b) How many more squares need to be shaded so that 70% of the grid is shaded?

The possible price for the items if the store sells $600 is (c) $40

From the question, we have the following parameters that can be used in our computation:

The supply-demand graph

If the store sells $600, then there is a supply worth of $600

The equation of the supply line is calculated as

y = mx + c

Where

c = y = 0

i.e. c = 100

So, we have

y = mx + 100

Using another point on the graph, we have

30m + 10 = 400

So, we have

m = 13

This means that

y = 13x + 100

For a supply of 600, we have

13x + 100 = 600

So, we have

13x = 500

Divide by 13

x = 38.4

Approximate

x = 40

Hence, the possible price for the items is (c) $40

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Answer: The length of BC ≈ 12.4 cm

Step-by-step explanation:

The first thing we need to do is to find the length of BD which we can solve for with the tangent of 20° which is the opposite side over the adjacent side.

We get tan20° = BD/8.

Solve for BD and you get BD = 8tan20°.

Now we will need to solve for the length of CD which we can get from the tangent of 40°.

We get tan40° = 8/CD

Solve for CD and you get CD = 8/tan40°.

Now that we have the lengths of BD and DC, we can simply add them together to get the length of BC.

(8tan20°) + (8/tan40°) ≈ 12.4 cm

Answer:

Step-by-step explanation:

−5+6−4

and

−4+(−5)+6

The actual distance represented by 23.7 cm on the map is 355.5 km.

To find the ratio of the amount of money Mabaso has to the amount of money Thabo has and the amount of money Ally has, we can divide each amount by the smallest amount (which is R35) to simplify the ratio.

Mabaso has R140, Thabo has R70, and Ally has R35.

The ratio of Mabaso's money to Thabo's money is:

R140 ÷ R35 = 4

The ratio of Mabaso's money to Ally's money is:

R140 ÷ R35 = 4

Therefore, the ratio of the amount of money Mabaso has to the amount of money Thabo has and to the amount of money Ally has is 4:1:1.

To calculate the percentage discount of a steel table, we need to find the difference between the original price and the discounted price, and then divide it by the original price. Finally, we multiply the result by 100 to get the percentage.

Original price: R750

Discounted price: R600

Discount: R750 - R600 = R150

Percentage discount: (R150 ÷ R750) × 100 = 20%

So, the table has a 20% discount on Black Friday.

To convert 125 grams to kilograms, we divide the amount in grams by 1,000 (since there are 1,000 grams in a kilogram).

125 g ÷ 1,000 = 0.125 kg

Therefore, 125 grams is equal to 0.125 kilograms.

If a green grocer packs 12 apples in a plastic bag and has 285 apples, we divide the total number of apples by the number of apples per bag to determine the number of bags needed.

Number of bags needed: 285 apples ÷ 12 apples/bag = 23.75 bags

Since we can't have a fraction of a bag, we round up to the nearest whole number. Therefore, the green grocer would need 24 bags.

If the scale of a map is 1,500,000 and the measurement on the map is 23.7 cm, we can use the scale to determine the actual distance.

1 cm on the map represents 1,500,000 cm in reality.

23.7 cm on the map represents x cm in reality.

x = 23.7 cm × 1,500,000 cm = 35,550,000 cm

To convert cm to km, we divide by 100,000 (since there are 100,000 cm in a kilometer).

35,550,000 cm ÷ 100,000 = 355.5 km

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The product of two linear functions having same variables will be a quadratic function where as the The product of two linear functions having different variables will be a linear function.

Linear function is the function whose degree is 1.

Degree of a function is the highest power of the variable of the function.

Let us take two examples.

1. Suppose the two linear functions are -

f(x) = 2x + 3 and g (x) = x + 5

The product of f(x) and g(x) will be

(2x + 3)(x + 5)

=2x (x + 5) + 3 (x + 5)

= 2x² + 10x + 3x + 15

= 2x² + 13x + 15

Here, f(x) and g(x) are the functions having same variables so there product is a quadratic function.

2. Suppose the two linear functions are -

f(x) = 2x + 3 and g (y) = y + 5

The product of f(x) and g(y) will be

(2x + 3)(y + 5)

=2x (y + 5) + 3 (y + 5)

= 2xy + 10x + 3y + 15

Here, f(x) and g(y) are the functions having different variables so there product is a linear function.

