If I have the quadratic parent
function and I move it to the
right 6 units, what is the new
question?

The inverse function of the given function f(x) = 12x + 10 is

h(x) = (x - 10)/12

Given, a function f(x)

f(x) = 12x + 10

we have to find the inverse of the function f(x) i.e. h(x).

let f(x) = y

y = 12x + 10

12x = y - 10

x = (y - 10)/12

inverse function of f(x) = h(x)

h(x) = (x - 10)/12

So, the inverse function of the given function f(x) is

h(x) = (x - 10)/12

Hence, the inverse function of the given function f(x) is

h(x) = (x - 10)/12

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Question 1

Since the x-coordinates are the same, the line is vertical. Therefore, the slope is undefined.

Question 2

Since the y-coordinates are the same, the line is horizontal. Therefore, the slope is zero.

You can occasionally start by isolating and replacing a variable that is squared in both equations if you're required to solve a system of equations without a starting linear equation.

If there isn't a linear equation to begin with, you can pick out and use a squared variable in both equations.

Start by dividing both sides of the supplied nonlinear equation by the variable's coefficient, for instance.

After you've done that and isolated a variable, carry on with the problem-solving by adding that variable to the other equation.

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The mistakes that Cindy made include:

The answer for Cindy's monthly car payments would be $609.63

To find the monthly payment. first convert the APR to a monthly rate and the number of years to months.

Monthly rate:

= 4% / 12

= 1 / 3%

Number of months:

= 4 x 12 months

= 48 months

The monthly payments is an annuity as it is constant and periodic. The monthly payment for Cindy's car can be found as:

= Cost of car / Present value of annuity factor, 1/3%, 48 months

= 27, 000 / 44.288833874953

= $609.63

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Answer:

$23.55

Step-by-step explanation:

First we will need to determine the total amount of sales Ryan and Carlos made. To do that we will multiply the amount of products sold by the product cost.

$2.75 x 12 = $33

Now we need to deduct the cost of supplies they need to pay back from their profits.

$33- $9.45= $23.55

Now we are left with Ryan and Carlos' total profit, which is $23.55

Answer: It indicates that the quadratic has a repeated real number solution.

Step-by-step explanation:

Factor the expression using the GCF 24y+88x

24y+88x

GCF is 8:

8(3y + 11x)

The function has the end behavior f(x) → -∞  as , x → -∞ as f(x) → +∞ , x → +∞

Since,  The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.

The degree and the leading coefficient of a polynomial function determine the end behavior of the graph.  And, if the function has  positive leading coefficient with odd degree then its end behavior is    f(x) → -∞  as , x → -∞ as f(x) → +∞ , x → +∞

Here, The given function has positive leading coefficient with odd degree.

Therefore,  by the definition of end behavior of a function,

The function has the end behavior f(x) → -∞  as , x → -∞ and, f(x) → +∞ , x → +∞

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Answer:

[tex]2 \sqrt[3]{3} [/tex]

Step-by-step explanation:

[tex]24 {}^{ \frac{1}{3} } [/tex]

[tex] \sqrt[3]{24} [/tex]

[tex] \sqrt[3]{8 \times 3} [/tex]

[tex] \sqrt[3]{8} \times \sqrt[3]{3} [/tex]

[tex] \sqrt[3]{2 {}^{3} } \times \sqrt[3]{3} [/tex]

[tex]2 \times \sqrt[3]{3} [/tex]

[tex]2 \sqrt[3]{3} [/tex]

Answer:

43x+3x+17y

Step-by-step explanation:

because 43x+17y+3x=43x+17y+3x

SAS - side angle side ,ASA - angle side angle

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure. The symbol of congruence is’ ≅’.

What we have been asked

how we tell if the triangle is SAS or ASA

SAS is for if two side and in between them the angle is equal for both the triangle.

ASA is for if two angle and in between them the side is equal for both the triangle.

look at the figure

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Answer:

[tex]f(h(x)) = ( \sqrt{x} - 3)^{2} + 4[/tex]

[tex]f(h(x)) = (x - 9) + 4[/tex]

[tex]f(h(x)) = x - 5[/tex]

Step-by-step explanation:

h(x) became x for function of f(x)

Answer:

60

Step-by-step explanation:

The measure of all exterior angles are the same. So, measure of each exterior angle = 360∘/6=60∘

Charmaine sends 34 message, Jose send 75 texts and Shen send 25 messages.

What is linear equation?

An equation is a mathematical statement, which has an equal sign (=) between the algebraic expression. Linear equations are the equations of degree 1. It is the equation for the straight line.

Let C be charmaine text, S be shen text, J be jose text.

C +J+ S=134

Shen send 9 messages fewer than charmine .

