I need help solving an answering this practice problems from my pre-calculus prep guide

First, replace f(x) by y. This is done to make the rest of the process easier.

Now, replace every x with y and a every y with an x:

Now, solve this equation for y. Then, we must move -8 to the left hand side as +8. It yields

Now, we can apply logarithms in both sides:

For the properties of logarithms, we have

then, we have

and we obtain

Finally, replace y with f^1. Then, the inverse funcion is

The graphs of the function and its inverse are:

Answer:

A: (-3,0)

B:(-3,-5)

C:(-6,0)

Step-by-step explanation:

invert the signs on all numbers to flip it 180 degrees, then add 4 to each y point to translate up 4

Answer

Interest = $5,250

Future value = $14,000

Explanation

Given:

Principal, P = $8,750

Rate, R = 3%

Time, T = 20 years

What to find:

The interest and future value.

Step-by-step solution:

The Interest

The interest can be calculated using the simple interest formula below.

The interest of $8,750 at 3% for twenty years is $5,250

The future value

Future value = Amount = Principal + Interest

Future value = $8,750 + $5,250

Future value = $14,000

Answer:

93.32 %

Step-by-step explanation:

88 - 82 = 6 points

  this is   6 /4 = z-score + 1.5  

     from z score table , this corresponds to .9332     or  93.32 %

The value of the missing variable x is; x = 37

Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line.

Now, from the given problem, we see that we have two parallel lines with a transversal crossing them Thus, we can say that the two given angles are corresponding angles and as such they are congruent. Thus;

3x + 4 = 115

3x = 115 - 4

3x = 111

x = 111/3

x = 37

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The reflection across x-axis has the following rule applied

The rotation of 180° about the origin has the rule

In this case, the new image are not the same, that is to say

Therefore, they are not the same.

Answer:

the answer is 3.5 i think

8+3+3+1+7+4+1+4+4= 35

35/10=3.5

John's paycheck is $2,000.

According to the question,

We have the following information:

John saves 2/5 of his take-home pay.

After 6 paychecks, he has saved $4,800.

Now, let's take John's paycheck to be $x.

Now, 2/5 of this paycheck will be $2x/5.

So, this is the amount saved from 1 paycheck of John.

Now, to find the amount saved in 6 paychecks will be:

6*(2x/5)

Now, we can equate this to the amount saved by John after 6 paychecks.

6*(2x/5) = $4,800

12x/5 = 4800

12x = (4800*5)

x = (4800*5)/12

Now, dividing 4800 by 12:

x = 400*5

x = $ 2000

Hence, the correct option is C ($2,000).

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         The number 5 in mathematics denotes a quantity or value of 5. Five is the entire number between four and six. Five is the name of the number. Sam the little shows off five fingers.

     The distance between 5 and 0 is the absolute value of 5. Then you go 1, 2, 3, 4, and 5. To the immediate right of zero, 5 is located. As a result, 5 has an absolute value of 5.

It denotes the sum of all succeeding integers, inclusively from 1 to 5.

That ' s 5! = 5*4*3*2*1 =120.

Also known as five factorials.

Ten-thousands

   Answer and justification A five-digit figure is one that is in the tens of thousands. This is due to the fact that 10,000 is the smallest positive whole number with five digits.

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All the three person earn $230.75 in all.

What is mean by Addition?

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

Given that;

You earn in selling items = $35.50

Newton earn 5 times as much you.

Descartes earns 0.1 times as much as Newton does.

Now,

You earn in selling item = $35.50

Newton earn in selling = 5 x $35.50

                                   = $177.5

Descartes earn in selling = 0.1 x $177.5

                                      = $17.75

So, Total earn = $35.50 + $177.5 + $17.75

                     = $230.75

Therefore, All the three person earn $230.75 in all.

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The monthly payment of $310 compounded monthly at 8% and 3% will have a principal of $15,288.71 and $17,252.23 respectively

The monthly payment is the amount paid per month to pay off the loan in the time period of the loan. When a loan is taken out it isn't only the principal amount, or the original amount loaned out, that needs to be repaid, but also the interest that accumulates.

In order to solve this question, we can use the formula of monthly payment we can use a simple formula for that

[tex]A = p \frac{r(1+r)^n}{(1+r)^n-1}[/tex]

In the first scenario, we can find the monthly payment at 8%

Substituting the values into the equation and solve

The principal at 8% is $152888.71 and the principal at 3% is at $17252.23

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Respuesta:

Si el número de yardas (Y) es igual al número de pies (F) dividido por 3, entonces podemos establecer la siguiente ecuación:

La gráfica de esta ecuación es una linea recta con pendiente 1/3 y que pasa por el origen, como sigue:

Consequently, it costs $62.70 to make cupcakes for two hours.

