Mathematics Middle School

What is the GCF of 28,56,and 84.
Also what is the GCF of 30,45, and 75.

Answers

Answer 1
1.) 28- all numbers listed are divisible by 28
2.) 15 (30/2, 45/3, and 75/5)

Answer 2

The gcf for the numbers 28, 56 and 84 is 28

Since

28: 1, 2, 4, 7, 14, 28

56: 1, 2, 4, 7, 8, 14, 28, 56

84: 1,2,3,4,6,7,12,14,21,28,42,84

Since the biggest number they all have is 14 so the gcf is 14.

The gcf for the numbers 30, 45, and 75 is 15

30: 1,2,3,5,6,10,15,30

45: 1,3,5,9,15,45

75: 1,3,5,15,25,75

Since the biggest number they all have is 15 so the gcf is 15.

Hope this helped

Related Questions

line m contains the points with coordinates (-4,1) and (5,8) and line n contains points with coordinates (6,-2) and (10,7) .are the lines parallel,perpendicular,or neither? justify your answer

Answers

M would be negative 4 and 1 becuase of the ratio

Write the sentence as an inequality.
Seven is at most the quotient of a number d and 5.

Answers

answer will be 7≤ d/5
answer: 7≤ d/5
hope this helps:D

plz give brainiest

A road sign gives drivers information about traffic on busy highways. One sign shows "15 miles in 20 minutes". What is this speed in miles pee hours?

Answers

First of all you need to work out 20 minutes in hours, this can be done by dividing 20 by 60:
20/60 = 1/3

Then you need to divide 15 by 1/3 to get the final speed:
15 / 1/3 = 45 miles per hour


He will need to be traveling at 45 miles per hour,
Hope this helps! :)
15/20 = mph/60

60 x 15 = 20 x mph

900 = 20 x mph

900/20 = mph

45mph is your answer.

after a reflection over the line y=x (8,11) is the image of point c. what is the original location of point c

Answers

the original points/point c would be (-8,11) bc the y stays the same and the x changes from its original to (in this case) negative to positive
 
(positive to negative/negative to positive for either the x or y)

hope this helps
Final answer:

The original location of point C before a reflection over the line y=x, given that the image of point C is at (8,11), would be (11,8) as coordinates are swapped during such a reflection.

Explanation:

To determine the original location of point C before a reflection over the line y=x, you would apply a simple transformation rule. For any reflection over the line y=x, the coordinates of a point are swapped. Thus, if the image of point C is at (8,11), the original location of point C would have the x-coordinate as 11 and the y-coordinate as 8.

The step-by-step process to find the original location of point C before the reflection is as follows:

Take the x-coordinate of the image and make it the y-coordinate of the original point.Take the y-coordinate of the image and make it the x-coordinate of the original point.The resulting point is the original location of C before the reflection.

Therefore, the original location of point C is (11, 8).

A real number greater than or equal to 5.5

Answers

A real number = x or any variable

It would be x ≥ 5.5

How many one thirds are in 7 halves?

Answers

Hello!

Here's how to solve this question without the use of a calculator.

[tex] 7 \times { \frac{1}{2} } = { \frac{7 \times 1}{2} } = { \frac{7}{2} } [/tex]

7/2 ÷ 1/3 = ?

Change division to multiplication.

[tex] { \frac{7}{2} } \times { \frac{3}{1} } = { \frac{7 \times 3}{2 \times 1} } = { \frac{21}{2} } [/tex]

21/2 = 10.5 ≈ 10 (rounded)

Thanks for posting your question in the community :)

X+3/6=x-6/3
x plus 3 divided by 6 equals x minus 6 divided by 3 solve for x

Answers

there is no solution because the Xs cancel out
Answer:  "x = 15 " .
_____________________________________________
Explanation:
_____________________________________________
Given:
_____________________________________________
 " (x + 3) / 6 = (x − 6) / 3 " ;    Solve for "x" ;
_____________________________________________
Multiply EACH SIDE of the equation by "6" ;
              to get rid of the "denominators" ("fractions") :
_____________________________________________
              →   6* { (x + 3) / 6 } = 6 * { (x − 6) / 3 }  ; 

to get:
_____________________________________________
                    →      x + 3 = 2(x − 6) ;
_____________________________________________

Note the "distributive property of multiplication"  :
_____________________________________________
         a(b + c) = ab +  ac ; 
         a(b − c) = ab − ac ;
_____________________________________________
As such:
_____________________________________________
   →  2(x − 6) = (2*x) − (2* 6) = 2x − 12 ;
_____________________________________________
So; we can rewrite the original equation:
_____________________________________________
                      "  x + 3 = 2(x − 6) " ;

        →  by substituting:  "2x − 12" ; [ in lieu of:  "2(x − 6)" ] ;  as follows:
______________________________________________________
                → x + 3 = 2x − 12 ; 

Now, we can subtract "x";  and can add "12" ; to EACH SIDE of the equation:

               → x + 3 − x + 12 = 2x − 12 − x + 12 ; 

               to get:   15 = x ; 

               ↔  x = 15 ; which is our answer.
______________________________________________



write each fraction or mixed number as a decimal.
1. 7/8 2. 7/15 3. 4 3/25

Answers

1.7.8
2. 7.15
3. 103.25

write three equivalent ratios for 10/12

Answers

10 to 12

10/12

and 

10:12


i hope this helps =)
5/6

20/24

30/36.


I interpreted the question this way:)

If 2/3 out of 3/3 of the pie is eaten what fraction remains

Answers

3/3 - 2/3 = 1/3 of the pie is left.
2/3 out of 3/3 is eaten

3/3 - 2/3 = 1/3

1/3 remains 

hope this helps

Jada has 7/8 cup of cheese. Her cheese bread recipe calls for 1/6 cup of cheese. How many times can she make her recipe with the cheese she had?

Answers

Divide 7/8 cup by 1/6 cup.

Write 7/8.  Then invert 1/6 and multiply the result:

7     6
-- * --- = 42/8 = 5 2/8 = 5 1/4.  She can make her recipe 5 times and have a bit of cheese left over.
8     1

A referee was standing on a certain yard line as the 1st quarter ended. He walked 41 3/4 yards to a yard line with the same number as the one he just left. How far was the refree from the nearest goal

Answers

Refer to the diagram shown below.

The American football field is 100 yds long, 53 1/3 yards wide, and has 10-yard touchdown zones at each end of the field.

Let x = distance of the referee at the end of the quarter from the nearest goal.
The distance between the same yard lines on either side of the  center line is
100 - 2x

This distance is the 41 3/4 yards that the referee walked. Therefore
100 - 2x = 41.75
-2x = 41.75 - 100 = -58.25
x = 29.125 yd  (or 29 1/8 yd)

Answer:
The referee was  29 1/8 yards (or 29.125 yards) from the nearest goal.

there was 2/3 of a pizza for 6 friends to share equally. What fraction of the pizza did each person get

Answers

Each person gets 1/9 of the pizza

Hope this helps!
Hello There!

[tex] \frac{2}{3} [/tex] x [tex] \frac{1}{6} [/tex] = [tex] \frac{2}{18} [/tex]
You can simplify that to
[tex] \frac{1}{9} [/tex]

Hope This Helps You!
Good Luck :) 

- Hannah ❤

PLEASE HELP!

Is it possible for a number to be a rational number that is not an integer but is a whole number? Explain

Answers

Every whole number is a rational number: for example, 3=31. So it is rational. Every whole number n can be written as a fraction of integers: n=n1. We aren't required to write it that way; we just need to know that it is possible to express every whole number as a fraction of integers, and hence it is rational.

What’s 28.2% of 92
Plz and thank you

Answers

28.2/100 = x/92

Multiply 92 by 28.2

2594.40

Then divide by 92

28.2

28.2% of 92 is 28.2

Hope this helps!

The value of given percent 28.2% of 92 is equal to 25.94

To calculate 28.2% of 92,  follow these steps:

Convert the percentage to a decimal by dividing it by 100. In this case, 28.2% becomes 0.282 (28.2 ÷ 100 = 0.282).

Multiply the decimal by the number you want to find the percentage of. here, 0.282 multiplied by 92:

0.282 ×92 = 25.944

Round the result to an appropriate number of decimal places. In this case, we'll round it to two decimal places:

28.2% of 92 is approximately 25.94.

