A point P(3, k) is first transformed by E¹[0, 2] and then by E²[0,3/2] so that the final image is (9, 12), find the value of k.​​

Even function:

A function is said to be even if its graph is symmetric with respect to the , that is:

Odd function:

A function is said to be odd if its graph is symmetric with respect to the origin, that is:

So let's analyze each question for each type of functions using examples of polynomial functions. Thus:

FOR EVEN FUNCTIONS:

1. When  becomes  

1.1 Effects on the y-intercept

We need to find out the effects on the y-intercept when shifting the function  into:

We know that the graph  intersects the y-axis when , therefore:

So:

So the y-intercept of  is one unit less than the y-intercept of

1.2. Effects on the regions where the graph is increasing and decreasing

Given that you are shifting the graph downward on the y-axis, there is no any effect on the intervals of the domain. The function  increases and decreases in the same intervals of

1.3 The end behavior when the following changes are made.

The function is shifted one unit downward, so each point of  has the same x-coordinate but the output is one unit less than the output of . Thus, each point will be sketched as:

FOR ODD FUNCTIONS:

2. When  becomes  

2.1 Effects on the y-intercept

In this case happens the same as in the previous case. The new y-intercept is one unit less. So the graph is shifted one unit downward again.

An example is shown in Figure 1. The graph in blue is the function:

and the function in red is:

So you can see that:

2.2. Effects on the regions where the graph is increasing and decreasing

The effects are the same just as in the previous case. So the new function increases and decreases in the same intervals of

In Figure 1 you can see that both functions increase at:

and decrease at:

2.3 The end behavior when the following changes are made.

It happens the same, the output is one unit less than the output of . So, you can write the points just as they were written before.

So you can realize this concept by taking a point with the same x-coordinate of both graphs in Figure 1.

FOR EVEN FUNCTIONS:

3. When  becomes  

3.1 Effects on the y-intercept

We need to find out the effects on the y-intercept when shifting the function  into:

As we know, the graph  intersects the y-axis when , therefore:

And:

So the new y-intercept is the negative of the previous intercept shifted one unit upward.

3.2. Effects on the regions where the graph is increasing and decreasing

In the intervals when the function  increases, the function  decreases. On the other hand, in the intervals when the function  decreases, the function  increases.

3.3 The end behavior when the following changes are made.

Each point of the function  has the same x-coordinate just as the function  and the y-coordinate is the negative of the previous coordinate shifted one unit upward, that is:

FOR ODD FUNCTIONS:

4. When  becomes  

4.1 Effects on the y-intercept

In this case happens the same as in the previous case. The new y-intercept is the negative of the previous intercept shifted one unit upward.

4.2. Effects on the regions where the graph is increasing and decreasing

In this case it happens the same. So in the intervals when the function  increases, the function  decreases. On the other hand, in the intervals when the function  decreases, the function  increases.

4.3 The end behavior when the following changes are made.

Similarly, each point of the function  has the same x-coordinate just as the function  and the y-coordinate is the negative of the previous coordinate shifted one unit upward.

Step-by-step explanation:

[tex] \frac{2}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } = \frac{2(2 - \sqrt{3} )}{1} = 4 - 2 \sqrt{3} [/tex]

Answer:

D.

Step-by-step explanation:

x = number of glasses of iced tea

y = number of glasses of lemonade

The total number of glasses is

x + y

The total number of glasses is 44

x + y = 44

This is not a choice, but the answer must be equivalent to this equation.

Solve for x by subtracting y from both sides.

x = 44 - y

Answer: D.

Answer:

142 [tex]cm^3\\[/tex]

Step-by-step explanation:

You have to do [tex](7*5)+(5*3)+(7*3)+(7*3)+(5*7)+(3*5)[/tex].

This equals 142 [tex]cm^3\\[/tex].

Answer:

The answer is 142cm

Step-by-step explanation:

Answer:

range

Step-by-step explanation:

Answer:

Yes, the triangles are similar by SAS

Step-by-step explanation:

Looking at the picture, we see that there are two triangles with side lengths of different sides. We can deduce that the scale factor is 1 2/3, because 8 divided by 4.8 is 1 2/3, and 10 divided by 6 is the same. Now that we have clarified that the triangles share the same scale factor, we notice that the angle is also the same, as mentioned in the picture. This leads us to say that the triangles are similar by the SAS similarity theorem (Side, Angle, Side). I hope this helped and please don't hesitate to reach out with more questions!

Answer:

13:11

Step-by-step explanation:

325:275

If divided by 5 all through, you get 65:55, then by 5 again you get 13:11

Answer:

13/11 = 1.1818

Step-by-step explanation:

Boys/girls = 325/275 = 13/11 = 1  2/11 = 1.1818

I don't know what simplest form means.

Answer:

???

Step-by-step explanation:

Answer:

[tex]b=80[/tex]°

Step-by-step explanation:

The central angles theorem states that the measure of an angle whose vertex is the center of the circle is equivalent to the arc surrounding it. One can apply this here by stating that the measure of the arc surrounding the (90) degree angle is (90) degrees.