S = C -9

C = S+9

And Jose sent 3 times more then shen

J =3S

We get,

S+9+3S+S=134

5S +9 = 134

5S = 134 -9

5S = 125

S = 25

C = 25 +9

= 34

J= 75

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Answer:

30 tadpoles

Step-by-step explanation:

the 3 part of the ratio relates to the number of swans, that is 18 , then

18 ÷ 3 = 6 ← value of 1 part of the ratio

Then

number of tadpoles = 5 × 6 = 30

Answer:

Separating the variables , using equality symbol , drawing boundary line in XY plane , shading the area are the four steps in graphing linear inequalities

Step-by-step explanation:

Mathematical expressions known as linear inequalities compare two expressions using the inequality symbol. The expression may be either a numerical or an algebraic expression, or it may be both.

Step 1: Always start by separating the variable y from the left side of the inequality.

Step 2: The equality symbol should be used in place of the inequality symbol

Step 3: Draw the boundary line from step 2 in the XY plane.

Step 4: The last step is to partially or completely shade the border line.

Separating the variables , using equality symbol , drawing boundary line in XY plane , shading the area are the four steps in graphing linear inequalities

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The reasons put into the correct order to justify solving the inequality:

-2(x + 6) < 3(x + 1) - Given

-2x - 12 < 3x + 3 - Distributive Property

-2x < 3x + 15 - Addition Property of Order

-5x < 15 - Subtraction Property of Order

x > 3 - Division Property of Order

Check how to solve:

-2(x + 6) < 3(x + 1)

Open the parenthesis

-2x - 12 < 3x + 3

Add 12 to both sides

-2x - 12 + 12 < 3x + 3 + 12

-2x < 3x + 15

Subtract 3x from both sides

-2x - 3x < 3x + 15 - 3x

- 5x < 15

divide both sides by -5

x > 3

Therefore, the solution to the given inequality -2(x + 6) < 3(x + 1) is x > 3.

The properties mentioned above are properties of inequalities and hold for all situations of inequalities as given.

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The heights of both trees at the time when they have an equal height are equal to 4 inches and 48 inches respectively.

In order to graphically solve the system of equations, we would first of all write a system of equations that models the situation. Additionally, we would assign variables to the height of Tree A t years after being planted and height of Tree B t years after being planted, and then translate the word problem into algebraic equation as follows:

Therefore, translating the word problem into algebraic equation, we have the following:

A = 32 + 4t

B = 16 + 8t

On a graph, we would plot the height of Tree A on the x-axis while height of Tree B would be plotted on the y-axis of the cartesian coordinate.

By critically observing the graph, the point of intersection which gives a solution to the system of equations include the following:

Height of Tree A, A = 4 inches.

Height of Tree B, B = 48 inches.

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Prime numbers are numbers greater than 1. They only have two factors, 1 and the number itself. This means 1 is a multiple of a prime number except prime number itself.

What are Prime Numbers?

Prime numbers are numbers greater than 1. They only have two factors, 1 and the number itself. This means these numbers cannot be divided by any number other than 1 and the number itself without leaving a remainder.

Numbers that have more than 2 factors are known as composite numbers.

A prime number is a natural number with exactly 2 divisors / factors: 1 and the number itself. Primes are always greater than 1 and they're only divisible by 1 and themselves. They cannot be made by multiplying two other whole numbers that are not 1 or the number itself.

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An open circle at 5 and a bold line starting at 5 and pointing to the right (>) is the correct representation of the inequality

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g 5 < 6, x ≥ 2, etc.

Given: the inequality –3(2x – 5) < 5(2 – x)

First, we have to solve for x in the inequality

–3(2x – 5) < 5(2 – x)

Clear the parenthesis:

-6x + 15 < 10 - 5x      (Note: This is one of the options to be selected)

Collect like terms:

-6x + 5x < 10 - 15

-x < -5

Divide both sides by -1:

x > 5              ( Note:  Dividing both sides by -1 will change the < to > )

This is what will determine our answer

Since our answer is x > 5.  An open circle will be at 5 and a bold line starts at 5 and is pointing to the right (>)

Therefore,  the correct representation of the inequality is "an open circle is at 5 and a bold line starts at 5 and is pointing to the right". Select 3rd and 4th option is the answer

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The domain and range of this square root function are: D: [–4, ∞) and R: [0, ∞).

In Mathematics, a domain can be defined as the set of all real numbers for which a particular function or relation is defined. This ultimately implies that, a domain is the set of all possible input values (x-values) for a function while a range is the set of all possible output values (y-values) of a function.

Based on the information provided, the function is represented as follows:

g(x) = √(x + 4)

Since a square root function doesn't exist for all negative values, the domain of this function is given by:

x + 4 ≥ 0

x ≥ -4

Domain = [-4, ∞]

Since we do not have a vertical translation, the range of this square root function is given by:

x ≥ 0

Range = [0, ∞]

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Answer:

[–4, ∞) and R: [0, ∞)

Step-by-step explanation:

I got it right on the test.

Part a

There are [tex]\frac{\pi}{180}[/tex] radians in a degree, so the angle of rotation in radians is [tex]\frac{930\pi}{180}=\frac{31\pi}{6}[/tex].

Part b

Using the arc length formula, the distance is [tex](31\pi/6)(3.5)=\frac{217\pi}{12}[/tex] inches.

Answer:

-4

Step-by-step explanation:

m = y2-y1 / x2-x1

m = -11-(-7) / 3-2

m = -11+7 / 3-2

m = -4 / 1

m = -4

m = -39-(-27) / 10-7

m = -39+27 / 10-7

m = -12 / 3

if you simplify if further,

m = -4 / 1

m = -4

Answer:

-4.

Step-by-step explanation:

The slope formula is y2-y1/x2-x1. if we plug in the numbers we can get the formula -11 - (-7)/ 3-2. This gets us -4/1 which equals -4. Therefore the slope of the equation is -4.

The state’s property tax rate is D. 0.069.

Property taxes are levied by cities, counties, and school districts on properties within their jurisdictions and used to fund services. All of these levies are added together to calculate the total tax rate (known as a mill rate) for a region. This rate is then multiplied by a property's assessed value so that people with more valuable properties pay more.

From the information, the person pays 2,849.84 in state property taxes every year and the property has an assessed value of $41,302.

The state property tax will be:

= Tax value / Property value × 100

= 2849.84 / 41302 × 100

= 0.069

In conclusion, the correct option is D.

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Answer:

D

Step-by-step explanation:

The common denominator of the complex fraction is (1/a - 1/b)/(1/a + 1/b) is a²b² which is option D.

The provided complex fraction is  (1/a - 1/b)/(1/a + 1/b).

Now, to find the common denominator,

Solving this complex fraction.

First multiplying each component of every bracket to every component of the other bracket,

= 1/a² + 1/ab - 1/ab - 1/b²

Now, simplifying the equation,

= 1/a² + 1/b²

= (a²+b²)/a²b²

The denominator is the lower part of the fraction.

Hence, the common denominator of the complex fraction is a²b².

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Complete question - What is the common denominator of 1/a + 1/b in the complex fraction (1/a - 1/b)/(1/a + 1/b)?

A)a2 b2

B)a – b

C)a + b

D)ab

Answer:

B = 24% - t(3%)

Step-by-step explanation:

You have you battery at 24% represented by B. you have your 3% which is your difference (d). and your hour which is t. For every hour you are subtracting 3%. So your equation would be B = 24% - t(3%)

Answer:

Equation: B = 23 - 3(t)

Step-by-step explanation:

24 is the percent after it was charged, the 3% is the difference, and your time, which is (t). You deduct 3% for each hour. As a result, your equation would be B = 24 - 3(t).

There were 24 women and 16 men riding the bus. An ordered pair of numbers a and b, written as a / b, is a ratio if b is not equal to 0.

The ratio of men to women is 2:3

this doesn't mean that there are only 2 men and 3 women

there could be:

2 men and 3 women

4 men and 6 women

6 men and 9 women

and so on

2 and 3 have to be multiplied by some number, call it x, to determine the exact number of men and women

2x / 3x is how to write the ratio

4 women got off the bus

2x is the number of men and 3x - 4 is the number of women

2x / (3x - 4) is the ratio now which equals 4/5

2x / (3x - 4) = 4/5

cross multiply

5 × 2x = 4 × (3x - 4)

10x = 12x - 16

10x - 12x = -16

-2x = -16

2x = 16

x = 16/2

x = 8

2 × 8 = 16 and 3 × 8 = 24, so the original ratio was 16/24 which is 2/3

4 women got off the bus

16 men and 24 - 4 = 20 women

16/20 = 4/5

Therefore, 16 men were on the bus and 24 women were on the bus

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The area of the trapezoid is equal to 7 square units.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the trapezoid in a two-dimensional plane is called the area of the trapezoid.

Given that the area of a trapezoid is given by the formula A = 1/2

h(b₁ + b₂). The given values are h = 2, b₁=3, and b₂=4.

The area of the trapezoid is calculated as,

Area = (1 / 2) x h(b₁ + b₂)

Area = (1 / 2 ) x 2 x ( 3 + 4 )

Area = 7

Area = 7 square units

Therefore, the area of the trapezoid is equal to 14 square units.

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The coordinates of the point after the two reflections are (0.3,-7/10).

A reflection is a mapping from an isometric hyperplane with a set of fixed points acting as the reflection's axis or plane from a Euclidean space to itself. A figure's reflection creates its mirror image of that figure in the plane or axis of the reflection.

Given that, the point (-0.3, 7/10) is reflected over the y-axis and then over the x-axis respectively.

The coordinates of the point after the reflection in the y-axis are:
(0.3, 7/10)

Now, the coordinates of the point after the reflection in the x-axis are:
(0.3, -7/10)

Hence, the coordinates of the point after the two reflections are (0.3,-7/10).

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