A student graphed f(x)=x and g(x)= f(x)-8 on the same coordinate grid. Which statement best describes how the graph of f and g are related?

The slope equation is given by:

To get the slope of the graph, we will pick two points along the line:

Let's pick the first point at (x, y) = (-6, 6)

Let's pick the second point at (x, y) = (0, -2)

We plug this into the slope equation, we have:

The slope (m) = -4/3

GIVEN:

We are given that IQ scores have a bell shaped distribution with a mean of 96 and a standard deviation of 17.

Required;

Using the emperical rule, what percentage of IQ scores are no more than 79?

Step-by-step explanation;

For a bell-shaped distribution, we already know that,

68% of the data set lies within one standard deviation

95% of the data set lies within two standard deviations

99.7% of the data set lies within three standard deviations

The condition given is that the IQ scores are no more than 79, hence;

Now we can see that the IQ score of 79 is 1 standard deviation to the left of the mean (that is to the left of 96).

We also take note that 68% of the data set lies within one standard deviation on either side of the mean.

Therefore, for the IQ scores to be 1 standard deviation from the mean, we would have;

Expressed as a percentage, we now have

ANSWER:

Therefore, 1.6% of IQ scores would be no more than 79.

Answer:

C. (2 x 50) + (2 x 25)

Explanation:

We are asked to give another form of the expression given.

Expanding the expression 2x(25+50) gives

Which matches the expression given in choice C; therefore C is the correct answer.

If Apple had their iphones on sale for 20% off during labor day weekend and the original cost of iphone is 345.00, the discount on the price during the labour weeked will be expressed as;

20% of 345

20/100 * 345

2/10 * 345

= 690/10

= 69.00

If there is a discount of 69.00 on the iphone price, the amount you would pay during labor day weekend will be 345.00-69.00 = 276.00

The correct answer is 276.000/100

The first step is to rotate point A(- 6, 8) 90 degrees counterclockwise. If a point, (x, y) is rotated 90 degrees counterclockwise, the new coordinate woule be (- y, x)

For point A, x = - 6, y = 8

Rotating point A 90 degrees counterclockwise, the new coordinate is

(- 8, - 6)

The next step is to reflect this point across the x axis. If a point is reflected across the x axis, the sign of the x coordinate remains the same while the sign of the y coordinate reverses. Thus, (x, y) becomes (x, - y)

Thus, the new coordinate of (- 8, - 6) after a reflection over the x axis is

A' = (- 8, - - 6)

A' = (- 8, 6)

The correct option is the third one

Given data:

Mean: 84 lb

Standard deviation: 12lb

Find % of hippos born weighing 25 poind or less.

1. Find the z-score corresponding to x=25:

2. Use a z-table to find the probability of x less or equal to 25 (z-score -4.92):

For a z-score of -3.50 or less the corresponding value is 0.0001

3. Multiply by 100 the value you get in step 2 to get the percentage:

The ratio of t shirts and shorts to sunglasses is, (t-shirts + shorts) : sunglasses

We have 25 t-shirts and 15 shorts, total 40 t-shirts and shorts. And 10 sunglasses.Then the ratio is:

4 t-shirts and shorts per 1 sunglass

Answer: B. 4 to 1

To find the height of a isosceles triangle having the angle between the equal sides and the opposite side of it use the next properties:

The line that describes the height of an isosceles triangle is a bisector of angle between equal sides, and also a bisector of opposite side (different side).

Using the right triangle formed and the next trigonometric ratio find h:

solve h:

Computing the last difference, we have:

Tin the last step, we have the difference:

Answer

From the picture above, we see that:

• mark obtains ,59,,

• the quotient is ,3x - 11,,

• and the remainder is ,59,,

• the answer to this long division is ,3x - 11 + 59/(2x+5)

Let n be the number of student in the class. Since there are 4 teams with 7 students per team, we can write this statements as

then, by moving 4 to the right hand side, we have

then, the total number of students is n=

In order to find the slope of the a line that connects the given points, use the following formula:

where (x1,y1) and (x2,y2) are the given points.

Replace the following coordinates in the formula for m:

(x1,y1) = (5,-1)

(x2,y2) = (8,-6)

Hence, the slope is -5/3

If ABCD is a rectangle, each of its four angles at the vertex is a right angle.

