Factor the polynomial: 8t^2 + 8t - 72

Answers

Answer 1

Final answer:

To factor the polynomial [tex]8t^2 + 8t - 72,[/tex] we first extract the common factor of 8, then factor the trinomial [tex]t^2 + t - 9[/tex] using the technique of finding two numbers that multiply to -72 and add up to 1, which are 9 and -8. Finally, we group and factor by grouping to get the factored form, 8(t - 8)(t + 9).

Explanation:

To factor the polynomial [tex]8t^2 + 8t - 72,[/tex], we will first look for the common factors and then apply factoring techniques. First, we can take out the common factor of 8:

8[tex](t^2 + t - 9)[/tex]

Next, we factor the trinomial inside the parentheses. We need two numbers that multiply to 8 * -9 = -72 and add up to 1. These numbers are 9 and -8. So, we can split the middle term based on these numbers:

[tex]t^2 - 8t + 9t - 9[/tex]

We group the terms to factor by grouping:

[tex](t^2 - 8t) + (9t - 9)[/tex]t(t - 8) + 9(t - 1)

Now we factor out the common binomial factor:

(t - 8)(t + 9)

Therefore, the factored form of [tex]8t^2 + 8t - 72,[/tex] is 8(t - 8)(t + 9).

Related Questions

A science fair poster is a rectangle 3 feet long and 2 feet wide. What is the area of the poster in square inches? Be sure to include the correct unit in your answer.

Answers

Area = length · width
Area = 3ft · 2ft
Area = 6ft²

hope this helps!

Shelby is organizing the 12 prize ribbons she won for athletic competitions. She has twice as many first place ribbons as she does second place ribbons. How many first place ribbons does she have?

Answers

I think she has for because 2x+x=12
3x=12
X=4

I would use the box method to solve this problem. Since she has twice as many, you add the 2 to the 1 to get three. Then you divide the total amount (12) by 3. So, 4 goes in each of the 3 boxes. This tells you that there are 8 first place ribbons and 4 second place ribbons. Hope this helps.

Distance between the points

Answers

To understand the distance formula, you first need to understand the Pythagorean Theorem. For a refresher, the theorem states that the square of the legs of a right triangle is equal to the the square of its hypotenuse (the side opposite the right angle), or in symbols:

[tex]a^2+b^2=c^2[/tex], where a and b are the lengths of the legs, and c is the length of the hypotenuse. In the context of the x-y plane, the legs of the triangle correspond to separate x and y values on the plane, and the hypotenuse corresponds to a straight line between two points on that plane.

To find the distance between the points you've listed, (2√5,4) and (1,2√3), we'll first need to find the "legs" of the triangle. To find the length of the x leg, we'll just need the distance between the x values of the points, which we find to be 2√5-1. We do the same for the y component, which ends up being 4-2√3. Now that we have our legs, we're ready to find the hypotenuse - or the distance.

Going back to Pythagorus's equation, we have:

[tex](2 \sqrt{5}-1)^{2}+(4-2 \sqrt{3})^{2}=d^2 [/tex]

where d, the hypotenuse of the triangle, means "distance."

To solve for d, we take the square root of both sides:

[tex]d= \sqrt{(2 \sqrt{5}-1)^2+(4-2 \sqrt{3} )^2} [/tex]

And from there, all that's left to do is solve the right side of the equation, which just ends up being rote calculation.