The total degree measure of a circle is (360). Thus one can form an equation and solve it to find the measure of the arc surrounding the angle (b). Call the arc surrounding angle (b); ([tex]b_1[/tex]).

[tex](b_1)+(90)+(110)=360[/tex]

Simplify,

[tex]b_1+200=360[/tex]

Inverse operations,

[tex]b_1+200=360[/tex]

[tex]b_1=160[/tex]

The peripheral angles theorem states that if the vertex of an angle formed between a tangent and a chord, is on the circumference (outer edge) of a circle, then the measure of the angle is equal to half of the measure of the surrouding arc. Please note that a chord is a line segment in a circle that intersects the circle in two points. A tangent is a line segment that intersects a circle at one point. One can apply this here by stating the following,

[tex]b=\frac{b_1}{2}[/tex]

Substitute,

[tex]b=\frac{160}{2}[/tex]

Solve,

[tex]b=80[/tex]

Answer:

[tex]y = \frac{1}{2} x + \frac{1}{2} [/tex]

Step-by-step explanation:

choose 2 points to find slope

(1,1) (-3,-1)

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

y-y1 = m(x-x1)

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

y = 1/2x + 1/2

guessing

y= 1/2x + 1/2

did y2 - y1/ x2-x1

which gave

-3

-6

also it passed through the y axis at +1/2

Answer:

Total amount of ticket free = £64.89

Step-by-step explanation:

Given:

Cost of theater ticket = £63 plus

Booking fee of theater ticket = 3%

Find:

Total amount of ticket free

Comutation:

Total amount of ticket free = Cost of theater ticket + Booking fee of theater ticket

Total amount of ticket free = 63 + 3%

Total amount of ticket free = 63 + 1.89

Total amount of ticket free = 64.89

Total amount of ticket free = £64.89

Answer:

The variable is y since it is a letter and is meant to hold value

The coefficient is 4 since in this equation 4 is multiplied by y

The exponent is 3 since it is after the variable

Hope This Helps!!!

Answer:

The coefficient is 4

The base and variable is y

The exponent is 3

Step-by-step explanation:

4y^3

The coefficient is 4

The base and variable is y

The exponent is 3

Answer:

B

Step-by-step explanation:

Answer:

[tex]x=15[/tex]°

Step-by-step explanation:

The sum of degree measures in a full angle (a circle) is (360) degrees. This means that the sum of all of the angles in this diagram is (360) degrees, as the angles form a full arc. Therefore, one can form an equation by adding up all of the angles and setting the equation equal to (360) degrees. Then one can substitute each angle value with the equation that is used to represent it, simplify, and use inverse operations to solve for the value of (x).

[tex](m<AMB)+(m<BMC)+(m<CMD)+(m<AMD)=(360)[/tex]

Substitute,

[tex](46)+(4x-2)+(9x+6)+(8x-5)=360[/tex]

Simplify,

[tex](46)+(4x-2)+(9x+6)+(8x-5)=360[/tex]

[tex]21x+45=360[/tex]

Inverse operations,

[tex]21x+45=360[/tex]

[tex]21x=315[/tex]

[tex]x=15[/tex]

Answer:

every single angle is 90°

Step-by-step explanation:

remember that,

4 angles will form if two lines intersect and the sum of those 4 angles is 360°

we are given the sum of 3 angles i.e 270

so one of the angles should be

[tex] \displaystyle {360}^{\circ} - {270}^{\circ}[/tex]

simplify substraction:

[tex] \displaystyle {90}^{\circ}[/tex]

therefore since one of the angles is 90° the intercepting lines are Perpendicular as a result every single angle formed by the two intercepting lines is 90°

Answer:

90°

Step-by-step explanation:

We know that sum of angle around a point is 360° . Here its already given that sum of three Angles out of 4 is 270°

Therefore :-

Measure of remaining one angle ,

Therefore the measure of the fourth angle is 90°

Answer:

(a) 525 g

Since they're proportional to each other:

[tex]\frac{20cm^{3} }{210g} =\frac{50cm^{3} }{Xg}[/tex]

Cross-multiply & solve:

[tex]20x=210*50\\20x=10500\\x=\frac{10500}{20} =525[/tex]

(b) 38 cm^3

Same thing, different numbers:

[tex]\frac{20cm^{3} }{210g} =\frac{Xcm^{3} }{399g}[/tex]

Cross-multiply & solve:

[tex]210x=20*399\\210x=7980\\x=\frac{7980}{210} =38[/tex]

Answer:

∠EFD

Step-by-step explanation:

Δ ABC similar ΔDEF

Trick is to keep the letters in the same order. A for D, B for E, and C for F

∠BCA

Where is the B?

second.

What's the second letter in other triangle?

E.

C is the third. F is the third in the other.

A is first. D is first.

Answer:

If you are camping in a rural setting and look up at the night sky, it can appear

If you are camping in a rural setting and look up at the night sky, it can appear as if there are many more stars visible compared to what you would see in a city or suburban area.

We have,

There is less light pollution in rural areas, allowing for a clearer view of the stars.

Here are some reasons why the night sky can appear different when camping in a rural setting:

Less light pollution:

Clearer atmosphere:

Different orientation:

Altitude:

Relaxation and focus:

Thus,

If you are camping in a rural setting and look up at the night sky, it can appear as if there are many more stars visible compared to what you would see in a city or suburban area.

Learn more about the night sky here:

https://brainly.com/question/28217744

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Answer:

125

Step-by-step explanation:

600=150+225+100+X=475+X

600-475=125=X

X=125

Answer: 325 I believe!

Step-by-step explanation:

ST = ST (Common)

RT = TQ (Given)

∠ RTS = ∠ SQT (Both 90°)

So, ∆ RTS ≅ ∆ QTS (By SAS congruency rule)

So, RS = QS (By C.P.C.T.)

=> 2x + 8 = 8x - 4

=> 8 + 4 = 8x - 2x

=> 12 = 6x

=> 12/6 = x

=> 2 = x

SR = 2x + 8 (Given)

=> SR = 2(2) + 8 (Putting the value of x)

=> SR = 4 + 8

=> SR = 12

Answer:

Step-by-step explanation:

Answer:

The distance between the two points is about 7.1 units.

Step-by-step explanation:

We want to find the distance between the two points (-3, 6) and (2, 1).

To find the distance between any two points, we can use the distance formula:

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

Let (-3, 6) be (x₁, y₁) and (2, 1) be (x₂, y₂). Substitute:

[tex]\displaystyle d=\sqrt{((2)-(-3))^2+((1)-(6))^2}[/tex]

Simplify:

[tex]\displaystyle d=\sqrt{(5)^2+(-5)^2}[/tex]

Evaluate:

[tex]d=\sqrt{25+25}=\sqrt{25(2)}=5\sqrt{2}\approx 7.1\text{ units}[/tex]

The distance between the two points is about 7.1 units.

Answer:

[tex](x -12)(x + 12)[/tex]

Step-by-step explanation:

Given

See attachment for chart

Required

The factors of [tex]x^2 - 144[/tex]

First, express [tex]x^2 - 144[/tex] as [tex]ax^2 + bx + c[/tex]

So, we have:

[tex]x^2 - 144 = x^2 + 0x - 144[/tex]

Compare the above expression to: [tex]ax^2 + bx + c[/tex]

We have:

[tex]ax^2 + bx + c = x^2 + 0x - 144[/tex]

So:

[tex]a =1[/tex]

[tex]b =0[/tex]

[tex]c = -144[/tex]

and

[tex]a * c = d * e[/tex]

Calculate ac

[tex]a* c = 1 * -144[/tex]

[tex]a* c = -144[/tex]

Rewrite as:

[tex]a* c = -12 * 12[/tex]

Recall that:

[tex]a * c = d * e[/tex]

Hence:

[tex]d = -12; e = 12[/tex]

So, on the x chart, we have:

        ac

d                  e

        b

This gives:

        -144

-12                  12

        0

The factors are

[tex](x + d)(x + e)[/tex]

[tex](x -12)(x + 12)[/tex]

Answer:

✔ (x – 12)

 and  

✔ (x + 12)

Step-by-step explanation:

Step-by-step explanation:

hope it helps thank you❤

Answer:

if you are supposed to find m<STR, then the answer is B

Step-by-step explanation:

Answer:

i thinkits c

Step-by-step explanation:

based on the info given

Answer: 286 possibilities

Step-by-step explanation:

It's a combination because the order of countries doesn't matter in this scenario.

[tex]_{n} C_{r} =\frac{n!}{r!(n-r)!}=\frac{13!}{10!(13-10)!}=\frac{13!}{10!(3)!}=\frac{13!}{10!(3)!}\\\\=\frac{6227020800}{3628800(6)}=\frac{6227020800}{3628800(6)}=\frac{6227020800}{21772800}=286[/tex]

I hope this is right

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

To learn more about probability click on,

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Answer:

B

Step-by-step explanation:

The sum of the inner angles of a quadrilateral is 360 degrees

135 + 110 + 68 + x = 360

313 + x = 360

x = 47 degrees

Answer:

47

Step-by-step explanation:

whole thing is 360 degrees

68 + 110 + 135 = 313

360 - 313 = 47

x looks small too (if you had to guess in a multiple choice question)

Answer:

A

Step-by-step explanation:

Start with the 3.

You know that there is a difference of 4 between (say) 2 and 5. The 3 is a sign that the sequence is increasing.  The members of the sequence are going up.

n - 1 means that the nth terms is calculated as an and uses the number of terms to be n-1. That means that the first term is a1 which is the starting point of the sequence.

The answer is an = a1 + (n-1)*d

d = 3

a1 = - 7

So let's try the formula out.

a4 = -7 + (4 - 1)*3

a4 = -7 + 3 * 3

a4 = -7 + 9

a4 = 2

Is 2 the 4th term in the series? Yes it is!