Determine if the two functions are similar by using transformations. Explain your reasoning.
I'm so confused please please please help and explain thoroughly.​

Answer:

i) 2 + 2x

ii) 154 = 2(2 + 2x + x)

iii) Length = 52m

Breadth = 25m

Step-by-step explanation:

Perimeter of swimming pool = 154m

Breadth = x

Length = 2 + 2x

Formula for finding perimeter = P = 2(l + b)

Therefore,

154 = 2 ( 2 + 2x + x)

154 = 4 + 4x + 2x

154 = 4 + 6x

154 - 4 = 6x

150 = 6x

150/6 = x

25 = x

With the value of x,

we can fInd the length and the breadth

Breadth = x

= 25

Length = 2 + 2x

= 2 + 2(25)

= 2 + 50

= 52

Answer:

- voluntary response sample

- convenience sample

Step-by-step explanation:

Any method of sampling can be biased depending on how they are cared out; however, both voluntary response and convenience are almost always biased. This is because in both the sample is not controlled. In voluntary response, there is no way to ensure that the sample will be representative of everyone since it is based on volunteers. Convenience is also biased because the sample is skewed towards whatever is convenient not what is fair and representative.

hello,

" a turning point is defined as the point where a graph changes from either  increasing to decreasing, or  decreasing to increasing"

a)

[tex]y=x^3+x^2-6x\\\\y'=3x^2+2x-6=0\\x=\dfrac{-2-\sqrt{76} }{6} \approx{-1.786299647...}\\or\\x=\dfrac{-2+\sqrt{76} }{6} \approx{1.1196329...}\\[/tex]

b)

Zeros are -3,0,2.

Sol={-3,0,2}

The solution of the graph function y=x³+x²-6x are -3 , 0 and 2

The link between lines and points is described by a graph, which is a mathematical description of a network. A graph is made up of certain points and the connecting lines. It doesn't matter how long the lines are or where the points are located. A node is the name for each element in a graph.

We have the function

y=x³+x²-6x

now, equating it to 0

x³+x²-6x = 0

x² + x - 6= 0

x² - 3x + 2x -6 =0

x(x -3) + 2(x -3)

x= 3 and -2

Now, ew can see from the that the equation is touching the x-axis at three points and it will represent three zeroes of the equation.

So, the solution of the graph are -3 , 0 and 2

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Answer:

Step-by-step explanation:

This is a right triangle because angle V is 90. Draw out a right triangle and put V at the 90 degree angle. It doesn't matter where you put U or T; you get the same cos value for T regardless of how you place your other 2 angles. The things you need to know are that UT is the hypotenuse of the triangle, side VU is across from angle T, and side TV is across from angle U.

The cos ratio is side adjacent to the reference angle over the hypotenuse.

Our reference angle is T, so we are looking for the side next to T that is NOT the hypotenuse. This side measures 33; the hypotenuse measures 65, so the tangent ratio of T is

[tex]tanT=\frac{33}{65}[/tex]

Answer:

[tex] \frac{3}{8} \: hours[/tex]

Step-by-step explanation:

Additional time =

[tex] \frac{1}{2} - \frac{1}{8} \\ = \frac{4}{8} - \frac{1}{8} \\ = \frac{3}{8} [/tex]

Answer:

3/8 hours is the time to Finnish

Hello,

[tex]\begin{array}{c|c|c|}&x&f(x)\\1&-4&-10\\2&-3&0\\3&-2&0\\4&-1&-4\\5&0&-6******\\6&1&0\\\end{array}\\[/tex]

y-intercept is -6

If x=0 then y=-6

Answer:

0.125

Step-by-step explanation:

It could be a lot of things, but if you mean the decimal form then it would be 0.125. Just divide 1 by 8.

Answer:

There is a non-removable discontinuity at x = 3

Step-by-step explanation:

We are  given that

[tex]f(x)=\frac{x^2+9}{x-3}[/tex]

We have to find true statement about given function.

[tex]\lim_{x\rightarrow 3}f(x)=\lim_{x\rightarrow 3}\frac{x^2+9}{x-3}[/tex]

=[tex]\infty[/tex]

It is not removable discontinuity.

x-3=0

x=3

The function f(x) is not define at x=3. Therefore, the function f(x) is continuous for all real numbers except x=3.

Therefore, x=3 is non- removable discontinuity of function f(x).

Hence, option B is correct.

Answer:

57°,123°,57°,123°

Step-by-step explanation:

as vertical angles are equal

so one angle=114/2=57°

other angle=180-57=123°

Answer:

pic pls

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given function is,

f(x) = -x² - 2x - 1

     = -(x² + 2x + 1)

     = -(x + 2)²

Comparing this equation with the vertex form of a quadratic function,

f(x) = a(x - h)² + k

Here, (h, k) is the vertex.

Vertex of the function is (-2, 0)

Leading coefficient of the function = -1

Therefore, parabola will open downwards.

Function will be increasing in the interval (-∞, -2).

Function will be decreasing in the interval (-2, -∞).

Domain of the function → (-∞, ∞)

Range of the function → (-∞, 0]

Answer:

Step-by-step explanation:

edge

Answer:

A. 100

Step-by-step explanation:

84

Step-by-step explanation:

c + 100 =180

c=180-100

c=80

100+96+d+c=360

100+96+d+80=360

276+d=360

d=360-276

d=84

Answer:

A) 100+55x > 150+51x

B) x>12.5

C)13

Step-by-step explanation:

Bc I said so lol :)

Answer:

again hello dude :D

answers are at the photos

GOOD LUCK :D

Step-by-step explanation:

greetings from Turkey ツ

Answer:

20 degrees.

Step-by-step explanation:

The interior angles of a triangle add up to 180 degrees. One of them, bottom right, is already shown as 70 degrees. You can find the bottom left angle by subtracting 110, the supplementary angle, from 180 (the number of degrees in a straight line). The top angle, 2x, is equal to 40 degrees. (180-70-70 = 40). 40/2 = x, so x = 20 degrees.

Answer:

C Infinitely many solutions

Step-by-step explanation:

i think! Good luck!!

Answer:

i) Point B is located at 0.

ii) The two points that are opposite are 5 / 5 and 10 / -5 and 5 / 5, 10 and -5, -10.

iii) Point D is located at 35.

iv) -20 is one tick mark to the left of point A.

Answer:

[tex]110 in^{2}[/tex]

Step-by-step explanation:

[tex]===========================================[/tex]

Formulas:

Area of a rectangle/square:

[tex]A=lw[/tex]

[tex]===========================================[/tex]

Squares(2):

5*5=25

Multiply by 2

50 in.

Rectangles(4):

5*3=15

Multiply by 4.

60 in.

Total:

Add.

50+60= 110 in2

I hope this helps!

Answer:

13/15

Step-by-step explanation:

P(A∪B) = P(A) + P(B) – P(A∩B)

            = 2/3 + 4/5 - 3/5

 Getting a common denominator

            2/3 *5/5 + 4/5*3/3  - 3/5 *3/3

             10/15 + 12/15 - 9/15

             13/15

Answer:

[tex] \frac{13}{15} [/tex]

Step-by-step explanation:

We know that,

P(AUB) = P(A) + P(B) - P(A n B)

So,

[tex]P(AUB) = P(A) + P(B) - P(A n B) \\ = \frac{2}{3} + \frac{4}{5} - \frac{3}{5} \\ = \frac{10 + 12 - 9}{15} \\ = \frac{22 - 9}{15} \\ = \frac{13}{15} [/tex]

hope this helps you.

Have a nice day!

Answer:

4:1

Step-by-step explanation:

The students eligible to ride the bus are: Marinna, Kaleb and Thomas

The distance between two points [tex](x_1,y_1),(x_2,y_2)[/tex] is,

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

An equation of circle with center at (h, k) and radius 'r' is,

[tex](x-h)^2 + (y-k)^2=r^2[/tex]

For given example,

Town hall is located downtown at point (0,0). A new school is located 3 miles north and 2 miles east of town hall.

Considering positive x-axis = East

negative x-axis = West

positive y-axis = North

negative y-axis =South

Also, locate the position of each student on the graph.

Then the given situation would as shown in following diagram.

We have been given, only students who live outside a 5-mile radius from the school are eligible to ride the school bus.

Using the equation of the circle,

the equation for the area within a circle of 5-mile radius from the school would be,

[tex](x-2)^2+(y-3)^2=5^2[/tex]

From the graph we can observe that, Marinna, Kaleb and Thomas live outside a 5-mile radius from the school.

Therefore, the students eligible to ride the bus are: Marinna, Kaleb and Thomas

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Answer:

11/15 = 73%

Step-by-step explanation:

because in total there are 15 cards and 4 of them is not green. You would want to see what is the probability of other colored carded after leaving out the green ones.

The probability that both cards drawn from the box are not green is 27/52.

To determine the probability that both cards drawn from the box are not green, we need to calculate the probability of each individual draw and multiply them together.

Initially, the box contains a total of 6 red index cards, 3 yellow index cards, and 4 green index cards.

For the first draw, there are a total of 13 cards in the box. Since we are interested in the probability of not drawing a green card, there are 13 - 4 = 9 non-green cards. Therefore, the probability of not drawing a green card on the first draw is 9/13.

For the second draw, there will be 12 cards left in the box. Since one green card has already been removed, there are now 12 - 3 = 9 non-green cards remaining. Thus, the probability of not drawing a green card on the second draw is 9/12.

To find the overall probability, we multiply the probabilities of each individual draw:

(9/13) * (9/12) = 27/52

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Answer:

The answer is 63+7k. :))

Answer:

7k+63

Step-by-step explanation:

Distribute the 7 into the expression 9+k

so 7*9=63

and 7*k=7K

Step-by-step explanation:

1. draw the parallelogram with side 20cm and 25cm respectively and also the diagonal as well.

2.Clearly it forms a triangle in the parallelogram with three known lengths of side.

