Rectangle ABCD is reflected over the x-axis, followed by a reflection over the y-axis, and then rotated 180 degrees about the origin. What is the location of point A after the transformations are complete?

Rectangle ABCD is shown. A is at negative 5, 1. B is at negative 5, 3. C is at negative 1, 3. D is at negative 1, 1.

(−5, 1)
(5, −1)
(−5, −1)
(5, 1)

It’s AB and DE so it would be b

Quadratic equations can be expressed in standard form or in vertex form.

The true statement about [tex]\mathbf{y = ax^2 + bx + c}[/tex] and [tex]\mathbf{y = a(x - h)^2 + k}[/tex] is that: the value of a remains the same

The original expression is given as:

[tex]\mathbf{y = ax^2 + bx + c}[/tex]

He wants to rewrite it as:

[tex]\mathbf{y = a(x - h)^2 + k}[/tex]

Expand the above equation

[tex]\mathbf{y = a(x - h)(x - h) + k}[/tex]

Open brackets

[tex]\mathbf{y = a(x^2 - hx - hx + h^2) + k}[/tex]

[tex]\mathbf{y = a(x^2 - 2hx + h^2) + k}[/tex]

Remove bracket

[tex]\mathbf{y = ax^2 - 2ahx + ah^2 + k}[/tex]

Compare the above equation to: [tex]\mathbf{y = ax^2 + bx + c}[/tex]

[tex]\mathbf{ax^2 = ax^2}[/tex]

[tex]\mathbf{-2ahx = bx}[/tex]

[tex]\mathbf{ah^2 + k = c}[/tex]

Analyzing the above equations

[tex]\mathbf{ax^2 = ax^2}[/tex]

Divide both sides by [tex]\mathbf{x^2}[/tex]

[tex]\mathbf{a = a}[/tex]

The above equation means that, the value of a remains unchanged.

Hence, option (c) is true

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Answer:

a. the distance of the home from a school

Step-by-step explanation:

The distance your home is from a flood plain can potentially increase your homeowner's insurance.  If your house is close to a flood plain, your insurance will increase.

The distance your home is from a fire station or a fire hydrant either one can lower your insurance.  If your home is within so many feet of a hydrant, you get a discount on your insurance; if it is close enough to a fire station, you get a discount as well.

Since the distance a home is from a school has no bearing on the cost of repairing or replacing the home, this will not affect your homeowner's insurance.

We are given that the slope is half the y-intercept and their sum is 1. Using these conditions we can solve for b and m (which represent y-intercept and slope) and we find that b=2/3 and m=1/3. Therefore, the equation of the line is y = 1/3x + 2/3.

The question is about finding the equation of a line from given conditions. We know that the equation of a line is typically written in the form y = mx + b, where m is the slope and b is the y-intercept. We are given two conditions: the slope is half the y-intercept, and their sum is 1.

Let's assume that the y-intercept is b and the slope is m. Now we can substitute the value of m from the first equation into the second. This gives us: b + b/2 = 1. Solving this, we get b = 2/3 and therefore, m = 1/3.

So, the equation of the line is y = 1/3x + 2/3.

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Answer:

The required equation is y + 3 = 4(x + 1)

Step-by-step explanation:

Since, the point slope form of a line passes through the point [tex](x_1, y_1)[/tex] having slope m is,

[tex]y-y_1 = m(x-x_1)[/tex]

Here,

[tex]x_1 = -1, y_1 = -3\text{ and }m = 4[/tex]

Hence, the equation of the line,

[tex]y+3 = 4(x+1)[/tex]

Or

[tex]y = 4(x+1) - 3[/tex]

The given expression V-15=-27 gives the value of v = -12.

Using operations like addition, subtraction, multiplication, and division, a mathematical expression is defined as a group of numerical variables and functions.

And we know that a mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The given expression is:

V-15=-27

To solve this equation:

Add 15 on both sides

v - 15 + 15 = - 27 + 15

v = -12

Hence,

The given expression gives the value of v = -12

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The recursive formula that represents the same geometric sequence as [tex]\( a_n = 3 \times 3^{n-1} \)[/tex] is option B: [tex]\( a_n = 3 \times a_{n-1} \).[/tex]

To find the recursive formula that represents the same geometric sequence as [tex]\( a_n = 3 \times 3^{n-1} \)[/tex], we need to find a recursive formula that generates the same sequence.

The formula [tex]\( a_n = 3 \times 3^{n-1} \)[/tex] can be rewritten as:

[tex]\[ a_n = 3 \times 3^{n-1} = 3 \times 3^n \times 3^{-1} = 3 \times \left(3 \times 3^{n-1}\right) \][/tex]

This indicates that each term is 3 times the previous term. So, the recursive formula should involve multiplying the previous term by 3.

Let's examine the options:

A. [tex]\( a_n = 9 \times a_{n-1} \)[/tex] - This represents multiplying the previous term by 9, not 3.

B. [tex]\( a_n = 3 \times a_{n-1} \)[/tex] - This represents multiplying the previous term by 3, which matches the original sequence.

C. [tex]\( a_n = 9 + a_{n-1} \)[/tex] - This represents adding 9 to the previous term, not multiplying it.

D. [tex]\( a_n = 3 + a_{n-1} \)[/tex] - This represents adding 3 to the previous term, not multiplying it.

Therefore, the recursive formula that represents the same geometric sequence as [tex]\( a_n = 3 \times 3^{n-1} \)[/tex] is option B: [tex]\( a_n = 3 \times a_{n-1} \).[/tex]

Answer: 1) Pizzeria must sell 78 pizzas for receiving the bonus.

2) The number of pizzas sold is decreased by Approximately 7.69 %.

Step-by-step explanation:

1) The number of pizza sold yesterday = 65,

The target for receiving the bonus = 20% more than the number of pizza sold yesterday

= 20% more than 65,

= 65 + 20% of 65    ( 1% = 0.01 ⇒ 20% = 0.2 )

= 65 + 0.2 × 65

= 65 + 13 = 78.

Hence, they must sell 78 pizzas for receiving the bonus.

2) If the actual number of pizza sold today = 60

⇒ Total reduction in the number of pizza = 65 - 60

= 5

Thus, the percentage decrease in the number of pizza

[tex]=\frac{\text{Total reduction}}{\text{The number of pizza sold yesterday}}\times 100[/tex]

[tex]=\frac{5}{65}\times 100[/tex]

[tex]=\frac{500}{65}=7.69230769\approx 7.69\%[/tex]

we have

[tex]x+y=11[/tex]

[tex]x=11-y[/tex] --------> equation A

[tex]4x^{2} -3y^{2}=8[/tex] ----> equation B

Substitute equation A in equation B

[tex]4(11-y)^{2} -3y^{2}=8[/tex]

therefore

the answer is the option B

[tex]4(11-y)^{2} -3y^{2}=8[/tex]

Answer: 24 video games

Step-by-step explanation: jasmine has 1,128 bucks originally. she gets some megadeth and metallica cd's (cause if she's got taste, that's probably what she got) and that adds up to 72 bucks. now she wants to buy a whole bunch of video games, which cost 43 each (imagine she got fortnite mod's. ew) so we put that in an equation-

$1,128 - $72 = $1,056

$1,056 divided by 43 equals 24.55813953488372.

when dealing with money, you always round down, so the total number of games she bought was 24

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