A translation is a transformation in which every point of the preimage is moved the same distance in the same direction.

To find the length and width of the rectangular porch, solve the equation (x+12)(x+5) = 120 for x. The length is x+12 feet, and the width is x+5 feet. Substitute the value of x to find the length and width.

To find the length and width of the rectangular porch, we need to solve the equation (x+12)(x+5) = 120 for x. Expanding the equation, we get x^2 + 17x + 60 = 120. Rearranging the terms and solving for x, we find x = 5. So the length of the porch is x+12 = 5+12 = 17 feet, and the width is x+5 = 5+5 = 10 feet. Therefore, the porch has a length of 17 feet and a width of 10 feet.

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The random Sample can be drawn the buying pattern on the online customers versus that of the walk in interview, the correct option is B.  

Sample is "a small and manageable version of a larger group".

According to the question,

The number of packs ordered by random samples through the online customers = 100

The number of packs ordered by random samples through the walk-in-interview =100

To find the inferences,

Online customers buy an average of five packs compared with walk-in customers, who buy an average of two packs.

Hence, the Option B.

To learn more about  sample  here

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For any two given points [tex](x_{1} ,y_{1} ) and(x_{2},y_{2})[/tex]

Rate of change =[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }.[/tex]

To find linear function with the greatest unit rate we find the rate of change of each points.

A) The given points are(2, 16) and (5, 10 )

Rate of change =[tex]\frac{10-16}{5-2}=\frac{-6}{2}=-3.[/tex]

B) The given points are :(2,14) and (6,12)

Rate of change=[tex]\frac{12-14}{6-2}=\frac{-2}{4}=\frac{-1}{2}.[/tex]

C) Points are (2,-24) and (5,-15)

Rate of change = [tex]\frac{-15+24}{5-2}=\frac{9}{3}= 3.[/tex]

D) Points are :(2,-12) and (6,-16)

Rate of change =[tex]\frac{-16+12}{6-2}=\frac{-4}{4}=-1.[/tex]

E) Points are  (2, -19 ) and (6, -17)

Rate of change =[tex]\frac{-17+19}{6-2}=\frac{-2}{4}=\frac{-1}{2}.[/tex]

Option C has the greatest rate of change.

The increasing linear function with the greatest unit rate is represented by the table in option B. The unit rate is 0.5.

The table that represents the increasing linear function with the greatest unit rate is option B (x y 2 14 6 12). In this table, as the value of x increases by 4, the value of y increases by 2. This gives us a unit rate of 2/4 or 0.5.

For the other options:

A. The unit rate is (-6)/3 = -2

C. The unit rate is 9/3 = 3

D. The unit rate is -4/4 = -1

E. The unit rate is (-17-(-19))/(6-2) = -2

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The cost to rent a movie is $2.25 and to rent a video game is $5.50, which was determined by solving a system of linear equations derived from the problem statement.

This problem is a classic example of a system of linear equations, and we can solve it using either substitution or elimination method. Let's denote the cost of renting a movie as 'm' and the cost of a video game as 'v'. From the problem statement, we know:

We can multiply the first equation by 2, giving us 4m + 6v = $42. Now if we subtract the second equation from this, we can solve for 'v':

Substitute 'v' back into the first equation to solve for 'm':

Therefore, the cost to rent a movie is $2.25 and to rent a video game is $5.50.

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Answer:

  0.15x

Step-by-step explanation:

15% of anything is 15/100 or 0.15 of it. You find that value by multiplying the "anything" by 0.15.

Since we don't know the value of x, the best we can do is show that the number of interest is x multiplied by 0.15.

Answer:

2.25

Step-by-step explanation:

Mary walks for 15 mins which is 0.75 mi. Jerry then starts jogging for 2 miles which is 30 minutes because he is jogging at 4 mph. This means Mary walked for 30 minutes which is 1.5 mi.

0.75+1.5=2.25

Answer:

3 kg/s

Step-by-step explanation:

Answer:

a = 2d/t²

Step-by-step explanation:

1- Divide by 1/2 on both sides:

(d ÷ 1/2 = d × 2/1 = 2d)

2d = at²

2- Divide by t² on both sides:

2d/t² = a

a = 2d/t²

You can do those two steps in one but I made it in two so it's easier to understand.

Answer:

The average number of deliveries per day is 16 deliveries.

Step-by-step explanation:

The mean of a data set is the average value within it. Means are used as a way of describing data and finding the central tendency. To calculate the mean of a data set, add all values of all data points, then divide the resulting number by the amount of data points.

13 + 15 + 17 + 19 + 16 = 80

80 / 5 = 16

So, the average number of deliveries made per day by Floral World is 16 deliveries.

Answer:

5/18

Step-by-step explanation:

5/8 ÷ 3/2

switch 3/2 to 2/3

5/12 × 2/3

10/36 divide each 2 5/18

Answer:

3x-4

Step-by-step explanation:

64 ounces

Step-by-step explanation:

The factors of the quadratic expression 2n^2 - 5n - 42 are found by looking for two numbers that multiply to -84n^2 and add up to -5n. The correct pair is 7n and -12n, leading to the factors (2n + 7) and (n - 6).

The factors of 2n^2 - 5n - 42 need to be determined by finding two numbers that multiply to 2n^2 times -42 (which is -84n^2) and add up to -5n. To factor this quadratic expression, we should look for a pair of numbers that meet these criteria.

Upon inspecting possible pairs, we find that 7n and -12n are the numbers that work since (7n) * (-12n) = -84n^2 and 7n + (-12n) = -5n. The quadratic trinomial can be expressed as:

2n^2 - 5n - 42 = (2n + 7)(n - 6)

By factoring this way, we have broken down the expression into its factors, which are (2n + 7) and (n - 6).

The factors of the quadratic expression [tex]\(2n^2 - 5n - 42\)[/tex] are [tex]\(2n + 7\)[/tex] and [tex]\(n - 6\)[/tex].

To find the factors of the quadratic expression \(2n^2 - 5n - 42\), we can use the factoring method. This involves finding two numbers that multiply to give the product of the coefficient of \(n^2\) (which is 2) and the constant term (which is -42), and also add up to the coefficient of \(n\) (which is -5).

The product of the coefficient of [tex]\(n^2\)[/tex] and the constant term is:

[tex]\(2 \times -42 = -84\)[/tex]

Now we need two numbers that multiply to -84 and add up to -5. These numbers are -12 and 7 because:

[tex]\(-12 \times 7 = -84\)[/tex]

[tex]\(-12 + 7 = -5\)[/tex]

Now we can rewrite the middle term of the quadratic expression using -12 and 7:

[tex]\(2n^2 - 12n + 7n - 42\)[/tex]

Next, we can factor by grouping. Group the first two terms and the last two terms:

[tex]\(2n(n - 6) + 7(n - 6)\)[/tex]

Notice that [tex]\(n - 6\)[/tex] is a common factor. We can factor this out:

[tex]\((2n + 7)(n - 6)\)[/tex].