Express the answer in terms of a natural logarithm. Y= (do not simplify)

SOLUTION

We want to tell the graph that represents the function

The graph of this function is shown below

Comparing this to what we have in the options,

we can see that the correct answer is option D

First, notice that the expression for f(f(x)) is the following:

notice that the first term is a quadratic expression with exponent 2. This means that f(f(x)) has 4 zeros.

Since f(x) has 2 zeros (since its quadratic), we have that M-m = 4-2 = 2, thus, M-m will never be 0, 1 or 3

ANSWER

The sphere is 10762 cubic centimeters bigger than the cube.

EXPLANATION

We want to find the difference in the volumes of the sphere and the cube.

To do this, we have to find the volumes of the sphere and cube and subtract that of the cube from the sphere.

The volume of a sphere is given as:

where r = radius

The radius of the sphere is 15 centimeters. Therefore, the volume of the sphere is:

The volume of a cube is given as:

where s = length of the side

The length of the side of the cube is 15 centimeters. Therefore, the volume of the cube is:

Therefore, the difference in the volumes of the sphere and cube is:

Therefore, the sphere is 10762 cubic centimeters bigger than the cube.

With the points (8. 4) (-6, -6) (-10, 12) (2,-4). What are the new points if the

scale factor of dilation is X?

we know that

The rule of the dilation of a point is equal to

(x,y) -------> (ax, ay)

with a scale factor a

so

In this problem

the scale factor is x

therefore

(8. 4) --------> (8x. 4x)

The answer is a donut.

A donut or Toroid is formed when you rotate an circle by a rotation axis displaced of the center of the circle.

Answer:

Step-by-step explanation:

donut

The polynomial that represents the rollercoaster, using the Factor Theorem, is given as follows:

y = 400(x - 1)²(x + 1)(x² + 0.1)(x + 5).

The Factor Theorem states that a polynomial function with zeros [tex]x_1, x_2, \codts, x_n[/tex], also represented by factors [tex]x - x_1, x - x_2, \cdots x - x_n[/tex] is given by the rule presented as follows:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient of the polynomial function with the given roots.

For this problem, the requirements are as follows:

The roots will be given as follows:

Hence the function is:

y = a(x - 1)²(x + 1)(x² + 0.1)(x + 5).

At x = 0, the function assumes a value of 250, hence the leading coefficient is obtained as follows:

0.5a = 200.

a = 400.

Thus the function is:

y = 400(x - 1)²(x + 1)(x² + 0.1)(x + 5).

Which has the desired features, as shown by the image at the end of the answer.

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we have the formula

substitute given values

Remember that

To divide complex numbers, multiply both the numerator and denominator by the conjugate of the denominator

the conjugate of the denominator is (-5-3i)

so

A) To do that we will draw a line inside the triangle that is perpendicular to the base as I have don above.

B) We will also do the same for B

This is a problem about combinations where the order doesn't matter. The solution is usually written as 7C2 (seven choose two) and has the value

Comment: 7C2 is the answer to the question "How many pairs (in our case, these pairs are seen as games played) can we form from a group of 7 things?".

We operate as follows:

The value of x is -3.

Given data:

The three numbers on the cards are 4, 5, 6.

The probability of picking an odd number and then picking an odd number is,

Thus, the probability of picking an odd number and then picking an odd number is 0.

Given:

Principal (P)=$200

Rate of interest (r) =4%

time (t)=30 years

Number of times compounded per year(n) = 12

Required- the amount.

Explanation:

First, we change the rate of interest in decimal by removing the "%" sign and dividing by 100 as:

Now, the formula for finding the amount is:

Put the given values in the formula, we get:

Solving further, we get:

Answer

The height of the trapezoid = 3 cm

Explanation

The area of a trapezoid is given as

Area = ½ (a + b) h

where

a and b = base lengths of the trapezoid

a = 9 cm

b = 7 cm

h = height of the trapezoid = ?

Area = 24 cm²

Area = ½ (a + b) h

24 = ½ (9 + 7) h

24 = ½ (16) h

24 = 8h

8h = 24

Divide both sides by 8

(8h/8) = (24/8)

h = 3 cm

Hope this Helps!!!

The given equation corresponds to a parabola:

The y-intercept of the parabola is the point when it crosses the y-axis, at this point x=0, to determine this value you have to replace the formula with x=0 and calculate the value of y:

Solve the exponent first, then the multiplication

The y-intercept for the given function is (0,-18)

Answer:

Statement 1. AB/DB = CB/EB

Reason 1: Given

Statement 2: ∠ABC = ∠BDE

Reason 2: Vertical angles

Statement 3: ∆ABC~∆DBE

Reason 3: SAS (side - angle - side)

Explanation:

It is given that AB/DB = CB/EB. So, we can say that the ratio of side AB to DB is equal to the ratio of side CB to EB. This made these sides similar.

Additionally, ∠ABC and ∠BDE are vertical angles because they are opposite angles formed when two lines intersect. Vertical angles have the same measure so, ∠ABC = ∠BDE.

Now, we can say that the triangles ABC and DBE are similar by SAS (Side-Angle-Side). Because two sides are similar and the angle between them is congruent.

Therefore, the answer is

Statement 1. AB/DB = CB/EB

Reason 1: Given

Statement 2: ∠ABC = ∠BDE

Reason 2: Vertical angles

Statement 3: ∆ABC~∆DBE

Reason 3: SAS (side - angle - side)

By means of the area formula for a square, the square has an area of 4 / 49 square meters (approx. 0.0816 square meters).

Herein we find a representation of a solid square in the figure, whose side length measure (l), in meters, is known, and whose area (A), in square meters, has to be found. Dimensionally speaking, the area unit is the square of length unit.  

The area formula of the square is shown below:

A = l²

If we know that the side length of the square has a measure of 2 / 7 meters (l = 2 / 7 m), then the area of the triangle is equal to:

A = (2 / 7 m)²

A = 4 / 49 m²

A ≈ 0.0816 m²

The area of the square is 4 / 49 square meters (approx. 0.0816 square meters).

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We know that:

Plugging the values given we have that:

Now, since the probability of the intersection is not zero this means that the events are non-mutually exclusive.

The formula for probabilty is given by; the Probability of an event(A) is the number of favorable outcomes divided by the total number of outcomes possible in a scenario. It can also be denoted by the formula:

In our problem we have 16 trains that are full and 4 which are not, therefore there are a total number of 20 trains in the Westford Station.

The number of favorable outcome is equal to the number of trains that are full since it is the one asked in our question as the one which is more favored to come, according to the question.

Therefore, the number of favorable outcome = number of full trains = 16, and

The Total number of Outcome = total number of trains that may pull over to Westford Station = 20

Therefore the experimental probability that a full train will pull over in the station is;

Therefore there is a probabilty of 4/5 or 80% that a full train will pull over the station.

The area enclosed by y² = 8 - x and (y + 1)² = −3 + x is 243.

We are given y² = 8 - x and (y + 1)² = −3 + x.

To sketch and calculate the area enclosed, find the intersection points:

y² = 8 - x ⇒ x = 8 - y²

Substitute x = 8 - y² in (y + 1)² = −3 + x:

(y + 1)² = −3 + 8 - y²

y² + 2y + 1 = −3 + 8 - y²

2y² + 2y - 4 = 0

y² + y - 2 = 0

(y - 1) (y + 2) = 0

y = 1, -2

Substitute y = 1, -2 in x = 8 - y²:

When y = 1, x = 8 - (1) ⇒ x = 7

When y = -2,  x = 8 - (-2)² ⇒ x = 4

Thus, the point of intersection is (4, -2) and (7, 1).

Graph of the region enclosed by y² = 8 - x and (y + 1)² = −3 + x:

The area of the enclosed region is given by:

A = [tex]\int \, \int \,dA[/tex]

[tex]=\int\limits^7_{-2} \, \int\limits^{3+ (y+1)^{2} } _{8 - y^{2} } \, dxdy[/tex]

[tex]=\int\limits^7_{-2} \, (x)^{3+ (y+1)^{2} } _{8 - y^{2} } \, dy[/tex]

[tex]=\int\limits^7_{-2} \, [{(3+ (y+1)^{2} )} -({8 - y^{2} })] \, dy[/tex]

[tex]=\int\limits^7_{-2} \, {(2 y^{2} + 2y -4) } \, dy[/tex]

[tex]=(\frac{2y^3}{3} + \frac{2y^2}{2} -4y)^7_{-2}[/tex]

[tex]=\frac{686}{3} + 49 - 28 + \frac{16}{3} - 4 - 8[/tex]

= 343

Hence, the area enclosed by y² = 8 - x and (y + 1)² = −3 + x is 243.

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The form of the equation of the circle is

(h, k) is the center

r is the radius

Let us compare it with the given equation to find the center and the radius

From the comparing

h = -1

k = 1

r^2 = 36

Find the square root of 36 to get r

The center is (-1, 1) and the radius is 6

The inequality that shows the possible contents of the box is 0.5c + 0.25l < 42

Inequality, defined as "the state of not being equal, particularly in status, rights, and opportunities," is a central concept in social justice theories. However, it is prone to misunderstanding in public debate because it means different things to different people. Some distinctions, however, are universal.

The expression 5x 4 > 2x + 3 resembles an equation, but the equals sign has been replaced by an arrowhead. It's an example of inequity. This means that the left part, 5x 4, is greater than the right part, 2x + 3. We'll be looking for x values for which the inequality holds true.

The definition of inequality is that two things are not equal.

One of the things could be less than, greater than, less than or equal to the other things, or greater than or equal to the other things.

p ≠ q means that p is not equal to q

p < q means that p is less than q

p > q means that p is greater than q

p ≤ q means that p is less than or equal to q

p ≥ q means that p is greater than or equal to q

Therefore, The inequality that shows the possible contents of the box is 0.5c + 0.25l < 42

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The general equation of a circle is given by

where (h,k) is the center of the circle and r is the radius

x² + y² -2x - 8y = 8

x² - 2x + y² - 8y = 8

(x² - 2x + ) + (y² -8y + ) = 8

Add square of half of the coefficient of x in the first paenthesis and the half of the square of the coefficient of y in the second parenthesis

Then add the two squaes at the right-hand side of the equation

(x² -2x +1 ) + (y² -8y + 16 ) = 8 + 1+ 16

(x-1)² + (y-4)² = 25

comparing this with the general equation

Center is ( 1, 4)

Radius is 5

Given:

The data set of the monthly rent paid by 7 tenants

990, 879, 940, 1010, 950, 920, 1430

We will find the mean of the data:

Mean = Sum/n

n = 7

Sum = 990+879+940+1010+950+920+1430 = 7119

Mean = 7119/7 = $1017

One of the tenants change from 1430 to 1115

The mean after the change will be as follows:

Sum = 990+879+940+1010+950+920+1115 = 6804

n = 7

Mean = 6804/7 = 972

So, the answer will be:

Mean before the change = 1017

Mean after the change = 972

(a + 15) •2

Multiply each term in the parentheses by 2

a*2 + 15*2

2a + 30

B) TS

1) Since these triangles are similar then we can write out the following ratios according to the Thales Theorem:

2) So these line segments must share the same ratio

3) Hence, the answer is TS

Answer:

TS

Step-by-step explanation:

Solution

- The constant being asked for is the slope of the graph.

- The formula for finding the slope of a graph is:

- The points on the graph that we will use are:

- Thus, we can find the constant as follows:

Final Answer

The constant(slope) is 1.5 (OPTION D)

The sum of all the angles in a triangle is always 180°.

We can write the equation and solve for the missing angle:

Solving for x:

The measure of the unknown angle is 72 degrees.

well, what's 40% of 20?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{40\% of 20}}{\left( \cfrac{40}{100} \right)20}\implies 8[/tex]

Problem

8 ( 11 - 2b ) = -4 ( 4b - 22 )

Solution

We can distribute the terms in the equation and we got:

88 -16b = -16b +88

If we add 16b in boh sides we got:

88 =88

Then for this case we can conclude that this equation has infinite solutions