Ben and Josh are in the same physical education class. Ben weighs twelve more pounds than josh. Together their weights add to 144. How much does each one weigh?

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.

Final answer:

To simplify an expression involving division of exponential terms with the same base, subtract the exponents of those terms. Numerical coefficients are divided normally while applying the subtraction rule to the exponents.

Explanation:

When simplifying the expression that involves division of exponentials, the correct action is to subtract the exponents. This rule applies when the bases of the exponential terms are the same. For example, when dividing [tex]a^m[/tex] by [tex]a^n[/tex], you would calculate a^(m-n). If we have numerical coefficients in front of the terms, we divide those normally, then apply the rule for exponents. An example is 4.5 × [tex]10^9[/tex] / [tex]10^6[/tex] = 4.5 × [tex]10^(9-6)[/tex] = 4.5 × [tex]10^3[/tex].

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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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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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".

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).

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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The given expressions need to be solved.

[tex]b[/tex] will include all numbers less than but not equal to [tex]0[/tex].

[tex]b[/tex] will include greater than but not equal to [tex]2[/tex].

The given expression is

[tex]6b-1<-7\\\Rightarrow 6b<-7+1\\\Rightarrow 6b<-6\\\Rightarrow b<-1[/tex]

So, [tex]b[/tex] will include all numbers less than but not equal to [tex]-1[/tex].

[tex]2b+1>5\\\Rightarrow 2b>5-1\\\Rightarrow 2b>4\\\Rightarrow b>\dfrac{4}{2}\\\Rightarrow b>2[/tex]

[tex]b[/tex] will include all numbers greater than but not equal to [tex]2[/tex]

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divide distance by speed

equation: time = distance / speed

120/8.5 = 14.117 seconds

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

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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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

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]

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.

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]

Answer:

Average change per day since then = $0.72

Step-by-step explanation:

Stock listing for Enam Telecom is given as

52 wk high    52 wk low   Symbol       Div.      Close      Net change

  122.866          64.77          ENM        3.45       99.14          4.74          

The lowest price $64.77 occurred 48 days ago.

Today's close for the stock was $99.14.

Now we have been asked to tell the approximate average change per day since then.

Therefore Average change per day = (closing value for today - closing value 48 days ago) ÷ (number of days)

Since closing value 48 days ago = 52 week low = $64.77

Now average change = [tex]\frac{(99.14-64.77)}{48}=0.72[/tex]

Therefore answer is $0.72 is the average change per day.

The approximate average change per day since the lowest price occurred is approximately $0.72, option B is correct.

To find the approximate average change per day since the lowest price occurred 48 days ago, we need to calculate the total change and divide it by the number of days.

The lowest price in the past year was 64.77, and the current price is 99.14.

The change in price is the difference between these two values:

Change = 99.14 - 64.77

= 34.37

Now, we divide the total change by the number of days:

Average Change per Day = Change / Number of Days

Average Change per Day = 34.37 / 48

Average Change per Day = 0.716

Hence, the approximate average change per day since the lowest price occurred is approximately $0.72.

Therefore, the correct option is b. $0.72.

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