Therefore, 28.2 percent of 92 is equal to 25.94.

learn more about percent here

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Mary never liked math and did poorly when she decided to think of it as a fun challenge her performance improved this is an example of

Answers

a competitive mindset seeing it as a challenge helps some people hope i helped

Answer:

Mary's improved math performance after seeing it as a fun challenge reflects a growth mindset, believing in the ability to develop skills through effort and dedication.

Explanation:

Mary's improved performance in math after deciding to think of it as a fun challenge is an example of the power of mindset, specifically a growth mindset. A growth mindset is the belief that abilities and intelligence can be developed through dedication and hard work. By shifting her perspective and viewing math as a fun challenge rather than something she was inherently bad at, Mary adopted a growth mindset. This change in mindset likely led her to approach math with more enthusiasm, effort, and persistence, ultimately resulting in improved performance.

g (a) = 4a ; Find g (2a)

Answers

this is how u do it...
ga=4a

Step 1: Divide both sides by a.

ag/a=4a/a. fraction

g=4
the answer is
4

If the unit selling price is 2.50 and the unit cost is 1.00 what action is needed to maintain the gross margin percentage when unit cost increase 0.25

Answers

The original gross margin is (2.50 / 1.00) - 1 = (2.5 - 1) = 1.5  =  150%

the cost increases 0.25, is an increase of (0.25 / 1.00) = 25%

  in order to keep the same gross margin, you need to increase the sale price by 25%

2.50*1.25 = 3.125

Then the gross margin is (3.125 / 1.25) - 1 = (2.5 - 1) = 1.5 = 150% ( same as original )

The population in the South in 2000was 100,236,820. In 2010 the population increased by 14.3% from 2000. How many people live in the south in 2010

Answers

First get the percentage of increase by changing 14.3 percent to a decimal and multiplying 100,236,820  by .143

100,236,820 x .143 = 14,333,865

Now add 100,236,820 by 14,333,865 
100,236,820 + 14,333,865 = 114,570,685

Elena drove 245 miles last week & 222 miles this week.she estimated that she drove about 475 miles bin both weeks.how did she estimate

Answers

she add both of her miles together 

Answer:

This estimate is based on the addition of both the miles of both weeks by rounding them off.

Step-by-step explanation:

Elena drove 245 miles last week & 222 miles this week.

She estimated that she drove about 475 miles in both weeks.

This estimate is based on the addition of both the miles of both weeks by rounding them off.

245 is rounded to 250

222 is rounded to 225

Now adding both [tex]250+225=475[/tex] miles.

Write 4,050 in expanded form.

Answers

4000 + 50 is the correct answer
4,050 in expanded form is 4000+50

a rectangle prism is 4 units high, 2 units wide, and 6 units long. what is its surface area in square units?

Answers

SA: 2(w × l + h × l + h × w)    w = 2, l = 6, h = 4

SA: 2(2 × 6 + 4 × 6 + 4 × 2)

SA: 2(12 + 24 + 8)

SA: 2(36 + 8)

SA: 2(44)

SA: 88

hope that helps, God bless!

Surface area of the rectangle prism is 88 sq. units.

Given:

height of the rectangle prism (h) = 4 units

width of the rectangle prism (w) = 2 units

length of the rectangle prism (l) = 6 units

Recall:

Formula for surface area of a rectangle prism is:

[tex]SA = 2(lw +wh +lh)\\[/tex]

Plug in the values:

[tex]SA = 2(6\times 2 +2\times4 +6\times4)\\SA = 2(12 + 8 + 24)\\SA = 2(44)\\SA = 88[/tex]

Therefore, the surface area of the rectangle prism is 88 sq. units.

Learn more about surface area of a rectangle prism here:

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Evaluate b2 − 4ac for a = −3, b = 5, and c = 2.

Answers

I believe the answer is -19
The answer is 49.
5^2= 25
-4*-3= 12
12*2= 24
24+25= 49

Can someone help me? (Algebra 1)

Answers

I believe real and rational.
Let's find out what the following terms mean, so we know what to choose from: 

 - An irrational number is a number that cannot be represented by a simple fraction. They can't be written as a ratio with two integers (like 55 = 55/1, 1.5 = 3/2, -.25 = -3/4). They are unable to repeat, and unable to end. Pi (3.1415926...) is a notable example of an irrational number. 1.7 as a fraction is 17/10. It can be written as a ratio with two integers, so it is not irrational. 

