Mathematics Middle School

please help Use the expression 8a + 16c.

Part A
Factor the expression using the GCF.
A. 2(4a + 8c)
B. 4(2a + 4c)
C. 8(a + 2c)
D. 16(12a + c)


Part B
What is the value of the expression when a = –5 and c = –1? Enter your answer in the box.

Answers

Answer 1
Part A.

C. 8 (a + 2c)


Explanation:
The answer is c because when you have this equation (below) you have find what both numbers are divisible by:


[tex]8a + 16c[/tex]

Both of these numbers are divisible by 8 (This number would be on the outside of the parenthesis).


[tex] \frac{8a}{8} + \frac{16c}{8} [/tex]

Now that you know they're both divisible by 8 you can start to put together your equation. So far you should have this:

8 (? +?)

Now to find the other numbers you have to think... what number multiplied by 8 will make it equal to 8a? The answer would be a. 8 times a = 8a. (Another way to do this is to just divide 8a by 8 same with 16)

Now your equation should look like this:

8 (a + ?)

Now do the same thing with the 16c as you did with the 8a. (either divide 16c by 8 or think of a number times 8 that will make it equal 16c) For this one I'm going to use the division method - so what is 16c ÷ 8? 16 ÷ 8 = 2 and finally just add the c. So your answer is 2c.

Your equation should not look like this:

8 (a + 2c)

You're done!



Part B.

-56


Eplanation:
To find this just plug in the numbers into the equation. a = -5 and c = -1.
For this I used the original equation :


[tex]8a + 16c[/tex]

Plug in the numbers....


[tex]8( - 5) + 16( - 1)[/tex]

And solve!


[tex] - 40 + - 16[/tex]

And finally....


[tex] - 40 + - 16 = - 56[/tex]

So the value of the equation if a were -5 and c were -1 would be -56!
Answer 2

The required expression is C. 8(a + 2c) and value of the expression when a = –5 and c = –1 is -56.

What is an expression?

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given the expression is

8a + 16c.

To find the Factor form of the given expression by using GCF.

We have,

8a + 16c.

Factors of each term:

8a = 2 x 2 x 2 x a

16c =  2 x 2 x 2 x 2 x c

The common factors are 2, 2 and 2. then Taking out the greater common factor (GCF) in the given expression;

GCF = 8

The answer is C. 8(a + 2c)

when a = –5 and c = –1

Then;

8(a + 2c)

8(-5 + 2(-1)) = 8 (-7) = -56

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Related Questions

a desert has both fruit and yogurt inside altogether the mass of the desert is 185g the ratio of the mass to fruit to the mass of yoghurt is 2:3 what is the mass of yoghurt?

Answers

fruit : yoghurt : total
2 : 3 : 2 + 3
2 : 3 : 5

5 parts = 185
1 part = 185 ÷ 5 = 37
3 parts = 37 x 3 = 111g

The mass of the yoghurt is 111g

The mass of the fruit is 74 grams and the mass of the yoghurt is 111 grams.

Given :

Total mass of the desert is 185 g.The ratio of the mass to fruit to the mass of yoghurt is 2:3.

Solution :

This question is solved by making a linear equation in one variable. Linear equations are nothing but yet another subset of "equations". Any linear calculations requiring more than one variable can be done with the help of linear equations. The standard form of a linear equation in one variable is of the form ax + b = 0. Here, x is a variable, and a and b are constants.

Now to form a linear equation first let x be the mass in gram. Than total mass of the desert is given by:

[tex]3x+2x=185[/tex]

[tex]5x = 185[/tex]

[tex]x = \dfrac{185}{5}[/tex]

x = 37 grams

Therefore the mass of the fruit = [tex]2 \times 37[/tex] = 74 grams and the mass of the yoghurt = [tex]3\times 37[/tex] = 111 grams.

