Mathematics High School

For the Transformation T, write the T^-1.

T : (x, y) (5x, 5y )
T^ -1 (x, y)

(x - 5, y - 5)
(5x - 1, 5y - 1)
(1/5x, 1/5y)

Answers

Answer 1
The 3rd selection is appropriate.

___
(1/5)(5x) = x, so the inverse transformation returns the original. Not so for the other choices.
Answer 2

Answer:  The correct option is

(C) [tex]T^{-1}(x,y)\rightarrow \left(\dfrac{1}{5}x,\dfrac{1}{5}y\right).[/tex]

Step-by-step explanation:  We are given a transformation T defined as :

[tex]T:(x,y)\rightarrow (5x,5y).[/tex]

We are to find the inverse transformation [tex]T^{-1}(x,y).[/tex]

From the given transformation, we have

[tex]T:(x,y)\rightarrow (5x,5y)\\\\\Rightarrow T^{-1}(5x,5y)=(x,y).[/tex]

Let us consider that

[tex]5x=z~~~~~~\Rightarrow x=\dfrac{z}{5},\\\\\\5y=t~~~~~~\Rightarrow y=\dfrac{t}{5}.[/tex]

Therefore, we get

[tex]T^{-1}(5x,5y)\rightarrow(x,y)\\\\\Rightarrow T^{-1}(z,t)\rightarrow \left(\dfrac{z}{5},\dfrac{t}{5}\right)\\\\\\\Rightarrow T^{-1}(x,y)\rightarrow \left(\dfrac{1}{5}x,\dfrac{1}{5}y\right).[/tex]

Thus, (C) is the correct option.

Related Questions

Which of the following mixed numbers is equivalent to 12.1 6 ?

Answers

Well, you don't have any options.
But a mixed number for 12.16 would be 12 4/25. Hope it helps! :)

Would it still be the same if the 6 was terminated?

You have a balance of $15,300 on your credit card with an 18% interest rate (1.5% per month). You pay $200 this month. Did your balance go up or down?
Will fan and medal

Answers

If balance is positive you will get $229.5 additionally So total balance will go up.
If balance is negative you charged $229.5 and you will add $200. So total balance will go down.
Balance went up.  
First, calculate the interest that will accumulate for 1 month on your current balance.
 15300 * 0.015 = 229.5 
 Right now, we can stop since it's obvious that $229.50 of interest is greater than the $200.00 you're paying for that month. The new balance on your card will be:
 $15,300 + $229.50 - $200 = $15,329.50

Two times a number minus 8 is less than 5.

Answers

here is your answer
2x-8<5

Suppose that y varies inversely with x. Write a function that models the inverse function. X= 15 when y= 2

Answers

The answer to this question is B: y = 30/x. I hoped I have helped you today!

Which of the following functions corresponds to the sinusoid shown?

4 sin 3x
-3 cos 4x
-4 cos 3x
3 sin 2x

Answers

Answer: the third option: -4cos(3x)

Justification:

1)  The amplitude of the function of the graph is [4 - (-4) ] / 2 = [4+4] / 2 = 8/2 = 4.

2) Therofore the coefficient that multiplies the trigonometric function is 4.

3) That leaves you the first and the third options:

4sin(3x) and - 4cos(3x).

4) The y intercept of the graph, f(0), is - 4.

Check f(0) for both 4 sin(3x) and 4 cos(3x)

4sin(0) = 0 => this is not the function

- 4cos(0) = -4 => this is the function and thw answer to the question.

Kathy is a repair technician for a phone company. each week, she receives a batch of phones that need repairs. the number of phones that she has left to fix at the end of each day can be estimated with the equation p=108−23d, where ppp is the number of phones left and ddd is the number of days she has worked that week. what is the meaning of the value 108108108 in this equation?

Answers

We have equation:
[tex]p=108-23d[/tex]

p = number of phones left to repair
108 = initial amount at the start of week
23 = number of phones repaired each day
d = number of days she worked that week
Final answer:

In the equation p=108−23d, the value 108 represents the total number of phones that Kathy receives each week for repair.

Explanation:

In the given equation p=108−23d, the number 108 represents the total number of phones that Kathy receives each week for repair.

This means that at the start of her work week, before she begins to fix any phones, she has 108 phones that need repairs.

As each day passes (represented by d), the number of phones that Kathy has left to fix decreases by 23, which is the number of phones she is able to repair in one day.

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In triangle ∆PQR, C is the centroid.



