Abigail drives at an average speed of 60 miles per hour for 3 hours. The graph shows her distance versus time. Which statements are true? Check all that apply. As Abigail’s time increases, her distance increases. As Abigail’s time increases, her distance decreases. At 2 hours, Abigail has traveled 120 miles. At 1.5 hours, Abigail has traveled 100 miles. At 3 hours, Abigail has traveled 180 mile

Final answer:

To reach the goal of selling more than 750 units this year, it will take more than 50 weeks.

Explanation:

To determine the number of weeks necessary to reach the company's year-end goal of selling more than 750 units, we can set up an inequality using the average rate of sales per week. Let x represent the number of weeks needed to reach the goal. The total number of units sold in x weeks can be calculated by multiplying the average rate of sales per week (15) by the number of weeks (x). So, the inequality would be: 15x > 750. To solve for x, divide both sides of the inequality by 15: x > 50. Therefore, it would take more than 50 weeks to reach the company's goal.

Final answer:

The inequality to solve for x, the number of necessary weeks, is 450 + 15x > 750.

Explanation:

To determine for x, the number of weeks necessary for Company XYZ to reach their goal of selling more than 750 units this year, we need to set up an inequality.

They have already sold 450 units and sell units at an average rate of 15 per week.

The company's target is more than 750 units.

Therefore, we can represent this scenario with the following inequality:

450 + 15x > 750

Here's how to solve for x:

Therefore, Company XYZ will need to sell for more than 20 additional weeks to exceed their goal of 750 units.

The volume and the surface area of the rectangular prism will be 66mm and 166mm² respectively.

Length = 11m

Width = 1mm

Height = 6mm

The volume of the rectangular prism will be:

= Length × Width × Height

= 11mm × 1mm × 6mm

= 66mm

The surface area of the rectangular prism will be:

= 2(wl + hl + hw)

= 2(11 + 66 + 6)

= 2(83)

= 166

Therefore, the surface area of the rectangular prism will be 166mm²

In conclusion, the volume and the surface area of the rectangular prism will be 66mm and 166mm² respectively.

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8*3 = 24 + 28 = 52 total square feet

he is painting at 8 sq m per hour

so A(t) = -8t +52

Answer:

[tex]A(t)=-8t+52[/tex]

Step-by-step explanation:

Let

A(t)------> the area to paint

t------> the time in hours

Step 1

Find the total area of the room

[tex]A=8*3+28=52\ m^{2}[/tex]

Step 2

Find the linear equation that represent the situation

[tex]A(t)=-8t+52[/tex]

By using what we know about intersecting lines, we will see that the correct options are:

In an intersection of two lines, if two angles are adjacent, then their measures must add to 180°. And if the angles are not adjacent, then the angles have the same measure.

a) 1 and 4 are not adjacent, so these angles have the same measure.

so if m<1 = 43, then m<4 = 43

The correct option is B.

b) 1 and 5 are equivalent (where we assume that JL and MP are parallel, so all the angles formed in the two intersections are equal).

Then if m<1 = 50,  m<5 = 50.

So the correct option is A.

c) The corresponding angles occupy equivalent positions.

For example:

etc.

The correct option is B.

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To determine two numbers where their difference is 16, and their ratio is 5:7, we let the smaller number be 5x and the larger one be 7x, solve for x with the equation 7x - 5x = 16, and find that the numbers are 40 and 56.

To find two numbers with a difference of 16 and a ratio of 5:7, first let's denote the smaller number as 5x and the larger number as 7x. The difference between the two numbers is 16, so we can write the equation 7x - 5x = 16.

Solving for x gives us 2x = 16 or x = 8. Thus, the two numbers we are looking for are 5x = 5 × 8 = 40 and 7x = 7 × 8 = 56.

Check: The difference between 56 and 40 is indeed 16, and the ratio of 40 to 56 simplifies to 5:7, confirming our solution.

Answer:

Inverse statement : "If you don't lift weights, then you will not be strong".