Edit: I'll go through the steps of that calculation here. We'll start by expanding each of the squared terms inside the radical:

[tex](2 \sqrt{5}-1)^2=(2 \sqrt{5}-1)(2 \sqrt{5}-1)=(2 \sqrt{5}-1)2 \sqrt{5}-(2 \sqrt{5}-1)[/tex]
[tex]=(2 \sqrt{5})^2-2 \sqrt{5}-2 \sqrt{5}+1=20-4\sqrt{5}+1[/tex]

[tex](4-2\sqrt{3})^2=(4-2\sqrt{3})(4-2\sqrt{3})=(4-2\sqrt{3})4-(4-2\sqrt{3})2\sqrt{3}[/tex]
[tex]=16-8\sqrt{3}-8\sqrt{3}+(2\sqrt{3})^2=16-16\sqrt{3}+12[/tex]

Putting those values back under the radical:

[tex] \sqrt{20-4\sqrt{5}+1+16-16\sqrt{3}+12} [/tex]

Collecting constants:

[tex] \sqrt{49-4\sqrt{5}-16\sqrt{3}} [/tex]

If you wanted an exact answer, this messy-looking thing would be it, and you can verify those results on WolframAlpha if you'd like. If you want an approximation, just enter that expression in to the online calculator of your choice, and it should give out the value of approx. 3.51325.

In general, if you want to solve for the distance between two points [tex](y_{1},x_{1}) [/tex] and [tex] (y_{2},x_{2}) [/tex], the formula is:

[tex]d= \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2} [/tex]

Can y’all plz help me ignore the writing part on the side of it plz show me the steps or tell me

Answers

Hello.

The Manager has concluded that 2 out of 25 light bulbs are faulty.The table he created represents the ratio of bulbs checked and which ones were found faulty.
A way that he could verify that the table is correct is by simplifying each ratio. If each of them turn out to 2:25, then the conclusion is correct.

The best answer that matches this is answer choice "C.)" as it also defines our method of verifying the table's validity (just the order of the ratio is reversed, and that's fine as long as the variables are matching as well). We can further prove that this answer is correct by making ratios of our table and simplifying them;
100:8; divide both sides by 4.
25:2
500:40; divide both sides by 20.
25:2
2,000:160; divide both sides by 80.
25:2
This ratio is always the simplified answer.

Your answer is: "C.)"

I hope this helps!

An art teacher has 192 containers of paint for 17 students. If the teacher wants to provide each student with an equal amount of containers, how many containers will be left over?

Answers

5 Left Each Student Gets 11

192 ÷ 7 = 27 r 3

there will be 3 containers left.

i had no paper so i had to write it on the table. XD haha

Balloons or bust sells balloons in 18 different colors. Each color comes in 3 sizes. They will inflate the balloon and tie on a gold, green, red,blue, pink or purple ribbon. How many different choices are there?

Answers

There are 270 different combonations
18x5x3=270

a utility bill shows that a household use 2001 gallons of water in a 5-day period. what was the average amount of water used by the households each day

Answers

400.2 is the average amount of water used each day

A telecommunication company has 7 satellites, two of which are sending a week signal. If two are picked at random without replacement, find the probability that both are sending a week signal

Answers

2/7 is the probability that the first satellite sends a weak signal. That leaves 6, one of which sends a weak signal. So the probability that the second also sends a weak signal is 1/6. Combine these and we get 2/7×1/6=1/21.

Hence, the probability that both are sending a weak signal is [tex]\frac{1}{21}.[/tex]

What is probability?

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

The probability of an event is a number between [tex]0[/tex] and [tex]1[/tex], where, roughly speaking, [tex]0[/tex] indicates the impossibility of the event and [tex]1[/tex] indicates certainty.

Since, [tex]\frac{2}{7}[/tex] is the probability that the first satellite sends a weak signal.

And leaves six, and one is sending a weak signal.

So, the probability that the second also sends a weak signal it has the probability [tex]\frac{1}{6}[/tex].

By Combining these and we get

[tex]\frac{2}{7}[/tex]×[tex]\frac{1}{6}[/tex] = [tex]\frac{1}{21}[/tex] .

Hence, the probability that both are sending a weak signal is [tex]\frac{1}{21}.[/tex]

To know more about probability

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Which expression results on a rational number?