- A real number is a number that represents any quantity in a number line. It includes all numbers. Every number is a real number. So, 1.7 is a real number. 

- A whole number is a positive number (including 0) that does not include any fractions, decimals, radicals, etc. Numbers such as 5, 32 and 73 are considered whole numbers. 1.7 is not a whole number, since it is a decimal. 

- A rational number is a number that can be written as a fraction. Values such as whole numbers (ex: 3/1), negative numbers (ex: -7/1), decimals that can be successfully written as a ratio (ex: .5) are rational numbers. Unlike irrational numbers, these can end (3.4) and repeat (3.3333333333...). 1.7 is able to be written out as a fraction with two integers and it ends. It is a rational number. 

- A natural number is a positive whole number. So, naturals are greater than 0. numbers such as 1,2,3 and onward are natural numbers. 1.7 is a decimal;  it is not considered a natural number. 

- Integers are all the positive and negative whole numbers including zero. 123, -5000, and 34 are random examples of an integer. 1.7 is a decimal, so it is not an integer. 

God Bless. You are going to do great in not only math, but in all your classes! 

A sketch of the line 2y-x=4 is shown.
The line cross with the axes at A and B.
Calculate the coordinates of A and B
Thank you.

Answers

 solution a, e M, is uniquely defined by the inequality (A'an – f', '' – an) < 0 ... Vane M, x, e M. (6.1.9) It is possible because a, e X, and a € X, Since M, C M for all n > 1, the sequence {a}} is compact, hence, there exists ¥ € M such that a' – 30 as n ... M = {a e X | p(x) = 0}, where b : X → R is a convex and continuous functional.

Given the following system of equations, identify the type of system. x + y = 4 x - y = 6

Answers

The following system of equations,  x + y = 4 x - y = 6 represents an Independent System.

What is the equation?

A formula that expresses the connection between two words on each side of an indication. A calculation with an integer multiple is referred to as an equation. Algebra is widely used in equations. In performing calculations but unsure of the precise amount, algebra is utilized.

When there is only one solution, a set of linear regression is persistent and independent. The diagrams of the platform's lines intersect at precisely one spot if this is the case. If a set of linear equations would have no resolutions, it is inconsistent. There is only one solution pair for an autonomous state (x,y). The sole solution is the intersection of the two lines. A system that is incongruous cannot be fixed.

Learn more about equation, Here:

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Solve for x.

−1/5(x−4)=−2

Answers

Solve for x.
−1/5(x−4)=−2

x=14
:)
x = 14  did u want to sovle for x or not

plz help...A hair salon charges a fixed rate of $25.00 for a haircut and then an additional $15 for any other services. Write a function to model the cost of services there and then determine how many services you had if you were charged $115

A)
f(x) = 15x + 25; f(6) = 115


B)
f(x) = 25x + 15; f(6) = 165


C)
f(x) = 15x + 25; f(6) = 125


D)
f(x) = 15x + 25; f(115) = 1750

Answers

The answer is A 
Hope this helps!!
the answer is a because it says you were charged 115 and thats the only one with 115 

Alvin’s family used 20.5 gallons of gas to Drive 492 miles. How many miles did they drive on each gallon of gas

Answers

Since they use 20.5 gallons in 492 miles you need to divide 492/20.5 which gives you 24

Answer: 24.0

Step-by-step explanation:

divide 492 and 20.5

If a television screen with a length-to-height ratio of 16:9 has an area of 576in, what is it's perimeter?

Answers

Final answer:

The perimeter of the television screen is 100 inches.

Explanation:

To determine the perimeter of a television screen with a length-to-height ratio of 16:9 and an area of 576 square inches, we need to find the length and the height of the screen first.

Using the ratio, we let the length be 16x and the height be 9x.

The area of a rectangle is given by its length times its height, so we have:

(16x) × (9x) = 57

144x² = 576

x² = 576 / 144

x² = 4

x = 2

Now we can find the actual dimensions:

Length = 16 × 2 = 32 inches

Height = 9 × 2 = 18 inches

The perimeter (P) of a rectangle is given by

P = 2 × (Length + Height)

P = 2 × (32 + 18)

P = 2 × 50

P = 100 inches

The perimeter of the television screen is 100 inches.

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