Graph the following function by moving the points to match two ordered pairs, including the x-intercept:
f(x) = log 1/8(x)

The measure of the perpendicular of the right-angle triangle will be 16.728 units.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

The sine of the angle is the ratio of perpendicular to the hypotenuse.

sin θ = Perpendicular / Hypotenuse

The angle is 42° and the measure of Hypotenuse is 25. Then the measure of the side 'x' will be given as,

sin θ = Perpendicular / Hypotenuse

sin 42° = Perpendicular / 25

Perpendicular = 25 x sin 42°

Perpendicular = 16.728

The measure of the perpendicular of the right-angle triangle will be 16.728 units.

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The slope is the measure of the steepness and direction of a line. You can predict whether lines in a coordinate plane are parallel, perpendicular, or none by finding the slope of the lines.

There are two distinct points on any line that can be used to calculate its slope. Between two distinct points on a line, the slope formula calculates the ratio of vertical and horizontal changes. In mathematics, the slope is calculated as the ratio of the rise to the run, or as the rise divided by the run. The slope is a measure of how steep a line is in a coordinate plane.

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The principal investment required to get a total amount of $17,757.16 from compound interest at a rate of 3.9% per year compounded continuously over 9 years is $12,500.75.

What is continuous compounding?

There is no cap on how frequently interest can accumulate thanks to continuous compounding. A balance can compound continuously an unlimited number of times, which means interest is earned on it constantly.

We have,

9 years in an account with a 3.9% annual interest rate compounded continuously,

an investment is worth a total of $17,757.16.

First, convert R as a percent to r as a decimal

r = R/100

r = 3.9/100

r = 0.039 per year,

Then, solve the equation for P

P = A / ert

P = 17,757.16 / e(0.039*9)

P = $12,500.75

Hence, the principal investment required to get a total amount of $17,757.16 from compound interest at a rate of 3.9% per year compounded continuously over 9 years is $12,500.75.

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Answer:

$12,500.75

Step-by-step explanation:

I got it right.

Answer:

Below

Step-by-step explanation:

y = 19/x^3       <===== solve for 'x'

x = cube rt (19/y)     < ====now switch the x and y's

y = cube rt ( 19/x)

Answer: f^-1(x) = 19^3/x

Step-by-step explanation:

Given that : f(x) = y = 19/x^3

x^3 = 19/y

y = (19)^3/x = f^-1(x)

think sometimes prob 4x5 i don't know

( x - 1 ) is the factor of f(x) as remainder is 0

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

According to the given information

The given polynomial is

f(x) = [tex]x^{3} + 4x^{2} +x -6[/tex]

According to the remainder theorem

( x - 1 ) will be the factor of f(x) , if f(1) is zero

So

= [tex]1^{3} + 4(1)^{2} + 1 -6[/tex]

= 1+4+1-6

= 6-6

= 0

So

( x - 1 ) is the factor of f(x) as remainder is 0

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Answer:

mode = 3

Step-by-step explanation:

the mode is the value that occurs most often in the data set

3, 7, 4, 6, 3, 5, 9, 40, 6, 3

the value 3 occurs most often , 3 times

then mode of data set = 3

Therefore , Angela needs to fill this cup 6/7 times.

A fraction represents a component of a whole or, more generally, any number of equal parts. As in one-half, eight-fifths, and three-quarters, a fraction in conversational English denotes the number of components of a specific size.

Here,

To her dough, Angela needs to add 12 cups of milk. She only has a measuring cup that holds 14 cups.

Thus, the number of times angela needs to fill  cup are = 12/14 times

thus ,

=> 12/14 =6/7

Therefore , Angela needs to fill this cup 6/7 times.

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Answer:61

Step-by-step explanation:

Answer:

200

Step-by-step explanation:

Because there were 110 people at the concert, that means only 110 seats were filled. So we can think of the problem as its own equation if we word it like this:

110     is    55%    of    how many seats

110     =   0.55    x      ?

Now to solve by dividing 110 by 0.55

110/0.55 = 200

Answer:

A split infinitive is a common grammatical mistake that can be hard for writers to spot. Many people think they are not a big deal, but they can often have a major impact on your writing and make it hard for a reader to understand what you have to say.

Step-by-step explanation:

Take, for example, this sentence:

I like to on a hot day eat a lot of ice cream.

Did you have to read it twice to be clear what it was saying? I know I did. But let's make just a little adjustment:

On a hot day, I like to eat a lot of ice cream.

Answer:

Answer:

16

Step-by-step explanation:

The given equation after a translation by 2 units upwards is y = 3.5x + 2.

