If you vertically shift the square root parent function, F(x)=√x, up nine units,what is the equation of the new function?O A. G(x) = √√xOB. G(x)=√x+9OC. G(x)=√x +9D. G(x)=√√√x - 9SUBMIT

The equation of the circle with endpoints of a diameter at (-14, -3) and (-4, -1) in standard form is (x + 9)² + (y + 2)² = 65/4, where the center is (-9, -2) and the radius is √(65)/2.

To find the equation of a circle in standard form, we need to know the center and the radius of the circle.

The midpoint of the diameter is the center of the circle, which can be found using the midpoint formula:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

Midpoint = ((-14 + (-4))/2, (-3 + (-1))/2)

Midpoint = (-9, -2)

The radius can be found by using the distance formula to find the distance between one of the endpoints and the center:

r = √((x2 - x1)² + (y2 - y1)²)/2

r = √((-4 - (-9))² + (-1 - (-2))²)/2

r = √(65)/2

Putting it all together, the equation of the circle in standard form is:

(x + 9)² + (y + 2)² = 65/4

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Along with proof of (a.) and (d.), (b.) Power tower: one level is a, (k + 1) levels is a raised to the power of a power tower with k levels, (c.) A(2, n) <= 2 ↑↑ n for all positive integers n, where ↑↑ denotes power tower notation.

The idea of a fully computable function that is not primitive recursive is illustrated by the recursively constructed mathematical function known as the Ackermann function. Since m and n are non-negative integers, it is commonly written as A(m, n).

a.) Prove using regular induction that \(A(1, n) \leq 2^n\) for all positive integers n:

Base Case: For n = 1, A(1, 1) = 2, which is equal to \(2^1\).

Inductive Hypothesis: Assume that \(A(1, k) \leq 2^k\) for some positive integer k.

Inductive Step: We need to show that \(A(1, k + 1) \leq 2^{(k + 1)}\). Using the recursive definition of A(m, n), we have \(A(1, k + 1) = A(0, A(1, k)) = 2^{(A(1, k))}\leq 2^{(2^k)}\) (by inductive hypothesis)\(< = 2^{(2^{(k + 1)})}\).

Therefore, by regular induction, we have proved that \(A(1, n) \leq 2^n\) for all positive integers n.

b.) A power tower with one level is defined as a, and a power tower with (k + 1) levels is defined as a raised to the power of a power tower with k levels.

c.) \(A(2, n) \leq 2\) ↑↑ n for all positive integers n, where ↑↑ denotes power tower notation.

d.) The recursive definition of a triple arrow-up notation for power towers is:

a ↑↑↑ 1 = a (base case)

a ↑↑↑ (k + 1) = a ↑↑ (a ↑↑↑ k) (recursive step)

This definition states that a triple arrow-up notation with one level is equal to the base value "a", and a triple arrow-up notation with (k + 1) levels is equal to "a" raised to the power of a triple arrow-up notation with "k" levels.

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Complete Question: ( Refer to image)

9514 1404 393

Answer:

  x-intercept: (-5, 0)

  y-intercept: (0, 5)

Step-by-step explanation:

The x-intercept is where the graph crosses the x-axis. The x-value there is -5. The y-value of any point on the x-axis is 0, so the point coordinates are (-5, 0).

The y-intercept is where the graph crosses the y-axis. The y-value there is 5. The x-value of any point on the y-axis is 0, so the point coordinates are (0, 5).

Answer:

Step-by-step explanation:

To find the equation of a line that is perpendicular to a given line and passes through a specific point, we need to follow a few steps:

Find the slope of the provided line.

The point-slope form of a line is given by: y - y1 = m(x - x1), where (x1, y1) represents the given point.

Substituting the values, the equation of the perpendicular line becomes:

y - 5 = (-1/m)(x - 2)

Simplifying the equation further, we can rewrite it in point-slope form:

y - 5 = (-1/m)x + (2/m)

Answer:

A

Step-by-step explanation:

To solve the equation 7x-3(x-6)=30, we need to use the distributive property to simplify the left-hand side of the equation:

7x - 3(x-6) = 30

7x - 3x + 18 = 30

4x + 18 = 30

Next, we need to isolate the variable term on one side of the equation. To do this, we can subtract 18 from both sides:

4x + 18 - 18 = 30 - 18

4x = 12

Finally, we can solve for x by dividing both sides by 4:

4x/4 = 12/4

x = 3

Therefore, the solution to the equation 7x-3(x-6)=30 is x = 3. Answer A is correct.

Answer:

its adding 3

Step-by-step explanation:

So if you had 6 cupcake two days ago, than yesterday there was 9, so tomorrow you should have 12 cupcake and so on

The requried pattern of cupcakes is given by adding 3 cupcakes each day and the pattern comes out as 6, 9, 12, 15, 18, 21, and so on for the subsequent day.

The sequence is a pattern of placing the values in a specified manner.

Here,
Assuming that the pattern is to add 3 cupcakes each day, the continuation of the pattern would be:

Two days ago: 6 cupcakes

Yesterday: 9 cupcakes

Today: 12 cupcakes

Tomorrow: 15 cupcakes

Day after tomorrow: 18 cupcakes

In five days: 21 cupcakes

And so on, the pattern would continue adding 3 cupcakes for each subsequent day.

