Find the inverse of function f.
f(x) = 9x + 7
O A.
OB.
f¹(x) =
O c.
f¹(x) =
O D. f¹(x) =
f¹(x) =
x - 7
7x + 9
-9x - 7
x -
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If BD bisects ∠ABC and ∠ADC, then AD is congruent to CD.

What is bisector of an angle?

In geometry, anything is said to have been bisected when it is split into two identical or similar parts, typically by a line. In that case, the line is known as the bisector. The types of bisectors that are most usually taken into account are segment bisectors and angle bisectors..

Since BD bisects ∠ABC, thus ∠ABD = ∠DBC.

Since BD bisects ∠ADC, thus ∠ADB = ∠BDC.

AA theorem: According to the AA similarity theorem, two triangles are similar if two of their triangles are congruent with two of their respective triangles' angles.

Consider △ABD and △DBC:

∠ABD = ∠DBC

∠ADB = ∠BDC

Therefore, △ABD ≅ △DBC

According to CPCT, AD ≅ CD.

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The number which can be raised by 3 to give the value of 11 is 2.224.

The idea of exponentiation, or repeated multiplication, is where the exponential function got its start, but more recent definitions—there are several that are equivalent—allow it to be rigorously extended to all real arguments, including irrational values.

Given:

The exponent to which 3 must be raised to obtain 11,

Assume the number is x then, According to the statement,

x³ = 11

x  = ∛11

x = 2.224

Thus, the number is 2.224.

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The expression which represents the correctly rewritten form of the given expression; 20x⁴y³ - 30x³y⁴ is; 5x³y³ ( 4x - 6y ).

It follows from the task content that the expression which correctly represents the rewritten form of the given expression be determined.

On this note, since the given expression is;

20x⁴y³ - 30x³y⁴

The greatest common factor of both terms in the expression is; 10x³y³ .

On this note, the expression can be factorised completely as follows;

10x³y³ ( 2x - 3y )

However, the expression which is equivalent to the expression above among the answer choices is;

5x³y³ ( 4x - 6y )

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The sales that Doug makes in the week is $3200.

From the information illustrated, Doug is a salesperson in a retail store and earns $75 per week plus 15% of his weekly sales and Doug makes $555 one week.

Let the sales be represented by x.

Based on the information, this will be:.

75 + (15% × x) = 555

75 + 0.15x = 555

Collect like terms

0.15x = 555 - 75

0.15x = 480

Divide

x = 480 / 0.15

x = 3200

The sales is $3200.

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The value of baseball card has increased by 160(%) percentage.

What is the percentage?

A number or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the word per cent means. The letter "%" stands for it.

Increase = New Number - Original Number

Then: we divide the increased number by the original number and multiply by 100.

Therefore, % increase = (Increase ÷ Original Number)× 100.

Given, the new price of a baseball card = $13

The original price of a baseball card = $5

Then from the above definition,

Increase = 13-5 = 8

% increase = (8/5)*100 = 160%

Hence, its value has increased by 160 percentage.

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Answer:

c. 502.65 in³

Step-by-step explanation:

For a cylinder:

V = πr²h

r = d/2 = 8 in. / 2 = 4 in.

V = 3.14159 × (4 in.)² × 10 in.

V = 502.65 in.³

Answer:

A,D,E

Step-by-step explanation:

A:

14/4 = 3.5

D:

7/2 = 3.5

E: 14/4 = 3.5

The constant of proportionality for the table is 3.5. Any other table that satisfies the equations x/y = 3.5 will have the same constant of proportionality.

To find the constant of proportionality, we can divide the y-values by the corresponding x-values and see if they are the same for all given points. In this case, if we divide 24.5 by 7, we get approximately 3.5. If we divide 31.5 by 9, we also get approximately 3.5. Therefore, the constant of proportionality is 3.5 for this table.

Now, we need to find the relationships that have the same constant of proportionality.

For example, if we have a table with the following values:

x1 y1

x2 y2

x3 y3

and the constant of proportionality is k, then we have the following equations:

x1/ y1 = k

x2/ y2 = k

x3/ y3 = k

So, any other table that satisfies these equations will have the same constant of proportionality as the given table.

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The true option is D

The intersection of angle bisectors are equidistant from the sides of the triangle

The intersection of all three of the triangle's interior angle bisectors is where a triangle's incenter is located. It can be thought of as the intersection of the triangle's internal angle bisectors.

According to the angle bisector theorem, a point is equally distant from both sides of an angle if it is on the angle's bisector.

According to the converse of the angle bisector theorem, a point is on the angle's bisector if it is both in the interior of the angle and equally distant from its sides.

According to the given information

Angle bisector intersection points are evenly spaced from the triangle's sides.

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Answer:

The answer is 140

Step-by-step explanation:

The first step is simple L x W which will give us.

L being 5 and W being 3.5 The equation is 5 × 3.5 = 17.5.

With that being said I just need to multiply that answer by 8 which gives us 140.

This means that he will need 140 ft of light in order to put light around each window.

Hope this helped :)

A car manufacturer wants to lean about the brand preferences, then the company should survey a sample of all electric car owners.

A survey is a set of questions used in human subject research with the goal of gathering specific information from a particular population. Surveys can be carried out via the phone, by mail, online, at street corners, and even in shopping centers. Surveys are employed to collect data or learn more in areas like demography and social research.

Survey research is frequently used to evaluate ideas, beliefs, and emotions. Surveys may have narrow, specialized objectives, or they may have more general, extensive objectives.

As the manufacturer wants to learn about the brand preferences of electric car owners that what type of things people like nowadays, or what kind of improvement he can do in his model or design or other things, he should prefer a sample of all electric car owners.

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Answer:

0.043

Step-by-step explanation:

I hope this helps you! Let me know if you have any questions! :)

Answer:

41° and 49°

Step-by-step explanation:

Two angles are said to be complements if the sum of their measures is 90 degrees. Since one angle is eight more than twice the other, we can set up the following equation to represent the situation:

2x + 8 = 90

Solving for x, we get:

2x = 82

 x = 41

Since the two angles are complements, their measures must add up to 90 degrees. Therefore, the measure of the other angle is 90 - 41 = 49 degrees.

Therefore, the two angles have measures of 41 and 49 degrees.

The domain of the function is { (x, y) ∈ R² | x² + y² ≥ 1 }

What is Domain of function?

A function's domain is the collection of all potential inputs. For instance, all real numbers are in the domain of f(x)=x², and all real numbers are in the domain of g(x)=1/x, with the exception of x=0. Special functions with more constrained domains can also be defined.

According to question

⇒ [tex]z = e^{\sqrt{x^{2}+ y^{2} -1 } }[/tex]

⇒ x² + y² - 1 ≥ 0

 ⇒ x² + y² ≥ 1

Hence, the Domain of f(x, y) is  { (x, y) ∈ R² | x² + y² ≥ 1 }

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The equivalent expression could be 4×3·4×4−s

Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.

Think about the numbers 3²+1 and 5×2. They both add up to 10. These two expressions are equivalent, so to speak.

Let's now have a look at some expressions with variables, such 5x+2.

It is possible to rewrite the expression as 5x+2=x+x+x+x+x+1+1.

The right side of the equation can be regrouped to 2x+3x+1+1, x+4x+2, or another combination. When the same value is used as x, all of these equations have the same result. These two expressions are equivalent, so to speak.

When two expressions have the same value regardless of the value of the variable(s) they contain, they are said to be equivalent.

Here, 4×3=12 and 4×4=16

therefore, 4×3·4×4−s is equal to the expression 12⋅16−s

4×3·4×4−s and 12⋅16−s  are equivalent expressions.

Hence, The equivalent expression could be 4×3·4×4−s

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The equivalent expression could be 4×3·4×4−s.

Here, 4×3=12 and 4×4=16

therefore, 4×3·4×4−s is equal to the expression 12⋅16−s

4×3·4×4−s and 12⋅16−s  are equivalent expressions.

Hence, The equivalent expression could be 4×3·4×4−s

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The translation from the parent function is defined according to the following option:

A translation of 5 units to the right.

The four possible translations are defined as follows:

The parent function in this problem is defined as follows:

f(x) = x².

The translated function is given as follows:

g(x) = (x - 5)².

Meaning that the translated function can be written as follows:

g(x) = f(x - 5).

Thus the transformation to the parent function is given as follows:

x -> x - 5.

Thus it was a translation right of five units, and the third option is the correct option.

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So, it will take the rider 5.1 seconds to reach a height of 50 ft above the ground after reaching the low point.

The circumference of the ferris wheel is equal to the diameter times pi, or 50*pi=157.08 ft. Since the ferris wheel makes one revolution every 40 seconds, the speed of the ferris wheel is 157.08/40=3.92 ft/sec.

