Mathematics Middle School

Which of these four sets of side lengths will form a right triangle?



Set 1
4 cm, 5 cm, 6 cm

Set 2
8 in., 12 in., 20 in.

Set 3
10 mm, 20 mm, 30 mm

Set 4
12 ft, 16 ft, 20 ft


Answers

Answer 1
set 4 is the correct answer because if you multiply 10 by 10 + 20 times 20, you will get 400 and when you multiply 30 by 30 you also get 400 which is equal to 400 there for you answer would be set 4.

Hope I helped if I did click the thx button ;)
Answer 2

Set of sides that will make right triangle is

Set 4 : 12 ft, 16 ft, 20 ft

What is Pythagoras theorem?

Pythagoras theorem states that in a right angled triangle square of the hypotenuse is equal to the sum of the square of perpendicular and square of base. The longest side is the hypotenuse.

Given measurements

Set 1:

4cm , 5cm , 6cm

By Pythagoras theorem

4² + 5² = 6²

16 + 25 = 36

41 ≠ 36

Pythagoras theorem is not satisfied,

this set of sides will not make right triangle

Set 2

8 in., 12 in., 20 in.

By Pythagoras theorem

8² + 12² = 20²

64 + 144 = 400

208 ≠ 400

Pythagoras theorem is not satisfied,

this set of sides will not make right triangle

Set 3

10 mm, 20 mm, 30 mm

By Pythagoras theorem

10² + 20² = 30²

100 + 400 = 900

500 ≠ 900

Pythagoras theorem is not satisfied

this set of sides will not make right triangle

Set 4

12 ft, 16 ft, 20 ft

By Pythagoras theorem

12² + 16² = 20²

144 + 256 = 400

400 = 400

Pythagoras theorem is satisfied

this set of sides will make right triangle.

Hence, Set 4 of sides 12 ft, 16 ft, 20 ft will form a right triangle.

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Related Questions

What is the slope of this line?

Answers

I started at (-2, 0) but you can start at any point on the graph that goes through the corner of the square (if that makes sense) like a point on the graph. From one point to the next, you go down one and one to the right, therefore the slope is a -1

Write the vertex form of the equation of the parabola which has a vertex of (0,0) and contains the point (1,2). A. Y=2x^2. B. Y=2(x-1)^2. C. Y=x^2. D. Y=(x+1)^2+1

Answers

General equation of parabola:  y-k = a(x-h)^2

Here the vertex is at (0,0), so we have y-0 = a(x-0)^2, or y = ax^2

All we have to do now is to find the value of the coefficient a.

(1,2) is on the curve.  Therefore, 2 = a(1)^2, or 2 = a(1), or a = 2.

The equation of this parabola is y = 2x^2.

The vertex form of the equation of a parabola with a vertex at (0,0) and passing through the point (1,2) is [tex]y=2x^2.[/tex]

The vertex form of a parabola is given by: [tex]y = a(x - h)^2 + k[/tex] where (h, k) is the vertex of the parabola.

In this case, the vertex is (0, 0), so h = 0 and k = 0.

Therefore, the equation becomes: [tex]y = a(x - 0)^2 + 0.[/tex] Simplifying further, the equation becomes: [tex]y = ax^2[/tex].

Now, we need to find the value of 'a.' To do this, we can use the given point (1, 2). Substitute these values into the equation:

[tex]2 = a(1)^2[/tex].

Therefore, 'a' is 2. So, the final equation in vertex form is: [tex]y = 2x^2.[/tex]

So, the correct answer is A. [tex]Y = 2x^2.[/tex]

there are 54 people at the party. 18 of them are wearing red, what percent of them are not wearing red

Answers

18 = number wearing red

54-18 = 36 not wearing red

36 out of 54 = 36/54

36/54 = 0.6666

0.6666 * 100 = 66.67%

Percent wearing red is 66.67%

There are 54 people at the party.

18 people are wearing red which means that 36 people are not wearing red

54 - 18 = 36

The fraction [tex]\frac{36}{54}[/tex] represents the 36 people at the party that are wearing no red. We can find what percent of the people at the party are not wearing red by turning [tex]\frac{36}{54}[/tex] into a percent.

[tex]\frac{36}{54}[/tex] can be reduced to [tex]\frac{2}{3}[/tex]  by dividing both the numerator and denominator by the greatest common factor of 36 and 54.

