suppose f(x)=x+3 find the graph of f(2x)

Answer:

The graph of g(x) is wider.

Step-by-step explanation:

Parent function:

[tex]f(x)=x^2[/tex]

New function:

[tex]g(x)=\left(\dfrac{1}{2}x\right)^2=\dfrac{1}{4}x^2[/tex]

Transformations:

For a > 0

[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]

[tex]\begin{aligned} y =a\:f(x) \implies & f(x) \: \textsf{stretched/compressed vertically by a factor of}\:a\\ & \textsf{If }a > 1 \textsf{ it is stretched by a factor of}\: a\\ & \textsf{If }0 < a < 1 \textsf{ it is compressed by a factor of}\: a\\\end{aligned}[/tex]

[tex]\begin{aligned} y=f(ax) \implies & f(x) \: \textsf{stretched/compressed horizontally by a factor of} \: a\\& \textsf{If }a > 1 \textsf{ it is compressed by a factor of}\: a\\ & \textsf{If }0 < a < 1 \textsf{ it is stretched by a factor of}\: a\\\end{aligned}[/tex]

If the parent function is shifted ¹/₄ unit up:

[tex]\implies g(x)=x^2+\dfrac{1}{4}[/tex]

If the parent function is shifted ¹/₄ unit down:

[tex]\implies g(x)=x^2-\dfrac{1}{4}[/tex]

If the parent function is compressed vertically by a factor of ¹/₄:

[tex]\implies g(x)=\dfrac{1}{4}x^2[/tex]

If the parent function is stretched horizontally by a factor of ¹/₂:

[tex]\implies g(x)=\left(\dfrac{1}{2}x\right)^2[/tex]

Therefore, a vertical compression and a horizontal stretch mean that the graph of g(x) is wider.

Answer:

Step-by-step explanation:

By applying the concept of transformation, the transformed function g(x) = √[(3/2) · x] is the consequence of applying a stretch factor of 3/2 on the parent function f(x) = √x.

In this question we have a parent function g(x) = √[(3/2) · x] and a transformed function f(x) = √x. Transformations are operations in which parent functions are modified in their relationships between inputs and outputs.

In this case, the difference between f(x) and g(x) occurred because of the application of a operation known as vertical stretch, defined below:

f(x) = g(k · x), k > 0     (1)

Where k is the stretch factor. There is a compression for 0 ≤ k < 1.

By applying the concept of transformation, the transformed function g(x) = √[(3/2) · x] is the consequence of applying a stretch factor of 2/3 on the parent function f(x) = √x. (Right choice: C)

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Answer:

Yes, because they are congruent by AAS (angle angle side)

Step-by-step explanation:

One of the congruence theorem is AAS. If you follow the sides of the triangle, you will see that they are marked with an angle, another angle, and a side being congruent. I hope this helps!

Answer:

-(6) x 8

ans: - 48

I believe that is the ans:

Answer:

-48

Step-by-step explanation:

   When we multiply a negative integer by a positive integer , we will get a negative integer.

(-6) * 8 = (-48)

negative integer  * negative integer = positive integer

(-2) * (-3) = 6

negative integer * positive integer  = negative integer

(-2) * 3 = (-6)

Positive integer *negative integer =  negative integer

2 * (-3) = (-6)

Answer:

Point-slope form of equation of a line that passes from (-1,3) and (0,0) is given as y-3=-3(x+1).

Slope-intercept form of equation is given as y=-3x.

Step-by-step explanation:

In the question, it is given that the line passes from (-1,3) and (0,0).

It is asked to write the point-slope form of the equation and rewrite it as slope-intercept form.

Step 1 of 2

Passing point of line is (-1,3).

Hence, [tex]$x_{1}=-1$[/tex] and

[tex]$$y_{1}=3 \text {. }$$[/tex]

Also, Passing point of line is (0,0).

