Solve 3(x - 2) < 18.

{x | x < 8}
{x | x > 8}
{x | x < -8}
{x | x > -8}

Answer:

The size of each section  is[tex]\frac{1}{32}[/tex] square yards

Step-by-step explanation:

Given:

Length of the fabric = 1/4 square yards

To Find:

The size of each section in square yards if divided into 8 equal sections

Solution:

Let the size of each section be x

Then

[tex]x = \frac{\text{length of the fabric}}{8}[/tex]

[tex]x = \frac{\frac{1}{4}}{8}[/tex]

[tex]x = \frac{1}{4} \times \frac {1}{8}[/tex]

[tex]x = \frac{1}{32}[/tex]

Then  the length of each section will be [tex]\frac{1}{32}[/tex] square yards

Kyra will make 9 cans from the sheet of metal.

Solution:

Height of the can (h) = 5 in

Radius of the can (r) = 6 in

The can is in the shape of a cylinder.

Surface area of the cylinder = [tex]2 \pi r^{2}+2 \pi r h[/tex]

Surface area of the can = [tex]2 \times3.14 \times 6^{2}+2 \times 3.14 \times 6\times 5[/tex]

                                       [tex]$=226.08+ 188.57[/tex]

                                       [tex]=414.65[/tex]

Surface area of the can = 414. 65 in²

Area of sheet of metal = 3750 in²

To find how many cans able to make:

[tex]$\text { Number of cans} =\frac{\text { Area of sheet metal }}{\text { Surface area of the can }}[/tex]

                         [tex]$=\frac{3750}{414.65}[/tex]

                         = 9.04

Number of cans = 9

Hence Kyra will make 9 cans from the sheet of metal.

Answer:

x = 40

Step-by-step explanation:

Since FG and HI are parallel and BC is a transversal, then

∠ GBE and ∠ GBE are same side interior angles and are supplementary, thus

3x + 20 + x = 180, that is

4x + 20 = 180 ( subtract 20 from both sides )

4x = 160 ( divide both sides by 4 )

x = 40

Answer:

That is math.

Answer:

When only solving for b you would multiple by the reciprocal of 1/18*b so you multiply 18 to both sides and b is equal to -108

Step-by-step explanation:

The given algebraic expression 9a1/2b14c3/2 appears to be a kind of factorization where a, b, c are variables raised to different powers. Unless values for these variables are provided, this expression can't be simplified further.

The expression 9a1/2b14c3/2 is considered as a form of factorization in mathematics where a, b, c denote variables, and the numbers 1/2, 14, 3/2 are their respective exponents. In other words, it's a product of the variables 'a', 'b', and 'c' raised to their respective powers. For instance, 'a' is under a square root (as signified by the power of 1/2), 'b' is raised to the power of 14, and 'c' is also under a square root but cubed (a power of 3/2).

Consequently, this expression doesn't seem to have a simpler or equivalent expression because the terms 'a', 'b', and 'c' are likely representing different entities, hence they can't be combined or simplified further. However, should there be values for 'a', 'b', and 'c', it's simply substituted into the expression and calculated accordingly.

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Answer:

[tex]\frac{120}{100}\times x=78[/tex] or [tex]12x=780[/tex]

Step-by-step explanation:

Given:

120% of x is equal to 78

We need to write an equation that shows the relationship of 120%, x, and 78

Solution:

We can write the 120% of x as:

⇒ 120% of x

Substitute [tex]\frac{120}{100}[/tex] in the place of 120%.

⇒ [tex]\frac{120}{100}\times x[/tex]

So, we write the equation as:

[tex]\frac{120}{100}\times x=78[/tex]

120 and 100 divided by 10.

[tex]\frac{12}{10}x=78[/tex]

Applying cross multiplication rule.

[tex]12x=780[/tex]

Therefore, equation shows the relationship of 120%, x, and 78.

[tex]\frac{120}{100}\times x=78[/tex] or [tex]12x=780[/tex]

Answer:

brainliest plsssssss

Step-by-step explanation:

answer is in the img below...

hope it helps you!!!!

Answer:

-2.1

Step-by-step explanation:

each line represents another 0.1, whether adding or subtracting.

after -22. there is one more tick mark, meaning it is -2.1

Answer:-2.1

Step-by-step explanation:

Each middle line is .1 and it is 1 under -2 so -2.1

Answer:

B is the correct option.

Step-by-step explanation:

Place the values from the given options in equations of f(n) and g(n).

Write the answer of each of the following.

For instance, option A gives:

f(6)= 31

g(6) = 24

Option B gives:

f(7)= 63

g(10)= 36

Option C gives:

f(5)= 15

g(8)=30

Option D gives:

f(5)=15

g(5)=21

Thus option B is correct because f(7) is greater than g(10).

Answer:

B. f(7) > g(10)

Step-by-step explanation:

f(7) = 2⁶ - 1 = 63

g(10) = 3×10 + 6 =36

since 63>36 then f(7) > g(10)

:)

The best way to rewrite the sentence is option D: "While he was driving on the highway, Paul saw a billboard advertising a music festival."

The original sentence is a bit awkward in its structure. Let's evaluate the options:

  This option is incorrect because it suggests that Paul was the one advertising the music festival while driving, which is not the intended meaning.

  This option is incorrect because it implies that the billboard itself was driving on the highway, which is illogical.

  This option maintains the original structure of the sentence, which is awkward and does not convey the intended meaning clearly.

  This option correctly places the modifier "advertising a music festival" next to "billboard," clarifying that it was the billboard, not Paul, advertising the music festival.

Answer:

Step-by-step explanation:

(f-g)(x) = [tex]x^{2}[/tex] + 2x + 8

Step-by-step explanation:

Step 1:

Formula for (f-g) (x) = f(x) - g(x)

Step 2:

Substitute values of f(x) and g(x) in the formula and solve

(f-g)(x) = (2x + 1) - ([tex]x^{2} -7[/tex])

(f-g)(x) = 2x + 1 - [tex]x^{2}[/tex] + 7

          = 2x + 8 [tex]- x^{2}[/tex]

          = [tex]x^{2}[/tex] + 2x + 8

Answer:

2 cups

Step-by-step explanation:

1/3 times 6 is 6/3, which is equal to two

Answer:

6/3 cups or simplified 2 cups

Step-by-step explanation:

Answer:

v = 16.

Step-by-step explanation:

This is one of the equations of motion  when acceleration is constant.

v = 6 + 2*5

= 16.

Answer: v=16

Step-by-step explanation:

v=6+2(5)

v=6+10

v=16

Answer:

15 inches

Step-by-step explanation:

Since the rectangles are similar then the ratios of corresponding sides are equal.

let x be the other dimension in the second photograph, then

[tex]\frac{4}{10}[/tex] = [tex]\frac{6}{x}[/tex] ( cross- multiply )

4x = 60 ( divide both sides by 4 )

x = 15

Thus the other dimension in the second photograph is 15 inches.

Answer:

(y = -8x - 6  and  y = 8x - 6) will have exactly one solution.

Step-by-step explanation:

1) Check number of solutions for A (using substitution)

y = -8x -6

y = -8x + 6

-8x - 6 = -8x + 6

+8x         +8x

0 - 6 = 0 + 6

-6 = 6 (since this is false, it would be no solution)

2) Check number of sultions for B (using substition)

y = -8x - 6

1/2y = -4x -3

y = -8x - 6 (Multiply both sides of second equation by 2 to cancel out fraction on left side)

-8x - 6 = -8x - 6

Since this is the same equation on both sides- when you cancel everything out it will be 0=0, meaning infinite solution

3) Check number of solutions for C (using substition)

y = -8x - 6

y = 8x - 6

-8x - 6 = 8x - 6

+8x   +6 = +8x +6

0 = 16x

x=0

The X value for the solution is 0, when we plug in this X value into one of the equations and solve for Y we will be able to get the Y coordinate

y = -8(0) - 6

y = -6

The solution for C will by (0,-6) which is one solution.

4) Check number of solutions for D (using substition)

y = -8x - 6

-y = 8x +6 --> y = -8x -6

muiltiply both sides of second equation by -1 to make the y positive

-8x - 6 = -8x - 6

Since this is the same equation on both sides- when you cancel everything out it will be 0=0, meaning infinite solution

Answer:

8k -3 is the answer my boiii

To solve the expression 8k - 9 divided by 3 for k = 7/8, substitute k with 7/8, multiply, subtract 9, and divide by 3 to get the result of -2/3.

The student asks to evaluate the expression 8k - 9 divided by 3 for k equals 7/8. Here's how to solve it step-by-step:

First, substitute k with 7/8 into the expression, which results in 8*(7/8) - 9.

Then apply multiplication to the first part: 8 * 7/8, which equals 7.

Next, subtract 9 from 7, yielding -2.

Finally, divide -2 by 3, to get -2/3 as the final result.

Therefore, when k is 7/8, the expression simplifies to -2/3.

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Answer:

Option C: (2, 1, 0)

Step-by-step explanation:

We are given a system of three equations. Usually, we eliminate a variable from the equations. Solve for the remaining two equations and determine the value of the third equation later.

Here, we are given the choices. So, we can readily substitute each option in the equations. The solution should satisfy all the three equations.

Option A: (3, 1, 0)

Equation (1): 3x + 3y + 6z = 9

⇒ 3(3) + 3(1) + 6(0) = 9 + 3 ≠ 9

Option A does not satisfy the first equation. So, it is eliminated.

Option B: (0, 1, 0)

Substituting in the first equation: 3x + 3y + 6z = 9

⇒ 3(0) + 3(1) + 6(0) = 3 ≠ 9

Option B does not satisfy as well. Hence, it is eliminated.

Option C: (2, 1, 0)

Substituting in 3x + 3y + 6z = 9

⇒ 3(2) + 3(1) + 6(0) = 9

It satisfies Equation 1. For this to be a solution, it should satisfy all the three equations. So, we check for equation 2 and 3.

Equation 2: x + 3y + 2z = 5

2 + 3(1) + 2(0) = 2 + 3 = 5

Equation 3: 3x + 12y + 12z = 18

3(2) + 12(1) + 12(0) = 6 + 12 = 18

Option C satisfies all the equations. So, it is the solution to the system.

On simple substitution, Option D can be eliminated as well.

Hence, the answer.

Answer:

He gained 31 yards minus 24 = which is 11 yards.

Step-by-step explanation:

If we gained 24 yards plus the 7 which is 31

So if he loss 20 yards that will be 11 yards left cause 31-24= 11

There's your answer. Hope this helps!

Step-by-step explanation:

[tex]10(5g+2h-3)-4(3g-4h+2) \\ \\ = 50g + 20h - 30 - 12g + 16h - 8 \\ \\ = 50g - 12g + 20h + 16h - 30 - 8 \\ \\ = 38g + 36h - 38[/tex]

Answer:

38(g - 1) + 36h

Step-by-step explanation:

10(5g + 2h - 3) - 4(3g - 4h + 2)

= 50g + 20h - 30 - 12g + 16h - 8

= 38g + 36h - 38

= 38(g - 1) + 36h

Answer:5

Step-by-step explanation:

In the Adams family with 10 children and a boy to girl ratio of 1:1, there are 5 girls.

The question asked is about the number of girls in the Adams family which has a total of 10 children and the ratio of boys to girls is given as 1:1. When a ratio is 1:1, that means there is an equal number of each. So in the case of the Adams family, there are equal numbers of boys and girls.

To find the number of girls, we simply divide the total number of children by 2. Therefore, the number of girls in the Adams family is 10 ÷ 2 = 5. So, there are 5 girls in the Adams family.

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Answer:

6 times 2 is 12, 6 times 4 is 24, 30 doesn't equal 36

Answer:

2 2/5

Step-by-step explanation:

12 x 1/5 = 2 2/5

Answer:

60 cents

Step-by-step explanation:

10x + 5(x+6)

15x = 30

x = 2

plug this back in the equation

20 + (5 x 8) = 60

Answer:

2 quarters and 5 dimes

Step-by-step explanation:

(2) 25 cent coins = 50 cents

(5) 10 cent coins = 50 cents

equals $1

Answer:

64.95

Hope this helps :-)

Answer:

4 pounds

Step-by-step explanation:

Do 70 - 39.56 = 30.44 To see how much she spent

Do 30.44 / 7.61 = 4 To see how many pounds of coffee she had bought

Answer:

4

Step-by-step explanation:

Amount spent on coffee = 70 - 39.56 = 30.44

One pound costs 7.61, how many will cost 30.44

7.61 : 1 = 30.44 : X

7.61 = 30.44/X

X = 30.44/7.61

X = 4

Answer: [tex]A(t) = 2,675(1.003)^{120}[/tex]

[tex]A(t) = 4,170(1.04)[/tex]

[tex]A(t) = 5,750(1.0024)^{20}[/tex]

Step-by-step explanation:

The exponential growth equation is given by :-

[tex]y=Ab^x[/tex] , where A = initial value , x= time period , b= growth factor.

The growth factor should be greater than 1.

From all the given options , the equations that are exponential :

[tex]A(t) = 2,675(1.003)^{120}[/tex]  , here b= 1.003

[tex]A(t) = 4,170(1.04)[/tex] , here b= 1.04

[tex]A(t) = 3,500(0.997)^{4t}[/tex]  , here b=  0.997

[tex]A(t) = 5,750(1.0024)^{20}[/tex]  , here b= 1.0024

[tex]A(t) = 1,500(0.998)^{127}[/tex]  , here b= 0.998

[tex]A(t) = 2,950(0.999)[/tex] , here b= 0.999

From the above exponential equations , only first  , second and fourth equation has b>1.

So , the models that could represent a compound interest account that is growing exponentially. are :

[tex]A(t) = 2,675(1.003)^{120}[/tex]

[tex]A(t) = 4,170(1.04)[/tex]

[tex]A(t) = 5,750(1.0024)^{20}[/tex]

Answer:

Step-by-step explanation:

Close to none because they are all the same price

The probability of a customer choosing a medium size popcorn with butter is 1/6, or about 16.67%.

To find the probability that a customer chooses a medium size popcorn with butter from the Village Theater, we need to consider the total number of possible outcomes and the number of favorable outcomes. Given there are small, medium, and large sizes, and each can be buttered or plain, there are 3 sizes  imes 2 types (buttered or plain), which results in 6 total possible outcomes. The event of choosing a medium size with butter is just one of these possible configurations.

Probability of choosing a medium size with butter = Number of favorable outcomes / Total number of possible outcomes = 1 / 6

The chance is 16.67%, which is the decimal 1/6 expressed as a percentage.

Answer: -0.2, -1/3, 0.4, 1.3, 5/3

Step-by-step explanation:

-1/3 is -.33 and 5/3 is 1.66 and then simply place them in order