Solve for y in terms of x:
[tex]4 {x}^{2} + 8 {x}^{2}y = 8 {x}^{3} [/tex]
A.
[tex] \frac{2}{2x - 1} [/tex]
B.
[tex] \frac{2}{2x + 1} [/tex]
C.
[tex] \frac{2x - 1}{2} [/tex]
D.
[tex] \frac{2}{2x - 1} [/tex]




​

Answer:

The graph of y = f(x) will shift left 6 units, as shown in figure a.

Step-by-step explanation:

A translation means we are able to move the graph of a function up or down - normally called Vertical Translation -  and right or left - commonly called Horizontal Translation.

If we replace the graph of y = f(x) with the graph of y = f(x + 6). It means we have added 6 units to the input, meaning the graph y = f(x) will shift left by 6 units as 6 is being added directly to the  x, so it is f(x + 6).

For example, if y = x² is the original function and of 6 is directly added to x i.e. f(x + 6), making it y = (x + 6)². So, we can easily observe that there will be a horizontal translation left of 8 units, as shown in figure a.

So, the graph of y = f(x) will shift left 6 units.

Keywords: graph shift, translation

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The graph of y = f(x) will shift left 6 units. The correct option is the third one.

For any function y = f(x), we define an horizontal translation of N units as:

y = f(x + N)

Where if:

N > 0, the translation is to the left.

N < 0, the translation is to the right.

Here we have:

y = f(x + 6)

So this is a translation of 6 units to the left.

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Answer:

Yes, y varies directly with x.

[tex]y=\frac{11}{8} x[/tex]

Step-by-step explanation:

[tex]\frac{y}{x}=\frac{11}{8} =\frac{22}{16} =\frac{33}{24}[/tex]

Hence [tex]y[/tex] varies directly with [tex]x[/tex].

[tex]\frac{y}{x}=\frac{11}{8} \\\\ y=\frac{11}{8} x[/tex]

Answer:

Step-by-step explanation:

x = number of cars

12x = 3.50x + 34

12x - 3.50x = 34

8.5x = 34

x = 34/8.5

x = 4 <=====he would have to sell 4 cars

In this case, Luke must sell [tex]\(\boxed{4}\)[/tex] cars for his revenue to equal his expenses.

To determine how many cars Luke must sell for his revenue to equal his expenses, let's define the variables and set up the equation.

Let x be the number of cars Luke sells.

Revenue:

Luke sells each car for $12, so his revenue for selling x cars is:

[tex]\[ \text{Revenue} = 12x \][/tex]

Expenses:

Luke's expenses include $3.50 per car and a fixed cost of $34 for tools. So his total expenses for x cars are:

[tex]\[ \text{Expenses} = 3.50x + 34 \][/tex]

We need to find the number of cars x such that his revenue equals his expenses:

12x = 3.50x + 34

To solve for x  subtract 3.50x  from both sides:

12x - 3.50x = 34

8.50x = 34

Now, divide both sides by 8.50:

[tex]\[ \text{Expenses} = 3.50x + 34 \][/tex]

x = 4

Therefore, Luke must sell [tex]\(\boxed{4}\)[/tex] cars for his revenue to equal his expenses.

Answer:

256

Step-by-step explanation:

Answer:

Step-by-step explanation:he rate of return on Karen investment is 10%. Explanation: Given that. Bought price = P = $78500. Sale price = S =$850,000.

The initial fee of a train ticket, given a constant fee per stop, can be calculated by finding the constant fee per stop and subtracting the total of this fee for a given number of stops from the total price for those stops. By this calculation, the initial fee is $2.50.

To determine the initial fee that is related to the price of a train ticket, which consists of an initial fee plus a constant fee per stop, we should first calculate the cost per stop. We can do this by subtracting the price of a ticket for 3 stops from the price of a ticket for 7 stops. So, we get $12.50 - $6.50 = $6.00. We find the difference in the number of stops, which is 7 - 3 = 4 stops. Divide the total price difference by the difference in the number of stops to get the constant fee per each stop: $6.00 / 4 stops = $1.50 per stop. Now we know the constant fee for each stop, so we subtract that from the total price for 3 stops to find the initial fee: $6.50 - ($1.50 * 3) = $2.50. So, the initial fee is $2.50.