Hence, [tex]$x_{2}=0$[/tex] and

[tex]$$y_{2}=0 \text {. }$$[/tex]

Substitute the above values to find the slope of line which is given by [tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]

[tex]$$\begin{aligned}m &=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\m &=\frac{0-3}{0-(-1)} \\m &=\frac{-3}{1} \\m &=-3\end{aligned}$$[/tex]

Hence, slope of the line is -3

Step 2 of 3

It is obtained that m=-3

[tex]$y_{1}=3$[/tex]

and [tex]$x_{1}=-1$[/tex]

Substitute the above values in point-slope form of equation given by [tex]$y-y_{1}=m\left(x-x_{1}\right)$[/tex]

[tex]$y-y_{1}=m\left(x-x_{1}\right)$\\ $y-3=-3(x-(-1)$\\ $y-3=-3(x+1)$[/tex]

Hence, point-slope form of equation given as y-3=-3(x+1).

Step 3 of 3

Solve y-3=-3(x+1) to write it as slope-intercept form given by y=mx+c

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

Hence, slope-intercept form of equation is given as y=-3x.

Answer:

'A prime number is a number which has exactly two factors i.e. '1' and the number itself. A composite number has more than two factors, which means apart from getting divided by 1 and the number itself, it can also be divided by at least one positive integer.'

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

What is the definition of prime & composite numbers?

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

A prime number can be evenly divided by 1 and itself. These are its only two factors.

A composite number can be evenly divided by 1, itself, and something else. In other words, composite numbers have more than 2 factors.

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

              [tex]\bf{\begin{cases}\bf{Primes\;have\;only\;2\;factors} \\ \bf{Composites\;have\;3\;or\;more\;factors} \end{cases}[/tex]

[tex]\LARGE\boxed{\bf{aesthetic\not1\theta l}}[/tex]

Answer:

Step-by-step explanation:

Step-by-step explanation for each question:

For Question 6, the range of a function is all the possible outputs of the function. Since the function can only take the inputs 0, 4, and 7, we can just plug in each into the formula and find their corresponding outputs.

g(0) = 0² - 9 = 0 - 9 = -9

g(4) = 4² - 9 = 16 - 9 = 7

g(7) = 7² - 9 = 49 - 9 = 40

Therefore the only possible outputs of function g, or the range, is {-9, 7, 40}.

For question 4, the input t is a given time, and h(t) is the height of the football at that time.

Hence, h(2.5) is the height of the football (in feet) at 2.5 seconds. The value 2.5 can be plugged into the function [tex]-16t^2+58t+2[/tex] to get the height. This gives us

[tex]-16(2.5)^2 + 58(2.5) + 2[/tex]

[tex]-16(6.25) + 58(2.5) + 2[/tex] [Squaring 2.5]

[tex]-100 + 145 + 2[/tex] [Multiplying]

[tex]47[/tex] [Combining all terms]

We find that the height of the football at 2.5 seconds is 47 feet.

For Question 5, the table of values show all the possible values x can be (or the domain), and what the output of the function f(x) would give for each.

A) f(-3) = 5, as the row with -3 for x has -5 for y.

B) f(0) = 0, as the row with 0 for x has 0 for y.

C) f(1) = -3, as the row with 1 for x has -3 for y.

The range of the function will be -9,7 and 40.

The domain denotes all potential x values, while the range denotes all possible y values.

Given equation;

g(x) = x²-9

The range of the given domain is found by putting the values one by one in the above equation as;

g(x) = x²-9

a)For x = 0

g(x) = 0²-9

g(x) =-9

b)For x =4

g(x) = 4²-9

g(x) =16-9

g(x) = 7

c)For x =7

g(x) = 7²-9

g(x) =49-9

g(x) = 40

Hence, the range of the function will be -9,7 and 40.

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Answer: h>0 and k>0

Step-by-step explanation:

If the circle is centered in Quadrant I, then both the x and y coordinates of the center are positive.

This means that h>0 and k>0.

Step-by-step explanation:

the sum of all angles in a triangle is always 180°.

so,

180 = 60 + 45 + angle4 = 105 + angle4

75° = angle4

C. Between E and F and between G and H the elevator could be travelling from a higher floor to a lower floor.

We have to justify all the options with respect to the graph :-

Option A : Between A and B, the elevator would be travelling from a lower floor to a higher floor. Also between C and D, the elevator would be travelling from a lower floor to a slightly higher floor.

So, this option is not correct.