Step-by-step explanation:

If a statement is defined as

p → q : If p is true, then q is true.

then the inverse of the given statement is

¬ p → ¬ q : If p is not true, then q is not true.

The given statement is "If you lift weights then you will be strong".

We need to find the inverse of the given statement.

Here,

p = you lift weights

q = you will be strong

The inverse of the given statement is "If you not lift weights, then you will not be strong".

volume = l x w x h

1.5 x 1.5 x 1.5 = 3.375 cubic feet

3.375 * 57 = 192.375 pounds

In his piggy bank, Dan has 10 nickels, 20 dimes and 5 quarters.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Assume that he had [x] nickels, [y] dimes and [z] quarters. Then we can write -

x = y + 5

x + y + z = 35

x/20 + y/10 + z/4 = 6

Now, the equation → x/20 + y/10 + z/4 = 6, can be written as → (x + 2y + 5z) = 120

We can write, the equations as -

x = y + 5

x + y + z = 35

x + 2y + 5z = 120

Solving the simultaneous equations, we get -

y + 5 + y + z = 35

2y + z = 30         Eq [1]

y + 5 + 2y + 5z = 120

3y + 5z = 115        Eq [2]

Plot Eq[1] and Eq[2] on graph. The point of intersection of both will give the values of y and z.

z = 20

y = 5

We can then find [x] as -

x = y + 5 = 10

x = 10

Therefore, in his piggy bank, Dan has 10 nickels, 20 dimes and 5 quarters.

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The approximate solution for the given system of equations y = 2x2 – 2 and y = –0.5x + 4 is C. x = 1. This is the value of x where the two graphs intersect, thus making both equations true.

The question is asking for the solution to the system of equations given by y = 2x2 – 2 and y = –0.5x + 4. Solving a system of equations means finding the value of x that makes both equations true. In other words, we're looking for the point where the two graphs intersect.

To find this value, we can set the two equations equal to each other and solve for x:

2x2 – 2 = -0.5x + 4

This simplifies to 2x2 + 0.5x - 6 = 0. Solving this quadratic equation can give us multiple solutions for x, but since the question is multiple choice, we can check which of the given options is a solution. Plugging the options into the equation reveals that option C. x = 1 is the correct answer, satisfying the equation.

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Answer:

Teachers 4 and Students 100, Teachers 5 and Students 125

Step-by-step explanation:

Going by the chart, by each teacher, the students are increasing by 25. The only ones to follow this pattern is 4:100 and 5:25

The sentence 'k is less than zero' can be translated into the inequality 'k < 0', where 'k' can be any value that is less than zero. The inequality for the word sentence 'k is less than zero' is k < 0.

The sentence 'k is less than zero' can be translated into an inequality as 'k < 0'. This is an inequality to represent a situation where 'k', a variable, takes values that are less than zero. It's a way of understanding the relationship of 'k' to zero in mathematical terms. For example, -1, -2, -3, etc. are all numbers that meet this less than zero inequality because they are less than zero.

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Final answer:

To find the point that maximizes P for the objective function P = 2x + 3y, calculate P at each vertex of the feasible region created by the constraints. Point A (0, 15) yields the highest value of P, which is 45. Therefore, point A (0, 15) is the correct answer.

Explanation:

To determine which point in the feasible region maximizes P for the objective function P = 2x + 3y, consider the given constraints: 2x + y ≤ 15, x + 3y ≤ 20, x ≥0, y ≥0. To find the maximum value of P, we need to check the value of P at all vertices of the feasible region formed by the constraints. In such linear programming problems, the maximum or minimum value of the objective function occurs at one of the vertices of the feasible region.

Let's test the given points against the objective function:

A. (0, 15) yields P = 2(0) + 3(15) = 45

B. (5, 5) yields P = 2(5) + 3(5) = 25

C. (8, 7) yields P = 2(8) + 3(7) = 37

D. (2, 6) yields P = 2(2) + 3(6) = 22

Comparing these values, we see that point A (0, 15) gives us the highest value of P, which is 45. Hence, the correct answer to the question is point A (0, 15).