2 ÷ 3 = 0.667

0.667 × 100 = 66.67%

Therefore, 66.67% of the people at the party are not wearing red

Which measure is equivalent to 2.5 liters? A)2.5 mL B)250 mL C) 2500 mL D)25,000 mL

Answers

we know that

[tex] 1L=1000mL [/tex]

we are given 2.5L

so, to find 2.5L into mL, we will have to multiply both sides by 2.5

[tex] 2.5*1L=2.5*1000mL [/tex]

now, we can simplify it

[tex] 2.5L=2500mL [/tex]

so, option-C.............Answer

Solve the system of equations. y = 7x + 43 y = 2x + 13 a. ( -6, 1) c. ( 6, 1) b. ( 6, -1) d. No solution

Answers

Hello there!

y = 7x + 43
y = 2x + 13

We wanna solve y = 7x + 43 for y in y = 2x + 13

What does that even mean? Well it simply means that we gonna replace y by 7x + 43.

y = 2x + 13

7x + 43 = 2x + 13

Subtract 2x on both sides

7x + 43 - 2x = 2x + 13 - 2x

5x + 43 = 13

Now we can subtract 43 on both sides

5x + 43 - 43 = 13 - 43

5x = -30

Then divide both sides by 5

5x/5 = -30/5

x = -6

Now since we have the value for x, we gonna use that value to find y.

We can do that by substituting -6 for x in y = 7x + 43

But what does that mean? It means that in y = 7x + 43, we gonna replace the x by -6

y = 7x + 43

y  = 7(-6) + 43

y = -42 + 43

y = 1

Thus,

The answer is: x = -6 and y = 1

The correct answer is option A (-6,1).

Let me know if you have questions about the answer. As always, it is my pleasure to help students like you.

7.Kristy baked 18 cookies. She took 2/3 of the cookies to work. How many cookies did she NOT take to work? 4 6 8 12

Answers

its 6
2/3 of 18 = 12
18-12=6
Here's the equation:
18 - 18 * 2/3
18 - 36/3
18 - 12
6
She didn't take 6 cookies to work.

What conclusions can you make about numbers in scientific notation with negative exponents?

Answers

A conclusion that you can make about numbers in scientific notation with negative exponents that the answer is going to be negative!

Circumference is 4 what is the radius and area of the circle

Answers

the radius is half the circumference which is 2

the area is pi times radius squared so you do pi times 2 to the 2nd power

[tex]\pi2 {?}^{2} [/tex]
and you will get 12.57

Need Help ASAP..GIVING 15 POINTS TO WHO ANSWERS.IF YOU COPY AND NOT ANSWER YOU WILL GET REPORTED
The original price for a clothes washer and dryer is $999. Which coupon is a better deal? A) SAVE 20% ON ANY WASHER/DRYER COMBO B) SAVE $200 ON ANY WASHER/DRYER COMBO C) SAVE $75 PLUS 5% OFF ON ANY WASHER/DRYER COMBO D) SAVE $50 PLUS 20% OFF ON ANY WASHER/DRYER COMBO

Answers

Its D. It equals out to 749.2 after you do 20% of 999 which is 199.8 while also subtracting the additional 50$ you save on it.

The diameter of a circular placemat is 15 inches. Devon wants to sew a border of lace around the placemat. If the lace he wants is sold by the foot, how many feet of lace will he need to purchase?

Answers

Circumference = πD = π(15) = 47 feet (Nearest feet)


Answer: 47 feet

The sum of the ages of two people is 32. The difference is their ages is 4. What is the age of the younger person ?

Answers

i believe the answer is 12
The age of the younger person is 14. 

solve the exponential equation
[tex] {10}^{ - x} = {7}^{4x} [/tex]

Answers

[tex]10^{-x}=7^{4x}\\ \ln 10^{-x}=\ln 7^{4x}\\ -x \ln 10=4x\ln 7\\ -x \ln 10-4x\ln 7=0\\ x(-\ln 10-4\ln 7)=0\\ x=0[/tex]

A probability close to 1/2 indicates a chance event is ________ to occur

Likely, unlikely, or neither likely nor unlikely

Please help

Answers

Neither likely nor unlikely, because there's a 50/50 chance either can happen

Mitch does not know the correct answer to two multiple choice questions. The choices are A,B,C, and D. If Mitch just guesses, what is the probability that Mitch will guess both answers correctly?

