I’m doing math homework and is about functions they said f(x)= x-3 and g(x)= √x-2

After I set them up I have this
am I supposed to just add the numbers or is there something else to do?

√ (x-3)-2

We can solve the inequality to get:

h ≤ -3

And its graph can be seen below.

Here we have the following inequality:

-(1/3)*h ≥ 8

To solve the inequality, we need to isolate h.

So we can multiply both sides by -3 (notice that this will change the sign of the inequality symbol)

So we will get:

-3*(-1/3)*h ≤ -3*h

h ≤ -3

Now to graph this, we need to draw a closed circle at -3, and draw an arrow that gose to the left.

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Answer:

Yes

Step-by-step explanation:

I think its yes.I think It's Yes.

The exponential function to describe the given sequence of numbers, 10, 60, 360, 2160, 12960, ... is aₙ = 10 × [tex]6^{n-1}[/tex].

The given series 10, 60, 360, 2160, 12960, ... is a geometric progression.

a = 10

The common difference r = 60/10 = 6

As we know the general formula of the nth term of a geometric series is

aₙ = a × [tex]r^{n-1}[/tex]

Now, put the values of a = 10, r = 6 and n in the general formula,

aₙ = 10 × [tex]6^{n-1}[/tex]

Therefore, the required exponential function to describe the given sequence of numbers, 10, 60, 360, 2160, 12960, ... is aₙ = 10 × [tex]6^{n-1}[/tex].

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A particle traveled a distance of 9.0×10¹² meters in 5.0 × 10⁷ seconds.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

If a particle traveled a distance of 9.0×10¹² meters at a rate of 1.8×10⁵meters per second.

And the distance,

= rate x time.

Rearranging the formula,

Time = Distance / rate

Time = 9.0×10¹² / 1.8×10⁵

Simplifying by using division operation,

Time = (9.0/1.8) × 10¹² × 10⁻⁵

Time = 5.0 × 10⁷

Therefore, the required specified time is  5.0 × 10⁷ seconds.

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Given:

A length of a side of an equilateral triangle = 32 cm

Formula Used:

If in an equilateral triangle with side length 'a' then,

Area of an equilateral triangle = [(√3)/4] × a2 

Calculations:

Area of an equilateral triangle = [(√3)/4] × 322

⇒ (1024 × √3)/4

⇒ 256√3 cm2

According to triangle inequality theorem a triangle with two sides 7 units and 17 units, has a third side which measures 10 units.

What is Triangle Inequality Theorem?

According to triangle inequality theorem, the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

The two sides of a triangle are -

a=7, b=x and c=17, where a, b and c are the sides of the triangle.

As, 17 is a bigger number so let it be the biggest side.

Now, according to triangle inequality theorem -

a + b = c

7 + x = 17

x = 17 -7

x = 10

Therefore, the third side of the triangle measures 10 units.

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Answer:  -100

Step-by-step explanation:   -7(15)+5

It said x=15 so put 15 in and solve from there and that would be -100

HOPE THIS HELPS ANY I JUST completed FUNCTIONS AND MAN IT WAS FUN

4.68

find unit rate by dividing 208 cents by 16 which is 13 than multiply by 36

Answer:

16 inches of ribbon cost- $2.08

36 inches of ribbon cost- ?

36*$2.08/ 16

$74.88/16

= $4.68

Thus, 36 inches of ribbon would cost $4.68

Elizabeth has a box that can hold exactly 24 unit cubes. It could also be said that her box has 24 cubic units. So, option D. is correct.

A cubic unit is a unit of measurement for volume. It represents the amount of space an object occupies in three dimensions: Length, Width and Height. It is often used to measure the volume of three-dimensional shapes such as cubes, square prisms, cylinders, and spheres. Cubic units are most commonly measured in cubic meters or cubic feet, but they can also be expressed in smaller units such as cubic centimeters or cubic inches.

The total volume of the box is 24 cubic units. A side of the box may measure 2 units x 3 units x 4 units = 24 cubic units.

Choice A is incorrect. This is because the area of ​​a shape is a measure of the two-dimensional space it occupies, and the volume of a shape is a measure of the three-dimensional space it occupies.

Choice B is incorrect. This is because the area of ​​a shape is a measurement of the two-dimensional space it occupies, not its volume.

Option C is incorrect because it states that the box has a volume of 12 cubic units, but it is not because the volume he has is 24 cubic units.

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The rate exists water being poured into the cup when the water level is 9 cm exists [tex]$$1458 \pi \mathrm{cm}^3 s^{-1}$$[/tex].

To determine the derivative of a composite function in differential calculus, apply the chain rule formula. If y = f(g(x)), then according to the chain rule, the instantaneous rates of change of the functions f and g with respect to x produce the instantaneous rate of change of f with respect to x.

A composition of functions, such as the composition of the functions f and g, f(g(x)), can be used to determine the derivative using the chain rule.

Let us set up the following variables:

R, Radius of conical cup (cm) = 30 cm

H, Height of the conical cup (cm) = 10 cm

Our aim is to find dV/dt when h = 9 and we are given dh/dt = 2

By similar triangles we have

r : h = R : H

r/h = 30/10

⇒ r = 3h

The volume of a cone is 1/3π r²h, So:

V = 1/3π r²h

simplifying the equation, we get

= 1/3π (3h²)h

= 1/3π 9h²h

= 3π h³

Differentiating wrt h we get:

dV/dh = 9π h²

Applying the chain rule we have:

dV/dt = (dV/dh)(dh/dt)

= 9π h² × 2

= 18π h²

If h = 9 then

[tex]$\left[\frac{d V}{d t}\right]_{h=9}=18 \pi\left(9^2\right)=1458 \pi \mathrm{cm}^3 s^{-1}$$[/tex].

Therefore, the rate exists water being poured into the cup when the water level 9 cm exists [tex]$$1458 \pi \mathrm{cm}^3 s^{-1}$$[/tex].

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Answer:

33 ounces

Explanation:

20% of 27.5 ounces is 5.5 ounces.

To find how much more juice the container has, we add 5.5 to 27.5, which equals to 33 ounces

Answer:

y = x - 2

Step-by-step explanation:

Here m is the slope and b is the y-intercept.

Choose any two points on the line.            

 (2,0)  ; (0,-2)

Now, find the slope.

        [tex]\sf \boxed{Slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]

                   [tex]= \dfrac{-2 - 0}{0 - 2}\\\\=\dfrac{-2}{-2}\\\\= +1[/tex]

m = 1.

Now, y = 1x +  b

The (2 , 0) passes through the line. Substitute x = 2 and y = 0 in the above equation and find the value of 'b'.

       0 = 1*2 + b

       0 =  2 + b

        -2 = b

Equation of line:

              y = x - 2

Answer:

5 kg.

Step-by-step explanation:

2 kg for $0.96 is more expensive than 5 kg for $1.95

Therefore, the inequality 1.85 < 15 can be used to find h.

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance. For instance, let's say you have 225 and want to purchase a new bicycle that costs $250.

When the expression's variables and constants are given values, the calculation it describes yields the expression's value. In an algebraic expression, numbers can be represented by letters.

The inequality 1.85 < 15 can be used to find h, the number of mini-hamburgers Betsy and her sister bought. This inequality represents the constraint that the total cost of the mini-hamburgers (1.85h) must be less than the amount of money they have to spend (15). To solve for h, you would divide both sides of the inequality by 1.85, giving you h < 8.1, so h can be any number less than 8.1.

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Earth's rotation is what causes day and night. As Earth rotates on its axis, half of the planet is facing the Sun, while the other half is facing away from the Sun.

The half of the planet facing the Sun experiences daylight, while the half facing away from the Sun experiences darkness. This cycle repeats itself every 24 hours, resulting in the day and night cycle that we experience.

Earth's rotation causes day and night by rotating on its axis, with half of the planet facing the Sun and the other half facing away from the Sun. This cycle of daylight and darkness lasts for  creating the day and night cycle that we observe.Earth's rotation is what causes day and night. As Earth rotates on its axis, half of the planet is facing the Sun, while the other half is facing away from the Sun.

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We can check if a function has an inverse function using horizontal  Line Test.

What is Function?

A relation between a collection of inputs and outputs is known as a function. In plain English, a function is an association between inputs in which each input is connect

horizontal  Line Test

Make f a function. Any horizontal line that crosses the f graph more than once indicates that f lacks an inverse. F does have an inverse if there are no horizontal lines that cross the graph of f more than once.

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Answer:

85+7.5v=160

7.5v=160-85

7.5v=75

V=75/7.5

V=10

Ryan would need to take 10 visits to get a free ticket.

The equation for new function is,

⇒ f (x) = ∛( 1/4x - 6) - 5

A relation between a set of inputs having one output each is called a function.

Given that;

The parent function is,

⇒ g (x) = ∛x

Now, After  reflected and stretched by 4, we get;

⇒ g (x) = f (1/4x) = ∛ 1/4x

And, After translated 6 units to the right, we get;

⇒ g (x) = f (x - 6) = ∛ 1/4x - 6

And, After 5 unit down, we get;

⇒ g (x) = h (x) - 5 = ∛( 1/4x - 6) - 5

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P= kd/u^2 is the equation which expresses the following relationship p varies derectly with d and inversly with the square of u.

Equation is a mathematical statement that expresses the equality of two expressions. An equation is written as an expression containing an equal sign, with each side of the equal sign representing a mathematical expression. The purpose of an equation is to show the relationship between two or more variables, such as a change in one variable resulting in a change in another. Equations are used to solve problems in mathematics, physics, economics, and many other fields.

The equation states that p is directly proportional to d, and inversely proportional to u squared. This means that as d increases, p increases, and as u increases, p decreases. The constant of proportionality, k, is a measure of the strength of the relationship between p, d, and u.

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The function [tex]$$f(x)= \begin{cases}1-x^2 & x \leqslant 1 \\ \ln (x) & x \geqslant 1\end{cases}$$[/tex]  is continuous on (-∞, ∞).

As per the given data the function f(x) is given by:

[tex]$$f(x)= \begin{cases}1-x^2 & x \leqslant 1 \\ \ln (x) & x \geqslant 1\end{cases}$$[/tex]

Here we have to determine that the function f(x) is continuous on (-∞, ∞)

If we show that f(x) is continuous at x = 1 then f(x) is continuous on (-∞, ∞)

What are continuous function?

A continuous function in mathematics is one where changes in the parameter cause constant changes in the function's value (i.e., a change without a leap). This shows that there are no abrupt changes in value or discontinuities.

To show f(x) is continuous at x = 1

[tex]\lim _{x \rightarrow 1^{-}} f(x)=\lim _{x \rightarrow 1^{+}}[/tex] f(x)

[tex]\rightarrow \lim _{x \rightarrow 1^{-}} f(x) & =\lim _{x \rightarrow 1^{-}}\left(1-x^2\right) \\[/tex]

= 1 - 1

= 0

[tex]\lim _{x \rightarrow 1^{+}} f(x) & =\lim _{x \rightarrow 1^{+}} \ln (x) \\[/tex]

= ln 1

= 0

Therefore  [tex]\lim _{x \rightarrow 1^{+}} f(x) & =\lim _{x \rightarrow 1^{-}} f(x)-0[/tex].

Hence f(x) is continuous on (-∞, ∞)

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The inverse of ∼P→∼Q is P->Q.

Given ∼P→∼Q

Its inverse, ∼(∼P)→∼(∼Q), means that P→Q.

If the hypothesis is correct but the conclusion is untrue, a conditional statement is false. If the statement in the example above read, "If you achieve good marks then you will not get into a good college," it would be untrue. A conditional statement that has been modified or rearranged is referred to as a related conditional. An if-then statement, also known as a conditional statement, is a set of hypotheses followed by a conclusion. It is noted that p→q. Read this: if p, then q.

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The ratio for cos (cosine) of angle θ is: cos(θ) =  adjacent side of θ / hypotenuse

We know that in right triangle the cosine of an angle is nothing but the ratio of the side adjacent of  given angle to the hypotenuse.

In right tirnagle for an angle θ, the ratio for cosine of angle θ would be:

cos(θ) =  adjacent side of θ / hypotenuse

Consider following right triangle PQR with angle PQR = 90 degrees

Here, PR is the hypotenuse.

Assume that angle QPR measure α degrees and angle PRQ measures θ degrees.

By definition of cosine of angle θ,

cos(θ) =  adjacent side of θ / hypotenuse

cos(θ) =  QR / PR

And by definition of cosine of angle α,

cos(α) =  adjacent side of α / hypotenuse

cos(α) = PQ / PR

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The monthly payment for this difference would be $1,361.21. An Adjustable Rate Mortgage (ARM) is a type of mortgage in which the interest rate on the loan changes over time.

An Adjustable Rate Mortgage (ARM) payment is based on various factors such as the loan amount, interest rate, and the terms of the ARM. The interest rate is usually tied to a specific financial index, such as the U.S.

Here is the calculation format for the difference in payments between year 2 and year 3 for Bart and April's mortgage:

Total amount to be paid for the mortgage: $315,000

Rate of interest: 5.85% (Depreciating rate)

Time = 2 years:

a. Remaining amount to be paid after 2 years:

Principal × (1 - Rate/100)^time

= $315,000 × (1 - 5.85/100)²

= $315,000 × (1 - 0.0585)²

= $279,223.01

Time = 3 years:

a. Remaining amount to be paid after 3 years:

Principal × (1 - Rate/100)^time

= $315,000 × (1 - 5.85/100)³

= $315,000 × (1 - 0.0585)³

= $262,888.46

Difference in payments from year 2 to year 3:

= Remaining amount after 2 years - Remaining amount after 3 years

= $279,223.01 - $262,888.46

= $16,334.55

The monthly payment for this difference would be $1,361.21, which is calculated by dividing the difference in payments by 12:

$16334.546/12 = $1361.21

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The domain and scope of the identity function are the same. Equation for the identity function is  f(x) = x, or y = x.

An statement, rule, or law in mathematics that specifies the connection between an independent variable and a dependent variable (the dependent variable. A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. Y=X2 is an illustration of this. You only receive one output for y if you enter anything for x. The fact that x is the input value leads us to argue that y is a function of x.

identity function are the same.

Equation for the identity function is

f(x) = x, or y = x.

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The seven different types of triangles are Equiangular Triangle , Acute Angled Triangle , Right Angled Triangle , Obtuse Angled Triangle , Equilateral Triangle , Isosceles Triangle and Scalene Triangle .

The Triangle is defined as a polygon with three sides having three vertices .

The Seven different types of Triangles are :

(i) Equiangular Triangle :

It is a type of triangle in which the measure of all the three sides of triangle are equal .

(ii) Acute Angled Triangle :

It is a type of triangle in which all the angles of triangle are acute , that means angle is less than 90 degree .

(iii) Right Angled Triangle :

It is the type of triangle in which the measure of one angle is 90 degree .

(iv) Obtuse Angled Triangle :

It is defined as a triangle in which one angle of the triangle is obtuse , that means the angle is greater than 90 and less than 180 degree .

(v) Equilateral Triangle :

It is a triangle in which the measure of all the sides of the triangle are equal .

(vi) Isosceles Triangle :

It is a type of triangle in which the measure of the two sides of the triangle are equal .

(vii) Scalene Triangle :

It is defined as a triangle in which the measure of all the sides of triangle are different ,

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P (X)= [tex]x^3+4 x^2-3x+2[/tex]  moreover, [tex]\frac{P(x)}{x - 1} = x^{2} + 5x +2[/tex] as a result, the actual claim is  [tex]$p(x)=(x-1)\left(x^2+5 x+2\right)+\frac{4}{x-1}$[/tex]

The likelihood of an event occurring is determined by probability:       P(A) = f / N. Probability and odds are related, but probability is necessary for odds to exist. Prior to calculating the likelihood that an event will occur, probability is required.

The steps listed below can be used to determine an event's likelihood: Step 1: Identify an event that has only one outcome. Step 2: Compile a list of all potential outcomes, including any positive ones. Step 3: Subtract the number of favourable outcomes from the total number of outcomes that are feasible. The probability of A or B is equal to p(A or B) = p(A) + p(B) if occurrences A and B are mutually exclusive (B). A probability is a number that expresses the possibility or likelihood that a specific event will take place.

Therefore the correct answer is option A ) [tex]$p(x)=(x-1)\left(x^2+5 x+2\right)+\frac{4}{x-1}$[/tex]

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The perimeter expression of a rectangle has a perimeter represented by the expression 4x−8 is 2(2x - 4)

From the question, we have the following parameters that can be used in our computation:

Perimeter = 4x - 8

Factor out 2 from the expression

So, we have the following representation

Perimeter = 2 * 2x - 2 * 4

So, we have

Perimeter = 2(2x - 4)

Hence, the perimeter is 2(2x - 4)

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The value of the legs of the triangle would be hypotenuse/√2.

You can use basic trigonometry to solve this problem. We know that the sine of the angle made by the hypotenuse and the base is equal to the ratio of perpendicular height and the hypotenuse, given that the angle is 45° the perpendicular will be equal to ⇒ hypotenuse × sin(45°).

That is perpendicular=hypotenuse/√2

Similarly, the cosine of the angle made by the hypotenuse and the base is equal to the ratio of base length and the hypotenuse, given that the angle is 45° the base will be equal to ⇒ hypotenuse × cos(45°)

That is base=hypotenuse/√2

Therefore, the value of the legs of the 45°-45°-90° triangle would be hypotenuse/√2.

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The value of x in this problem is 2.

Our given algebraic equation is 2.5 ( 6x - 4 ) = 10 + 4 ( 1.5 + 0.5x) and in this, we have to find the final value of x.

Use the transposing method to isolate the variable x and then solve for it.

distribute brackets on both sides of the equation.

= 2.5*6x - 2.5*4 = 10 + 4*1.5 + 4*0.5x

= 15x - 10 = 10 + 6 + 2x

collect terms in x to the left side and numeric values to the right side.

= 15x - 2x = 10 + 6 + 10

= 13x = 26

= x = 26/13 = 2

Therefore the final value of x in this equation will be 2.

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