If PX = 25, find PQ



If CY = 9, find PC and PY



If QC = 12, find ZC and ZQ

not 100% sure how to figure this out

Answers

Given that P is the Centroid of the triangle PQR, it then follows that:
PZ = ZR          ... (Equation 1)
QY = YR         ... (Equation 2)
PX = XQ         ... (Equation 3)

QUESTION 1
If PX = 25, find PQ 
From the diagram, PQ = PX + XQ

Remember, PX = XQ         ... (Equation 3)
Therefore, PQ = PX + XQ = PX + PX
⇒ PQ = PX + PX
PQ = 2(PX)

Since PX = 25
PQ - 2(25)
PQ = 50


QUESTION 2
If CY = 9, find PC and PY 

We know that the centroid of a triangle divides each median into segments with a 2:1 ratio, therefore:

PC = 2(CY)
Since CY = 9,
PC = 2(9)
PC = 18

From the diagram, we see that,
PY = PC + CY
PC = 18, CY = 9
PY = 18 + 9
PY = 27


QUESTION 3
If QC = 12, find ZC and ZQ

Again, going by the fact that the centroid of a triangle divides each median into segments with a 2:1 ratio,

ZC = QC/2
Since QC = 12
ZC = 12/2
ZC = 6

From the diagram, we see that
ZQ = ZC + QC
ZC = 6, QC = 12
ZQ = 6 + 12
ZQ = 18

Express the difference in the means as a multiple of their ranges.

Answers

Answer:

Hence, the difference in mean is represented as:

                         12=2.5×5

where 5 is the range and 12 is the difference in the mean.

Step-by-step explanation:

Shade plant Height (in.)

7    11     11      12      9      12      8     10

Minimum value=7

and Maximum value=12

Range=Maximum value-Minimum value

This means that Range is: 12-7=5

Also, the mean is calculated as follows:

[tex]Mean=\dfrac{7+11+11+12+9+12+8+10}{8}\\\\\\Mean=\dfrac{80}{8}\\\\\\Mean=10[/tex]

Sun Plant heights (in.)

21    24    19    19     22    23    24    24

Minimum value=19

and Maximum value=24

Range=Maximum value-Minimum value

This means that Range is: 24-19=5

Also, the mean is calculated as follows:

[tex]Mean=\dfrac{21+24+19+19+22+23+24+24}{8}\\\\\\Mean=\dfrac{176}{8}\\\\\\Mean=22[/tex]

Difference in mean is: 22-10=12

Also, the range of both the set is:  5

Hence, the difference in mean could be expressed as:

       12=5×n

Hence, n=2.5

The expression (12 = 5×2.4) represents the difference in the means as a multiple of their ranges if the mean for the first data set is 10 and for the second data set is 22.

What is mean?

It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.

For the first data:

The mean can be calculated as follows:

[tex]\rm Mean = \frac{\sum x}{n}[/tex]

[tex]\rm Mean = \frac{7 + 11+ 11+ 12 + 9+ 12+ 8+ 10}{8}[/tex]

Mean(1st data set) = 10

For range:

The minimum value in the data set = 7

The maximum value in the data set = 12

Range = 12 - 7 ⇒ 5

For the second data set:

The mean can be calculated as follows:

[tex]\rm Mean = \frac{\sum x}{n}[/tex]

[tex]\rm Mean = \frac{21 + 24 + 19 + 19 + 22 + 23 + 24 + 24}{8}[/tex]

Mean(2nd data set) = 22

For range:

The minimum value in the data set = 19

The maximum value in the data set = 24

Range = 24- 19 ⇒ 5

Difference in means = 22 - 10 ⇒  12

Since the range is the same for both the data set.

From the problem:

12 = 5×n

n = 2.4

Thus, the expression (12 = 5×2.4) represents the difference in the means as a multiple of their ranges if the mean for the first data set is 10 and for the second data set is 22.

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What is the coefficient of 12a+5

Answers

The coefficient is 12a because it has a variable (a).
The coefficient of the expression 12a+5 is 12. The coefficient is always the number that has a variable (in this case it is the letter “a”)
I hope this helped! :-)

An equilateral triangle has a length of 18 feet, determine the length of the triangle

Answers

Hello Delanew,

Do you mean the altitude of the triangle, since you are already given the length?

If you are looking for an altitude, you can start by drawing it in your triangle. You will see that it divides the triangle into two 30, 60, 90 triangles. The short leg of the triangle is 6, so using the rules for a 30, 60, 90 triangle the longer leg (your altitude) would be 6 square roots of 3. Or about 10.39.

If this isn't what you are looking for, let me know.
I can try and help.

Good luck!
The remaining lengths within an equilateral triangle are all the same. Each of the side lengths are also 18 feet, hence the name equal lateral sides.

If a circle has a radius of 20.5 cm, what is its circumference?

Answers

according to my math the answer is 128.81 cm.
2[tex] \pi [/tex]r 
2[tex] \pi [/tex]20.5
after calculating, you should get-
128.8 cm

F left parenthesis x right parenthesis equals 9 x cubed plus 2 x squared minus 5 x plus 4 and g left parenthesis x right parenthesis equals 5 x cubed minus 7 x plus 4. what is f left parenthesis x right parenthesis minus g left parenthesis x right parenthesis? show all of your steps and write your final answer in factored form.

Answers

The answer is 2x(2x²+x+1).

When we subtract polynomials we combine like terms:
(9x³+2x²-5x+4)-(5x³-7x+4)

9x³-5x³=4x³
2x²- 0 = 2x²
-5x--7x=-5x+7x=2x
4-4=0

This gives us 
4x³+2x²+2x

Each of these is divisible by 2, and each has an x, so we factor those out:
2x(                        )

4x³/2x = 2x²:
2x(2x²                   )

2x²/2x=x:
2x(2x²+x               )

2x/2x = 1:
2x(2x²+x+1)

From 1980 to 1990, the consumer price index (CPI) increased from 82.4 to 130.7. If a gallon of apple juice cost $0.95 in 1980 and the price of apple juice increased at the same rate as the CPI from 1980 to 1990, approximately how much did a gallon of apple juice cost in 1990?

A. $0.56
B. $0.82
C. $1.51
D. $1.31

Answers

Answer: C $1.51

To solve this, start with a proportion. Put the CPI numbers on the left and the apple juice prices on the right.

You will have:

82.4/130.7 = 0.95/x

Cross multiply to solve and you will get the price of the juice is $1.51.

Answer:

The cost of the gallon of the apple juice is approximately $1.51 in 1990. (Option C)

Step-by-step explanation:

As it can be assumed that the increase of the gallon of apple juice is proportional to the increase of the CPI, we can state that the rate of the price of 1990 to the price of 1980 is the same than the rate of the CPI in 1990 to the CPI in 1980:

$130.7 / $82.4 = Pg (1990)/ $0.95

Where Pg (1990) is the apple juice gallon cost for 1990. By solving the equation above:

$130.7 / $82.4 * $0.95 = Pg (1990)

Pg (1990) = $1.5068 ---> Pg (1990) = $1.51

Solve for x. Simplify completely.
x^2-9=55

Answers

Simplifying x2 + -9 = 55 Reorder the terms: -9 + x2 = 55 Solving -9 + x2 = 55 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x2 = 55 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = 55 + 9 x2 = 55 + 9 Combine like terms: 55 + 9 = 64 x2 = 64 Simplifying x2 = 64 Take the square root of each side: x = {-8, 8}

Find the hypotenuse of a right triangle if the legs are: 5 and 12

Answers

Use Pythagoras which is c*squared = a*squared + b*squared
In this case a would be 5 and b would be 12. If you add these into the equation and then square root your answer, that should be the hypotenuse of the triangle. Hope I helped, have a nice day :)
You use pythagorus theorem. 5squared plus 12squared equals 169. So what squared is equal to 169? The answer would be 13

IS THIS CORRECT!!!!!!!!!!!!!

Answers

 For this case, the first thing we must do is define variables.
 We have then:
 x: number of devices.
 Y: plan charge
 For the current plan we have: 
 [tex]y = 175 [/tex]
 For the new plan we have:
 [tex]y = 4.5x + 94 [/tex]
 Since we want the new plan to be smaller than the current plan, then we have:
 [tex]175\ \textgreater \ 4.5x + 94 [/tex]
 From here, we clear the value of x:
 [tex]4.5x \ \textless \ 175 - 94 x \ \textless \ 81 / 4.5 x \ \textless \ 18[/tex]
 Answer:
 x <18
 Note: The graph is correct
Answer:

The graph is the region (-∞,18)

i.e. the shaded region to the left of 18 and open circle at 18.

Step-by-step explanation:

It was given that the cost of the current plan is: $ 175 per month.

Also, the flat rate of new plan is: $ 94

Also, cost of 1 device is: $ 4.50

cost of x device is: $ 4.50x

Total cost of the new plan for x devices is: $ (94+4.50x)

Now we are asked to find the inequality such that the total cost of new plan is less than the current plan i.e.

94+4.50x < 175

i.e. 4.50x < 175-94

i.e.  4.50x < 81

i.e. x<18

Hence,the graph would be a line to the left of 18 with open circle at 18, since the inequality is strict.

Think about parallel and perpendicular lines. In what profession might a person rely upon this information? Describe how that person would apply these concepts? @malcolmmcswain,

Answers

An engineer relies heavily on the use of perpendicular and parallel lines. they use these lines to draw concepts, plot graphs, and find solutions to problems that arise.

Does anyone know these two answers?

Answers

Problem 1:

The vertical line and the horizontal line are perpendicular to each other, so they form right angles.

x + 61 = 90

x = 90 - 61

x = 29

Problem 2:

Vertical angles are congruent. They have the same measure.

m<1 = m<2 = 93 deg
Hello there!

Question #1

(90-61)= 29

x=29

Question #2

Vertical angles are across from each other. This would show us that we would have to subtract.

360-93=(267).

(267)÷ (3)= 89.

But then, we would have t understand that these vertical angles could always be congruent which would mean that they're the same size (93)

Jon is launching rockets in an open field. The path of the rocket can be modeled by the quadratic function h(t) = -16t^2 + 96t, where h(t) is the height in feet any time t in seconds. After how many seconds will the rocket reach a height of 80 feet for the second time

Answers

It will reach 80 feet for the second time after 5 seconds.

We set the equation equal to 80 feet:
80= -16t² + 96t

When solving quadratics, we want it equal to 0, so we subtract 80 from both sides:
80-80= -16t² + 96t - 80
0= -16t² + 96t - 80

We use the quadratic formula to solve:
[tex]t=\frac{-96\pm \sqrt{96^2-4(-16)(-80)}}{2(-16)} \\ \\t=\frac{-96\pm \sqrt{9216-5120}}{-32} \\ \\t=\frac{-96\pm \sqrt{4096}}{-32} \\ \\t=\frac{-96\pm 64}{-32} \\ \\t=\frac{-96+64}{-32} \text{ or } 0=\frac{-96-64}{-32} \\ \\t=1 \text{ or } t=5[/tex]

A cab driver told Bernice her fare came to a total of $7.75. She pays with a $10 bill. How much change should she get?

Answers

She would get $2.25 back from the driver.
2.25 back from the driver

Please help me! I'm so lost t-t!!

Factor completely.

x^2−8x+15

Enter your answer in the box.

Answers

factor out x² and find factors of 15 that give you -8

x² - 8x + 15
x             -5
x             -3

(x-5)(x-3)

x = 5, 3

hope this helps

One number is equal to the square of another. find the numbers if both are positive and their sum is 18921892.

Answers

If n is the number, the sum is
.. n^2 +n = 1892
The solution to this quadratic is
.. n = 43

Your numbers are 1849 and 43.

_____
The product n^2 +n can be written as n(n+1). Since n is fairly large,
.. n + 1/2 ≈ √(n*(n +1))
.. √1892 ≈ 43.497 ≈ 43 1/2
so n = 43.
There are more formal ways to get this result exactly, but it is often convenient to use a square root like this to get you close to the number of interest.

A circle is drawn within a square as shown.



What is the best approximation for the area of the shaded region?

Use 3.14 to approximate pi.


21.5 cm²

78.5 cm²

100 cm²

178.5 cm2

Answers

these questions are really simple
square10×10= 100
circle πr^2= π(10/2)^2=78.54
100-78.54=21.46≈ 21.5cm2

u should practice more, otherwise future mathematics will kill u XD

Answer:

21.5 I TOOK THE TEST

Step-by-step explanation:

what is 83/4 as an mixed number

Answers

83/4 

think of 83 as 80 + 3
80/4 = 20
3/4= 3/4
20+3/4 = 20 3/4 thats your mixed number  or 20 and 3/4 twenty and three fourths
Hello!

A mixed number is a number that consists of a whole number and a fraction.

The numerator of a fraction is how many of the denominator there are, and the denominator is thr whole (total amount).

In this improper fraction, the whole is 4, and the numerator is greater than the denominator.

The question is, how many wholes of 4 can be made with that numerator?

First, divide the numerator by the denominator to find the whole number.

83 ÷ 4 = 20.75

This means that the whole number is 20.

Next, multiply this whole number by the denominator, and then subtract that from the original numerator to find the new numerator.

83 - (4 × 20) = 3

Finally, place the new numerator over the old denominator.

ANSWER:

83/4 = 20 3/4 as a mixed number.

