The zeroes of the function are:
A) -2 and 0
B) 0 and 4
C) -2, 0, and 4

Answer:

The correct answer is $12

Step-by-step explanation:

To check, subtract 12 from 31

31 - 12 =19

Multiply 19 by 2

19 x 2 =38

Add 12

38 + 12 =50

a^m × a^n = a^(m+n)

means that when you take a number, a, multiplied by itself m times, and multiply that by the same number a multiplied by itself n times, it's the same as taking that number a and raising it to a power equal to the sum of m and n.

To prove this, we can verify it numerically:

Let us take,

a = 10

m = 2

n = 5

Now,

10² × 10⁵ = 10²+⁵

100 × 100000 = 10⁷

10000000 = 10000000

Another example,

Let us take,

a = 2

m = 0

n = 3

Now,

2⁰ × 2³ = 2⁰+³

1 × 8 = 2³

8 = 8

Earn $910 for a 40​-hour work week at the same hourly​ rate.

It is often used to express a change in one quantity over another quantity, such as speed, growth, or the relationship between two numbers.

There are many types of rates, some examples include:

Interest rate: The percentage of an amount of money that is charged as interest for borrowing or lending money.

Tax rate: The percentage of income or the value of a good or service that is charged as tax.

Growth rate: The rate at which a quantity increases over time, such as the growth rate of a population or the growth rate of an economy.

Speed: the rate at which an object moves, measured as the distance it travels per unit of time.

Rates are often expressed as a percentage or as a decimal. For example, an interest rate of 5% means that for every $100 borrowed, $5 must be paid back as interest. Similarly, a growth rate of 2% means that a quantity is increasing by 2% per unit of time.

It's important to note that rates are often used in mathematical and statistical calculations and it is crucial to understand the context of the rate to correctly interpret it.

To find the hourly rate, we can divide the weekly earnings by the number of hours worked: $635.60 ÷ 28 hours = $22.70/hour

To find the earnings for a 40-hour work week, we can multiply the hourly rate by the number of hours worked: $22.70/hour x 40 hours = $910.

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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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Answer:

Step-by-step explanation:

        (x, y) translates to (x+4, y-2) the image point is  (x', y')

  A(4,2) B(0, 0) → A'(4+4, 2-2)  B'(0+4, 0-2) → A'(8, 0) B'(4, -2)

C(-3, -3) D(4, 2) →C'(-3+4, -3-2) D'(4+4, 2-2) →C'(1, -5) D'(8, 0)

         E(0, 2)     → .           E'(0+4, 2-2) .          →E'(4, 0)

         F(-2, 5) .  → .           F'(-2+4 , 5-2) .         →F'(2, 3)

Answer:

Step-by-step explanation:

Since the cannonball is fired at an angle of 45°, it will have the same horizontal and vertical velocities.

Let x be the distance it travels before it is 600 feet above ground. At this point, its vertical displacement will be 600 feet, and we can use the formula for vertical displacement:

y = v0*t + (1/2)at^2

Since there is no initial vertical velocity and we are ignoring gravity, a = 0 and the equation simplifies to:

y = 0*t + 0 = 600

Solving for t, we get:

t = sqrt(2y/a) = sqrt(2*600/0) = undefined

This means that the cannonball will never be 600 feet above ground if we ignore gravity. Since this is not realistic, we cannot answer this question without additional information or by assuming that gravity is acting on the cannonball.

The original dimensions of the piece of metal were 15 inches by 20 inches.

To solve this problem, we can use the given information to set up an equation. Let's assume that the width of the rectangular piece of metal is x inches. According to the problem, the length of the piece of metal is 5 inches longer than its width, so the length would be (x+5) inches.

When squares with sides 1 inch long are cut from the four corners, the width and length of the resulting box will be reduced by 2 inches each. Therefore, the width of the box will be (x-2) inches and the length will be ((x+5)-2) inches, which simplifies to (x+3) inches.

The height of the box will be 1 inch since the flaps are folded upward.
Now, let's calculate the volume of the box using the formula Volume = length * width * height.

Substituting the values, we have:

234 = (x+3)(x-2)(1)

Simplifying the equation, we get:

234 = x^2 + x - 6

Rearranging the equation, we have:

x^2 + x - 240 = 0

Now, we can solve this quadratic equation either by factoring or by using the quadratic formula. Let's use factoring to find the values of x.

Factoring the equation, we have:
(x+16)(x-15) = 0
Setting each factor equal to zero, we get:
x+16 = 0 or x-15 = 0
Solving for x, we have:
x = -16 or x = 15
Since the width cannot be negative, we take x = 15 as the valid solution.
Therefore, the original dimensions of the piece of metal were 15 inches in width and (15+5) = 20 inches in length.

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Answer:

0.00046 acres

1.85806 square meters

2,880 square inches

Answer:

20 square feet

Step-by-step explanation:

Area=Length x Width

4 x 5 = 20

Answer:

1500+

Step-by-step explanation:

The rule demonstrating the logical equality of the two claims. -((w V p) ^(-91q1w)) DeMorgan's law has the form -(w V p) v-(-91qAw).

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Answer:

Roberto can buy 7 videogames.

Step-by-step explanation:

Given that Roberto has $ 200 in spending money and he wants to buy some video games that cost $ 25.50 each, to determine the number of games he can buy, the following inequality must be resolved:

25.50X = 200

X = 200 / 25.50

X = 7.84

Thus, since the whole number is 7, with $ 200 you can buy 7 video games, and there will be $ 21.5 (200 - 178.5) left over.

Answer:

50 + 100n  

Step-by-step explanation:

The cost is the cost of the visit plus the cost of the cavities

50 + 100n  where n is the number of cavities

Answer:

P = 50 + 100*n

Step-by-step explanation:

1. The visit is $50

2. Additional cavity is $100

3. n cavities would cost 100*n

Answer:

y=1/4x-3

Step-by-step explanation:

Answer:

0.33333.......

Step-by-step explanation:

one cannot be divided completely so it goes on forever

Answer:

0.33333333333......................( and goes on )

18 ans 2,639.064

19 ans 1,437.607

22 ans 7,872.433

23 ans 2,950.190

Answer:

It is D.

Step-by-step explanation:

Hoped this helped have an amazing day!

The domain of the quadratic function in this problem is given as follows:

All real values.

The domain of a function is the set of all the possible input values that can be assumed by the function.

On the graph, the domain of the function is given by the values of x of the function.

A quadratic function has no restrictions on the domain, hence it is defined by all the real values.

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(a) The errors made by the student are:

Incorrectly expanding 49(2) as 24 instead of 98.

Mistakenly factoring the quadratic equation as (y - 8)(y - 1) instead of

\(y^{2} - 9y + 8.\)

(b) The exact solution to the equation is x = 7/11.

(a) The student made two errors in their solution:

Error 1: In the step \("22x + 49(2) = 0,"\) the student incorrectly expanded 49(2) as 24 instead of 98. The correct expansion should be 49(2) = 98.

Error 2: In the step \("y^{2} - 9y + 8 = 0,"\) the student mistakenly factored the quadratic equation as (y - 8)(y - 1) = 0. The correct factorization should be \((y - 8)(y - 1) = y^{2} - 9y + 8.\)

(b) To find the exact solution to the equation, let's correct the errors made by the student and solve the equation:

Starting with the original equation: \(22x + 4 - 9(2) = 0\)

Simplifying: 22x + 4 - 18 = 0

Combining like terms: 22x - 14 = 0

Adding 14 to both sides: 22x = 14

Dividing both sides by 22: x = 14/22

Simplifying the fraction: x = 7/11

Therefore, the exact solution to the equation is x = 7/11.

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Approximately 37.5% of the data are greater than 28, 33.3% of the data are less than 23, 91.7% of the data are greater than 17.5, and 62.5% of the data are between 17.5 and 28.

To answer the questions, we can analyze the given data set.

First, let's count the number of data points that satisfy each condition:

Greater than 28:

There are 9 data points greater than 28 (29, 29, 29, 30, 29, 29, 28, 28, 28).

Less than 23:

There are 8 data points less than 23 (20, 18, 15, 17, 17, 15, 17, 19).

Greater than 17.5:

There are 22 data points greater than 17.5.

Between 17.5 and 28:

There are 15 data points between 17.5 and 28.

Now, let's calculate the approximate percentage for each condition:

Percent greater than 28:

The total number of data points is 24. Approximately, 9 out of 24 data points are greater than 28.

Percentage =\((9 / 24) \times 100 = 37.5\)%.

Percent less than 23:

Approximately, 8 out of 24 data points are less than 23.

Percentage = \((8 / 24) \times 100 = 33.3\)%.

Percent greater than 17.5:

Approximately, 22 out of 24 data points are greater than 17.5.

Percentage = \((22 / 24) \times 100 = 91.7\)%.

Percent between 17.5 and 28:

Approximately, 15 out of 24 data points are between 17.5 and 28.

Percentage = \((15 / 24) \times 100 = 62.5\)%.

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Answer:

30

Step-by-step explanation:

5x6=30

The piecewise function graphed is defined as follows:

A piecewise function is a function that has multiple definitions, depending on the input of the function.

Between x = -6 and x = -3, the function is linear with a slope of -1, hence:

y = -x + b.

When x = -4, y = 0, hence the intercept b is found as follows:

0 = 4 + b

b = -4.

Hence:

y = -x - 4, -6 <= x <= -3.

For x between -3 and 2, the function is constant at y = 2, hence:

y = 2, -3 < x <= 2.

For x between 2 and 6, the function is linear with a slope of 0.5(when x increases by 2, y increases by 1), hence:

y = 0.5x + b.

When x = 6, y = -1, hence the intercept b is given as follows:

-1 = 0.5(6) + b

b = -4.

Hence:

y = 0.5x - 4, 2 < x <= 6.

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18 is the correct answer

Answer:

22

Step-by-step explanation:

Using the expression to determine the value of c

121 = (c/2)²

find c

121 = c²/4

c² = 121 * 4

c = √121*4

c = √484

c = 22

Hence the value of c is 22

Answer:

175%

Step-by-step explanation:

70 = p * 40

p = 1.75 or 175%

Answer:

Step-by-step explanation:

175%

The area of a rectangle does double when dilated by a scale factor of 2, the Perimeter does not double. It increases by a factor of 2.

Brendan's statement that when a rectangle with a length of 6 cm and a width of 4 cm is dilated by a scale factor of 2, the perimeter and area of the rectangle are doubled is incorrect. While the area of the rectangle does indeed increase by a factor of 2 when dilated, the perimeter does not necessarily double.

Brendan's statement and understand the concept of dilation:

1. Perimeter: The perimeter of a rectangle is the sum of all its sides. In this case, the original rectangle has a length of 6 cm and a width of 4 cm, resulting in a perimeter of 2*(6 cm + 4 cm) = 20 cm. If we dilate this rectangle by a scale factor of 2, the new rectangle will have a length of 2 * 6 cm = 12 cm and a width of 2 * 4 cm = 8 cm. The perimeter of the new rectangle is 2*(12 cm + 8 cm) = 40 cm. As we can see, the perimeter has not doubled; it has increased by a factor of 2.

2. Area: The area of a rectangle is calculated by multiplying its length by its width. For the original rectangle with a length of 6 cm and a width of 4 cm, the area is 6 cm * 4 cm = 24 cm². When we dilate the rectangle by a scale factor of 2, the new rectangle will have a length of 2 * 6 cm = 12 cm and a width of 2 * 4 cm = 8 cm. The area of the new rectangle is 12 cm * 8 cm = 96 cm². The area has indeed doubled, as Brendan mentioned.

Therefore, while the area of a rectangle does double when dilated by a scale factor of 2, the perimeter does not double. It increases by a factor of 2. It is crucial to differentiate between the effects of dilation on the area and the perimeter of a shape to have a clear understanding of geometric transformations.

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Answer:

- sinu

Step-by-step explanation:

using the difference identity for sine

sin(a - b) = sinacosb - cosasinb

then

sin(u - π )

= sinucosπ - cosusinπ

= sinu(- 1) - cosu(0)

= - sinu - 0

= - sinu

The correct answer is B. The sample represents a proportion of the population.

A point estimate is a single value used to estimate a population's unknown parameter. The sample proportion (denoted by p), in the context of determining the population proportion, is a widely used point estimate. The sample proportion is determined by dividing the sample's success rate by the sample size.

The sample must be representative of the population for it to be a reliable point estimate of the population proportion. To accurately reflect the proportions of various groups or categories present in the population, the sample should be chosen at random.

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