Answers

where are the answers

Which symbol correctly compares the two fractions use <, > or = 2/4 and 3/8

Answers

2/4>3/8_________________________________________

2/4>3/8———————-____________________________

An international company has 13,600 employees in one country. If this represents 19.3% of the company's employees, how many employees does it have in total?

Answers

Hi there! To solve this question, we can write and solve a proportion. Let’s set it up like this: 13,600/x = 19.3/100. We do this, because we’re looking for the total amount of people, which would be the whole. We already have the part. Cross multiply the values in order to get 1,360,000 = 19.3x. Now, divide each side by 19.3 to isolate the variable. When you do, you get x is approx. 70,466.3212 or 70,466 when rounded to the nearest whole number. Plus, you can’t have a fraction of a person, anyway. The company has a total of 70,466 employees.

A car detailing company charges $30 plus $18 per hour. Another company charges $25 plus $20 per hour. How long is a job that costs the same no matter which company is used? (There should be a variable on both sides of the equal sign/equation)

Answers

The startup equation for this would be 30 + 18h = 25 + 20h. Subtract 20h from both sides to get 30 - 2h = 25. Now, you should subtract 30 from both sides. When you do, you get -2h = -5. Divide each side by -2 to isolate the h. h = 2.5. A job that costs the same no matter which company is used is 2.5 (2 1/2) hours long.

In a survey about favorite breakfast foods, 3/8 of those surveyed chose cereal , 0.125 chose yogurt, 0.1875 chose fruit, 5/8 chose toast which got the least number of votes.

Answers

yogurt i hope im right :)

Final answer:

The given question is a comparison of fractions and decimals to determine the smallest number. When all values are converted to decimals for easier comparison, we find that the smallest number is 0.125, which represents the people who chose yogurt as a breakfast food, hence, yogurt got the least number of votes.

Explanation:

The given values in the problem represent different proportions of people's choices for breakfast. The question wants to find the breakfast food with the least number of votes. To do this, we need to understand the numerical values. All are fractions and decimal numbers that represent parts of 1 whole (or 100 percent). Here, the numbers are 3/8 for cereal, 0.125 for yogurt, 0.1875 for fruit, and 5/8 for toast. Converting all to either decimals or fractions for comparison, we get 0.375 for cereal, 0.125 for yogurt, 0.1875 for fruit, and 0.625 for toast.

Comparing these numbers, 0.125 (yogurt) is the smallest number. Therefore, among the given choices, the least number of people chose yogurt for their breakfast food.

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She spent 1/4 of her money on a shirt and 2/5 on shoes. What fraction of money has been spent

Answers

1/4 = 5/20
2/5 = 8/20

8/20 + 5/20 = 13/20 has been spent

on Saturday 2832 tourists visited the zoo on Friday 1475 tourists visited the zoo estimate the number of tourists who visited the zoo on the two days by first rounding the numbers to the nearest thousand

Answers

Rounded to the nearest thousand would be 4000

A stamp collector bought 160 stamps for $25.00. The purchase included 5¢ stamps, 15¢ stamps, and 25¢ stamps. The number of 15¢ stamps is three times the number of 5¢ stamps. How many of each type of stamp was purchased?

Answers

5- 30
15- 90
52- 40
Questions?

Final answer:

The stamp collector purchased 40 5¢ stamps, 120 15¢ stamps, and 0 25¢ stamps.

Explanation:

To solve this problem, let's assign variables to the number of each type of stamp purchased. Let x be the number of 5¢ stamps, y be the number of 15¢ stamps, and z be the number of 25¢ stamps. We are given that the number of 15¢ stamps is three times the number of 5¢ stamps, so we can write this as y = 3x. We also know that the total number of stamps is 160, so we have the equation x + y + z = 160.