Since the rider starts at a height of 30 ft above the ground and ends up 50 ft above the ground, the total change in height is 50-30=20 ft. Since the speed of the ferris wheel is 3.92 ft/sec, it will take the rider 20/3.92=5.1 seconds to reach a height of 50 ft above the ground after reaching the low point.

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Using the z-distribution, the 99% confidence interval for the true population mean textbook weight is ( 89.772 , 64.228 )

The confidence interval is:

= μ ± z ( σ / [tex]\sqrt{n}[/tex] )

Where,

μ X is the sample mean.

z is the critical value.

n is the sample size.

σ is the standard deviation for the population.

In this problem, we have a 99% confidence level, hence [tex]\alpha =0.99[/tex] , z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2}[/tex] = 0.995,

So the critical value z- distribution is z = 2.575.

The other parameters are given as follows:

Mean μ = 77

Standard deviationσ = 7

Sample size two side n = 2

Hence the lower and upper bound of the interval are given, respectively, by:

= μ ± z ( σ / [tex]\sqrt{n}[/tex] )

= μ + z ( σ / [tex]\sqrt{n}[/tex] )   ,     μ - z ( σ / [tex]\sqrt{n}[/tex] )

= 77 + 2.575 ( [tex]\frac{7}{\sqrt{2} }[/tex] ) ,    77 - 2.575 ( [tex]\frac{7}{\sqrt{2} }[/tex] )

= 77 + 2.575 ( [tex]\frac{7}{1.41}[/tex] ) ,   77 - 2.575 ( [tex]\frac{7}{1.41}[/tex] )

= 77 + 2.575 ( 4.96 ) , 77 - 2.575 ( 4.96 )

= 77 + 12.772 ,             77 - 12.772

= ( 89.772 , 64.228 )

Therefore,

Using the z-distribution, the 99% confidence interval for the true population mean textbook weight is ( 89.772 , 64.228 )

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The domain of the relation is {4,8} and the range of the relation is {n,q,m}.

A function or relation's domain is the set of all potential independent values that it can have.

Suppose that the relation S is defined as follows.

S= {(4,n), (8,q), (4,m)}

The first term at the point represents the input and the second term at the point represents the output.

So,

the input values are 4,8 and 4 and their respective outputs are n, q and m,

The collection of all conceivable independent values that a function or relation may take is known as its domain.

So, the domain is {4,8}.

The range of a function or relation is the set of all possible dependent values the relation can produce from the domain values.

So, the range is {n,q,m}

Therefore, the domain is {4,8} and the range is {n,q,m}.

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Answer:

3. 32, 28, 30

4. 38, 142

Step-by-step explanation:

3. (x + 3) + (x - 1) + (x + 1) = 90

3x + 3 = 90

3x = 87

x = 29

angle 1: x + 3 = 29 + 3 = 32

angle 2: x - 1 = 29 - 1 = 28

angle 3: x + 1 = 29 + 1 = 30

4. x + (x + 104) = 180

2x + 104 = 180

2x = 76

x = 38

angle 1: x = 38

angle 2: x + 104 = 38 + 104 = 142

Answer:

Step-by-step explanation:To find the zeros of the quadratic function f(x) = 2x² + 3x - 2, we can use the zero-product property, which states that if the product of two factors is zero, then at least one of the factors must be zero.

We can write the function as follows:

f(x) = 2x² + 3x - 2 = 0

We can then factor the quadratic as follows:

f(x) = 2(x-1)(x+1) = 0

Since the product of the factors is zero, at least one of the factors must be zero. Therefore, the zeros of the quadratic are x = 1 and x = -1.

Since, We catch the other car if our speed of our car is 60mph.

When you catch up, the distance traveled is the same

Let us consider x as the velocity.

Therefore, our velocity is x + 10

We know that:

Distance = rate x time

According to the question:

r = uncle's rate

30 min = 30/60 hr = uncle's time

25 min = 25/60 hr =  your time

and

Uncle's distance = Your distance

Now,

(r)(30/60) = (r + 10)(25/60)

⇒ (r)(1/2) = (r + 10)(5/12)

⇒ r/2 = 5r/12 + 50/12  

⇒ 6r = 5r + 50

⇒ r = 50  

Now,

Uncle's rate = 50 mph

and, putting the values:

Your rate = 50 + 10 = 60 mph

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Answer: If Ben has 7 more baseball cards than Sara, and Sara has x baseball cards, you can represent the number of baseball cards Ben has with the expression x + 7. This means that Ben has x baseball cards plus an additional 7 baseball cards.

For example, if Sara has 5 baseball cards, then Ben has 5 + 7 = 12 baseball cards.

The depth of the submarine after 8 minutes is -123.6 feet below sea level.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Depth of the submarine after y minutes.

= -270 + 18.3y

The depth of the submarine after 8 minutes.

= -270 + 18.3 x 8

= -270 + 146.4

= -123.6

Thus,

The submarine is at -123.6 feet below sea level.

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Answer:

x = -58

Step-by-step explanation:

18 + x = -40

-18 -18

x = -58

Answer:We may rewrite f(x) = (x-1)^2

We stretch by having 3(x-1)^2

We reflect about the y axis by changing x to -x:   3(-x-1)^2 = 3(x+1)^2

We  move to the left by adding 2 to x: 3(x+2+1)^2 = 3(x+3)^2

Step-by-step explanation:A way to verify this:  Consider y = x^2 to be the unit parabola.  f(x) = (x-1)^2 moves the unit parabola one to the right, so it is symmetric about x = 1; We then vertically stretch it by a factor of 3; reflection about the y-axis moves the parabola to be symmetric about x = -1;  moving to the left by 2 means the parabola is now symmetric about x = -3; thus, we have a stretched unit parabola symmetric about x = -3, so g(x) = 3(x+3)^2

We may write g(x) = 3x^2 + 18x + 27, also.

Therefore ,the solution to this equation question is option C) 220 .

In an equation, it is said that the values of two mathematical expressions are equal. The equality of two variables is established via a mathematical formula. It is denoted by the equal ('=') sign. For example, the formula is 8+2=12-2. The aforementioned equation indicates that the left and right sides of the equation are equal. In light of this, an equation is a claim that "this equals that."

Here,

S is the total families

thus,

S = 60 + 85 + 70 + 95 = 310.

I + II + III + IV = X

S = I + 2 II + 3 III + 4 IV

S - I = 2 II + 3 III + 4 IV

310 - 130 = 180 = 2 II + 3 III + 4 IV

Make III & IV = 0 to increase X.

2 II therefore equals 1800. II = 90

X max = 130+90 = 220

Therefore ,the solution to this equation question is option C) 220 .

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The graph of the equation, y = -19x + 10 is shown below.

If the equation of a line is expressed in slope-intercept form as y = mx + b, it means that:

Given a line has the equation, y = -19x + 10, therefore;

the slope (m) = -19.

the y-intercept (b) = 10.

Therefore, the graph of the line is shown in the attachment below and it cuts the y-axis at 10.

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Answer:

x = -1

Step-by-step explanation:

To solve this equation, you can use the process of polynomial algebra.

First, you can rearrange the terms on the left side of the equation so that all the terms with an x^2 coefficient are on one side and all the other terms are on the other side. You can do this by adding x^2 to both sides of the equation:

5x^2 - 2x - 6 + x^2 = -x^2 + 6x + x^2

This gives you:

6x^2 - 2x - 6 = 6x

Now, you can rearrange the terms on the right side of the equation in the same way:

6x^2 - 2x - 6 = 6x^2 - 6x

To solve for x, you can now use the process of polynomial algebra to combine like terms on each side of the equation. This gives you:

6x^2 - 2x - 6 = 6x^2 - 6x

Combining like terms on the left side of the equation gives you:

6x^2 - 6x - 6 = 6x^2 - 6x

Combining like terms on the right side of the equation gives you:

6x^2 - 6x - 6 = 6x^2 - 6x

Now, you can subtract 6x^2 - 6x from both sides of the equation to obtain:

-6x - 6 = 0

Dividing both sides of the equation by -6 gives you:

x + 1 = 0

Finally, you can solve for x by subtracting 1 from both sides of the equation, which gives you:

x = -1

Therefore, the solution to the original equation is x = -1.

Answer:

n=1

Step-by-step explanation:

(-y + 3) + (2y - 4) = (ny - 1)

-y + 3 + 2y - 4 = ny - 1

-y + 2y + 3 - 4 = ny - 1  -> combine like terms on the left side of the equation

y - 1 = ny - 1 ==> simplify

y - 1 + 1 = ny - 1 + 1  

y = ny  ==> solve for n

y/y = ny/y

1 = n ==> n=1