Juan always saves the same amount of money from his weekly allowance. This table shows how much he has saved in dollars at different times. Which equation represents the situation, where ex is the time and why is the amount saved?

The parent quadratic function is 2 unit right and 3 units up.

Given function is

f(x) = (x-2)² +3

= x² - 2² - 2×x×2 + 3

= x2 - 4 - 4X + 3

= X² - 4X -1

Parent function g(x) = x²

The parent function is shifted to 2 units in right and 3 units up.

Parent function transformations are shown in blue. This is a 1 unit shift down. Mirroring of the x-axis is done functionally by multiplying the superordinate function by the negative function.

A parent function is the simplest function that satisfies the definition of a particular function type. For example, consider linear functions that form a family of functions.

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Disclaimer:- your question is incomplete, Please see below for the complete question.

Which phrase best describes the transformation(s) of the following graph from the parent quadratic function? f(x)=(x-2)^2+3

The price charge is $235 and the maximum revenue is $165675.

It is a plane curve that is mirror-symmetrical. It is approximately U-shaped. It is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed-line. It is the locus of a fixed point that moves on a plane. It has many important applications. In Mathematics, the parabola plays a crucial role.

Number of members in club = 360

Monthly membership is of $350

For $ 1 price decrease and 3 people joinining

Membership charge will be = 350-x

Members will be 360+3x

Revenue equation will be

R (x) (350-1x)(360+3x)=0

126,000-360x+1050x-3x² =0

126,000+690x- 3x²-=0

This is a parabolic equation. Maximize the function to get

Differentiate to get the parabola vertex

R'(x) = 690-6x

So, 690-6x =0

x =115

Therefore, the price charge is

350-115 = $235

The number of members is

3360+115 = 705

The maximum revenue is given as

$235 × 705=$165675

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Answer:

y= 1/5x -7

Step-by-step explanation:

1/5 is the slope

-7 is the y-intercept

The length of AC is 2.96 units using trigonometric ratio.

What are the trigonometric ratios?

Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant are the six trigonometric ratios. A branch of mathematics called trigonometry in geometry deals with the sides and angles of a right-angled triangle.

Given that angle A = 65° and AB = 7 units.

The base of △ABC is AC, height is BC, and hypotenuses is AB.

Cosine of angle is the ratio of base to hypotenuses.

Thus cos  65° = AC/AB

Substitute AB = 7

cos  65° = AC/7

Multiply both sides by 7:

7 × cos  65° = AC

Putting cos  65° = 0.42261826174

7 × 0.42261826174 =AC

AC = 2.95832783218

AC = 2.96 (nearest hundredth)

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The order pair (3, 14) is from the given scatter plot.

Scatter plots are used to observe and plot relationships between two numeric variables graphically with the help of dots. The dots in a scatter plot shows the values of individual data points.

• A scatter plot with increasing values of both variables can be said to have a positive correlation.

• A scatter plot with an increasing value of one variable and a decreasing value for another variable can be said to have a negative correlation.

In the given scatter plot, the order pair with x-coordinate 3 is 14

So, the order pair is (3, 14)

Therefore, the order pair (3, 14) is from the given scatter plot.

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Answer:

11.10 or 11.1

Step-by-step explanation:

1. 15 x 0.075= 1.125 or 1.13

2. 15-1.13=13.87

3. 13.87 x 0.20= 2.774 or 2.77

4. 13.87 -  2.77 = 11.10 or 11.1

Answer:

f(x) = 4(1.15)6.

Step-by-step explanation:

The GPA of a student who studies for 15 hours a week is 2.935.

What is a GPA?

Grade point average, or GPA, is a conventional method of evaluating academic performance in the United States on a scale of 0 to 4.

How to calculate GPA?

To calculate your GPA, divide the total number of grade points earned by the total number of letter-graded units undertaken.

Here,

We have an equation y = 0.164x + 0.475

put x= 15

we get,

y = 0.164* 15 + 0.475

y = 2.935

Hence, The GPA of a student who studies for 15 hours a week is 2.935

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Answer:

4 people will be on the last chair.

Step-by-step explanation:

60 divided by 5 is 12. There will be 12 full seats. 64 - 60 is 4 so there will be 4 more on the last chair.  

Hope this helped!

The translation rule is (x, y) ---> (x+8)(x-4).

What is translation rule?

A translation is a type of transformation that moves each point in a figure the same distance in the same direction. The second notation is a mapping rule of the form (x,y) → (x−7,y+5).

A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other.

Given,

let A =(x, y) ----> (x+9,y-2) and B =(x, y) ----> (x-1,y-2)

which means A is translated 9 units right and 2 units down

and B is translated 1 unit left and 2 units down.

Therefore, rule for composition is A+B

= (x, y) ------> (x+9-1, y-2-2)

(x,y) -----> (x+8,y-4)

which means translation is 8 units right and 4 units down.

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Answer: D.

Hope it helps

The value of [tex]a^{2} +\frac{1}{a^{2} }[/tex] if  [tex]a=\frac{2+\sqrt{5} }{2}[/tex] is solved to be

The equation is solved by substituting for a in the given equation [tex]a^{2} +\frac{1}{a^{2} }[/tex]

[tex]a^{2} +\frac{1}{a^{2} }[/tex]

substituting for a

[tex](\frac{2+\sqrt{5} }{2})=(1+\frac{\sqrt{5} }{2})[/tex]

[tex](1+\frac{\sqrt{5} }{2})^{2} =(1+\frac{\sqrt{5} }{2})*(1+\frac{\sqrt{5} }{2})=1+2\frac{\sqrt{5} }{2} +\frac{5}{4}=\sqrt{5} +\frac{9}{4}=4.48607[/tex]

= 4.8607 + 1/4.48607

= 5.0664

Substituting the value of a in the equation and solving resulted to 5.1

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In linear equation, 10 feet and 8 inches will require 4.6 pints.

What are instances of linear equations?

For 10 feet and 8 inches,          

12 inches = 1 foot,

therefore 8 inches = 8/12 foot = 0.6 foot

10 feet 8 inches = 10 + 0.6 = 10.6 feet

6 feet 8 inches required 3 pints

1 foot would have required (3/6.8) pints

10.6 feet will then require   (3/6.8)*10.6 = 4.6 pints.

Therefore 10 feet and 8 inches will require 4.6 pints.

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Apply the trigonometric functions:

Sin B = opposite side / hypotenuse:

Where:

B : angle

Opposite sid

Answer: 3.86587352821

Step-by-step explanation: This cannot be solved by hand, you need a calculator for this!

The aspect ratio for a computer screen is

if the width equals 13.5, then the height is:

Answer:

2^25/2

Step-by-step explanation:

We express them as a power of 2 using laws of indices

Answer:

Of 20,000 people that apply, 6300 actually enroll.

Step-by-step explanation:

70% of 20,000 is 14,000

45% of 14,000 is 6,300

Answer:

17.1

Step-by-step explanation:

Exponential Functions:

y=ab^x

a=starting value = 310

r=rate = 6.4%=0.064

Exponential Decay:

b=1−r=1−0.064=0.936

Write Exponential Function:

y=310(0.936)^x

Put it all together

Plug in y-value:

100=310(0.936)^x

100/310 = 310(0.936)^x/310

​

Divide both sides by 310

0.322581=0.936^x

\log 0.322581=\log 0.936^x

Take the log of both sides

log0.322581=xlog0.936

Use power rule to bring x to the front

log0.322581/log0.936 = xlog0.936/log0.936

​

Divide both sides by log(0.936)

17.106221=x

x≈17.1

17.12 will it take until there are 100 grams of the element remaining

Two or more expressions with an Equal sign is called as Equation.