By making use of functions, We have: n(h) = 3h, The cost in terms of hours h is given by C(3h) = 60+1.35h, and Lisa's cost for making cupcakes for 2 hours is $62.70

According to the question, Lisa makes 3 dozen cupcakes an hour. To calculate how many she makes in h hours, we will apply the equality postulate as stated.

3 dozens = 1 hour

Hour = n(h)

Cross Multiplying,

n(h) × 1 = 3×h

n(h) = 3h

Therefore, n(h) = 3h is the function that predicts the number of cupcakes Lisa produces in h hours.

We shall locate the composite function C(n(h)) to obtain the cost function in hours.

C(n(h)) = C(3h) (3h)

If C(n) = 60 + 0.45n, then

By replacing n with 3h in the function as indicated, C(3h) is obtained;

C(3h) = 60+0.45(3h) (3h)

C(3h) = 60+1.35h

Thus, 60+1.35h is the cost function expressed in hours.

We will change h = 2 into the calculation C(h) = 60+1.35h to obtain the cost of baking cupcakes for 2 hours.

C(2) = 60+1.35(2) (2)

C(2) = 60+2.70

C(2) = 62.70

Consequently, it costs $62.70 to make cupcakes for two hours.

Complete Question:

Lisa specializes in baking lemon cupcakes. She bakes 3 dozen cupcakes every hour. The cost (in dollars) of making n cupcakes is given by the function C(n) = 60 + 0.45n. The function that models the number of cupcakes Lisa makes in h hours is n(h)=___. The cost in terms of hours h is given by ___. Lisa's cost for making cupcakes for 2 hours is___

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The parachutes speed during free fall will be : 990 feet per second

Given: A parachute speed during a free fall = 135 miles per hour.

This means Unit rate = 135 miles per hour

= 135 × [tex]\frac{5280}{60X60}[/tex] feet per second

Because it is given that 1 mile = 5280 feet per second

= [tex]135 X \frac{5280}{3600}[/tex]

On dividing 5280 by 3600

we get:

= 135 × 1.46

= 198.00 feet per second

Thus in 5 seconds the parachutes speed during free fall will be :

990 feet per second.

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Given:

Variable r

To determine the what variable r represents, we first note that it is a common way to indicate a correlation value. We also note that coefficient of determination, r^2, is simply the square of the sample correlation coefficient (i.e., r).

Therefore, variable r means:

The sample correlation coefficient

SOLUTION:

This can be simplified to give;

1) Gathering the data

282 miles

2 1/2 hour We can rewrite that as 2.5

2) Let's use a proportion, or rather a formula for that

282 miles ------- 2.5

x -------------------- 1

2.5x = 282

x=282 /2.5

x =112.8 miles per hour

In one 1 hour, this train is able to get 112.8 miles if this train maintains its velocity

We have the following equation:

y - 4 = 1/3 (x + 2)

We clear y in order to be more unterstandable:

y - 4 = 1/3 (x + 2)

y = 1/3 (x + 2) + 4

y = 1/3 x + 2/3 + 4

y = 1/3 x + 2/3 + 12/3

y = 1/3 x + 14/3

In order to find the answer we are going to determine x value when y = 4:

y = 1/3 x + 14/3

4 = 1/3 x + 14/3

4 - 14/3 = 1/3 x

12 - 14 = x

-2 = x

Then, it passes through the point (-2 , 4), so we can discard options A and B (because it doesn't pass through (2, 4))

We know a linear equation is given by:

y = mx + b, where m and b are numbers: m is the slope of the line and b the y-intercept.

In this case y = 1/3 x + 14/3, the slope is 1/3. We know m is given by

m = Δy/Δx

Since in this case

m = 1/3 = Δy/Δx

Then

Δx = 3 and Δy = 1

That means that if it changes 3 units on the x-axis, then it changes 1 unit on the y-axis

Answer

x = √6

Explanation

We will first sketch this triangle.

Let the short leg of the triangle be x

In a right-angle triangle, the side opposite the right angle is the Hypotenuse, the side opposite the given angle that is non-right angle is the Opposite and the remaining side is the Adjacent.

So, after noting the three sides in a right triangle, we will then use trignometric ratios to solve for any of the unknown. If the non-right-angle angle given is θ, the trignometric ratios in short forms are written as

SOH, CAH and TOA

SOH means Sin θ = (Opp/Hyp)

CAH means Cos θ = (Adj/Hyp)

TOA means Tan θ = (Opp/Adj)

So, the one to be used depends on the sides of the triangle that are provided.

For this triangle, using the angle 60° as the non-right-angle angle

Hypotenuse = ?

Opposite = 3√2

Adjacent = x

Angle = 60°

TOA means Tan θ = (Opp/Adj)

Tan 60° = (3√2)/x

Tan 60° = √3

Tan 60° = (3√2)/x

√3 = (3√2)/x

Cross multiply

x = (3√2)/(√3)

x = (√3) (√2)

x = √6

Hope this Helps!!!

Answer:

x = √6

Step-by-step explanation:

ANSWER:

Regular pay is $383.2

Overtime rate is $14.37

Overtime pay is $114.96

Gross pay is $498.16

STEP-BY-STEP EXPLANATION:

Assuming the overtime multiplier is 1.5 and the standard work week is 40 hours. Therefore, we calculate the regular payment like this:

The overtime rate would be the value of the normal payment times the overtime multiplier, like this

Then we multiply the number of additional hours to the 40 hours allowed, that is, 8 (48 - 40), for which one gives overtime pay

Now the gross pay would be the sum of the regular payment with the overtime payment:

The value of x is 7 and the measure of unknown angle is 64°.

The angles of triangle are given 76°, (9x+1)° and 40°.

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

Now, sum of three angles of a triangle is

76°+(9x+1)°+40°= 180°

⇒ 116+9x+1 = 180

⇒ 9x + 117 = 180

⇒ 9x = 63

⇒ x = 7

So, 9x+1=64°

Therefore, the value of x is 7 and the measure of unknown angle is 64°.

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therefore the center of the hyperbole is (0,0) and it's symmetry axis is the y-axis and the x-axis. The intercepts are (0,-1) and (0,1)

Answer:

[tex]\frac{x}{3}[/tex] or x/3 or x÷3

Given:

The change in volume by time is, (dV/dt) = 10 cubic feet per minute.

The diameter and height of the right circular one are equal, 2r = h.

Height of the pile is, h = 21 ft.

The objective is to find the rate of increase in height of the pile.

Explanation:

The general formula of volume of cone is,

From the given data, radius of the cone can be calculated as,

Substitute the value of r in equation (1).

To find rate of increase in height of the pile:

Now, differentiate equation (2) with respect to time t.

Substitute (dV/dt) and h in equation (3).

On plugging the obtained values in eqation (3),

Hence, the rate of increase in height of the pile is 0.029 ft/min.

Given: A farmer is going to divide her40 acre farm between two crops

To Determine: How many acres of each crop should the farmer plant to maximize her profit

Solution

The graph of the inequalitiesis as shown below

Neglecting the negative axis, the point that will maximize the profit are te points shown above with their coordinates

The coordinates will maximum profits are

Substitute the 3 points into the profit functions to determine thepoint that will given the maximum profit

Hence, the point that will maximize profit is (35, 0), which is

35 acres of crop A, and

0 acre of crop B

The measure of an angle and its complement differ by 22 degrees and the larger is 56°

The total of the two angles' measurements determines their complement and supplement. The pair of angles is said to be complimentary if the product of the two angles equals the measurement of a right angle.

1. If the total of two angles equals 90°, the angles are considered to be complements of one another.

2. Let x° and y° be the two angles. Since they complement one another, the two angles' sum will be 90 degrees.

= x + y = 90°. (Assume equation 1 is used.)

3. The two angles differ by 22 degrees, hence the equation will be,

= x - y = 22°. (Put equation 2 in.

4. To determine the values of x and y, solve equations 1 and 2.

Add equations 1 and 2 together.

= x + y + x - y = 90 + 22,

= 2x = 112°,

= x = 56°.

5. In equation 1, change the value of x.

= 56° + y = 90°,

= y = 90 -56,

= y = 34°.

So, the measure of the two angles is 56°, and 34°.

And the larger angle is  56°

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Given:

m∠A = (4x - 2) degrees

m∠B = (11x + 17) degrees

Let's find the value of x if the angles A and B are complementary angles.

Complementary angles are angles that sum up to 90 degrees.

Hence, we have:

m∠A + m∠B = 90

(4x - 2) + (11x + 17) = 90

Let's solve for x.

• Remove the parentheses:

4x - 2 + 11x + 17 = 90

• Combine like terms:

4x + 11x - 2 + 17 = 90

15x + 15 = 90

• Subtract 15 from both sides:

15x + 15 - 15 = 90 - 15

15x = 75

• Divide both sides of the equation by 15:

Therefore, the value of x = 5

ANSWER:

x = 5

Answer:

Step-by-step explanation:

Answer:

R90° transformation results in an image point that is (6, -8).

The plane is divided into four infinite areas known as quadrants, each of which is bounded by two half-axes, using two-dimensional Cartesian axes.

These are commonly numbered from 1 to 4, and are denoted by Roman numerals: the coordinates for I are I (+, +), II (-, +), III (-, -), and IV (+, -).

We are aware that there are four quadrants: I (x, y), II (-x, y), III (-x, -y), and IV (-x, -y) (x, -y)

We can infer that the points are in quadrant III from the supplied point, which is (-6, -8). (-x, -y).

Now, if we turn right 90 degrees and enter sector IV (x, -y), the supplied point will change to (6, -8)

hence, following the transformation of R90°, we have the image point is (6, -8).

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