Use a graphing utility to graph the function and to approximate any relative minimum or relative maximum values of the function. (Round your answers to the nearest integer. If an answer does notexist, enter DNE.)

Answer:

125 teachers

Explanation:

We were given that:

20% of teachers teach advanced writing skills = 20/100 = 0.2

Number of writing teachers = 25

The total number of teachers = x

We will obtain the number of teachers in the school as shown below:

Hence, the total number of teachers in the school is 125

Inequalities are expressions that refer to non-equivalent quantities. Inequalities can express less than, more than, less than or equal to, more than or equal to.

The type of inequalities and symbols are:

So, there are four types of inequalities, for example:

Each inequality is different from the other, this means that the symbol used represents a type of inequality.

At last, among the choices, the inequalities are

However, variable inequalities mean that the inequalities must have a variable in it. So, they are:

Therefore, the variable inequalities are b, c, and d.

Let x be the rate of water output by the Thompson family and let y be the rate of water output by the Kim family.

We know that the Thompson family sprinkler was used for 25 hours, Kim's family sprinkler was used for 35 hours and that there was a combined total output of 1075 L of water; then we have the equation:

We also know that the combined water output was 35 L per hour, then:

Hence we have the system of equations:

To solve this system we solve the second equation for y:

And we plug this value in the first equation and solve for x:

Once we have the value of x we plug it in the expression of y:

Therefore we have that:

which means:

Thompson family's sprinkler: 15 L per hour

Kim family's sprinkler: 20 L per hour.

Considering the expression 6+(x+3)^2. the table of at least SIX different values of the expression is

x               y

0            15

1             22

2            31

3            42

4            55

5            70

The table is completed by substituting the values of x in the given expression as follows

6 + (  x + 3 )^2

for x = 0, y = 6 + ( 0 + 3) ^2 = 15

for x = 1, y = 6 + ( 1 + 3) ^2 = 22

for x = 2, y = 6 + ( 2 + 3) ^2 = 31

for x = 3, y = 6 + ( 3 + 3) ^2 = 42

for x = 4, y = 6 + ( 4 + 3) ^2 = 55

for x = 5, y = 6 + ( 5 + 3) ^2 = 70

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We will determine the density of the rock as follows:

So, the density of the rock is 7 g/cm^3.

Answer:

Explanation:

Here, we want to know the amount of water the bucket can hold when full

Let us have the volume as x liters

Mathematically:

Given:

Logarithmic expressions in options.

Required:

Select correct calculated option.

Explanation:

1). ln 1 = 0

2).

3)

4).

5).

Answer:

Hence, option A and E are correct.

The ratio 4 : 5 means that in every 9 liters of oil, we will have 4L of synthetic oil and 5L of natural oil.

Divide the 531 by 9 to get how many times we have to amplify the ratio:

Multiply the ratio by 59:

Meaning that for the 531L of oil, 236L would be synthetic and 295L natural.

Answer: 236 Liters.

Given:

The objective is to find the shortest distance between house and library.

Consider the given triangle as,

Here, A represents the house, B the grocery and C the library.

Since it is a right angled triangle, the distance between the house and the library can be calculated using Pythagoras theorem.

Apply the given values in the above formula,

If Natasha walks through Grocery store,

By comparing the two ways, ACHence, the hypotenuse distance AC, between house and library is the closest distance.

Collect like terms

Equation of the line:

y = mx+b

where:

m= slope

b= y-intercept

First, we have to find the slope:

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

Since we have:

(x1,y1) = (8,7)

(x2,y2)= (0,0)

Replacing:

m = (0-7)/ (0-8) = -7/-8 = 7/8

Now, that we have the slope:

y = 7/8 x +b

We can place the point (8,7) in the equation and solve for b:

7 = 7/8 (8) +b

7=7 +b

7-7=b

b=0

Since the y-intercept=0

The final equation is:

y= 7/8x

So,

Let's remember that:

The three point postulate states that:

Through any three noncollinear points, there exists exactly one plane.

The Plane-Point Postulate states that:

A plane contains at least three noncollinear points.

As you can notice, the diagram illustrates that:

Given that a plane exists, then, there are three collinear points.

That's the three point postulate.

By formula,

Midpoint between two points PQ =

So, (-1,-4) (option 3)

Given

To Determine: The angle function

Solution

The information can be represented as shown below

From the diagram below

Remember that 3, 4 and 5 is a Pythagorean triple, since:

Since one side of the given right triangle has a length of 3 and the hypotenuse has a length of 5, then, the remaining leg b must have a length of 4.

Therefore:

The angles A and B can be found using trigonometric identities.

Remember that the sine of an angle equals the quotient of the lengths of the side opposite to it and the hypotenuse of the right triangle.

The side opposite to A has a length of 3 and the length of the side opposite to B is 4. Then:

Use the inverse sine function to find A and B:

Then, to the nearest tenth:

Therefore, the answers are:

A shortcut for a 90° counterclockwise rotation:

• If the point (h, k) is rotated 90° counterclockwise rotation, then the final point will be (-k, h).

Answer:

Therefore the coordinates would be:

• X,(-5, 3) → ,X',(-3, -5)

• Y,(-1, 1) → ,Y',(-1, -1)

• Z,(-8, -4) → ,Z',(4, -8)

Then, the rule is (x, y) → (-y, x).

Data Given:

Nurses = 1 1/2 of each doctor

This can be interpreted as

If there are 6 doctors in the day shift, then there will be

=>

This means that I will have to schedule 9 nurses for the day shift on Friday

The median of the given data set will be 35.

So, The variability metrics for each class are listed below:

The further classifications: Class A; Class B;

Greater variability in the data set is suggested by class B's wider interquartile range and mean absolute deviations.

Set A's median will be:

Therefore, the median of the given data set will be 35.

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The given situation can be written in an algebraic way:

Say x the width of the rectangle and y its height.

- The width of a rectangle is 8 inches less than its length:

x = y - 8

- The area of the rectangle is 9 square inches:

xy = 9

In order to find the values of y and x, you first replace the expression

x = y - 8 into the expression xy = 9, just as follow:

you apply distribution property, and order the equation in such a way that you obtain the general form of a quadratic equation:

Next, you use the quadratic formula to solve the previous equation for y:

here you have a = 1, b = -8 and c = 9. By replacing these values you obtain:

Hence, you have two solutions for y:

y1 = 4 + 5 = 9

y2 = 4 - 5 = -1

You select only the positive solution, because negative lengths do not exist in real life. Hence, you have y = 9.

Finally, you replace the value of y into the expression x = y - 8 to obtain x:

Hence, the width and length of the given recgtangle are:

width = 1 in

length = 9 in

The radius of cone is r = 6 cm.

The height of cone is h = 9 cm.

The formula for the volume of cone is,

Substitute the values in the formula to determine the volume of cone.

Thus, volume of cone is 339.3 cm^3.

SOLUTION

Now, we don't know the scores for his first three tests. But we are told that the average score for the first three tests was 80.

So, let the scores of the first three tests be a, b, and c. That means

Also, let's assume the total score for his first three tests was x, This means that

Comparing with the first equation it means that

Now we are asked "What must he score on his next test to raise his average to 84?"

So this means the total tests becomes 4. Hence

So he must score 96 to raise his average score to 84.

Hence, the answer is 96

In order to find the polar equation of the ellipse, first let's find the rectangular equation.

Since the directrix is a vertical line, the ellipse is horizontal, and the model equation is:

Where the center is located at (h, k), the directrix is x = -a/e and the eccentricity is e = c/a.

So, if the eccentricity is e = 1/5 and the directrix is x = -7, we have:

Now, let's calculate the value of b with the formula below:

Assuming h = 0 and k = 0, the rectangular equation is:

Now, to convert to polar form, we can do the following steps:

Another way of writing this equation in polar form is:

Where p is the distance between the focus and the directrix.

Since the foci are located at (±c, 0) = (±7/25, 0) and the directrix is x = -7, the distance is:

So the equation is:

Answer

Option B is correct.

SAS | 2 sides and the angle between them in one triangle are congruent to the 2 sides and the angle between them in the other triangle, then the triangles are congruent.

Explanation

We have been told that the two triangles have two sets of sides that are congruent to each other.

And we can see that the angle between those congruent sides for the two triangles is exactly the same for the two triangles.

So, it is easy to see that thes two triangles have 2 sides that are congruent and the angle between these two respective sides are also congruent.

Hope this Helps!!!

SOLUTION

Write out the formula

where A= apothem and P= perimeter of the regular polygon

The area of the regular polygon is

We have the next information

100 mg of menthol

every minute the amount of menthol in your body is cut in half

we have the next variables

x= minutes

y= amount of menthol in mg remaining in your body

so the equation that can we model is

then we have that It is safe to take a new cough drop after the level of menthol in your body is less than 5 mg

y= 5mg

in order to know the time we need to solve the equation above

then we isolate the x

after 5 minutes you can take another cough drop

Solution

Step 1

The volume of a triangular prism = Cross-sectional area x Length

Step 2

Step 3:

When 1 foot is added to each dimension of the prism.

The new dimensions becomes Base = 7, Height = 8 and length = 11

Step 4

Find the percent increase in volume

Final answer

46.7