Let f(x)= sqrt x. Find (g)x, the function that is f(x) shifted up 2 units and left 5 units

Ok, so

We have the next system of equations:

The first equation is a line, and the second one is a parable.

If we graph, we would get the following:

Then, we notice that there's two intersection points between both graphs.

These points are located at ( -1 , -3 ), and ( 2 , -6)

Therefore, there are two solutions for this problem.

x = -1 and y = -3,

x = 2, and y = -6

Now, how to graph each equation?

First one, take the line y = -x-4

Notice that this equation tells us that the line given has its intersection with y-axis at ( 0 , -4 )

We also know that a line is formed with two points, so we could replace by any "x" number and see which value "y" takes.

For example:

If x = 1,

y = -1-4, which is y = -5

So we got other point: ( 1, -5).

Now, we just join both points and we get the line, like this:

And that's how you can graph the line.

Now, how could we graph the parable?

We know that we have to take three points to join to graph a parable. So, first, we would find its intersections with x - axis, if we equal the equation to zero.

x² – 2x - 6 = 0

If we solve this equation, we obtain that x could take two different values.

To solve it, we use the next equation:

x = 1 - √7 or

x = 1 + √7.

Then, we actually have two points.

Now, finally, we could find its vertex.

If we find the vertex of the parable, we notice that it is located in (1,-7)

Now, we just join these three points as this:

And if we put these graphs together, we obtain the first graph I drew, and notice that the solution for the system is the intersection between both functions.

Answer:

slope = -1/2

Y-intercept = (0,2)

Step-by-step explanation:

If he initially had 30 liters of fuel, and his car's fuel efficiency is  cubic centimeters per kilometer. The calculation will give us the estimated volume of fuel that remains in Carson's tank by the end of the drive, in liters is: 30- 100/1000×120

Given data:

Distance = 120 kilometers

Liters of fuel = 30 liters

Using this formula to find the remaining volume

Remaining volume = I - E × D

Where:

I = Initial volume

E = Fuel efficiency

D = Distance

First step is to formula an equation that will be use to find the remaining volume

Equation =  30- 100/1000 ×120

Now let use the formulated equation to find the remaining volume

Remaining volume = 30- 100/1000 × 120

Remaining volume = 30- 12

Remaining volume = 18

Therefore  30- 100/1000×120 can be used to determine the remaining volume.

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The equation which represents the proportionality relationship is:

y=16x.

Given, we have the pairs as:

(1,16),(2,32) and (3,48)

calculate the value of y/x for the ordered pairs:

For (1,16), the value of y/x is = 16/1 = 16

For (2,32), the value of y/x is = 32/2 = 16

For (3,48), the value of y/x is = 48/3 = 16

now, compare ratios:

for each ordered pair, y/x = 16

Since, k=y/x, you know that the constant of proportionality , k is 16.

Substitute 16 for k in the equation for a proportional relationship.

y = kx

y = 16x

Hence we get the equation as y=16x.

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Find x in the following expressions:

9^x = 3 in this case, x has to be 1/2 (square root) in order to render 3 as an answer, given that 3^2 = 9

Then x = 1/2 in this first case

Second case:

3^x = 1 In this case, we use the property of exponent zero, which always renders 1

Last case x^3 = 9

Let's begin by listing out the information given to us:

The magnitude, r, of the vector, v , is given to be 4/5.

The direction angle is given to be 114 degrees.

A vector component is written in the form of:

We are going to use the given magnitude and direction angle to obtain the values of a and b.

Thus, we have:

Substitute for b into eqn i); thus we have:

Substitute for a= 0.325 into any of the equations, we have:

Hence, the vector, v, in terms of i and j is:

If a caterpillar eats 1400% percent of its birth mass in one day. The caterpillar's birth mass is 14m grams.

Given data:

Birth mass in one day = 1400%

Hence, we need to formulate an equation and then use the formulated equation to find or determine the caterpillar's birth mass in m grams

1400 / 100m

Now let find the birth mass in m grams using the equation

1400/100m

= 14m grams

Therefore we can conclude that 14m grams is the birth mass.

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Answer:  14m and 1400/100

Step-by-step explanation: just do it !!

Solution

We want to complete the square of

Firstly, let us look at how to complete a square.

Consider the illustration below

Thus, we have

Answer:

5 three hour classes and 27 four hour classes

Step-by-step explanation:

Convert these words into equations

Since one hour is 36, we can write two expressions for the 2 different classes: 108x and 144y (the amount of money from those classes)

x is the number of 3 hour classes, y is the number of 4 hour classes

Since the amount of money the studio makes is 4428, 108x+144y=4428

Since there are a total of 32 classes, x+y=32

So we now have the equations x+y=32 and 108x+144y=4428

Solve for x in the first equation (in order to substitute it into the second one)

we get x=32-y

plugging this into the second equation gives

108(32-y)+144y=4428

3456-108y+144y=4428

Combining like terms gives 36y=972

y=27

So there are 27 four hour classes, and 5 three hour classes( because 32-27=5)

Data

number of commuters = 7900

percent needed = 1%

Rule of three

7900 ------------------------ 100%

x

Answer:

The answer is it is true.hope the day is saved

Answer:

1.49 × 101.

100+40+9

1.49 × 103.

Step-by-step explanation:

is this Right?

Answer:

C. 5,007 and 0.5007

Explanation:

Given the two numbers:

From the given options:

All other options do not satisfy the condition.

The correct choice is C.

The distance Rhea travelled is the perimeter around the triangle.

The first step in finding the perimeter is finding the side lengths and for that, the following distance formula is used.

where (x_1, y_1) and (x_2, y_2) are the coordinates of the two points.

The distance between L(-1,6) and M(-4,2) is

Similarly, the distance between L(-1,6) and K(2,2) is

And the distance between M(-4, 2) and L(2,2) is

Therefore, the perimeter of the triangle is

Hence, Rhea travelled 16 km.

Answer:

225 miles on 3rd day

Step-by-step explanation:

400 + 125 + x /3 = 250

multiply each by 3 to get 400 +125 +x = 750

subtract 525 each to get x =  225

The sum of three consecutive numbers is 111.

Consecutive Numbers: Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers. For example: 1, 2, 3, 4, 5, 6, and so on are consecutive numbers.

Let the three consecutive numbers are : x , x + 1, x +2

Since the sum of three consecutive number is 111

x + (x +1 ) + (x +2) = 111

Simplify :

x + x + 1 + x + 2 = 111

x + x + x + 1 + 2 = 111

3x + 3 = 111

3x = 111 - 3

3x = 108

x = 108/3

x = 36

So, the first number is x : x = 36

Second number is : x + 1= 36 + 1 = 37

Third Number is : x + 2 = 36 + 2 = 38

Numbers are : 36, 37, 38

Smallest number in 36, 37 & 38 is 36

Smallest number = 36

Answer : 36

Answer:

Step-by-step explanation:

The scale factor here is 3 : 2.

The scale factor is defined as the difference between the new image's and the old image's sizes. A fixed point in the plane is the center of dilation. The definition of the dilation transformation depends on the scale factor and the center of dilation.

A stretched image results from a scale factor of higher than 1.

The image shrinks when the scale factor falls between 0 and 1.

The resulting image is consistent with the source image if the scale factor is 1.

As a result of the dilation modifications, the following characteristics of forms don't change:

The figure's angles are all identical.

The figure's midpoints on its sides and the midpoint of the dilated shape are both preserved.

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7.5 components yellow paint should be mixed with 5 parts violet paint.

Moss green is created by combining violet and yellow paint in a 2 to 3 ratio. You're interested in learning how many parts of yellow paint to combine with five parts of violet paint.

