If T: (x, y) → (x + 6, y + 4), then T-1: (x,y) → _____.

( x/6, y/4 )
( x - 4, y - 6)
(-6 x, -4 y)
( x - 6, y - 4)

Answers

Answer 1

T is a linear transformation from R²→R² with basis {(1,0),(0,1)}
T: (x,y)→(x+6,y+4)

A function from one vector space to another that preserves the underlying (linear) structure of each vector space is called a linear transformation.

Then the vector (1,0) goes to (1+6,4)=(7,4)=7(1,0)+4(0,1)

and the vector (0,1) goes to (6,1+4)=(6,5)=6(1,0)+5(0,1)

So, the matrix of the transformation is

[tex]\left[\begin{array}{ccc}7&6\\4&5\end{array}\right][/tex]

The inverse of the matrix is

[tex]\left[\begin{array}{ccc}\frac{5}{11}&\frac{-6}{11}\\ \\\frac{-4}{11}&\frac{7}{11}\end{array}\right][/tex]

So, the Inverse Transformation is given by

[tex]T^{-1}(x,y)=\left[\begin{array}{ccc}\frac{5}{11}&\frac{-6}{11}\\ \\\frac{-4}{11}&\frac{7}{11}\end{array}\right]\left[\begin{array}{ccc}x\\y\end{array}\right] =(\frac{5x-6y}{11}, \frac{-4x+7y}{11})[/tex]

So, no option is correct. And the answer is

[tex]T^{-1}(x,y)=(\frac{5x-6y}{11}, \frac{-4x+7y}{11})[/tex]

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Related Questions

Solve the following inequality |x| < 13

Answers

Answer:

x < 13 and x > -13

Step-by-step explanation:

Split the absolute value equation into 2 equations to account for the positive and negative answers possible with absolute values.

Write the positive value first by removing the absolute value symbol.

x < 13

Flip the inequality and make the 13 negative for the other side.

x > -13

A solid right pyramid has a square base with an edge
length of x cm and a height of y cm.
X
Which expression represents the volume of the
pyramid?
O1/3 xy cm³
O1/3 x²y cm³
O1/2 xy² cm³
O1/2 x²y cm³

Answers

The correct answer is option D which is the volume of the square pyramid will be  [tex]V = \dfrac{1}{2}x^2y\ cm^3[/tex].

What is a square pyramid?

A solid made up of a square base and four triangles connected side by side and meet at the same edge is called a square pyramid.

Given that:-

The side of the square base is x cmThe height of the pyramid is y cm.

The volume of the pyramid will be calculated as:-

Volume = [tex]\dfrac{1}{2}[/tex] x Length of square pyramid x Height

Volume = [tex]\dfrac{1}{2}[/tex]  x (x)² x y

Volume = [tex]\dfrac{1}{2}[/tex] x²y

Therefore the correct answer is option D which is the volume of the square pyramid will be  [tex]V = \dfrac{1}{2}x^2y\ cm^3[/tex].

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The figure below shows a square ABCD and an equilateral triangle DPC:

ABCD is a square. P is a point inside the square. Straight lines join points A and P, B and P, D and P, and C and P. Triangle D

Ted makes the chart shown below to prove that triangle APD is congruent to triangle BPC:

Statements Justifications
In triangles APD and BPC; DP = PC Sides of equilateral triangle DPC are equal
In triangles APD and BPC; AD = BC Sides of square ABCD are equal
In triangles APD and BPC; angle ADP = angle BCP Angle ADC = angle BCD = 90° so angle ADP = angle BCP = 60°
Triangles APD and BPC are congruent SAS postulate
What is the error in Ted's proof? (1 point)

He writes the measure of angles ADP and BCP as 60° instead of 45°.
He uses the SAS postulate instead of AAS postulate to prove the triangles congruent.
He writes the measure of angles ADP and BCP as 60° instead of 30°.
He uses the SAS postulate instead of SSS postulate to prove the triangles congruent.

Answers

Answer:

Which of the following completes Ted's proof?

In square ABCD; angle ADC = angle BCD

In square ABCD; angle ADP = angle BCP

In triangles APD and BPC; angle ADC = angle BCD

In triangles APD and BPC; angle ADP = angle BCP\

ax +by = 16
3x+2y=64

In the system of equations, a and b are constants. if the system has infinitely many solutions, what's the value of ab?

