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A string of lights is 69 1/3 feet long. The lightbulbs are spaced 8 inches apart. The diagram shows the beginning of the string and the end of the string. What is the total number of lightbulbs on the string of lights?

The polynomial function which represents the number of vehicles ( x ) that go through the drive-thru each hour f ( x ) is given by the function f ( x ) , where f ( x ) = 0.4048x² + 16.9762x + 2.1429

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Daniel keeps track of the number of vehicles that go through the drive-thru each hour

Let the number of hours be x

Let the total number of vehicles that passes be y

Now , the values of x = { 1 , 2 , 3 , 4 , 5 , 6 , 7 }

The values of y = f ( x ) = { 18 , 38 , 60 , 78 , 93 , 117 , 143 }

Let the polynomial equation be represented as f ( x )

Now , the value of f ( x ) is calculated from the curve fitting model of hyperbola , where

f ( x ) = 0.4048x² + 16.9762x + 2.1429

when x = 3

f ( 1 ) = 0.4048 ( 3 )² + 16.9762 ( 3 ) + 2.1429

On simplifying , we get

f ( 1 ) = 3.6432 + 50.9286  + 2.1429

f ( 1 ) ≈ 60

Hence , the polynomial equation is f ( x ) = 0.4048x² + 16.9762x + 2.1429

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Answer:

I think answer is 87<180 or maybe 87<12*15

9514 1404 393

Answer:

  f(x) = 6x +1

Step-by-step explanation:

Differences in x-values (first row) are 1, 1, 1.

Differences in y-values (second row) are 6, 6, 6.

The constant ratio of differences (6/1) tells you the function is linear, and has a slope of m = 6/1 = 6.

Using the first point in the form ...

  y = mx + b

we have ...

  y = 6x + b

  7 = 6·1 + b . . . . (x, y) = (1, 7)

  1 = b . . . . . . subtract 6

Then the equation can be written ...

  y = 6x +1

In functional form, this is ...

  f(x) = 6x +1

Answer:

The result when x^3-8x^2+19x-14 is divided by x^2-2x−2 is

[tex]x-6 +\frac{9x -26}{x^{2} -2x-2}[/tex] .

Step-by-step explanation:

Seems the divisor in the question is x^2-2x−2. If so, the solution to the division is shown using the long division method in the attachment below.

The result is

[tex]\frac{x^{3}-8x^{2} +19x -14}{x^{2} -2x-2} = x-6 +\frac{9x -26}{x^{2} -2x-2}[/tex]

Answer:

$68,213

Step-by-step explanation:

The median is the middle value number.

So you need median for Virginia.

First lets see how index and income are connected.

To do this divide the income by the index to see if you have a constant value you can use.

535.434783 = Arkansas

535.381944 = Alabama

535.58 = Arizona

535.669236 = Alaska

535 is constant in all of these.

Let's multiply the index by 535.

127.2*535 =68212.5

For median income, you need a whole number so lets round up.

68213

So Virginia would have a median income rate of $68,213

If you have anymore questions, don't be afraid to reach out and I hope that helps!

Answer:

∠one  and ∠seven

Step-by-step explanation:

Answer:

We know that:

Price of a taco = $4

Price of a burrito = $6.50

x = number of tacos sold

y = number of burritos sold.

We must have that:

x + y ≤ 150  (Because she only has supplies to make 150 tacos or burritos, but she can sell less than that)

And also we know that she must sell at least $780, then:

x*$4 + y*$6.50 ≥ $780

Now we found the system of inequalities:

x + y ≤ 150

x*$4 + y*$6.50 ≥ $780

To solve it graphically, we just need to find each one of the region solutions for each equation, and the intersection of these regions will be the solution for the system.

To graph them may be easier to write them as lines, you can do it as follows:

y ≤ 150 - x

y ≥ ($780 - x*$4)/$6.50

in the first equation, we will shade the area below the line, and in the second equation, we will shade the area above the line.

You can see the image below.

Where the accepted solutions are the ones in the darker part, and we only restrict this to positive values of x (because of how we defined the variable x)

Then looking at the image, we can see that one solution can be the point

x = 20, y = 120

Answer:

-2/11

Step-by-step explanation:

y2-y1/x2-x1

8-10 / -5 -(-16)

-2/-5 + 16

-2/11

Answer:

See explanation

Step-by-step explanation:

for -2x+4=4 the slope is y=2x-4

for -3x+2y=6 the slope is y=3/2x+3

for -3x+2y=6 the y-intercept is y=3 or (0,3)

(you can plug into desmos to check :) )

Answer:

1. x = 7

2. x = -5

Step-by-step explanation:

1. Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation: 2*x+5*(6*x-9)-(179)=0

Pull out like factors  6x - 9  =   3 • (2x - 3)

 (2x +  15 • (2x - 3)) -  179  = 0

Pull out like factors: 32x - 224  =   32 • (x - 7)

Solve: x-7 = 0

Add  7  to both sides of the equation  = 7

2. Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation: -40-(6*x-5*(-4*x-18))=0

Pull out like factors: -4x - 18  =   -2 • (2x + 9)

 -40 -  (6x -  -10 • (2x + 9))  = 0

Pull out like factors:  -26x - 130  =   -26 • (x + 5)

-26 • (x + 5)  = 0

Solve: x+5 = 0

Subtract  5  from both sides of the equation: x = -5

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Thanks!

