write an equation of a line with the given slope and y-intercept m= -5, b-3

A is 16 and B is 28.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Given

A:B = 4:7

A + B = 44

Let the common factor between A and B is x

then

4x + 7x = 44

11x = 44

x = 4

Therefore,

A = 16

B = 28

Hence, 16 and 28 are A and B respectively.

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Final answer:

The slope of the line through points P(5,7) and Q(-1,7) is calculated to be 0, indicating a horizontal line.

Explanation:

To find the slope of the line through points P(5,7) and Q(-1,7), we can use the formula for the slope of a line through two points: slope (m) = (y2 - y1) / (x2 - x1). In this case, the coordinates for P are (x1, y1) = (5, 7) and the coordinates for Q are (x2, y2) = (-1, 7).

Plugging these values into the slope formula, we get:

m = (7 - 7) / (-1 - 5)

m = 0 / (-6)

m = 0

So the slope of the line is 0, which means that the line is horizontal.

[tex]\text{Answer: The fence post will be }3\frac{5}{8}\ feet\text{ far above the ground when it is placed in the hole.}[/tex]

Explanation:

Since we have given that

Length of hole dug for a fence post is given by

[tex]2\frac{3}{8}\ feet=\frac{19}{8}\ feet[/tex]

Length of the fence post = 6 feet

we need to find the length of the fence post above the ground is seen when it is placed in the hole.

So, Length of the fence post above the ground is given by

[tex]6-\frac{19}{8}\\\\=\frac{48-19}{8}\\\\=\frac{29}{8}\\\\=3\frac{5}{8}\ feet[/tex]

[tex]\text{Hence, the fence post will be }3\frac{5}{8}\ feet\text{ far above the ground when it is placed in the hole.}[/tex]

The set which is the subset of every set is:

                   Empty set or null set.

Set--

A set is a well defined collection of the distinct objects.

The number of objects in the set is the cardinality of the set.

The set whose cardinality is zero is known as the empty set or the null set.

i.e. it is the set which is having zero element i.e. no element.

Such a set is unique.

Also, the null set or the empty set is the subset of every set.

Answer:

1. A line passes through (2, −1) and (4, 5).

Which answer is the equation of the line?

−3x+y=−7

2. A line has slope −3/4 and y–intercept 5.

Which answer is the equation of the line?

y=−3/4x+5

3. There are 6 quarters in a jar. Jill adds 2 quarters to the jar every day.

Which linear equation represents the total amount of quarters in the jar after x days?

y = 2x + 6

4. Which answer is an equation in point-slope form for the given point and slope?

Point: (1, 9); Slope: 5

y−9=5(x−1)

Step-by-step explanation:

Frank has memorized 6 words which is two-thirds of his vocabulary list, so by dividing 6 by 2/3, we find out that the total number of words on the list is 9.

Frank has memorized 6 words on his Latin vocabulary list, which is two-thirds of the total number of words. To find out the total number of words on the list, we can set up a proportion where 6 words corresponds to 2/3. Therefore, we need to find a number that, when multiplied by 3/2 or 1.5, gives us 6.

We can set up the equation like this: 2/3 * total words = 6 words. To find the total words, we divide 6 by 2/3:

total words = 6 ÷ (2/3)

total words = 6 * 3/2

total words = 9

So, the vocabulary list has a total of 9 words.

10 trees /  2 hours = 5 trees per hour

150 trees /  5 per hour = 30 hours

[tex]\left(-\dfrac{2}{3}\right)\left(\dfrac{1}{6}\right)=-\dfrac{1}{3}\cdot\dfrac{1}{3}=-\dfrac{1}{9}[/tex]

Answer:

17

Step-by-step explanation:

You are to follow the clues. Since it is 2 digits and is prime, go through the prime numbers between 10 and 20. They are 11, 13, 17, and 19. Then you find the factors of 34 which are 1×34 2x17. That leaves only 1 possible answer: 17

The skateboarder's rate of ollies per minute would be 68 ollies per minute. The skateboarder's rate of ollies per hour would be 4080 ollies per hour.

To find the rate of ollies per minute, we need to divide the number of ollies completed in 30 seconds by the number of seconds in a minute. In this case, the skateboarder completed 34 ollies in 30 seconds, so the rate of ollies per minute would be:

Rate per minute = (34 ollies / 30 seconds) × (60 seconds / 1 minute) = 68 ollies per minute

To find the rate of ollies per hour, we need to divide the number of ollies completed in 30 seconds by the number of seconds in an hour. In this case, the skateboarder completed 34 ollies in 30 seconds, so the rate of ollies per hour would be:

Rate per hour = (34 ollies / 30 seconds) × (3600 seconds / 1 hour) = 4080 ollies per hour

Answer:  Option 'B' is correct.

Step-by-step explanation:

Since we have given that

"A number is divisible by 2 if even."

It means that if the number is even , then that number is always be divisible by 2.

So, the conclusion of the conditional is that

"If a number is even, then the number is divisible by 2."

Hence, Option 'B' is correct.

Answer: Bookshelf can hold 15 books.

Step-by-step explanation:

Given : The length of the book shelf = [tex]28\dfrac{1}{8}[/tex] inches

In improper fraction ,  [tex]28\dfrac{1}{8}=\dfrac{8(28)+1}{8}=\dfrac{225}{8}[/tex]

i.e. Length of the book shelf = [tex]\dfrac{225}{8}[/tex] inches

Similarly, Thickness of a book = [tex]1\dfrac{7}{8}=\dfrac{8(1)+7}{8}=\dfrac{15}{8}[/tex] inches

Now, the number of books the shelf can hold =  Length of the bookshelf ÷Thickness of a book

[tex]=\dfrac{225}{8}\div\dfrac{15}{8}\\\\=\dfrac{225}{8}\times\dfrac{8}{15} \\\\=\dfrac{225}{15}=15[/tex]

Hence, the bookshelf can hold 15 books.