2x + 4y = 22

What is the y-intercept?

Answer:

x = -31.5

Explanation:

We are given that the quotient of x and -1.5 is 21

This means that:

[tex]\frac{x}{-1.5} =21[/tex]

To get the value of x, we will multiply both sides of the equation by -1.5

This means that:

[tex]\frac{x}{-1.5} * -1.5=21*-1.5[/tex]

x = -31.5

Note that the value of x must be negative because we are dividing by a negative number and the quotient is positive (-ve/-ve is +ve and +ve/-ve is -ve)

Hope this helps :)

The value of x is -31.5.

Quotient means the result of dividing a number by another number. For example, the quotient of 4 and 2 is 2.

The information provided in this question can be represented with this equation:

[tex]\frac{x}{-1.5}[/tex] = 21

In order to determine the value of x, multiply both sides of the equation by -1.5.

x = 21 x - 1.5

x = -31.5

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108/2=54*60= 34min40sec     then 108/5=21*60=13min

sorry if this is incorrect your question was a little confusing                                                                           

The Equations are 2x = 108 and 3y = 108.

Drain A takes 54 minutes and Drain B takes 36 minutes to empties the pool.

When comparing two different kinds of numbers with distinct units, a rate is a ratio that is employed. The unit rate, on the other hand, shows how many units of one quantity are equal to one unit of another.

Given:

Drain A empties a pool at a rate of 2 gal/min.

Drain B empties a pool at a rate of 5 gal/min.

One pool has 108 gal of water in it.

So, let Drain A empties the pool in x minutes and Drain B in y minutes.

Then, Drain A:

2x = 108

x= 54 minutes

and, Drain B:

3y = 108

y= 36 minutes

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A relation is any set of ordered pairs.

For example, {(5,9), (1,2), (8,11), (10,20), (4,7)}

A function is a special type of relation where each x-coordinate has exactly 1 y-coordinate.

To find the unit price, divide the cost by the number of ounces for each brand. Brand X has a unit price of $0.15 per ounce, while Brand Y has a unit price of $0.16 per ounce. Brand X is the better buy because it has a lower unit price.

To find the unit price of each brand, we need to divide the cost by the number of ounces for each brand.

Brand X: Unit Price = $2.40 / 16 ounces = $0.15 per ounce

Brand Y: Unit Price = $1.92 / 12 ounces = $0.16 per ounce

Therefore, Brand X is the better buy because it has a lower unit price.

A word problem is,

"A member of the school track team ran for a total of 179.3 miles in practice over 61.5 days. About how many miles did he average per day?

Division is the process of splitting a number or an amount into equal parts.

here, we have,

a word problem that involves dividing by a decimal .include a picture of solution using a model

given by,

"A member of the school track team ran for a total of 179.3 miles in practice over 61.5 days. About how many miles did he average per day?"

(Explanation is attached)

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The correct expression to determine how fast a mule deer runs in miles per hour is one-fourth mile over twenty-five seconds = 36 miles per hour.

To find the speed of the mule deer in miles per hour, we need to convert the time from seconds to hours and then use the formula for speed, which is distance divided by time.

First, let's convert 25 seconds into hours. There are 3600 seconds in an hour, so:

25 seconds * (1 hour / 3600 seconds) = 25/3600 hours

Now, we know that the mule deer runs one-fourth of a mile in 25 seconds. To find the speed in miles per hour, we divide the distance by the time in hours:

Speed (mph) = Distance (miles) / Time (hours)

Using the conversion above, we have:

Speed (mph) = (1/4 mile) / (25/3600 hours)

To simplify this, we multiply the numerator and denominator by 4 to get rid of the fraction in the numerator:

Speed (mph) = (1 mile) / (25/900 hours)

Now, we multiply the denominator by 900 to get the time in hours:

Speed (mph) = (1 mile) / (25/900 * 900 hours)

Speed (mph) = (1 mile) / (25 hours)

Next, we need to find out how many 25-hour intervals there are in one hour. To do this, we divide 1 by 25:

Speed (mph) = 1 mile * (1/25 hours)

Speed (mph) = 1/25 miles per hour

Since there are 25 intervals of 1/25 hours in one hour, the mule deer can cover 25 intervals of 1/4 mile in one hour:

Speed (mph) = 25 * (1/4 mile) per hour

Speed (mph) = 25/4 miles per hour

Speed (mph) = 6.25 miles per hour

However, this result does not match any of the options given in the question. It seems there was a mistake in the calculation. Let's correct it:

Speed (mph) = (1/4 mile) / (25/3600 hours)

Speed (mph) = (1/4) / (25/3600)

Speed (mph) = (1 * 3600) / (4 * 25)

Speed (mph) = 3600 / 100

Speed (mph) = 36 mph

This is the correct calculation. Therefore, the expression that represents the speed of the mule deer in miles per hour is one-fourth mile over twenty-five seconds equals 36 miles per hour.

Answer:

The lowest common denominator is 12

Step-by-step explanation:

use the photo math method

Step-by-step explanation:

The distance between the rooftops of two buildings, one 47 feet high and the other 31 feet high with a 12 feet gap between them, is 20 feet, as calculated using the Pythagorean theorem.

To determine the distance between the rooftops of two buildings with different heights, we should envision a right-angled triangle where the buildings form the two vertical legs, and the distance between them forms the base.

The height difference of the buildings gives us one leg of the triangle (47 feet - 31 feet = 16 feet), and the distance between them gives us the other leg (12 feet).

Using the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides, we can calculate the length of the hypotenuse, which is the distance between the rooftops.

The formula is c = ( √{a² + b²} ), where a and b represent the legs of the triangle, and c represents the hypotenuse.

For our problem:

Leg a (height difference): 16 feet

Leg b (distance apart): 12 feet

Plug the values into the formula:

c = √{16² + 12²}

c = √{256 + 144}

c = √{400}

c = 20 feet

So, the distance between the rooftops of the buildings is 20 feet.

Fractional equivalent of 2/300 is 1/150 .

Decimal equivalent of 2/300 is 0.0066.

Given,

2/300

Here,

To get the fractional equivalent of 2/300

Divide numerator and denominator by the common factor,

2 / 2= 1

300 / 2= 150

Simplified fractional form,

= 1/150.

Decimal equivalent of 2/300,

Divide 2 by 300

So,

2/300 = 0.0066

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Answer: 639

Step-by-step explanation:

Given: The number of people that belong to a certain social website=412

Since they are increasing at the rate of 5% every month .

The number of members of after x months is given by exponential growth function, i.e. [tex]y=A(1+r)^x[/tex], where A is the initial amount , r is the growth rate

From question, A=412

r=5%=0.05

x=9 months

Therefore, [tex]y=412(1+0.05)^9=412(1.05)^9=412\times1.551=639.1356\approx639[/tex]

hence, there will be 639 members agter 9 months.

The solution is Option D.

The unit rate of the cost per box is given by the equation A = $ 2.50

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

The selling price of 2 boxes of cookies = $ 5

So , the cost of 1 box of cookies A = selling price of 2 boxes of cookies / 2

Substituting the values in the equation , we get

Cost of 1 box of cookies A = 5/2

Cost of 1 box of cookies A = $ 2.50

Therefore , the value of A is $ 2.50

Hence , the unit rate of box of cookies is $ 2.50

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Answer: 1 5/12

Step-by-step explanation:

2 1/3 = 7/4

3 3/4 = 15 / 4

The amount they eat = The amount they picked - The amount they remained

The amount they eat = 15 / 4 - 7/3

=45-28 / 12

=17/12

= 1 5/12