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The given quesiton is incomplete, the complete question s given below,

I had 6 cupcakes two days ago, and 9 yesterday. Assume it to be series. What will be the number of cupcakes that I will have two days from today??

Answer:

What exactly is the question?

On the first day on Joanne's new wage, she worked for 18 hours.

Given that, Joanne's waitressing job gave her a raise of $2 per hour.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

The first day on her new wage, she worked half of a full a workday and made $36.

Number of hours she worked = Total money she made/Money paid per hour

= 36/2

= 18 hours

Therefore, on the first day on Joanne's new wage, she worked for 18 hours.

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Answer:

0.55555556

Step-by-step explanation:

Answer:

The probability that the lacrosse goalie will make at least 10 saves is 0.558.

Step-by-step explanation:

Let X denote the number of saves the lacrosse goalie will successfully make.

It is provided that the probability of the lacrosse goalie making a successfully save is, p = 0.80.

It is assumed that all save attempts are independent.

Suppose that the lacrosse goalie attempts to make n = 12 saves.

The random variable X follows a binomial distribution with parameters n = 12 and p = 0.80.

Compute the probability that the lacrosse goalie will make at least 10 saves as follows:

\(P(X\geq10 )=P(X=10)+P(X=11)+P(X=12)\)

                 \(={12\choose 10}(0.80)^{10}(0.20)^{2}+{12\choose 11}(0.80)^{11}(0.20)^{1}+{12\choose 12}(0.80)^{12}(0.20)^{0}\\\\=0.2835+0.2062+0.0687\\\\=0.5584\\\\\approx 0.558\)

Thus, the probability that the lacrosse goalie will make at least 10 saves is 0.558.

Answer: 2,594.4 is your answer for fund A and 165.6 is your answer for Fund B

Step-by-step explanation:

A first course in differential equations with modeling applications ninth edition is a textbook that covers the basics of differential equations and their applications in mathematical modeling.

It begins with an introduction to the concepts of differential equations, including the definition, solution methods, and the concept of modeling. It then covers topics such as first-order linear equations, higher-order linear equations, systems of linear differential equations, and nonlinear equations. It also has a chapter on boundary-value problems, which is a type of differential equation that involves a set of boundary conditions that must be satisfied for the solution to be valid.

In order to solve differential equations with boundary-value problems, we must first define the boundary conditions that must be satisfied for the solution to be valid. This involves setting up the boundary conditions in terms of the dependent and independent variables of the equation. We then solve the equation using the boundary conditions and the equation itself. The solution is then used to calculate values for the independent and dependent variables at the boundary points. Finally, we can verify the solution by substituting the calculated values into the equation and seeing if the solution is valid.

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Answer:

Rs 40950

Step-by-step explanation:

P = Rs. 130000

R = 21% per annum

T = 1 year + 6 months / 12

= 12 months + 6 months / 12

= 18 / 12

= 1.5 years

SI = (P × T × R) / 100

= (130000 × 1.5 × 21) / 100

= 4095000 / 100

= 40950

Answer:

the first wheel ever built

Answer:

The first wheel ever built

Step-by-step explanation

(*) Sorry for my late answer but I hope this helps others that are looking for this.

100% in the test :)

Answer:

The probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068

Step-by-step explanation:

We use the Exponential distribution,

Since we are given that on average, 5 pregnant women with high blood pressure come per week,

So, average = m = 5

Now, on average, 5 people come every week, so,

5 women per week,

so, we get 1 woman per (1/5)th week,

Hence, the mean is m = 1/5 for a woman arriving

and λ = 1/m = 5 = λ

we have to find the probability that it takes higher than a week for a high BP pregnant woman to arrive, i.e,

P(X>1) i.e. the probability that it takes more than a week for a high BP pregnant woman to show up,

Now,

P(X>1) = 1 - P(X<1),

Now, the probability density function is,

\(f(x) = \lambda e^{-\lambda x}\)

And the cumulative distribution function (CDF) is,

\(CDF = 1 - e^{-\lambda x}\)

Now, CDF gives the probability of an event occuring within a given time,

so, for 1 week, we have x = 1, and λ = 5, which gives,

P(X<1) = CDF,

so,

\(P(X < 1)=CDF = 1 - e^{-\lambda x}\\P(X < 1)=1-e^{-5(1)}\\P(X < 1)=1-e^{-5}\\P(X < 1) = 1 - 6.738*10^{-3}\\P(X < 1) = 0.9932\\And,\\P(X > 1) = 1 - 0.9932\\P(X > 1) = 6.8*10^{-3}\\P(X > 1) = 0.0068\)

So, the probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068

Answer:

\(2-\sqrt{3}\)

Step-by-step explanation:

\(tan15 = tan(45 - 30)=\frac{\tan{45}-\tan{30}}{1+\tan{45}\tan{30}}\\\\=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}\\\\\\=\frac{\sqrt{3}-1}{\sqrt{3}+1}\\\\\\\)

\(=\frac{(\sqrt{3}-1)^2}{3-1}\\=\frac{3+1-2\sqrt{3}}{2}\\=2-\sqrt{3}\)

Answer:

There isn't an image...

