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PLEASE GIVE A STEP BY STEP EXPLANATION!!!


The linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x):

Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 points)


Part B: Solve for k in each type of transformation. (4 points)


Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x). (4 points)

Answer:

Area: 15.53 square inches

Perimeter: 15.71 inches

Step-by-step explanation:

Area:

So the area of the rectangle is pretty easy to find and is just the width * height. In this case it's 4 * 3 which is 12. Now the area of a circle is [tex]\pi r^2[/tex]. But since this is a semi circle it's half of that which is [tex]\frac{\pi r^2}{2}[/tex]. The diameter of the semicircle is 3 as it sits on top of the rectangle. The radius is half of the diameter so the radius is 1.5. Now plug that into the equation and you get [tex]\frac{(3.14) (1.5)^2}{2} = 3.5325[/tex]. Now add that to 12 and you get 15.5325. Round that number to the nearest hundredth and you get 15.53. So that's the area.

Perimeter:

Pi is the ratio of any circle's circumference to the diameter. Or in other words the circumference is equal to the diameter * 3.14. The diameter is 3 which you multiply by 3.14 to get the circumference of a circle. This will get you 9.42 but since it's a semicircle, the circumference is half of this value which is 4.71. The perimeter of the rectangle is just 2 times the width + 2 times the height. This is not completely the case in this shape since one of the sides of the rectangle is not a side of the two shapes joined together. Which is the side that is parallel to the side of length 3 inches. So the perimeter is going to be 2(4) + 3. This gives you 11 which you add to the 4.71 and get 15.71

The graphed trigonometric function is the one in option a.

The key parts that we can see on the graph are:

From this we know that the correct option is either a or b.

Now we can evaluate options a and b in x = 0 and see which one is equal to zero.

for a:

y = sin(0 - pi/2) + 1 = sin(-pi/2) + 1 = -1 + 1 = 0

for b:

y = cos(0 + pi/2) + 1 = 0 + 1 =  1

Then we can see that option a is the correct option.

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Answer:

x = | 1 |

Step-by-step explanation:

how are u in college doing this???

Answer:

1

Step-by-step explanation:

(x+8)=9

x+8=9

x=9-8

x=1

If f(x)=x²+2 and g(x)=x²+5 then the domain of  the (fog) (x) is (-∞,∞).

Given the f(x)=x²+2 and g(x)=x²+5

We have to find the domain of  the (fog) (x)

The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0.

then,(fog) (x)= (x²+5)²+ 2

                    =x⁴+25+10x²+2

                    = x⁴+27+10x²

Now on any real value of x the value of (fog) (x) exists therefore (fog) (x) can take all the values of the real number.

So domain (fog) (x)= (-∞,∞).

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The cost of 11-minute call between these two cities after 5 p.m is: 142.

Given:

Charges for long distance=65% or .65

Cost=20 cents per minutes

Number of call minutes=11 minutes

Hence:

Cost =20 cents ×11 minutes times 0.65

Cost =143 cents

Therefore the cost of 11-minute call between these two cities after 5 p.m is: 142.

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Answer:

The total number of registered doctors in this year are 307345.

Step-by-step explanation:

Let the total number of doctors who registered in this year are x

Given that the total number of female doctors in total registered doctors are 54400

According to the question 17.7 percent of the total registered doctors are the female doctors

Hence the total number of  registered doctors who are females are 17.7% of x

which is written as 17.7*x÷100

According to the question 17.7x÷100= 54400

as we are given that the total number of female doctors are 54400

now

17.7x = 54400×100

x= 54400×100÷17.7

x= 307344.633 ≈ 307345

Therefore there are 307345 doctors who registered that year.

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Answer:

1/7

Step-by-step explanation:

Alternative Form: 0.142857, 7^-1

According to second equation of kinematics

Take positive value

Answer:

2.7 s  (1 d.p.)

Step-by-step explanation:

Use the Constant Acceleration Equations where:

Given:

[tex]\begin{aligned}\text{Using }s & =ut+\dfrac{1}{2}at^2\\\implies 55 & =11.8t+\dfrac{1}{2}(6.39)t^2\end{aligned}[/tex]

Rearrange the equation to equal zero:

[tex]\implies 3.195t^2+11.8t-55=0[/tex]

Quadratic Formula

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]

Use the quadratic equation to solve for t:

[tex]\implies a=3.195, \quad b=11.8, \quad c=-55[/tex]

[tex]\implies t=\dfrac{-11.8 \pm \sqrt{11.8^2-4(3.195)(-55)} }{2(3.195)}[/tex]

[tex]\implies t=2.694780675, -6.388051411[/tex]

As time is positive:

[tex]\implies t=2.694780675... \:\text{s}[/tex]

[tex]\implies t=2.7 \: \text{s (1 d.p.)}[/tex]

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Answer: [tex]2\left(x-\frac{1}{4} \right)^{2}[/tex]

Step-by-step explanation:

[tex]2x^{2}-x+\frac{1}{8}\\\\=2\left(x^{2}-\frac{1}{2}x \right)+\frac{1}{8}\\\\=2\left(\left(x-\frac{1}{4} \right)^{2}-\frac{1}{16} \right)+\frac{1}{8}\\\\=2\left(x-\frac{1}{4} \right)^{2}-\frac{1}{8}+\frac{1}{8}\\\\=\boxed{2\left(x-\frac{1}{4} \right)^{2}}[/tex]

step-by-step explanation:

#1: simplify both sides of the equation.

2(x+3)−4x=x

(2)(x)+(2)(3)+−4x=x

2x+6+−4x=x

(2x+−4x)+(6)=x

−2x+6=x

−2x+6=x

***

#2: subtract x from both sides.

−2x+6−x=x−x

−3x+6=0

***

#3: subtract 6 from both sides.

−3x+6−6=0−6

−3x=−6

***

step 4: divide both sides by -3.

−3x/-3 = -6/-3

solution x = 2

thomas age:44

huilan age: 29

Step-by-step explanation:

h = t + 15

t + t + 15 = 73

2t = 73 - 15

2t = 58

t = 29

Answer:

4

Step-by-step explanation:

4

The possible values of x are:

x = -1/2 + i/2

x = -1/2 - i/2

A basic quadratic equation, or a second-order polynomial equation with a single variable, is represented by the equation x : ax² + bx + c = 0, where a≠0 for the variable x. As it is a second-order polynomial equation, which is ensured by the algebraic fundamental theorem, it must have at least one solution.

To find the possible values of x in equation 8x² + 4x = -1, we need to solve for x.

First, we can rearrange the equation to get:

8x² + 4x + 1 = 0

We can solve this quadratic equation using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation in standard form (ax² + bx + c).

In this case, a = 8, b = 4, and c = 1. Substituting these values into the quadratic formula, we get:

x = (-4 ± √(4² - 4(8)(1))) / 2(8)

x = (-4 ± √(16 - 32)) / 16

x = (-4 ± √(-16)) / 16

x = (-4 ± 4i) / 16

where i is the imaginary unit, which is defined as the square root of -1.

Therefore, the possible values of x are:

x = (-4 + 4i) / 16

x = (-4 - 4i) / 16

These values can also be simplified as:

x = -1/2 + i/2

x = -1/2 - i/2

So the possible values of x are complex numbers, specifically x = -1/2 ± i/2.

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Step-by-step explanation:

the answer is 38/24 so the final answer is 19/12

Answer:

vector VW= w - v

vector WV= v - w

Step-by-step explanation:

there are no figures to solve the question so i'll just write the formula..

vector VW= w - v

vector WV= v - w

The integral of [tex]f(x)[/tex] over the interval [tex][-a,a][/tex] corresponds to the area of a semicircle of radius [tex]a[/tex], so

[tex]\displaystyle \int_{-a}^a f(x) \, dx = \frac{\pi a^2}2[/tex]

The integral over [tex][a,3a][/tex] corresponds to the negative area of a trapezoid with height [tex]a[/tex] and base lengths [tex]2a[/tex] and [tex]a[/tex], so

[tex]\displaystyle \int_a^{3a} f(x) \, dx = -\frac{a(2a+a)}2 = -\frac{3a^2}2[/tex]

Then combining the integrals, we have

[tex]\displaystyle \int_{-a}^{3a} f(x) \, dx = \frac{\pi a^2}2 + \left(-\frac{3a^2}2\right) = \frac{(\pi-3)a^2}2[/tex]

When [tex]a=9[/tex], the integral evaluates to

[tex]\displaystyle \int_{-9}^{27} f(x) \, dx = \frac{(\pi-3)\times81}2 \approx \boxed{5.7345}[/tex][/tex]

It can be modeled by an exponential function because each time x increases by 1, f(x) is multiplied by 4.

This means the base of the exponential function is 4, and since f(x)=3 when x=0, [tex]f(x)=3(4)^{x}[/tex]

The amount of the  interest revenue that  Princess will record in 2022 on this lease is:$413,553.82.

First step

Lease value payments after first payment:

Lease value payments=  $5,588,516- $716,000

Lease value payments= $4,872,516

Second step

Lease value payments after second payment:

Lease value payments=$4,872,516+ ($4,872,516×9%) - $716,000

Lease value payments=$4,872,516+$438,526.44-$716,000

Lease value payments=$4,595,042.44

Third step

2022 Interest revenue=$4,643,787.6×9%

2022 Interest revenue=$413,553.8196

2022 Interest revenue=$413,553.82 (Approximately)

Therefore the amount of the  interest revenue that  Princess will record in 2022 on this lease is:$413,553.82.

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Answer:

[tex] \frac{1}{7} [/tex]

If the number of multiple-choice questions is x and the number of short answer questions is y, then:

[tex]x+y=28\\\\3x+5y=100[/tex]

Answer:

Suppose the heights of 18-year-old men are approximately normally distributed, with mean 71 inches and standard deviation 4 inches.

(a) What is the probability that an 18-year-old man selected at random is between 70 and 72 inches tall? (Round your answer to four decimal places.)

z1 = (70-71)/4 = -0.25

z2 = (72-71/4 = 0.25

P(70<X<72) = p(-0.25<z<0.25) = 0.1974

Answer: 0.1974

(b) If a random sample of thirteen 18-year-old men is selected, what is the probability that the mean height x is between 70 and 72 inches? (Round your answer to four decimal places.)

z1 = (70-71)/(4/sqrt(13)) = -0.9014

z2 = (72-71/(4/sqrt(13)) = 0.9014

P(70<X<72) = p(-0.9014<z<0.9014) = 0.6326

Answer: 0.6326

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Explanation:

We have two concentric circles. Think of a bulls-eye on a dart board. The inner circle is the garden itself. The outer circle is the garden plus the surrounding pathway. What we're interested in is the area of the outer ring, which is the area of the garden path only.

To find this ring area, we'll need to find the area of each circle.

A = area of the smaller circle

A = pi*r^2

A = pi*12^2

A = 144pi

Notice how I took half of the 24 yard diameter to get the radius of 12 yards.

B = area of the larger circle

B = pi*r^2

B = pi*15^2

B = 225pi

Subtract the two results

C = area of the outer ring, aka the garden path only

C = B - A

C = 225pi - 144pi

C = (225-144)pi

C = 81pi

We're told to use 3.14 in place of pi

C = 81*pi

C = 81*3.14

C = 254.34

The garden path has an area of roughly 254.34 square yards.

1 bag of sand covers 8 square yards.

So we'll need (254.34)/(8) = 31.7925 = 32 bags of sand

Answer:

[tex]\frac{2}{3}|2-x|=\frac{1}{15}[/tex]

Step-by-step explanation:

[tex]\frac{1}{5} + \frac{2}{3} |2-x| = \frac{4}{15} \\\\\frac{1}{5}*(\frac{3}{3}) = \frac{3}{15}\\\\\frac{3}{15}-\frac{3}{15} + \frac{2}{3}|2-x| =\frac{4}{15}-\frac{3}{15}\\\\\frac{2}{3}|2-x|=\frac{1}{15}[/tex]

Step-by-step explanation:

1) the required equation in common form is:

(x-x₀)²+(y-y₀)²=r², where (x₀;y₀) - coordinates, where Michael is standing; r - the social distance;

According to the common form and given coordinates (x₀=-5; y₀=2; r=6) it is possible to make up the required equation:

(x+5)²+(y-2)²=6².

2) if the distance between two friends is:

[tex]d=\sqrt{(-5-1)^2+(2-1)^2}=\sqrt{37}, \ then[/tex]

this distance is longer than social (6 ft). For more info see the attachment.

Step-by-step explanation:

first function, f(x) = 5x-3 goes with option B

2nd function, 4- 4x goes with option A

3rd function goes with option D

4th goes with option C

Answer:

10000×(1+5%)^(15×2)=43219.4238

Answer:

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

Answer:

Answer is 6

Step-by-step explanation:

Let the number be ×

Twice a number is 2×

Twice a number increase by 8 is 2×+8

hence the equivalent will be

2×+8=20

2×=12

×6

Answer:

6

Step-by-step explanation:

Let n be the unknown number.

"Twice a number" means to multiply the number by 2:  

⇒ 2n

"Increase by 8" means to add 8:

⇒ 2n + 8

"Is 20" means equals 20:

⇒ 2n + 8 = 20

Therefore, the equation is:  2n + 8 = 20

To solve, subtract 8 from both sides:

⇒ 2n + 8 - 8 = 20 - 8

⇒ 2n = 12

Divide both sides by 2:

⇒ 2n ÷ 2 = 12 ÷ 2

⇒ n = 6

Therefore, the unknown number is 6.

The transformation of a function may involve any change. The function with the graph are given below.

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.

If the original function is y = f(x), assuming horizontal axis is input axis and vertical is for outputs, then:

Horizontal shift (also called phase shift):

Vertical shift:

Stretching:

The real graph of the function is f(x)=x², now if the graph of the given function can be found by using the transformation rule as shown above. The function with the graph are given below.

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Answer:

19 small frames and 3 large frames

Step-by-step explanation:

follows the steps in the attached