3.Using the cosine rule : c^2=b^2+c^2 -2bc cos c to find the obtuse angle.

9514 1404 393

Answer:

  114.8°

Step-by-step explanation:

The angles can be found using the Law of Cosines. It tells you ...

  c² = a² +b² -2ab·cos(C)

Then angle C can be found to be ...

  C = arccos((a² +b² -c²)/(2ab)) = arccos((20² +25² -38²)/(2·20·25))

  C = arccos(-419/1000) ≈ 114.77°

The measure of the obtuse angle is about 114.8°.

Step-by-step explanation:

does this mean the sale price includes the tax already ?

then we need to find 13% of the original price before taxes.

that would be done by saying that $101.94 are actuality 113% of the original price (original price = 100%, and then 13% are added).

101.94 = 113%

1% = 101.94/113

13% = 101.94 × 13/113 ≈ $11.73

that means it of the total sales price of $101.94, $11.73 would be the included taxes.

but if this means that 101.94 = 100% of the original price before taxes, we need to calculate the 13% based on that

101.94 = 100%

1% = 101.94/100

13% = 101.94 × 13/100 ≈ $13.25

and then the total price to be paid is

101.94 + 13.25 = $115.19

Answer:

the distance is 16

Step-by-step explanation:

Hi there!

We are given point A (-4,-13) and point B (-4,3). We need to find the distance between those two points

the distance formula is given as [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex] where ([tex]x_{1}[/tex],[tex]y_{1}[/tex]) and ([tex]x_{2}[/tex], [tex]y_{2}[/tex]) are points

we are given 2 points, which is what we need for the formula. However, let's label the values of the points to avoid any confusion

[tex]x_{1}[/tex]=-4

[tex]y_{1}[/tex]=-13

[tex]x_{2}[/tex]=-4

[tex]y_{2}[/tex]=3

now substitute those values into the formula. Remember: the formula uses SUBTRACTION.

[tex]\sqrt{(-4--4)^2+(3--13)^2}[/tex]

simplify

[tex]\sqrt{(-4+4)^2+(3+13)^2}[/tex]

now add the values inside the parenthesis that are under the radical

[tex]\sqrt{(0)^2+(16)^2}[/tex]

raise everything under the radical to the second power

[tex]\sqrt{0+256}[/tex]

add under the radical

[tex]\sqrt{256}[/tex]

now take the square root of 256

[tex]\sqrt{256}[/tex]=16

so the distance between point A and point B is 16

Hope this helps! :)

Answer:

15 is 30 percent of 50 hope this helps

Answer:

Step-by-step explanation:

Tangent line is:

Perpendicular line to this has a slope of -3 and passes through  point (1, 2).

Its equation is:

Using the second line passing through the center, find the coordinates of the center:

Solve the system by elimination:

Then

The center is (0, 5) and radius is the distance from center to point (1, 2):

The equation of circle:

Answer:

It has to be...

Step-by-step explanation:

$55*x because that will be the total

Answer:

the answer to the expression is u=4

Answer:

a) A score of 65 is in the 79.67th percentile.

b) A score less than 70 is below the 95.25th percentile.

c) 20.33% of the scores are greater than 65.

d) 95.25% of scores are less than 70.

e) 45.25% of the scores are between 50 and 60.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The mean is 60 and the standard deviation is 6.

This means that [tex]\mu = 60, \sigma = 6[/tex]

a. what is the percentile rank of the score 65?

This is the p-value of Z when X = 65.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{65 - 60}{6}[/tex]

[tex]Z = 0.83[/tex]

[tex]Z = 0.83[/tex] has a p-value of 0.7967.

Thus: A score of 65 is in the 79.67th percentile.

b. what is the percentile of the score less than 70?

Below the p-value of Z when X = 70. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{70 - 60}{6}[/tex]

[tex]Z = 1.67[/tex]

[tex]Z = 1.67[/tex] has a p-value of 0.9525.

Thus: A score less than 70 is below the 95.25th percentile.

c. what is percent of the scores is greater than 65?

The proportion is 1 subtracted by the p-value of Z when X = 65.

From item a, when X = 65, Z has a p-value of 0.7967

1 - 0.7967 = 0.2033

0.2033*100% = 20.33%

20.33% of the scores are greater than 65.

d. what percent of scores is less than 70?

The proportion is the p-value of Z when X = 70, which, from item b, is of 0.9525.

0.9525*100% = 95.25%

95.25% of scores are less than 70.

e. what percent of the score is between 50 and 60?

The proportion is the p-value of Z when X = 60 subtracted by the p-value of Z when X = 50.

X = 60

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{60 - 60}{6}[/tex]

[tex]Z = 0[/tex]

[tex]Z = 0[/tex] has a p-value of 0.5.

X = 50

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{50 - 60}{6}[/tex]

[tex]Z = -1.67[/tex]

[tex]Z = -1.67[/tex] has a p-value of 0.0475.

0.5 - 0.0475 = 0.4525

0.4525*100% = 45.25%

45.25% of the scores are between 50 and 60.