The rules for translating an equation in both vertical and horizontal directions are:

The given equation is y = 3.5x

The equation after translation by 2 units upward is obtained by using the rule we have y = f(x) + m.

⇒ y = 3.5x + 2

The graphs for the given equation and the translated equation are shown in the graph below.

For the pair that show translation in both equations, substituting x = 0, we get

y = 3.5x ⇒ y = 3.5(0) = 0; So, the point is (0,0)

and

y = 3.5x + 2 ⇒ y = 3.5(0) +2 = y = 2; So, the point (0,2)

Therefore, the required pair is (0,0) and (0,2).

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The number of ways that we can remove the balls one at a time from the box is 1307674368000

Given,

The number of balls in a box;

5 red balls

6 blue balls

4 green balls

We have to find the number of ways the balls can removed from the box one at a time;

Here,

Order is indistinguishable, so combination can be followed;

Combination formula;

ⁿCr = n! / r1(n - r)!

Here,

Total number of balls in the box = 5 + 4 + 6 = 15 balls

Then.

¹⁵C₁₅ = 15! / 15! (15 - 15)! = 15! = 1307674368000

That is,

We can remove the balls one at a time from the box in 1307674368000 ways.

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Answer:

a value that is not yet known

The total amount they will pay would be $95.557

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

Given that the cost of their meal was $75.99. Tax on the meal is 6.75% and they left a 19% tip on the cost of the meal.

Cost of meal = $75.99

The tax amount = 6.75% of 75.99

                  = ( 6.75/100 ) x 75.99

                  = $5.129

Tip amount = 19% of 75.99

                  = (19/100) x 75.99

                  =  $14.438

Thus, the Total amount they will pay

= $75.99 + $5.129 + $14.438 = $95.557

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Answer:

A and B

Step-by-step explanation:

-(5/3) = -1.67

-5/3 = -1.67

5/-3 = -1.67

5/3 ≠ -1.67

-5/-3 ≠ -1.67

-(-5/3) ≠ -1.67

The reasoning above makes it very evident that the hyperbola's coordinate is (8, -1)

The hyperbola is open upward and downward because the expression 'y' has a positive leading coefficient. In comparison to the usual equation, the hyperbola's center is found to be at (2, -1) and its 'a' point, 6, and 'b' point is 8. A smooth curve that lies in a plane and is classified as a hyperbola in mathematics by either its geometric characteristics or by equations for which it is the solution set. Two parts of a hyperbola, referred to as connected components or branches, are mirror reflections of one another and resemble two infinite bows.

Given,

((x-2)²/36)-((y+1)²/64)=1

We know that the standard form of a parabola is:

((x-k)²/a²)-((y-h)²/b²)=1

Center for the given hyperbola is (2, -1)

And a=6, b=8

And the coordinates for the center of the hyperbola are x=8, y= -1

Therefore, (x, y)=(8, -1)

The reasoning above makes it very evident that the hyperbola's coordinate is

(8, -1)

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10x-61/12 is the difference of  (7x-[tex]6\frac{2}{3}[/tex]) - (-3x + [tex]4\frac{3}{4}[/tex]).

An expression is combination of variables, numbers and operators.

The given expression is (7x-[tex]6\frac{2}{3}[/tex]) - (-3x + [tex]4\frac{3}{4}[/tex])

7x-[tex]6\frac{2}{3}[/tex]+3x- [tex]4\frac{3}{4}[/tex]

7x-20/3+3x-19/4

Add the variable terms and constant terms.

10x-20/3-19/4

The LCM of 3 and 4 is 12/

10x-4-57/12

10x-61/12

Hence, 10x-61/12 is the difference of  (7x-[tex]6\frac{2}{3}[/tex]) - (-3x + [tex]4\frac{3}{4}[/tex]).

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The domain for the given function is {-1, 2, 33, 32}.

A function's or relation's domain is the set of all possible independent values that the relation can take. It is the sum of all possible inputs.

A function's or relation's range is the set of all possible dependent values that the relation can produce from the domain values. It is the sum of all possible outputs.

When dealing with sets of ordered pairs, we simply divide the pairs into x- and y-coordinates. The domain is formed by the x-coordinates, which are independent values. The y-coordinates are the dependent values, i.e. they define the range.The domain in the set of ordered pairs {(a,b); (c,d); (e,f); (g,h)} is the set of the first number in each pair (those are the x-coordinates): {a,c,e,g}. The range is the set of all the pairs with the second number (the y-coordinates): {b,d,f,h}.

