The domain of a function f(x) is x< 4, and the range is y≤ 0. What are the
domain and range of its inverse function, f-¹ (x)?
A. Domain: x≤0
Range: y< 4
B. Domain: x<0
Range: y≤ 4
C. Domain: x24
Range: y> 0
D. Domain: x < 4
Range: y≤ 0

An acute triangle is a triangle with three acute angles, whereas an obtuse triangle is a triangle with one obtuse angle and two acute angles.

An obtuse angle is a angle which is more than 90°.

In our problem, the triangle has a 110° angle, and 110°>90°; therefore, the answer is obtuse triangle

Let's draw the figure to better understand the problem.

The number of people that can attend Jordan's party is 50 people.

The equation that represents the total amount that would be spent at the party would be a linear equation. A linear equation increases at a constant rate.

The form of the linear equation would be:

Total amount = rental fee + (charge per hour of the Dynamic DJ x number of hours he plays) + (cost per person of Roscoe's rentals x number of people)

$800 = $400 + ($50 x 4) + ($4 x p)

$800 = $400 + $200 + $4p

$800 = $600 + $4p

$800 - $600 = $4p

$200 = $4p

p = $200 / $4

p = 50 people

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Explanation:

For the given equation

For Erika to resolve the question

Step 1: We will take the logarithm of both sides

Step 2: Simplify the expression

Thus

Step 3: Solve for x

As per given by the question,

There are given two figure on coordinate grid, figures 1 and 2.

Now,

From concept of similar figure:

Similar figure means, that have the same shape and exactly the same in every way, on the other hand;

The similar figure means they are same shape but not the same size, then these figure is also called similar figure.

Now,

From concept of the congruent figure:

The congruent means, that two figure exactly the same that means, we can say that they are congruent, when both figure have same shape and same size.

So,

According to both concept, similar and congruent;

The given figure 1 and 2 is simililar, because of same shape. But due to different size, both figure have not congruent.

So, the given figures 1 and 2 is similar, but not congruent.

Hence, the option first is correct.

The value of x is 10 and the length of SU is 50.

Here SU is the line and T is the mid-point of the line

So from this we have

SU = ST + TU

ST = TU

SU = 2ST = 2TU

ST = 3x - 5 and TU = 2x + 5

As ST = TU

3x - 5 = 2x + 5

x = 10

SU = 2ST

     = 2( 3x - 5)

     = 2( 3 × 10 - 5)

     = 2( 30 - 5)

     = 2× 25

     = 50

Therefore the value of x is 10 and the length of SU is 50.

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The given expression is

y = (x²-7x)^5 (3x^5-5x)

To differentiate, we would apply the product rule which is expressed as

(fg)' = f'g + fg'

Let f = (x²-7x)^5 and g = (3x^5-5x)

f' = 5(2x - 7)(x²-7x)^4

g' = 15x^4 - 5

By applying the product rule, it becomes

y' = 5(2x - 7)(3x^5-5x)(x²-7x)^4 + (15x^4 - 5)(x²-7x)^5

You have one box that is 2 and 5/11

feet tall and a second box that is 2.45 feet tall. Write the decimal expansion for

2 and 5/11. If you stack the​ boxes, about how tall will the stack​ be​

we have that

If you stack the​ boxes,

we have

2.45+2.45=4.90 ft

Answer:

x+8 - 6/x+3

Step-by-step explanation:

a) Point = could be any point A to D = for example A

b) Line : AD

Could be any line named by the endpoints.

c) Segment: Fragment of a line

AB

d) Ray: part of a line that has a fixed star but no end:

BE

e) Angle : Could be any angle, the middle letter is where the angle rests.

f) 3 collinear points: A,B,C

3 points that are in the same line

g)Opposite rays: same end point but opposite directions

BE and BC

h) Plane: infinite set of points forming a connected flat surface.

ABDC

i) 3 non collinear points: AEC

Three points that aren't on the same line

j) another name for m

Answer:

1187.49

Step-by-step explanation:

[tex]P(40)=0.023(40)^3-0.289(40)^2+3.068(40)+55.170=1187.49[/tex]

SOLUTION:

Case: Distance time graph

Method:

a) the students speed from the 3rd to 5th minute

b) the times during the bike ride did the student come to a stop

d and h

8 minutes and 23 minutes

c) the students speed increase during.

b to c. 1 and 3 minutes

e to f. 11 and 15 minutes

f to g. 15 and 17 minutes

If the cost to park in garage can be modeled by the equation P = 3+ch

Part A

The equation to find the number of hours a person parked h = (P-3) / c

Part B

If c = $2.25 and number of hours h =6 hours, then the cost to park in garage is $16.5

Part C

If P = $25.50, the person parked 10 hours if the cost per hour is $2.25

The flat fee of parking = $3

The cost to park in garage can be modeled by the equation

P = 3+ch

Where c is the hourly rate to park

h is the number of hours parked in the garage

Part A

The equation to find the number of hours a person parked is

P = 3+ch

c × h = P-3

h = (P-3) / c

Part B

c = $2.25

h = 6 hours

P = 3 + 2.25×6

= 3 + 13.5

= $16.5

Part C

P = $25.50

c = 2.25

h = (P-3)/c

= (25.50-3)/2.25

= 10 hours

Hence, if the cost to park in garage can be modeled by the equation P = 3+ch

Part A

The equation to find the number of hours a person parked h = (P-3) / c

Part B

If c = $2.25 and number of hours h =6 hours, then the cost to park in garage is $16.5

Part C

If P = $25.50, the person parked 10 hours if the cost per hour is $2.25

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Looking at the diagram of the triangular prism and its net, we can see that

a = width of the base = 5 cm

b = the slant height = 13 cm

c = length of the base = 15 cm

Inequality: [tex]x-7\ge 15[/tex]

Solution: [tex]x\ge 22[/tex]

Inequality is a mathematical statement which depicts the relation between two or more mathematical variable or quantities which involves in relation which is not equal or inequal.

Given the statement is "A number decreased by 7 is at least 15"

Let the number be the variable x.

Now decreased by 7 = x-7

Suitable inequality sign for at least statement is [tex]\ge[/tex]

So the required inequality is given by,

[tex]x-7\ge15[/tex]

Solving the same we get,

[tex]x-7+7\ge 15+7[/tex]

[tex]x\ge 22[/tex]

Thus the number is [tex]x\ge 22[/tex]

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The division of the two numbers in scientific notation is equal to 1.91*10^15

To solve this problem, we have to divide the two numbers in scientific notation and to do this, we can simply apply division law of indices here;

We can first divide 6.1 by 3.2.

This will give us 1.90625 which is approximately 1.91.

Then applying the law of indices and subtract the power from one another. This becomes 20 - 5 = 15

The final value will be 1.91 * 10^15

The division of 6.1*10^20 by 3.2*10^5 is equal 1.91 *10^15

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Given:

The graph of the function f is given and the function g is as:

Required:

To graph the function g.

Explanation:

The graph of the function f(x+2), shift the graph f(x) left 2 units by subtracting 2 from the x-coordinates of the points on the graph of f.

The graph of the function

here

So the graph of g has undergone a vertical shrinking by a factor of

The graph of the function

reflect the graph of

across the x-axis by multiplying the y coordinate of the points on the graph of

by -1.

Thus the graph of the function

is as:

Final Answer:

The graph of the function g is attached in the explanation part.

Anlges A and D are right angles becuase they measure 90

Angle C is Acute because it is smaller than 90

Angle B is Obtuse because it is grather than 90

In the year 2006, the total average credit card debt for a U.S. household was 10370 dollars.

We are given the expression that gives an approximate value of the total average credit card debt in a U.S. household (in dollars), t years after 1995 as;

420t + 5750

where t represents number of years after the year 1995. Thus, for the year 2006, the value of t is;

t = 2006 - 1995

t = 11 years

Thus;

f(11) = 420(11) + 5750

f(11) = 10370 dollars

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The domain of the function is [1, ∞) and the range of the function is [0,∞).

Domain and range:

The domain and range of a function are  refers the set of all the inputs and outputs a function can give respectively.

Basically, domain takes all the possible input values from the set of real numbers whereas the range takes all the output values of the function.

Given,

Here we have the function

y = √x - 1

Now, here we need to find the domain and range of the function.

The given function is rewritten as,

√x - 1 > 0

Square both sides then we get,

x - 1 > 0

Add 1 on both sides then we get,

x > 1

Therefore, the domain is [1, ∞).

Similarly, let us consider, y ≥ 0

Therefore, the range is [0,∞).

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Answer:

12 is the number that comes after 11 and before 13. 12 represents the number between 11 and 13. 12 is a composite number.

Step-by-step explanation:

12 is the number that comes after 11 and before 13.

12 represents the number between 11 and 13. 12 is a composite number.

Answer:

See below

Step-by-step explanation:

Slope of given line is 1      y = (1) x + 2

 parallel line has same slope

    so it will start to look like this    y = (1) x   + b

        sub in the point 5,7 to find b = 2

final answer y=x+2

Given the expression below

Step 1: Using PEMDAS rule

P=> Parenthesis

E=>Exponent

M=>Multiplication

D=>Division

A=>Addition

S=> Subtraction

From the rule above, we will start our simplification with the parenthesis

Step 1: simplify (5-4)

Step 2: Expand 2(1)=> 2x1, then simplify (6-2(1))

Step 3: Expand 6(4)=>6 x 4

Step 4: Add 8 and 24

Hence, the final answer is 32

Answer: your answer would be 32

Step-by-step explanation:

using PEMDAS we would first go by parentheses and use the order by each step.

Let f(x) = 9x - 8. Find (f o f)(1).​

we know that

(f o f)(1).=f(f(1))

step 1

find f(1)

f(1)=9(1)-8

f(1)=1

substitute

f(f(1))=f(1)=1

therefore

the answer is 1

The equation which satisfied the given expression after simplification are (a) 3x = 24 and (c) 3(x - 2) = 18.

How simplification method work?

In mathematics, the simplification method is used for the equation formation for the problem statements. And it also convert the complicated expression into simpler one to make the calculation easy.

According to the question, the given equation can be simplified by using simplification method and it is written below:

The given equation is: 3x - 6 = 18

3x = 18 + 6 = 24 ⇒ 3x = 24

Similarly, 3x - 6 = 18

3(x - 2) = 18

Hence, the equation which satisfied the given expression after simplification are (a) 3x = 24 and (c) 3(x - 2) = 18.

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Answer: f(3) = 0.84375

Step-by-step explanation:

f(3) is asking for the value of the function when x = 3, not multiplying f by 3. (f(x) is basically the output, y)

So we just plug in 3 for x and simplify (use PEMDAS)

f(3) = 2(0.75)^3

f(3) = 2(0.421875)

f(3) = 0.84375

Answer:

[tex]\frac{27}{32}[/tex]

Step-by-step explanation:

It may be a bit easier to represent 0.75 as a fraction, since we can use the following property of exponents: [tex](\frac{a}{b})^x = \frac{a^x}{b^x}[/tex]

We can represent 0.75 as: [tex]\frac{3}{4}[/tex]

And substituting this into the function we get: [tex]f(x)=2(\frac{3}{4})^x[/tex]

calculating the value when x=3, we get: [tex]f(3)=2(\frac{3}{4})^3[/tex]

using the property previously stated we get: [tex]f(3)=2(\frac{3^3}{4^3})[/tex]

Raising each value to the exponent we get: [tex]f(3)=2(\frac{27}{64})[/tex]

When we multiply by two, we can simplify by splitting up 64, into two factors: 2 and 32, to get: [tex]\frac{2*27}{32*2}[/tex]

From here it's easy to see that we can cancel out the values 2, to get: [tex]\frac{27}{32}[/tex]

Which is our answer!

Since BCE is an inscribed angle, it measures half the measure of the inscribed arc.

Angle BCE inscribes the arc BE of 180°, we have:

Therefore the correct option is 1)

Rodger biked 30 miles in 2 hours. Write this rate as a unit rate.​

__________________________________

30 miles / 2 hours = 15 miles/hour

_________________________________________

Answer

15 miles/hour