1) Is F increasing on the interval (2.10)? 2) List the interval(s) on which F is increasing. Justify your answer. 3) List the intervalis) on which F is decreasing Justify your answer. 4)List the value(s) of x at which has a local maximum. Justify your answer.5) List the value(s) of x at which F has a local minimum. Justify your answer. 6) Find the X -intercepts 7) Find the Y-intercepts.

D= {m, n, p, q}

E= {3,6,8}

a) D x E = { (m, 3), (m, 6), (m, 8), (n, 3), (n,6), (n,8), (p, 3), (p, 6), (p, 8), (q, 3), (q, 6),

(q, 8) }

b) We need to know what a proper subset is.

Proper subset

A proper subset of a set A is a subset of A that is not equal to A. In other words, if B is a proper subset of A, then all elements of B are in A but A contains at least one element that is not in B.

From the above definition, we can say R is a proper subset of D x E because there are element in D x E that is NOT in R.

Given:

Number of sides in octagon = 8

Length of apothem = 14.1

Side length = 11.7

Required: Area

Explanation:

The area of a regular polygon is one-half the product of its apothem and its perimeter.

Here, the area of the regular octagon is

Final Answer: Area of the regular octagon is 659.88 square units.

We have to graph the solution set for the inequality:

The first step is to graph the function that divides the solution region from the other region. This line correspond to the equality within this inequality:

If we rearrange it we can find two points to graph it:

When x=0, then y is:

Then, the y-intercept is at y=3.

When y=0, then x is:

Now we now that the x-intercept is at x=9/2.

We have two points from the line, so we can graph it as:

Now, we know the line that limits the solution region.

As the inequality includes the equal sign, we know that this limit is included in the solution region.

The only thing left is to find is if the solution region is above this line or if it is below.

One easy way to test it is to select a point from one of the regions and replace (x,y) in the inequality: if the inequality stands true, then this point is in the solution region and we then now on which side the solution region is.

In this case, we can test with point (0,0) to make it easier:

As the inequality is true for this point, we know that the solution region includes (0,0).

Then, we know that the solution region is below the line.

We then can graph it as:

The mean absolute deviation is given by:

where xi represent each data, x bar the mean and n the number of data we have. Then:

Therefore the mean absolute value is 2 and the answer is C.

The half-life of a radioactive substance is given 3 hours.

Given the initial amount of substance is 800 grams. After 3 hours, the substance becomes half that is 400 grams. Then again after 3 more hours, the substance becomes half again that is 200 grams. Again after three hours, the substance becomes half that is 100 grams.

Thus, the amount of radioactive material after 9 hours is 100 grams.

dentify the percentage of change and increase or decrease 75 people to 25 people increase or decrease find the percent of change round to the nearest tenth of a percent ​

we have that

75 people represent the 100 % so

Applying proportion, find out how much percentage represent the difference (75-25=50)

so

100/75=x/50

solve for x

x=(100/75)*50

x=66.7 %

therefore

The given expression is

We will use the rule

Since 81 = 3 x 3 x 3 x 3, then

We will use the rule

Given:

The polynomial is

Required:

Find the zeros. Then determine the multiplicity at each zero and state whether the graph displays the behavior of a touch or a cross at each intercept.

Explanation:

The zeros of polynomial are

Now,

So, graph is crossing at -0.5

Answer:

Hence, fourth option is correct.

Solution

- The illustration described can be sketched as follows:

- From the above diagram, we can observe that the ramp forms a right-angled triangle with the ground.

- The Opposite of the triangle is 2.8 feet, the angle made by the ramp with the ground is 5 degrees., whilethe length of the ramp is labeled as x.

- Thus, we can apply SOHCAHTOA to find the value of x as follows:

Final Answer

The length of the ramp is 10.82 feet

The fraction given is 2/6.

The first five multiples of the denominator are as follows;

The other fraction is 7/10.

The first five multiples of the denominator are as follows;

Basically, you simply multiply the denominator by any series of numbers, in this case from 1 to 5. Therefore you'll have

6 x 1 = 6, 6 x 2 = 12, and so on. The same principle applies to the other denominator, that is 10.

we have

6x^3+ 23x^2 - 6x -8 : (3x-2)

step 1

Verify if (3x-2) represents a factor

If (3x-2) is a factor

then

3x-2=0 ------> x=2/3

Substitute the value of x=2/3 in the given expression

6(2/3)^3+23(2/3)^2-6(2/3)-8

6(8/27)+23(4/9)-4-8

(16/9)+(92/9)-12

12-12=0

that means

(3x-2) is a zero of the given function

therefore

Given the linear function:

y = ax + b

And it undergoes a horizontal shift of 5 units

Let the original line be f(x) and the new line be g(x)

g(x) = f(x - 5)

The vertical change will be the horizontal change times a, using the definition of slope.

Thus, since the horizontal change here is 5 units, the vertical change is 5a units

ANSWER:

E) a vertical change of 5a units

Answer:

4 g / cm^2

Explanation:

The density is defined is

where m is the mass of the object and V is its volume.

Now in our case, we see that the cube weighs M = 240 g and has a volume of

With the value of M and V in hand, we now calculate the density

which is our answer!

SOLUTION:

We are to show that the given polynomial function has a real zero between the numbers given.

At x = -2, we substitute -2 for x in the given function;

At x = -1, we substitute -1 for x in the given function;

CONCLUSION:

Since the function f went from -72 to +3 over the interval of -2 to -1, that means it must have passed through zero.

Given that

Given that AB = 12, BC =18, AC =24 and RS =16, RT=x

We now use the ratio of the corresponding sides to find side RT( the value of x).

Hence,

Therefore, the value of x (RT) is 32

Perimeter of a plane shape is the sum of all lenth of side of outer boundary.

Perimeter = 110cm

perimeter = 8.6 + 34.6 + 8.6 + 17.3 + 11.6 + 11.6 + 11.6 + x

110 = 103.9 + x

x = 110 - 103.9

x = 6.1cm

To solve this problem we need to create an equation, where the unkown variable, x, represents the cost for the love seat. We know that the sofa costs $75 less than the love seat, therefore we have:

The cost for both pieces of furniture together is equal to $600. So if we add them we have:

We can swap the expression for y on the second equation.

Now we know that the love seat costs $337.5. We will use the first equation to find the cost of the sofa.

The sofa costs $262.5.

Given: A function-

Required: To determine the absolute maxima and minima of the function.

Explanation: The given function is-

Differentiating the function,

Setting f'(x)=0 gives-

So we have to check the function at the boundary points of the interval [-5,1] and x=0 as follows-

Hence, the absolute maximum is 5 at x=o, and the minimum is -95 at x=-5.

Final Answer: The absolute maximum value is 5, and this occurs at x=0.

The absolute minimum value is -95, and this occurs at x=-5.

The polynomials are classified as shown in the image below

The quadrilateral is a parallelogram (the opposite sides are parallel and equal)

The total number of coins in the wallet, is:

Since there are 8 nickels and 4 pennies, there are 12 coins which are either nickels or pennies. Then, the probability of picking a nicle or a penny, is:

Multiply 3/5 by 240 to find the expected amount of times that a nicke or penny will be drawn:

18.92 pounds of peanut and 25.08 pounds of nut shack should be used to make the mixture

the cost per pound for the nut shack = $6.80

let the amount of pounds of nut shack used in the mixture = n

the cost per pound for the peanuts = $4.80

let the amount of pounds for the peanuts used in the mixture = p

We want to obtain 44 pounds of mixture which sells for $5.94 per pound

sum of pounds mixture = 44

amount of pounds of nut shack used in the mixture + amount of pounds for the peanuts used in the mixture = 44

cost per pound for the nut shack (amount used) + cost per pound for the peanuts (amount used) = cost per pound of the mixture (amount of mixture)

6.80(n) + 4.80(p) = 5.94(44)

using substitution method:

from equation 1, we can make n the subject of formula

n = 44 - p

substitute for n in equation (2):

substitute for p in equation 1:

18.92 pounds of peanut and 25.08 pounds of nut shack should be used to make the mixture

Answer:

The missing side length is 56

Step-by-step explanation:

1680 = 1/2 · (64 + x) · 28

1680 · 2 = 28 · (64 + x)

3360 = 1792 + 28x

28x = 3360 - 1792

28x = 1568

x = 1568 ÷ 28

x = 56

Hope this helps.

A parallelogram is a quadilateral that has two pairs of parallel sides. The opposite sides of a parallelogram are equal.

Given the points:

Q(-1,3), R(3,0), and S(-2,-1)

a) When placed in quadrant I, let's find the point T that forms a parallellogram.

Here the distance QS and RT must be equal.

Use the distance formula:

The point of T that forms a parallellogram when placed in quadrant I is:

T(4, 4)

From point R

b) When placed in Quadrant II, let's find the point T that forms a parallellogram.

We have:

T(-6, 2)

From point Q, make a movement 5 units left and 1 unit down

The point of T that forms a parallellogram when placed in quadrant II is:

T(-6, 2)

c) When placed in quadrant IV, let's find the point T that forms a parallelogram.

We have:

T(2, -4)

From point R, make a movement of down 4 units and left 1 unit.

The point of T, that forms a parallelogram when placed in quadrant IV is:

T(2, -4)

ANSWER:

a) (4, 4)

b) (-6, 2)

c) (2, -4)

Step 1:

When we multiply a function by a positive constant, we get a function whose graph is stretched or compressed vertically in relation to the graph of the original function. If the constant is greater than 1, we get a vertical stretch; if the constant is between 0 and 1, we get a vertical compression.

Step 2

Parent function y = f(x)

In general, a vertical stretch is given by the equation

y=bf(x). If b>1, the graph stretches with respect to the y-axis, or vertically. If b<1, the graph shrinks with respect to the y-axis.

The function becomes y = 1.4f(x) when trainsform vertically

The function is shifted 3 units to the left and it becomes y = 1.4f(x + 3)

Final answer

y = 1.4f(x + 3)

Answer:

I'm assuming this is a greatest to least, but in case it was not, I put least to greatest, too.

Step-by-step explanation:

Greatest to least:

6/5, 8/9, 0.5, 40%

Least to greatest:

40%, 0.5, 8/9, 6/5

Hope this helps!

1) Consider that the 1st Quartile corresponds to 25%, the Median is equivalent to 50% of the data, the Third Quartile to 75% of the data as the sketch below:

Notice that the Median is that bar inside the box, also known as the 2nd Quartile.

2) So the percentage of the data greater than the median is:

SOLUTION

We have been given the height of each lateral triangular face of the roof h as 13.4 ft and the length of the square base of the pyramid as 21.5 feet

We want to know if the area of the square base is the same as the area of each triangular lateral face

Area of the square base is

Area of the four triangular lateral face becomes

From our calculations, the area of the square base is 462.25 square-feet,

While the area of the four lateral face triangle of the roof is 576.2 square-feet

Hence the roofer is incorrect

The given figure is of a rectangle which is enclosed in the large rectangle.

Area of rectangle = Length x Width

Dimension of large rectangle, 10 and 20.

Area of larger rectangle = 10 x 20

Area of larger rectangle = 200

Dimension of the small rectangle, 14 and 6.

Area of small rectangle = 14 x 6

Area of small rectangle = 84

Area of shaded region = Area of large rectangle - Area of small rectangle

Area of shaded region = 200 - 84

Area of shaded region = 116

Area of shaded region is 116 unit²