Given,

The set of ordered pair =   {(-1,5) , (2,3), (33,6), (32,7)}

then,

the Domain = {-1, 2, 33, 32}

Range = {5, 3, 6, 7}

Thus, the domain for the given function is {-1, 2, 33, 32}

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Answer:

-x² -10x -26

Step-by-step explanation:

Substitute x in f(x) with x + 5:

f(g(x)) = - (x+5)² - 1

= - (x² + 10x + 25) -1

= -x² -10x -25 -1

= -x² -10x -26

Answer:Use it as it is or fit non-normal distribution

Step-by-step explanation:

888030 ways are there for teachers to select the students.

What is the combination?

A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.

Here, we have

A teacher selects 7 students from her class of 27 students.

We have to find how many ways are there for her to select the students of the chosen students.

The order of selecting the students does not matter here so the number of ways to select 7 students from the class of 27 to work together on a project is:

C(27,7) = 27!/(7!*(27-2)! = 888030

Hence, 888030 ways are there for teachers to select the students.

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Answer:

121°

Step-by-step explanation:

x + 6 + 3x -15 + 5x + 36 = 180

9x + 27= 180

9x = 180 - 27

9x = 153

9/9 x = 153/9

x = 17

mC = 5·17 + 36

85 + 36

121°

Answer: y = 8 , x = 4

Step-by-step explanation:

gosh darn i haven done this since algebra 1 !!

since both equations equal y, we can make them equal to each other since y = y

-2x +16 = 2x (im just gonna simplify without all the extra steps sorry)

x = 4 (this is the first answer)

now we can plug in x to find y

y = 2(4)

y = 8 (second answer)

im sorry if the grammar is horrid its 3 am

Answer:

0.44

Step-by-step explanation:

Answer:

$575 after 5 years

Step-by-step explanation

3% of 500= 15

15 × 5= 75

500 + 75= $575

After dilation, the size of the image will change and the shape of the image will be same

Dilating an image means the changing the size of the image, but the shape of the image will be same

Dilation is the process of changing the size of the image without changing the shape of the image

The image after the dilation is called as the pre image.

The dilation can be done by using the scale factor or normally increase or decrease the size,

If the dilation of an image done by scale factor, the size is increased or decreased according to the value of scale factor. If it is greater than 1 the size increases and if it is between 0 and 1 the size decreases

Therefore, size of the image will change after the dilation

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The constant of proportionality that relates the number of servings to cups of cheese is  0.25.

According to the question,

Sarah used 2.5 cups of cheese in a dish that serves 10 people, this can be written as :

let the c be the cups of cheese : c = 2.5 cups of cheese

let n be the number of the people that is been served

Then the equation can be written as :

c ∝ n

then we can bring in the proportionality constant sign as ;

then c = kn

then we can introduce the given figures into the equation as ;

=> 2.5=k (10)

the we can determine the value of the constant as :

=> k=2.5/10 = 0.25

Hence, constant of proportionality relates the number of servings to cups of cheese is 0.25

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f(-2) = 254 , meaning if the company sells shirts -2 , they would make a profit of 254 dollars. This interpretation is true in the context of the problem.

f(12) = 266 , meaning if the company sells shirts 12 , they would make a profit of 266 dollars. This interpretation is true in the context of the problem.

f(17.5) = 270.25, meaning if the company sells shirts 17.5 , they would make a profit of 270.25 dollars. This interpretation is true in the context of the problem.

Based on the observations above, it is clear that an appropriate domain for the function is x ≥ - 2.

Functions and values given the function that represents elevation, in feet, of Jayden hikes expressed as:

f(x)=(x+2)²+250.

If the domain value of the function is -4, then;

f(-4)=(-4+2)²+250

f(-4) = 4 + 250

f(-4) = 254

f(-4) = 254 means If Jayden hikes 4 miles to the south, his elevation would be 254 feet. This interpretation is true in the context of the problem

If the domain value of the function is -4, then;

f(2)=(2+2)²+250

f(2) = 16 + 250

f(2) = 266

f(2) = 266 means If Jayden hikes 2 miles to the north, his elevation would be 266 feet. This interpretation is true in the context of the problem

If the domain value of the function is 2.5, then;

f(2.5)=(2.5+2)²+250

f(2.5) = 20.25 + 250

f(2.5) = 270.25

f(2.5) = 270.25 means If Jayden hikes 2.5 miles to the north, his elevation would be 270.25 feet. This interpretation is true in the context of the problem

Determining the domain

The domain exist for the value of (x+2)² ≥ 0

x + 2 ≥ 0

x ≥ - 2

Based on the observation above, it is clear that an appropriate domain of the function is x ≥ - 2

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