Proportion

There are various ways to express the proportion. The unknown value is often placed in the numerator. (x is the quantity of yellow paint in parts)

Yellow: violet equals 3: 2; x; and 5

The ratio, expressed as a fraction, is

3/5=x/5

5*3/2=X  multiply by 5

15/2=x=7.5 simplify

7.5 parts yellow paint to 5 parts violet paint.

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The fraction of the students in the band that play either the flute or the clarinet is 4/5.

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Subtracting a negative number is the same as adding that number. In this case,

The tax owed by Ethan is $6,521.25.

Ethan's total income was $58,000. There was a deduction of $9,000. Ethan's net income is $49,000. The tax table is attached below. Now we will calculate the tax as per the table.

From $0 to $9,275, the tax is 10%, i.e., $9,27.5.

From $9,276 to $37,650, the tax is 15%, i.e., $4,256.25.

From $37,651 to $49,000, the tax is 25%, i.e., $2,837.5.

The payable tax is the sum of the above calculated taxes. The payable tax is $8,021.25. There is a tax credit of $1,500. The tax owed is the difference between the payable tax and the tax credit. The tax owed is $8,021.25-$1,500 = $6,521.25.

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The meaning of the y-intercept in this situation is that: D. when the cab travels 0 miles, the total fee will be $10.00.

Mathematically, the slope of a straight line can be calculated by using this formula;

[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

From the table, we have the following parameters:

Points (x, y) = (2, 5) and (13.00, 17.50)

Next, we would calculate the slope as follows:

Slope = (17.50 - 5)/(13.00 - 2)

Slope = 12.50/11.

Slope = 1.14.

Mathematically, the standard form of the equation of a straight line is given by;

y - y₁ = m(x - x₁)

Where:

Substituting the given parameters into the standard equation, we have;

y - 13.00 = 1.14(x - 2)

y - 13.00 = 1.14x - 2.28

y = 1.14x - 2.28 + 13.00

y = 1.14x + 10.72

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Let's begin by identifying key information given to us:

This figure is a cylinder. The formula for its volume is:

Height (h) = 2 m,

Diameter (d) = 5 × h = 5 × 2 = 10 m; radius (r) = d/2 = 10/2 = 5 m

pi = 3.14

The volume of the cylinder is calculated as shown below:

We have a table of values which contains different x-values and their related f(x).

We are searching for f(9), then we have to observe the value of the function f(x) when x=9.

In the table of values we can observe when x=9, then f(x)=8.

So f(9)=8

Step-by-step explanation:

please write the question properly

Since all the points proportional to (2,5) follow the equation 2y = 5x, (x,y) is a solution to y=5/2x

Accordingly 2y= 5x is the same as y/x = 5/2 . Since the equation y = 5/2x is a line with y-intercept equal to 0 , there is a line which passes through points (x,y) and (2,5). The true statements are: first, third and fifth statements.

Line segment IK includes Point J. The length of the segment IK=15 and IJ=13. The length of the segment JK is 2.

Given that,

Line segment IK includes Point J.

We have to determine the length of segment JK.

We have length of the segment IK=15 and IJ=13.

Two unique points on a line define the boundaries of a line segment. A line segment is also known as a part of a line that connects two locations. A line and a line segment vary in that a line has no ends and can continue indefinitely in any direction.

We can write as,

IK=IJ+JK

15=13+JK

JK=15-13

JK=2

Therefore, The length of the segment JK is 2.

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According to the given graph, after 70 seconds it ran 40 units of distance, after 100 seconds it ran 160 units of distance. So, the points we are going to use to find the rate of change are: (70, 40) and (100, 160).

Now, we use the following formula.-

Replacing the points, we have.

SOLUTION

Step1: Write out the parameters in the question

Let the number of hot dogs be h

The cost of a hot dog is $3

The cost of the bottle of water is $2

The total amount spent by jeff is $ 14

Step2: Write the inequality

The total amount spend should be less than or equal to the total amount

then

The cost of the hot dog is

The inequality will be the sum of the cost of the hot dog and the bottle of water

Hence option G is the correct op