Given that  element with a mass of 310 grams decays by 6.4% per minute.

we need to find the time will it be until there are 100 grams of the element remaining

y=abˣ

a=starting value = 310

r=rate = 6.4%=0.064

Exponential Decay:

b=1−r

=1−0.064

=0.936

Plug in these values in the formula

y=310(0.936)ˣ

100=310(0.936)ˣ

Divide both sides by 310

100/310 = (0.936)ˣ

0.322581=0.936ˣ

Apply log on both sides

log 0.322581=xlog0.936

Divide both sides by log0.936

log0.322581/log0.936 = xlog0.936/log0.936

17.106221=x

Hence, 17.12 will it take until there are 100 grams of the element remaining

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Answer:

For b, you just start at (0,-5)(go down 5 on the y-axis), and go one up, one over to the right, and for c, just start at (0,0) and go right one, up 2

Step-by-step explanation:

Answer:

y= 2x-3

Step-by-step explanation:

4/2 OR 2 is the slope

-3 is the intercept  

The equation used to determine y, the number of water bottles remaining at the music festival x hours after 5:00 P.M will be;

⇒ y = - 500x + 5500

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The table shows the linear relationship between the number of water bottles remaining and the number of hours since 5:00 P.M.

Now,

Find the linear equation for the given table as;

Take number of hours = x

And, Number of remaining bottles = y

So, Two points for the linear equation as;

⇒ (x, y) = (1, 5000) , (2, 4500)

Thus, The linear equation for the table is,

⇒ y - y₁ = (y₂ - y₁) / (x₂ - x₁) (x - x₁)

⇒ y - 5000 = (4500 - 5000) / (2 - 1) (x - 1)

⇒ y - 5000 = - 500 (x - 1)

⇒ y - 5000 = - 500x + 500

⇒ y = - 500x + 500 + 5000

⇒ y = - 500x + 5500

Thus, The equation used to determine y, the number of water bottles remaining at the music festival x hours after 5:00 P.M will be;

⇒ y = - 500x + 5500

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Answer:

y=3x-11

Step-by-step explanation:

In this question, we will use the point slope form:

Which has the equation:

[tex]y-y_1=m(x-x_1)\\subsitute:\\y+5 = 3(x-2) , (y--5=+5)\\y+5=3x-6\\y=3x-11[/tex]

Hope this helps!

To simplify

First of all, Octavia error can be spotted from the correct steps below

Step1: Expand the expression

Step2: Collect like terms

Step 3: Simplify by using exponents laws

Step 4: Combine the terms.

The value is

Her error was that she didn't apply the exponents' law properly.

One of the laws she violated was

Her mistake was that she did

So she missed it from our step 1 above

From the graph given, we are asked to find the equation of line, with our answer in point slope form.

from the graph:

y = 9, x = 10

y1 = 5, x1 = 6

recall, the equation of a line is:

y = mx + b

slope m = y - y1/x - x1

m = 9 - 5/10 - 6

m = 4/4

m = 1

y = 1x + b

y = x + b

using the point slope form:

y - y1 = m(x - x1)

Where:

y = y coordinate of second point

y1 = y coordinate of point one

m = slope

x = x coordinate of second point

x2 = x coordinate of point one.

Therefore, the point slope equation is:

y - 5 = 1(x - 6)

y - 5 = x - 6

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-8})\hspace{10em} \stackrel{slope}{m} ~=~ 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-8)}=\stackrel{m}{ 4}(x-\stackrel{x_1}{(-4)}) \implies y +8= 4 (x +4) \\\\\\ y+8=4x+16\implies {\Large \begin{array}{llll} y=4x+8 \end{array}}[/tex]

To find the area of the whole figure, we can divide it into two rectangles, the smaller rectangle has dimensions of 5 inches by 8 inches.

The bigger rectangle has dimensions of 9 inches by 15 inches.

Then, we add