Option B : Between B and C, the elevator wouldn't go higher. And also the same would happen in between D and E.

So, this option is not correct.

Option C : Between E and F, the elevator would be travelling from higher floor to lower and also between G and H.

So, this option is correct.

Option 4 : Between F and G, there would not have much changes. So it will be omitted.

So, this option is not correct.

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Answer: after t hours, the distance d between the hikers is

d^2 = (.24t)^2 + (.17t)^2 - 2(.24t)(.17t)cos109.167°

so, find t when d = 0.0568182

Step-by-step explanation:

Using the Central Limit Theorem, the percentage that is expected to be the closest to the actual percentage is:

A. The Tribune, at 68%.

It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard error [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].

From this, a larger sample size leads to a smaller error estimate. Since the Tribune had the largest sample size, option A is correct.

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Answer:  x = -5/2 and x = -3/2

Step-by-step explanation:

(2x + 5)2 = 4x (x + 5) +25

   4x + 10 = 4x² + 20x + 25

   [minus 4x on both sides.]

            10 = 4x² + 16x + 25

   [minus 10 on both sides.]

            0 = 4x² + 16x + 15

ac = 4(15) = 60,then find the factors that add up to 16, which is 6 and 10.

            0 = 4x² + 6x + 10x + 15

            0 = 2x(2x + 3) + 5(2x + 3)

            0 = (2x + 5)(2x + 3)

2x + 5 = 0                                 2x + 3 = 0

       2x = -5                                    2x = -3

         x = -5/2                                    x = -3/2

[tex]\huge\text{Hey there!}[/tex]

[tex]\textbf{Assuming you meant: }\mathsf{(2x + 5)^2 = 4x(x + 5) + 25}[/tex]

[tex]\textbf{If so, simplify both sides of your equation you're working with}[/tex]

[tex]\mathsf{ 4x^2 + 20x + 25 = 4x^2 + 20x + 25}[/tex]

[tex]\textbf{SUBTRACT }\rm{\bf 4x^2}\text{ \bf to BOTH of the SIDES}[/tex]

[tex]\mathsf{4x^2 + 20x + 25 - 4x^2 = 4x^2 + 20x + 25 - 4x^2}[/tex]

[tex]\textbf{Simplify it!}[/tex]

[tex]\mathsf{20x + 25 = 20x + 25}[/tex]

[tex]\textbf{SUBTRACT 20x to BOTH of the SIDES}[/tex]

[tex]\mathsf{20x + 25 - 20x = 20x + 25 - 20x}[/tex]

[tex]\large\textbf{SIMPLIFY IT! (as well)}[/tex]

[tex]\mathsf{25 = 25}[/tex]

[tex]\textbf{SUBTRACT 25 to BOTH of the SIDES}[/tex]

[tex]\mathsf{25 - 25 = 25 - 25}[/tex]

[tex]\textbf{Lastly, SIMPLIFY THAT!}[/tex]

[tex]\textbf{We get: }\mathsf{0 = 0}[/tex]

[tex]\large\textsf{This means that your \boxed{\textsf{solutions}} are \bf REAL NUMBERS.}[/tex]

[tex]\huge\textsf{Therefore, your answer should be: }\\\boxed{\mathsf{All\ \underline{\underline{REAL\ NUMBERS}}\ are\ solutions.}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

(×-4) (x + 4)

Step-by-step explanation:

first of all, recognize that the polynomial expression is a difference of two squares.

thus

X^2-16

(x -4)(x+4)

⊱________________________________________________________⊰

[tex]\\[/tex][tex]\\[/tex]

Answer:

Step-by-step explanation:

[tex]\large\begin{gathered} \sf{To \ factor \ this \ polynomial, \ we \ must \ first \ recognise \ it. \ Isn't \ it \ the \ difference} \\ \sf{of \ two \ squares?} \\ \rm{It \ is! } \\ \sf{Polynomials \ like \ (a^2-b^2) are \ factored \ like \ this\!\!:} \\ \sf{(a+b)(a-b).} \\ \sf{Similarly, \ (x^2-16) \ is \ factored \ as \ (x+4)(x-4). \end{gathered}[/tex]

Done!!

⊰_____________________________________________________⊱

[tex]\\[/tex][tex]\\[/tex]

[tex]\boldsymbol{\rm{\triangleright\overbrace{C}\triangleleft\underbrace{A}\triangleright\overbrace{L}\triangleleft\underbrace{L}}\triangleright\overbrace{\stackrel\bigstar{I}}\triangleleft\underbrace{G}\triangleright\overbrace{R}\triangleleft\underbrace{A}\triangleright\overbrace{P}\triangleleft\underbrace{H}\triangleright{Y}}}[/tex]

Answer:

No. The correct equation is

y= 1/2 x - 2

Step-by-step explanation:

See picture

Answer:

AC = 6√3 in

Step-by-step explanation:

Join OC. Now ΔAOC is an isosceles triangle as OA = OC =radius.

 ∠A = ∠C = 30.

 ∠A + ∠C +  ∠AOC = 180 {angle sum property of traingle}

 30 + 30 + ∠AOC  = 180°

                 ∠AOC = 180 -60

                 ∠AOC = Ф = 120°

Find the length of radius using the bellow formula.

         [tex]\sf \boxed{\bf Arc \ length = \dfrac{\theta}{180}\pi r}[/tex]

            Ф = 120°

                Arc length = 4π

            [tex]\sf 4\pi =\dfrac{120}{180}*\pi *r\\\\ r =\dfrac{4\pi * 180}{120*\pi }\\\\ r = 6 \ in[/tex]

[tex]\sf \boxed{\bf chord \ length = 2rSin \ \dfrac{\theta}{2}}[/tex]

                         [tex]\sf b = 2*6*Sin \ \dfrac{120}{2}\\\\ b = 2 *6 * Sin \ 60^\circ\\\\ b = 2 * 6 * \dfrac{\sqrt{3}}{2}\\\\ \b = 6\sqrt{3}[/tex]

[tex]\sf \boxed{\bf AC = 6\sqrt{3} \ in}[/tex]

Puja Limbu had the better performance than Raju Limbu.

Such question are generally solved using percentages.

In mathematics, a percentage is a number or ratio that represents a fraction of 100. It is often denoted by the symbol "%" or simply as "percent" or "pct." For example, 35% is equivalent to the decimal 0.35, or the fraction.

Percentage of Raju limba = [tex]\frac{11}{15}[/tex] X 100 = 73.3%

Percentage of Puja Limba = [tex]\frac{8}{10}[/tex] x 100 = 80%

As percentage of Puja Limba is greater than that of Raju Limba .

Hence performance of Puja Limba is better

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3:8:1

3/12 x 144= 36

8/12 x 144= 96

96+36= 132

144-132= 12

12/12=1

Therefore, the ratio of Alyssa's nickels to dimes to quarters is 3:8:1

The value of a is (c) 86

The given parameter is:

Angle C = 86

By vertical angle theorem, we have:

Angle A = Angle C = 86

This implies that:

Angle A = 86

The arc A subtends angle A

This means that:

Arc A = 86

Hence, the value of a is (c) 86

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The percentiles are: P40 = 33, P70 = 45, and P89 = 54.1, while the quartiles are Q1 = 28.5 and Q3 = 47.5

The sorted dataset is:

22, 22, 24, 25, 26, 27, 27, 30, 30, 32,

33, 33, 35, 37, 38, 38, 40, 42, 44, 44,

45, 47, 48, 48, 49, 52, 55, 58, 62, 68

The number of data elements is:

N = 30

The 40th percentile (P40)

This is calculated using:

Element = (40% * N)th

So, we have:

Element = (40% * 30)th

Evaluate

Element = 12th

The 12th element is 33

Hence, the value of P40 is 33

The 70th percentile (P70)

This is calculated using:

Element = (70% * N)th

So, we have:

Element = (70% * 30)th

Evaluate

Element = 21st

The 21st element is 45

Hence, the value of P70 is 45

The 89th percentile (P89)

This is calculated using:

Element = (89% * N)th

So, we have:

Element = (89% * 30)th

Evaluate

Element = 26.7th

The element is calculated as:

Element = 26th + 0.7 * (27th - 26th)

