Why is 2i * -2i equal to 4, and not -4i?

Answer:

[tex]\dfrac{1}{3}[/tex].

Step-by-step explanation:

In quadrilateral QRST, Q(-1,0), R(5,0), S(3.5,-6), T(-2.5,-6).

In quadrilateral Q'R'S'T', Q'(-1,2), R'(1,2), S'(0.5,0), T'(-1.5,0).

Distance formula:

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

Using distance formula , we get

[tex]QR=\sqrt{(5-(-1))^2+(0-0)^2}=\sqrt{6^2}=6[/tex]

[tex]Q'R'=\sqrt{(1-(-1))^2+(2-2)^2}=\sqrt{2^2}=2[/tex]

Now,  

[tex]\text{Scale factor}=\dfrac{Q'R'}{QR}[/tex]

[tex]\text{Scale factor}=\dfrac{2}{6}[/tex]

[tex]\text{Scale factor}=\dfrac{1}{3}[/tex]

Therefore the scale factor is [tex]\dfrac{1}{3}[/tex].

The given transformation of quadrilateral QRST to quadrilateral Q'R'S'T'

are a dilation and a translation, therefore,  QRST is similar to Q'R'S'T'.

[tex]\mathrm{The \ scale \ factor \ of \ the \ dilation\ between \ QRST \ and \ Q'R'S'T' \ is} \ \dfrac{1}{3}[/tex]

Reasons:

The vertices of the quadrilateral are;

Quadrilateral QRST

Q(-1, 0)

R(5, 0)

S(3.5, -6)

T(-1, 2)

Quadrilateral Q'R'S'T'

Q'(-1, 2)

R'(1, 2)

S'(0.5, 0)

T'(-1.5, 0)

The given transformation that gives quadrilateral Q'R'S'T' from quadrilateral  QRST are a dilation and a translation.

Required:

The scale factor of the dilation

Solution:

[tex]\mathrm{The \ scale \ factor \ of \ the \ dilation} = \dfrac{\mathrm{Length \ of \ \overline{Q'R'} }}{\mathrm{Length \ of \ \overline{QR}} }[/tex]

Length of [tex]\overline{Q'R'}} }[/tex] = 1 - (-1) = 2

Length of [tex]\overline{QR}} }[/tex] = 5 - (-1) = 6

Therefore;

[tex]\mathrm{The \ scale \ factor \ of \ the \ dilation} = \dfrac{2}{6} = \dfrac{1}{3}[/tex]

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Work Shown:

(11a - 2b + 7c) - (3a - 9b + 5c)

11a - 2b + 7c - 3a + 9b - 5c ... see note below

(11a-3a) + (-2b+9b) + (7c-5c)

8a + 7b + 2c

note: don't forget to distribute the negative through to every term inside the parenthesis

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▹ Answer

8a + 7b + 2c

▹ Step-by-Step Explanation

(11a - 2b + 7c) - (3a - 9b + 5c)

Remove the parentheses

11a - 2b + 7c - (3a - 9b + 5c)

Collect like terms

8a - 2b + 7c + 9b - 5c

Final Answer

8a + 7b + 2c

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

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Answer:

[tex]f(-1) = 3[/tex]

[tex]f(2) = 6[/tex]

[tex]f(12) = 41[/tex]

Step-by-step explanation:

Given

The piece wise function can be split to:-

[tex]f(x) = -2x[/tex]   [tex]x\leq -10[/tex]

[tex]f(x) = x + 4[/tex]   [tex]-10<x\leq 2[/tex]

[tex]f(x) = 4x - 7[/tex]   [tex]x> 2[/tex]

Required

f(-1), f(2) and f(12)

To solve for each of these functions, we first check the range they fall into, then we execute the corresponding function

-1 is within the range of [tex]-10<x\leq 2[/tex]

Hence; we make use of [tex]f(x) = x + 4[/tex]  

Substitute -1 for x

[tex]f(-1) = -1 + 4[/tex]

[tex]f(-1) = 3[/tex]

2 is within the range of [tex]-10<x\leq 2[/tex]

Hence; we make use of [tex]f(x) = x + 4[/tex]  

Substitute 2 for x

[tex]f(2) = 2 + 4[/tex]

[tex]f(2) = 6[/tex]

12 is within the range of [tex]x> 2[/tex]

Hence; we make use of [tex]f(x) = 4x - 7[/tex]  

Substitute 12 for x

[tex]f(12) = 4(12) - 7[/tex]  

[tex]f(12) = 48 - 7[/tex]

[tex]f(12) = 41[/tex]

Answer:

w-2

Step-by-step explanation:

To file your return, you'll need the following on hand: Your W-2: This form will come from your company and list not only your salary for the year but the amount of taxes withheld along the way. You're required to file your W-2 along with your taxes, so if you're a salaried employee, this form is non-negotiable.

The document you need to have on hand when preparing to file your tax return is Form W-2. The correct option is D.

A tax return is a document filed with the tax authorities by individuals or businesses to report their income, expenses, and other relevant financial information in order to calculate their tax liability or refund.

It is usually filed once a year, and the information on it is used to determine whether the taxpayer owes additional taxes or is eligible for a refund.

Form W-2 is a form that an employer provides to an employee at the end of the year that shows the employee's total earnings as well as the amount of taxes withheld from those earnings.

It is a necessary document for accurately preparing and filing an individual's tax return.

Thus, the correct option is D.

For more details regarding tax return, visit:

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#SPJ7

Answer:

-1/10115

Step-by-step explanation:

Let x be the rational number.

-7/85 × x = 1/17

x = 1/17 ÷ -7/85

x = 1/(17 × -7 × 85)

x = 1/(-10115)

x = -1/10115

The rational number is -1/10115.

Answer:

- 5/7

Step-by-step explanation:

-7/85*x= 1/17

x= 1/17 ÷ (-7/85)

x= - 1/17 × 85/7

x= - 5/7

Answer:

Slope = rise / run

= -12 / 1500 (It's -12 and not 12 because a drop means it's decreasing)

= -0.008

Answer:

00 to 99 are 100 numbers.

If you match the first number only, you win $200. The Probability for this is 1/100.

If you match the first two numbers and not the third, you win $5000. The Probability for this is 1/50.

If you match all three numbers, you win $100,000. The Probability for this is 3/100.

And, If you are a customer, You will think is fair for you.

But if you are the lottery tickets company, you will think is not fair for you.

It depends who you are. 

the game isn't fair because 100,000/3=3333 1/3, so each number should be worth $3333.3333...... dollars but you can't really give 1/3 dollars so the game is impossible to be fair. Also, if you match the first two numbers you apparently get $5000. That's also not fair because each number is worth $50 dollars more than if you get the first number matched. So, the game isn't fair but it will be pretty much impossible to be fair.

Answer:

30a

Step-by-step explanation:

4a-a x 3a +7a

3a x 10a

30a

The given expression is:

By applying multiplication, we get

→ [tex]4a - 3a^2+7a[/tex]

By applying addition, we get

→ [tex]-3a^2+11a[/tex]

By taking "a" as common, we get

→ [tex]a (-3a+11)[/tex]

Thus the answer above is right.

Learn more about simplification will be:

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Answer:

y = -4

Step-by-step explanation:

-2x + 5y = 8

Let x=-14

-2(-14) +5y = 8

28 +5y = 8

Subtract 28 from each side

28-28 +5y = 8-28

5y = -20

Divide by 5

5y/5 = -20/5

y = -4

Answer:

1) -2q-5= -11

-2q = -11+5

q = -6/-2 =3

2) 3(8+k) = 33

24 + 3k = 33

3k = 33-24

K = 9/3 = 3

3) 4/6=x/9

By cross multiplication

4x9 = Xx6

36 = 6x

So, x = 6

4) 6(y+3)=24

6y + 18 = 24

y = (24-18)/6 = 1

5)4k+8=26

4k = 26-8

k = 18/4 = 4.50

6)8y=6+2y

8y - 2y = 6

6y = 6

So, y = 1

7)3x-7=20

3x = 20+7

x = 27/3 = 9

Answer: See below attachment

Answer:

hope this helps you :) have a good day

Answer:

f^-1(x) is 6x + 48

f(x) = 1/6x - 8

To find f^-1(x) equate f(x) to y

That's

f(x) = y

y = 1/6x - 8

Next interchange the terms

We have

x = 1/6y - 8

Make y the subject

Multiply through by 6

We have

6x = y - 48

y = 6x + 48

Therefore f^-1(x) is 6x + 48

Hope this helps you

Answer:f(-1/6)-8

Step-by-step explanation:

cuz

Answer:

D

Step-by-step explanation:

BIG BRAIN

Makes no sense yea put D like it’s gonna be the answer for d on mine

Answer:

A. One solution.

B. x = 3.

Step-by-step explanation:

4(2x - 5) = 4

4*2x + 4*-5 = 4

8x - 20 = 4

8x = 24

x = 3.

The given equation has one solution and the solution to the given equation is 3

Linear equation has a leading degree of 1. Given the equation

4(2x - 5) = 4

Divide both sides by 4

4(2x-5)/4 = 4/4
2x - 5 = 1

Add 5 to both sides

2x = 1 + 5

2x = 6

x = 3

Hence the given equation has one solution and the solution to the given equation is 3

Learn more on linear equation here: https://brainly.com/question/14323743

Step-by-step explanation:

you make x the subject of formula for all the questions.

firstly you divide both sides of the equation by a, this way the a will cancel it self out of the equation

x+b= c/a

then you take '+b' to the other side of the equation over the = sign, this makes +b sign to change it then becomes -b

x=c/a -b

2. 7(x-a)=b

you divide both sides of the equation by 7.

x-a=b/7

then you take -a to the other side of the equation it becomes +a

x=b/7+a

NOTE: always eliminate the number/letter beside the bracket first. it unlocks the bracket. the number or letter is joined to a bracket by multiplication so we divide to eliminate it

Answer:

3.5 mi = 18480 ft

Step-by-step explanation:

There are 5,280 feet for every one mile. Because there are 3.5 mile, you would multiply 5,280 x 3.5, getting 18480 feet.

Answer:

18480 feet

Step-by-step explanation:

1 mile is equal to 5280 feet. so then 3 1/2 miles is equal to 18480 feet.

Hope this helps!

Answer:

m∠A = 2x = 2*20 = 40

m∠B = 3x = 3*20 = 60

m∠C= 4x = = 4*20 = 80

Step-by-step explanation:

we know sum of angles of triangle is 180 degrees

given

m∠A : m∠B : m∠C = 2:3:4

let the angle be

m∠A = 2x

m∠B = 3x

m∠C= 4x

we have taken such angle by applying rule of indices where

a:b:c = ax:bx:cx

which means that if we multiply all term of ratio by same number ratio remains same

thus,

2x+3x+4x = 180

9x = 180

x = 180/9 = 20

Thus,

m∠A = 2x = 2*20 = 40

m∠B = 3x = 3*20 = 60

m∠C= 4x = = 4*20 = 80

Answer:

It's a valid sample because the first five people were selected to participate.

Step-by-step explanation:

True because random people who saw the advertisement responded. By chance, not every person who saw the advertisement answered, therefore it was random, but it would be more random if he decided to reject the second, fourth, sixth, and eighth person, and only the first, third, fifth, seventh, and ninth were chosen.

Answer:

AC=2.06cm

Step-by-step explanation:

AC^2=AD^2+CD^2

AC^2=1.5^2+1.4142^2

AC^2=2.25+2=4.25

....

[tex] \sqrt{ac {}^{2} } [/tex]

=

[tex] \sqrt{4.25 = } 2.06[/tex]

Answer:

AC=2.06 cm

Step-by-step explanation:

Answer:

statements 2 and 3

B

Step-by-step explanation:

Answer:

Yes the Quadrilateral is a Parallelogram.

Step-by-step explanation:

A parallelogram can be defined as a quadrilateral i.e a geometric shape with four sides that has opposite sides parallel and equal in length.

From the question, we are given the following points

P(2, 2), Q(1, -3), R(-4, 2), S(-3, 7)

Given points: (x1, y1) and (x2, y2)

The formula would be

√(x2 - x1)² +(y2 - y1)²

a) P(2, 2), Q(1, -3)

Length PQ = √(1 - 2)² +(-3 - 2)² = √-1² + -5² = √26

b) R(-4, 2), S(-3, 7)

Length RS = √(-3 - (-4))² + (7 - 2) ² = √ 1² + 5² = √26

c) R(-4, 2), Q(1, -3)

Length RQ = √(1 - (-4))² + (-3 - 2)² = √5² + 5² = √(25 + 25) = √50

d) S(-3, 7), P(2, 2)

Length SP = √(2 - (-3))² + (2 - 7)² = √5² +(-5)² = √(25 + 25) = √50

From the above solution, we can see that

Length PQ = Length RS

Length RQ = Length SP

This means the opposite sides are parallel and equal in length, hence it is a Parallelogram.

Answer:

Step-by-step explanation:

m∠1=m∠3

m∠2=m∠4

3*(m∠1+m∠3)=m∠2+m∠4

3*(m∠1+m∠1)=m∠2+m∠2

3×2 m∠1=2 m∠2

m∠2=3 m∠1

now m∠1+m∠2=180°

m∠1+3 m ∠1=180

4 m∠1=180

m∠1=180/4=45°

m∠3=45°

m∠2=180-m∠1=180-45=135°

m∠4=135°

Answer:

Step-by-step explanation:

Your answer is c

the absolute value of -2x would be positive 2x making x =2 and -2

"translated 5 units up" means y becomes y+5. We just add 5 to whatever the y coordinate is to shift the point 5 units up.

To shift 3 units left, we subtract 3 from whatever the x coordinate value is. So we go from x to x-3.

Put this together and the translation rule is [tex](x,y) \to (x-3, y+5)[/tex]

Answer:

31.25

Step-by-step explanation:

There are about 31 quarters in a the jar so if you need to round do accordingly! Have a good day

Answer:

31 quarters

Step-by-step explanation:

Have an equation set

Then you solve the equation you get 31.25

Round the number since you can't have 31.25 quarters it just doesn't make sense.

Round it to 31

Therefore your answer is 31 quarters

Hope this Helps!

Answer:

Part 1:  [tex]2l+2w=34[/tex]       Part 2:  10.5 Units

Step-by-step explanation:

We can find perimeter of a rectangle using formula [tex]2l+2w=P[/tex]. We are given [tex]w[/tex], which is 6.5. Put this into the equation.

[tex]2l+2(6.5)=342l+13=34\\2l=21\\l=10.5[/tex]

So, length(l) of the rectangle is 10.5 units.

Answer:

10.5

Step-by-step explanation:

The perimeter of rectangles is calculated by adding all lengths together

34 units = length + length + width +width

since width is given as 6.5 units

2l + 2 × 6.5 = 34 (l : length)

2l + 13 = 34

2l = 21

l = 10.5

Answer:

Step-by-step explanation:

Let the angles be 2x , 6x , 9x , 13x

We know that the sum of quadrilateral is 360°

Now,

[tex]2x + 6x + 9x + 13x = 360[/tex]

Calculate the sum

[tex]30x = 360[/tex]

Divide both sides of the equation by 30

[tex] \frac{30x}{30} = \frac{360}{30} [/tex]

Calculate

[tex]x = 12[/tex]

Replacing the value,

2x = 2 * 12 = 24°

6x = 6 * 12 = 72°

9x = 9 * 12 = 108°

13x = 13 * 12 = 156°

So, the angles are 24° , 72° , 108° , 156°

Hope this helps...

Good luck on your assignment...

Answer:

Below in bold.

Step-by-step explanation:

2+6+9+13 = 30.

Now there are 360 degrees in a a quadrilateral.

So the value of the shortest angle = 2/30 * 360

= 1/15 * 360

= 24 degrees.

In the same way the value of the other 3 angles is:

6/30 * 360,  9/30 * 360 and 13/30 * 360

= 72, 108 and 156 degrees.

Answer:

Flipped across the y-axis and then rotated -90 degrees

Step-by-step explanation: