Part A: The area of a square is (25x2 − 10x + 1) 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 (81x2 − 9y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work. (5 points)

Answers

Answer 1
Before getting started, let's look at notation. My guess is that by (25x2-10x+1) you mean "25 x squared plus 10x plus 1." Usually to show the exponent (x squared) we use  the ^ symbol so that means for Part A you are being asked to factor 25x^2 -10x + 1. We can also use a program like equation editor (part of Word) so that the expressions look like they would if you wrote then by hand in your notebook. I will do PART A using "^" and PART B using an editor that will make the notation look as it does in your notebook so you see both ways.

PART A:
As the expression given is the area of a square (and in a square the sides are all of equal length) when we factor (write as a product) this expression we should get two identical factors. If you remember how to distribute twice (teachers usually use the term F.O.I.L.) this question is asking you to go backwards...the expression is what you get when you "FOIL" so what were the two terms before?

25x^2 --> What can you multiply to get 25x^2? Since the terms have to be identical that's 5x. That is (5x)(5x) gives 25x^2.

Next we look at the last term (1) and think what can you multiply by itself to get 1? That's 1 as (1)(1)=1.

This means that the expression 25x^2 -10x + 1 = (5x+1)(5x+1) = (5x+1)^2.
The side of the square is 5x+1

PART B:
Here you are asked to factor [tex]81 x^{2} -9 y^{2} [/tex]. You might notice that [tex]81 x^{2}[/tex] is a perfect square. [tex]81 x^{2} =(9x)(9x)[/tex]. Similarly, [tex]9 y^{2} =(3y)(3y)[/tex]. We are dealing with the difference (notice the subtraction sign between the terms) of squares.

How do we factor the difference of squares? It is: (square root of first term + square root of second term)(square root of first term - square term of second). In symbols it is: [tex] a^{2} - b^{2} =(a+b)(a-b)[/tex].

In our case, we get [tex]81 x^{2} -9 y^{2} =(9x+3y)(9x-3y)[/tex].

If you forget or don't see that it is the difference of squares you can still figure it out by reasoning it out. What two terms give you the first when multiplied and what two terms give you the second?



Related Questions

You want to buy a jet ski 5 years from now, and you plan to save $600 per year, beginning today. you will deposit your savings in an account that pays 8% interest. how much will you have 5 years from now?

Answers

600(1+0.08/5)^5=649560.3
The valur of Rs 600will decline to 649560.3in 5 years interest is 8%

Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. The Balance after the fifth year from now is 3801.56.


What is simple interest?

Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,

SI = PRT

where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.

The balance in the accounts can be calculated as,

Balance after the first year,

A = 600×(1.08) = 648

Balance after the second year,

A = (600+648)(1.08) = 1248(1.08) = 1347.84

Balance after the third year,

A = (1347.84+600)(1.08) = 1947.84 (1.08) = 2103.67

Balance after the fourth year,

A = (2103.67+600)(1.08) = 2703.67 (1.08) = 2919.96

Balance after the fifth year,

A = (2919.96+600)(1.08) = 3519.96 (1.08) = 3801.56

Hence, the Balance after the fifth year from now is 3801.56.

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Two events, X and Y, are independent of each other. P(Y) = 5/6 and P(X and Y) = 1/3. What is P(X) written as a decimal? Round to the nearest tenth, if necessary.

Answers

For independent events,
P(X ∩ Y) = P(X)* P(Y)
=>
1/3 = P(X)*(5/6)
solve for P(X) =>
P(X) = (1/3)*(6/5) = 2/5 = 0.4

Answer:option C

Step-by-step explanation: edge

you have a large container of olive oil. You have used 22 1/2 quarts of oil. Twenty-five percent of the olive oil remains. How many quarts of olive oil remain?

Answers

Solution:

we are given that

You have a large container of olive oil. You have used [tex]22 \frac{1}{2}[/tex] quarts of oil.

Twenty-five percent of the olive oil remains.

we have been asked to find how many quarts of olive oil remain?

Let there were x quarts of olive oil.

It mean , we can write

[tex]x-22 \frac{1}{2}=\frac{1}{4}*x[/tex]

[tex]x-\frac{1}{4}*x=22 \frac{1}{2}[/tex]

[tex] \frac{3x}{4}=22 \frac{1}{2}[/tex]

[tex] 3x=4*22 \frac{1}{2}[/tex]

[tex] x=\frac{4}{3}* \frac{45}{2}[/tex]

[tex] x=30[/tex]

Hence quarts of olive oil remain [tex] =30-\frac{45}{2}=\frac{15}{2}=7\frac{1}{2}[/tex]

When ordering hot cocoa, Jackson is asked if he wants milk chocolate, dark chocolate, or chocolate mint flavor. He also must choose between a small or large mug, and has the option of adding marshmallows. How many ways can Jackson order his hot cocoa? A). 10
B).6
C).7
D).12

Answers

There are 12 ways that Jackson can order his hot cocoa.
So, the answer is 12.

i hope this helps :)

There are 12 ways Jackson can order his hot cocoa by choosing from three flavors, two mug sizes, and the option of adding marshmallows. Option D is correct,

To find the total number of ways Jackson can order his hot cocoa, we need to consider all the possible combinations of choices he has.

1. Flavor: Jackson has 3 options: milk chocolate, dark chocolate, or chocolate mint flavor.

2. Mug Size: Jackson has 2 options: small or large mug.

3. Marshmallows: Jackson has 2 options: with or without marshmallows.

To find the total number of combinations, we multiply the number of options for each choice:

[tex]\[ \text{Total combinations} = \text{Number of options for flavor} \times \text{Number of options for mug size} \times \text{Number of options for marshmallows} \]\[ \text{Total combinations} = 3 \times 2 \times 2 \]\[ \text{Total combinations} = 12 \][/tex]

So, there are 12 ways Jackson can order his hot cocoa. Therefore, the correct answer is option D) 12.

Round 6 4/9 to nearest whole number

Answers

6.0
4/9 is .44444 so round down not up
Check to see if 4/9 is greater than 0.5
4/9 = 0.4444444 which is less than 0.5
The closest whole number is 6.

Is 2 miles greater too 3,333 yards or is 3,333 yards greater than 2 miles?

Answers

2 miles = 3,520 yd
So 2 miles is greater than 3,333 yd
Hope this helps:D
have a great rest of a brainly day!
"AB84"

Engineers must consider the breadths of male heads when designing motorcycle helmets. men have head breadths that are normally distributed with a mean of 6.0 in and a standard deviation of 1.0 in. (based on anthropometric survey data from gordon, churchill, et al.). if one male is randomly selected, find the probability that his head breadth is less than 6.2 in. use 4 decimals for your answer.

Answers

Answer: 0.9772 (the answer above wasn't the right one;)


Using z-score formula, the probability that a male's head breadth is less than 6.2 inches, would be approximately 57.9261%.

What is z-score formula?

When you have multiple samples and want to describe the standard deviation of those sample means (the standard error), you would use this z score formula:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

This z-score will tell you how many standard errors there are between the sample mean and the population mean.

We have been given that men have head breadths that are normally distributed with a mean of 6.0 inches and a standard deviation of 1.0 inches. We are asked to find the probability that a man's breadth is less than 6.2 inches.

First of all, we will find z-score corresponding to sample score of 6.2 as:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

where,

z = Z-score,

x = Sample score,

[tex]\mu[/tex] = Mean,

[tex]\sigma[/tex] = Standard deviation.

Upon substituting our given values in z-score formula, we will get:

[tex]z=\frac{6.2-6.0}{1.0}[/tex]

[tex]z=\frac{0.2}{1.0}[/tex]

z = 0.2

Now, we need to find the probability that a z-score is less than 0.2.

Using normal distribution table, we will get:

P(z < 0.2) = 0.57926

0.579261 ≈ 57.9261 %

Therefore, the probability that a male's head breadth is less than 6.2 inches, would be approximately 57.9261%.

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solve.
[tex] \sqrt{3 x - 11} - \sqrt{x} + 5 = 6[/tex]

Answers

Solve for x:
5 - sqrt(x) + sqrt(3 x - 11) = 6

Subtract 5 from both sides:
sqrt(3 x - 11) - sqrt(x) = 1

(sqrt(3 x - 11) - sqrt(x))^2 = -11 + 4 x - 2 sqrt(x) sqrt(3 x - 11) = -11 + 4 x - 2 sqrt(x (3 x - 11)) = 1:
-11 + 4 x - 2 sqrt(x (3 x - 11)) = 1

Subtract 4 x - 11 from both sides:
-2 sqrt(x (3 x - 11)) = 12 - 4 x

Raise both sides to the power of two:
4 x (3 x - 11) = (12 - 4 x)^2

Expand out terms of the left hand side:
12 x^2 - 44 x = (12 - 4 x)^2

Expand out terms of the right hand side:
12 x^2 - 44 x = 16 x^2 - 96 x + 144

Subtract 16 x^2 - 96 x + 144 from both sides:
-4 x^2 + 52 x - 144 = 0

The left hand side factors into a product with three terms:
-4 (x - 9) (x - 4) = 0

Divide both sides by -4:
(x - 9) (x - 4) = 0

Split into two equations:
x - 9 = 0 or x - 4 = 0

Add 9 to both sides:
x = 9 or x - 4 = 0

Add 4 to both sides:
x = 9 or x = 4

5 - sqrt(x) + sqrt(3 x - 11) ⇒ 5 - sqrt(4) + sqrt(3×4 - 11) = 4:
So this solution is incorrect

5 - sqrt(x) + sqrt(3 x - 11) ⇒ 5 - sqrt(9) + sqrt(3×9 - 11) = 6:
So this solution is correct

The solution is:
Answer:  x = 9

Ted researched the price of airline tickets and discovered a correlation between the price of a ticket and the number of miles traveled. After recording his data on a scatter plot, he determined the equation for the line of best fit is y = 300 + 0.45x. How can you tell from the equation that the correlation between the cost of a plane ticket and the number of miles traveled is positive? What does a positive correlation tell you about the dependent and independent variables?

Answers

D) the expected change in price of the ticket for each mile traveled
.45 represents a positive slope... if you are using usatestprep it should be D

Please help!!! Will get brainliest!!! For b.Zoom in.

Answers

the answer is 1/30 1:30 are both correct because you have 30 choices and only 1 of those is the 4 so 1/30

How does one find the equation y=ax²+bx+c when you are only provided with the coordinates of the turning point, (-6,-9)? Note: a is +1 or -1

Answers

Start with vertex form and eliminate parentheses.
.. y = a(x -h)^2 +k . . . . . . where (h, k) is the vertex
The value of "a" will be greater than zero if the parabola opens upward, as shown.

Using this form, your equation is
.. y = 1*(x +6)^2 -9
.. y = x^2 +12x +36 -9
.. y = x^2 +12x +27 . . . . . . the desired form

Write two equivalent fractions for 2/3

Answers

8/12
and 10/15
 They both equal 2/3 when they reduce


Hope this helped you:)

Suppose a family starts out 50 miles from home at time t = 0. They travel away from home at a constant speed of 45 miles an hour. What's the equation that tells you how far they'll be from home t hours later? (Assume d is distance in miles.) A. d = 45t + 50 B. d = 45t C. d = 50t D. d = 50t + 45

Answers

50 miles, t=0 is the start
45 miles each 1 hour

A. d= 45•t+50
At t = 0  d = 50.
At time = 1 hour , d = 50 + 45(1)
At time = 2 hours, d = 50 + 45(2)

So its d = 50 + 45t  or  d = 45t + 50

Choice A is the correct one.

The area of a trapezoid is found using the formula A=1/2h(b^1+b^2), where b^1 and b^2 are the parallel sides of the trapezoid and h is the height. The area of a trapezoid is 18km^2 , with bases 5 km and 7 km. What is the height, in

Answers

The height is 0.666 kilometers or 666 meters

Answer:

40

Step-by-step explanation:

Just did it on Time4Learning. Please give brainliest.










Which equation has solution x = -3?
A) 2x - 7 = -1
B) 3x + 8 = 1
C)
1
2
x + 8 = 10
D)
1
2
(2x - 6) = -6

Answers

The answer is C

for X=-3

The answer is C.
X= -3

Luca has a box of dog toys. There are 3 bones, 5 balls, and a stuffed animal. What is the ratio of balls to stuffed animals?

Answers

5:1 is your answer, 
Hope this helps :)

Answer:

5.1

Step-by-step explanation:

I Has This Study Island Before

the equation of a line that goes through the points (0,0) and (300000,365)

Answers

[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 0 &,& 0~) % (c,d) &&(~ 300000 &,& 365~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{365-0}{300000-0}\\\\\\ \cfrac{365}{300000}\implies \cfrac{73}{60000}[/tex]

[tex]\bf \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-0=\cfrac{73}{60000}(x-0)\implies y=\cfrac{73}{60000}x[/tex]

dividing mixed fractions

Answers

a) 2 1/3 = 7/3
   7/3 / 1/4 = 7/3 x 4/1 = 28/3 = 9 and 1/3

b) 4 2/5 = 22/5
   1 1/5 = 6/5
22/5 / 6/5 = 22/5 x 5/6 = 110/30 = 3 and 2/3

In a game, the two players scored a total of 121 points. One player had 13 more points than the other player.  How many points did the player with the fewer points score?

Answers

We are going to write the following variables:
 x: points for player 1
 y: points for player 2
 We write the following system of equations:
 x + y = 121
 y = 13 + x
 Solving the system we have:
 Step 1:
 x + (13 + x) = 121
 2x + 13 = 121
 x = (121-13) / (2)
 x = 54
 Step 2:
 y = 13 + 54
 y = 67
 Answer:
 the player with the fewer points scores 54 points

2 (x-4)=22
[tex]2(x - 4) = 22[/tex]

Answers

[tex]\bf 2(x-4)=22\implies x-4=\cfrac{22}{2}\implies x-4=11\implies x=11+4 \\\\\\ x=15[/tex]

Answer:

x=15

Step-by-step explanation:

To get the answer I thought, what times 2 equals 22 and i got 11. 15-4=11. so i figured x=15.

Will ran four miles on his first day of training. The next day he ran one-third that distance. How far did he ran the second day?

Answers

4/1 times 1/3 is 4/3 or 1 1/3 miles on the second day of training.
To solve, we multiply the distance he ran on the first day by 1/3. This lets us find out how far he ran the second day.

4mi*1/3=1 1/3mi

Will ran 1 1/3 miles on the second day.

HURRY PLEASE!!!! I WILL GIVE BRAINLIEST!!!!!!!


A school sold small and large boxes of fruit for a fundraiser. One student sold 5 small boxes and 13 large boxes for $232. Another student sold 12 small boxes and 7 large boxes for $218. Their sales can be represented in two equations where x represents the price of the small boxes and y represents the price of the large boxes. Which constants can be multiplied by the equations so one variable will be eliminated when the systems are added together? Check all that apply.


1 The first equation can be multiplied by –12 and the second equation by 5 to eliminate x.

2 The first equation can be multiplied by 5 and the second equation by 12 to eliminate x.

3 The first equation can be multiplied by –7 and the second equation by 13 to eliminate y.

4 The first equation can be multiplied by 7 and the second equation by –13 to eliminate y.

5 The first equation can be multiplied by 12 and the second equation by –5 to eliminate x.

6 The first equation can be multiplied by 7 and the second equation by 13 to eliminate y.

Answers

Answer:

A,C,D,E

Step-by-step explanation:

An equation is formed of two equal expressions. The correct options are 1, 3, 4, and 5.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given that One student sold 5 small boxes and 13 large boxes for $232. Another student sold 12 small boxes and 7 large boxes for $218. Also, x represents the price of the small boxes and y represents the price of the large boxes. Therefore,

The equation for the first student can be written as,

5x + 13y = 232

The equation for the second student can be written as,

12x + 7y = 218

Now, the multiplication that can be done to eliminate the variables are,

1.) The first equation can be multiplied by –12 and the second equation by 5 to eliminate x.

3.) The first equation can be multiplied by –7 and the second equation by 13 to eliminate y.

4.) The first equation can be multiplied by 7 and the second equation by –13 to eliminate y.

5.) The first equation can be multiplied by 12 and the second equation by –5 to eliminate x.

Hence, the correct options are 1, 3, 4, and 5.

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Steve opened a bank account.he plans to deposit $35 every month.write an equation that models the total amount of money,t,deposited after m months

Answers

35m because 35 dollars multiplied by m months

A pizza parlor uses square prisms for their pizza boxes. Due to the crust rising, the height of their boxes is always 2 inches. Additionally, the volume of the pizza box must be 450 cubic inches to fit their standard-sized pizza. A worker determined that the equation below could be used to find the side length, x, of the box needed to reach that volume.

Answers

We are to find the side length of the box

Volume = Length * Breadth * Height


Volume of box = 450 cubic inches

Height of box = 2 inches

Length of box = x

Since it is a square prism, Breadth = Length = x


Therefore,

Volume = Length * Breadth * Height

⇒ 450 = 2 * x * x

⇒ 450 = 2x²

⇒ 2x² = 450


Divide the equation by 2

2x²/2 = 450/2

x² = 225

⇒√x² = √225

x = 15

The side length of the box is 15 inches


Answer:

The solutions are -15 and 15, but only 15 is a reasonable side length.

Step-by-step explanation:

Got it right on the test.

6 surfaces 2 small stand tall what shape

Answers

its called a rectangular prism

I hope this helps

A gift box in the shape of a triangular prism has a volume of 36 cubic inches, a base height of 4 inches, and a height of 3 inches. What is the length of the base?

Answers

Answer:

6 inches is the base

Step-by-step explanation:

So you have to think back to what the formula to volume is. From there plug in numbers until you get your answer

Sayed gave an answer of 6 6/7 for the problem 4 2/7 x 1 3/5. using estimates, is this a reasonable answer?

Answers

Answer:
His estimation is correct

Explanation:
First, we will convert the mixed number to fractions as follows:
4[tex] \frac{2}{7} [/tex] = [(7*4)+2] / 7 = [tex] \frac{30}{7} [/tex]

1[tex] \frac{3}{5} [/tex] = [(5*1)+3] / 5 = [tex] \frac{8}{5} [/tex]

Then, we will do the multiplication as follows:
[tex] \frac{30}{7} [/tex] * [tex] \frac{8}{5} [/tex]
 = [tex] \frac{30*8}{7*5} [/tex]
 = [tex] \frac{240}{35} [/tex]
 = [tex] \frac{48}{7} [/tex]

Finally, converting the [tex] \frac{48}{7} [/tex] into a mixed number, we will find that it is equivalent to 6[tex] \frac{6}{7} [/tex]

Hope this helps :)





A classmate believes that a triangle can have both a right angle and an obtuse angle. Which of the following statements would you use to convince him that he is incorrect?

Answers

You can only have obtuse

Sum of internal angles in a triangle is 180 degree.

∠A + ∠B + ∠C = 180°

Now we have three cases:

Case 1 : For right anlge triangle.

in this case one angle is 90°. and rest of two angle's sum is 90 degree

it means measure of rest two anles is less than 90 degree.

So, this type trianlge holds one right anlge and two acute angle.

Case 2: If one angle is Obtuse angle(more than 90°)

In this case , rest of two angle's sum is less than 90°

So, this type trianlge holds one obtuse anlge and two acute angle.

Case 3: All angles are acute

In this case all three anles are less than 90°

So, triangle has one obtuse angle, that means rest of two anlges must be less than 90°


Which is greater 9/8ths or 2 halves?

Answers

The correct answer is  [tex]\frac{9}{8}[/tex] is greater than 2 halves.

To compare 9/8ths and 2 halves, we need to convert them to equivalent fractions with the same denominator, and then compare their numerators.

[tex]\text{Step 1: Convert 2 halves to an equivalent fraction with the denominator of 8}[/tex]

[tex]2\text{ halves} = 2 \times \left(\frac{4}{8}\right) = \frac{8}{8}[/tex]

[tex]\text{Step 2: Compare the numerators of }\frac{9}{8}\text{ and }\frac{8}{8}[/tex]

[tex]\text{Since }9 > 8\text{, therefore, }\frac{9}{8} > \frac{8}{8}[/tex]

Therefore, [tex]\frac{9}{8}[/tex] is greater than 2 halves.

A store advertises that it is offering a 14% discount on all articles purchased at the store. if yao pays $670.80 for an article, what was the marked price for the article?

Answers

The answer is $576.888
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