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we know that

if two lines are perpendicular, then the product of their slopes is equal to minus one

so

[tex]m1*m2=-1[/tex]

Step 1

Find the slope of the given line

we have

[tex]3y=-4x+2[/tex]

Solve for y

Divide by [tex]3[/tex] both sides

[tex]3y/3=(-4x+2)/3[/tex]

[tex]y=-\frac{4}{3}x+ \frac{2}{3}[/tex]

the slope of the given line is [tex]m1=-\frac{4}{3}[/tex]

Step 2

Find the slope  of a line that is perpendicular to the given line

we have

[tex]m1=-\frac{4}{3}[/tex]

[tex]m1*m2=-1[/tex]

[tex]m2=-1/m1[/tex]

substitute the value of m1

[tex]m2=-1/(-4/3)=\frac{3}{4}[/tex]

therefore

the answer is

the slope is [tex]\frac{3}{4}[/tex]

The slope of a line that is perpendicular to a line of the given equation is [tex]\frac{3}{4}[/tex]

Given the following equation;

To find the slope of a line that is perpendicular to a line of the given equation:

In Mathematics, the slopes of two lines are said to be perpendicular when the product of these slopes is equal to negative one (-1).

Mathematically, this is given by:

[tex]m_1 \times m_2 = -1[/tex]   ...equation 1.

First of all, we would determine the slope of the given equation:

[tex]3y =-4x +2\\\\y = \frac{-4x}{3} + \frac{2}{3}[/tex]

Slope, [tex]m_1[/tex] = [tex]\frac{-4}{3}[/tex]

Substituting slope 1 into eqn 1, we have:

[tex]\frac{-4}{3} \times m_2 = -1\\\\-4m_2 = -3\\\\m_2 = \frac{3}{4}[/tex]

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The angular velocity of the wheel is 6π rad/sec.

Angular velocity is the speed at which the angle between two bodies changes as an item rotates or revolves around an axis.

In one revolution,

The angular velocity is 2π rad/sec.

In 30 revolutions,

The angular velocity is 2π x 30 rad/ 10sec.

The angular velocity is 60π rad/sec.

The SI unit of angular velocity is radians per second.

Hence, The wheel's angular velocity is 6 rad/sec.

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It takes Stella 1.4 minutes to write a full page, calculated by setting up a proportion based on her rate of writing [tex]\frac{1}{7}[/tex] of a page in 1/5 of a minute.

Stella writes  [tex]\frac{1}{7}[/tex] of a page in  [tex]\frac{1}{5}[/tex] of a minute. To calculate how many minutes it takes her to write a full page, we can set up a proportion. Since 7/7 would make a full page, we'd need Stella to write seven times as much as she does in 1/5 of a minute. So, the math to find the time for a full page looks like this:

[tex]\frac{1}{7}[/tex] page :  [tex]\frac{1}{5}[/tex]  minute = 7/7 page : x minutes

Now multiply both sides by (1/5) minutes to isolate x:

[tex]\frac{1}{7}[/tex] /   [tex]\frac{1}{5}[/tex] = 1/x

Cross multiply to solve for x:

[tex]\frac{1}{7}[/tex] * x =  [tex]\frac{1}{5}[/tex]

x =  [tex]\frac{1}{5}[/tex]  /  [tex]\frac{1}{7}[/tex]

x =  [tex]\frac{1}{5}[/tex]  * (7/1)

x = 7/5 minutes

x = 1.4 minutes

Therefore, it takes Stella 1.4 minutes to write a full page.

The scale factor used to find the dimensions of the scale drawing is 1/12. This is found by dividing the dimensions of the drawing by the dimensions of the actual flower bed, confirming both scale factors for length and width are equal.

The student is asking about determining the scale factor used to create a scale drawing from the actual dimensions of an object, which in this case is a flower bed. To find the scale factor, we compare the dimensions of the drawing with those of the actual object. For the given dimensions of the drawing, which are 3 inches by 7 inches, and the actual dimensions being 36 inches by 84 inches, we can find the scale factors for the length and width separately and confirm they are the same.

For the length, the scale factor is calculated as:
Scale factor for length = Length of drawing / Length of actual object
Scale factor for length = 3 inches / 36 inches = 1/12

For the width, the scale factor is calculated as:
Scale factor for width = Width of drawing / Width of actual object
Scale factor for width = 7 inches / 84 inches = 1/12

Thus, the scale factor for the scale drawing is 1/12. This means that each unit of measurement in the drawing represents 12 units in the actual flower bed.

1. The expression that represents the dimensions of the small box is (2x³ + 4x²).

2. The expression that represents the dimensions of the large box is (3x³ + 36x² + 105x).

3. The difference in the volumes of the two boxes is (x³ + 32x² + 105x)

1.