Answers

Both chances to success are 1/4. If you want the first AND the second to be successful, you have to multiply the chances, so the answer is

1/4 * 1/4 = 1/16

Final answer:

Mitch has a 1/16 probability of guessing both multiple-choice answers correctly when randomly guessing among four options.

Explanation:

If Mitch guesses on two multiple-choice questions with choices A, B, C, and D, the probability of guessing both correctly is calculated as follows: The probability of correctly guessing one question is 1/4 (since there are 4 possible choices, and only one is correct). To find the probability of guessing both correctly, we multiply the probabilities of each independent event. Thus, the probability of guessing the first question correctly AND the second question correctly is 1/4 × 1/4 = 1/16.

Solving for Circumference of a Penny A penny is 1.9 cm wide. What is the circumference of a penny? Approximate using mc001-1.jpg = 3.14 and round the answer to the nearest tenth if necessary.

Answers

Rounding to the nearest tenth, the circumference of a penny is approximately 6.0 cm.

To find the circumference of a penny, we use the formula for the circumference of a circle:

Circumference = π * diameter

Since the penny's width is given (which is the same as the diameter), we can plug in the values:

Circumference = 3.14 * 1.9 cm

Now, calculate the circumference:

Circumference ≈ 5.966 cm

Rounding to the nearest tenth, the circumference of a penny is approximately 6.0 cm.

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Graph the data from the table below. Describe the parent function as linear, square root, cube root, cubic, or quadratic.

Answers

The function rule is g(x) = 2*sqrt(x) which is a transformation of the parent function f(x) = sqrt(x)

The g(x) function has been scaled by a factor of 2. In other words, each point on g(x) is twice as high as its corresponding point on f(x). Specifically for example, the point (1,1) has been doubled to (1,2). Overall, this vertically stretches out the parent function graph.

Both the parent function f(x) and the other g(x) curve are square root functions. 

See the attached image. The blue curve goes through the given points from the table. The red curve is the parent function. 

Mrs. Sloan is purchasing 3.4 pounds of trail mix that costs $4.25 per pound. How much change will Mrs. Sloan receive if she gives the cashier $20.00.

a. $14.45 b. $5.55 c. $12.55 d. $7.45

Answers

STEP 1:
multiply number of pounds purchased by price per pound

= 3.4 pounds * $4.25 per pound
= $14.45 total cost


STEP 2:
subtract total cost of purchase (step 1) from amount she gave cashier ($20.00)

= $20.00 - $14.45
= $5.55 amount received back from cashier


ANSWER: (B) $5.55 received back

Hope this helps! :)

PLEASE HELP ASAP WILL GIVE BRAINLIEST!!!!!!
Mr. McClellan compared the weights (in pounds) of pairs of elk antlers dropped at Mount St Helens NVM and Rocky Mountain NP. He tabulated them in the following data table.
Weight of elk antler pairs at Mount St Helens NVM:
{34, 34, 30, 30, 30, 28, 28, 26}
Weight of elk antler pairs at Rocky Mountain NP:
{40, 38, 36, 36, 36, 36, 34, 32}
(a) Create a line plot for each data set.
(b) Calculate the mean and MAD for each area of collection.
(c) Calculate the means-to-MAD ratio for the two areas of collection.
(d) What inference can be made about the areas in regard to weight of dropped elk antlers? Explain

Answers

A) The two line plots are attached.

B) In order to calculate the mean, you have to sum all the values and divide it by the number of values:
m(MSH) = (34 + 34 + 30 + 30 + 30 + 28 + 28 + 26) ÷ 8 
              = 240 ÷ 8
              = 30

m(RM) = (40 + 38 + 36 + 36 + 36 + 36 + 34 + 32) ÷ 8
           = 288 ÷ 8
           = 36

In order to calculate the mean absolute deviation (MAD), you need to calculate the absolute values from the mean, sum them up and divide it by the number of values; the absolute values of the difference from the mean are:
MSH = {|34-30|, |34-30|, |30-30|, |30-30|, |30-30|, |28-30|, |28-30|, |26-30|}
        = {4, 4, 0, 0, 0, 2, 2, 4}

RM = {|40-36|, |38-36|, |36-36|, |36-36|, |36-36|, |36-36|, |34-36|, |32-36|}
     = {4, 2, 0, 0, 0, 0, 2, 4}

Therefore,
MAD(MSH) = (4 + 4 + 0 + 0 + 0 + 2 + 2 + 4) ÷ 8
                   = 16 ÷ 8
                   = 2

MAD(RM) = (4 + 2 + 0 + 0 + 0 + 0 + 2 + 4) ÷ 8
                = 12 ÷ 8
                = 1.5

C) In order to calculate the mean-to-MAD ratio, you need to simply divide the mean by the MAD:
r(MSH) = 30 ÷ 2 = 15

r(RM) = 36 ÷ 1.5 = 24

D) We can say that in Mount St Helens NVM elk antlers pairs are lighter but with a bigger variability (which means that they tend to be weight differently from each other), while in Rocky Mountain NP elk antlers pairs are heavier, but with less variability (which means that they tend to be similar to each other).

A) The two line plots are attached.


B) In order to calculate the mean, you have to sum all the values and divide it by the number of values:

m(MSH) = (34 + 34 + 30 + 30 + 30 + 28 + 28 + 26) ÷ 8 

             = 240 ÷ 8

             = 30


m(RM) = (40 + 38 + 36 + 36 + 36 + 36 + 34 + 32) ÷ 8

          = 288 ÷ 8

          = 36


In order to calculate the mean absolute deviation (MAD), you need to calculate the absolute values from the mean, sum them up and divide it by the number of values; the absolute values of the difference from the mean are:

MSH = {|34-30|, |34-30|, |30-30|, |30-30|, |30-30|, |28-30|, |28-30|, |26-30|}

       = {4, 4, 0, 0, 0, 2, 2, 4}


RM = {|40-36|, |38-36|, |36-36|, |36-36|, |36-36|, |36-36|, |34-36|, |32-36|}

    = {4, 2, 0, 0, 0, 0, 2, 4}


Therefore,

MAD(MSH) = (4 + 4 + 0 + 0 + 0 + 2 + 2 + 4) ÷ 8

                  = 16 ÷ 8

                  = 2


MAD(RM) = (4 + 2 + 0 + 0 + 0 + 0 + 2 + 4) ÷ 8

               = 12 ÷ 8

               = 1.5


C) In order to calculate the mean-to-MAD ratio, you need to simply divide the mean by the MAD:

r(MSH) = 30 ÷ 2 = 15


r(RM) = 36 ÷ 1.5 = 24


D) We can say that in Mount St Helens NVM elk antlers pairs are lighter but with a bigger variability (which means that they tend to be weight differently from each other), while in Rocky Mountain NP elk antlers pairs are heavier, but with less variability (which means that they tend to be similar to each other).


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how do i solve 3 (2y-4)=8y+9-9y

Answers

3(2y - 4) = 8y + 9 - 9y

Distribute 3:
6y - 12 = 8y + 9 - 9y

Combine like terms:
6y - 12 = -y + 9

Add y to both sides:
7y - 12 = 9 

Add 12 to both sides:
7y = 21

Divide both sides by 3:
y = 3
The first step for solving this equation is to distribute 3 through the parenthesis.
6y - 12 = 8y + 9 - 9y
Collect the like terms with y.
6y - 12 = -y + 9
Move the variable to the left side and then change its sign.
6y + y - 12 = 9
Now move the constant to the right side and change its sign.
6y + y = 9 + 12
Add the terms on the left side of the equation.
7y = 9 + 12
Add the numbers on the right side.
7y = 21
Lastly,, divide both sides of the equation by 7 to find your final answer.
y = 3
This means that y = 3 is the correct answer to your question.
Let me know if you have any further questions.
:)

What do you call a person who makes face all day long

Answers

A clockmaker is the answer

What method could have been used to collect the data?

Answers

11. The method used for data collection was observation. This is because recording the heights involves measurements which can be recorded through observation of heights of 11 students who were involved in the research. 

Answer: Observation.

12. Other data that could be recorded from the students that could be used to make a box plot include:
-age of the students
-weight of the students
-exam scores
-grades in which they belong to

the number of people who attended the spring festival is 799 more than 8 thousands. how many people attended the festival?

Answers

8×1000 +799 = 8,799 people attended the festival.

In this question, we are given the information about total number of people but in word equation.

We are given that, 799 more from 8 thousand attend the festival.

When we are given more, we add the number to the number from which it is more.

Here, we will add 799 to 8,000 in order to calculate total number of people who attended the festival

Thus, total number of people who attended the festival = 8,000 people + 799 people = 8,799 people.


