Find (f/g) (x). include any restrictions on the domain.
(image attached

Answer:

X = 17

Step-by-step explanation:

Since M = N then,

(3x - 22) = (2x-5)

What we can do next is get the X's on one side and the numbers on the other side of the equal sign

Let's subtract 2x from both sides

3x - 2x is just X, so

X - 22 = -5

Now we can add 22 to both sides. -5+22 = 17

X = 17

Plug in 17 to make sure

(3x - 22) = 3(17)-22 = 51-22 = 29

(2x-5) = 2(17)-5 = 34 - 5 = 29

The required function is continuous at x = -5 when c = 4.

If it is possible to draw the curve without encountering any breaks, the function is considered to be continuous in the interval. If every point in the interval satisfies the function, the function is said to be continuous.

For the function to be continuous at x = -5, the value of the function f(-5) must be equal to the value of c. That is,

f(-5) = c

Since f(x) = 4 when x = 1, we have

f(-5) = 4

Therefore,

c = 4

So the function is continuous at x = -5 when c = 4.

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Answer:

Step-by-step explanation:

10π cm * 12 cm = 120π cm² ≈ 377 cm²

The graph of y = 10 + 20x that represents the situation is shown in the attachment.

A graph of a linear equation is a straight line on a coordinate plane that represents all the solutions to the equation. A linear equation can be written in the form of y = mx + b, where m is the slope of the line and b is the y-intercept.

The slope and y-intercept determine the position and direction of the line on the coordinate plane. Points on the line satisfy the equation, and any x and y values that satisfy the equation can be plotted on the graph to form the line. The graph of a linear equation can be used to visualize relationships between variables and to make predictions about the values of the variables based on the line.

Thus, the equation y = 10 + 20x will have a graph that has a y-intercept of 10 and a slope of 20. The graph is shown below.

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Answer:

what the person above said pls give the brainliest

Step-by-step explanation:

Answer:

When we multiply by a power of 10 (such as 10, 100, 1000, 10000, etc.), the number of digit zeros in the power of 10 is the number of places we move the decimal point to the right.

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Step-by-step explanation:

A bottle of tomato juice contains 247. 5 mg of vitamin C and A bottle of grape juice contains 258 mg are in one serving of each type of juice is 45mg and 86mg.

A bottle of tomato juice contains 247. 5 mg of vitamin C and has 5. 5 servings so,

247.5/5.5 = 45 mg

A bottle of grape juice contains 258 mg of vitamin C and has 3 servings so,

258/3 = 86 mg

Water-soluble vitamin C, sometimes referred to as ascorbic acid and ascorbate, is present in citrus and other fruits and vegetables. It is also available as a dietary supplement and as an ingredient in topical "serums" used to cure melasma (dark pigment spots) and facial wrinkles. Scurvy is treated and prevented with it.

Vitamin C is a necessary nutrient that aids in collagen development, tissue healing, and the enzymatic synthesis of certain neurotransmitters. It is necessary for the operation of various enzymes and is crucial for the immune system. Additionally, it serves as an antioxidant. The majority of animals can produce their own vitamin C.

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The amount of light that passes through a camera lens is determined by the aperture, which is the size of the opening in the lens that lets light in. changing from f/1.4 to f/8 reduces the amount of light that can pass through the lens by a factor of 32.49,

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The correct two expressions have the same solution are,

⇒ 230p - 1010 = 650p - 400 - p

⇒ 23p - 101 = 65p - 40 - 0.1p

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ 2.3p - 10.1 = 6.5p - 4 - 0.01p

Now, We can simplify as;

⇒ 2.3p - 10.1 = 6.5p - 4 - 0.01p

Multiply by 10 both side,

⇒ 23p - 101 = 65p - 40 - 0.1p

And, ⇒ 2.3p - 10.1 = 6.5p - 4 - 0.01p

Multiply by 100 both side,

⇒ 230p - 1010 = 650p - 400 - p

Thus, The correct two expressions have the same solution are,

⇒ 230p - 1010 = 650p - 400 - p

⇒ 23p - 101 = 65p - 40 - 0.1p

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The complete question is this;

Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4

The amount of the old monthly payment = $879

The amount of the new monthly payment = $724.5

Then the small amount of principal that has been paid = -17.57%

Given that,

Natan Nave bought a home with a 13% adjustable rate mortgage for 20 years.

