Which is the graph of the piecewise function f(x)?


f(x) = StartLayout Enlarged left-brace 1st row 1st column negative x + 1, 2nd column x less-than-or-equal-to 0 2nd row 1st column x + 1, 2nd column x greater-than 0 EndLayout

The question is about comparing Angela's 12% commission structure against her friend's $750 fixed salary plus 5% commission. The answer examines how the volume of sales would affect their respective incomes.

This problem is about comparing commission rates and overall income. If Angela worked on a straight 12% commission, it means that she earns 12% of the total sales she makes. Her friend, however, has a fixed salary of $750, in addition to earning 5% of his total sales as commission. To compare their incomes, we would need to know the total sales each of them makes. Generally, the more sales they make, the more beneficial the commission system becomes.

For example, if Angela made $1000 in sales, she would earn $120 (12% of $1000). If her friend made the same amount in sales, he would earn $800 ($750 salary + $50 from 5% of $1000). However, if they only made $100 in sales, Angela would earn $12, and her friend would earn, $755. So, the best system depends on the volume of sales.

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Answer: 25

Step-by-step explanation:

If two shapes are similar , then the ratio of their sides are also similar.

From the shapes given:

[tex]\frac{x}{50}[/tex] = [tex]\frac{20}{40}[/tex]

[tex]\frac{x}{50}[/tex] = [tex]\frac{1}{2}[/tex]

2x = 50

x = 25

Answer:

Perimeter of triangle ABC = 5(3+13) = 5 x 16 = 80

Angle A = 30°, Angle B = 60°

Therefore Angle C = 90°

Pythagorean triplet = 40/3, 96/3, 104/3

Area of triangle ABC = 1/2 x b x h

= 1/2 x 40/3 x 96/3

= 1920/9

= 213.3 cm^2

Hope this helps!

The area of the triangle is found by recognizing that it is a special 30-60-90 triangle with sides in the ratio of 1: √3 : 2. The area, using these ratios and the given perimeter, is calculated as 25√3 square units.

This problem pertains to the area of a triangle. Because we know the two acute angles of triangle ABC, it is a 30-60-90 triangle. This is a special type of right triangle where the sides are in a particular ratio. In a 30-60-90 triangle, the sides across from the 30°, 60° and 90° angles are in the ratio of 1: √3 : 2.

Given that the perimeter is 5(3 + √13), we can set up the ratio for the sides as x, x√3, and 2x. Adding these together equals the perimeter: x + x√3 + 2x = 5(3 + √13). Solving this equation, we find x = 5.

The area of a triangle is calculated using the formula 1/2*base*height. Using the sides of the triangle, 5, 5√3, and 10, we will use the side across from the 90° angle (10) as the base and the side across from the 60° angle (5√3) as the height, giving us a triangle area of 1/2 * 10 * 5√3 = 25√3 square units.

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Answer:

B

Step-by-step explanation:

15% = 0.15

1 - 0.15 = 0.85

[Plug in the p and s]

Answer:

Domain : {-2, -1, 0, 4}

Range: {-2, 2, 3, 4}

Answer:

b,c

Step-by-step explanation:

Answer:

6 shaded squares and 4 unshaded....shaded = 60%

Step-by-step explanation:

a grid with 100 squares, 6 are shaded....6/100 = 0.06 = 6%

a grid with 100 squares, 36 are shaded....36/100 = 0.36 = 36%

6 shaded squares and 4 unshaded...6:4...added = 10

shaded = 6/10 = 0.6 = 60% <====

4 shaded squares and 6 unshaded...4:6...added = 10

shaded = 4/10 = 0.4 = 40%

Answer: The answer is C

Answer:

x intercept is 6/13

y intercept is -6

Step-by-step explanation:

x intercepted when y is zero.

y intecepted when x is zero...

Answer:

$ 1.10

Step-by-step explanation:

p + r = 1.45....p = 1.45 - r

2p + r = 1.80

2(1.45 - r) + r = 1.80

2.90 - 2r + r = 1.80

-2r + r = 1.80 - 2.90

-r = - 1.10

r = 1.10 <=== a ruler costs $ 1.10

p + r = 1.45

p + 1.10 = 1.45

p = 1.45 - 1.10

p = 0.35 .......a pencil will cost $ 0.35

By setting up simultaneous equations based on the purchases of Phoebe and Ioeh and solving them, we find that the cost of the ruler is £1.10.

To determine the cost of the ruler, we need to set up two equations based on the given information about Phoebe and Ioeh's purchases and use the method of simultaneous equations.

Let's assume 'R' represents the cost of the ruler and 'P' represents the cost of one pencil.

According to the question:

To find the cost of the ruler, we can solve these equations simultaneously. Subtract the first equation from the second to eliminate R and find P:

1. R + 2P = £1.80
2. R + P  = £1.45

Subtract equation 2 from equation 1:

2P - P = £1.80 - £1.45
P = £0.35

Now that we know one pencil costs £0.35, we can substitute P back into either equation to find R. Let's use the first equation:

R + P = £1.45
R + £0.35 = £1.45
R = £1.45 - £0.35
R = £1.10

Thus, the ruler costs £1.10.

A charter is to a city government as a state constitution is to a state government.

Answer: Option D

Explanation:

Apart from the national level constitution, in the United States of America, every state has its own constitution. They are more detailed when compared to the national constitution as they tend to have more words or content when compared to the national level constitution.

The shortest one belongs to Vermont and the longest one belongs to Alabama. These constitutions tell how the government of each state must function and carry out its day to day activities.

Answer:

therefore the correct options are:

B. the equation is an exponential decay equation.

F. $28000 represents the initial cost of an automobile that depreciates 27% per year  over the course of t years.

Step-by-step explanation:

i) the cost of an automobile is given by the equation is

 C(t) = [tex]28000\times(0.73)^{t}[/tex], where C(t) represents the cost and t represents the time in years

ii) the above equation is an exponential decay equation. It is a decay equation because growth rate is 0.73 which is less than 1 and greater than zero.

ii) when t = 0 then the cost is C(0) = 28000 represents the initial cost.

iii) from the equation in i) we can understand that the cost depreciates 27% per year over the course of t years.

therefore the correct options are:

B. the equation is an exponential decay equation.

F. $28000 represents the initial cost of an automobile that depreciates 27% per year  over the course of t years.

Answer:

Part 1)Is a inconsistent system

Part 2) Is a consistent independent system

Part 3) Is a consistent dependent system

see the attached figure

Step-by-step explanation:

we know that

If a system has at least one solution, it is said to be consistent .  

If a consistent system has exactly one solution, it is independent .  

If a consistent system has an infinite number of solutions, it is dependent

If a system not have solution, it is said to be inconsistent

Part 1) we have

[tex]x+5y=-2[/tex]

[tex]x+5y=4[/tex]

This system of linear equations has two parallel lines (their slopes are equal) with different y-intercept

so

The lines don't intersect

The system has no solution

therefore

Is a inconsistent system

Part 2) we have

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

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

we know that

If two lines have different slopes, then the lines intersect at one point and the system of equations has one solution

In this problem, the lines have different slopes )m=3 and m=2)

so

The system has one solution

therefore

Is a consistent independent system

Part 3) we have

[tex]3x+y=4[/tex] ----> equation A

[tex]-6x-2y=-8[/tex] ----> equation B

Multiply equation A by -2 both sides

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

[tex]-6x-2y=-8[/tex] ----> equation C

Compare equation B and equation C

Are identical lines

so

The system has infinity solutions

therefore

Is a consistent dependent system

Answer:

A system of equations is shown below: x + y = 3 2x − y = 6 The x-coordinate of the solution to this system of equations is _____. I'm thinking it could be X=3

Step-by-step explanation:

The value of the y-coordinate of the solution to the system of equations is; y = 1.

According to the question;

The equations given are;

By solving the pair of equations simultaneously; we have;

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Answer:

y = abx. Where a ≠ 0, the base b ≠ 1 and x is any real number ... When given a percentage explanation:

Josh bought a total of 1,800 grams of fruit. This includes 1.5 kg of oranges (converted to 1,500 grams), 150 grams of grapes, and 15,000 centigrams of apples (converted to 150 grams). The weights were converted to grams to find the total weight.

The subject of the question you've asked pertains to Mathematics, specifically to the topic of weight measurement and addition. We have to convert different measurements to a uniform unit and then sum them up to find the total weight of all the fruits bought by Josh at the farmer's market.

To solve the problem presented in the question: Josh bought 1.5 kilograms of oranges, 150 grams of grapes, and 15,000 centigrams of apples. We want to find out the total weight of fruits in grams. First, we need to convert kilograms and centigrams to grams, since kilograms and centigrams are not directly compatible with grams. We know that 1 kilogram equals 1,000 grams, and 1 centigram equals 0.01 grams.

So, converting Josh's purchases to grams:

Oranges: 1.5 kg × 1,000 = 1,500 grams

Grapes: 150 grams (already in grams, no conversion necessary)

Apples: 15,000 cg × 0.01 = 150 grams

Now, we simply add all the weights in grams:

1,500 grams (oranges) + 150 grams (grapes) + 150 grams (apples) = 1,800 grams of fruit in total.

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First represent your 3 consecutive integers as follows.

X ⇒ first integer

X + 1 ⇒ second integer

X + 2 ⇒ third integer

Since their sum is 84, our equation reads x + (x + 1) + (x + 2) = 84.

Simplifying on the left side we get 3x + 3 = 84.

Now subtract 3 from both sides to get 3x = 81.

Dividing both sides by 3, we find that x = 27.

Finally, make sure you list all your answers.

If x is 27 then x + 1 is 28 and x + 2 is 29.

Answer:

27 + 28 + 29 = 84

Step-by-step explanation:

Let the three consecutive integers be x +1, x+2 and x+3

Thus,

[tex](x + 1) + (x + 2) + (x + 3) = 84[/tex]

Remove the brackets

[tex]x + 1 + x + 2 + x + 3 = 84[/tex]

Group the like terms

[tex]x + x + x + 1 + 2 + 3 = 84[/tex]

[tex]3x + 6 = 84[/tex]

To make 3x subject of formula, subtract 6 from both sides of the equation thus,

[tex]3x + 6 - 6 = 84 - 6[/tex]

[tex]3x = 78[/tex]

Divide through by 3

[tex] \frac{3x}{3} = \frac{78}{3} [/tex]

[tex]x = 26[/tex]

Since x = 26

[tex]x + 1 = 26 + 1 = 27[/tex]

[tex]x + 2 = 26 + 2 = 28[/tex]

[tex]x + 3 = 26 + 3 = 29[/tex]

Therefore, the three consecutive integers are 27, 28 and 29

Check

[tex]27 + 28 + 29 = 84[/tex]

Answer:

[tex]y = \frac{5}{2} + \frac{19}{2}[/tex]

Step-by-step explanation:

From the question;

We are required to determine the equation of a line that passes through points (-7,-8) and (-5,-3).

Note that we can get the equation of a line when;

Therefore, since we are given two points where the line is passing through we can get the equation;

First, we determine the slope of the line;

slope = change in y ÷ change in x

That is;

[tex]slope=\frac{(-3--8)}{(-5--7)}[/tex]

        [tex]=\frac{5}{2}[/tex]

Second, we take another point (x,y) and one of the points, in this case, we take (-5,-3).

Therefore;

[tex]\frac{y+3}{x+5}=\frac{5}{2}[/tex]

[tex]2(y+3)=5(x+5)\\2y + 6 = 5x +25\\2y= 5x + 19\\y = \frac{5}{2} + \frac{19}{2}[/tex]

Therefore, the equation of the line is [tex]y = \frac{5}{2} + \frac{19}{2}[/tex]

Answer:

therefore the given equation is linear but it is not proportional.

