I need help with my pre-calculus homework, please show me how to solve them step by step if possible. The image of the problem is attached. The homework was a pdf so the choices can't expand, my teacher told me to just write the transformation of the given function in the format.

the answer is:

Student G earns less money per hour than student F

Answer: 31 electricians

Step-by-step explanation:

We could set up a ratio for this problem. It takes 14 electricians 18 days to wire a new housing subdivision, so it would take 24 electricians x days to do the same job. 14/18 = 24/x. We can then cross multiply to find x.

X = 30.8 or approximately 31.

The total distance that Kim walked in 3 days is 6 2/3 miles. We would convert this distance to mixed numbers. To do this, we would multiply 6 by 3 and add 2. The denominator would still be 3. It becomes

20/3 miles

If she walked 20/3 miles in 3 days, the number of miles that she walked per day would be

total distance/number of days

It becomes

(20/3) / 3

If we change the division sign to multiplication, it means that we would flip 3 such that it becomes 1/3. Thus, we have

20/3 * 1/3 = 20/9

= By converting to mixed numbers, we would find how many 9's are in 20. It is 2. The remainder is 20 - 18 = 2

Thus, the answer is

2 2/9 miles per day

Answer:

50 + 6x = 62

Explanation:

If x represents the cost of one box of pencils and the teacher got snacks for $50, purchased 6 boxes of pencils, and spent a total of $62, we can write the equation that models the above situation as shown below;

The equations that are equivalent to the formula PV = nRT are  V = nRT/P,  n = PV/RT and R = PVnT. Option B, C and D

From the information given, we have that;

The Ideal Gas law is represented as;

PV = nRT

Given that;

Subject of formula is described as the variable expressed in terms of other variables in an equation.

It is made to stand on its own on one end of the equality sign.

Let's make 'V' the subject of formula

Divide both sides by the coefficient of V which is the variable 'P', we have;

V = nRT/P

Making 'R' the subject of formula, we have

R = PV/ nT

Making 'n' the subject of formula, we have;

n = PV/RT

Hence, the equations are options B, C and D

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The complete question:

In physics, the Ideal Gas Law describes the relationship among the pressure, volume, and temperature of a gas sample. This law is represented by the formula PV = nRT, where P is the pressure, V is the volume, T is the temperature, n is the amount of gas, and R is a physical constant. Which of the equations below are equivalent to the formula PV = nRT? Select all that apply. A. P = VnRT B. V = nRT/P C. n = PV/RT D. R = PVnT E. T = nR/PV

Answer:Pv=NRT

Step-by-step explanation:

If the amount of time spent is lesser than or equal to 250, so the price is $29, so we have the first part of the piecewise equation:

Then, for an amount of time greater than 250, the extra minutes are charged by 0.35 per minute, and this extra cost will add the fixed cost of $29, so the second part of the equation is:

The option that shows the correct piecewise equation is option A.

The faster motorcycle travelled 240 miles and the slower motorcycle travelled 120 miles .

In the question ,

let the time travelled by the slower motorcycle be "t" .

given , the faster one travelled 1 hour longer ,

So , the time travelled by faster motorcycle = "t+1" hour .

the speed of slower motorcycle = 60 miles per hour .

the speed of faster motorcycle = 80 miles per hour .

So , the distance covered by slower motorcycle = speed * time

                                                                                 = 60*(t)

the distance covered by the faster motorcycle = 80*(t+1) .

given that faster motorcycle travels twice the distance of the slower motorcycle

So According to the question

80*(t+1) = 2*60*(t)

simplifying further , we get

80t + 80 = 120t

120t - 80t = 80

40t = 80

t = 2 hours

distance covered by slower motorcycle = 60(2) = 120 miles

distance covered by faster motorcycle = 80(2+1) = 80*3 = 240 miles .

Therefore , The faster motorcycle travelled 240 miles and the slower motorcycle travelled 120 miles .

The given question is incomplete , the complete question is

One motorcycle travels 80 miles per hour and the second motorcycle  travels 60 miles per hour,  if the faster motorcycle travels 1 hour longer than the slower motorcycle and it also travels twice the distance of the slower motorcycle . What distance does each of the motorcycle travel ?

