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Factor the polynomial: 8t^2 + 8t - 72
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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).
what is 1/10 of .1 thank you
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1/10 of 1/10 is 1/100
1/100 = 0.01
0.01 is your answer
hope this helps
Write 0.8 as a fraction.
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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
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.
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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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What are the missing angles?
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2y=60
i believe this is the correct answer
3y=90
y=30
2y=60
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)
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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.
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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]
Distance between the points
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[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
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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!
What is 4/5 - 2/3?
Someone please answer.
I have to write up to 20 characters so yh.
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So, 12/15 - 10/15.
Then, subtract to get 2/15.
Hope it helped :)
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?
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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
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A satellite makes 4 revolutions of the earth in one day. How many revolutions would it make in 6 1/2 days?
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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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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.
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Area = 3ft · 2ft
Area = 6ft²
hope this helps!
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
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Hope this helps :)
What is the positive square root of 36? Enter your answer in the box.
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√36 = 6 because 6 x 6 = 36
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?
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18x5x3=270
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?
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3x=12
X=4
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?
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there will be 3 containers left.
i had no paper so i had to write it on the table. XD haha
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?
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15- 90
52- 40
Questions?
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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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
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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
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?
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Find the measure of angel b
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140+x=180
x=40
Which expression results on a rational number?
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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
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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
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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]
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Write the solution to the inequality in set - builder notation:
5r + 8 < 63
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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
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2/5 = 8/20
8/20 + 5/20 = 13/20 has been spent
Which symbol correctly compares the two fractions use <, > or = 2/4 and 3/8
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Solve the inequality.Explain all steps and Identify the properties used. n/-3 + 5>4
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then you can just times by -3 to get n on it's own
n>-3(4-5)
n>-3*-1
n>3
[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!