So, we have:

Element = 52 + 0.7 * (55 - 52)

Element = 54.1

Hence, the value of P89 is 54.1

The 1st quartile (Q1)

This is calculated using:

Element = (1/4 * N)th

So, we have:

Element = (1/4 * 30)th

Evaluate

Element = 7.5th

The element is calculated as:

Element = 7th + 0.5 * (8th - 7th)

So, we have:

Element = 27 + 0.5 * (30- 27)

Element = 28.5

Hence, the value of Q1 is 28.5

The 3rd quartile (Q3)

This is calculated using:

Element = (3/4 * N)th

So, we have:

Element = (3/4 * 30)th

Evaluate

Element = 22.5th

The element is calculated as:

Element = 22nd + 0.5 * (23rd - 22nd)

So, we have:

Element = 47 + 0.5 * (48- 47)

Element = 47.5

Hence, the value of Q3 is 47.5

The 5th quartile (Q5)

There is no such thing as Q5 i.e. the 5th quartile

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The price of each taco is $10.5

What is unitary method?

We can solve this question by unitary method.
The unitary method is a method of finding the value of one unit and then finding the value of the required number of units. While solving a problem it is important to recognize the units and values.

In this question, 10 tacos cost $105.
Let's represent the cost of 1 taco as [tex]x[/tex]
10 tacos =$ 105
1 taco = [tex]x[/tex]
10[tex]x[/tex] = 105
[tex]x[/tex] = [tex]\frac{105}{10}[/tex]

[tex]x[/tex] = 10.5
Each taco cost $10,5
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Answers:

====================================================

Explanation:

Here are all the ways to multiply to 18 when using integers only:

Sum each pair of factors to find out a possible value of b.

Therefore, the possible values of b are

which are the final answers.

----------------------

An example:

Let's say b = 11. This would mean [tex]x^2+bx+18[/tex] becomes [tex]x^2+11x+18[/tex]

It would factor to [tex](x+2)(x+9)[/tex] since it was stated earlier that:

2+9 = 11

2 * 9 = 18

You can use the FOIL rule, distributive property, or the box method to confirm that [tex]x^2+11x+18 = (x+2)(x+9)[/tex] is a true equation for all real numbers x.

This same idea applies for the other values of b.

----------------------

If you're curious why this works, consider multiplying the two factors (x+p) and (x+q)

Use the FOIL rule to get [tex](x+p)(x+q) = x^2+qx+px+pq = x^2+(p+q)x + pq[/tex]

The middle term [tex](p+q)x[/tex] has the components add to the coefficient, while those same two components multiply to get the last term. This is why when factoring we're looking for two numbers that multiply to 18, and also add to the value of b (which in the case of the last example was 11).

The population in the year 2020 is 4628

The given parameters are:

Initial, a = 12910

Rate, r = 5%

Since the population decreases, then we make use of an exponential decay function.

This is represented as:

f(n) = a * (1 - r)^n

So, we have:

f(n) = 12910 * (1 - 5%)^n

Evaluate the difference

f(n) = 12910 * 0.95^n

2020 is 20 years from 2000.

So, we have:

f(20) = 12910 * 0.95^20

Evaluate

f(20) = 4628

Hence, the population in the year 2020 is 4628

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Answer:

20cm

Step-by-step explanation:

You divide by 12

The estimation goal is to estimate a population parameter. The estimation process uses sample statistics.

The goal of hypothesis testing is testing to claim whether it is right or wrong.

The hypothesis testing also uses statistics to determine whether or not a treatment has an effect.

The estimation goal is to estimate a population parameter. The estimation is used to determine how much effect a treatment has.

To estimate a parameter, a sample statistics of the parameter is used.

Thus, the estimation is to estimate a population parameter.

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[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

An equation is shown. What is the value of n? [tex]\bf{n=1:17}[/tex] is shown

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

[tex]\bf{n=1:17}[/tex] | divide

[tex]\bf{n=\dfrac{1}{17}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{Result:}[/tex]

          [tex]\bf{=n=\dfrac{1}{17}}[/tex]

[tex]\boxed{\bf{aesthetic \not101}}[/tex]