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Explanation

Step 1

we have a perpendicular line, its slope is

two lines are perpendicular if

replace

so, our slope is 3/2

Step 2

using slope=3/2 and P(-5,2) find the equation of the line

ANSWER :

EXPLANATION :

Obtuse angles (90°–180°) are those that fall within this range. Right angles are those that have a 90 degree angle ( = 90°). Straight angles are those that have a 180 degree ( = 180°) angle.

Any angle more than 90 degrees is deemed obtuse: A straight angle is one with a 180° measurement. A zero angle is one with a measurement of 0°: Angles with measures that add up to 90 degrees are said to be complementary angles: Angles with measures that add up to 180° are referred to as supplementary angles.

We now understand that an obtuse angle is one that is greater than 90 degrees but less than 180 degrees. Obtuse angle examples include 110°, 135°, 150°, 179°, 91°, and more. As a result, all angles between 90° and 180° are obtuse angles.

Hence obtuse angle is one of the angle which is not correct 100 degree angle

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(a)Recall that the circumference of a circle is given by the following formula:

Where d is the diameter of the circle.

Substituting d=14 ft in the above formula, we get:

(b) Recall that the area of a circle is given by the following formula:

Substituting d=14 ft in the above formula, we get:

Answer:

(a)

Exact solution:

Approximation:

(b) Exact solution:

Approximation:

If two lines are parallel, it means that they have the same slope. The given lines are

y = 2x - 4 and y = x - 4

The slope intercept form of a straight line is expressed as

y = mx + c

Where

m represents slope

c represents y intercept

By comparing both equations with the slope intercept form,

For y = 2x - 4

Slope, m = 2

For y = x - 4

Slope, m = 1

We can see that the slopes are not eaual. Thus, the lines are not parallel.

Also, we can conclude that there is no line that passes through the point (3,5) that is parallel to both lines

There is no line that passes through the point (3,5) that is parallel to both lines.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

If two lines are parallel, it means that they have the same slope. The given lines are

y = 2x - 4 and y = x - 4

By comparing both equations with the slope-intercept form,

For y = 2x - 4

Slope, m = 2

For y = x - 4

Slope, m = 1

We can see that the slopes are not equal. Thus, the lines are not parallel.

Also, we can conclude that there is no line that passes through the point (3,5) that is parallel to both lines.

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The resulting rational number is √100

Rational numbers:

A rational number is a number that can be represented a/b where a and b are integers and b is not equal to 0.

Given,

Here we have the following list of numbers

√75, -√25, 2√7, √100, √0.36, √0.0144, √3/7 , -√36/49

Now, we need to identify whether these are the rational numbers or not.

AS per the definition of rational number,

When we take the  root for the value √75, we get 8.660 that is a non-whole square root, 8.660 is not a rational number.

The value -√25 takes the negative value so it is not a rational number.

The number 2√7, this one also produce on-whole square root, so this one is not a rational number.

The value of √100 is 10, and it is a rational number.

The value of √0.36 is 0.6 which is less than 0, so it is not a rational number.

The value of √0.0144 is 0.012 which is less than 0, so it is not a rational number.

The value of √3/7 this one also produce on-whole square root, so this one is not a rational number.

The value -√36/49 takes the negative value so it is not a rational number.

Therefore, the rational number is √100.

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Given: The equation below

To Determine: The slope, the vertical and horizontal intercept, and the graph of the equation

Solution

The general slope-intercept form of a straight line is as shown below

Let us compare the general slope-intercept form of a straight line to the given

The vertical intercept is the point where the x values is zero

The vertical intercept is y = 5, with coordinate (0, 5)

The horizontal intercept is the point where the y value is zero

The horizontal intercept is x = 5/2, with coordinate (5/2, 0)

The graph of the equation is as shown below

Answer Summary

(a) slope = -2

(b) Vertical intercept, y = 5

(c) Horizontal intercept, x = 5/2

start expanding the squared expression using the square of a binomial,

then,

replace in the original function

apply distributive and simplify

Answer:

