The logarithmic functions, f(x) and g(x), are shown on the graph.
What is the equation that represents g(x)? Explain your reasoning.

Answer:

See attached image

Step-by-step explanation:

Every step holds except for step 5

In mathematics, it deals with numbers of operations according to the statements.

Here,
Step 1 is the result of the distribution of -5 while opening the parenthesis, So, Step 1 holds the distributive property.

Step 2, states adding like terms across each side, so combining as terms hold,

Step 3, Addition over the equal sign. So it also holds

Step 4, subtraction of 12 over the equal sign. So subtraction of the terms also holds.

Step 5, does not hold because the number 12 gets divided by 8 it is not an associative property.

Thus, Every step holds except for step 5.

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The altitude of the trapezoid, based on the given parameters is 5 units

From the question, we have the following parameters about the trapezoid

Base length 1 of the trapezoid = 6

Base length 2 of the trapezoid = 10

Area of the trapezoid = 40

Altitude of the trapezoid = h

The area of the trapezoid is calculated using

Area = 0.5 * (Sum of the two base lengths) * Altitude of the trapezoid

Substitute the given parameters in the above formula

40 = 0.5 * (6 + 10) * h

Evaluate the sum of 6 ad 10 (do not approximate)

40 = 0.5 * (16) * h

Evaluate the product of 0.5 and 16 (do not approximate)

40 = 8 * h

Divide both sides by 8 (do not approximate)

h = 5

Hence, the altitude of the trapezoid, based on the given parameters is 5 units

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Answer:

5 units

Step-by-step explanation:

The given case of Gallup asking the same 50 people how many hours had they worked at a job in the past 7 days. is an example of dependent sample.

The measured values in relation in a dependent sample (also called a paired sample).

Some characteristics of dependent sample are-

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Applying the trigonometry ratios, the missing lengths for right triangle ABC are: 12 and 8√3.

Trigonometric ratios are defined as the values of all trigonometric functions based on the right-angled triangle's side ratio. The trigonometric ratios of any acute angle in a right-angled triangle are the ratios of its sides to that angle.

Reference angle (∅) = 60

Adjacent = 4√3

Opposite = ?

tan 60 = opp/adj

tan 60 = Opp/4√3

√3 = opp/4√3

Opposite = √3 × 4√3

Opposite = 12

Reference angle (∅) = 60

Adjacent = 4√3

Hypotenuse = ?

cos 60 = adj/hyp

cos 60 = 4√3/hyp

hyp = 4√3/cos 60

hyp = 4√3/1/2

hyp = 4√3 × 2

hyp = 8√3

Therefore, applying the trigonometry ratios, the missing lengths for right triangle ABC are: 12 and 8√3.

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Answer:

[tex]\textsf{19.} \quad S_{20}=1490[/tex]

33.  None of these are correct.

Step-by-step explanation:

General form of an arithmetic sequence:

[tex]a_n=a+(n-1)d[/tex]

where:

Given values:

Substitute the given values into the formula and solve for a:

[tex]\implies 27=a+(20-1)(-5)[/tex]

[tex]\implies 27=a+(19)(-5)[/tex]

[tex]\implies 27=a-95[/tex]

[tex]\implies a=27+95[/tex]

[tex]\implies a=122[/tex]

Sum of the first n terms of an arithmetic series:

[tex]S_n=\dfrac12n[2a+(n-1)d][/tex]

where:

Given values:

Substitute the given values into the formula and solve:

[tex]\implies S_{20}=\dfrac{1}{2}(20)[2(122)+(20-1)(-5)][/tex]

[tex]\implies S_{20}=10[244-95][/tex]

[tex]\implies S_{20}=10[149][/tex]

[tex]\implies S_{20}=1490[/tex]

Sum of the first n terms of a geometric series:

[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]

where:

Given values:

Substitute the given values into the formula and solve:

[tex]\implies S_6=\dfrac{1458\left(1-\frac{1}{3}^6\right)}{1-\frac{1}{3}}[/tex]

[tex]\implies S_6=\dfrac{1456}{\frac{2}{3}}[/tex]

[tex]\implies S_6=\dfrac{1456 \cdot 3}{2}[/tex]

[tex]\implies S_6=2184[/tex]

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The value to increase is keeping A constant and decreasing the value of B

Fractions are written as a ratio of two integers. For instance a.b is a fraction where a and b are integers.

In the fraction a/b, the numerator is and the denominator is b. If the value of the denominator is decreasing the fraction will increase but if the value of the denominator is increasing the fraction will decrease.

Given the expression A + 2/B, the higher the value of B provided such that that A is constant, the higher the expression. Hence the expression that will cause the value to increase is keeping A constant and decreasing the value of B

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If a diameter intersects a chord of a circle at a perpendicular then the chord is bisected.

The solution to the problem:

A circle's chord is intersected perpendicularly by its diameter, which also passes through the center of the circle. The chord and diameter are perpendicular. Any line that is perpendicular to a chord on the circle and passes through its center divides it. The chord is divided equally by the diameter.

Therefore, the chord is bisected.

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Solving a linear equation, we will see that after 9 days he cuts the last section.

We know that the initial length of the piece of cloth is 20m, and the taylor each day cuts a piece of 2 meters of it.

So, the length as a function on the number of days, is:

L(x) = 20m - 2m*x

Here we just need to solve:

L(x) = 2m

Because the last cut is when the long piece measures 4 meters (in that case he does one cut and has the two final pieces of 2 meters).

Solving that, we get:

20m - 2m*x = 2m

20m - 2m = 2m*x

18m/2m = x = 9

After 9 days he cuts the last section.

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the graphed equation is:

y = -|x| + 1

On the graph, we can see an absolute value equation, which opens downwards, and passes through the points (1, 0) and (0,1).

The general absolute value equation is:

y = a*|x - b| + c

Because the vertex is at the point (0, 1), we know that:

b = 0, c = 1

Replacing that we get:

y = a*|x| + 1

Now, this must be zero when we evaluate in x = 1, then:

0 = a*|1| + 1

a = -1

Then the graphed equation is:

y = -|x| + 1

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Answer:

3.89

Step-by-step explanation:

if 15.2 gallons cost 59.13.What about 1

then we just divide 59.13 by 15.2 to get the cost of 1 gallon

The correct equation that shows the area of painted area is

A=[tex]x^{2} -8x-16[/tex].

Given that the length of the  floor,x,is atleast 12 feet.The width of the floor is 4 feet less than the length.There is a right angle of height x-4 and base 8 feet. The rectangle inside has length of 8 feet and width be 4 feet.

We are required to find the painted area of the theater room in square feet.

To find the painted area of the theater the following steps must be followed:

1) Find the area of the theater room.

length =x

Breadth=x-4

Area=x(x-4)

=[tex]x^{2} -4x[/tex]

2) Area of the right triangle.

Height=x-4

Base=8

Area=1/2 *8*(x-4)

=4(x-4)

=4x-16

3) Find the area of the rectangle inside labeled closet.

Length=8

Width=4

Area=8*4

=32

Area=Area of theater room-Area of of right triangle-Area of closet.

=[tex]x^{2} -4x[/tex]-4x+16-32

=[tex]x^{2} -8x-16[/tex]

Hence the correct equation that shows the area of painted area is

A=[tex]x^{2} -8x-16[/tex].

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Answer:

A = x(x − 4) − 0.5(8)(x − 4) − 3(7)

Work:

x = length, making the width (x-4)

The stage closet will be (x-4)(8)(1/2)

The rectangle is 7(3)

which makes the painted area x(x-4) - 4(x-4)

thus giving us

x(x − 4) − 0.5(8)(x − 4) − 3(7)

Step-by-step explanation:

hope this helps :)

Answer:

6 - 16y

Step-by-step explanation:

2(3 – 8y) = 2 × 3 - 2 × 8y = 6 - 16y

The condition for the expected value in the goodness of fit test is that the expected frequency is at least 5.

According to the statement

we have to find the condition of the expected values in the case of testing of goodness-of-fit test.

So, For this purpose we know that the

The goodness of fit test is of a statistical model describes how well it fits a set of observations. Measures of goodness of fit typically summarize the discrepancy between observed values and the values expected.

So, The main condition of the expected value for the goodness of fit test is

For each​ category, the expected frequency is at least 5.

Without this condition the test is not possible, so overall this the main condition related the goodness of fit test.

So, The condition for the expected value in the goodness of fit test is that the expected frequency is at least 5.

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The statement that best describes the relationship between triangles ABD and CBD is 'Triangles ABD and CBD are congruent by the SSS Congruence postulate'. Option A

It is important to note the following;

"Two triangles are similar when their corresponding angles are equal and corresponding sides are in equal proportion."

The SSS congruence states that ; "Two triangles are congruent if all three sides of a triangle are congruent to corresponding three sides of other triangle."

SSS similarity postulates that;  "Two triangles are similar if all the three sides of a triangle are in proportion to the three sides of another triangle."

SAS similarity postulates that ; "Two triangles are similar if the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle between the two sides in both the triangle are equal."

SAS congruence postulates that ; "Two triangles are congruent if two sides and the angle between these two sides of one triangle are congruent to the corresponding two sides and the included angle of a second triangle."

For given question,

We have been given triangles ABD and CBD.

B is the midpoint of line AC

⇒ AB = BC

For triangles ABD and CBD,

side AB = side CB; since, B is the midpoint of line AC

side BD = side BD ; they have common sides

side AD = side CD = 15 units each

So, by SSS postulates of triangle congruence triangles ABD and CBD are congruent triangles.

Therefore, the statement that best describes the relationship between triangles ABD and CBD is 'Triangles ABD and CBD are congruent by the SSS Congruence postulate'. Option A

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Answer:

-20

Step-by-step explanation:

He went back 20 and not forward 20.  Everyone would want a penalty if you got to go forward.

Type of model best fits the given situation linear.  Since it has a constant of +3 everyday.

What is a linear equation in math?

the membership of the local pta increases by 3 members a day for each day during the month of September.

Since it has a constant of +3 everyday.

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There are 59 integer solutions

Such questions are best solved by writing cases and calculating the total number of cases. So beginning with

1)  x = -3. The possible combinations are as follows:-

-3 2 13

-3 3 12

-3 4 11

-3 5 10

-3 6 9

-3 7 8

-3 8 7

-3 9 6

-3 10 5

-3 11 4

10 combinations

2) x = -2

-2 2 12

through

-2 11 3

10 combinations

3) x = -1

-1 2 11

through

-1 10 3

9 combinations

4) x = 0

0 2 10

through

0 9 3

8 combinations

as we can see from the pattern at x =1  we get 7 combinations, at x =2  we get 6 combinations, at x=3 we get 5 combinations and at x =4  we get 5 combinations.

Thus total number of combinations 4+5+6+7+8+9+10+10 = 59 integer solution.

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The solution of the assumed equation is

θ = 135 + 360k

and

θ = -45 + 360k (or 315 + 360k)

Assuming the equation is

csc^2(θ) = 2cot(θ) + 4

and not

Assuming the equation to be:

csc^2(θ) = cot^2(θ) + 1

Solving these equations usually begins with algebra and/or trigonometry. ID for transforming equations to have one or more equations of the form:

trigfunction(expression) = number

It is not always easy to understand how to perform the desired transformation. If it's not obvious, first use the trigonometric identity to reduce the number of different arguments or functions in the equation. In this expression, all arguments are θ. Therefore, there is no need to reduce the number of arguments. But he has two different functions, csc and cot.

csc^2(θ) = cot^2(θ) + 1

Substituting the right side of this equation into the left side of the equation, we get: :

cot^2 (θ) + 1 = 2 cot(θ) + 4

Now that we have only one function cot and one argument θ, we are ready to find the form we need. Subtracting the entire right-hand side from both sides gives:

cot^2(θ) - 2cot(θ) - 3 = 0

The left-hand side factorizes:

(cot(θ)-3)(cot (θ) ) + 1 ) = 0

Using the properties of the zero product,

cot(θ) = 3 or cot(θ) = -1

These two equations are now in the desired form.

The next step is to write the general solution for each equation. The general solution represents all solutions of the equation.

cot(θ) = 3

Note that 3 is not a specific angle value for cot. That's why you need a calculator. Your computer probably doesn't have the crib button, so you'll need to switch it to tan

Since tan is the reciprocal of cot, if cot = 3...

tan(θ) = 1/3

Inverse tan tan^-1(1/3) can be used to find the reference angle. You should get a reference angle of 18.43494882 degrees. Using this reference angle and cot (and tan) being positive in the 1st and 3rd quadrants, we get the general solutions

θ = 18.43494882 + 360k

and

θ = 180 + 18.43494882 + 360k

.

θ = 198.43494882 + 360k

where

cot(θ) = -1

-1 should be recognized as a special angle value for cot. So you don't need a calculator. This reference angle is 45 degrees. Using this reference angle, cot is negative in the 2nd and 4th quadrants, so

θ = 180 - 45 + 360k

and

θ = -45 + 360k (or 360 - 45 + 360k) the general solution for

must get. to:

θ = 135 + 360k

and

θ = -45 + 360k (or 315 + 360k)

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The x-intercept of the function g(x) = -5(x - 3)^2 is (3, 0) and the vertex of the function g(x) = -5(x - 3)^2 is (3, 0)

The function is given as:

g(x) = -5(x - 3)^2

Set g(x) to 0, to determine the x-intercept.

-5(x - 3)^2 = 0

Divide through by -5

(x - 3)^2 = 0

Take the square root of both sides

x - 3 = 0

Add 3 to both sides

x = 3

Hence, the x-intercept of the function g(x) = -5(x - 3)^2 is (3, 0)

The function is given as:

g(x) = -5(x - 3)^2

A quadratic function is represented as:

g(x) = a(x - h)^2 + k

Where, the vertex is

Vertex = (h, k)

By comparing g(x) = a(x - h)^2 + k and g(x) = -5(x - 3)^2, we have

(h, k) = (3, 0)

Hence, the vertex of the function g(x) = -5(x - 3)^2 is (3, 0)

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Mrs. Corrubi takes 7.5 hours to complete the job alone.

Directly proportional: as one amount increases, another amount increases at the same rate. Direct variation means when one quantity changes, the other quantity also changes in direct proportion

Inversely Proportional: when one value decreases at the same rate that the other increases. An increase in the quantity A leads to a decrease in quantity B and vice versa.

Let the number of hours taken by Mrs Corrubi to do a particular work be x.

∴ The number of hours taken by Mr Corrubi to do a particular work will be 2x.

So according to the condition,

1/x + 1/2x = 1/5

(2+1)/2x = 1/5

3/2x = 1/5

2x = 15

x = 7.5 hours.

Thus Mrs. Corrubi takes 7.5 hours to complete the job alone.

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Answer:

ur answer is B

Step-by-step explanation:

Answer:

B

As root over 72 is 8.48 and after we round off we get 8.5 so no B is correct

The correct option is (D) one of the non-fiction books on the bottom shelf and a second non-fiction book from the bottom shelf.

To find which 2 books describe a pair of dependent events:

Therefore, the correct option is (D) one of the non-fiction books on the bottom shelf and a second non-fiction book from the bottom shelf.

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Answer: 1/2

Step-by-step explanation:

The probabilities must add to 1, so:

[tex]P(x < 9) +P(X=9)+P(X > 9)=1\\\\\frac{1}{6}+P(X=9)+\frac{1}{3}=1\\\\P(X=9)=\boxed{\frac{1}{2}}[/tex]

Answer:

35

Step-by-step explanation:

Angle QRS is an inscribed angle, so measure of angle QRS is half the measure of the intercepted arc, arc SPQ. Therefore arc SPQ is 125*2 = 250 degrees, and arc QRS is 360 - 250 = 110 degrees.

Angle QPS is an inscribed angle, and arc QRS is its intercepted arc. Therefore angle QPS is 110/2 = 55 degrees. Since PS is the radius of the circle, angle PQS, the angle inscribed in the semicircle, is 90 degrees. Since interior angles of the triangle QPS add up to 180 degrees, angle QSP is 180 - 90 - 55 = 35 degrees.

Angles QSP and UST are vertical angles, and by the vertical angles theorem, they are congruent. Therefore x = 35.

Hello and Good Morning/Afternoon:

Let's take this problem step by step:

Let's write out the equation we would hypothetically use to convert 410 kilometers to meters:

  [tex]410 kilometers * \frac{1000 meters}{1 kilometers}[/tex]

Let's see if there are any errors:

              ⇒ we want to get rid of the kilometer symbol

                   ⇒ which is done in this problem

                        [tex]410 kilometers * \frac{1000 meters}{1 kilometers}=\frac{410 kilometers}{1 kilometers}*1000 meters = 410000meters[/tex]

Thus the answer is true

Answer: True

Hope that helps!

Answer: [tex]\frac{2x\sqrt[4]{y^{2}}}{3}[/tex]

Step-by-step explanation:

[tex]\sqrt[4]{\frac{16}[81}} \sqrt[4]{\frac{x^{11}y^{8}}{x^{7}y^{6}}}\\\\=\frac{2}{3} \sqrt[4]{x^{4}y^{2}}\\\\=\frac{2x\sqrt[4]{y^{2}}}{3}[/tex]

The new dimensions of the flower bed are 4√2 and 6√2

The dimensions of the initial rectangular flower bed are given as:

Length = 4ft

Width = 6 ft

The area of the new flower bed is twice the area of the old one.

This means that

New Area = Old Area * 2

Substitute the dimensions of the old area in the above equation

New Area = 4 * 6 * 2

Express 2 as √2 * √2

This gives

New Area = 4 * 6 * √2 * √2

Rewrite the above equation as:

New Area = 4√2 * 6√2

The area of a rectangle is

Area = Length * Width

This means that:

Length = 4√2 ft

Width = 6√2 ft

Hence, the new dimensions of the flower bed are 4√2 and 6√2

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Answer: 6x8

Step-by-step explanation:

(4+x)(6+x)=2*24

x^2+10x+24=48

subtract 48 on both sides

x^2+10x-24=0

Solve using the quadratic formula

-10±√(100+96)÷2

simplifies to

-(10±14)÷2 = 2, -12

-12 doesn't work though because the sides can't be negative.

So x=2

To check, add both sides by 2:

2(4x6)=6x8=48

Answer:

Laplace transforms turn a Differential equation into an algebraic, so we can solve easier.

y'= pY-y(0)

y"=p²Y - py(0)- y'(0)

Substituting these in differential equation :

p²Y -py (0)  -y' (0)-6(pY-y(0)) + 13Y

Substituting in the initial conditions given , fact out Y, and get:

Y( p²-6p+13) = -3

Y=-3/ p²-6p+13

now looking this up in a table to Laplace transformation we get:

y=-3/2.e³т sin(2t)

for the last one, find the Laplace of t∧2 . which is 2/p³

pY - y(0)+ 5Y= 2/p³

Y= 2/p³(p+5)

Taking partial fractions:

Y=-2/125(p+5) + 2/125p - 2/25p² + 2/5p³

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Answer:

The integral transform that converts a function of a real variable to a function of a complex variable is called Laplace transform. first we need to substitute y' and y" in differential equation then finding Laplace transformation and at last taking partial fractions.

Given:                              y'= pY-y(0)

                                         y"=p²Y - py(0)- y'(0)

Putting y' and y" in differential equation :

                               p²Y -py (0)  -y' (0)-6(pY-y(0)) + 13Y

Substituting in the initial conditions given , fact out Y, and get:

                                 Y( p²-6p+13) = -3

                                                    Y=-3/ p²-6p+13

by Laplace transform we get:

                                  y=-3/2.e³т sin(2t)

for the last one, find the Laplace transform of t∧2 . which is 2/p³

                                  pY - y(0)+ 5Y= 2/p³

                                                     Y= 2/p³(p+5)

Taking partial fractions:

                                Y=-2/125(p+5) + 2/125p - 2/25p² + 2/5p³

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The store will break even after selling 35 books.

To find  what is the break-even point for this bookstore:

Given:

Let, n be the number of books.

Total costs = 12n + 105

The selling price of each book = $15

Total revenue = 15n

For breaking even, costs = revenue.

Therefore, the store will break even after selling 35 books.

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