Answers

Answer:

The system has infinitely many solutions when a = 3/4 and b = 1/2

Given

System of linear equations

ax +by = 163x+2y=64

To find

Values of a and b that leads to infinitely many solutions

Solution

The linear system of equations has infinitely many solutions when lines overlap, so both have same slope and y-intercept.

We can solve it in two different ways

1. Note that when the first equation is multiplied by 4, it has same value of constant as the second equation, which is 64.

4ax + 4by = 643x + 2y = 64

When compared it gives us:

4a = 3 ⇒ a = 3/44b = 2 ⇒ b = 2/4 = 1/2

2. Convert both equations from standard to slope-intercept form and compare:

ax + by = 16by = -ax + 16y = - (a/b)x + 16/b

3x + 2y = 642y = - 3x + 64y = - (3/2)x + 32

Work out values of a and b:

16/b = 32 ⇒ b = 16/32 ⇒ b = 1/2- (a/b) = - 3/2 ⇒ a/b = 3/2 ⇒ a = 3b/2 ⇒ a = 3(1/2)/2 ⇒ a = 3/4

What is the length of segment AB?
7
9
18
25

Answers

Answer:

Nobody likes a short, one-word-answer. Let’s make sure other people understand everything.

Step-by-step explanation:

By lisa Simpson

Answer:

9

Step-by-step explanation:

help me nowwwwwwwwww

Answers

The angle measurements the carpenter needs to cut the carpet to make it fit in his room are 144°, 144°, 144°, 144°, 144°, 90°, and 90°

Angles in a polygon

From the question, we are to determine the angle measurements that the carpenter needs to cut the carpet to make it fit in his room

The diagram shows a heptagon with two of its angles, a right-angle each, and the remaining angles have equal values, x.

First, we will calculate the sum of angles in a heptagon

The sum of angles in a polygon is given by the formula

Sum of angles in a polygon = (n-2)180°

Where n is the number of sides

For a heptagon, n = 7

∴ Sum of angles in a heptagon = (7-2)180°

= 5×180°

= 900°

Now, considering the given diagram, we can write that

x + x + x + x + x + 90° + 90° = 900°

5x + 180° = 900°

5x = 900° - 180°

5x = 720°

x = 720°/5

x = 144°

Hence, the angle measurements the carpenter needs to cut the carpet to make it fit in his room are 144°, 144°, 144°, 144°, 144°, 90°, and 90°

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What is the volume of the cone shown below?
A. 1344 cu. units
B. 504 cu. units
C. 4032 cu. units
D. 2016 cu. units

Answers

Answer: Choice A) 1344π  cubic units

Work Shown:

r = 8 = radius

h = 63 = height

V = volume of the cone

[tex]V = \frac{1}{3}\pi*r^2*h\\\\V = \frac{1}{3}\pi*8^2*63\\\\V = \left(\frac{1}{3}*8^2*63\right)\pi\\\\V = \left(\frac{1}{3}*63*8^2\right)\pi\\\\V = \left(21*64\right)\pi\\\\V = 1344\pi\\\\[/tex]

Side note: You could write the symbol π as "pi" without quotes.

if the ratio of the sides of a triangle are 13:14:15 and its perimeter is 84 cm, find the area of the triangle.​

Answers

Answer:

The ratio of sides of triangle = 13:14:15

perimeter = 84 CM

perimeter of a triangle = Sum of all sides

let the sides of a triangle be 13x, 14x and 15x

84 = 13x + 14x + 15x

84 = 42x

x = 2

13x = 13* 2 = 26 CM

14x = 14*2 = 28 CM

15x = 15*2 = 30 CM

Can someone help me please and thxxx

Answers

Answer:

C

Step-by-step explanation:

cos 30=12/x

[tex]x = 8 \sqrt{3} [/tex]

cos60=y/x

[tex]y =4 \sqrt{3} [/tex]

Answer:

x = [tex]8\sqrt{3}[/tex]

y = [tex]4\sqrt{3}[/tex]

Step-by-step explanation:

• tan 60° = 12/ y         [tan θ = opposite/ adjacent]

y = 12/ tan 60°  

y = [tex]4\sqrt{3}[/tex]

• x² = y² + 12²             [Pythagoras's theorem]

x² = ( [tex]4\sqrt{3}[/tex] )² + 144

x = [tex]\sqrt{(4\sqrt{3})^{2} \space\ + \space\ 144}[/tex]

x = [tex]8\sqrt{3}[/tex]

Which answers describe the shape below?
(MULTIPLE ANSWERS)
(Picture above)

A. Quadrilateral
B. Parallelogram
C. Rectangle
D. Trapezoid
E. Rhombus
F. Square​

Answers

Answer:

it is a trapezoid and a quadrilateral

Explaination -

Square is a quadrilateral of 4 equal side and 4 equal angles so it is not square as all sides are unequal and all angles are also unequal

rhombus is a quadrilateral which has equal sides 4 equal angles and it's diagonal bisects each other.

rectangle has two opposite sides equal and parallel and each Ange equal as 90°

parallelogram is a quadrilateral in which a pair of opposite sides are parallel and equal and the remaining sides are unequal

it is a quadrilateral and a trapezoid

How could you solve this problem?
2 × 3 × 4
Check all that are true.

Multiply 3 × 4 to get 12 and then multiply 12 × 6.

Multiply 2 × 3 to get 6 and then multiply 6 × 12.

Multiply 3 × 4 to get 12 and then multiply 12 × 2.

Multiply 2 × 3 to get 6 and then multiply 6 × 4.

Multiply 2 × 3 to get 6, multiply 3 × 4 to get 12, and then multiply 6 × 12.

Answers

2x3x4 = 24 so the only statements that are correct are the 3rd and 4th ones as they are the only ones that equal 24.

Step-by-step explanation:

multiply 2×3 to get 6 and then multiply 6×4

or

multiply 3×4 to get 12 and then multiply 12×2

Triangle N P O is shown. Line O N extends through point M to form exterior angle P N M. Angle N P O is 38 degrees. Angle P O N is 39 degrees. Exterior angle P N M is x degrees.
Which statement about the value of x is true?

x > 38
x < 39
x < 77
x > 103

Answers

The correct option is Option A:  x > 38° this statement about x value is true.

Given in triangle ΔNPO the angle ∠ PNM is the exterior b to the interior angle ∠ PNO of the triangle.

Given the angle ∠NPO= 38°

∠PON= 39°

As we know the exterior angle is the sum of the two farthest interior angles of the triangle.

Then we can write the angle ∠PNM as

So, ∠PNM = ∠NPO + ∠PON

⇒ x = 38° + 39° = 77° {Given that ∠ PNM = 38° and ∠ PON = 39°}

{Since the exterior angle of an interior angle is equal to the sum of the other two interior angles of a triangle}

As x=77°

which satisfies the relation x=77° >38°.

Therefore,The correct option is Option A:  x > 38° this statement about x value is true.

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give me the answer
Given below is a magic square. Place the numbers
70 – 21 25 24 , ,, 95 –133 95 38
in the appropriate squares so that sum in each row, column and
diagonal is equal

Answers

The appropriate numbers to fill in the magic squares are;

Row 2, Column 2 = 21/133

Row 2, Column 3 = 24/38

Row 3, Column 2 = 70/95

Row 3, Column 3 = 25/95

How to use magic squares?

To solve this magic square, we will follow the procedures below;

Step 1; Convert all the numbers into lowest forms.

Step 2; Find the sum of any column or row which is 34/19.

Step 3; Put the numbers given in such positions that the sum of each row, column and diagonal is equal.

Step 4; Write the numbers in their original form.

When we follow those steps above, we will arrive at the following figures;

Row 2, Column 2 = 21/133

Row 2, Column 3 = 24/38

Row 3, Column 2 = 70/95

Row 3, Column 3 = 25/95

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There are 8 kids at a birthday party. If there are 6 girls and 2 boys at a party what fraction of the kids are girls?

Answers

Okay, so out of 8 kids, we know that 6/8 are girls and 2/8 are boys. Its asking us what fraction of the kids are girls. The denominator (the bottom part of the fraction will be the amount of kids at the party, 8) and the top part, the numerator, will be 6 as there are 6 girls at the party of the 8 attendees.

So the fraction is 6/8. However we can reduce this by dividing both sides of the fraction by a common factor, 2!

So your final answer is
3/4.


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3/4 of the kids are girls

There are only red sweets and yellow sweets in a bag.
There are n red sweets in the bag.
There are 8 yellow sweets in the bag.
Sajid is going to take at random a sweet from the bag and eat it.
He says that the probability that the sweet will be red is
7
10
(a) Show why the probability cannot be
7
10

Answers

Red sweets

_______

Total number =

N÷n+8

Probility is 7/10=n÷n+8

10n= 7n+56

3n=56

N= 56/3 but it has to be a whole number so 7/10

Write an inequality for the given statement: The sum of twice a number and 12 is no more than 24.
A. 2x+12>24
B. 2x+12 < 24
C. 2x+12224
D. 2x+12 ≤ 24

Answers

Answer:

D)

Step-by-step explanation:

Carolyn bought two brands of socks. She bought a total of 5 pairs. One brand cost $2 each and the other brand cost $3 each. She spent $13. Find the number of pairs each brand of socks she bought

Answers

Answer:

Step-by-step explanation:

Declaration

Let Brand A number of 2.00 socks= x

Let Brand B number of 3.00 socks = y

Equations

Number of socks : x + y = 5

Cost of socks: 2x + 3y = 13

Solution

Multiply top equation by 2

2(x+ y = 5)

2x + 2y = 10

Write the new equation under the cost of socks equation

2x + 3y = 13

2x + 2y = 10       Subtract.

y = 3

She spent 3 dollars on 1 pair of socks.

Now she needs to calculate the number of 2.00 dollar socks

2x + 3y = 13

2x + 3*3 = 13                Combine the left

2x + 9 = 13                   Subtract 9 from both sides.

2x +9-9 = 13-9             Combine

2x = 4                          Divide by 2

2x/2 = 4/2

x = 2

Answer

#2 dollar socks = 2

#3 dollar socks = 3

Select the correct answer. Simplify the polynomial expression. 3x(-2x+7) -5(x-1)(4x-3)

Answers

Answer:

The simplified form is -26x^2 + 56x -15

Step-by-step explanation:

We need to solve the expression:

3x(-2x+7)-5(x-1)(4x-3)

Multiplying the terms outside the bracket with the terms inside the bracket.

=-6x^2+21x-5(x(4x-3) -1(4x-3))

= -6x^2+21x-5(4x^2-3x-4x+3)

= -6x^2+21x-5(4x^2-7x+3)

Now multiply -5 with the terms inside the bracket

= -6x^2+21x -20x^2 +35x -15

Now, Combining the like terms:

= -6x^2 -20x^2 +21x+35x -15

Adding the like terms

= -26x^2 + 56x -15

So, the simplified form is -26x^2 + 56x -15

-26^2+56x-15 yea that should be the answer


If c = 7, then the value of b is...

Answers

Answer:

3.5

Step-by-step explanation:

The triangle shown is a 30-60-90 special right triangle. All right triangles that have a 30-degree angle will be, but if needed you can use the equation: 180 - (90 + 30) = x, to find the missing angle.

Special Right Triangles

Special right triangles are useful because they allow us to easily find missing sides without having to use sin, cos, or tan. All special right triangles have formulas that can be used to find missing sides.

Formulas

30-60-90 triangles have 3 sides: the hypotenuse (c), the short leg (b), and the long leg (a).

The formulas are as follows:

c = 2bb = 0.5ca = b[tex]\sqrt{3}[/tex]

Solving for b

We are already given c, so the easiest way to find b is to use the formula b = 0.5c. Just plugin the c-value.

b = 0.5(7)

Once simplified the final answer is

b = 3.5

Please help i dont get this at all so please i will highly appreciate it .Thank youuu!!!

Answers

Answer:

D

Step-by-step explanation:

Can line r be parallel to line s and line p be parallel to line q at the same time ? Explain

Answers

Yes, the line r is parallel to the line s and the line p is parallel to the line q.

Parallel lines are straight lines that do not intersect at any point.They never meet. They are always in the same distance. But they are not always ways inIf two lines AB and CD are parallel, then it can be represented by AB || CD. Some examples: Cricket stumps, white lines of zebra crossing, opposite boundaries of an rectangular box, etc.

Here the given lines are p, q, r, s.

Line p and q are parallel to each other.

and the line p is parallel to the line q.

Therefore, Yes, the line r is parallel to the line s and the line p is parallel to the line q.

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A.P.E.X Algebra 1 Sem 2

Answers

Answer:

Data Set C

Step-by-step explanation:

You can see that the data is best fit and better looking and fitting to the line in the data set C.

Using circle P with a radius of 7 cm, find the EXACT
measure/length for each of the following.
8.
9
10
11.
12
The diameter of circle P
The circumference of circle P
The area of circle P
The length of RS
The area of sector MPR
P
45
30
S
M
R

Answers

Answer:

8. 14

9. 14π

10. 49π

11. 1.75π

12. [tex]\frac{49}{12}[/tex] π

Step-by-step explanation:

If the radius is 7, the diameter is 14.

Circumference is pi * diameter, so 14π

Area is π r², so 49π

Arc length is [tex]\frac{n}{360}[/tex] * 2πr, so [tex]\frac{45}{360}[/tex] * 14π = 1.75π

Sector Area is [tex]\frac{n}{360}[/tex] * πr², so [tex]\frac{30}{360}[/tex] * 49π = [tex]\frac{49}{12}[/tex]π

Triangle N P O is shown. Line O N extends through point M to form exterior angle P N M. Angle N P O is 38 degrees. Angle P O N is 39 degrees. Exterior angle P N M is x degrees.

Which statement about the value of x is true?
x > 38
x < 39
x < 77
x > 103

Answers

The measure of the exterior angle PNM will be x < 77. Then the correct option is C.

What is the triangle?

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

Triangle NPO is shown.

Line ON extends through point M to form exterior angle PNM.

Angle NPO is 38 degrees.

Angle PON is 39 degrees.

Let the exterior angle PNM is x degrees and the interior angle PYO be y.  

Then we have

38 + 39 + y = 180°

                y = 103°

And we know that the sum of interior and exterior angle is a triangle is 180 degrees.

   x + y < 180

103 + x < 180

         x < 77

Then the correct option is C.

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(please help) Find the value of A

Answers

Step-by-step explanation:

(6a + 10)° = (3a + 55)°

6a - 3a = 55 - 10

3a = 45

a = 45/3

a = 15° IS THE ANSWER

1 peasant changed rabbits to hens and 2 rabbits were equal to 3 hens, each hen produced the eggs that were equal to ⅓ of the total number of hens, the peasant sold the eggs, 9 eggs will cost as many pennies as each hen that produced the eggs and totally he got 72 pennies so how many hens and how many rabbits he had?

Answers

The peasant had 28 hens and 42 rabbits

How to determine the number of hens and rabbits?

Represent hens with h, eggs with e and rabbits with r.

So, we have:

2r = 3h

e = 1/3h

Make h the subject in e = 1/3h

h = 3e

He got 72 pennies.

So, we have:

r + h = 72

Multiply through by 2

2r + 2h = 144

Substitute 2r = 3h in 2r + 2h = 144

3h + 2h = 144

Evaluate the sum

5h = 144

Divide by 5

h = 28.8

Remove decimal

h = 28

Recall that:

2r = 3h

So, we have:

2r= 3 * 28

Divide by 2

r = 3 * 14

Evaluate the product

r = 42

Hence, the peasant had 28 hens and 42 rabbits

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Adam wins $30 in a "spot the ball" competition. He decides to save the money and opens a saving account with the $30. After his win, he continues to put $8 into his savings account each week. Identify a rule for the linear function that describes Adam's savings. Use the rule to find the amount Adam saved during the first 5 weeks.

Answers

Answer:

$110

Step-by-step explanation:

$30-$8=$22 each week

$22×5weeks=$110

How would you answer this question?

Answers

Answer:

32

Step-by-step explanation:

the pattern of sticks from the first 3 diagrams is

7 , 12 , 17 ,..

note the pattern increases by 5 each time , then continue by adding 5 to the previous value.

4th = 17 + 5 = 22

5th = 22 + 5 = 27

6th = 27 + 5 = 32

can someone help me here pls thanks!​

Answers

Using proportions, it is found that the measure of the inscribed angle B is of 30º.

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In a circle, the inscribed angle is half the measure of the outside angle. Hence, in this problem, the measure of angle B is of 50% of 60º, hence:

m<B = 0.5 x 60º = 30º.

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Answer:

Using proportions, it is found that the measure of the inscribed angle B is of 30º.

Step-by-step explanation:

Is in between 2 number on the number line

Answers

Answer:

3 and 4

Step-by-step explanation:

well you can approximate by squaring values

2^2 = 4

3^2 = 9

4^2 = 16

the value should fall somewhere between 3 and 4 since the square root of 9 is 3 and the square root of 16 is 4

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