Answer:

w=8 inches

Step-by-step explanation:

w( 2w - 4) = 96

Answer:

A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

The scale is: 1 cm = 3.26 meter

Step-by-step explanation:

Given

Height of Pyramid in Painting = [tex]H_p = 45 cm[/tex]

Actual Height of Pyramid = [tex]H_a = 146.5m[/tex]

In order to find the scale, we can find the ratio between actual height and height in painting.

The ratio can be found by dividing the actual height by height in painting

[tex]Scale = \frac{H_a}{H_p}\\= \frac{146.5}{45}\\=3.25555 m/cm[/tex]

Rounding off to nearest hundredth

= 3.26

This means that the scale is:

1 cm = 3.26 meter

Answer:

x=48

Step-by-step explanation:

2x+6=96

subtract 6 from both sides

2x=96

divide both sides by 2

x=48

Answer:

x = 88

Step-by-step explanation:

Answer:

y=10

Step-by-step explanation:

Answer:

4%

Step-by-step explanation:

dude if you got a whole number and a decimal, the whole number is going to be greater (as long as it isn't negative)

Answer:

The first and second one are functions, the rest are not

Step-by-step explanation:

Answer:

They actually can all be functions

Answer:

C

Step-by-step explanation:

Answer:

(b)

Step-by-step explanation:

Answer:

The dimensions of rectangle are:

Width = 16 inches

Length = 106 inches

Step-by-step explanation:

Perimeter of rectangle = 244 inches

Let Width of rectangle = w

Length of rectangle = w+90

We need to find the dimensions (length and width) of the carpet

The formula used will be: [tex]Perimeter=2(length+width)[/tex]

Putting values and making equation:

[tex]244=2w+2(w+90)\\Solving:\\244=2w+2w+180\\244=4w+180\\Switching\:sides\\4w+180=244\\Subtracting\:180\:from\:both\:sides\\4w=244-180\\4w=64\\Dividing\:both\:sides\:by\:4\\\frac{4w}{4} =\frac{64}{4}\\w=16[/tex]

So, we get w = 16

The width w = 16 inches

Now, finding length = w+ 90 = 16+90 = 106 inches

Therefore the dimensions of rectangle are:

Width = 16 inches

Length = 106 inches

Answer:

m=-4/3

Step-by-step explanation:

y2-y1

x2-x1

x1=−5 ,

y1=0,

x2=−2,

y2=−4.

m=(−4)−(0)(−2)−(−5) =−4/3=−4/3.

Answer:

The first step you would have to do would be get 4x by itself

Step-by-step explanation:

So it would be 4x +5 = 21

-5 and -5

So it would be 4x = 16

Answer:

D. 48

Step-by-step explanation:

4pi r^2

4 × 3 × 2^2 = 48

Answer:

The answer is D.

Step-by-step explanation:

You only have to substitute π value and r value into the formula :

[tex]s.a = 4\pi {r}^{2} [/tex]

[tex]let \: \pi = 3,r = 2[/tex]

[tex]s.a = 4 \times 3 \times {2}^{2} [/tex]

[tex]s.a = 12 \times 4[/tex]

[tex]s.a = 48 \: {m}^{2} [/tex]

Answer:

Number line C

Step-by-step explanation:

First, you isolate x. This gives you x>=3+4 or x>= 7. Next, you find a number line greater than or equal to which cancels out A and D. Now whichever line starts on 7, is the answer which is C

Answer:

C

Step-by-step explanation:

If you solve the equation your answer will be x≥7

This is a less than or equal to 7 so the point on the graph will be closed (or filled in) which means your closed point goes on 7 and goes down the line to the left because of the direction of the sign. (less than)

Answer:

No, y=5 is NOT a linear function.

Step-by-step explanation:

In order for a linear function to be true, it need to include a slope-intercept. For example, a commonly used equation, y = mx+b y = m x + b, is an example of a linear function, since it meets both the variables of m and b and criteria of x and y. In this case, when drawing out y=5 on a graph, marking it down reveals no slope.

I hope this helped to answer your question.

We now know that y = 5 is not a linear function as it cannot be written as y = MX + b.

As, in the description it is cleary said that linear functions can be represented in y = MX + b form, and y = 5 cannot be represented in the same form.

Therefore, y = 5 is not a linear function as it cannot be written as y = MX + b.

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Answer: 50

Step-by-step explanation: 9 divided by 3 plus 4 times 6 plus 8 equals 50

Answer:

35

Step-by-step explanation:

9 ÷ 3 + 4 · 6 + 8

Do 9 ÷ 3 first

3

Plug this value back into the equation

3 + 4 · 6 + 8

Do 4 · 6 next

24

Plug this value back into the equation

3 + 24 + 8

Add 3 to 24

27

Plug this value back into the equation

27 + 8

Add

35

Hope this helps :)

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Answer:

if you want to simplify it, it would be -5 + 12

but if you want to finish the problem then the answer would be positive 7 or just 7

Step-by-step explanation: