I need this for an exam of mine and I don't understand how to solve it

The domain of f + g is (-∞, ∞).

The domain of ff is (-∞, ∞).

The domain of f/g is (-∞, 1) ∪ (1, ∞).

To find the domain of the given functions, we need to consider any restrictions that may occur. In this case, we have the functions f(x) = x + 2 and g(x) = x - 1. Let's determine the domains of the following composite functions:

f + g:

The function (f + g)(x) represents the sum of f(x) and g(x), which is (x + 2) + (x - 1). Since addition is defined for all real numbers, there are no restrictions on the domain. Therefore, the domain of f + g is (-∞, ∞), which includes all real numbers.

ff:

The function ff(x) represents the composition of f(x) with itself, which is f(f(x)). Substituting f(x) = x + 2 into f(f(x)), we get f(f(x)) = f(x + 2) = (x + 2) + 2 = x + 4. As there are no restrictions on addition and subtraction, the domain of ff is also (-∞, ∞), encompassing all real numbers.

f/g:

The function f/g(x) represents the division of f(x) by g(x), which is (x + 2)/(x - 1). However, we need to be cautious about any potential division by zero. If the denominator (x - 1) equals zero, the division is undefined. Solving x - 1 = 0, we find x = 1. Thus, x = 1 is the only value that causes a division by zero.

Therefore, the domain of f/g is all real numbers except x = 1. In interval notation, the domain can be expressed as (-∞, 1) ∪ (1, ∞).

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Answer:

alternate interior angles theorem

Step-by-step explanation:

The alternate interior angles theorem states that when two parallel lines are cut by a transversal, the resulting angles produced are a pair of congruent alternate interior angles.

Given the image attached below, both line k and line l are parallel to each other and also, line t is the transversal, therefore the resulting congruent alternate interior angles produced are:

∠ 4 ≅ ∠6, ∠1 ≅ ∠7

Answer:

Step-by-step explanation:

A. Alternate interior angles theorem.

Answer:

√13

Hope that helps! :)

Step-by-step explanation:

An irrational number is a number that is non-terminating and non-recurring.

√13 is an irrational number because it cannot be expressed as either a terminating or a repeating decimal.

Option C is the correct answer.

An irrational number is a number that is non-terminating and non-recurring.

We have,

3

This is an integer so it is not an irrational number.

17

This is also an integer so it is not an irrational number.

6

This is also an integer so it is not an irrational number.

√13  = 3.6-55512755..

It is a non-terminating and non-recurring number so it is an irrational number.

0.2971

It is a terminating number so it is not an irrational number.

Thus,

√13 is an irrational number because it cannot be expressed as either a terminating or a repeating decimal.

Option C is the correct answer.

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Answer: I think its 10%

Step-by-step explanation: I hope that helps

Answer:

5

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

A base angle

B leg

C vertex angle

D leg

E base angle

F base

in any isosceles triangle there are 2 congruent legs and 2 congruent base angles.

the base angles are opposite the congruent legs

the remaining side, the base is the 3rd side of the triangle

the vertex angle is formed by the 2 congruent legs

Answer:

C. 36

There are 150 cups total, and 60 blue cups

\(150/60=0.4\)

Multiply that by the number of cups he picked up

\(0.4*90=36\)

A sample size of approximately 506 voters should be drawn to ensure that the sample proportion of voters who are satisfied with their representative is approximately normally distributed.

In order to determine the sample size needed for a normal distribution of sample proportions, we can use the formula:

n = (² * p * q) / E²

Where:

n is the sample size

Z is the z-score corresponding to the desired level of confidence (typically 1.96 for a 95% confidence level)

p is the estimated proportion of voters satisfied with their representative (0.77)

q is the complement of p (1 - p)

E is the desired margin of error (usually represented as a decimal value)

By plugging in the given values, we can calculate the sample size:

n = (1.96² * 0.77 * 0.23) / (0.05²)

n = 506.06

Therefore, a sample size of approximately 506 voters should be drawn to ensure that the sample proportion of voters who are satisfied with their representative is approximately normally distributed.

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Answer:

\(\huge\boxed{2}\)

Step-by-step explanation:

Given Polynomial is:

\(3x^2 + 6x = 0\)

Degree of polynomial is the highest power on the variable.

Here 2 is the highest power on the variable, So, it is the degree of polynomial.

a. The surface area of the outer square pyramid is 11.25 square centimeters. b. The side length of the inner square pyramid is 2.25 centimeters.

a. To find the surface area of the outer square pyramid, we need to calculate the area of each of its faces and add them together. The outer square pyramid has four triangular faces and a square base.

Area of a triangular face = (1/2) x base x height

Area of a triangular face = (1/2) x 1.5 cm x 3 cm = 2.25 cm²

The area of the square base can be found using the formula for the area of a square:

Area of square base = side length²

Area of square base = 1.5 cm x 1.5 cm = 2.25 cm²

Therefore, the total surface area of the outer square pyramid is:

Surface area = 4 x area of triangular face + area of square base

Surface area = 4 x 2.25 cm² + 2.25 cm²

Surface area = 11.25 cm²

Therefore, the surface area of the outer square pyramid is 11.25 square centimeters.

b. The dimensions of the inner square pyramid have a ratio of 2:3 to the dimensions of the outer square pyramid. Let's call the side length of the inner square pyramid "x". Since the ratio of the dimensions is 2:3, we know that the side length of the outer square pyramid is (3/2)x.

The volume of a square pyramid can be calculated using the formula:

Volume = (1/3) x base area x height

Since the two pyramids are similar, the ratio of their volumes is the cube of the ratio of their corresponding side lengths:

Volume of inner pyramid / Volume of outer pyramid = (x / (3/2)x)³ = (2/3)³

We also know that the volume of the outer pyramid is:

Volume of outer pyramid = (1/3) x base area x height

The height of the two pyramids is the same, since they are stacked on top of each other, so we can write:

Volume of inner pyramid / Volume of outer pyramid = (1/3) x base area of inner pyramid / (1/3) x base area of outer pyramid

Simplifying this expression, we get:

(x / (3/2)x)³ = (1/3) x² / (1/3) (3/2x)²

Solving for x, we get:

x = (3/2)²

x = 2.25

Therefore, the side length of the inner square pyramid is 2.25 centimeters.

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The complete question is :

a. For the outer square pyramid, the side length of the base is 1.5 centimeters and the height of one of the triangular faces is 3 centimeters. What is the surface area of the outer square pyramid?

b. The dimensions of the inner square pyramid have a ratio of 2:3 to the dimensions of the outer square pyramid. What are the dimensions of the inner square pyramid?

Answer: 42 kmh

Step-by-step explanation:

Speed = distance / time

= 189 / 4.5

= 42 kmh

Answer:

Average Speed = 42 km/hr

Step-by-step explanation:

Given:

Distance = 189 km

Time = 4.5 hours

Required:

Average Speed = ?

Formula :

Average Speed = Total Distance Covered/ Total Time Taken

Solution:

Putting the givens

Average Speed = 189/4.5

Average Speed = 42 km/hr

Using the formula of area of a circle, about 226.08in² has been eaten

The diameter of the pizza is given as 24 inches. To calculate the area of the entire pizza, we need to use the formula for the area of a circle:

Area = π * r²

where π is approximately 3.14 and r is the radius of the circle.

Given that the diameter is 24 inches, the radius (r) would be half of the diameter, which is 12 inches.

Let's calculate the area of the entire pizza first:

Area = 3.14 * 12²

Area = 3.14 * 144

Area ≈ 452.16 square inches

Now, if half of the pizza is consumed, we need to calculate the area of half of the pizza. To do that, we divide the area of the entire pizza by 2:

Area of half of the pizza = 452.16 / 2

Area of half of the pizza ≈ 226.08 square inches

Therefore, if half of the pizza is consumed, approximately 226.08 square inches of pizza would be eaten.

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Answer:

0.0236 m per minute,

Step-by-step explanation:

Volume of the cone V = 1/3 π r^2 h.

Diameter = 2r = 2h so r = h

and V = 1/3 π h^3

So  the rate of change of volume with height =

dV / dh =  π h^2.

We are given that dV/dt = 6.

So the rate of change of height: dh/dt = dV/dt * dh/dV

= 6 * 1/ π h^2

When  h = 9

dh/dt = 6 / 81π m per minute

= 0.0236 m per minute,

Answer:

Choice 3 and 5

Step-by-step explanation:

Answer: A,B,E

Step-by-step explanation:

Just trust me

3x + 4y = 25 is an example of a line that is parallel to the supplied line.

Equations are mathematical expressions that have two algebraic expression on either side of an equals (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left hand side = right hand side) is a fundamental mathematical formula. For an unknown quantity represented by an unknown variable, equations can be solved to determine its value. It is clear that a statement is not an equation if there is no "equal to" sign in it. The phrase will be regarded as an expression.

Given that : line that is parallel to the line 3x + 4y = 32 and contains

the point (7,1).

3x + 4y = 32 is the equation for given line

This type of line is called a slope intercept. The line has a slope of m=\(\frac{-3}{4}\).

The slope of parallel lines is equal. As a result, all lines with slope m=\(\frac{-3}{4}\).will be perpendicular to one another.

3x + 4y = 25 is an example of a line that is parallel to the supplied line.

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we have the following:

Answer:

70 dollars

Step-by-step explanation:

he has only 70%left of his initial savings so that make 70%*100=7*10=70usd

the PERT weighted average is 9 days

PERT can be defined as an estimating technique that uses a weighted average of three numbers to get a final estimate.

The formula for finding the PERT weighted average is given as;

PERT weighted average = (Optimistic + (4 X Most Likely) + Pessimistic)/6

We have;

Substitute the values into the formula

PERT weighted average  = \(\frac{6 + 4(8) + 16 }{6}\)

PERT weighted average  = \(\frac{54}{6}\)

PERT weighted average  = 9 days

Thus, the PERT weighted average is 9 days

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The table provides information about three events related to rolling three dice. There are eight possible outcomes in total, the probability of this event is 3/8.

In the first event, the sum of the three dice rolls is 10. Looking at the table, we see that three outcomes meet this condition: (4, 3, 3), (3, 4, 3), and (3, 3, 4). Since there are eight possible outcomes in total, the probability of this event is 3/8.

The second event involves rolling an even number on the first die, a number greater than 4 on the second die, and an even number on the third die. From the table, we observe that two outcomes satisfy this condition: (6, 5, 4) and (6, 6, 4). Therefore, the probability of this event is 2/8 or 1/4.  

The third event requires obtaining an odd number on the first die, a number less than or equal to 3 on the second die, and an even number on the third die. We find only one outcome that fulfills this condition: (1, 2, 4). Hence, the probability of this event is 1/8.  

To summarize, the first event has a probability of 3/8, the second event has a probability of 1/4, and the third event has a probability of 1/8.

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Answer:

\(\sqrt{2^{5} }\) is correct

Step-by-step explanation:

Answer:

8a+2

Step-by-step explanation:

add up all the A's then add up the numbers

The required vertex form of the given equation is a) \(4(x-6)^2 +10\) is correct

the function  \(y=4x^2+24x+154\) is given,

vertex form of a equation \(y=ax^2+bx+c\) is given by \(y=a(x-h)^2+k\).

since \(y=4x^2+24x+154\)
Now h = - b/2a

   h = -N

Now at x = 0
  k = 10
vector form can be given by  \(4(x+6)^2 +10\)

The question is incomplete. The question could be:

what is the correct vertex form of equation \(y=4x^2+24x+154\)?
a)\(4(x+6)^2 +10\)
b)\(4(x-6)^2 -26\)
c)\(4(x-6)^2 -134\)
d)\(4(x-6)^2 +154\)

Thus, the vector form of the given function is \(4(x+6)^2 +10\)

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The following time Joey's age is greater than Zoe's, his two numbers add up to 11 years.

Consider Chloe to be c years old and Joey to be c+1 years old. After n years, Chloe and Zoe will be n + c and n + 1 respectively.

Based on the given conditions,

(n + c) ÷ (n + 1) = 1 + [(c - 1) ÷ (n + 1)]

n is an integer for 9 non-negative integers.

C – 1 hence has 9 positive divisors.

Either \(p^{8}\) or \(p^{2} q^{2}\) is the prime factorization of c-1 < 100

Since c - 1 < 100, is

c - 1 = \(2^{2} *3^{2}\)

c - 1 = 36,

c = 36 + 1

We can calculate the coefficient,

c = 37

We can infer that Joey is 38 years old as of right now.

Assume that after k years, Joey's age is multiplied by Zoe's age, making Joey and Zoe k + 38 and k + 1 years old, respectively.

So,

We can write,

(k + 38) ÷ (k + 1) = 1 + [(38 - 1) ÷ (k + 1)]

K is an integer for some positive integers.

Since 37 can be divided by k + 1,

k = 36 is the only viable option.

Using the assumption that Joey will be k + 38 = 74 years old, the result is 7 + 4 = 11.

Therefore,

11 years is the sum of Joey's two digits the next time his age is a multiple of Zoe's age.

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Answer:  Brian gets $39.2 more over Colin.

Step-by-step explanation:

Given: Total tip amount = £78.40

The ratio of the share of tips for Pawl, Colin and Bria  is 2:1 :5.

Let tip amount for Pawl = 2x, tip amount for Colin = x , tip amount for Bria = 5x

Then, 2x+x+5x= 78.40

\(\Rightarrow\ 8x = 78.40\\\\\Rightarrow x=\dfrac{78.40}{8 }\\\\\Rightarrow x=9.8\)

Tip for Colin = $ 9.8 , Tip for Bria = 5($9.8)= $49

Difference = $(49-9.8) = $ 39.2

Hence, Brian gets $39.2 more over Colin.

Answer:

In ko add krne k baad 10 se multiple kro

Answer:

If the sum of two numbers is 128band their difference is 16 then find the number

Answer:

perseveration

Step-by-step explanation:

The term you are looking for is "perseveration."