Which graph represents the system of inequalities? {y+3/4x<2 {y−1≥2x

The $2 and $3 profits from the sale of sandwiches and wraps respectively, and the equation that is used to calculate the profit gives;

1. The equation is; [tex] \displaystyle{y = 490 - \frac{2}{3} \cdot x}[/tex]

The slope, m = [tex] \displaystyle{ - \frac{2}{3}}[/tex]

The y–intercept, c = 490

2. The graph can be drawn by joining the y–intercept to a point found by moving along the slope from the y–intercept

3. [tex] \displaystyle{f(x) = 490 - \frac{2}{3} \cdot x}[/tex]

4. Please find attached the graph of the number of wraps to the number of sandwiches

5. Please find attached the combined graph of the two functions

The similarity is the common slope

The difference is the y–intercept

The slope is the ratio of the rise to the run of the graph.

The given function is; 2•x + 3•y = 1470

Where;

x = The number of sandwich sold

y = The number of wraps sold

The profit per sandwich sale = $2

Profit per each wrap sale = $3

1. The slope and intercept form is; y = m•x + c

Where;

m = The slope

c = The y–intercept

Therefore, 2•x + 3•y = 1470 gives;

3•y = 1470 - 2•x

y = (1470 - 2•x)÷3 = 490 - (2/3)•x

[tex] \displaystyle{y = \frac{1470-2\cdot x}{3} = 490 - \frac{2}{3} \cdot x}[/tex]

Therefore;

By comparison, we have;

2. Using the slope and intercept method to graph the line involves the following steps.

3. The equation in function notation is; [tex] \displaystyle{f(x) = 490 - \frac{2}{3} \cdot x}[/tex]

The meaning of the function is that the number of wraps sold is given by the difference between 490 and two thirds of the number of sandwiches sold, or that as the number of sandwiches sold increases by by 1, the number of wraps sold decreases by 2/3

4. The graph can be created using a spreadsheet application

Please find attached the graphs of the function

5. With a profit next month of $1,593, we have;

2•x + 3•y = 1593

Which gives;

[tex] \displaystyle{y = 531 - \frac{2}{3} \cdot x}[/tex]

Given that the equation of the graph of the previous month is y = 490 - (2/3)•x, we have;

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The answer would be C. y = 3/4 x - 9

this line has the same slope => ¾

The sequence of the decorative fence boards would be 66.48 feet which is the infinite geometric sequence.

The geometric series defined as a series represents the sum of the terms in a finite or infinite geometric sequence. The successive terms in this series share a common ratio.

The nth term of a geometric progression is expressed as

Tₙ = arⁿ⁻¹

Where a is the first term, r is the common ratio

The first fence board will be 2 feet tall, and each successive fence board will be 25% taller than the previous fence board which is given in the question.

aₙ = arˣ⁻¹   (n ≠ 0)

a₁ = 2

x = (1 +25%) = 125%

n = 10

aₙ = 2 × (125%)

The sum of the terms in a finite or infinite geometric sequence as

Sₙ = a₁ + a₂ + ... +aₙ

= a₁(1 -xⁿ)/(1-x)

= 2(1 -1.25¹⁰)/(1-1.25)

= 2(-8.31)/(-0.25)

=  66.48 feet

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Answer:

f(n)=8n-63

15th term=57

Step-by-step explanation:

goes up by 8 each time therefore the coefficient of n is 8

take for example the 1st term,8n would be 8, to get to -55 from 8 you would have to subtract 63, therefore the nth term is 8n-63.

Answer:

3. parallel

4. they have the same slope

They will together take 18 minutes to finish the sanitization work together.

It is mentioned that Liana can sanitize the guest room in 45 minutes only and Gab, her brother, can do the same in 30 minutes.

Let they take y minutes to finish the work together.

Let the total work be m

Workdone by Liana in 45 mintues = m

∴Workdone in 1 minute = m / 45

Workdone by Gab in 30 minutes = m

∴Workdone by Gab in 1 minute = m / 30

Let the total time taken by them = x minutes.

Total time taken by them together = m / 45 + m / 30

∴ [tex]\frac{m}{45} +\frac{m}{30} = \frac{m}{x}[/tex]

⇒ [tex]\frac{1}{45} +\frac{1}{30} = \frac{1}{x}[/tex]

LCM of 45 and 30 is 90

⇒ [tex]\frac{2}{90} +\frac{3}{90} = \frac{1}{x}[/tex]

⇒ [tex]\frac{5}{90}= \frac{1}{x}[/tex]

⇒ [tex]\frac{1}{18}= \frac{1}{x}[/tex]

⇒ x = 18 minutes

Hence they both can do the same given work in 18 mintues.

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Answer:

1) −1/3,1

Step-by-step explanation:

Answer:

22 is 20% of 110

Step-by-step explanation:

a machine can pack a 3 ft by 3 ft by 1 ft carton with packing material in 3 seconds Then it would take 32 seconds to fill a carton that measures 4 ft by 4 ft by 6 ft

1) we calculate the volume of the first carton:

volume=length x width x height

volume=3 ft * 3 ft * 1 ft=9 ft³

Therefore:

A machine can fill 9 ft³ in 3 seconds.

2) we calculate the volume of the second carton.

volume=length x width x heigth

volume=4 ft * 4 ft * 6 ft=96 ft³

3) we calculate the time that the machine needs for fill the second carton with packing material by the rule of three.

9 ft³---------------------3 seconds

96 ft³--------------------      x

x=(96 ft³ * 3 seconds) / 9 ft³=32 seconds.

Hence , a machine can pack a 3 ft by 3 ft by 1 ft carton with packing material in 3 seconds Then it would take 32 seconds to fill a carton that measures 4 ft by 4 ft by 6 ft

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The total bill of 3.18 pounds of grapes, 1.35 pounds of peaches, and 2.48 pounds of apples is $ 8.4.

Given that,

I bought 3.18 pounds of grapes, 1.35 pounds of peaches, and 2.48 pounds of apples.

Grocery Store Prices:

Grapes $1.29 per pound

Peaches $1.19 per pound

Apples $1.09 per pound

Therefore the total bill is = $ [(3.18 pounds x 1.29 per pound) + (1.35 pounds x 1.19 per pound ) + ( 2.48 pounds x 1.09 per pound)]

= $ ( 4.10 + 1.60 + 2.70)

=$ 8.4

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Answer:

1st[tex]7532 + 100y ^{2} + 100y^{2} - 1100[/tex]

2nd

[tex]200y ^{2} + 6432[/tex]

final answer

[tex]a = 200[/tex]

[tex]b = 6432[/tex]

Answer:

110 degrees?

Step-by-step explanation:

35+35= 70 right?

So then would have to subtract the 70 from 180  because that is total length of an angle to get 110 degrees

110 degrees

I might be wrong, because it might be different with triangles

Answer:

U = 110

Step-by-step explanation:

The formula for finding missing angle is.

a + b + c = 180   or in this case   S + U + T = 180.

You already have the measurement of two angles so plug those in.

35 + U + 35 = 180

Now all you have to do is simplify and solve it.

35 + 35 + U = 180  

70 + U = 180   you simplify by adding together 35.

U = 110     to cancel out 70 and isolate U you subtract 70 to both sides.

On solving the inequality we get -6>5 which is not possible; hence there is NO SOLUTION possible for s.

We solve the given inequality for s as follows

2(4s-3) ≥ 5+8s

⇒8s - 6≥ 5 +8s

⇒ -6 > 5               (on subtracting 8s from both sides)

the last statement shows that variables cancel out from both sides of the inequality and we get -6>5 which is not possible. Because -6>5 is not possible or false, hence no value of s will be able to satisfy the given inequality. Thus the answer for s is NO SOLUTION.

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Answer: 20 x 1 x 0.1 + 8 + 1

              2 + 8 = 10

The edge lengths of a cube that has a 1.728 cm³ volume is 1.2 cm

The volume of a cube is the given by the length of one edge raised to the power of 3

The volume of a cube, V = Length, L × Width, W × Height, H

Given that the lengths of the edges of a cube are equal, we have!

Length, L = Width, W = Height, H

Which gives;

The volume of a cube, V = L × L × L = L³

Therefore, for the given cube, we have;

L³ = 1.728 cm³

1.728 = 1728/1000

(a + b)³ = a³ + 3•a²•b + 3•a•b² + b³

Taking a = 10, and b = 3, we have;

(10 + 2)³ = 10³ + 3×10²×2 + 3×10×2² + 2³ = 1728

Therefore;

1728/1000 = (10 + 2)³/10³ = 12³/10³

Which gives;

L³ = 12³/10³

[tex] \displaystyle {L = \sqrt[3]{ \frac{{12}^{3} }{ {10}^{3} } } = 1.2}[/tex]

The edge lengths of the cube, L = 1.2 cm

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Answer:

10/9

Step-by-step explanation:

We can calculate f(3) and g(-4)

f(3) = 4*3 - 2 = 12 - 2 =10

and g(-4) = -2 * (-4) + 1 = 8 + 1 = 9

Then it is easy to calculate f(3)/g(-4):

f(3)/g(-4) = 10/9

where we use the values which we calculated before.

⇒In the equation f(x) given f(3) plug in the value 3 in the place of x and simplify

[tex]f(3)=4(3)-2\\f(3)=12-2\\F(3)=10[/tex]

⇒For g(-4) in the place of x plug in -4 in the equation of g

[tex]g(-4)=-2(-4)+1\\g(-4)=8+1\\g(-4)=9[/tex]

Now we can find the value of  of the problem as done BELOW:

[tex]\frac{f(3)}{g(-4)} \\\frac{f(3)}{g(-4)} =\frac{10}{9}[/tex]

1. The value of the expression 5/8 - (-2/8) will be 7/8.

2. The value of the expression  -3 1/5 + (-6 1/2) will be -97/10.

3. The value of the expression 5/8 - (-2/8) will be 7/8.

What is Addition?

The process of combining the two or more number is called Addition.