To find the initial fee, we need to determine the additional cost per stop. We can do this by using the formula y = mx + b, where y represents the price of the ticket, x represents the number of stops, m represents the constant fee per stop, and b represents the initial fee.

Using the given data, we can set up two equations using the points (3, 6.50) and (7, 12.50).

By subtracting these two equations, we can determine the value of b, which represents the initial fee. Thus, the initial fee is $3.

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Answer:

D.3

Step-by-step explanation: The full line is equivelent to 3 if you look

Answer:

3/5

Step-by-step explanation:

Answer:

slope = [tex]\frac{3}{5}[/tex]

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

y + 4 = [tex]\frac{3}{5}[/tex](x - 7) ← is in point- slope form

with slope m = [tex]\frac{3}{5}[/tex]

Answer:

The given expression at p = 5 can be written as:

[tex]4(p^4)  > 2p -3[/tex]

Step-by-step explanation:

Here, the given expressions are:

[tex](4p^4 ), (2p-3)[/tex]

Now, substitute the value of p = 5 in both the given expressions, we get:

[tex]4(p^4)  = 4(5^4)  = 4 (625)   =  2,500\\\implies 4(p^4) = 2,500[/tex]

Similarly,

[tex](2p-3)  = 2(5) - 3 = 10 -3 = 7\\\implies 2p - 3  = 7[/tex]

So,now comparing  both the values at p = 5, we get:

2,500 > 7

[tex]\implies 4(p^4)  > 2p -3[/tex]

Hence, the given expression at p = 5 can be written as:

[tex]4(p^4)  > 2p -3[/tex]

Answer:

g>=-12

Step-by-step explanation:

g+11>=-1

g>=-1-11

g>=-12

Answer:

The answer can be calculated by doing the following steps;

Step-by-step explanation:

Answer:

The approximate length of the radius is 3 feet

Step-by-step explanation:

Given:

circumference of a circle = 18.41 feet

To Find:

approximate length of the radius = ?

Solution:

Let the radius of the circle be r

We know that the circumference of the circle C is given by the formula

C =[tex]2 \pi R[/tex]

Substituting the values, we get

18.41 =[tex]2\times \pi \times R[/tex]

Rearraning the above equation we get

R=[tex]\frac{14.41}{ 2\times \pi}[/tex]

R=[tex]\frac{18.41}{6.28}[/tex]

R= 2.93

R= 3 (approx)

One roll of plain costs $20 and one roll of shiny costs $20 also.

Step-by-step explanation:

Let,

Cost of one roll of plain = x

Cost of one roll of shiny = y

According to given statement;

2x+2y=80     Eqn 1

8x+10y=360    Eqn 2

Multiplying Eqn 1 by 4

[tex]4(2x+2y=80)\\8x+8y=320\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 2

[tex](8x+10y)-(8x+8y)=360-320\\8x+10y-8x-8y=40\\2y=40[/tex]

Dividing both sides by 2

[tex]\frac{2y}{2}=\frac{40}{2}\\y=20[/tex]

Putting y=20 in Eqn 1

[tex]2x+2(20)=80\\2x+40=80\\2x=80-40\\2x=40[/tex]

Dividing both sides by 2

[tex]\frac{2x}{2}=\frac{40}{2}\\x=20[/tex]

One roll of plain costs $20 and one roll of shiny costs $20 also.

Keywords: linear equation, elimination method

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Answer:

Step-by-step explanation:

[tex]-2-2(-7+b)=-8b+24\qquad\text{use the distributive property}\\\\-2+(-2)(-7)+(-2)(b)=-8b+24\\\\-2+14-2b=-8b+24\qquad\text{combine like terms}\\\\(-2+14)-2b=-8b+24\\\\12-2b=-8b+24\qquad\text{subtract 12 from both sides}\\\\12-12-2b=-8b+24-12\\\\-2b=-8b+12\qquad\text{add}\ 8b\ \text{to both sides}\\\\-2b+8b=-8b+8b+12\\\\6b=12\qquad\text{divide both sides by 6}\\\\\dfrac{6b}{6}=\dfrac{12}{6}\\\\b=2[/tex]

Question:

At noon a tank contains 6 cm of water after several hours it contains 3 cm of water what is the percent decrease of water in the tank

Answer:

The percent Decrease of water in the tank  is 50%

Step-by-step explanation:

Given:

Initial amount of water in the tank at the noon = 6 cm

amount of water remained in water after several hours = 3 cm

To Find:

The percent decrease =?

Solution:

The percent decrease in the tank

=>[tex]\frac{\text {water present after some hours }}{\text {initial water contained in the tank }} \times 100[/tex]

Substituting the values

=>[tex]\frac{3}{6} \times 100[/tex]

=>[tex]\frac{1}{2} \times 100[/tex]

=>[tex]\frac{100}{2}[/tex]

=> 50

Answer:

2020

Step-by-step explanation:

This is an example of what is called an "infinite continued fraction".

For the repeated fraction:

y = 2019 / (2 + 2019 / (2 + 2019 / (2 + 2019 / ...

We can rewrite using substitution:

y = 2019 / (2 + y)

Solving for y:

y (2 + y) = 2019

2y + y² = 2019

y² + 2y + 1 = 2020

(y + 1)² = 2020

y + 1 = ±√2020

y = -1 ± √2020

Since the repeated fraction must be positive, y = -1 + √2020.

Therefore:

x = (1 + y)²

x = (1 + -1 + √2020)²

x = 2020

Answer:

The left side continues up, and the right side continues down.

Step-by-step explanation:

[tex]f(x) = -9x^3 + 8x^2 - 16x + 3[/tex]

To find the end behavior, determine the highest degree and leading coefficient

Highest degree is 3  and leading coefficient is -9

highest degree 3 is odd and leading coefficient is negative

As x->-infinity , y -> infinity

As x->infinity , y ->-infinity

The left side continues up, and the right side continues down.

Answer:

Correct answer is C.

Step-by-step explanation:

Answer:

y = 0.7865x + 0.2413  

Step-by-step explanation:

[tex]\begin{array}{rrc}\mathbf{x} & \mathbf{y} & \mathbf{\log(y)}\\1 & 13 & 1.114\\2 & 55 & 1.740\\3 & 349 & 2.543\\4 &2407 & 3.381\\5 &16813 & 4.226\\\end{array}[/tex]

I plotted both your original and transformed data in Excel and asked it to display the regression equation for the transformed data.

Your original data are the blue line plotted against the left-hand axis.

Your transformed data are the red line, plotted against the right-hand axis.

The linear regression equation is

y = 0.7865x + 0.2413

The answer is y = 0.7865x + 0.2413  

The Linear regression equation for the transformed data:

We transform the predictor (x) values only. We transform the response (y) values only. We transform both the predictor (x) values and response (y) values.

Find the linear regression equation for the transformed data?

(1, 13) 1.114

(2, 55) 1.740

(3, 349) 2.543

(4, 2407) 3.381

(5, 16, 813) 4.226

X            Y           Log(y)

1              13           1.114

2             55         1.740

3             349       2.543

4             2407     3.381

5             16813    4.226

The linear regression equation is y = 0.7865x + 0.2413  

The graph is plotted below:

Original data are the blue line plotted against the left-hand axis and transformed data are the red line, plotted against the right-hand axis.

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Answer:

45% of 31 days is 13.95 days, theres your answer.

Answer:

k=3

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]

In this problem we have

[tex]y=3x[/tex]

therefore

The constant of proportionality  is k=3

Answer:

k=3

Step-by-step explanation:

i went on knan and it worked

[tex]\text{The constant of variation is a fancy word for rate of change}\\\\\text{You're trying to find the rate of change in this scenario, which would}\\\text{be your constant of varaition}\\\\\text{To find this, we need to know how much he makes each hour}\\\\\text{Find this by dividing 175 by 15:}\\\\175\div15= 11.666\\\\\text{Round to the nearest hundredths}\\\\11.67\\\\\boxed{\text{Constant of variation: 11.67}}[/tex]

Based on the information given the constant of variation is 11.67.

Using this formula

Constant of variation=Amount earned/Time

Where:

Amount earned=$175

Time=15 hours

Let plug in the formula

Constant of variation=$175/15

Constant of variation=11.66

Constant of variation=11.67 (Approximately)

Inconclusion  the constant of variation is 11.67.

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Answer:

the answer is D.) 4/3

Step-by-step explanation:

when you look for a slope that is perpendicular to the slope you are given you take the reciprocal and change the sign

Answer:

4/3

Step-by-step explanation:

Because perpendicular means negative reciprocal.

Answer:

Step-by-step explanation:

4/5-(-3/10)=4/5+3/10=8/10+3/10=11/10

5.5-8.1=-2.6

-5-5/3=-15/3-5/3=-20/3

-8 3/8-10 1/6=-67/8-61/6=-445/24

-4.62-3.51=-8.13

The equation which represents the amount of minutes.m that it will take to fill the pool is 200 = 60 + 10m

Which equation represents the amount of minutes ( m) that it will take to fill the pool?

Let

m = amount of minutes that it will take to fill the pool

Gallons of water in the pool = 60 gallons

Capacity of the pool = 200 gallons

Additional gallons added per minutes = 50 gallons / 5

= 10 gallons per minutes

The equation:

200 = 60 + 10m

200 - 60 = 10m

140 = 10m

Divide both sides by 10

m = 140/10

m = 14 minutes

Therefore, it takes Anita 14 minutes to fill the pool.

Please see the attachment below.

All the information is in the problem you just have to format it into an equation.

Point slope form: [tex]y_{2}- y_{1}=m(x_{2}- x_{1})[/tex] where "m" is the slope.

The equation would look like...

y+9=-2(x-10)

The money can you accumulate over the course of a year if you opt to save the money instead will be $82.68.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

It is also known as the product. If the object n is given to m times then we just simply multiply them.

Assume you drink eight sodas per week & they cost $1.59 each.

We know that there are 52 weeks in a year.

The money can you accumulate over the course of a year if you opt to save the money instead will be

⇒ $1.59 × 52

⇒ $82.68

The money can you accumulate over the course of a year if you opt to save the money instead will be $82.68.

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Answer:

0.1513...

Step-by-step explanation:

Answer:

I think its 19,000/1

Step-by-step explanation:

I don't think there is any explanation :)

To compare the two plans and find the amount of driving for which they cost the same, we can set up an equation and solve for x. The two plans cost the same for 450 miles of driving.

To compare the two plans and find the amount of driving for which they cost the same, we need to set up an equation. Let's assume the amount of driving is represented by the variable x. The total cost for Plan 1 can be calculated as:

Total cost = $46 + $0.13x

The total cost for Plan 2 can be calculated as:

Total cost = $55 + $0.11x

We can set the two equations equal to each other and solve for x:

$46 + $0.13x = $55 + $0.11x

$0.02x = $9

x = $9 / $0.02 = 450

Therefore, the two plans cost the same for 450 miles of driving.

Answer:

60 I think

Step-by-step explanation:

1100-400=700 12×60=720

59 hours

She has to save $700

If r and p are perpendicular:

1 + 2 = 90°

3 = 90°

4 + 5 = 90°

6 = 90°

If any one of these are true, r and p must be perpendicular

Answer:

Yes

Step-by-step explanation:

First you will have to find out the scale

Then you will find out the numbers that are

Perpendicular

Answer:

411

1000 is divisible by 4, 600 is divisible by four, and 44 is divisible by for: add up you get 250+150+11

Step-by-step explanation:

411

Using place value, the quotient of 1,644 and 4 is: 411.

Given the dividend, 1,644, to divide it by the divisor, 4, break down 1,644 using place value, and divide by 4 separately.

1,644/4 = (1,000 ÷ 4) + (600 ÷ 4) + (44 ÷ 4)

1,644/4 = (250) + (150) + (11)

1,644/4 = 411

Therefore, using place value, the quotient of 1,644 and 4 is: 411.

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