Step-by-step explanation:

i) Is y = 4x - 5 proportional or non- proportional.

ii) therefore we can see that the equation is the same as the equation for a line, therefore the given equation is linear but it is not proportional.

Answer:

$112.7

Step-by-step explanation:

15%=0.15

0.15*98=14.7

98+14.7=112.7

Answer:

Part A) Circumference

Part B) C=π D

Part C) The distance traveled in one rotation is 628.32 feet

Step-by-step explanation:

Part A) we know that

The distance around the circle is equal to the circumference.

The Ferris Wheel have a circular shape

so

To find out the distance around the Ferris Wheel you should use the circumference

Part B) What is the formula needed to solve this problem?

we know that

The circumference is equal to multiply the number π by the diameter of the circle

so

C=π D

Part C) What is the distance traveled in one rotation?

we know that

One rotation subtends a central angle of 360 degrees

The distance traveled in one rotation is the same that the circumference of the Ferris wheel

we have

[tex]D=200\ ft[/tex] ----> diameter of the Ferris wheel

substitute in the formula of circumference

[tex]C=\pi (200)\\C=200\pi\ ft[/tex]

assume

[tex]\pi=3.1416\\C=200(3.1416)=628.32\ ft[/tex]

therefore

The distance traveled in one rotation is 628.32 feet

Answer:

m > 124

Step-by-step explanation:

switch sides, add 91 to both sides then simplify :)

You need to isolate/get the variable "m" by itself on one side of the equation

33 < m - 91    Add 91 on both sides to get m by itself

33 + 91 < m - 91 + 91

124 < m    [124 is less than m]

Answer:

Therefore the expression for y when x is 2 is

[tex]y=\dfrac{48}{6}\times 2[/tex]

Step-by-step explanation:

Given:

y varies directly as x, and y is 48 when x is 6

Means  Direct Variation.

Therefore,

[tex]y=kx[/tex]

Where,

k = Constant of Proportionality

To Find:

y when x = 2

Solution:

First step we need to Find Constant of Proportionality

So put y = 48 and x = 6

Substituting the values we get

[tex]48=k\times 6\\\\k=\dfrac{48}{6}[/tex]

Now When x = 2 and [tex]k=\dfrac{48}{6}[/tex] y will be

[tex]y=\dfrac{48}{6}\times 2[/tex]

Therefore the expression for y when x is 2 is

[tex]y=\dfrac{48}{6}\times 2[/tex]

Answer:

B

Step-by-step explanation:

You can solve this by using the vertical line test. When you do the vertical line test, the vertical line should only pass through one point on the function. That means that there can to be only one value of x for every y. Set B is the only set where the x value doesn't repeat.

In the provided sets of ordered pairs, B and D are considered functions. A function is a relation where each input corresponds to exactly one output, and in sets B and D, this requirement is met.

In mathematics, a relation is considered a function if and only if every input (also called the domain or the x-coordinate) corresponds to exactly one output (also called the range or the y-coordinate). In the language of ordered pairs, an ordered pair presents itself as (x, y). If x repeats with a different y in the set, then the relation is not a function.

So let's examine the sets of ordered pairs given:

Therefore, the set of ordered pairs which are functions are B and D.

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Answer:

The value of the given expression -9w+9 when w=15 is -126

Step-by-step explanation:

Given expression is -9w+9

To find the given expression when w=15:

That is put w=15 in the given expression we get

-9w+9=-9(15)+9

=-135+9 ( adding the like terms )

=-126

Therefore the value of the given expression -9w+9 when w=15 is -126

Paolo wrote the following equation for the perimeter of a rectangle.

P=2(l+w)

Which equation is equivalent to the equation Paolo wrote?

The equivalent equations are:

[tex]w = \frac{p-2l}{2}\\\\l = \frac{p-2w}{2}\\\\p = 2l+2w[/tex]

Given that:

The equation for perimeter of rectangle written by Paolo is:

P = 2(l + w)

where

l = length side of rectangle

w = width side of the rectangle

We have to find the equivalent equation

Let us solve the equation for "w"

[tex]P = 2(l + w)[/tex]

Divide by 2 both sides

[tex]\frac{P}{2} = \frac{2(l+w)}{2}\\\\\frac{P}{2} = l + w[/tex]

[tex]\text{Subtract L on both sides of equation }[/tex]

[tex]\frac{P}{2} - l = l + w - l\\\\\frac{P}{2} - l =w[/tex]

[tex]w = \frac{p-2l}{2}[/tex]

Similarly solving for "l" we get,

[tex]l = \frac{P-2w}{2}[/tex]

Also, given equation can be written as,

[tex]P = 2(l+w)\\\\P = 2l + 2w[/tex]

Thus the equivalent equations are found

Final answer:

The equivalent equation to Paolo's originally written P=2(t+W) for a rectangle's perimeter should be P=2t+2u, assuming 't' stands for width and 'u' for length. The area function a(t) for the rectangle based on width and fixed perimeter is valid within the domain 0 <= t <= L/2.

Explanation:

The question pertains to the formation of equivalent equations to express the perimeter of a rectangle. Paolo wrote the equation P=2(t+W). However, it seems there may have been a typographical error as the correct variables should have been 't' for width and 'u' for length. Given this, the equivalent equation to Paolo's should be P = 2t + 2u, also stated as P = 2(t + u) which confirms the relationship between perimeter, length, and width for a rectangle.

From the provided context, it's also understood that the function representing the area of the rectangle, when written in terms of width (t), is a(t) = t(L/2 - t), which is valid within the domain 0 <= t <= L/2. This function helps in determining the maximum area of the rectangle for a given perimeter (L).

Answer:

[tex]v = 15 \\ c = v \div 5[/tex]

Step-by-step explanation:

It could be this

Answer:

Therefore  40 milliliter of 50% fungicide solution is required

Therfore  60 milliliter of 10% fungicide solution is required

Step-by-step explanation:

i) Let the 10% fungicide solution have x milliliter and the 50% fungicide solution have y milliliter.

ii) Therefore 10x + 50y = 26(x + y)

                      x + y = 100

iii) form the first equation in ii) we get

                   16 x  = 24 y   Therefore [tex]x = \frac{24}{16} y = \frac{3}{2} y[/tex]

iv) substituting the value obtained in iii) in the second equation in ii) we get

      [tex]\frac{3}{2} y + y = \frac{5}{2} y = 100[/tex]

  Therefore y = 100 ÷ 2.5 =  40 milliliter

   Therfore x = 100 - 40 = 60 milliliter

Answer:

Step-by-step explanation:

V=πr²h

=3.14*6*6*10

=1130.4 cm³

New cylinder:

h = 15cm

V= 1130.4  cm³

πr²h = 1130.4

3.14*r²*15=1130.4

r²=1130.4/15*3.14

r²=24

r=√24

r=4.898 = 4.9 cm

The radius be to meet the client's need is 4.9 cm.

Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies.

Volume is sometimes referred to as capacity.

We have,

Radius of cylinder (r)= 6 cm

Height of cylinder (h) = 10 cm

and, Height of new cylinder (H)  = 15 cm

Radius of new cylinder = R cm

Now, Volume of cylinder can be compared as

πr²h = πR²H

6 x 6 x 10 = R² x 15

360 / 15 = R²

R² = 24

R= 4.9 cm

Thys, the radius is 4.9 cm.

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Answer:

The answer is that 90 couples remain at the party after 11 pm

Step-by-step explanation:

Number of people who went to the couples only party at 9 pm = 250

Number of people who left the party at 11 pm = 70

How many couples remained at the party?

People that remained at the party = 250 - 70 = 180

Couples that remained at the party = 180/2 = 90

The answer is that 90 couples remained at the party after 11 pm