Then the angle at D is a right angle (measure of 90 degrees).

The right angle is divided in two angles, <1 and <2, by the diagonal, so <1 and <2 are complementary.

Then, we can write:

Then, with the value of x we can calculate m<1 and m<2:

Answer:

x = 7

m<1 = 35º

m<2 = 55º

SOLUTION

We want to draw the graph of

The graph is shown below

Domain of the function.

The domain is determined from the x-axis. The function is defined for all values of x, hence the domain is negative infinity to positive infinity.

The domain in interval notation is

The Range of the funtion.

The range is determined from the y-axis. Looking at the graph, the graph has a horizontal asymptote drawn at y = - 1, and the y-values run below and does not exceed this -1, telling us it is between negative 1 and negative infinity.

Hence the range in interval notation is

To calculate the variance in this case, we need to use the variance for a discrete variable and its probability.

The equation we need to use in this case is:

Where x_i is each value in the first row and P(x_i) is each value in the second row.

First, let's calculate each square difference:

Now, we need to multiply each for its corresponding P(x):

Finally, we sum them all to get the variance:

So, the variance to one decimal place is 2.4.

The volume of the new structure is given by:

Therefore, the dimensions of block D must be given by:

ANSWER

The cost of apples is a function of their weight.

EXPLANATION

On the cartesian plane, the horizontal axis is the x-axis and the vertical axis is the y-axis.

The values on the y-axis are the values of the dependent variable while the values on the x-axis are the values of the independent variable.

This implies that, generally, for a function, y is a function of x.

Therefore, the cost of apples is a function of their weight.

From the statement, we know that the road:

• rises Δy = 6 m,

• over a distance Δx = 80 m.

The slope of the road (m) and gradient angle (θ) are given by:

Replacing the data of the problem, we get:

The gradient angle of the road is approximately 4.289°.

As mentioned in the question, Line a and Line b are parallel to each other and these two lines are cut by the transversal line c.

Since line b is cut by the transversal line c forming the angles measuring 64° and y°, these angles are called linear pairs. The sum of the angles of a linear pair is 180°. Hence, we can say that:

From that equation, we can solve for the value of y.

Therefore, the value of y is 116°.

On the other hand, angle x and angle y are what we call alternating exterior angles. By definition, alternating exterior angles are congruent. Hence, the value of x is also 116°.

Why are x and y alternating exterior angles? X and Y are alternating exterior angles because first, they are angles found outside lines a and b, hence, the word exterior. Also, angles x and y do not lie on the same side of the transversal. Hence, the word alternating.

ANSWER

r = -0.8 or 2

EXPLANATION

We have the absolute value equation:

3 |3 - 5r| - 3 = 18

First, let us isolate the absolute value:

3 |3 - 5r| = 18 + 3

3 |3 - 5r| = 21

Divide through by 3:

|3 - 5r| = 21 / 3

|3 - 5r| = 7

An aboslute value equation can have two meanings, it could mean that the value in the absolute value function is positive or negative.

That means that we can split the function as follows:

3 - 5r = 7 or 3 - 5r = -7

Collect like terms:

-5r = 7 - 3 or -5r = -7 - 3

-5r = 4 or -5r = -10

Divide through by -5:

r = 4 / -5 or r = -10 / -5

r = -0.8 or 2

That is the value of r.

Given the function:

Let's find the zeros of the function.

To find the zeros of the function, take the following steps.

Step 1:

Set the function to zero

Step 2:

Factor the left side of the equation

Factor x out:

Now factor using the AC method:

We have the factors:

x, x+2, x+4

Step 3:

Equate the individual factors to zero.

Thus, we have:

Step 4:

Solve each equation for x to get the zeros

• x = 0

• x + 2 = 0

Subtract 2 from both sides:

x + 2 - 2 = 0 - 2

x = -2

• x + 4 = 0

Subtract 4 from both sides:

x + 4 - 4 = 0 - 4

x = -4

Therefore, the zeros of the function are:

x = 0, -2, -4

ANSWER:

The Solution.

Representing the problem in a diagram, we have

The rectangular window has two diagonals, and both diagonals are equal in length. If the length of one of them is 15 feet (as stated in theHence, the length of the

Time taken by Nina to complete the chapter = was 6 hours.

Amount of chapter completed in 1 hour = 1/6.

Mandy takes the time to complete the chapter = 2 hours.

Amount of chapter completed in 1 hour = 1/2.

Amount of chapters completed by both in 1 hour is calculated as,

Thus the amount of time taken by both of them to complete the chapter is

We will have that the initial diameter will be:

So, the initial diameter has to be 19/32 inches.

We can translate a function on its two axis. If we want to translate it on the vertical axis we need to add or subtract the constant that determines the translation by the end of the function, as seen below:

If the constant is positive, then the function will be translated up, if its negative it'll be translated down.

We can also shift the function on its horizontal axis. To do that we have to add a constant in the argument of the function as seen below:

If the constant is negative, the shift will happen on the right direction. If the constant is positve, the shift will be on the left direction.

The function given to us is:

This falls on the second type of translation and the constant is negative, therefore there is a shift to the right by 4 units. The correct answer is b.

order to determine the rate of change of the given function, use the following formula:

m = (y2 - y1)/(x2 - x1)

where (x1,y1) and (x2,y2) are any two points of the line.

Use, for example:

(x1,y1) = (0,250)

(x2,y2) = (20,500)

replace the previous values of the coordinates into the expression for m:

m = (500 - 250)/(20 - 0)

m = 250/20

m = 12.5

Hence, the correctstament is:

C. After her raise, Natasha makes $12.50 an hour.

Two values of y will be y = 4.7 and y = 3.7

a. First we will take equation 1 that is

x - 9y = 10

x = 10 + 9y

from here we get x as 10 + 9y and now we will put it in equation 2 which is

3[tex]y^{2}[/tex] = 4x + 7

3[tex]y^{2}[/tex] = 4 ( 10 + 9y ) + 7

3[tex]y^{2}[/tex] = 40 + 36y + 7

3[tex]y^{2}[/tex] - 36y - 47 = 0

Here we can clearly see that  3[tex]y^{2}[/tex] - 36y - 47 = 0

b. Formula of finding roots of a quadratic equation is

y = ( -b ± [tex]\sqrt{b^{2} - 4ac}[/tex] ) / 2a

Put value of b , a and c in the formula.

b = -3

a = 3

c = -47

y = ( 3 ± [tex]\sqrt{9^{2} - 4 * 3 * 47 }[/tex] ) / 2 * 3

By solving this we get

y = ( 3 + 25.4 ) / 6               and               y = ( 3 - 25.4 ) / 6

Therefore two values of y will be y = 4.7 and y = 3.7

To know more about quadratic equations

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ANSWER

EXPLANATION

We want to factor the expression given:

To do this, we use the difference of two squares method:

Therefore, we have:

That is the answer.

Arithmetic Sequence

In an arithmetic sequence, each term can be obtained as the sum of the previous term plus a fixed number, called the common difference.

To find if this is an arithmetic sequence, we subtract every consecutive term. If the result is constant, we have a common difference.

Let's subtract the second term minus the first term:

d = 2/4 - 1/4 = 1/4

Let's subtract the third term minus the second term:

d = 3/4 - 2/4 = 1/4

Let's subtract the fourth term minus the third term:

d = 4/4 - 3/4 = 1/4

Now we are sure this is an arithmetic sequence. The formula for the nth term of an arithmetic sequence is:

an = a1 + (n-1) d

Substituting:

Thus, the general term is

an = n/4

To calculate the next term, we set n=5:

a5 = 5/4

Summarizing:

Rule: an = n/4

Next term: 5/4

Multiplying 9/8 and the first equation we get:

Adding the above equation and the second equation of the system we get:

Adding like terms, we get:

Therefore:

Subtituting x=1 in the first equation, we get:

Solving the above equation for y, we get:

Answer:

In order to determine the probability of generating 25938 in exact order, let's determine first how many ways can we generate 5-digit numbers from 1 - 9.

So, for our first number, we have 9 numbers to choose from.

For our second number, we only have 8 numbers to choose from since digits cannot be repeated.

For our third number, we only have 7 numbers to choose from.

For our 4th number, we now have 6 numbers only available

Lastly, for our 5th number, only 5 numbers are available.

So, there are 15, 120 ways of generating 5-digit numbers out from 1-9 without digits being repeated. Out of these 15,120 ways, only one is 25938.

Hence, the probability that a randomly generated number is 25938 is:

or in decimal form,

or in percent form.