X+4y=6 y=-x+3 solve each system of linear equations by substitution

Answer:

1/4 or one quarter

Step-by-step explanation:

Say a complete pie is represented by a whole or a number 1

Assuming half of the pie was eaten

We have a leftover of 1/2

Now tom ate 1/2 of left over

Which is 1/2 of 1/2

1/2*1/2=

1/4

Answer:

The monthly payment would be £450.

Step-by-step explanation:

Given formula for the cost of buying a car,

Cost = 12 × monthly payment + deposit,

Here,

Cost of the car = £ 8000,

Deposit = £ 2600,

By substituting the values,

8000 = 12 × monthly payment + 2600

⇒ 12 × monthly payment = 8000 - 2600

⇒ 12 × monthly payment = 5400

⇒ Monthly payment = [tex]\frac{5400}{12}[/tex] = £450

Answer:

18.45

Step-by-step explanation:

75% of 20 peaches is 15 peaches. To find this, divide 15 by 0.75.

To find the total number of peaches represented by 75%, you can divide the known amount (15 peaches) by 0.75. This is because 75% can be written as the decimal 0.75.

Dividing 15 peaches by 0.75 gives us:

15 ÷ 0.75 = 20 peaches

So, 75% of 20 peaches is 15 peaches.

To find the total number of peaches where 75% of them is 15 peaches, a proportion is set up and solved to discover that the total is 20 peaches.

The question "21. 75% of ________ peaches is 15 peaches" is asking us to find the total number of peaches if 75% of that total is equivalent to 15 peaches. To solve this, we need to set up a proportion where 75% is to 15 peaches as 100% is to the total number of peaches. We represent the total number of peaches by the variable x.

Here is the proportion set up as an equation: 0.75 * x = 15. To find x, divide both sides of the equation by 0.75, which gives us x = 15 / 0.75. When we calculate this, we get x = 20. So, the total number of peaches is 20.

To check our work, we can confirm that 75% of 20 is indeed 15 by multiplying 20 by 0.75, which equals 15. Hence, the statement "21. 75% of 20 peaches is 15 peaches" is correct and answers the student's question.

Answer:

Yes possible

Step-by-step explanation:

Given is a fraction 5/6

We are to decompose it into 3 fractions with different numerators

First let us convert 5/6 into equivalent fraction as

[tex]\frac{5}{6} =\frac{1+4}{6} =\frac{1}{6} +\frac{2}{3}[/tex]

Let us break 2/3 into sum of two other fractions

[tex]\frac{2}{3} =\frac{6}{9} =\frac{2}{9}+\frac{4}{9}\\=\frac{2}{9}+\frac{8}{18}[/tex]

Thus we can write

5/6 = 1/6+2/9+8/18

as a sum of 3 fractions with different denominators.

Hence answer is possible.

The system of equations to determine the price of the speaker system at each distributor is t = 3d - 280 and t - d = 288. Solving these equations will give the prices at Schools'R'Us (t) and The Warehouse (d).

To find the price of the speaker system at each distributor, we need to set up a system of equations based on the information provided. Let's denote the cost of the speaker system at Schools'R'Us as t, and the cost of the same speaker system at The Warehouse as d.

According to the problem statement, we have the following relationship between the two prices:
t = 3d - 280. (1)

The difference in price between the two systems is also given as $288, forming the second equation:
t - d = 288. (2)

Therefore, the system of equations that we can use to determine the price of the speaker system at each distributor is:

Solving this system of equations will provide the values for t and d, representing the prices of the speaker systems at Schools'R'Us and The Warehouse, respectively.

The width of the car on the scale drawing is 16 inches.

To find the width of the car on the scale drawing, we can set up a proportion using the scale of the drawing and the actual width of the car.

The scale of the drawing is 1 inch = 1/2 foot. The actual width of the car is 8 feet. So the proportion is: x/1 inch = 8/1/2 foot.

To solve for x, we multiply both sides of the proportion by 1 inch: x = 8/1/2 inch. Simplifying the right side of the equation, we get x = 16 inches. Therefore, the width of the car on the scale drawing is 16 inches.

The width of the car on the scale drawing is 16 inches.

To find the width on the scale drawing, we need to use the scale provided in the question. The scale is given as 1 inch = 1/2 foot. This means that for every inch on the drawing, it represents 1/2 foot of the actual object.

Given that the actual width of the car is 8 feet, we need to convert this measurement to inches using the scale factor. Since 1 foot is equal to 12 inches, 1/2 foot is equal to 6 inches (because 12 inches / 2 = 6 inches).

Now, we can set up a proportion to find the width on the scale drawing:

[tex]\[ \frac{1 \text{ inch}}{1/2 \text{ foot}} = \frac{\text{width on drawing}}{8 \text{ feet}} \][/tex]

To solve for the width on the drawing, we multiply both sides of the equation by 8 feet: [tex]\[ \text{width on drawing} = \frac{1 \text{ inch}}{1/2 \text{ foot}} \times 8 \text{ feet} \][/tex]

Since 8 feet is equal to 16 halves of a foot (because 8 * 2 = 16), we can simplify the equation:

[tex]\[ \text{width on drawing} = 1 \text{ inch} \times 16 \][/tex]

[tex]\[ \text{width on drawing} = 16 \text{ inches} \][/tex]

Therefore, the width of the car on the scale drawing is 16 inches.

C is your answer to this problem.

Answer: D) 52.5

Step-by-step explanation:

The equation for inverse variation between two quantities x and y is given by :-

[tex]k=yx[/tex], where k is the constant of variation, for this relationship. (1)

Given : Sarah studies indicate that there is an inverse relationship between TV time and GPA, and that a student who watched 15 hours of TV per week can be expected to have a GPA of 3.5.

Then from (1) the constant of variation is given by :-

[tex]k=15\times3.5=52.5[/tex]

Hence, the required answer is option D) 52.5 .

Final answer:

The constant of variation, k, for the inverse relationship between TV time and GPA, where 15 hours of TV results in a GPA of 3.5, is 52.5.

Explanation:

Sarah is researching the connection between the time students spend watching television and their performance in school, finding an inverse relationship between TV time and GPA. For a student who watched 15 hours of TV per week and has a GPA of 3.5, we can determine the constant of variation, k, in this inverse relationship.

The relationship can be represented as GPA = k / TV time. To find k, we plug in the known values: 3.5 = k / 15 hours. To solve for k, multiply both sides by 15: k = 3.5 × 15, which gives us k = 52.5.

Therefore, the constant of variation k for the inverse relationship between the time spent watching TV and GPA is 52.5.