Which side lengths form a right triangle?
Choose all answers that apply:
(Answers in picture)
Answers
Option (C). 2, 2, √8, forms a right triangle.
Explanation:A right triangle is a triangle that has one angle measuring 90 degrees.
According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Therefore, to determine if a set of side lengths forms a right triangle, we can check if the sum of the squares of the two shorter sides is equal to the square of the longest side.
Option A: 4, 8, 124^2 + 8^2 = 16 + 64 = 80
12^2 = 144
The sum of the squares of the two shorter sides is not equal to the square of the longest side. Therefore, this does not form a right triangle.Option B: 2, 3, √5
2^2 + 3^2 = 4 + 9 = 13
(√5)^2 = 5
The sum of the squares of the two shorter sides is not equal to the square of the longest side. Therefore, this does not form a right triangle.Option C: 2, 2, √8
2^2 + 2^2 = 4 + 4 = 8
(√8)^2 = 8
The sum of the squares of the two shorter sides is equal to the square of the longest side. Therefore, this forms a right triangle.
Based on the calculations above, only option C, 2, 2, √8, forms a right triangle.
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The correct answer is: C. [tex]\(2, 2, \sqrt{8}\)[/tex]
Step 1
To determine which sets of side lengths form a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Step 2
Let's check each option:
A. [tex]\(4, 8, 12\)[/tex]
- [tex]\(4^2 + 8^2 = 16 + 64 = 80\)[/tex]
- [tex]\(12^2 = 144\)[/tex]
- [tex]\(80 \neq 144\)[/tex]
Therefore, option A does not form a right triangle.
Step 3
B.[tex]\(2, 3, \sqrt{5}\)[/tex]
- [tex]\(2^2 + 3^2 = 4 + 9 = 13\)[/tex]
- [tex]\((\sqrt{5})^2 = 5\)[/tex]
- [tex]\(13 \neq 5\)[/tex]
Therefore, option B does not form a right triangle.
Step 3
C. [tex]\(2, 2, \sqrt{8}\)[/tex]
- [tex]\(2^2 + 2^2 = 4 + 4 = 8\)[/tex]
- [tex]\((\sqrt{8})^2 = 8\)[/tex]
- [tex]\(8 = 8\)[/tex]
Therefore, option C forms a right triangle.
Related Questions
Madeline uses fewer than 5 coins to pay 60 cents. Draw coins to show one way she could pay 60 cents.
Answers
What is the value of x? (The shape is a rectangle with the top side labelled 40 and the bottom side labelled 5x + 10)
Enter your answer in the box.
**I got 26)
x = 26
Answers
5x+10=40
subtract 10 on both sides
5x=30
divide on both sides
5x/5=30/5
x=6
A bag contains 4 red, 3 yellow, 3 blue, and 2 white marbles, for a total of 12 marbles. If Lucia randomly picks two marbles from the bag without putting the first marble back, what is the probability that the first marble is red and the second is white?
Answers
[tex] |\Omega|=12\cdot11=132\\
|A|=4\cdot2=8\\\\
P(A)=\dfrac{8}{132}=\dfrac{2}{33}\approx6\% [/tex]
Answer:
2/33
Step-by-step explanation:
Gloria Trench checked her gas mileage and found that she had used 16.6 gal of gas to travel 372 mi. At this rate, how many gallons will she use to travel from San Francisco to Washington, D.C., a distance of 2,850?
Answers
Using the rate of miles per gallon for Gloria's car, we calculated that she will need approximately 127.2 gallons of gas to travel from San Francisco to Washington, D.C.
Explanation:To solve this problem, we'll use the principle of ratios.
First, we find the rate of miles per gallon for Gloria's car by dividing the distance travelled by the gallons used:
372 miles ÷ 16.6 gallons = 22.4 miles per gallon
With this information, we can calculate how many gallons Gloria will need to travel from San Francisco to Washington D.C., which is a distance of 2850 miles:
2850 miles ÷ 22.4 miles per gallon = 127.2 gallons
So, Gloria will use approximately 127.2 gallons of gas to travel from San Francisco to Washington, D.C., at her current rate.
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Samantha works at a nursery where she pots plants. It takes her 1 1/2 hours to pot 12 plants. How many plants can Samantha pot in hour?
Answers
Samantha can pot 8 plants in one hour.
To calculate how many plants Samantha can pot in one hour, we need to determine the rate at which she pots plants. She currently pots 12 plants in 1 1/2 hours, which is equal to 1.5 hours.
To find the rate, we divide the number of plants by the number of hours:
12 plants /1.5 hours=8 plants per hour
Therefore, Samantha can pot 8 plants in one hour.
A 15 oz can of peaches costs $1.99 and a 24 oz can of peaches cost $2.55. How much is the price per ounce of the 15 oz can of peaches
Answers
=$1.99 ÷ 15 ounces
=$0.13
The price per ounce of the 15 ounce can is $0.13.
Hope this helps! :)
Match the pre-image, and its clockwise rotation, with the coordinates of its image. 1. (5, 2); 90° (-2, -5) 2. (5, 2); 180° (2, -5) 3. (5, 2); 270° (-2, 5) 4. (-5, 2); 90° (5, 2) 5. (-5, 2); 180° (-5, -2) 6. (-5, 2); 270° (2, 5) 7. (-2, 5); 90° (-5, 2) 8. (5, -2); 180° (5, -2)
Answers
2. (-5,-2)
3. (-2,5)
4. (2,5)
5. (5,-2)
6. (-2,-5)
7. (5,2)
8. (-5,2)
Each 90° clockwise turn takes a point (x,y) and transforms it to (y,-x). For a 180° turn you would do this process twice in a row; for a 270° turn, three times in a row.
Answer:
(2,5) = (-5,2); 90°
(2,-5) = (5,2); 90°
(-2,-5) = (-5,2); 270°
(5,-2) = (-5,2); 180°
(-2,5) = (5,2); 270°
(5,2) = (-2,5); 90°
(-5,2) = (5,-2); 180°
(-5,-2) = (5,2); 180°
Each 90° clockwise turn takes a point (x,y) and transforms it to (y,-x). For a 180° turn you would do this process twice in a row; for a 270° turn, three times in a row.
Hope this helps!
∵∅Levi∅∵
∵ФωФ∵
In what quadrant does point R lie?
A.
Quadrant I
B.
Quadrant II
C.
Quadrant III
D.
Quadrant IV
Answers
Answer:
Option: D
Point R lie on the Quadrant IV (i.e. quadrant fourth)
Step-by-step explanation:
Clearly from the given graph the point R lie on the fourth quadrant as the fourth quadrant is defined as the region such that any point on it with the given coordinates ; the x-value of any point is positive and y-value of any point is negative.
The coordinates of Point R from the given Graph has coordinates (5,-5).
Hence point R lie on the fourth quadrant.
Hence option D is correct.
Two lines intersect at a point, forming ∠1 , ∠2 , ∠3 , and ∠4 .
∠1 and ∠2 are supplementary angles.
∠2 and ∠4 are vertical angles.
m∠1=120°
What is the measure of ∠4 ?
a.30°
b.60°
c.90°
d.120°
please help i will mark brainliest
Answers
________________________________________
Because at whatever location, ∠2 and ∠4 are vertical angles;
and all vertical angles have equal measurements.
Given: m∠1 is 120°, and ∠1 is supplementary to ∠2 ;
then m∠1 + m∠2 = 180° .
So, m∠2 = (180 - 120)° = 60° .
As aforementioned:
m∠4 = m∠2 = 60° ; which is: Answer choice: [B]: " 60° " .
___________________________________________________
Answer:
" 60° " .
Step-by-step explanation:
a) Wilma used to make 10.50 per hour, but then she got an 8% raise. How much does Wilma make per hour now?
1) $11.00
2) $11.14
3) $11.34
4) $11.54
b) You went to the store and bought some DVDs. The cost of the DVDs was 45.80. The sales tax is 5%. How much is your total cost?
1) $48.09
2) $48.19
3) $48.29
4) $48.39
c) What is 2/3 of 30?
1) 10
2) 15
3) 20
4) 25
d) Arrange in order from least to greatest: 1/2, 3/4, 5/7, 13/14
1) 1/2 < 3/4 < 5/7 < 13/14
2) 1/2 < 5/7 < 3/4 < 13/14
3) 3/4 < 5/7 < 13/14 < 1/2
4) 13/14 < 1/2 < 3/4 < 5/7
e) Which property is demonstrated by this equation? 3(1 + 2) = (1 + 2)3
1) Commutative property
2) Associative property
3) Distributive property
f) Which property is demonstrated by this equation? 2 + 3 = 3 + 2
1) Commutative property
2) Associative property
3) Distributive property
g) Which property is demonstrated by this equation? 3 • (1 • 2) = (3 • 1) • 2
1) Commutative property
2) Associative property
3) Distributive property
please answer fast
Answers
Simplify 4 sqrt 6 / sqrt 30 by rationalizing the denominator. Please show steps.
Answers
so it basically looks like
4√6
¯¯
√30
?
then you multiply both sides by √30
4√6 x √30 = 4√180 which simplified = 24√5
√30 x √30 just equals 30
so the answer is
24(√30) / 30
simplified = 4(√5) / 5
Hope this helps!!
~Girlygir101~
24√5/√30 is the simplified form of the expression 4√6/√30
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is 4√6/√30
We have to rationalizing the denominator.
Multiply numerator and denominator by √30
4√6/√30 × √30/√30
4√6×30/30
4√180/30
4.6√5/√30
24√5/√30
Hence, 24√5/√30 is the simplified form of the expression 4√6/√30
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What is the 32nd term of the arithmetic sequence where a1 = −33 and a9 = −121? −396 −385 −374 −363
Answers
The formula to find the general term of an arithmetic sequence is,
[tex] a_{n} =a_{1} +(n-1)d [/tex]
Where [tex] a_{n} [/tex]= nth term and
[tex] a_{1} [/tex] = First term.
Given, a9 = −121. Therefore, we can set up an equation as following:
[tex] -33+(9-1)d = -121 [/tex] Since, a1 = -33
- 33 + 8d = -121
-33 + 8d + 33 = -121 + 33 Add 33 to each sides of the equation.
8d = -88.
[tex] \frac{8d}{8} =\frac{-88}{8} [/tex] Divide each sides by 8.
So, d = - 11.
Now to find the 32nd terms, plug in n = 32, a1 = -33 and d = -11 in the above formula. So,
[tex] a_{32} = -33 +(32 -1) (-11) [/tex]
= -33 + 31 ( -11)
= - 33 - 341
= -374
So, 32nd term = - 374.
Hope this helps you!
Please help use the diagram of the right triangle above
Answers
TanB = b / a
We clear the value of b:
b = a * TanB
Substituting the values we have:
b = 10 * Tan (60)
b = 17.32 m
Answer:
b = 17.32 m
option a.
I WILL GIVE BRAINLEST. Use the irregular polygon below. show all work.
a. find the perimeter.
b. find the area.
Answers
Rebecca gives gifts to 12 employees. Each gift is in a box 12 inches by 10 niches by 3 inches. How much wrapping paper does Rebecca need to completely cover the boxes?
A. 360in squared
B. 1,720in squared
c. 4,464in squared
D. 14,400 in squared
Giving brainiest to the most accurate answer. (please include your work)
Answers
Answer:
C is the answer. C= 4,464in squared.
Step-by-step explanation:
All you would have to do is multiply all the numbers together and then choose your answer
Rebecca needs 4,464 square inches of wrapping paper to completely cover the boxes.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
Each box has six sides, and the dimensions of each side are:
12 x 10, 12 x 10, 12 x 3, 12 x 3, 10 x 3, and 10 x 3 inches.
The total surface area of each box is:
2(12 x 10) + 2(12 x 3) + 2(10 x 3) = 240 + 72 + 60
= 372 square inches.
Since there are 12 boxes, the total surface area of all the boxes is:
= 12 x 372
= 4,464 square inches.
Therefore,
Rebecca needs 4,464 square inches of wrapping paper to completely cover the boxes.
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Choosing a graph to fit a narrative
Answers
the October meeting of the yearbook club had 21 people attend. That was 3 times as many people as the number of people who came to the september meeting. How many people were at the September meeting?
Answers
Sept meeting = 21 ÷ 3 = 7
7 people were at the September meeting.
Alcia received a $75 gift certificate for her birthday. She went to a boutique to buy some T- shirts at $7 each and some socks for $2.50 a pair. If T represents the number of T-Shirts, and S represents the number of pairs of socks she bought, write an inequality that would determine the number of T-shirts and pairs of socks she could buy. HURRY PLEASE
Answers
T represents the number of T-Shirts
S represents the number of pairs of socks she bought
Each T-shirt cost $7, so 'T' T-Shirts will cost 7T
Each Pairs of socks cost $2.5, so 'S' pair of socks cost 2.5S
[tex] Total \; cost\; =\; T-shirts \; cost \; +\; Pair \; of \; socks\; cost \\ \\ Total \; Cost \; =\; 7T+2.5S\\ \\ [/tex]
Total cost should be less than or equal to 75 dollars.
Conclusion:
The inequality that would determine the number of T-shirts and pairs of socks she could buy is given below:
[tex] 7T+2.5S\leq 75 [/tex]
A cylinder has a volume of 136 cubic centimeters. What is the volume of a cone with the same height and the same diameter
Answers
V_cone = 1/3 pi r^2 h. If that's the case the only difference is that the Cone's volume is 1/3 that of the cylinder
V_cone = 1/3 V_cylinder
V_cone = 1/3 136 cubic cm.
V_cone = 45.33 cubic cm.
LM=7, LN=10, MN=5, What can you conclude about the angle measures
Answers
.. ∠L ≈ 27.66°
.. ∠M ≈ 111.80°
.. ∠N ≈ 40.54°
The smallest angle will be opposite the shortest side; the largest angle will be opposite the longest side.
Given the lengths stated, we conclude that triangle LNM is a right triangle. Angle LNM would be the right angle, and angles NML and NLM can be calculated with trigonometry if necessary.
Explanation:Given the lengths of triangle LNM with LM = 7, LN = 10, and MN = 5, we can infer that this triangle is a right triangle. This is concluded through the use of the Pythagorean theorem, which defines that in any right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. Specifically, in this case, we can observe that 10² (LN) equals to 7² (LM) + 5² (MN), because 100 equals 49 + 25. Consequently, since LN is the hypotenuse, angle LNM is the right angle, and angles NML and NLM can be found using trigonometric functions if needed.
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Carlie’s Cell Phone Store has a gross income of $1,287,684 and deductions of $598,982. What is the federal corporate income tax? Round to the nearest whole dollar.
Answers
1.) $1,287,684 - $598,982 = $688,702
Due to Tax Cuts and Jobs Act of 2017, corporate tax rate is fixed at 21%. Hence:
2.) $688,702 * .21 = $144,627.42 or $144,627
Laura’s cell phone service costs $65 per month, plus an additional $0.10 per text message sent. The table below shows the cost for Zach’s cell phone service based on the number of texts messages he sends. How much cheaper is Zach’s cell phone service than Laura’s when no text messages are sent?
Answers
When no text messages are sent, Zach's cell phone service is $55 cheaper than Laura's each month.
Explanation:Laura's cell phone service costs $65 per month regardless of how many text messages she sends. On the other hand, Zach's cell phone service cost is represented by the variable equation $10 = $2× QRT + $.05 × QPC. However, since no text messages are sent in this scenario, the number of text messages (QPC) is 0. Therefore, all the terms in the equation that involve QPC becomes zero. Hence, Zach's cell phone service costs $10 per month when no text messages are sent. So if we compare Laura's cell phone costs to Zach's without sending any text messages, Zach is paying $65 - $10 = $55 less than Laura each month.
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how do you solve twelve less than the quotient of a number and 7 is -2
Answers
Remark
One of the things you need to do is learn to read phrase by phrase.
What is the quotient of a number and 7? That meas you have a number, x, and it is divided by 7. What you do that the answer you get is the quotient.
x/7 is what you know so for. Now the first part says you take 12 away from that.
x/7 - 12 is what you have after doing that.
The result you get is - 2
x/7 - 12 = - 2 Add 12 to both sides
x/7 - 12 + 12 = - 2 + 12
x/7 = 10 Now multiply by 7
x = 10 *7
x = 70 <<< Answer the number is 70
help me with these please will give brainliest and lots of points
Answers
Some answers you may need to round off as needed
Errol uses 1/3 can of wet dog food for his dog money each day how many dog servings will he get from five cans of dog food
Answers
Hope this helps!
♤MidnightQueen
is 34.653 greater than, less than, or equal to 3.4653
Answers
The difference between 34.653 and 3.4653 is positive thus,34.653 > 3.4653.
What is a number system?
The number system is a way to represent or express numbers.
A decimal number is a very common number that we use frequently.
Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.
As per the given, 34.653 and 3.4653
If the difference of x - y is positive then, x - y > 0 or x > y
Since 34.653 - 3.4653 > 0
34.653 > 3.4653
Hence "The difference between 34.653 and 3.4653 is positive thus,34.653 > 3.4653".
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How to do I don't know how to do can u help me pls.
Thanks you
Answers
So, we have 2185 student in Rose.
