1. Is the following a function?
2. Write a function that represents the following description:
“After 8 hours, a person earned $148 in wages”
3. Let f(x)=x and g(x)=x-13
Find (f+g)(9)
4. Paige is paying off her car loan. The function that models how much she has left to pay is P(m) = 6000 -300m where m is the number of months since Paige took out the loan. What was the original amount of her loan?

Answer:

A. The modulus is 5√2.

B. It lies in quadrant 3

Step-by-step explanation:

Given a complex value z = x = iy

The modulus is expressed as;

|z| = √x²+y²

Given the complex number z = -5 - 5i

|z| = √(-5)²+(-5)²

|z| = √25+25

|z| = √50

|z| = √25 * √2

|z| = 5√2

For the argument;

theta = arctan(-5/-5)

theta = arctan 1

theta = 45degrees

since tan is positive in the third quadrant, hence it lies in quadrant 3

Answer:

B

Step-by-step explanation:

5t^2-(3-6t-8t^2)

=5t^2-3+6t+8t^2

=13t2-3+6t

Answer:

[tex]\boxed {\boxed {\sf B. \ 13t^{2} -3+6t}}[/tex]

Step-by-step explanation:

We are given this expression and asked to simplify:

[tex]5t^2-(3-6t-8t^2)[/tex]

First, distribute the -1. Multiply each term in the parentheses by -1 or switch the sign of every term inside the parentheses.

[tex]5t^2+ (-1*3)+(-1*-6t)+(-1*-8t^2)[/tex]

[tex]5t^2+(-3)+(6t)+(8t^2)[/tex]

[tex]5t^2-3+6t+8t^2[/tex]

Next, combine like terms. We see that two terms have a t², so they are like terms. We can add them together.

[tex](5t^2+8t^2)-3+6t[/tex]

[tex]13t^2-3+6t[/tex]

The simplified expression is 13t²-3+6t and Choice B is correct.

If a company found that raising the price of its muffins resulted in an absolute value of.35 < 1, then the demand for muffins is inelastic.

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Step-by-step explanation:

The axis of symmetry is the vertical line that goes through the vertex, dividing the parabola into two equal parts. If h is the x-coordinate of the vertex, then the equation for the axis of symmetry is x=h

Answer:

The temperature at 9 am = -14.7°F

Between 9am and 12 pm = -14.7 + 17.8 = 3.1°F

Between 12pm and 3 pm = 3.1+5.1 = 8.2°

Between 3pm and 6 pm = 8.2-14.5 = -6.3°F

The required value of x is 17 for the given equation 11 = x - 6.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The equation is given in the question, as follows:

11 = x - 6

We can determine the value of x by adding 6 to both sides of the equation.

As per the question, we have

⇒ 11 = x - 6

⇒ 11 + 6 = x - 6 + 6

⇒ x = 11 + 6

Apply the addition operation, and we get

⇒ x = 17

Therefore, the required value of x is 17.

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Definition of Ray:

'A part of a line that has one endpoint and extends indefinitely in one direction'.

The correct statement is A.

A ray is a part of the line having one fixed point and the other point does not have an end. It means that a ray has one terminating end and the other end is extending infinitely.

Given definitions of ray:

A. a part of a line that has one endpoint and extends indefinitely in one direction.

B. the set of all points in a plane that are a given distance away from a given point.

C. lines that lie in the same plane and do not intersect.

D. a part of a line that has two endpoints.

Only statement A satisfies the definition of ray.

Hence, the definition of ray is described by statement A.

A part of a line that has one endpoint and extends indefinitely in one direction.

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Answer:

2/100=0.02

0.02*15=33.3

111+33.3

144.3

The Sides of triangle when only the angles of triangles are given can be found by using the Law Of Sines .

What is Law Of Sines ?

The Law Of Sines states that  the ratio of sides of a triangle and their respective Sine angles are equivalent to each other. The other names by which the law of sines is known  are Sine Law, Sine Rule and Sine Formula.

The Sine Law  is used to find unknown side of an oblique triangle. The oblique triangle is defined as a triangle that is not a right triangle.

Let a , b and c be the sides of a triangle ABC , and A , B and C be the angles .

So , by Sine Law : [tex]\frac{a}{SinA}=\frac{b}{SinB}=\frac{c}{SinC}[/tex] ;

Therefore , The Law Of Sines help in finding the sides of triangle that has only angles .

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The measures of three angles are 40.5°, 43.5° and 95.8°.

Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

The formula for sine rule is sinA/a=sinB/b=sinC/c

Given that, an interior designer plans to use triangular tiles that are 8 cm×9 cm×13 cm for a backsplash.

Using cosine rule, we get

9²= 8²+ 13²- 2(8)(13) cos θ (angle opposite 9 cm side.)

81=64+169-208 cos θ

81-233=-208 cos θ

-208 cos θ=-152

cos θ=-152/(-208)

cos θ=0.7307

θ=43.7°

Using sine rule,

The formula for sine rule is sinA/a=sinB/b=sinC/c

sinA/8 =sin43°/9=sinC/13

sinA/8 =0.7307/9

sinA/8=0.0811

sinA=0.6495

A=40.5°

So, ∠A+∠B+∠C=180°

40.5°+43.7°+∠C=180°

∠C=95.8°

Therefore, the measures of three angles are 40.5°, 43.5° and 95.8°.

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The cost of a senior citizen ticket is $3 and the cost of a child ticket

is $9.

If a system of equations only contains two linear equations with two variables, the system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution.

There are only three matching forms of solution for a given system of equations because there are only three different ways that two straight lines in the plane can graph.

From the given information the two linear equations in 'x' and 'y' can be formed as,

2x + 8y = 78 and 4x + 8x = 84.

Now, Subtracting equation 1 from equation 2 we'll have,

2x = 6.

x = 3 and hence y = 9.

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Answer:

The answer will bee 6.6666666667 well with nine zeros

Manuel was incorrect, because the perimeter of a flower bed is [tex]51\frac{1}{4}[/tex] feet not [tex]25\frac{5}{8}[/tex] feet.

The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).

Given that, Manuel says [tex]25\frac{5}{8}[/tex] feet of fencing is enough for a rectangular flower bed that measures [tex]9\frac{7}{8}[/tex] feet by [tex]15\frac{3}{4}[/tex] feet

Here, perimeter =2([tex]9\frac{7}{8}[/tex] +  [tex]15\frac{3}{4}[/tex]) feet

= 2(79/8 + 63/4)

= 2(79/8 + 126/8)

= 2(205/8)

= 410/8

= [tex]51\frac{1}{4}[/tex] feet

Manuel was incorrect, because the perimeter of a flower bed is [tex]51\frac{1}{4}[/tex] feet not [tex]25\frac{5}{8}[/tex] feet.

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A one million sided shape called as Megagon.

We know that a polygon is noting but a closed two-dimensional figure which is enclosed by line segments.

These line segments are known as sides.

A polygon has at least three straight sides and angles.

Polygons are classified mainly into four categories. Regular polygon, Irregular polygon, Convex polygon and Concave polygon

We know that a polygon with n sides is called n-gon.

For n = 1000000, i.e., a polygon with one million sides is called as Megagon.

A number of edges and vertices = 1000000

And the internal angle of megagon is about 179.99 degrees.

Therefore, a shape with  1 million sides is known as a Megagon

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Answer:

B

Step-by-step explanation:

The inequality that represents negative one third is greater than or equal to the product of negative two fifths and a number is: B. negative one third is greater than or equal to negative two fifths y where y is greater than or equal to five sixths.

In Mathematics, an inequality simply refers to a mathematical relation that can be used to compare two (2) or more numerical values, numbers, and variables in an algebraic equation, especially based on any of the following inequality symbols:

Note: Let the variable y represent the unknown number.

Next, we would translate the word problem "negative one third is greater than or equal to the product of negative two fifths and a number" into an algebraic inequality as follows;

-1/3 ≥ -2/5 × y

-1/3 ≥ -2y/5

Multiplying both sides of the algebraic inequality by -5/2, we have:

-1/3 × -5/2 ≥ -2y/5 × -5/2

5/6 ≤ y

y ≥ 5/6.

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Answer:

-25, -19, -15, -4, 5, 7, 22

Step-by-step explanation:

-25, -19, -15, -4, 5, 7, 22 is the order from least to greatest

The bigger the negative number, the smaller it is; that is why the order is

-25, -19, -15, -4, 5, 7, 22

yes, (-2,4) is the solution of the system of equation 4x² - 4y = 0.

To check whether the given points are the solution of the given system of equation 4x² - 4y = 0. We have to put the values of x = -2 and y = 4 in the given equation. If we get the result equals zero then (-2, 4) is the solution of 4x² - 4y = 0 and if the result is a non-zero number then (-2, 4) is not the solution of 4x² - 4y = 0.

⇒4x² - 4y = 0

⇒4(-2)² - 4 × 4 = 0

⇒4 × 4 - 4 × 4 = 0

⇒0 = 0

Here we get the result equal to zero, hence (-2,4) is the solution of the system of equation 4x² - 4y = 0.

--This question is incomplete, the complete question is

''Is (-2,4) a solution of the system of equation 4x² - 4y = 0?''--

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Answer:

a. 49/2

b. -2/9

If I make any mistakes, I'm sorry.

Answer:

110.25π sq cm

Step-by-step explanation:

circumference 2πr= 21π cm

so r = 21/2= 10.5 cm

area of circle = πr^2

=π (10.5)^2

=110.25 sq cm

The options that shows expressions which are functions in the ranges they are defined are;

Option A: f(x) = 2x + 5

Option B:  f(x) = x² + 1

Real numbers are defined as the combination of rational and irrational numbers, in the number system. This means that, all the arithmetic operations can be performed on real numbers and they can be represented in the number line.

Now, integers are defined as whole numbers that can be positive, negative or zero.

a) We are told that the input of real numbers must yield only real numbers. Yes this is true because any real number we put in for x in f(x) = 2x + 5 will yield an output that is also a real number.

b) We are told that the input of real numbers must yield only real numbers. Yes this is true because any real number we put in for x in f(x) = x² + 1 will yield an output that is also a real number.

c) We are told that the input of real numbers must yield only real numbers. No this is not true because if we put -1 which is a real number for x in the denominator, we will get an undefined function.

d) We are told that the input of integers must yield only integers. No this is not true because if we put 1 for x which is an integer, we will get a fraction which is not an integer.

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Answer:

Since 3⁵= 243 you can just multiply by 3 to find 3⁶

Answer:

You can multiply 243 by 3 to get the answer to 3^6

Step-by-step explanation:

Answer:

6,720 inches or 560 feet

Step-by-step explanation:

20 x 14 x 24 = said number above.

Remember volume is just length times width times height.

Answer: William Wordsworth, a prominent figure in the Romantic movement, believed that nature had an immense value and could have a profound impact on the human spirit. In his poem "I Wandered Lonely as a Cloud," he wrote, "Nature never did betray the heart that loved her," which is a claim that nature is a constant source of comfort and inspiration. In this poem he praises nature and its ability to be a source of beauty and joy.

One could argue that Wordsworth's claim is true based on the evidence that nature can have a positive impact on mental and physical health. Studies have shown that spending time in nature can reduce stress, improve mood, and boost overall well-being. Additionally, nature can be a source of inspiration for many artists and poets, including Wordsworth himself, who drew inspiration from the natural world for his poetry.

On the other hand, one could argue that Wordsworth's claim is idealistic and may not apply to everyone or every situation. Some people may not find nature as comforting or inspiring, especially those who live in urban areas with limited access to natural spaces. Additionally, there are negative impacts of human activities on nature, such as pollution and deforestation, which can make it harder for some people to find value in nature.

Overall, while Wordsworth's claim that "Nature never did betray the heart that loved her" is a strong statement, and it holds true for many people, but it's a personal perspective that may not apply to everyone. Each individual has their own relationship with nature and it's not always a constant source of comfort, however, it's a treasure that we should take care of, respect and appreciate in order to achieve a better quality of life.

Step-by-step explanation:

Answer:

y=-52

Step-by-step explanation:

-5*9=-45

-5*9=-45 +7=

y=-52

Answer:

Step-by-step explanation:

ASA requires that both triangles have two angles and the included side to be congruent.

We have one side and an adjacent angle and need the second angle adjacent to the marked side to be congruent as well

It is the ∠BAC of ΔABC and ∠DPF of ΔPDF or simply ∠A and ∠P.

The required phrase to translate the expression x + 7 is, A number increases by 7 or an Addition of number and 7.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Given expression x + 7,
The expression can be translated as a number increase by 7 or the Addition of the number and 7.

Thus. the required phrase to translate the expression x + 7 is, A number increases by 7 or an Addition of number and 7.

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