Find the interquartile range for each set of data.
Set 1: 21, 5, 14, 10, 8, 17, 2

Answer:

a^15 * 2^9

Step-by-step explanation:

(a^5 * 2^3)^3 =

= (a^5)^3 * (2^3)^3

= a^(5 * 3) * 2^(3 * 3)

= a^15 * 2^9

Answer: the second choice 3.

Answer:

3. a^15*2^9

Step-by-step explanation:

We know that (a * b) ^c = a^c * b^c

(a^5 * 2^3)^3

a^5^3 * 2^3^3

And we know that a^b^c = a^(b*c)

a^(5*3) * 2^(3*3)

a^15 * 2^9

Answer:

580

Step-by-step explanation:

Let's translate this word for word.

87 is 15% of what number

87 = 15% times x

87=.15 times x

[tex]87=.15 \cdot x[/tex]

Divide both sides by .15

[tex]\frac{87}{.15}=\frac{.15x}{.15}[/tex]

Cancel out the common factor of .15 on the right; that is .15/.15=1.

[tex]580=x[/tex]

580 is the number

Answer:

580

Step-by-step explanation:

Alright. Translate that into math, and you get:

87=15/100x

multiply both sides by x

8700/15=x

x=8700/15

x=580

Check:

580*15/100

58*15/10

870/10

87

BINGO!

To graph the equation y > 2x, start by graphing the line y = 2x and shading the region above it.

To graph the equation y > 2x, we start by graphing the line y = 2x. This line has a positive slope (b > 0) and passes through the origin (0, 0). Since we want to graph y > 2x, we need to shade the region above the line.

Draw the line y = 2x as a solid line. Then, shade the region above the line to indicate that y is greater than 2x.

Answer: Graph (a) matches the given inequality y > 2x.

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Answer:

The x-intercepts are (4,0) and (-1/3,0).

Step-by-step explanation:

f or any relation/function will intersect the x-axis when y is 0.

Set that's what we will do is set y to 0 and solve for x.

0=3x^2-11x-4

I'm going to attempt to factor.

a=3

b=-11

c=-4

We need to find two numbers that multiply to be ac and add up to be b.

ac=-12=-12(1)

b=-11=-12+1

Let's factor 3x^2-11x-4 by grouping.

3x^2-11x-4

3x^2-12x+1x-4       ; I replaced -11x with -12x+1x

Group the first 2 pairs and group the last two pairs like so:

(3x^2-12x)+(1x-4)

Now factor what you can from each pair:

3x(x-4)+1(x-4)

Now you have two terms, both with the common factor (x-4) so factor it out:

(x-4)(3x+1)

Now let's go back to solving:

3x^2-11x-4=0

This is the same as solving:

(x-4)(3x+1)=0  (because this is just the factored form of the original equation.)

Now this means either x-4=0 or 3x+1=0.

We need to solve both.

x-4=0 can be solved by adding 4 on both sides resulting in x=4.

3x+1=0 requires two steps.

3x+1=0

Subtract 1 on both sides:

3x=-1

Divide both sides by 3:

x=-1/3

The x-intercepts are (4,0) and (-1/3,0).

Answer:

The negative x-intercept is at (-1/3 , 0).

The positive x-intercept is at (4 , 0).

Explanation:

Where does f(x) = 3x2 – 11x – 4 intersect the x-axis?

The negative x-intercept is at (-1/3 , 0).

The positive x-intercept is at (4 , 0).

Set f(x) equal to zero so

3x2 – 11x – 4 = 0

Plug in a. b, and c into the quadratic formula

and get 2 solutions:

1/3 and -4

take the opposite signs and put it in the x intercepts

Answer:

Length of larger piece: 7 m

Total length of carpet is: 19 m

Step-by-step explanation:

Let the smaller piece have length x.

Let the larger piece have length y.

"The length of the smaller piece is 5 meters greater than the length of the larger piece."

x = y + 5

"If the length of the smaller piece is 12 meters"

x = 12

x = y + 5

12 = y + 5

7 = y

y = 7

The larger piece has length 7 meters.

The total length of the carpet is x + y = 12 m + 7 m = 19 m

To find the length of the larger piece of carpet, use the equation x + 5 = 12, and solve for x. Substitute the total length of the carpet for x in the formula to find the length of the larger piece.

The problem involves finding the length of the larger piece of carpet when the length of the smaller piece and the total length of the carpet are known. Let's assume the length of the larger piece is x meters. According to the problem, the length of the smaller piece is 5 meters greater than the length of the larger piece, so the length of the smaller piece can be represented as x + 5 meters. The total length of the carpet is the sum of the lengths of the smaller and larger pieces, so we can create the equation: x + (x + 5) = total length. Given that the length of the smaller piece is 12 meters, we can substitute x + 5 with 12 in the equation and solve for x:

x + (x + 5) = total length

x + x + 5 = total length

2x + 5 = total length

2x = total length - 5

x = (total length - 5) / 2

Now we have the formula to calculate the length of the larger piece. Simply substitute the total length of the carpet into the formula to find the length of the larger piece.

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Answer:

The length is 5 times the width

Step-by-step explanation:

Let

W ----> the width of the rectangle

L ----> the length of the rectangle

we know that

The area of rectangle is equal to

[tex]A=LW[/tex]

In this problem we have

[tex]L=5x[/tex] ----> equation A

[tex]W=x[/tex] ----> equation B

substitute equation B in equation A

[tex]L=5W[/tex]

therefore

The length is 5 times the width

Circumference is 62.8

To find the circumference, the formula is 2πr

The radius is half so we must multiply by 2 which is 20.

And finally, you multiply by π (3.14) and you will get 62.8 cm.

In conclusion, the answer is 62.8 cm.

The Circumference of the Circle is 62.8 cm

The Circumference (or) perimeter of circle = 2πr

where, r is the radius of the circle. π is the mathematical constant

Given:

Radius- 10 cm

Now, the Circumference of Circle

= 2πr

=2 x 3.14 x 10

= 2 x 31.4

= 62.8 cm

Hence, the Circumference of the Circle is 62.8 cm

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Answer:

C) 2744 cm

Step-by-step explanation:

To find the volume of a cube you have to use this equation:

V = a^3

Now plug in the number:

V = 14^3

14^3 or 14*14*14 = 2,744

The volume is 2,744 cm

Answer:

1) 2744cm^3

2)1176cm^2

Step-by-step explanation:

1)Since it's a square, the sides are all equal length. And volume=base×width×height

thus we can multiply 14×14×14=14^3=2744cm^3

2)for surface area we can find the area of on side and multiply it by 6 because the square has six equal sides. thus, area=base×height so, area=14×14=14^2=196cm^2

Now we multiply it by 6 which is equal to 1176cm^2

To find the average, you add all of the numbers and divide by the number of numbers (If that makes sense)

We can use variables (x) to solve for the last number.

268+258+271+x/4 = 266

Multiply both sides by 4

268+258+271+x = 266*4

268+258+271+x = 1064

Add the three numbers together

797+x = 1064

Subtract both sides by 797

x = 267

Her fourth pregnancy must last 267 days.

Answer:

267

Step-by-step explanation:

So we want to find the average of 4 numbers:

268, 258, 271, and x

The average of those 4 numbers is represented by the fraction:

[tex]\frac{268+258+271+x}{4}[/tex]

Now we also wanting this average to be equal to 266.  We need to find x such that that happens.

So we have the following equation to solve:

[tex]\frac{268+258+271+x}{4}=266[/tex]

Multiply both sides by 4:

[tex]268+258+271+x=4(266)[/tex]

Do any simplifying on both sides:

[tex]797+x=1064[/tex]

Subtract 797 on both sides:

[tex]x=1064-797[/tex]

Simplify:

[tex]x=267[/tex]

Answer:

1873

Step-by-step explanation:

just add them up

The restaurant sold a total of 1837 orders of eggs.

To calculate the total number of orders of eggs sold by the breakfast restaurant, we need to add up all the individual orders for each type of eggs.

Scrambled eggs: 889 orders

Poached eggs: 313 orders

Fried eggs: 594 orders

Hard-boiled eggs: 41 orders

Now, let's add these numbers together:

889 + 313 + 594 + 41 = 1837 orders

Therefore, the restaurant sold a total of 1837 orders of eggs.

Answer:

x is 50 degrees

Step-by-step explanation:

If you subtract 65 twice from 180 you get this answer. The line is a straight line making it equal 180 degrees

The correct answer is 50

Answer:

temperature of city a=5

temperature of city b=4

Step-by-step explanation:

Given:

Let temperature of city A= a

temperature of city B=b

As given:

4a=8+3b

a-2b=-3

rearranging 2nd equation we get:

a=-3+2b

substituting above in 1st equation we get:

4(-3+2b)-3b=8

8b - 12 = 3b + 8

8b-3b=12+8

5b = 20

b = 4

Now substituting b=4 in 4a = 8 + 3b , we get

4a = 8 + 3b

4a = 8 + 3(4)

4a = 8 + 12

4a = 20

a = 20/4

a = 5

temperature of city a and city b on that day is 5C and 4C respectively!

Answer:

The temperature of the city a was 5 °C and b was 4 °C.

Step-by-step explanation:

First we have to write the equations based on the description, this is:

[tex]4a=8+3b\\a-2b=-3[/tex]

Now that we have the equations, we can replace the second in the first:

[tex]4(2b-3)=8+3b[/tex]

Now we can find the value of b:

[tex]8b-12=8+3b[/tex]

[tex]8b-3b=8+12[/tex]

[tex]5b=20[/tex]

[tex]b=\frac{20}{5}[/tex]

[tex]b=4\\[/tex]

Now with the value of b and the second equation we can get the value of a:

[tex]a-2(4)=-3[/tex]

[tex]a-8=-3[/tex]

[tex]a=8-3[/tex]

[tex]a=5[/tex]

The temperature of the city a was 5 °C and b was 4 °C.

Answer:

Final answer: a-2b+3c

Step-by-step explanation:

5ab/5b= a

-10b^2/5b= -2b

15bc/5b= 3c  

Answer:

a - 2b + 3c

Step-by-step explanation:

Factor the numerator by factoring out 5b from each term, that is

[tex]\frac{5b(a-2b+3c)}{5b}[/tex]

Cancel the 5b on the numerator/ denominator, leaving

a - 2b + 3c

(4x+3y)(4x-3y)

Multiply the two brackets together

4x(4x)(4x-3y)(-3y)(4x)(3y)(-3y)

16x^2-12xy+12xy-9y^2

16x^2-9y^2

Answer is 16x^2-9y^2

[tex]\huge{\boxed{16x^2-9y^2}}[/tex]

Use the FOIL method.

First term in each binomial: [tex]4x*4x=16x^2[/tex]

Outside terms: [tex]4x*-3y=-12xy[/tex]

Inside terms: [tex]3y*4x=12xy[/tex]

Last term in each binomial: [tex]3y*-3y=-9y^2[/tex]

Add these all together. [tex]12xy-12xy+16x^2-9y^2=\boxed{16x^2-9y^2}[/tex]

Answer:

101

Step-by-step explanation:

3^4 = 81

4 x 5  20

81 +20 = 101

Answer:

101

Step-by-step explanation:

[tex]3^{4}[/tex] = 81 and 4 x 5 =20, so 20+81= 101.

Answer:

the answer is -2 and would be plotted on -2 on a number line

Answer: 364.7 pounds

Step-by-step explanation: Multiply the number of kilograms, 165, by the number of pounds per kilogram, 2.21.

165 x 2.21 = 364.65

Round to the nearest tenth.

364.7 pounds in 165 kilograms.

The number of pounds in 165 kilograms is approximately 363.2 pounds. Rounding to the nearest tenth, the number of pounds in 165 kilograms is approximately 363.2 pounds.

To find the number of pounds in 165 kilograms, we can use the conversion rate of 1 kilogram is approximately equal to 2.21 pounds. We can set this up as a proportion: 1 kilogram / 2.21 pounds = 165 kilograms / x pounds. Cross-multiplying, we get x pounds = (165 kilograms * 2.21 pounds) / 1 kilogram. Simplifying, x pounds = 363.15 pounds. Rounding to the nearest tenth, the number of pounds in 165 kilograms is approximately 363.2 pounds.

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Answer:

At (4, 0), (6, 0)

Step-by-step explanation:

[tex]x^2 - 10x + 24 = 0\\(x-6)(x-4) = 0\\x_1 = 6\\x_2 = 4[/tex]

Answer:

answer C:  (x - 1) is also a factor of P(x).

Step-by-step explanation:

Synthetic division is the best approach here.  Given that one factor is x - 9, we know that 9 is the appropriate divisor in synthetic division:

9    )    5    -51      k       -9

                 45    -54      (9k - 486)

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

           5     -6   (k - 54)  (-9 + 9k - 486)

and this remainder must = 0.  Find k:  -9 + 9k - 486 = 0, or

                                                                      9k = 486 + 9 = 495

                                                                      Then k = 495/9 = 55

Look at the last line of synthetic division, above:

5   -6   (k - 54)    0

Substituting 55 for k, we get:

5   -6     1          

These are the coefficients of the quotient obtained by

dividing P(x) by (x - 9).    They correspond to 5x^2 - 6x + 1.

We must factor this result.

Let's start with 5x + 1, and check whether this is a factor of 5x^2 - 6x + 1 or not.  If 5x + 1 is a factor, then the related root is -1/5.  Let's use -1/5 as the divisor in synthetic div.:

-1/5    )       5       -6        1

                           -1        7/5

         ----------------------------

                 5        -7       12/5       Here the remainder is not zero, so -1/5 is

                                                    not a root and 5x + 1 is not a factor.

Now try x - 5.  Is this a factor of 5x^2 - 6x + 1?  Use 5 as divisor in synth. div.:

5    )     5      -6      1

                    25    95

     ------------------------

         5         19     96  Same conclusion:  x - 5 is not a factor.

Try x = -1:

-1     )    5     -6     1

                    -5     11

        ----------------------

            5       -11     12.  The remainder is not zero, so (x + 1) is not a factor.

Finally, try x = 1:

1     )    5    -6     1

                  5    -1

      --------------------

          5     -1      0

Finally, we get a zero remainder, and thus we know that x - 1 is a factor of P(x)

Answer C is correct:  x - 1 is a factor of P(x)

To solve this question, we can apply the Remainder Theorem. According to the Remainder Theorem, if a polynomial \( P(x) \) is divided by \( x - c \), the remainder of the division is \( P(c) \).
Given:
\( P(x) = 5x^3 − 51x^2 + kx − 9 \)
We are told that when \( P(x) \) is divided by \( x − 9 \), the remainder is 0. Therefore, according to the Remainder Theorem:
\( P(9) = 5(9)^3 − 51(9)^2 + k(9) − 9 = 0 \)
Let's compute \( P(9) \):
\( P(9) = 5(729) − 51(81) + 9k − 9 \)
\( P(9) = 3645 − 4131 + 9k − 9 \)
\( P(9) = 9k − 495 = 0 \)
To solve for \( k \):
\( 9k = 495 \)
\( k = 495 / 9 \)
\( k = 55 \)
Now, we know that P(x) with \( k = 55 \) has no remainder when divided by \( x − 9 \).
The updated polynomial \( P(x) \) is:
\( P(x) = 5x^3 − 51x^2 + 55x − 9 \)
To determine which of the given options is a factor of \( P(x) \), we will test each option by plugging in the roots of these factors into the polynomial \( P(x) \) and checking if it yields zero.
A) For \( x − 5 \), the root is \( x = 5 \):
\( P(5) = 5(5)^3 − 51(5)^2 + 55(5) − 9 \)
\( P(5) = 5(125) − 51(25) + 275 − 9 \)
\( P(5) = 625 − 1275 + 275 − 9 \)
\( P(5) = 625 − 1009 \)
\( P(5) ≠ 0 \) (This factor does not yield zero, so it is not a factor of \( P(x) \).)
B) For \( x + 1 \), the root is \( x = -1 \):
\( P(-1) = 5(-1)^3 − 51(-1)^2 + 55(-1) − 9 \)
\( P(-1) = -5 − 51 − 55 − 9 \)
\( P(-1) = -120 \)
\( P(-1) ≠ 0 \) (This factor does not yield zero, so it is not a factor of \( P(x) \).)
C) For \( x − 1 \), the root is \( x = 1 \):
\( P(1) = 5(1)^3 − 51(1)^2 + 55(1) − 9 \)
\( P(1) = 5 − 51 + 55 − 9 \)
\( P(1) = 60 − 60 \)
\( P(1) = 0 \) (This factor yields zero, so it is a factor of \( P(x) \).)
D) For \( 5x + 1 \), the root is \( x = -1/5 \):
\( P(-1/5) = 5(-1/5)^3 − 51(-1/5)^2 + 55(-1/5) − 9 \)
\( P(-1/5) = -1/25 − 51/25 − 55/5 − 9 \)
Since the coefficients add up to a non-zero value, we can tell that it's not going to be zero; therefore, it is not worth computing the whole expression.
\( P(-1/5) ≠ 0 \) (Hence, this is also not a factor of \( P(x) \).)
The only option that gives a remainder of zero when its root is substituted into \( P(x) \) is C, \( x - 1 \). Therefore, the correct answer is:
C- x − 1

Answer:

8.  $114

10.  60 stamps

Step-by-step explanation:

8.

