Question 3: 12 points
3. The area of a rectangle is 45x8y9 square yards. If the length of the rectangle is 5x3y4 yards,
find expression represents the width of the rectangle in yards?


please help!! i will mark you brainiest

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:

The given expression is

[tex]3 + (\frac{(2+8)2}{4} \times(\frac{1}{2} )^4)= \hspace{0.3cm}3 +( \frac{10 \times 2}{4}\times \frac{1}{2^4} ) \hspace{0.3cm} = \hspace{0.2cm} 3 + ( \frac{5}{16})[/tex] = 3.3125

Step-by-step explanation:

The given expression is

[tex]3 + (\frac{(2+8)2}{4} \times(\frac{1}{2} )^4)= \hspace{0.3cm}3 +( \frac{10 \times 2}{4}\times \frac{1}{2^4} ) \hspace{0.3cm} = \hspace{0.2cm} 3 + ( \frac{5}{16})[/tex] = 3.3125

Answer:6  1/8

and i took the same test

Answer:

64.95

Hope this helps :-)

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: -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

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

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:

x=5p-3/2py

Step-by-step explanation:

Im not entirely sure on this answer.

Your goal is to isolate x. So first subtract 3y on both sides resulting in 2xp=10-3y. Then u divide each side by 2p to get x by itself to get x=5p-3/2py.

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:

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:

-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:

Therefore she make 1.43 batches per hour.

Step-by-step explanation:

Given,  Molly can make 2.5 batches  in 1.75 hours.

Therefore she make [tex]=\frac{2.5}{1.75}[/tex]   batches=1.43 batches per hour.

Answer:

h = 14

Step-by-step explanation:

7h - 5 (3h - 8) = -72

7h - 15h + 40 = -72

-8h + 40 = -72

-8h = -112

h = 14

Answer:

14

Step-by-step explanation:

7h-5(3h-8)=-72

7h-15h+40=-72

-8h+40=-72

-8h=-72-40

-8h=-112

8h=112

h=112/8

h=14

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:

[tex]\frac{9x^6}{4}-\frac{3x^5}{2}+\frac{x^4}{4}[/tex]

Step-by-step explanation:

We want to simplify:

[tex](6x-2)^2(0.5x)^4[/tex]

We expand to get:

[tex](36x^2-24x+4)*\frac{x^4}{16}[/tex]

We expand further to get:

[tex]\frac{9x^6}{4}-\frac{3x^5}{2}+\frac{x^4}{4}[/tex]

[tex]f(x)=3x^2 \\ \\ g(x)=x+2[/tex]

In this case we have the composition of two function called [tex]f(x)[/tex] and [tex]g(x)[/tex] that results in another function [tex]h(x)[/tex]. So:

[tex]h(x) =(f\circ g)(x)[/tex]

Another way to write this function is:

[tex]h(x)=f(g(x)) \\ \\ So \ g(x) \ becomes \ the \ domain \ of \ f[/tex]

One possibility for [tex]f(x)[/tex] and [tex]g(x)[/tex] is:

[tex]f(x)=3x^2 \\ \\ g(x)=x+2[/tex]

Because [tex]h(x)=f(g(x))[/tex] is:

[tex]h(x)=3(x+2)^2[/tex]

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Answer:

(Options 2,2,3)

There are 6 observed toll fee values.

It costs $3.40 to travel 76 miles.

The predicted value for traveling 30 miles is $1.61.

Answer:

There are 6 observed toll fee values.

It costs $3.40 to travel 76 miles.

The predicted value for traveling 30 miles is $1.61.

Step-by-step explanation:

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:

90

Step-by-step explanation:

890÷5=178

178-88=90

Answer:

90

Step-by-step explanation:

890/5=78

178-88=90

90 = difference

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!!!!

To find the values of p that satisfy |18 - 2p| > 8, we solve two separate inequalities, leading to the solutions p < 5 and p > 13. Hence, among the options provided, -10, -5, and 15 are the correct solutions.

To solve the inequality |18 – 2p| > 8, we need to consider two cases because the absolute value measures distance from zero on a number line, either in the positive or negative direction.