Step-by-step explanation:

The linear equation written in the slope-intercept form is:

y = (-3/5)*x

The correct option is C.

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Here we can see that the line crosses through the poin (0, 0), so the y-intercept is 0.

b = 0

y = a*x + 0

y = a*x

To find the value of a, we can use another point on the graph.

We can see that the linear equation passes through (5, - 3), replacing these values:

-3 = a*5

-3/5 = a

Then the linear equation is just:

y = (-3/5)*x

The correct option is C.

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Answer:

3 1/3

Step-by-step explanation:

8-5=3=3 1/3.

hope u understand

Answer:

No, he does not have enough money to buy the grapes because he only has 15$ when in total the the grapes are $28.35.

Step-by-step explanation:

Answer:

ya-yb=yc+ca

Step-by-step explanation:

Distribute y and c to the values inside the parenthesis.

ya-yb=yc+ca

Answer: 16

Step-by-step explanation:

The trigonometric functions are sin A = 12/13, sin B = 5/13, cos A = 5/13, cos B = 12/13, tan A = 12/5, and tan B = 5/12 as fractions.

Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.

The trigonometric functions are given in the question

Apply the sine ratio on the given right triangle

⇒ sin(θ) = Perpendicular/hypotenuse

sin A = BC/AB

sin A = 12/13

sin B = AC/AB

sin B = 5/13

Apply the cosine ratio on the given right triangle

⇒ cos(θ) = Base/hypotenuse

cos A = AC/AB

cos A = 5/13

cos B = BC/AB

cos B = 12/13

Apply the tangent ratio on the given right triangle

⇒ sin(θ) = Perpendicular/Base

tan A = BC/AC

tan A = 12/5

tan B = AC/BC

tan B = 5/12

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Answer:

y = x + 18

Step-by-step explanation:

slope:

  m = (y₂ - y₁) / (x₂ - x₁)

      = (10 - 18) / (-8 - 0)

      = -8 / -8

      = 1

y-intercept using m from above and anyone of given points, let's use (0, 18):

  y = mx + b

  (18) = 1(0) + b

  b = 18

Using m and b from above form equation of line:

  y = mx + b

  y = 1x + 18 or y = x + 18

\(\boxed{\begin{minipage}{5cm}\sf{2(x+3)=-4(x+1)}\\\sf{2x+6=-4x-4}\\\sf{6x+6=-4}\\\sf{6x=-10}\\\sf{x=-10/6}\\\sf{x=-5/3}\end{minipage}}\)

The required simplified value of the given expression is 16x¹². Option B is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
=(2x³)⁴

As we know that,
[xᵃ]ᵇ = xᵃˣᵇ

So,
(2x³)⁴ = 2⁴x³ˣ⁴
        = 16x¹²

Thus, the required simplified value of the given expression is 16x¹².

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Answer:

Terminating

Step-by-step explanation:

Answer:

Terminating

Step-by-step explanation:

it doesn't repeat bc 89/100 = 0.89

The angle formed by the two hands have a measure less than 1/4 turn

From the question, we have the following parameters that can be used in our computation:

A clock with the hour hand at 12 and the minute hand at 2

The turn represented by the above is represened as

Turn = (2 * 30)/360

When simplified, we have

Turn = 1/6

Next, we have

Angle at the turn = 1/4

1/6 is less than 1/4

This means that the angle formed by the two hands have a measure less than 1/4 turn

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Answer:

1,3

2,4

5,7

6,8

Step-by-step explanation:

congruent  angles are angles across from each other and they equal the same

Answer:

\(\lim_{x \to 0} \frac{12xe^x-12x}{cos(5x)-1}=-\frac{24}{25}\)

Step-by-step explanation:

Notice that \(\lim_{x \to 0} \frac{12xe^x-12x}{cos(5x)-1}=\frac{12(0)e^{0}-12(0)}{cos(5(0))-1}=\frac{0}{0}\), which is in indeterminate form, so we must use L'Hôpital's rule which states that \(\lim_{x \to c} \frac{f(x)}{g(x)}=\lim_{x \to c} \frac{f'(x)}{g'(x)}\). Basically, we keep differentiating the numerator and denominator until we can plug the limit in without having any discontinuities:

\(\frac{12xe^x-12x}{cos(5x)-1}\\\\\frac{12xe^x+12e^x-12}{-5sin(5x)}\\ \\\frac{12xe^x+12e^x+12e^x}{-25cos(5x)}\)

Now, plug in the limit and evaluate:

\(\frac{12(0)e^{0}+12e^{0}+12e^{0}}{-25cos(5(0))}\\ \\\frac{12+12}{-25cos(0)}\\ \\\frac{24}{-25}\\ \\-\frac{24}{25}\)

Thus, \(\lim_{x \to 0} \frac{12xe^x-12x}{cos(5x)-1}=-\frac{24}{25}\)