Using these equations, we can set up a system of equations:

y = 3x

x + y + z = 160

We can substitute the first equation into the second equation to eliminate y:

x + 3x + z = 160

Combining like terms, we get 4x + z = 160. We can rearrange the equation to solve for z:

z = 160 - 4x

Now we can substitute this expression for z back into the second equation:

x + 3x + 160 - 4x = 160

Simplifying, we get 4x = 0. Solving for x, we find x = 40. Plugging this value back into the equation y = 3x, we get y = 120. Finally, we can find z by substituting x and y into the equation z = 160 - 4x:

z = 160 - 4(40) = 160 - 160 = 0.

So, 40 5¢ stamps, 120 15¢ stamps, and 0 25¢ stamps were purchased.

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Solve the equation. If there is no solution, write no solution. 4|n| – 19 = 13
A. n = 8 or n = –8
B. n = 28 or n = –36
C. no solution

Answers

A works if you substitute 8 in for 'n', however it doesn't if you put in -8. The answer should still be 8, because the absolute value of a number cannot be negative.

Hope this helps :)

A satellite makes 4 revolutions of the earth in one day. How many revolutions would it make in 6 1/2 days?

Answers

26.
1 day/24 hours, makes 4 revolutions.
4 x 6 = 24,
1/2 of 4 = 2.
24+2 = 26.
26 revolutions, if my answer is wrong someone please correct me.

A satellite makes 26 revolutions of the earth in 6 1/2 days.

What is fraction?

"A number expressed as a quotient, in which a numerator is divided by a denominator. "

What is unitary method?

"It is a method of finding the value of a single unit, and based on that value we can find the required value."

For given question,

A satellite makes 4 revolutions of the earth in one day.

⇒ 1 day = 4 revolutions

We need to find the number of revolutions in 6 1/2 days.

We can write the fraction [tex]6 \frac{1}{2}[/tex] as,

[tex]6 \frac{1}{2}[/tex] days

= [tex]\frac{13}{2}[/tex] days

= 6.5 days

By unitary method, for 6.5 days the number of revolutions would be,

= 6.5 × 4

= 26

Therefore, a satellite makes 26 revolutions of the earth in 6 1/2 days.

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What is the positive square root of 36? Enter your answer in the box.

Answers

the answer to this question is going to be negative 6

answer is 6

√36 = 6 because 6 x 6 = 36

Write the solution to the inequality in set - builder notation:
5r + 8 < 63

Answers

First, the inequality needs to be solved. The first step is to subtract 8 from both sides of the inequality, leading to 5r < 55. Dividing 5 out from both sides, this will leave r < 11. Next, to form a set notation, the inequality is written in such form: {r | r < 11}.

What is 4/5 - 2/3?
Someone please answer.
I have to write up to 20 characters so yh.

Answers

Change 4/5 - 2/3 so that the denominator is th same. Let’s try 15.
So, 12/15 - 10/15.
Then, subtract to get 2/15.

Hope it helped :)

this is the answer to your question 2/15

Find the measure of angel b

Answers

52+88+x=180
140+x=180
x=40

What are the missing angles?

Answers

y=30
2y=60

i believe this is the correct answer

y +90+2y=180
3y=90
y=30
2y=60

Please help. I don’t understand any of this.

Answers

If the two triangles are congruent (not just similar), then QS and TV would be equal. Thus, 3v + 2 = 7v - 6.

Solving this equation for v: 4v = 8, and v = 2.

Then QS = 3(2) + 2, or 8, and TV should be the same: 7(2) - 6 = 8.

Answer:

If the two triangles are congruent (not just similar), then QS and TV would be equal. Thus, 3v + 2 = 7v - 6.

Solving this equation for v: 4v = 8, and v = 2.

Then QS = 3(2) + 2, or 8, and TV should be the same: 7(2) - 6 = 8.

Step-by-step explanation:

Tanya spent $8.15 on 5 cans of tuna. She used a coupon that gave her 35¢ off each can. What was the price of a can of tuna without the coupon? Enter your answer in the box.