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triangle XYZ has vertices X(6,-2.3), Y(7.5,5), and Z(8,4). when translated X' has coordinates (2.8,-1.3). Write a rule to describe this transformation. Then find the coordinates of Y' and Z'.

Answers

Final answer:

The transformation is a translation where you subtract 3.2 from the x-coordinate and add 0.7 to the y-coordinate. Using this rule, Y' is (4.3, 5.7) and Z' is (4.8, 4.7).

Explanation:

The student is asking about a translation transformation in a coordinate plane. Given the original and translated coordinates for point X, we can determine the translation rule by calculating the differences between the coordinates.

The x-coordinate has changed from 6 to 2.8, a decrease of 3.2, and the y-coordinate has changed from -2 to -1.3, an increase of 0.7. Thus, the translation rule is to subtract 3.2 from the x-coordinate and add 0.7 to the y-coordinate.

To find the translated coordinates for points Y and Z, we apply the same rule:

Y'(Y after translation) will have coordinates (7.5 - 3.2, 5 + 0.7) which simplifies to (4.3, 5.7).Z'(Z after translation) will have coordinates (8 - 3.2, 4 + 0.7) which simplifies to (4.8, 4.7).

In summary, Y' is (4.3, 5.7) and Z' is (4.8, 4.7).

To find the translation rule, we used the given coordinates of X and X' to determine a translation vector of (-3.2, 1). Using this rule, the coordinates of Y' are (4.3, 6) and Z' are (4.8, 5).

Given the vertices of triangle XYZ: X(6, -2.3), Y(7.5, 5), and Z(8, 4), and knowing that vertex X when translated has coordinates X'(2.8, -1.3), we need to determine the translation rule.

First, find the translation vector by comparing the coordinates of X and X'.The translation from X to X' is (2.8 - 6, -1.3 + 2.3) which equals (-3.2, 1).Therefore, the translation rule is: (x, y) → (x - 3.2, y + 1).Apply this rule to the coordinates of Y and Z to find Y' and Z'.For point Y(7.5, 5):
Y' = (7.5 - 3.2, 5 + 1) = (4.3, 6).For point Z(8, 4):
Z' = (8 - 3.2, 4 + 1) = (4.8, 5).

Hence, the coordinates of the translated points are Y'(4.3, 6) and Z'(4.8, 5).

here is the complete question-Triangle XYZ has vertices X(6, -2.3), Y(7.5, 5), and Z(8, 4). When translated, X` has coordinates (2.8, -1.3). Write a rule to describe this transformation. Then find the coordinates of Y' and Z'.

Chantelle is going on an 8 day hike of 82.5 miles. she plans to hike 8.25 hours everyday for each of those 8 days. how many miles will she covet each hour of her trip?

Answers

Final answer:

Chantelle will cover 1.25 miles each hour of her hike.

Explanation:

To find out how many miles Chantelle will cover each hour of her trip, we need to divide the total distance of 82.5 miles by the total time of 8.25 hours per day for 8 days.

First, we calculate the total time of the trip by multiplying the hours per day (8.25) by the number of days (8): 8.25 hours/day x 8 days = 66 hours.

Next, we divide the total distance by the total time: 82.5 miles / 66 hours = 1.25 miles/hour.

Therefore, Chantelle will cover 1.25 miles each hour of her hike.

Angles ABC is dilated using scale factor of 2. what happens to its angle measures?

Answers

Hello,

When you are dilating a shape you are simply making the sides larger or smaller. However, the angles will remain the same.

Imagine a stop sign being made twice as large. The side would be twice a long, however all of the angles will remain the same.

Good luck,
MrEQ

Joe walked 4/9 of a mile in 4/5 of an hour. What is his unit rate in miles per hour? 4/9 over 4/5 = 5/9 mile per hour 4/5 over 4/9 = 1 and 4/5 miles per hour 4/9 over 4/5 = 1 and 4/5 miles per hour 4/5 over 4/9 = 5/9 mile per hour

Answers

Joe walks at approximately .56 mph.

