What is the equation of the new function

Answer:

C

Step-by-step explanation:

Whenever you see | | with a NEGATIVE NUMBER it ALWAYS goes to the positive for example |-5| will be converted to 5 because its a negative number now if it is a positive number it stays the same for example |5| is still 5 because its positive Therefore, It is C. 8

Hope this helps!

dj~

Correct option is (C) 8

When we take the absolute value of any negative number say '-x' the number simplifies to just the magnitude of the number i.e 'x'

Thus |-8| would be '8'

Therefore absolute value of -8 is 8

Answer:

Step-by-step explanation:

Hello :)

Sorry I cant draw a graph on here but I can explain this to you. So if you have a calculator on you (a scientific one) you can use the table mode by pressing mode and then table. If you do not have a calculator then the axis on the graph you have needs to be substituted where x is.

If the axis is from -3 to 3 you need to enter every single value from -3 to 3 and substitute where x is

EG - (-3)^2-6(-3)+5 that is 32

Keep following for the rest of the values (it depends on your scale)

In this case we have

32,21,12,5,0,-3,-4 these each correspond and these are values on the y axis.

These each correspond to -3,-2,-1,0,1,2,3 in this exact order.

Plot the Graph with the values from this so on the x axis you will have -3 and on the y axis you will have 32 and so on.

This allows you to plot your graph

Answer:

Step-by-step explanation:

We can factor the equation to find the zeros

y = x^2 − 6x + 5

0 =   x^2 − 6x + 5

0 = (x-5) (x-1)

Using the zero product property

x-5 = 0      x-1 =0

x=5   x=1

The zeros are at (1,0) and (5,0)

The vertex is 1/2 way between the zeros

1+5 = 6  6/2 =3

The x coordinate of the vertex is 3

Substituting into the equation

y = 3^2 -6(3) +5

y = 9-18+5

y= -4

The vertex is at (3,-4)

We know it is symmetric around x=3

The y intercept is (0,5)

Answer:

1/12

Step-by-step explanation:

Answer:

r = 6 m

Step-by-step explanation:

The circumference of a circle is given by

C = 2 * pi *r

Substitute in what we know

37.68 = 2 * 3.14 * r

37.68 = 6.28 r

Divide each side by 6.28

37.68/6.28 = 6.28 r/6.28

6 = r

Answer:

Step-by-step explanation:

Start with our equation:

s=2(lw+wh+hl)

Plug in our values for l, w, and h:

s=2(12*9+9*2+2*12)

Simplify:

s=300

Answer:

1:16

Step-by-step explanation:

Convert the basketball players height to inches:

6 ft = 12 x 6 = 72 inches.

72+8 = 80 inches tall

Now divide his actual height by the scaled height:

80 / 5 = 16

The scale can be 1:16 , which means 1 inch equals 16 inches.

it takes 1.6 hour to go 8 miles.

Speed of toy car = 5mph
distance = 8 miles
times =??

Speed is ratio of distance to the time.

Speed = distance/time
time = distance/speed
time = 8/5
time = 1.6

Thus, it takes 1.6 hour to go 8 miles.

Learn more about speed here:
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set f(x) equal to y

y = 19/ x^3

swap x and y

x = 19/y^3

make y the subject

xy^3 = 19

y^3 = 19/x

[tex]y = \sqrt[3]{ \frac{19}{x} } [/tex]

then just replace y with f^-1(x)

[tex]f(x) = \sqrt[3]{ \frac{19}{x} } [/tex]

hope this helped! have a good day ~ •lipika•

The inverse of the function F(x) is:

          [tex]\sqrt[3]{\dfrac{19}{x}}[/tex]

We are given a rational function F(x) as:

[tex]F(x)=\dfrac{19}{x^3}[/tex]

The steps to find the inverse function of a given function f(x) are as follows:

1.   Put f(x)=y

2.  Interchange the value of x and y

3.  Solve for y.

Hence, we find the inverse of F(x) as follows:

[tex]F(x)=y[/tex]

i.e.

[tex]\dfrac{19}{x^3}=y[/tex]

Now we interchange x and y

i.e.

[tex]\dfrac{19}{y^3}=x[/tex]

Now we solve for y as follows:

[tex]y^3=\dfrac{19}{x}\\\\i.e.\\\\y=\sqrt[3]{\dfrac{19}{x}}[/tex]

      Hence, the inverse function is:

                 [tex]\sqrt[3]{\dfrac{19}{x}}[/tex]

Answer: $27,000

Step-by-step explanation:

In order to calculate what his salary is this year, you need to divide $3,600 / 12% since $3,600 equals 12%. $3,600 / .12 = $30,000. If his salary is $30,000 it was 3,000 less last year, or $27,000.