Answers

Each can of tuna would cost $1.98 because you would do .35x5 then your total plus 8.15 and that would be the total without coupons then you would divide your grand total by 5 for the exact price of one can without the coupon

Answer: $1.98

Step-by-step explanation:

Given: The total amount Tanya spent on cans of tuna = $8.15

Also, she used a coupon that gave her 35 cents off each can.

Therefore, The total discount on 5 cans =[tex]5\times35=175\ cents[/tex]

Since, $1=100 cents or 1 cent= 0.01 dollar

Therefore, the total discount on 5 cans=[tex]0.01\times175=\$1.75[/tex]

Now, the price of 5 cans of tuna without the coupon=[tex]\$8.15+1.75=\$9.90[/tex]

The price of a can of tuna without the coupon=[tex]\frac{9.90}{5}=\$1.98[/tex]

Write 0.8 as a fraction.

Answers

Using the place value chart, we can see that the decimal 0.8 is eight-tenths, so we can write 0.8 as the fraction [tex]\frac{8}{10}.[/tex] We are able to simplify so we will divide the numerator and the denominator by 4.

Image is provided.

Therefore, the decimal 0.8 can be written as [tex]\frac{4}{5}[/tex].

Answer:

4/5

Step-by-step explanation:

0.8=8/10=4/5

Your cousin is taking the train to Washington to visit her parents. She has at most $15.00 to spend on snacks and reading materials. Granola bars cost $1.15 each, and magazines cost $1.25. If your cousin buys the same number of granola bars and magazines, how many can she buy?

Answers

I think 6 of each. I divided 15 by 2, got $7.50. You can buy exactly six magazines w that, and 6.5 granola bars. So six of each.

Solve the inequality.Explain all steps and Identify the properties used. n/-3 + 5>4

Answers

n/-3>4-5
then you can just times by -3 to get n on it's own
n>-3(4-5)
n>-3*-1
n>3

For this..
[tex]\frac{n}{-3}+5 \ \textgreater \ \mathrm{Apply\:the\:fraction\:rule}:\ \frac{a}{-b}=-\frac{a}{b} \ \textgreater \ -\frac{n}{3}+5 \ \textgreater \ \frac{n}{3}+5\ \textgreater \ 4[/tex]

[tex]\mathrm{Subtract\:}5\mathrm{\:from\:both\:sides} \ \textgreater \ -\frac{n}{3}+5-5\ \textgreater \ 4-5 \ \textgreater \ \ \textgreater \ -\frac{n}{3}\ \textgreater \ -1[/tex]

[tex]\mathrm{Multiply\:both\:sides\:by\:}3 \ \textgreater \ 3\left(-\frac{n}{3}\right)\ \textgreater \ 3\left(-1\right) \ \textgreater \ \mathrm{Simplify} \ \textgreater \ -n\ \textgreater \ -3[/tex]

[tex]\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)} [/tex]
[tex]\left(-n\right)\left(-1\right)\ \textless \ \left(-3\right)\left(-1\right) \ \textgreater \ \ \textgreater \ \mathrm{Simplify} \ \textgreater \ n\ \textless \ 3[/tex]

Hope this helps!

what is 1/10 of .1 thank you

Answers

0.1 = 1/10

1/10 of 1/10 is 1/100

1/100 = 0.01

0.01 is your answer

hope this helps

I need help ASAP i'm doing math and we are do Addition with mixed numbers

A freight train is loaded with 12 1/2 tons of corn, 11 1/3 tons of oats, and 6 1/4 tons of wheat.how many tons of grain is it carrying? Note: Corn, oats, and wheat are considered grain

A) 29 1/12
B) 30 1/12
C) 29 11/12
D) 30 1/6

Answers

The answer is 30 1/2 because you have to multiply each denominator which you should get 12.
150/12
75/12
136/12
Than you can easily add them together to get 361/12 which you would need to simplify to get the correct answer

I believe the awnser would be B) 30 and a half

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