We have the next given set for distances (in miles) to the nearest for 13airport families:

10, 13, 15, 15, 20, 26, 27, 28, 30, 32, 34, 37, 39

The minimum is the least number value. Then:

Minimum =10

In this case, we have 13 data, so :

- The middle number is the median:

10, 13, 15, 15, 20, 26, 27, 28, 30, 32, 34, 37, 39

Now, the lower quartile is given by the next equation:

Replacing:

The lower quartile is in the fourth position:

Lower quartile = 15

The upper quartile is given by the next equation:

The upper quartile is located in the 11th position:

Upper quartile = 34

The interquartile range is given by:

IQR=upper quartile - lower quartile

IQR=34-15

The interquartile range =19

Given:

Cost of a CD = $14.50

Markup =30%

If markup 30% then:

So the cost is:

markup cost is 18.85

Given:

The point is (-2,3).

The parallel line is y=4x+2.

This is of the form

where slope m=4.

We know that the slope of the parallel lines is equal.

Thus we get the slope m =4 for the required line.

Consider the line equaiton

Substitute x= -2,y=3, and m =4 in the equation to find the value of b.

Adding 8 on both sides of the equation, we get

We get b=11.

Substitute m=4 and b=11 in the equation, we get

Hence the line equation that passes through the point (-2,3) and parallel to y=4x+2 is

Sidney will use 57 cups of soda for 19 cups of ice cream.

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

From the table,

The ratio of cups of ice cream to cups of soda.

3.5 cups ice cream = 10.5 cups of soda

Divide both sides by 3.5.

1 cup of ice cream = 3 cups of soda

Multiply 19 on both sides.

19 cup of ice cream = 57 cups of soda

Thus,

57 cups of soda.

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We have four numbers. We have to know that negative numbers are "smaller" than positive numbers, and when numbers are far away from zero are even "bigger".

The least number is -27/36. It is a negative number.

We can also see that we have some fractions. A fraction is a part of "a whole".

So, as we can see 6 is not a fraction. Therefore, 6 is the greatest number from this list.

So we have the least and the greatest: -27/36 and 6, respectively.

We also need to compare 18/40 and 5/20. What fraction is bigger?

In order to compare them, we need to have two fractions with the same denominator. Then, the fraction with the greatest numerator is "bigger" than the other fraction.

Let us see:

If we divide the numerator and the denominator of 18/40 by 2, we have:

18/2 = 9

40/2 = 20

Then, the equivalent fraction is 9/20 (or 9/20 is equivalent to 18/40). Now, we can compare them:

9/20 and 5/20. So, which one is the greatest? The one with the greatest numerator: 9/20.

Our final list is this way, from least to the greatest as follows:

-27/36, 5/20, 18/40 (9/20), 6.

By identifying the intercepts in the given image, we conclude that the solutions of the system of equations are points B and F.

When we have a system of 2 equations:

y = f(x)

y = g(x)

To solve it graphically, we have to graph both functions in the same coordinate axis and see in which points the graphs intercept (if they do). Each of these interceptions in the form (x, y) will be a solution for the equation f(x) = g(x) = y

In this case, we can see a line and a parabola (each of these is a different equation from the system), and we can see that the graphs intercept at points F and B (i think, the image is really small). Then the two solutions of the system of equations graphed are the points F and B

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Answer:

solution: F and B

NOT solution: the rest of the letters

Step-by-step explanation:

I did the work on imagine math

=====================================================

Explanation:

mu = 500 = mean

sigma = 100 = standard deviation

We'll need the z score for x = 620

z = (x - mu)/sigma

z = (620-500)/100

z = 1.20

The task of finding P(x > 620) is equivalent to P(z > 1.20)

Use a Z table or a Z calculator to find that

P(Z < 1.20) = 0.88493

which leads to

P(Z > 1.20) = 1 - P(Z < 1.20)

P(Z > 1.20) = 1 - 0.88493

P(Z > 1.20) = 0.11507

This converts to 11.507% and rounds to 11.5%

About 11.5% of the students score higher than a 620 on the SAT.

-------------------------

Another approach:

Open your favorite spreadsheet program. The command we'll be using is called NORMDIST. The template is this

NORMDIST(x, mu, sigma, 1)

If you were to type in [tex]\text{=NORMDIST(620,500,100,1)}[/tex] then you'll get the area under the normal distribution to the left of x = 620

This means [tex]\text{=1-NORMDIST(620,500,100,1)}[/tex] will get us the area to the right of 620. The result of that calculation is approximately 0.11507 which leads to the same answer of 11.5% as found earlier.

When using a spreadsheet, don't forget about the equal sign up front. Otherwise, the spreadsheet will treat the input as text and won't evaluate the command.

-------------------------

Another option is to use a TI83 or TI84 calculator.

Press the button labeled "2nd" in the top left corner. Then press the VARS key. Scroll down to "normalcdf"

The template is

normalcdf(L, U, mu, sigma)

The mu and sigma values aren't anything new here. But the L and U are. In this case L = 620 is the lower boundary and technically there isn't an upper boundary since it's infinity. Unfortunately the calculator wants a number here, so we just pick something very large. You could go for U = 99999 as the stand in for "infinity". The key is to make sure it's more than 3 standard deviations away from the mean.  

So if you were to type in [tex]\text{normalcdf(620,99999,500,100)}[/tex] then the calculator will display roughly 0.11507, which is in line with the other answers mentioned earlier.

As you can see, there are many options to pick from. Searching out "normal distribution calculator" or "z calculator" will yield many free options. Feel free to pick your favorite.

Given

AD = 6.4

BD = 3.6

Find

AC,BC and DC

Explanation

Using Pythogoras theorem in triangle ADC

Using PT in triangle BDC

Adding equation (1) and (2)

Using PT in triangle ABC

Equating above 2 equations

Putting this value of DC in equation (2)

Final Answer

AC = 8

BC = 6

DC = 4.8

Answer:

5x+3

Step-by-step explanation:

Three more than means we add 3

The product of 5 and a number means some number multiplied by 5 call it 5x

so three more than 5x is 5x+3.

Answer:

a. The total weight

b. 2 times the weight of Jet

c. The weight of Fido

d. The total weight

Explanation:

We know that Fido weighs 10 pounds more than Jet and together they weigh 46 pounds. So, if j represents Jet's weight, the bar model is:

Now, we can answer each part as:

a. 46 represents the total weight of the small dogs

b. 2j represents 2 times the weight of Jet

c. j + 10 represents the weight of Fido because its weight is the weight of Jet j added to 10.

d. 2j + 10 also represents the sum of the weights of the small dogs.

So, the answers are:

a. The total weight

b. 2 times the weight of Jet

c. The weight of Fido

d. The total weight

Answer

Initial animal population, P₀ = 25,000

1. Rate of change = 15% = 0.15

2. Animal left in 10 years?

To calculate the animals left in 10 years, we use the formula:

P(t) = P₀ (1 - r)^t in t years

t = 10, P₀ = 25,000, r = 15% = 0.15)

P₍₁₀₎ = 25000 (1 - 0.15)¹⁰

P₍₁₀₎ = 25000 (0.85)¹⁰

P₍₁₀₎ = 25000 (0.1969)

P₍₁₀₎ = 4922.50

Therefore, 4922.50 animals will be left in 10 years.

Question:

Solution:

Answer:

Step-by-step explanation:

one dollar of the first day = 3^0

three dollars on the second day = 3^1

nine dollars on the third day = 3^2

twenty-seven dollars on the fourth day = 3^3

Numbers increase 3 times a day, it is an exponential function, powers of 3

The function is going to be:

In order to calculate the area of the triangle, given the length of its three sides, we can use Heron's formula:

Where p is the semi-perimeter.

So, calculating the value of p and then the area of the triangle, we have:

Rounding to the nearest square foot, the area is 170 ft².

we are asked to determine the area of a circle with a diameter of 6 cm. To do that we will use the following formula for the area of a circle:

Replacing the value of the radius:

Replacing the value of pi:

Solving the operations: