Donavon and three friends go to a fair. They each spend one half of their money on rides. ​ Then, they each spend​ $3 on food. At the end of the​ day, Donavon and his friends have a total of​ $8 remaining. How much money did each person bring to the​ fair?

Answer:

32 hours

Step-by-step explanation:

Let after x hours the charges of A and B are same,

Given,

For painter A,

Fixed charges = $ 376,

Additional charges per hour = $ 12,

So, the total charges for x hours = ( 376 + 12x ) dollars

For painter B,

Fixed charges = $ 280,

Additional charges pet hour = $ 15,

So, the total charges for x hours = ( 280 + 15x ) dollars

Thus,

376 + 12x = 280 + 15x

12x - 15x = 280 - 376

-3x = -96

x = 32

Hence, for 32 hours their cost will be same.

To solve the apple picking problem, we assigned variables and formulated an equation based on the relationships between the amounts each person picked. Solving the equation revealed that Andrew picks 252 pounds of apples.

Let Maria's apple pick be x pounds. According to the question, Andrew picks three times as many apples as Maria, which makes Andrew's pick 3x pounds. Jane, on the other hand, picks two times as many apples as Andrew, resulting in Jane's pick being 2(3x) or 6x pounds. Now, we know that the total weight of the apples picked by all three is 840 pounds.

We can express this as an equation:

x + 3x + 6x = 840

This simplifies to 10x = 840.

To find x, we divide both sides by 10:

x = 840 / 10

x = 84 pounds

Since Andrew picks 3x pounds, we multiply 84 by 3 to find Andrew's pick:

Andrew's pick = 3 × 84 = 252 pounds of apples.

Thus, the rates form a proportion as the rates of both are equal.

proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

Here,
The unit rate of sits-up = 90 / 2 = 45 sits-up per minute
Friend unit rate of sits-up = 135 / 5 = 45 sits-up per minute

From the above expressions, it is clear that rates form a proportion as rates of both are equal.

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The solution to system of equation  y = 4x - 3 and y = - x - 13 is (- 2, - 11).

If a system of equations only contains two linear equations with two variables, the system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution.

There are only three matching forms of solution for a given system of equations because there are only three different ways that two straight lines in the plane can graph.

Given, A system of equations y = 4x - 3 and y = - x - 13.

If we subtract these two equations,

  y = 4x  - 3

- (y = -x - 13)

__________

0 = 5x + 10.

5x = - 10.

x = -2 and hence y = - 11.

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Answer:

Equivalent Expression of given Expression is 84x - 16y - 10.6.

Step-by-step explanation:

Given Expression is :

[tex]2(14x-3y+28x+12.2-5y-17.5)[/tex]

We have to find: Equivalent Expression

To find Equivalent expression we simplify the given expression.

Consider,

[tex]2(14x-3y+28x+12.2-5y-17.5)[/tex]

Group like terms,

[tex]\implies2(14x+28x-3y-5y+12.2-17.5)[/tex]

Now solve like terms,

[tex]\implies2(42x-8y-5.3)[/tex]

Now, using Distributive Property

[tex]\implies2\times42x-2\times8y-2\times5.3[/tex]

[tex]\implies84x-16y-10.6[/tex]

Therefore, Equivalent Expression of given Expression is 84x - 16y - 10.6.

Answer:

a

Step-by-step explanation:

Answer:

Ques 1)

B) 3/2

Ques 2)

B) (-2,1)

Step-by-step explanation:

Ques 1)

We know that the coordinates of points S are (-2,-8)

and the coordinates of the point Q are: (8,7)

We know that the slope of a line passing segment with end points (a,b) and (c,d) are given as:

[tex]slope=\dfrac{d-b}{c-a}[/tex]

Here we have:

(a,b)=(-2,-8) and (b,d)=(8,7)

Hence, the slope is:

[tex]Slope=\dfrac{7-(-8)}{8-(-2)}\\\\Slope=\dfrac{7+8}{8+2}\\\\Slope=\dfrac{15}{10}\\\\Slope=\dfrac{3}{2}\\(Since\ both\ the\ numerator\ and\ denominator\ are\ divisible\ by\ 5)[/tex]

Hence, the slope of a line connecting point S to point Q is:

3/2.

Ques 2)

We know that solution of a system of equation is the point where the two system meet if it has a unique solution.

From the graph of the system of equation we could observe that the two lines intersect each other in the second quadrant and we know that the point in the second quadrant has x-value negative and y-value positive.

Hence, the point that is the solution of the given system of equations is:

B) (-2,1)

To find out how many grams of strawberries are left, subtract the used grams from the total grams. Therefore, 430 grams of strawberries are left.

To determine how many grams of strawberries are left, we need to subtract the remaining grams from the total amount:

So, 430 grams of strawberries are left.

Answer:

Option D) 5/21 pizza is left.

Step-by-step explanation:

Bill has 2/3 of his pizza left from lunch. If he eats 3/7 more of pizza then we have calculate the pizza left.

Let the size of a pizza is x. Now 2x/3 pizza is left with Bill after lunch.

Therefore pizza eaten by Bill = x - 2x/3 = x/3

Now Bill eats 3/7 more of pizza has been eaten by Bill.Therefore total pizza left is

x - x/3 - 3x/7 = x(1 - 1/3 - 3/7) = x( 21 - 7 - 9)/21 = 5x/21

So 5/21 part of pizza is left.