Lily School has 307 more students than Rose, so Lily has,
2185 + 307 = 2492 Students in Lily School.
Since question a. is asking you to round off to the nearest ten, your answer to part a is 2490.
For part b. add 2185 and 2490.
2185 + 2490 = 4675 students.
The questions want you to round to the nearest hundredth, so,
4700 is the answer to part b.
For simplicity, let L and R represent the numbers of students in Lily school and Rose school, respectively. The first sentence tells you
.. R = 2185
The second sentence tells you
.. R = L - 307
a) This question asks you the value of L. Use the given information to find it.
.. 2185 = L -307
.. 2185 +307 = L
.. 2492 = L
You are asked to round this number to the nearest 10. This means you look at the 1s digit (2) and decide if it is 5 or more (it is not). If it is, you add 1 to the tens digit (here, you don't) and then report the number with the 1s digit made zero:
.. There are 2490 pupils in Lily school.
b) This question asks you the total number in both schools. That will be
.. L +R = 2492 +2185 = 4677
You are asked to round this number to the nearest 100. This means you look at the 10s digit (7) and decide if it is 5 or more (it is). If it is, you add 1 to the hundreds digit (here, you do) and then report the number with the 10s and 1s digits made zero:
.. There are 4700 pupils total in the two schools.
If you can, help me with 3 through 9 for brainliest. Do what you can thanks
Answers
2. Once again you just have to find the areas of the individual shapes and then add them together. So, 8×4 added to (4+4)×4 added to 12×12. So the area would be 32+32+144 which is 208.
3. First work out the triangles area: (12-8)×((16-10)/2) which equals 12. And then add it to the rectangles area: 16×8 which is 128. So the area is 140.
4. Find out the area of the circles: 3.14×1.5^2 which is 7.065. This is the area for a full circle and as there is 4 halves in the picture, multiply this number by 2, giving a total circle area of 14.13. Then simply add the square area which is 3×3. So the total area is 23.13.
It's the same for the last two. Seperate 5 into a triangle, long rectangle down the bottom and a squarish one up top. Work out the individual areas for these three shapes and then just add them.
For 6 just work out the semicircle, rectangle and triangle areas and add them once more.
Hope that helps! :)
Cut the figure into a rectangle and triangle. You are left with a rectangle with length 6 and width 3, and a triangle with base 15 - 3 = 12 and height 6 + 6 = 12.
A = lw
A = (6)(3)
A = 18 ft^2
So the area of the rectangle is 18 square feet.
A = 1/2bh
A = 1/2(12)(12)
A = 72 ft^2
So the area of the triangle is 72 square feet. Add the two areas together to find the total area of the figure:
18 + 72 = 90 ft^2
So the area of the figure is 90 square feet.
#4
Cut the figure into three rectangles.
4 * 8 = 32
4 * 8 = 32
12 * 12 = 144
32 + 32 + 144 = 208 ft^2
#5
Cut the figure into a rectangle and a triangle.
16 * 8 = 128
1/2 * 6 * 4 = 12
128 + 12 = 140 ft^2
#6
Cut the figure into a square and 4 semi-circles.
3 * 3 = 9
1/2 * 3.14 * 1.5^2 = 3.5325 * 4 = 14.13
9 + 14.13 = 23.13 ft^2
#7
Cut the figure into two rectangles and a triangle.
10 * 8 = 80
4 * 4 = 16
1/2 * 2 * 4 = 4
80 + 16 + 4 = 100 ft^2
#8
Cut the figure into a semi-circle, rectangle, and triangle.
6 * 4 = 24
1/2 * 3 * 2 = 3
1/2 * 3.14 * 2^2 = 6.28
24 + 3 + 6.28 = 33.28 ft^2
To measure the distance from the U.S. to Istanbul, Turkey you would most likely use __________.
Answers
1. The United States System using miles
2. The Metric System using kilometers
However, the best answer to the question is MILES, because you would use miles to find the distance when traveling.
Ken has 6 different colors of marbles he has 9 marbles of each color how many marbles does Ken have in all
Answers
Final answer:
Ken has a total of 54 marbles in all.
Explanation:
To calculate the total number of marbles Ken has, we need to multiply the number of colors of marbles by the number of marbles of each color. Ken has 6 different colors of marbles and 9 marbles of each color. To find the total, we perform the multiplication:
6 colors imes 9 marbles per color = 54 marbles.
Hence, Ken has a total of 54 marbles in all.