A building inspector needs to determine if two walls in a new house are built at right angles, as the buildingcode requires. He measure and find the following information. Wall 1 measures 12 feet, wall 2 measures 14feet, and the distance from the end of wall 1 to the end of wall 2 measures 18 feet. Do the walls meet at rightangles? Explain

Given:

The function

Required:

State where the inflection points, critical points, concave up and down points.

Explanation:

Inflection points are points where the function changes concavity, i.e. from being "concave up" to being "concave down" or vice versa.

A graph is said to be concave up at a point if the tangent line to the graph at that point lies below the graph in the vicinity of the point and concave down at a point if the tangent line lies above the graph in the vicinity of the point.

A critical point is a point in the domain of the function where the function is either not differentiable or the derivative is equal to zero.

The graph is

Now,

Answer:

answered the question.

Polynomial:

Factored form:

a) The digits and letters of the pasword can not be repeated, then, to determine the number of uniques passwords you use the following formula:

Given:

he needs 33 feet of bordertrim for the living room, 27 feet of border trim for the bedroom, and 39 feet of border trim for thedining room.

Required:

How many yards of border trim does she need?

She needsyards of border trim.

Explanation:

The first step to determine the total sum of border trims in feet

33 feet+27 feet+ 39 feet=99feet

Next step is to convert feet into yard

Required answer:

32.99 yards (approx)

The question only supplied us with the mass of the new baby which is:

This mass is too bizzarre & unrealistic for

(6x-6)²

The correct option is fourth option

Explanations:

From the data, re-arranging in ascending order, the median of the data is 58.

The upper quartile is 62, while the lower quartile is 54

From the options, only the 4th options represent a box plot of median 58, upper quartile of 62 and lower quartile of 54. This makes it the correct option

Let x be how much student pays for one hour to use the telescope

Let y be how much student pays for one hour to use the supercomputer.

Equation for student 1:

Equation for student 2:

Use both equations above as a system of equations to solve x:

1. Solve y in the equation for student 1:

2. Substitute the y in the second equation by the value you get in step 1:

3. Solve x:

Elias is 6 years older than Marcos

This can be interpreted as: e = m + 6

Together they are 42 years old

This can be interpreted as: e + m = 42

The answer is

e = m + 6

e + m = 42

Solving the equations, we have

e = m + 6

e + m = 42

Substitute e = m + 6 into the second equation

m + 6 + m = 42

2m + 6 = 42

2m=42-6

2m = 36

m=36/2

m=18

Substitute m = 18 into the first equation

e = m + 6

e = 18 + 6

e = 24

Given data

Subject: Find the equation of the parabola after the change.

We know the graph of the parabola.

Ifrom the given graph it can be seen that is is shifted right side.

So the equation for the given graph,

When we shift the parabola right hand side, the equation is given as,

The graph of y = (x-k)^2+h is the resulting of shifting the graph of y = x^2.

here, k is the unit to the righ hand and h is units up.

From the given graph we can observe that the y = x^2 graph is shifting or translated in the right hand side and it is alos shifted up.

We can compare the given equation with equation (1).

Therefore, the correct option is (B).

The formula for time is: T (period) = 1 / f (frequency)

We have two functions, f(x) and g(x) and we have to find (f/g)(x).

Let h(x) = (f/g)(x).

We can write it like this:

(f/g)(x) is defined for all x but g(x)=0.

We can find the values of x for which (f/g) is not defined as:

So we can conclude that (f/g)(x) is defined for all real numbers.

Answer: (f/g)(x) = (-10x^3+12x^2-6x+7)/(14x^2+1)

Explanation

We can find how much larger is the first coin than the second coin by finding the difference between the areas of the two coins.

The area is given as;

Therefore,

Answer

Therefore the first coin is bigger than the second by

Solution

The room had 5 green tables, 11 yellow tables, 12 blue tables, and 7 purple tables.

Probability that the first person to enter the room will be randomly seated at a yellow table

Hence the correct answer is 11/35

According to the given data we have the following data set:

3, 9, 12, 4, 6, 40, 25, 14, 10​

The first quartile, Q1, is the median of the lower half not including Q2

Therefore, in this case the Q1 would be 5

Solution:

From the graph;

The line passes through the points

To find the equation of a straight line, the formula is

Substituting the values of the coordinates into the formula above

Hence, the equation of the line is

Option B

The number of gallons can be determined as,

Thus, the number of gallons is 25.

So,

First of all, remember that two lines are parallel when their slopes are equal.

We want to find an equation of the line passing through the point (-6,7) that is parallel to the line:

For this, first remember that any line has the following main form:

Where "m" is the slope and "b" is the y-intercept.

Given that the line that we want to find is parallel, its slope is 1/3.

So, what we're going to do is to replace the point (x,y) = (-6,7) and the slope m = 1/3 in the main equation to find the value of b and then replace.

This is:

Therefore, the equation is:

Solution

8th percentile

N=14

Now we need to arrange the data from the smallest to the biggest

(Ascending order)

17, 21, 38, 46, 54, 61, 61, 66, 68, 70, 79, 81, 82, 82

Therefore, the 8th percentile is 21

This means that approximately 8% of the data lies below 21 when the data are ranked

Part B

74th percentile

N= 14

Therefore, the 74th percentile is 79

This means that approximately 74% of the data lies below 79 when the data are ranked

Equation of the line

The equation of the line in slope-intercept form is:

y = mx + b

Where m is the slope and b is the y-intercept.

We are given the slope of a line m=2 and the y-intercept b=5.

Substituting:

y = 2x + 5

This is the required equation for the line

Answer:

Explanation:

25 students share a class set of 100 markers.

However, 5 students were absent, thus:

20 students shared 100 makers.

INFORMATION:

We have the next expression:

And, we must:

a.) Convert the exponential function below to its corresponding logarithmic function

b.) Write the log form from Part A into the expanded log form

STEP BY STEP EXPLANATION:

a.) To convert it to its corresponding logarithmic function, we must use the next

In our case,

Now, replacing in the formula

b.) To write the expanded log form of part A, we must use the properties of log

1. We can separate the multiplications using the first property

2. We can delete the exponent of the logarithms using the third property

ANSWER:

a.) The logarithmic function would be:

b.) The expanded log form would be:

Explanation

Step 1

remember

then

Step 2

make the multiplication:

To multiply decimals, first multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor. Finally, put the same number of digits behind the decimal in the product.

so

I hope this helps you

Let:

x = Investment in the first year

y = Investment in the second year

Since connor had 91.00 to invest:

Using the simple interest formula:

For 16%:

For 14%:

After one year, the total interest earned was $13.74. so:

So:

From (1):

Replace (3) into (2):

Replace the value of y into (3):

He invested $50 at 16% and $41 at 14%

Explanation:

The total number of people on the table is given below as

Step 1:

The probability that a class attendee is a member of the gym and is attending a Boot Camp class is given below as

Step 2:

The probability of non-member of the gym and is attending a yoga class

Hence,

The probability that a class attendee is a member of the gym and is attending a Boot Camp class or non-member of the gym and is attending a yoga class will be

Hence,

The final answer is

We know that KLMN is a parallelogram

Parallelograms have the following properties (to highlight a few):

I. Opposite sides are congruent (same) i.e. KN = LMN

II. Opposite angles are congruent (same) i.e. K = M & L = N

III. Consecutive angles are supplementary (they add up to 180 degrees) i.e. N + K = 180 degrees & L + M = 180 degrees

Therefore, N & K are supplementary angles

To find:

Convert each degree measure to radian measure.

Solution:

It is known that to convert a degree measure to radian measure, we have to multiply the value by pi/180. So, the answers are as follows:

(a, b) = (-4, -1)

Given that:

We have:

Therefore, we say a = -4, b = -1

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

Length = 1300 mm = 1.3 m, Width = 900 mm = 0.9 m

The area of a rectangle is given by:

To obtain the relationship between x and y, the following steps are advised:

Step 1: Starting with the values in table 1, divide the values of y by the corresponding values of x, as follows:

Since the value of the ratio of y to x is not constant (ranging from 4, to 5, and to 6), it means that x and y are NOT proportional.

Therefore, for Table 1, x and y are NOT proportional

Step 2: Proceeding with the values in table 2, divide the values of y by the corresponding values of x, as follows:

Since the value of the ratio of y to x is constant ( 3, all through), it means that x and y are proportional.

Therefore, for Table 2, x and y are proportional

Thus: y is 3 times x, for table 2