Let Dylan have d, Mike have m, and Jeremy have j

3 of them have 171, so we can write:

1. [tex]d + m + j = 171[/tex]

Mike has twice as Dylan, so we can write:

2. m = 2d

Jeremy had three times as Mike, so:

3. j = 3m

We can write equation 3 as m = j/3

Also, if we put this into equation 2, we have:

j/3=2d

d=j/6

Now we have d and m in terms of j. We put it into equation 1 and solve for j:

[tex]\frac{j}{6} + \frac{j}{3} + j = 171\\\frac{3j+6j+18j}{18}=171\\\frac{27j}{18}=171\\27j=18*171\\27j=3078\\j=\frac{3078}{27}\\j=114[/tex]

Jaime has $114

10.

amount of stamps Maddy has is m and amount Simon has is s

Maddy had twice as many stamps as Simon:

m = 2s

Also

After Maddy sold 60 stamps, Sinom had twice as many stamps as Maddy:

s+60=2(m-60)

We put the first equation in the second and solve for s:

s+60=2(m-60)

s+60=2(2s-60)

s+60=4s-120

180=3s

s=60

THus, m = 2(60) = 120

So maddy had 120 - 60 = 60 more stamps than Simon

Answer:

Part 1) The equation tells us that Terry started at an elevation of 2,600 ft

Part 2) The elevation is decreasing by 50 feet each second

Step-by-step explanation:

we have

[tex]E(t)=2,600-50t[/tex]

where

E(t) is Terry's elevation in feet

t is the time in seconds

Part 1) Find the E intercept of the equation

The E-intercept is the value of E when the value of t is equal to zero

so

For t=0

substitute

[tex]E(0)=2,600-50(0)[/tex]

[tex]E(0)=2,600\ ft[/tex]

therefore

The equation tells us that Terry started at an elevation of 2,600 ft

Part 2) Find the slope of the equation

we have

[tex]E(t)=2,600-50t[/tex]

This is the equation of the line into slope intercept form

The slope m is equal to

[tex]m=-50\ ft/sec[/tex]

The slope is negative, because is decreasing

therefore

The elevation is decreasing by 50 feet each second

The subject of this question is Physics. The given equation represents Terry's elevation while skiing down a steep hill.

The subject of this question is Physics. The given equation E(t) = 2600 - 50t represents Terry's elevation in feet after t seconds while skiing down a steep hill.

To better understand the equation, let's break it down step-by-step:
- The constant term 2600 represents Terry's initial elevation at t = 0 seconds.
- The coefficient of t, -50, represents the rate at which Terry's elevation decreases as time passes. This means that Terry's elevation decreases by 50 feet for every second that goes by.

Based on this equation, Terry's elevation will progressively decrease as time passes.

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Answer:

Option A.) 1.30

Step-by-step explanation:

we know that

The secant of x is 1 divided by the cosine of x:

so

sec(40°)=1/cos(40°)

using a calculator

sec(40°)=1.30

Answer:

A.) 1.30

Step-by-step explanation:

If the cosine value is 40*, the secant value to the hundredths degree is 1.30.

sec(40°)=1.30

Answer:

Step-by-step explanation:

The coordinates of the intersection of the line are the solution of the system of equations.

[tex]\underline{+\left\{\begin{array}{ccc}x-y=1\\y-x=1\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad0=2\qquad\bold{FALSE}[/tex]

The system of equations has no solution. Therefore, the lines are parallel (the intersection does not exist).

Answer:

12.5

Step-by-step explanation:

divide 25 by 2

To find the area of the painted part, subtract the area of the missing sector from the area of the entire circle.

The area of the painted part of the figure can be found by subtracting the area of the missing sector from the area of the entire circle. To find the area of the missing sector, we need to know the central angle of the sector. Once we have the central angle, we can use the formula for the area of a sector to calculate the area of the missing sector. Finally, we subtract the area of the missing sector from the area of the entire circle to find the area of the shaded part.