His salary last year was 27,000

Steps:

find what 3,600 is 12% of.

we do this by is over of equals percent over a hundred

this gives us 30,000 dollars

next we subtract the 3000 dollars more he earned

this gives us 27,000 dollars

312 people bought balcony seats and 396 people bought ground seats.

The length is 12 feet

The width of the garden is 5 feet

After that the total edging is telling us the area

We know that

So

60 = length x 5

Length = 60 / 5

Length = 12 feet

Simplify : ( 5 + 4i ) + ( 3 - 2i ) = ?

Simplify by combining the real and imaginary parts of each expression.

= 8 + 2i

Hope this helps,

Davinia.

x2=400

x=√400

=20

20^2=400

The solutions to the equation x² = 400 are x = 20 and x = -20, obtained by taking the positive and negative square roots.

The given equation is x² = 400. This is a simple quadratic equation, and we can solve it by taking the square root of both sides. Any positive number n has two square roots: positive root √n and negative root -√n. So this results in two equations: x = √400 and x = -√400.

Solving these, we find that x = 20 and x = -20. So, the solutions to the equation x² = 400 are x = 20 and x = -20.

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Answer:

[(2 + √3)/4] = 0.9330127

Step-by-step explanation:

We know that

cos (pi/12) ^ 2 =

cos (pi/12)* cos (pi/12)  =

[(√6 + √2)/4]*[(√6 + √2)/4] =

(0.9659)*(0.9659) = 0.9330127

[(2 + √3)/4] = 0.9330127

Answer:

The answer is 2760000

Step-by-step explanation:

Answer:2760000

Step-by-step explanation:

There are 4 people. They average 68, so the total key chains are 68 x 4 = 272.

Tarun has 78, so the other three people have a total of 272 - 78 = 194.

Let Marcus = X

James has half as many as Marcus, so he is 0.5X

Yahya is (x + 0.5x)-28 = 1.5X-28

Now add them together to equal 194:

X + 0.5x + 1.5x -28 = 194

Simplify:

3x -28 = 194

Add 28 to each side:

3x = 222

Divide both sides by 3:

x = 222 / 3

x = 74

Marcus = x = 74 key chains.

James = 0.5x = 0.5(74) = 37 key chains.

Yahya = 1.5x-28 = 1.5(74) -28 = 111-28 = 83 key chains.

Tarun = 78 key chains.

Check: 74 + 37 + 83 + 78 = 272 ( matches the total above).

the original price is "x", or 100%.

but we know that if we reduce "x" by 20%, namely 100% - 20% = 80%, the 80% of "x" is really £50, what is "x" or the 100% anyway?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 50&80 \end{array}\implies \cfrac{x}{50}=\cfrac{100}{80}\implies \cfrac{x}{50}=\cfrac{5}{4}\implies 4x=250 \\\\\\ x=\cfrac{250}{4}\implies x=62.5[/tex]

Answer:

{x ∈ ℝ : x ≥ π/6 +2πn and x ≤ π/6 + 2πn and n ∈ ℤ}

Step-by-step explanation:

sinx can run from -1 to +1

2sinx can run from -2 to +2

2sinx -1 can run from -3 to +1

However, the square root is imaginary when x < 0. So, the condition is

2sinx -1 ≥ 0

2sinx ≥ 1

sinx ≥ ½

x ≥ π/6 (30°)

So, in the interval [0, 2π], π/6 ≤ x ≤ 5π/6

However, the sine is a cyclic function and repeats itself every 2π.

Over all real numbers, the condition is (π/6 +2πn) ≤ x ≤ (5π/6 + 2πn).

The domain is then

{x ∈ ℝ : x ≥ π/6 +2πn and x ≤ π/6 + 2πn and n ∈ ℤ}

The original price was $120.00.

30 percent of $120.00 is $36 and if you add those together they equal $156.00.

I hope that makes sense and was helpful.

Answer:

$22554.45

Step-by-step explanation:

Since we are given a function to use to find the cost of the car, we first need to find the difference in the years 2017 and 2010

2017 - 2010 = 7

So our value for t will be 7.

We can use the formula because it still falls under the expected increase within the 10 year range.

So now let's substitute t in the function.

[tex]f(7) = 15000*(1.06)^{7}[/tex]

[tex]f(7) = 22554.45[/tex]

So it will cost the company $22554.45 to build the car in 2017.

The cost to build the car in 2017 is $22,554.45.