Given that;

The expression are;

1. 5/8 - (-2/8)

2. -3 1/5 + (-6 1/2)

3. 5/8 - (-2/8)

Now, Solve the expression as;

1. 5/8 - (-2/8) = 5/8 + 2/8

                   = 7/8

Thus, The value of the expression 5/8 - (-2/8) will be 7/8.

2. -3 1/5 + (-6 1/2) = - 16/5 - 13/2

                          = -32/10 - 65/10

                          = - 97/10

Thus, The value of the expression  -3 1/5 + (-6 1/2) will be -97/10.

3. 5/8 - (-2/8) = 5/8 + 2/8

                   = 7/8

Thus, The value of the expression 5/8 - (-2/8) will be 7/8.

So, The solution are;

1. The value of the expression 5/8 - (-2/8) will be 7/8.

2. The value of the expression  -3 1/5 + (-6 1/2) will be -97/10.

3. The value of the expression 5/8 - (-2/8) will be 7/8.

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Length of the golf club where Bruce plays = 7,040 yards

Solution:

1. Let's convert 7,040 yards to miles:

1 yard = 0.000568182 mile

Now, we can use Direct Rule of Three, as follows:

Yards Miles

1 0.000568182

7,040 x

2. Solve for x:

1 * x = 0.000568182 * 7,040

x = 4 miles

Polynomial equation 3 -x + 2x -4 + 2x is equivalent to 6 +(-x) + 2x + (-7) + 2x

The example of a first-degree polynomial is f(x) = MX + b of a linear function.

Consider a equation 1, to 6 +(-x) + 2x + (-7) + 2x, and simplify it.

6 +(-x) + 2x + (-7) + 2x

= 6 -x + 2x -7 + 2x

Take likely terms and add or subtract according to the equation.

6-7-x+2x+2x

-1+3x

Consider 3 – x + 2x – 4 + 2x as equation 2.

3 – x + 2x – 4 + 2x

Take likely terms and add or subtract according to the equation.

= -1+ 3x

Here equation 1 is equal to equation 2.

∴6 +(-x) + 2x + (-7) + 2x = 3 – x + 2x – 4 + 2x

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Answer:

58.2 degrees

Explanation:

The given problem is illustrated using the diagram below:

The angle the ramp makes with the sidewalk is labeled x above.

Using trigonometry:

The angle the ramp makes with the sidewalk is 58.2 degrees.

Answer:

5.625

Step-by-step explanation:

450÷80 I hope I'm right and it helps if not I'm sorry.

Barbara has 10 shirts with long sleeves

100% of Barbara's shirts is 25

Given: 60% of Barbara's shirts are short sleeves.

That means, 1.0 - 0.6 = 0.4 --> 40% of Barbara's shirts are long sleeves.

We need to find: 40% of 25

0.4 * 25 = 10

10 long sleeved shirts

Answer: See attached.

Step-by-step explanation:

     To graph this, we will look at the pieces they gave us. Slope-intercept form equations are written in y = mx + b.

   ➜ The slope, m, is the pitch of the line. It's "rise over run" and helps us know where the plot points. For this problem, we will rise one value and move 6 values right to the next point.

     ➜ The y-intercept, b, is where the line intercepts the y-axis. It helps us know where the first point goes (0, y). For this problem, we will graph (0, 4).

     Using these details, we will graph the line. View attached.

The estimated probability that the sum of five dice will be 26 is 0.0053

Estimated Probability: Estimated probability is an approximation, or estimate, of theoretical probability. The larger the number of trials, the more accurate we expect this approximation to be. If E consists of a single outcome s, we refer to P(E) as the probability of the outcome s, and write P(s) for P(E)

N = Number of Repeated Process = 10,000

n = Number of times the sum of the five tosses equaled 26 = 53

The estimated probability that the sum of the five dice will be 26 = n/N

Where n = 53

And N = 10,000

Using the above formula, we have the following:-

n/N becomes

n/N = 53/10,000

n/N = 0.0053

Hence, the estimated probability that the sum of five dice will be 26 is 0.0053

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Answer:

76:9

Step-by-step explanation:

because because because

The two linear functions has different slopes, the blue line has a slope of 2 and the magenta line has a slope of 1, and the same intercept, both have an intercept of 0.

In this problem we find the picture of two linear equations set on Cartesian plane. Linear functions are polynomials of the form:

y = m · x + b

Where:

To find all similarities and differences between the two lines we must compare each expression with the equation of the line. Based on this strategy we find the following conclusions:

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The number of liters that are in 13.39 gallons is 51.5 liters

In order to determine the liters that are in 13.39 gallons, divide the amount of gallons by the unit of conversion.

Division is the mathematical process of grouping a number into equal parts using another number. The sign used to represent division is ÷. Division is one of the basic mathematical operations. Other  mathematical operations are addition, subtraction and division.

Number of liters in 13.39 gallons = 13.39 / 0.26 = 51.5 liters

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Answer:

100

Step-by-step explanation:

He is walking and he go 12 kilometer total 312 so 312 divided by 12