Example:

If the circle has a radius of 5 units and the central angle of the missing sector is 60 degrees, we can calculate:

Area of missing sector = (60/360) * π * 5^2

Area of the shaded part = π * 5^2 - (60/360) * π * 5^2

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Step-by-step explanation:

In ∆ABC, if <A is 90° and <B is 45° then hypotenuse is BC.

Now,

Cos B= base/height

Cos B= AB/ BC

BC= AB/cos 45°.

Answer:

17 sqrt 2

Step-by-step explanation:

trust me the length is 24.04163 which equals 17√2

www.calculator.net has a triangle calculator if u think im wrong just look up triangle calculator

Answer:

15%

Step-by-step explanation:

Answer:

30 inches

Step-by-step explanation:

By definition,

volume of a pyramid = (Base Area x height ) / 3

or

500 = (50 x h ) / 3

50h = (500) (3)

h = (500)(3) / (50) = 30 inches

Answer:

h=30in

Step-by-step explanation:

The height of a pyramid whose volume is 500 cubic inches and whose area base is 50 square inches is 30inches.

Formula: V = Ab h/3

h=3 V/Ab = 3 ⋅ 500/50 = 30 inches

Step-by-step explanation:

The first polygon, ABCD, should be rotated around DA' axis and then create a function f'(x)=f(x) +5 to transpose ABCD poligon into A'B'C'D' position

The second polygon, MNOP, rotate around MP axis and half the size ( Area)

Step-by-step explanation:

1b) First, reflect ABCDE over the x-axis.

(x, y) → (x, -y)

Then, translate 5 units to the right and 3 units down.

(x, -y) → (x+5, -y-3)

1c) Instead of reflecting over the x-axis, we can reflect ABCDE over the y-axis.

(x, y) → (-x, y)

Then, rotate about the origin 180 degrees.

(-x, y) → (x, -y)

Finally, translate 5 units to the right and 3 units down.

(x, -y) → (x+5, -y-3)

2b) First, rotate MNOP 90 degrees clockwise about the origin.

(x, y) → (y, -x)

Then, scale by 1/2.

(y, -x) → (y/2, -x/2)

Finally, translate 3.5 units to the left and 2.5 units down.

(y/2 - 3.5, -x/2 - 2.5)

2c) We can form a second method by changing the order of transformations.

First translate MNOP 5 units to the right and 7 units down.

(x, y) → (x + 5, y - 7)

Then scale by 1/2.

(x + 5, y - 7) → (x/2 + 2.5, y/2 - 3.5).

Finally, rotate 90 degrees about the origin.

(y/2 - 3.5, -x/2 - 2.5)

3b) First, rotate EFGH 45 degrees counterclockwise about the origin.

(x, y) → (½√2 (x - y), ½√2 (x + y))

Then scale by ⅓√2.

(½√2 (x - y), ½√2 (x + y)) → (⅓ (x - y), ⅓ (x + y))

Finally, translate 13/3 units to the right and 1 units down.

(⅓ (x - y), ⅓ (x + y)) → (⅓ (x - y) + 13/3, ⅓ (x + y) - 1)

3c) Again, we can form a second method by changing the order of the transformations.

Let's keep the first step the same, rotating EFGH 45 degrees counterclockwise about the origin:

(x, y) → (½√2 (x - y), ½√2 (x + y))

Then translate 13/√2 units to the right and 3/√2 units down.

(½√2 (x - y), ½√2 (x + y)) → (½√2 (x - y) + 13/√2, ½√2 (x + y) + 3/√2)

Finally, scale by ⅓√2.

(½√2 (x - y) + 13/√2, ½√2 (x + y) + 3/√2) → (⅓ (x - y) + 13/3, ⅓ (x + y) + 1)

4b) First, rotate XYZ 45 degrees clockwise about the origin.

(x, y) → (½√2 (x + y), ½√2 (y - x))

Then translate 5-√2 units to the right and 4√2 units up.

(½√2 (x + y), ½√2 (y - x)) → (½√2 (x + y) + 5 - √2, ½√2 (y - x) + 4√2)

4c) Instead, let's translate XYZ 5 units to the left and 3 units up.

(x, y) → (x - 5, y + 3)

Then rotate 45 degrees clockwise about the origin:

(x - 5, y + 3) → (½√2 (x + y - 2), ½√2 (y - x + 8))

Finally, translate 5 units to the right.

(½√2 (x + y - 2), ½√2 (y - x + 8)) → (½√2 (x + y - 2) + 5, ½√2 (y - x + 8))