1. Identify the given function:

[tex]\[ f(t) = 15000 \times (1.06)^t \][/tex]

2. Substitute [tex]\( t = 7 \)[/tex] into the function:

[tex]\[ f(7) = 15000 \times (1.06)^7 \][/tex]

3. Calculate [tex]\( (1.06)^7 \):[/tex]

[tex]\[ (1.06)^7 \approx 1.50363 \][/tex]

4. Multiply by the initial cost:

[tex]\[ f(7) = 15000 \times 1.50363 \approx 22554.45 \][/tex]

Answer:

This ordered pair is NOT a solution of the equation.

Step-by-step explanation:

First, it is important to note that ordered pairs consist of (x, y) so in this case

x = 15 and y = -3.  And that any variable directly next to a number calls for multiplication.  So, plugging in the variables the equation would look like

"-3 = 5 x 15"  

To see if 5 x 15 = -3 we will multiply them.  5 x 15 actually equals 75 not -3.  So we know this ordered pair is NOT the solution for the problem.  

Answer:

x = -1/2

Step-by-step explanation:

4(x + 3) = 9x + 16 + 3x

Distribute the 4

4x +12 = 9x+16+3x

Combine like terms

4x+12 = 12x+16

Subtract 4x

4x-4x+12 = 12x-4x+16

12 = 8x+16

Subtract 16

12-16 = 8x+16-16

-4 =8x

Divide by 8

-4/8 =8x/8

-1/2 =x

Answer:

13 miles

Step-by-step explanation:

divide 391 minutes by 17, to find out how many minutes for 1 mile.

its 23 min= 1 mile.

do 23 multiplied by 13 to get your desired amount of time, which is 299 min.

It will travel 12.65 miles

see the image

Answer:

3467.2

Move the decimal to the right three times, then put the decimal between the 3rd and 4th place.

Answer:

If not, stop and use Steps for Solving an Exponential Equation with Different Bases. Step 2: Rewrite the problem using the same base. Step 3: Use the properties of exponents to simplify the problem. Step 4: Once the bases are the same, drop the bases and set the exponents equal to each other.

To ensure the cost doesn't exceed $49, the chemistry club can rent the meeting room for fewer than 7 hours.

The subject is Mathematics, and it's likely for High School level. This problem deals with the concept of linear inequalities. Here, the total cost of renting the room is given by the equation:

y = 14 + 5t,  where t represents the number of hours the room is rented. The chemistry club wants to spend less than $49, so we have the inequality: 14 + 5t < 49. Subtract 14 from both sides to get 5t < 35. Finally, divide both sides by 5 to solve for t, ending up with: t < 7. Therefore, the chemistry club could rent the meeting room for fewer than 7 hours to keep the cost under $49.

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4+1/5 could be modeled using the diagram

To find the equation of a line that is perpendicular to another line, we need to consider the fact that perpendicular lines have slopes that are negative reciprocals of each other. The given line has a slope of 1, so the perpendicular line will have a slope of -1. Using the point-slope form of a line, we can find the equation of the perpendicular line by plugging in the given point and slope.

To find the equation of a line that is perpendicular to another line, we need to consider the fact that perpendicular lines have slopes that are negative reciprocals of each other. The given line has a slope of 1, so the perpendicular line will have a slope of -1.

Using the point-slope form of a line, y - y1 = m(x - x1), we can plug in the values of the given point (-12, 10) and the slope (-1) to find the equation:

y - 10 = -1(x - (-12))

y - 10 = -1(x + 12)

y - 10 = -x - 12

y = -x - 2

Therefore, the equation of the line that is perpendicular to y = x - 2 and passes through the point (-12, 10) is y = -x - 2.

Answer:

(A) 9

Step-by-step explanation:

First, change the percentage sign into decimal: 51% = 51/100 = 0.51

Multiply 0.51 with 18

0.51 x 18 = 9.18

Note that it is asking for an estimate, and so round to the nearest whole number.

9.18 rounded to the nearest whole number is 9

(A) 9  is your answer.

~

Answer:

(A)9

Step-by-step explanation:

If you weren't using a calculator, you know that half, or 50% of 18 is 9, and if it is 51% it will also be around 9. Therefore A is the correct answer.

Answer:

121.7

Step-by-step explanation:

73

+48.7

=121.7

121.7

-73

=48.7

To add 73 and 48.7, align them based on the decimal point and add each column from right to left to get the result of 121.7.

The task is to add 73+48.7. The best way to go about this is to align the numbers vertically, taking the decimal point into account:

Now, add each column from right to left. In the first column, we have 0+7, which equals 7. In the next column, we have 3+8, which equals 11. Write down the 1 and carry over the 1 on top of the next column. In the last column, we have 7 (from the carried-over value and the number 7); add it to 4, which equals 11. The final result is 121.7.

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