First, we solve the inequality when the expression inside the absolute value is positive:

Next, we solve the inequality when the expression inside the absolute value is negative:

Combining the solutions from both cases, the values of p that satisfy the original inequality are p < 5 and p > 13. Among the given options, -10, -5, and 15 are the values that are solutions to the inequality.

Final answer:

The values of p that satisfy the inequality |18 - 2p| > 8 are p < 5 and p > 13; therefore, from the given options, -10 and -5 are the correct solutions.

Explanation:

The student needs to determine which values of p satisfy the inequality |18 – 2p| > 8. To solve this, we consider two separate cases because the absolute value function defines a piecewise function. The two cases are when the expression inside the absolute value is positive and when it is negative.

For the first case (18 - 2p > 0), we solve 18 - 2p > 8, which simplifies to -2p > -10, and upon dividing by -2 and flipping the inequality sign, we get p < 5. For the second case (18 - 2p < 0), we solve -(18 - 2p) > 8, which simplifies to -18 + 2p > 8, leading to 2p > 26, and upon dividing by 2, we get p > 13.

Therefore, the solution to the original inequality consists of all the values p < 5 and p > 13. Checking the provided options against these conditions, only -10 and -5 fall within p < 5, so they are the solutions to the inequality.

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:

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)

:)

180 students voted for blue and 60 students voted for green

Solution:

Let "x" be the total number of votes

From given,

[tex]\frac{5}{8}[/tex] of the votes were for blue

[tex]Blue\ votes = \frac{5}{8}x[/tex]

Therefore,

[tex]Remaining = 1 - \frac{5}{8}x = \frac{8x-5x}{8} = \frac{3x}{8}[/tex]

Given that,

5/9  of the remaining students voted for green

So we get,

[tex]Green\ votes = \frac{3x}{8} \times \frac{5}{9} = \frac{5x}{24}[/tex]

[tex]Green\ votes = \frac{5x}{24}[/tex]

So we have now accounted for 5/8 (blue) + 5/24 (green) of the votes

Therefore,

[tex]Remaining = 1-(\frac{5x}{8} + \frac{5x}{24}) = 1 -(\frac{15x+5x}{24})= 1 -\frac{20x}{24} = \frac{24x-20x}{24}\\\\Remaining = \frac{4x}{24}\\\\Remaining = \frac{1x}{6}[/tex]

48 students voted for red

Therefore, remaining 1/6 votes for 48

Let "x" be the total number of votes

Then we can say,

1/6 of "x" is equal to 48

[tex]\frac{1}{6} \times x = 48\\\\x = 48 \times 6\\\\x = 288[/tex]

Number of votes for Blue:

[tex]Blue\ votes = \frac{5}{8} \times x = \frac{5}{8} \times 288\\\\Blue\ votes = 180[/tex]

Number of Green votes:

[tex]Green\ votes = \frac{5}{24} \times x = \frac{5}{24} \times 288\\\\Green\ votes = 60[/tex]

Thus 180 students voted for blue and 60 students voted for green

Answer:

whats the statement

Step-by-step explanation:

Final answer:

The inverse statement is 'If you cannot vote, then you are not over 18,' but practical exceptions exist. The 26th Amendment ensures those over 18 have the right to vote, illustrating the importance of voting as a democratic right. Encouraging voter registration and participation among eligible citizens is crucial for maintaining a vibrant democracy.

Explanation:

The inverse of the statement 'If you are over 18 then you can vote' would logically be 'If you cannot vote, then you are not over 18'. However, this inversion doesn't always hold true in practice due to various voting laws and conditions, such as registration requirements and citizenship. The right to vote is a fundamental aspect of democracy, emphasized by constitutional amendments and various voting rights acts that seek to protect this privilege. For instance, the 26th Amendment to the U.S. Constitution, ratified on March 23, 1971, prohibits the denial of the right to vote for U.S. citizens eighteen years of age or older based on age.

To encourage political participation, it is vital for eligible citizens to register to vote and exercise their right. This act of voting allows individuals to have a say in how their government is run and who represents their interests. Discussions about lowering the voting age further, to include 16 and 17-year-olds, in local, state, or national elections have sparked debates about civic engagement and the readiness of younger citizens to participate in the electoral process.

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:

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