He paid $11. 72 monthly per thousand on his original loan.

At the end of 4 years he owes the bank $75,000.

Now that interest rates have gone down to 10%

The bank will renew the mortgage at this rate or Natan can pay $75,000.

Natan decides to renew and will pay $9. 66 monthly per thousand on this loan.

Per thousand value = 75000/1000 = 75

What was the old monthly payment,

$[tex]11.72*75[/tex] = $879

What is the new monthly payment,

$[tex]9.66*75[/tex] = $724.5

What is the percent decrease in his monthly payment (to the nearest tenth),

= [tex](\frac{9.66}{11.72} )-1 *100[/tex]

= -17.57%

Therefore,

The amount of the old monthly payment = $879

The amount of the new monthly payment = $724.5

Then the small amount of principal that has been paid = -17.57%

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A clockwise rotation of 144° about the origin will map the pentagon onto itself. Option(c) is the correct answer.

The number of sides (n) of the pentagon is:

n =5

The pentagon will not be plotted onto itself when reflected across the x-axis because the pentagon has 5 sides (an odd number of sides).

To draw the pentagon onto itself, the pentagon has to be rotated.

The angle of rotation is:

θ [tex]= \frac{360}{n}[/tex]

θ  [tex]=\frac{360}{5} = 72[/tex]

Other possible angles of rotation must be multiple of 72. i.e.

θ= 72, 144, 216, 288...

Hence, a clockwise rotation of 144° about the origin will map the pentagon onto itself.

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The complete question is:

A regular pentagon is centered about the origin and has a vertex at (0, 4). Which transformation maps the pentagon to itself?

a. A reflection across line m

b. A reflection across the x-axis

c) A clockwise rotation of 144 degrees about the origin

Answer: $2.15

Step-by-step explanation: Let x represent the price of a pen.

5x + (x - 1.30) = 11.60

6x - 1.30 = 11.60

6x = 12.90

x = 2.15

the angle bisector theorem formula yields the value x=10.

The angle bisector theorem states that RU/RT=US/ST or a/b = x/y. A line or ray known as an angle bisector divides an angle in a triangle into two identically sized parts.

The geometry concept known as the angle bisector theorem examines the ratios of the two segments that a line that bisects the opposing angle splits a triangle's side into. It contrasts their relative lengths with the ratios of the other two sides of the triangle.

Side ratio: RU/RT=US/ST

3x/40 = x+2/16

6x=5x +10

x=10

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The polynomial that satisfies the conditions is: p(t) = (1/4)(t - 1)² (t - 2)³

This polynomial has a root of multiplicity 2 at t = 1 and a root of multiplicity 3 at t = 2, and also satisfies p(0) = 2 and p'(0) = 1.

The other root of p(t) can be found by factoring the polynomial further, but since the degree of the polynomial is 6, it will have 3 additional roots, which can be found using various mathematical methods such as the Rational Root Theorem or numerical methods.

Polynomials are mathematical expressions that involve variables raised to a power and are combined using addition and subtraction operations. The degree of a polynomial is the highest power of the variable in the expression.

A zero of a polynomial is a value of the variable for which the polynomial evaluates to zero. The multiplicity of a zero is the number of times the factor (t - zero) appears in the polynomial's factorization.

Given the conditions that the polynomial p(t) has a zero of multiplicity 2 at t = 1 and a zero of multiplicity 3 at t = 2, we can write p(t) as the product of factors (t - 1)² and (t - 2)³:

p(t) = a(t - 1)² (t - 2)³

where a is some constant. To find the value of a, we use the fact that p(0) = 2 and p'(0) = 1. We evaluate p(0) and p'(0) using the polynomial expression above, then solve for a.

First, we find p(0):

p(0) = a(0 - 1)² (0 - 2)³ = a(-1)² (-2)³ = a * 8

Next, we find p'(0):

p'(t) = 2a(t - 1)(t - 2)³ + a(t - 1)² * 3(t - 2)²

p'(0) = 2a(-1)(-2)³ + a(-1)² * 3(-2)² = 16a + 12a = 28a

Now that we have expressions for p(0) and p'(0), we can solve for a:

p(0) = a * 8 = 2 => a = 1/4

p'(0) = 28a = 1 => 28 * 1/4 = 1

So the polynomial that satisfies the conditions is:

p(t) = (1/4)(t - 1)² (t - 2)³

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The following equations are organized for P as a function of Q

1) P = 20-8Q

2) p = [tex]\dfrac{12-Q}{3}[/tex]

3) p = 9 - 4Q

A function in mathematics is, technically speaking, a relation between a set of inputs and a set of potential outputs, where each input is related to exactly one output. Examples of functions in mathematics typically range from integers to integers or from real numbers to real numbers.

Additionally, it is a relation or a process that links each element x of a set X to the codomain of the function and to a single element y of a different set Y (typically the same set).

1) Q = 20-P

Q + P = 20

P = 20-Q

2) Q=12-3P

Q +3P = 12

3P = 12-Q

p = [tex]\dfrac{12-Q}{3}[/tex]

P = 4 - 1/3Q

3) 8Q = 18 -2p

8Q + 2p = 18

2p = 18 - 8Q

p =  [tex]\dfrac{18-8Q}{2}[/tex]

p = 9 - 4Q

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Complete question:

The solution for the given expression [tex]\frac{x^{2} + y^{2} }{x^{3} + y^{3} } - \frac{1}{x + y}[/tex] will be [tex]\frac{xy}{x^{3} + y^{3} }[/tex].

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given an expression [tex]\frac{x^{2} + y^{2} }{x^{3} + y^{3} } - \frac{1}{x + y}[/tex]

We will solve this equation using the simplification methods,

Since,

a³ + b³ = (a +b)(a² +b² - ab)

From this formula;

=> [tex]\frac{x^{2} + y^{2} }{x^{3} + y^{3} } - \frac{1}{x + y}[/tex]

=> [tex]\frac{x^{2} + y^{2} }{(x + y)(x^{2} + y^{2} - xy) } - \frac{1}{x + y}[/tex]

taking 1/(x +y) common,

=> 1/(x +y) { (x² + y²)/(x² +y² - xy) - 1}

=>  1/(x +y) { xy/(x² +y² - xy)}

=> xy/(x³ +y³)

Therefore, [tex]\frac{xy}{x^{3} + y^{3} }[/tex] will be the simplified form of the given Equation.

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Paying only the minimum balance each month will take the longest period of time to pay off the credit card debt.

Simple interest is defined as the percentage of earnings on the lending for a period of time.

Paying only the minimum balance each month will take the longest period of time to pay off the credit card debt. This method is often referred to as "minimum payment plan." By making only the minimum payment each month, the credit card holder will pay mostly interest, and very little of the principal balance. This will result in a longer period of time to pay off the debt, as the outstanding balance will only decrease slowly each month.

In contrast, making fixed payments each month, regardless of the minimum payment, will result in paying off the debt more quickly. Snowballing payments according to the highest interest rate or the lowest balance will also help pay off the debt more quickly, as these methods prioritize paying off the credit cards with the highest interest rate or the lowest balance first.

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To Calculate the Sum or Difference : x = 12

When two or more numbers or terms are added together, the total is the outcome or answer.

Consequently, the sum is a method of assembling objects.

The process of combining two or more numbers to create a new result or total is known as the sum, to put it another way.

Where Samantha's age at the moment is y and her age in five years is a. In light of the fact that she will turn 17 in 5 years, she is currently 12 years old. Consequently, y in this situation equals 12.

In summary, a = age in 5 years, and y = age right now (12)

Based on the given condition, Write :

x = 17 - 5

Calculate the Sum or Difference : x = 12

x = 12.

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The solution is Option A.

The value of the equation is x = -13/15 and x = 0

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

15x² + 13x = 0   be equation (1)

On simplifying the equation , we get

Subtracting 13x on both sides of the equation , we get

15x² = -13x

Divide by x on both sides of the equation , we get

15x = -13

Divide by 15 on both sides of the equation , we get

x = - ( 13/15 )

So , when x = 0

0 = 0

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

x = -13 ± √ ( 169 - 4 ( 15 ) ( 0 ) ) / 2 ( 15 )

x = -13 ± √ ( 169 - 0 ) / 30

x = ( -13 ± 13 ) / 30

So , we have 2 solutions to x ,

x = ( -13 - 13 ) / 30

x = -26 / 30

x = -13/15

And , x = ( -13 + 13 ) / 30

x = 0/30

x = 0

Hence , the solutions to the equation is x = -( 13/15 ) and x = 0

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Let's call the amount of Deep Thought granola mixed "x" (in pounds). The amount of Oat Dream granola mixed would then be 20 - x (in pounds).

We know that Deep Thought granola is 25% nuts and dried fruit and Oat Dream granola is 10% nuts and dried fruit. We also know that the desired mix of 20 pounds of granola should be 19% nuts and dried fruit.

Therefore, we can set up the following equation to find the amount of Deep Thought and Oat Dream granola to be mixed:

0.25x + 0.10(20 - x) = 0.19 * 20

Expanding the right side of the equation and solving for x, we get:

0.25x + 2 - 0.1x = 3.8

0.15x = 1.8

x = 12

So, we would mix 12 pounds of Deep Thought granola and 8 pounds of Oat Dream granola to get 20 pounds of granola that is 19% nuts and dried fruit.

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A normal distribution with a mean of 10 and standard deviation of 25, the z score for the value of 35 is 1.

A mean = 10

Standard Deviation = 25

We have to determine the z score for the value of 35. So X = 35.

The relationship between a value and a set of values' mean is described by the statistical measurement known as the Z-score. Standard deviations from the mean are used to measure Z-score. A Z-score of 0 indicates that the data point's value is equal to the mean score.

The formula is:

Z = (X - mean)/Standard Deviation

Now putting the values

Z = (35 - 10)/25

Z = 25/25

Z = 1

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Answer: this is the basic d

Step-by-step explanation idf k man comletely honest, i just searched that shi up and i saw that so yeah...

There must be at least one x-value that makes the function undefined if r(x) is a rational function.

If r(x) is a rational function in simplest form where the degree of the numerator is 2 and the degree of the denominator is 2, then it is possible for the function to be undefined for some values of x.

A rational function is defined as the quotient of two polynomials, and when the degree of the numerator is equal to the degree of the denominator, it is possible for the denominator to equal zero for some values of x, which would make the function undefined for those values.

This means that there must be at least one x-value that makes the function undefined. To determine these x-values, we need to find the zeros of the denominator and set the denominator equal to zero, then solve for x.

The x-values that make the denominator equal to zero are known as the vertical asymptotes of the function, and they are the x-values for which the function is undefined.

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The values are 0,27,27,1000 and dependent values.

A function is a mathematical rule that assigns a unique output to each input value. The input values are called the independent variables, and the output values are called the dependent variables. The relationship between the input and output values is defined by a mathematical expression or a set of instructions.

f(0) = |0|^3 = 0^3 = 0

f(-3) = |-3|^3 = 3^3 = 27

f(3) = |3|^3 = 3^3 = 27

f(-10) = |-10|^3 = 10^3 = 1000

f(a-3) = |a-3|^3 = (a-3)^3 if a >= 3, and -(a-3)^3 if a < 3

f(ah) = |ah|^3 = (ah)^3 if h >= 0, and -(ah)^3 if h < 0

So, depending on the values of a and h, the value of f(a-3) and f(ah) will change. For example, if a = 5 and h = -1, then f(a-3) = f(2) = |2|^3 = 8 and f(ah) = f(-5) = |-5|^3 = 125.

Therefore, The values are 0,27,27,1000 and dependent values.

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The values are 0,27,27,1000 and dependent values.

A function is a mathematical rule that assigns a unique output to each input value. The input values are called the independent variables, and the output values are called the dependent variables. The relationship between the input and output values is defined by a mathematical expression or a set of instructions.

f(0) = |0|³= 0³ = 0

f(-3) = |-3|³ = 3³ = 27

f(3) = |3|³ = 3³ = 27

f(-10) = |-10|³ = 10³ = 1000

f(a-3) = |a-3|³ = (a-3)³ if a >= 3, and -(a-3)³ if a < 3

f(ah) = |ah|³ = (ah)³ if h >= 0, and -(ah)³ if h < 0

So, depending on the values of a and h, the value of f(a-3) and f(ah) will change. For example, if a = 5 and h = -1, then f(a-3) = f(2) = |2|³ = 8 and f(ah) = f(-5) = |-5|³ = 125.

Therefore, The values are 0,27,27,1000 and dependent values.

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The area of the triangle with the given vertices is 6.6.

The formula for finding the area of a triangle given its vertices is A = 1/2 abs(x1y2 + x2y3 + x3y1 - x2y1 - x3y2 - x1y3). To calculate the area of the given triangle, we substitute the coordinates of each vertex into the formula. First we find the three cross-products: x1y2 = 0 * 6 = 0, x2y3 = 2.8 * 6 = 16.8, and x3y1 = 5 * 0 = 0. Then, we find the two products of the y-coordinates: x2y1 = 2.8 * 0 = 0, and x3y2 = 5 * 6 = 30. Lastly, we find the product of the x-coordinates: x1y3 = 0 * 6 = 0. Adding all these up, we get 0 + 16.8 + 0 - 0 - 30 - 0 = -13.2. We then take the absolute value of the result, abs(-13.2) = 13.2. Finally, we multiply the result by 1/2 to get the area of the triangle, A = 1/2 abs(-13.2) = 1/2 * 13.2 = 6.6. Therefore, the area of the triangle with the given vertices is 6.6.

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The y-intercept represents the initial temperature, and the rate of change gives how the temperature changes per minute.

So the correct options are A and D.

Here we have a relation that shows how the temperature changes as a function of time.

So if F(x) is the temperature and x is the time, the y-intercept is given by:

F(0)

So the y-intercept is the initial temperature, the correct option is A.

And the rate of change tells us how the temperature changes as the time passes, so we can define the rate as "the change in temperature per minute" like on option D.

These are the correct options.

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The standard parameterization for the tangent line :

x = 12t + 18 , y = 3t + 13 , z = 54t + 54

parametric equation, a type of equation that employs an independent variable called a parameter (often denoted by t) and in which dependent variables are defined as continuous functions of the parameter and are not dependent on another existing variable.

as given,

r(t) = (2t^2) i + (3t + 4) j + (2t^3) k, t = t₀ = 3

so, [tex]x = 2t^{2}, y = 3t + 4 , z = 2t^{3}[/tex]

[tex]\frac{dx}{dt} = 4t, y=3, z=6t^{2}[/tex]

r'(t) = <4t, 3, [tex]6t^{2}[/tex]>

and at t =3,

r'(t=3) = <12, 3, 54>

we have to find the tangent line to the curve at t=3,

x = 18, y = 13, z = 54

for t=3, (x, y, z) = (18, 13, 54)

finally,

x = 12t + 18

y = 3t + 13

z = 54t + 54

Thus, the standard parameterization for the tangent line :

x = 12t + 18 , y = 3t + 13 , z = 54t + 54

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The standard parameterization for the line tangent to the curve is

x=12t+18 , y=3t+9 , z=54t+54  

In parameterization the variables are independent variables , whereas continuous functions are dependent variables , that is it is dependent on another functions. The given curve is r(t)=(2t^2)i+(3t+4)j+(2t^3)k and given t=t0=3

Given , r(t)=(2t^2)i+(3t+4)j+(2t^3)k

r'(t)=(4t)i+3j+(6t^2)k

and also given t=t0=3

r(t=t0=3) => (18 , 9 , 54)

r'(t=t0=3) => (12 , 3 , 54)

The standard parameterization for the tangent line can be given by using r(t) and r'(t) . so by that we came to know the required standard parameterization.

x=12t+18

y=3t+9

z=54t+54

Therefore, the about mentioned x, y, z are the standard parameterization for the tangent line of given curve.

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The two points that would line of fit go through to best fit the data is (1, 9) and (10, 1).

Scatterplots are the plotting of set of points on a vertical axis and an horizontal axis. The shows the correlation extent between the numbers of the observed quantities.

Given a scatterplot.

There are 10 points which are marked in the scatterplot.

We have to identify the points which are closely related to the general trend of the line.

Those points will be best passing through the line of best fit.

Here the graph will be negative, since the values on the vertical line are decreasing with the increase in the values on horizontal.

Hence the two points are (1, 9) and (10, 1).

Hence the two points are (1, 9) and (10, 1).

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Colleen had 90 points after ten turns, which was calculated by subtracting 170 from her initial 260 points.

The expression to find how many points Colleen had after her ten turns is 260 - 170 = 90. This expression can be written mathematically as P = 260 - 170, where P is the total points after ten turns. To solve this equation, we first subtract 170 from 260. This yields a total of 90 points, which is the number of points Colleen had after her ten turns. The calculation can be summarized as follows:

P = 260 – 170

P = 90

Therefore, after ten turns,Colleen had 90 points after ten turns, which was calculated by subtracting 170 from her initial 260 points.

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The center is called rectangle point X. The distance from the corner of the rectangle to the center (BX) can be found using the Pythagorean theorem is 21.74 to the nearest tenth be 21.7.

The Pythagorean theorem defined that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the right triangle is constructed by sides AB, BC, and BX, with BX being the hypotenuse. So, we can apply the Pythagorean theorem as follows:

        BX² = AB² + BC²

Plugging in the values for AB and BC:

        BX²= 12² + 18²

        BX² = 144 + 324

        BX² = 468

Finally, taking the square root of both sides gives us the length of BX:

        BX = √(468)

        BX = 21.74 to the nearest tenth = 21.7

The description above involves finding the length of the diagonal of a rectangle that goes from one corner of the rectangle to its center. This length is similar to as BX in the definition. To find BX, the Pythagorean theorem is used.

The Pythagorean theorem defined that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the right triangle is constructed by sides AB, BC, and BX, with BX being the hypotenuse.

By substituting the values of AB and BC, the equation BX² = AB² + BC² can be solved to find the length of BX. Finally, taking the square root of the solution gives the length of BX to the nearest tenth.

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Answer:  r and b are both positive or both negative

Reason:

The correlation coefficient r is between -1 and 1

[tex]-1 \le r \le 1[/tex]

If r = -1, then we have perfect negative correlation. All points are on the same straight line that goes downhill as you move to the right. This slope is negative. If -1 < r < 0, then we still have negative slope but the points aren't all on the same line.

If r = 1, then the slope is positive. The regression line moves upward as you move to the right. All points are on this line. If 0 < r < 1, then the points aren't on the same line but we have a positive slope.

If r = 0, then we have no linear correlation at all. Either the points are randomly scattered or they fall on a curve (eg: parabola).

In short: