The midpoint of ab is =m, −3−2 . one endpoint is =a, 2−8 . find the coordinates of the other endpoint,
b.

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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divide distance by speed

equation: time = distance / speed

120/8.5 = 14.117 seconds

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

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).

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]

Triangle JKL is obtuse triangle.

Triangle XYZ is acute triangle.

An obtuse triangle is a type of geometric figure with three sides and three angles. In an obtuse triangle, one of the angles measures more than 90 degrees (∠A, ∠B, or ∠C > 90°). The other two angles are acute angles, measuring less than 90 degrees each. Consequently, the sum of the angles in an obtuse triangle is greater than 180 degrees.

what is the acute triangle

An acute triangle is a type of geometric shape defined by its angles. It consists of three sides and three angles, all of which are acute angles, meaning each angle measures less than 90 degrees (∠A, ∠B, and ∠C < 90°)

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To graph the parabola [tex]f(x) = -1/3x^2 + 4/3x - 16/3[/tex], plot the vertex at (2, -4), note the axis of symmetry at x = 2, and create a downward-opening parabolic shape on a coordinate plane.

To graph the parabola given by the function [tex]f(x) = -1/3x^2 + 4/3x - 16/3[/tex], follow these steps:

1. Identify the vertex: The vertex of a parabola in the form of [tex]y = ax^2 + bx + c[/tex] is given by (-b/2a, f(-b/2a)). In this case, a = -1/3 and b = 4/3. Calculate the x-coordinate of the vertex using -b/2a:

  x-coordinate of the vertex = -b / (2a) = -(4/3) / (2 * (-1/3)) = 2.

  Now, find the corresponding y-coordinate by plugging the x-coordinate back into the function:

[tex]f(2) = (-1/3)(2)^2 + (4/3)(2) - 16/3 = (-4/3) + (8/3) - 16/3 = -12/3 = -4.[/tex]

  So, the vertex is at (2, -4).

2. Find the axis of symmetry: The axis of symmetry is a vertical line that passes through the vertex. In this case, it's the vertical line x = 2.

3. Calculate additional points: To create a more accurate graph, you can choose additional x-values and calculate their corresponding y-values. For instance, you can select x-values to the left and right of the vertex.

  - For x = 0:

    [tex]f(0) = (-1/3)(0)^2 + (4/3)(0) - 16/3 = -16/3.[/tex]

  - For x = 4:

    [tex]f(4) = (-1/3)(4)^2 + (4/3)(4) - 16/3 = -64/3 + 16/3 - 16/3 = -64/3.[/tex]

4. Plot the points: Plot the vertex (2, -4) and the additional points you calculated on a coordinate plane.

5. Draw the parabola: Connect the points smoothly to form the parabolic shape. Since the leading coefficient (-1/3) is negative, the parabola opens downward.

6. Label the axis of symmetry: Label the vertical line x = 2 as the axis of symmetry.

Your graph of the parabola f(x) = -1/3x^2 + 4/3x - 16/3 should resemble a downward-opening parabola with the vertex at (2, -4) and the axis of symmetry at x = 2.

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By substituting '12' into the given linear equation 'y = 10x - 18', we find that figure 12 in this tile pattern would be 102.

The given pattern follows the linear equation y = 10x - 18. To find the value of figure 12, smaller 'x' with '12' in the equation: y = 10 * 12 - 18 = 102. Therefore, figure 12 in this tile pattern would be 102.

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Final answer:

The framer can make at most 4 complete picture frames from the usable length of the board, after deducting the scratched section, and each frame using 1 2/3 feet of the board.

Explanation:

The picture framer has a board that is 10 1/12 feet long. However, part of this board is unusable due to scratches, and that section is 2 3/8 feet. Therefore, the usable length of the board is 10 1/12 feet - 2 3/8 feet. Each picture frame requires 1 2/3 feet of this board. To find out how many complete picture frames can be made, we need to divide the usable length of the board by the length required for each frame.

First, convert the mixed numbers to improper fractions:

Total length of the board: 121/12 feet

Scratched section: 19/8 feet

Frame length: 5/3 feet

After subtracting the scratched section from the total length, we have:

(121/12) - (19/8) = (968/96) - (228/96) = 740/96 feet

Now we divide the usable length by the frame length:

(740/96 feet) / (5/3 feet) = (740/96) * (3/5) = 740/160 = 4.625

Since we cannot have a partial frame, the framer can make at most 4 complete picture frames.

Answer:

The complex number  6(cos 330° + i sin 330°) in the form of a+bi is:

3√3-3 i

Step-by-step explanation:

6(cos 330° + i sin 330°)

= 6(cos(360°-30°)+ i sin(360°-30°))

=6(cos30°- i sin30°)   (since, 360°-30° lies in fourth quadrant and cos is positive there and sin is negative)

=[tex]6(\dfrac{\sqrt{3}}{2}-i\dfrac{1}{2})[/tex]

Distributing 6, we get

=3√3-3 i

Hence, the complex number  6(cos 330° + i sin 330°) in the form of a+bi is:

3√3-3 i

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.

f(x) = 7x-5

 find f(-10)

 replace x with -10

 so you have 7(-10)-5

7*-10=-70 - 5 = -75

 so f(-10) = -75

f(x) = 7x-5

find f(-10)

replace x with -10

so you have 7(-10)-5

7*-10=-70 - 5 = -75

so f(-10) = -75

Answer:

There will be 150 defective cars among the set of 10,000 cars

Step-by-step explanation:

For every 200 cars 3 are defective

Let X numbers of car be defective out of 10000 cars

There is a proportional relationship between the two

Thus,

[tex]\frac{3}{200} = \frac{X}{10,000} \\X = \frac{(10,000)(3)}{(200)} = 50 * 3\\= 150[/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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