4/9= .444...
4/5= .8

.444 miles /.8 hours= x miles /1 hour
x= .56 mph

If Joe walked 4/9 of a mile in 4/5 of an hour then the unit rate is  5/9 miles/hour.

What is Division?

A division is a process of splitting a specific amount into equal parts.

The distance walked by Joe is 4/9 of a mile.

The time taken by Joe to walk 4/9 of a mile is 4/5 of an hour.

We need to find the unit rate in miles per hour.

To find this we just need to divide 4/9 by 4/5.

Rate = Distance/Time

Distance = 4/9 miles

Time = 4/5 hour

Rate  = 4/9 ÷ 4/5

Rate = 4/9 × 5/4

Rate = 5/9 miles/hour.

Hence, if Joe walked 4/9 of a mile in 4/5 of an hour then the unit rate is  5/9 miles/hour.

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9x+10y=29
10x+9y=28
Solve by elimination

Answers

[tex](9x + 10y = 29)9[/tex]
[tex](10x + 9y = 28) - 10[/tex]

[tex]81x + 90y = 261[/tex]
[tex] - 100x - 90y = - 280[/tex]
[tex] - 19x = - 19[/tex]
[tex]x = 1[/tex]
[tex]9(1) + 10y = 29[/tex]
[tex]9 - 9 + 10y = 29 - 9[/tex]10y=20
y=2

a picture of a school mascot is 18 in. Wide and 24 in. Long. It is enlarged proportionally to banner size. If the width is enlarged to 63 in., what is the length of the banner?

Answers

3.5. All you do is divide 63/18.
84 inches. Cross multiply or use the rule of three

The area of a trapezoid is 18sq. ft and the sum of its bases is 6 ft. Find the area of a square whose side is equal to the height of the trapezoid.

Answers

Area = (L1 + L2)*h/2
Area = 18
L1 + L1 = 6
h = ???

18 = (L1 + L2)*h/2
18 = (6) * h/2 Multiply both sides by 2
36 = 6h Divide by 6
36/6 = h
h = 6
So the square is 6 by 6
Area square = s^2 where s is the side of the square.
Area = 6^2 = 36 

Area = (L1 + L2)*h/2

Area = 18

L1 + L1 = 6

h = ???

18 = (L1 + L2)*h/2

18 = (6) * h/2 Multiply both sides by 2

36 = 6h Divide by 6

36/6 = h

h = 6

So the square is 6 by 6

Area square = s^2 where s is the side of the square.

Area = 6^2 = 36 

so your answer will be 6^2 = 36 

find the area of a triangle with sides a=5 b=8 c=11

Answers

The answer is either 20 or 27.5.

If the base is 5, then the area is 20.
If the base is 11, then the area is 27.5.

Hope I helped☺☺

What is the answer to problem 13

Answers

answer D <<<<
You are correct

option d is correct as its values comes out to be 39 which is same as given expression


i deserve brainliest please

YOU WILL GET 50 POINTS IF YOU EXPLAIN HOW YOU GOT THE ANSWER TO THIS PROBLEM. I WILL MARK YOU AS BRAINLIEST TOO. THANK YOU :)
Phil used 3 gallons of paint to cover 1,125 square feet of a wall. at this same rate, what is the total area of the wall, in square feet, that Phil will cover using 5 gallons of paint ?

A) 675 square feet
B) 1,575 square feet
C) 1,800 square feet
D) 1,875 square feet

Thank you :)

Answers

your answer is D 1,875 square feet
step1: divide 1,125/3=375
step2: multiply 375*5=1,875
you divide to get the ratio you multiply to get the total area he will cover
hope this helped have a great day
The answer is D 1875 square feet
My work:
First I divided 1125 by 3 to get 375 then I
Multiplied 375 by 5 and got 1875 so the
Answer is D

Hope I helped if so Mark me as brainliest

7.2 + ( -5.55) = -5.5 + 7.2 identify what property is shown

Answers

i am not sure if i'm right but if you had function operation in your options then its the answer

How would 4,609,912,073 be written in word form? A. four billion, six hundred nine million, nine hundred twelve thousand, seven hundred three B. four billion, six hundred nine million, nine hundred twelve thousand, seventy-three C. four million, six hundred ninety-nine thousand, one hundred seventy-three D. fourteen million, nine hundred twelve thousand, seven hundred three

Answers

Your answer is B. four billion, six hundred nine million, nine hundred twelve thousand, seventy-three

a women has a ladder that is 13 ft long. if she sets the base of the ladder on level ground 5ft from the side of a house, how many feet above the ground will the top of the ladder be when it rests against the houlad

Answers

It is convenient to remember that 5-12-13 is a Pythagorean triple.

Her ladder is 12 ft above the ground where it rests on the house.

_____
Using the Pythagorean theorem, you are given the hypotenuse as 13 ft and one leg as 5 ft. Then the other leg is
.. √(13^2 -5^2) = √(169 -25) = √144 = 12

Final answer:

Using the Pythagorean theorem, it is determined that the ladder reaches 12 feet up the side of the house when the base is placed 5 feet away.

Explanation:

To solve for the height at which the ladder reaches the house, we can use the Pythagorean theorem, which relates the lengths of the sides of a right triangle.

In this scenario, the ladder represents the hypotenuse (c), the distance from the base of the ladder to the house gives one leg of the triangle (a), and the height the ladder reaches up the side of the house is the other leg (b).

Let a = 5 ft (distance from the ladder's base to the house).Let c = 13 ft (length of the ladder).We need to find b (the height the ladder reaches the house).

According to the Pythagorean theorem, a² + b² = c². Plugging in our known values allows us to solve for b²:

a² = 5² = 25.c² = 13² = 169.Subtract a² from c² to get b²: 169 - 25 = 144.Take the square root of b² to find b: √144 = 12.

Therefore, the top of the ladder will be 12 feet above the ground.

find the value of this pronumeral

Answers

Answer:

x = 70 ; 

y = 50  .
_____________________________________________________
Explanation:
_____________________________________________________
y = 50 ; since vertical angles are congruent.


180 – (50 + 60) = x ;  since all angles in any triangle add up to 180 degrees. 

↔  x = 180 – (50 + 60) = 180 – (110) = 70.
_____________________________________________________

HELP ME PLZ

Using V = lwh , find an expression in factored form for the volume of this prism. Explain the general steps you used to arrive at this answer.

Answers

You are asked to use the volume formula V = lwh which basically means to find the volume by multiplying the length, width and height of the prism. These are all given to you as expression so you are asked to multiply the expressions. That is, find: [tex]( \frac{ x^{2} -x}{4x+1} )( \frac{2x-5}{1} )( \frac{24 x^{2} +6x}{x-1} )[/tex]

First factor each of the expressions in the numerators and then multiply those in the numerators putting them over those in the denominator. It turns out those in the denominators (in this problem) cannot be factored. When you do this you are left with:
[tex]\frac{(x)(x-1)(2x-5)(6x)(4x+1)}{(4x+1)(x-1)} [/tex]

You can divide out (sometimes called cancelling out) those terms expressions that are in both the numerator and the denominator. That leaves you with:
[tex]\frac{(x)(2x-5)(6x)} {1}[/tex] which we can clean up by multiplying x and 6x in the numerator.

Thus, the volume of the prism is: [tex]6 x^{2} (2x-5)[/tex]
We do not multiply this out because it is now written as a product and thus factored (as you were asked).

The volume of the prism with the given dimensions is;

V = 12x³ - 30x²

We are given that the formula for the volume of a cube is;

V = Lwh

where;

L is length

w is width

h is height

We are given;

L = (24x² + 6x)/(x -1)

w = 2x - 5

h = (x² - x)/(4x + 1)

This means that;

V = [(24x² + 6x)/(x - 1)] × (2x - 5) × [(x² - x)/(4x + 1)]

Now, let us factorize the terms that can be factorized;

(24x² + 6x)/(x - 1) can be factorized into; [6x(4x + 1)/(x - 1)]

Similarly;[(x² - x)/(4x + 1)] can be factorized into [x(x - 1)/(4x - 1)]

Using the factorized terms to get the volume now;

V = [tex]\frac{6x(4x + 1)}{x -1} * (2x - 5) * \frac{x(x - 1)}{4x + 1}[/tex]

(x - 1) will cancel out and also 4x + 1 will cancel out to give;

V = 6x * x * (2x - 5)

V = 6x²(2x - 5)

V = 12x³ - 30x²

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please help and explain how u got your answer :)

Answers

square=base times height
square=area of 16
triangle=base times height divided by 2
triangle=24/2
triangle =12
28yd^2
Fins the area of the square, find the area of the triangle, then add those two areas together.

Square Area= a^2
=(4)^2
=16 yards squared

Triangle Area= 1/2 base * height
add 4 yards + 4 yards to equal whole side of triangle
=1/2 (6)(4+4)
=1/2(6)(8)
=1/2(48)
=24 yards squared

Add the area of the square and the area of the triangle together.
=16 + 24
=40 yards squared

ANSWER: 40 yards squared (second choice)

Hope this helps! :)

Which measurement is the closest approximation of the rectangle’s area? A. 15 m² B. 30 m² C. 40 m² D. 50 m²

Answers

6m x 8.5m ≈ 6 x 9 ≈ 54 ≈ 50m² (Answer D)
Hello!

The formula for area of a rectangle is:

A = l × w

We must multiply the length by the with to find the area. Substitute:

A = 8.5 × 6

A = 51

Now, 51 isn't in the given answer options, but that's because the question asks for the closest APPROXIMATION of the area.

ANSWER:

D. 51 m^2 is the closest approximation of the area.

pls help and show some steps

Answers

To solve this equation, simply plug in the value of h = 0 feet, as this would be the height the object will be on the ground. It would be 0.

Afterwards, solve the equation by factoring the quadratic function.

16t^2 - 64t - 80 = 0.
8(2t^2 - 8t - 10) = 0

2t^2 - 10t + 2t - 10 = 0

2t(t - 5) + 2(t - 5) = 0

(2t + 2)(t - 5) = 0

T = 5 and t = -1.

Since time can’t be negative, there is only one solution, t = 5.

It would be about 5 seconds.

If 2(x + 3) = x + 10, then x equals what

Answers

Final answer:

To solve the equation, we first distribute the 2 on the left, then collect like terms and finally isolate x. The solution to the equation 2(x + 3) = x + 10 is x = 4.

Explanation:Solution for the Equation

To solve the equation 2(x + 3) = x + 10, we will first distribute the 2 on the left-hand side of the equation to get 2x + 6. Therefore, the equation becomes: 2x + 6 = x + 10.

The next step is to collect like terms. To do this, we subtract x from both sides, which gives us: x + 6 = 10.

Finally, to solve for x, we subtract 6 from both sides of the equation: x = 4. Hence, the solution to the equation 2(x + 3) = x + 10 is x = 4.

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Final answer:

x = 4

Explanation:

To solve the equation 2(x + 3) = x + 10, we first expand the left side of the equation:

2 × x + 2 × 3 = x + 10

2x + 6 = x + 10

Now subtract x from both sides to move all x terms to one side:

2x - x + 6 = 10

1x + 6 = 10

Subtract 6 from both sides to solve for x:

x = 10 - 6

x = 4

Thus, the solution to the equation is x = 4. Checking the solution, we substitute x back into the original equation:

2(4 + 3) = 4 + 10

2(7) = 14

14 = 14

What is the value of the following function when x = 0?

Answers

The value is nothing because it has to be equal to zero.

Hope this helps:)

Answer:

It’s y=-2 on edge

Mr. Saba owns two food trucks. He rents two spots at the state fair. This table shows the number of tacos the two food trucks sold each day for 10 days.

Food Truck 1 721 658 437 527 601 468 425 431 508 515
Food Truck 2 462 471 426 654 647 732 701 684 632 698

Which conclusion can be drawn from the data?

The medians for the two taco trucks are the same
.
The two food trucks sold the most tacos on Day 3.

The range between the maximum and minimum values for taco truck 2 is greater than the range between the maximum and minimum values for taco truck 1.

On average, food truck 1 sold more tacos over the 10 days than food truck 2.

Answers

using the data for each truck lets calculate, 

median for truck 1 - 511.5
median for truck 2 - 650.5

lets consider each statement 
A.medians for both trucks are the same - wrong 
median for 1 and 2 are 511.5 and 650.5 respectively 

B. the two trucks sold most number of tacos on 3rd day 
truck 1 sold 437 on day 3 but highest number it sold was 721 on day 1
truck 2 sold 426 on day 3 but highest number was 732 on day 6
therefore this statement too is wrong 

C.
truck 1 - range between maximum(721) and minimum(425) = 296
truck 2 - maximum (732) and minimum (426) difference = 306
the range between maximum and minimum in truck 2 is 306 thats greater than range between maximum and minimum in truck 1, that's 296
therefore this statement is correct

D.
total number of tacos for each truck - 
truck 1 - 5291
truck 2 - 6107
food truck 1 sold less than truck 2 therefore this statement too is wrong 

Answer: C)  The range between the maximum and minimum values for taco truck 2 is greater than the range between the maximum and minimum values for taco truck 1.

Find the area of the triangle or quadrilateral.

Answers

To find the area of a trapezoid, use this formula:

A = 1/2 · h · (b₁ + b₂)
A = area
h = height
b₁ = base 1
b₂ = base 2

Plug in the numbers given for trapezoid AWEV
1/2 · 3 · (3 + 6)
Then solve
1/2 · 3 · 9 = 13.5

The area of trapezoid AWEV = 13.5 ft²

Follow the same steps for the second trapezoid (Trapezoid EFGH)

A = 1/2 · h · (b₁ + b₂)
A = area
h = height
b₁ = base 1
b₂ = base 2

Plug in the numbers given for trapezoid EFGH
1/2 · 4 · (13 + 8)
Then solve
1/2 · 4 · 21 = 42

The area of trapezoid EFGH = 42 ft²

I really need the answer I’ve been stuck on this all day

Answers

Hello!

You do 72/6 which is 12.

So the answer is 12

Hope this helps!
formula A=bh
The area is 72
72=6*b
Base= 12

Write a problem that uses a fraction greater than 1

Answers

two is greater than one
A problem that uses a fraction greater than one could be 15/4 plus 1/4

The period T of a pendulum in seconds depends on its length L in feet, and is given by the formula T=

Answers

This is a matter of plugging in. Specifically 7 for L.

T = 2πsqrt(7/32)
T = (6.28319...)(0.46771...)
T is about 2.93871 seconds

Given: ΔABC; a= 10; b = 4, and c = 11. Find the measurement of ∠B to the nearest tenth of a degree. A) 21.3° B) 24.7° C) 25.1° D) 31.4°

Answers

A) 21.3° is the answer, you must do the angle version of the law of cosines.

Can the sides of a triangle have lengths 7.2, 13.3, and 19.3?
yes or no

Answers

No They Cannot I Believe :D
No a triangle can’t have those lengths

Help I don’t understand

Answers

Rotation about a point does not change any dimensions. C'D' = CD = 2.8 units.

help me please!!!!!!

Answers

3276800/8 = 409600 (how many bacteria in an hour)

Then just multiply that number by the amount of hours you want to solve for 

9 hours = 3686400
10 Hours = 4096000
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