Diane is baking cookies. She bakes four dozen sugar cookies, three dozen butter cookies, and two dozen chocolate chip cookies. She gives away 2 dozen sugar cookies, 2.5 dozen butter cookies, and 1.5 dozen chocolate chip how many cookies does she have left? ( Give an exact number of cookies).

Answers

Total of 36 cookies left. 48+36+24=108. 108-24-30-18=36

THIS IS SUPER EASY I NEED HELP

Answers

[tex]\left(\dfrac{1}{2}\right)^5=\dfrac{1^5}{2^5}=\dfrac{1}{32}[/tex]

[tex]2^5=2\cdot2\cdot2\cdot2\cdot2=32[/tex]

Answer: [tex]\left(\dfrac{1}{2}\right)^5=\dfrac{1}{32}[/tex]
(1/2)^5 is equivalent to 

(1/2) x (1/2) x (1/2) x (1/2) x (1/2)

The answer is .03125 or 1/32

PLZ Help me!!! 20 Points! Plz, know the answers!
Jack needs to save $125 to go to a concert. He has saved $35. He makes $7.50 an hour at his job. With x representing the number of hours, which equation and solution can be used to show how many hours Jack must work in order to have enough money to go to the concert?
A. 125x + 35 = 750; x = 5.75
B. 35x + 125 = 750; x = 18
C. 7.5x + 35 = 125; x = 12
D. 35−7.5x=125;x=6

Answers

Jack needs to save $125 but he has saved $35.
He makes $7.50 an hour at his job.
With x representing the number of hours

so equation

7.5x + 35 = 125
7.5x = 90
     x = 12

answer
C. C. 7.5x + 35 = 125; x = 12 
the answer is C because $125 is the total needed minus the $35 he already has saved brings it down to $90 he still needs, divided by $7.50 an hour equals 12 hours he would need to work.

Two numbers multiply to be -15 and adds to be 2 what are the numbers?

Answers

Assuming x and y are the two numbers,
[tex]x + y = 2 \\ x \times y = - 15[/tex]

[tex]x + y = 2 \\ x = 2 - y[/tex]

Substitute that into
[tex](2 - y) \times y = - 15 \\ 2y - {y}^{2} = - 15 \\ {y}^{2} - 2y - 15 = 0 \\ (y - 5)(y + 3) = 0 \\ y = 5[/tex]

Substitute that into
[tex]x = 2 - 5 \\ x = - 3[/tex]

Answer : The two numbers are 5 and - 3.

Hope this helps. - M

write the worlds as an algebraic expression. the width plus twelve. how do i do it?

Answers

Answer: X + 12

Reason/Explanation:
It's asking us to write the words as an algebraic expression. "The width plus twelve." For starters, we don't know what the width is, so we use a variable, X. Now we add 12. So we use X + 12. The width is X, plus twelve.

-DustinBR
X + 12 correct

You have to find x then add 13

Jess is building a skateboarding ramp in the shape of a triangular prism with the dimensions shown. If Jess wants to cover all faces of the ramp with plywood, how much plywood will he need?

96 square feet
144 square feet
156 square feet
168 square feet

Answers

we know that
surface area of the triangular prism=2*area of the base+perimeter of base*height

area of the base=b*h/2
b=3 ft
h=4 ft
area of the base=3*4/2----> 6 ft²

perimeter of the base=3+4+5-----> 12 ft
height of the prism=12 ft

surface area of the triangular prism=2*6+12*12-----> 12+144---> 156 ft²

the answer is
156 ft²

Answer:

C) 156

Step-by-step explanation:

a triangle with an area of 202.5 has a height that measures 15 find its base

Answers

the area = 1/2 * base * height

202.5 = 1/2 *  base * 15

measure of the base =  202.5 / (1/2 * 15)

=   27 answer

Which of the binomials below is a factor of this trinomial ? X^2 + x + 12

Answers

That trinomial can't be factored. You would have to complete the square to factor it and even then your answer would be an imaginary number. 

x² + x + 12 = 0
x² + x = - 12
x² + x + 1/4 = - 12 + 1/4
x² + x + 1/4 = - 11 3/4
x² + x + 1/4 = - 47/4

(x + 1/2)² = - 47/4 
x + 1/2 = +/- √(- 47/4) 
x + 1/2 = +/- [tex] \frac{47}{4}i [/tex]

x = 1/2 +/- [tex] \frac{47}{4}i [/tex]

If the constant was a negative, it would be factor-able (is that a word?). 

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