Small box:

x inches,

(x+ 2) inches and

(2x) inches

Volume = length × width × height

= x × (x + 2) × (2x)

= (x² + 2x) × 2x

= 2x³ + 4x²

2.

Large box:

(x+5) inches,

(x + 7) inches and

(3x) inches.

Volume = length × width × height

= (x + 5) × (x + 7) × (3x)

= 3x³ + 36x² + 105x

4.

Difference in volume = Large box - Small box

= (3x³ + 36x² + 105x) - (2x³ + 4x²)

= 3x³ + 36x² + 105x - 2x³ - 4x²

= x³ + 32x² + 105x

Therefore, x³ + 32x² + 105x is the expression which represents the volume of the box.

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Joe used 1/5 of the timber for the first garden and 3/8 for the second garden. After converting these fractions to have a common denominator, we found that 23/40 of the timber was used. Therefore, 17/40 of the timber remains for the third garden.

The student is asking how much of the timber remains after Joe has used some for two gardens. Joe uses 1/5 of the wood for the first garden and 3/8 for the second garden. To solve this, we first add the fractions of wood used for both gardens to find out the total used fraction:

1/5 + 3/8

To add these fractions, we first need to find a common denominator, which in this case is 40. So we convert the fractions:

8/40 + 15/40} = 23/440

Now we subtract the used fraction from the total amount of timber, which is 1:

1 - 23/40 = 40 / 40 - 23 / 40= 17 / 40

Thus, 17/40 of the wood remains for the third garden.

To find the perpendicular components of a displacement vector with a magnitude of 20 meters, use trigonometry and the Pythagorean theorem.

The question asks for the perpendicular components of a displacement vector with a magnitude of 20 meters. Perpendicular components of a vector can be determined using trigonometry. Let's assume the vector has components Ax and Ay.

Using the Pythagorean theorem, Ax^2 + Ay^2 = 20^2. Since the components are perpendicular, we can set up a right triangle and solve for the components using the sine and cosine functions. For example, if one component is Ax = 10 meters, the other component Ay can be calculated using Ay = sqrt(20^2 - 10^2) = 10*sqrt(3) meters. Similarly, if one component is Ay = 10 meters, the other component Ax can be calculated using Ax = sqrt(20^2 - 10^2) = 10*sqrt(3) meters.

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Let

x-------> the number of tickets

y------> the profit in dollars

Let

[tex]A(0,-400)\ B(40,0)[/tex]

Find the slope of the linear equation

The slope is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute

[tex]m=\frac{0+400}{40-0}[/tex]

[tex]m=10\frac{\$}{ticket}[/tex]

the linear equation is

[tex]y=10x-400[/tex]

Statements

case A) The y-intercept represents the cost per ticket

The statement is false

The cost per ticket  represent the slope of the linear equation

The y-intercept is the value of the profit for a number of tickets equal to zero

In this problem the y-intercept is the point [tex](-400,0)[/tex]

case B) The slope represents the money spent before the sale of the first ticket

The statement is False

The slope represents the cost per ticket

the money spent before the sale of the first ticket is the y-intercept

case C) The sports club must sell more than [tex]40[/tex] tickets to make a profit

The statement is True

Because

we know that

For [tex]x=40\ tickets[/tex]

the value of the function is

[tex]y=0[/tex]

in the linear equation

[tex]y=10x-400[/tex]

For [tex]x>40\ tickets[/tex]

the profit will be

[tex]y > 0[/tex] --------> see the graph

therefore

the answer is

The sports club must sell more than [tex]40[/tex] tickets to make a profit

Answer:

the first 2 are false and the last one is true.

Step-by-step explanation:

I took the test :)

To find out how much more money is needed for the Atlanta playground, add the amounts raised by each school and subtract from the total amount needed. The schools have raised $12,324, so they still need about $1676. Therefore, $1676 more is required to meet the goal.

Let's calculate how much money the schools have already raised:

First, add these amounts together:

Next, subtract the total amount raised from the total money needed:

Therefore, the town of Atlanta still needs to raise about $1676 for the new playground.

A. We are given that they already drove 420 miles and an additional of 65 miles per hour. Therefore distance covered is:

d = 420 + 65 t

where d is distance and t is time

B. If they drove 8 hours per day for 2 days, then total time is t = 16 hours, hence:

d = 420 + 65 * 16

d = 1460 miles

Answer: C) Yes, the figure can be rotated 180°.

Step-by-step explanation:

Here,the given figure is a rectangle, and we know that a rectangle has order of rotational symmetry of 2.

The 180° and 360° rotations will map it onto itself.

So, from the given options, the right answer is C) Yes, the figure can be rotated 180°.