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The probability that Julie will be a captain, given that she makes the team is 1/3.

Given,

Number of students trying out for a soccer team = 40

Case of probability,

P(A) = n(A)/n(S)

n(A) = number of favourable outcomes, n(S) is the total number of events in the sample space.

Given ,

18 of 40 students will make the soccer team.

⇒ n(S) = 18

Let event A: Julie will be a captain, given that she makes the team

⇒ n(A) = 3

So, the probability that Julie will be a captain, given that she makes the team,

= P(A) = n(A)/n(S)

= P(A) = 3/18

= P(A) = 1/6

Therefore, the probability that Julie will be a captain, given that she makes the team is 1/3.

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The equation that represents the total cost of the membership will be y = 5x + 265.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

A local rec center offers a yearly membership for $265. The center offers aerobics classes for an additional $5 per class.

Let 'x' be the number of aerobics classes and 'y' be the total cost. Then the equation is given as,

y = 5x + 265

The equation that represents the total cost of the membership will be y = 5x + 265.

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The estimated number of cars without insurance from a sample of 180 cars is 18.

Insurance is a form of risk management that protects individuals and businesses from financial losses due to unexpected events such as accidents, theft, or natural disasters. It provides a safety net to individuals and businesses by compensating them for losses or damages that are covered by a policy. Types of insurance include life, health, auto, property, liability, and business insurance. Insurance also helps businesses to minimize their risk by transferring the risks to insurance companies, which then pay for any covered losses.

We can calculate the estimated number of cars without insurance from a sample of 180 cars by taking the average of the four days and multiplying it by 3, since there are three times as many cars in the larger sample as in the smaller sample.
Therefore, the estimated number of cars without insurance from a sample of 180 cars is (6+8+10+8)/4 x 3
= 18.

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Step-by-step explanation:

Realize that:

speed = distance / time and thus

time = distance / speed

Then the whole journey of 40/60 hours is the sum of (let's call them t1 and t2)

cycling: t1 = 2/y hours

running: t2 = 4/(y-4) hours

so we must simplify t1+t2=40 minutes (a.k.a. 4/6 hours):

2/y + 4/(y-4) = 4/6

let's multiply the first term by (y-4)/(y-4) and the second term by (y/y):

\(\frac{2(y-4)}{y(y-4)} + \frac{4y}{y(y-4)} = \frac46\)

since they now share a common denominator:

\(\frac{2(y-4) + 4y}{y(y-4)} = \frac46\)

\(\frac{6y-8}{y(y-4)} = \frac46\)

cross-products:

\(6 (6y-8) = 4y(y-4)\)

further simplification:

\(36y - 48 = 4y^2 - 16y\)

\(4y^2 - 52y + 48 = 0\)

\(y^2 - 13y + 12 = 0\)

q.e.d.

The perimeter of the shape is 10 inches.

It's important to note that the perimeter of a shape or calculated by adding all the sides together.

In this case, this is a rectangle and the perimeter will be:

Perimeter = 2(length + width)

Length = 4 inches

Width = 1 inch

Perimeter = 2(length + width)

Perimeter = 2(4 + 1)

Perimeter = 10 inches.

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To find the height of the shuttle, we can use trigonometry and the concept of similar triangles. The height of the shuttle is approximately 468.675 meters.

Let's assume that the height of the shuttle is represented by 'h' meters. From the information given, we know that the distance between the camera and the launch pad is 750 meters, and the angle of elevation from the camera to the shuttle is 32 degrees.

Using trigonometry, we can set up the following equation:

tan(32°) = h / 750

To find the value of h, we can rearrange the equation:

h = tan(32°) * 750

Using a calculator, we can find the value of tan(32°) ≈ 0.6249.

Now we can calculate the height of the shuttle:

h ≈ 0.6249 * 750

h ≈ 468.675 meters

Therefore, the height of the shuttle is approximately 468.675 meters.

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The percent change in the number of water bottles the company manufactured from February to April is 19.5%, to the nearest percent.

A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.

The total number of water bottles the company manufactured in February, March, and April.

In February, the company manufactured 4,100 water bottles. In March, the company manufactured 7% more water bottles than in February, which is 7/100 * 4,100 = 287 water bottles.

Therefore, the total number of water bottles the company manufactured in March is 4,100 + 287 = 4,387 water bottles. In April, the company manufactured 500 more water bottles than in March, which is 4,387 + 500 = 4,887 water bottles.

This is calculated as (4,887 - 4,100) / 4,100 = 0.195 or 19.5%.

Therefore, the percent change in the number of water bottles the company manufactured from February to April is 19.5%, to the nearest percent.

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The measure of angle x in each of the triangles is:

1) 20°

2) - 49°

3) 8°

4) 33.33°

5) 10°

6) 3°

7) 1°

8) 2°

9) 6°

1) The measure of the inner angles in the triangle are 100°, 40°, and 2x°.

The sum of all angles in the triangle is equal to 180°.

Therefore,

100° + 40° + 2x = 180°

140° + 2x = 180°

2x = 40°

x = 20°

2) The measure of the inner angles in the triangle are 99°, 37°, and (- x - 5)°.

The sum of all angles in the triangle is equal to 180°.

Therefore,

99° + 37° + ( - x - 5 )° = 180°

136° + (- x - 5)° = 180°

( - x - 5 )° = 44°

x = - 49°

3) The measure of the inner angles in the triangle are 60°, 60°, and ( - 12 + 9x)°.

The sum of all angles in the triangle is equal to 180°.

Therefore,

60° + 60° - 12 + 9x = 180°

120° - 12° + 9x = 180°

108° + 9x = 180°

9x = 72°

x = 8°

4) The measure of the inner angles in the triangle are 36°, 46°, and ( 2 - 3x)°.

The sum of all angles in the triangle is equal to 180°.

Therefore,

36° + 46° - 2° + 3x° = 180°

82° - 2° + 3x° = 180°

80° + 3x° = 180°

3x = 100°

x = 33.33°

5) The measure of the inner angles in the triangle are 71°, 50°, and ( 6x - 1 )°.

The sum of all angles in the triangle is equal to 180°.

Therefore,

71° + 50° - 1° + 6x° = 180°

121° - 1° + 6x° = 180°

120° + 6x° = 180°

6x = 60°

x = 10°

6) The measure of the inner angles in the triangle are 45°, 90°, and ( 8x + 21 )°.

The sum of all angles in the triangle is equal to 180°.

Therefore,

45° + 90° + 21° + 8x° = 180°

156° + 8x° = 180°

8x = 24°

x = 3°

7) The measure of the inner angles in the triangle are 85°, 64°, and ( 4x + 27 )°.

The sum of all angles in the triangle is equal to 180°.

Therefore,

85° + 64° + 27° + 4x° = 180°

176° + 4x° = 180°

4x = 4°

x = 1°

8) The measure of the inner angles in the triangle are 44°, 104°, and ( 7x + 18 )°.

The sum of all angles in the triangle is equal to 180°.

Therefore,

44° + 104° + 18° + 7x° = 180°

166° + 7x° = 180°

7x = 14°

x = 2°

9) The measure of the inner angles in the triangle are 125°, 25°, and ( - 5x )°.

The sum of all angles in the triangle is equal to 180°.

Therefore,

125° + 25° - 5x° = 180°

150° + 5x° = 180°

5x = 30°

x = 6°

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Answer:

The length is 8 inches and the width is 3 inches

Step-by-step explanation:

Let w represent the width.

The length can be represented by 2w + 2

Use the area formula, A = lw, and plug in the area and the expressions for the length and width:

A = lw

24 = (2w + 2)(w)

Simplify and solve for w:

24 = 2w² + 2w

2w² + 2w - 24

Divide everything by 2:

w² + w - 12

Factor:

(w + 4)(w - 3)

Set equal to 0 and solve for each factor:

w + 4 = 0

w = -4

w - 3 = 0

w = 3

Since the width cannot be negative, the width has to be 3.

Next, find the length by plugging in 3 as w:

2w + 2

2(3) + 2

= 8

So, the length is 8 inches and the width is 3 inches

Answer:

\(\textsf{1)}\quad y = \dfrac{4}{3}x-\dfrac{13}{3}\)

\(\textsf{2)} \quad y = \dfrac{3}{2}x-6\)

Step-by-step explanation:

To find the equation of a line parallel to the line joining (1, 2) and (-2, -2) and passing through (4, 1), we first need to find the slope of the line joining (1, 2) and (-2, -2).

\(\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-2-2}{-2-1}=\dfrac{-4}{-3}=\dfrac{4}{3}\)

Parallel lines have the same slope, so the slope of the parallel line is m = 4/3.

Substitute the found slope and point (4, 1) into the point-slope formula:

\(\begin{aligned} y - y_1 &= m(x - x_1)\\\\y - 1 &= \dfrac{4}{3}(x - 4)\\\\y - 1 &= \dfrac{4}{3}x-\dfrac{16}{3}\\\\y &= \dfrac{4}{3}x-\dfrac{13}{3}\end{aligned}\)

Therefore, the equation of the line parallel to the line joining (1, 2) and (-2, -2) and passing through (4, 1) is:

\(\boxed{y = \dfrac{4}{3}x-\dfrac{13}{3}}\)

\(\hrulefill\)

To find the equation of a line perpendicular to the line joining (2, -3) and (-1, -1) and passing through (2, -3), we first need to find the slope of the line joining (2, -3) and (-1, -1).

\(\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-1-(-3)}{-1-2}=\dfrac{2}{-3}=-\dfrac{2}{3}\)

The slopes of perpendicular lines are negative reciprocals, so the slope of the parallel line is m = 3/2.

Substitute the found slope and point (2, -3) into the point-slope formula:

\(\begin{aligned} y - y_1 &= m(x - x_1)\\\\y - (-3) &= \dfrac{3}{2}(x - 2)\\\\y+3&= \dfrac{3}{2}x-3\\\\y &= \dfrac{3}{2}x-6\end{aligned}\)

Therefore, the equation of the line perpendicular to the line joining (2, -3) and (-1, -1) and passing through (2, -3):

\(\boxed{y = \dfrac{3}{2}x-6}\)

Answer:

a is g(x) b is f(x)

Step-by-step explanation:

because a increases faster

Answer:

Step-by-step explanation:

Let the number be n

The statement

the difference of a number and eight is written as

n - 8

It's multiplied by 6

That's

6( n - 8)

The result is 12

So we have the final answer as

Hope this helps you

Answer:

33

Step-by-step explanation:

22-6+17=33

this is correct i think

g(x) is the inverse of f(x)

\(f(x) = {x}^{2} \)

\(g(x) = \sqrt{x} \)

Answer: 5 1/2

Step-by-step explanation:

12 5/6 - 7 1/3

Find an equivalent fraction for 7 1/3

12 5/6 - 7 2/6

5 3/6

Simplify

5 1/2

12 5/6 - 7 1/3

12-7= 5 and

5/6-1/3= {lcm of 6 and 3}

5-2/6= 3/6

3/6 = 1/2

final answer = 5 1/2

Answer:

Step-by-step explanation:

4(30+5)

4(30)+4(5)

120+20

140

Answer:

Step-by-step explanation:

201.06ft²

Answer:

Step-by-step explanation:

Answer:

5 ft

Step-by-step explanation:

30/6 = 5

20/4 = 5

25/x = 5

25/5 = 5

x = 5

Answer:

5 feet

Step-by-step explanation:

the triangles are scaled by the factor of 5

Answer:

x = -3±sqrt( 5)

Step-by-step explanation:

(x + 3)^2-5=0

Add 5 to each side

(x + 3)^2-5+5=0+5

(x + 3)^2 = 5

Take the square root of each side

sqrt((x + 3)^2 )=±sqrt( 5)

x+3 = ±sqrt( 5)

Subtract 3 from each side

x+3-3 = -3±sqrt( 5)

x = -3±sqrt( 5)

Answer:

I think it is 0.50d + 0.25

PLZ CORRECT ME IF I AM WRONG PLEASE AND THANK YOU

Step-by-step explanation:

Answer:

Step-by-step explanation:

0.25 (2d+1)=

0.50d+0.25 <===

Answer:

Step-by-step explanation:

For step explanation:

1. write the problem

2. distinguishing the neg sign

3. distributing 3

4. moving like terms next to each other through commutative property

5.  Combining like terms

6. getting rid of parentheses