (again, negative because it's a drop)

Now add these two drops together:

Total Change in Temperature = (-2º) + (-3º) = -5º

So, the total change in temperature is a decrease of 5 degrees Celsius (ºC).

To know more about change in temperature, refer here:

https://brainly.com/question/30046334

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Lee weighs 130 4/5 pounds. He lost 5.2 pounds then gained 3 pounds. What is Lee's
current weight? Write an expression and solve.

Answers

Answer:

128.6 pounds

Step-by-step explanation:

130 4/5 - 5.2 + 3

=, 128.6pounds

I really need help now

Answers

Answer:

i believe and know the answer is x = - 10

Step-by-step explanation:

i did it on paper dont want to explain i have worked my brain to much

Diyoshana, Hemant and Rupesh got different answers for this problem: {-10-3(10÷2)}-4.

Diyoshana's answer was 1, Hemant's answer was -29, and Rupesh's answer was 21

a). Which student had the correct answer?
b). Show and explain how other two students got their answers. What errors did they make?

My opinion on this:
this is a way to long question

I'm giving 20 points for this​

Answers

Answer:

a)hemant is correct

b) they didn't solve this according to BoDMAS so they got wrong answer

a) The student Hemant's answer -29 is the correct answer, b) The errors they make is the change of sign in the first step.

What is simplification of an expression?

Simplification of an expression is the process of writing an expression in the most efficient and compact form without affecting the value of the original expression. It involves, multiply out the brackets and then simplify the resulting expression by collecting the like terms.

For the given situation,

The expression is {-10-3(10÷2)}-4

⇒ [tex][-10-3(\frac{10}{2} )]-4[/tex]

⇒ [tex][-10-3(5)]-4[/tex]

⇒ [tex][-10-15]-4[/tex]

⇒ [tex][-25]-4[/tex]

⇒ [tex]-29[/tex]

a) The student Hemant's answer -29 is the correct answer.

b) The student Diyoshana did mistake in sign in step 1 as

⇒ [tex][-10+3(\frac{10}{2} )]-4[/tex]

⇒ [tex][-10+15]-4[/tex]

⇒ [tex]5-4[/tex]

⇒ [tex]1[/tex]

The student Rupesh did mistake in sign in step 1 as

⇒ [tex][10+3(\frac{10}{2} )]-4[/tex]

⇒ [tex]25-4[/tex]

⇒ [tex]21[/tex]

Hence we can conclude that a) The student Hemant's answer -29 is the correct answer, b) The errors they make is the change of sign in the first step.

Learn more about simplification of an expression here

https://brainly.com/question/11444405

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PLEASE HELP ILL GIVE 10 POINTS X2

Answers

I’m still thinking about the equation part give me a second

I really need help on this!!!!!
Why is the sum of the interior angles in a triangle different in Euclidean geometry vs Riemannian geometry?

Answers

Answer:

n spherical geometry angles are defined between great circles. ... The sum of the interior angles of a triangle ALWAYS exceeds 180 degrees. In Euclidean Geometry, two lines that intersect form exactly one point. However, in Spherical Geometry, when there are two great circles, they form exactly two intersecting points.

Step-by-step explanation:

Answer:

in riemannian geometry there is only one parallel to the given line.euclud second postulate is a straight line of fininit length that can be continued continuously without bounds

Write the first five terms of a sequence that has 8 as its second term.

Answers

Step-by-step explanation:

im kinda busy can I answer your questions later??

work out the following product,giving your answer as product of prime factor in power a) of the following product is in your answer as a product of prime factor in power 480 x 175 ​

Answers

85.3ft (26m) x 45.93ft (14m).

10 sqrt 45

please show how you did it

Answers

[tex]10\sqrt{45}=10\sqrt{9\cdot5}=10\sqrt{3^2\cdot5}=\\\\=10\cdot3\sqrt5=\boxed{30\sqrt5}[/tex]

if you can figure everything out that amazing,but one by one is alright as well​

Answers

Answer:

x=14°

SEE the IMAGE FOR SOLUTION

420 hg = _____ cg
please help me

Answers

Answer:

420 hg = __4200000___ cg

Step-by-step explanation:

please mark me brainliest

Question is in picture

Answers

[tex]|2x|\geq1\\\\2x\ge1 \ \ \text{or} \ \ 2x\leq-1\\\\\huge\boxed{x\geq\frac{1}{2} \ \ \text{or} \ \ x\leq-\frac{1}{2}}[/tex]

Nevaeh rolls a standard six-sided die, numbered from 1 to 6. Which word or phrase
describes the probability that she will roll a 7?
certain
unlikely
Submit Answer
impossible
likely
DOLL

Answers

Answer:

Step-by-step explanation:

If she had two dice, a seven is the most common roll you can get, although the odds are still against you.

To get a seven with just 1 die is impossible.

IF x=1, y= -3 ,find the value of 5x 2square + 3xy -y 2square ​.
Please help me in full details

Answers

Step-by-step explanation:

sorry man i wish i could help

Can I get a bit of help

Answers

she can count the number of row and the number of square in each row, or she can add 6 and 8

HELPPP PLS THIS IS DUE TOMARRROW

Answers

Answer:

It is second bubble

for explanation

○One

○Two

○Three

○Four

Answer:

(-10)+3 1/2 = -6 1/2

Step-by-step explanation:

It first points to the left. Which means subtracting. It shows that it starts at zero so, keep that in mind. Then it points to the right which means your adding 3 1/2. So you would start at zero and subtract 10. (-10). Then you would add 3 1/2. +3 1/2

(-10) + 3 1/2

To then make -6 1/2

What is the distance between these two points?

Answers

Answer:

Step-by-step explanation:

4,8

Answer: sqrt 145

Step-by-step explanation:

(2,7) (-6,-2)

d = sqrt [(x-x)^2+(y-y)^2]

d = sqrt[(-6-2)^2+(-2-7)^2]

d = sqrt(8^2 + -9^2)

d = sqrt (64+81) = sqrt 145

Here’s a challenge start with the 1st number 15 subtract it by 3 multiply by 4x (solve it too) and then divide or add by 5.70 and explain what you did :) thank you (I’ll mark smartest for whoever does this challenge (btw you guys have over 6 years lol) to answer

Answers

15-3=12
12*48= 576 (x = 48)
576/5.70=101

A 5000​-seat theater has tickets for sale at ​$28 and ​$40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of ​$153,200​?

Answers

Answer:

There are 3,900 tickets of $28 each and 1,100 tickets of $40 each sold.

Step-by-step explanation:

x = the number of $28 tickets

y = the number of $40 tickets

x + y = 5000

28x + 40y = 153200

x = 3,900 tickets

y = 1,100 tickets

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