Suppose you earn 15$ for each car you wash. Which function describes the relationship between your total earnings E and the number of cars you wash, c?
A) E(c) = c + 15
B) E(c) = 15c
C) c = 15E
D) E(c) = c - 15

Answers

E(c)=15c because 15 is the cost of each car washes and c is the number of car washes
the answer is B. by multiplying them you get the whole income. i think:)

The lowest altitude of an altocumulus cloud is about 3^8 feet. The highest altitude of an altocumulus cloud is about 3 times the lowest altitude. What is the hugest altitude of an altocumulus cloud? Write your answer as a power.,

Answers

3(3^8) equals 9^8 feet.

The highest altitude of an altocumulus cloud is [tex]3^{9}[/tex] feet.

The lowest altitude mentioned is [tex]3^{8}[/tex] feet. To find the highest altitude, we should multiply the lowest altitude by 3. Therefore, the highest altitude will be

3 x [tex]3^{8}[/tex]

which can also be written as

[tex]3^{1}[/tex]x [tex]3^{8}[/tex]  

Applying the rule of exponents where you add the exponents when you multiply the bases that are the same, we get the highest altitude as [tex]3^{9}[/tex] feet.

write the rule for the table as an algebraic expression.
the table shows
in : x | 2 | 3 | 4 | 5
out: y 5 | 7 | 9 | 11 | plz answer

Answers

For this case what you should do is write the table in a software that allows you to graph each ordered pair.
 You can use Excel, for example, to graph the ordered pairs in the table.
 We observe that when graphing the behavior of the ordered pairs is linear.
 The equation of the line is:
 y = 2x + 1
 Answer:
 The rule for the table as an algebraic expression is:
 y = 2x + 1

!!!!!HELP PLEASE!!!
Which of the following statements is NOT true?
A. Every function can be represented by a graph in the Cartesian plane.
B. Another name for an x-intercept is a real zero.
C. A function can have several y-intercepts.
D. A function can have infinitely many x-intercepts.

Answers

Hey there!

The answer to your question is " A function can have several y-intercepts". This statement is not true.

The following are true:
-
Every function can be represented by a graph in the Cartesian plane.
-
Another name for an x-intercept is a real zero.
and
A function can have infinitely many x-intercepts.

Final answer:
Option "C."

Hope this helps you.
Have a great day!

Final answer:

The statement that is NOT true is that a function can have several y-intercepts.

Explanation:

NOT true statement: C. A function can have several y-intercepts.

In a Cartesian plane, a function typically has only one y-intercept, where it crosses the y-axis.

A y-intercept represents the point where the function intersects the y-axis, indicating the value of the function when the input is zero.

helpppppppppppppppppppppppppppppp

Answers

Answer:

first option: Harulo is correct because the angle is coterminal with 3π / 4 and the reference angle is π / 4.

Explanation:

1) 19 π/4 = 4π + 3 π/4, which is 4 complete turns and 3/4 of turn.

2) 3 π/4 is in the third quadrant, so the reference angle is π - 3 π/4 = π/4

3) sin (π/4) = sin (3π/4) = (√2) / 2

4) csc (π/4) =  1 / [ sin (3π/4) ] = 1 / [ (√2) / 2 ] = 2 / (√2) = √2, which shows the validity of the statement and csc(19π/4) = √2.

A(n)=−5+6(n−1)a, left parenthesis, n, right parenthesis, equals, minus, 5, plus, 6, left parenthesis, n, minus, 1, right parenthesis find the 12^\text{th}12 th 12, start superscript, t, h, end superscript term in the sequence. answer

Answers

Final answer:

The 12th term in the sequence is 61.

Explanation:

The given sequence is defined by the formula A(n) = -5 + 6(n-1), where n represents the term number. To find the 12th term, substitute n = 12 in the formula.

A(12) = -5 + 6(12-1) = -5 + 6(11) = -5 + 66 = 61

Therefore, the 12th term in the sequence is 61.

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The 12th term of the arithmetic sequence is calculated using the formula A(n) = -5 + 6(n-1) by substituting n with 12, resulting in the term being 61.

The 12th term of the sequence can be found using the arithmetic sequence formula provided. We will use the clarified formula A(n) = -5 + 6(n-1) to find the 12th term.

Firstly, plug in the value of n = 12 into the formula to compute the 12th term:

A(12) = -5 + 6(12-1)A(12) = -5 + 6(11)A(12) = -5 + 66A(12) = 61

Therefore, the 12th term in the sequence is 61.

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