Use the Pythagorean theorem to find the missing length in the right triangle

Answer:

Step-by-step explanation:

In the rectangular complex number -9√3 + 9i, which has a standard form a + bi, the a = -9√3 and the b = 9. We need this in polar form (r, θ) where

[tex]r=\sqrt{a^2+b^2}[/tex] and filling in:

[tex]r=\sqrt{(-9\sqrt{3})^2+(9)^2 }[/tex] (notice we do not put the i in there with the 9).

[tex]r=\sqrt{243+81}[/tex] so

r = 18. Now let's move on to the angle, which is a little more difficult. The angle is found in the inverse tangent ratio:

[tex]tan^{-1}(\frac{b}{a})[/tex] so filling that in, we have:

[tex]tan^{-1}(\frac{9}{-9\sqrt{3} })=\frac{1}{-\sqrt{3} }[/tex] Since tangent is the side opposite over the side adjacent, y is positive and x is negative in the second quadrant. This is a 30 degree angle in QII, which has a reference angle of 150 degrees. This angle in radians is [tex]\frac{5\pi}6}[/tex], so the polar form of that number is (18, [tex]\frac{5\pi}{6}[/tex])

Answer:

its d

Step-by-step explanation:

i guessed lol

Answer:

h = 5/2

Step-by-step explanation:

[tex]\frac{3}{4} *\frac{1}{2} *h=\frac{15}{16} \\\\\frac{3}{8} *h=\frac{15}{16}[/tex]

divide both sides by 3/8

[tex]h=\frac{5}{2}[/tex]

Answer:

I would answer but I have no numbers to give the answer

Answer:

area of circle is 2πr²

= 2 x 3.14 x 8 x 8

= 402 cm

Answer:

If you take 32 percent of a number and get 64, then what is that number? In other words, you know that 32 percent of a number is 64 and you want to know what that initial number is. Therefore, the answer to "64 is 32 percent of what number?" is 200, and you can also derive that 32 percent of 200 equals 64.

Step-by-step explanation:

200

Step-by-step explanation:

32% x = 64

(32/100)x= 64

0.32x=64

x=64÷0.32

x=200

Answer:

26.2

Step-by-step explanation:

From the given diagram;

Opposite side IJ = 22

Hypotenuse HI = x

Angle of elevation = 57degrees

Using the SOH CAH TOA;

sin theta = opposite/hypotenuse

sin theta = IJ/HI

sin57 = 22/x

x = 22/sin57

x = 22/0.8387

x = 26.2

Hence the legnth of HI is 26.2

Answer:

a. Total of 45 students.

b. 18 Boys.

Answer:

There are 45 students and 18 boys in the class

Answer:

Aidan saved 115.67 over five weeks.

Step-by-step explanation:

After x weeks:

The amount of money saved by Aidan is given by:

[tex]y(x) = 17.63x + 27.52[/tex]

How much aidan saved over five weeks?

This is y when x = 5. So

[tex]y(x) = 17.63x + 27.52[/tex]

[tex]y(5) = 17.63*5 + 27.52 = 115.67[/tex]

Aidan saved 115.67 over five weeks.

Answer: Hi the Range is 4

Step-by-step explanation: The range of a data set in statistics is the difference between the largest and the smallest values. While range does have different meanings within different areas of statistics and mathematics, this is its most basic definition, and is what is used by the provided calculator. Using the same example:

18, 16, 19, 15, 17

19,18,17,16,15

19-15= 4

Answer:

Jomar needs to study for 3 hours on Thursday to be prepared for his test.

Step-by-step explanation:

If we want to make the average a certain amount of time over a certain number of days, we can first figure out the number of days and total amount needed. Here, we can see that the average is 1 hour and 30 minutes, and there are 6 days (Saturday-Thursday). Therefore, as

average = total / length, we can multiply both sides by length to get

average * length = total

Plugging 1.5 hours in for average and 6 days for length, we get

1.5 * 6 = 9 hours as the total amount needed to get an average of 1.5 hours a day

Our total so far is 2 hours for Saturday, 2 hours for Sunday, and 2 hours for Monday. This adds up to 6 hours, and we need 9. The difference between 9 and 6 is 3, meaning that Jomar needs to study for 3 hours on Thursday to be prepared for his test.

Answer:

3 : 7

Step-by-step explanation:

24/56 = 3 / 7

Answer:

3:7 helpful answer to your question have a nice evening

Answer:

$0

Step-by-step explanation:

Answer:

a y intercept (0,8)

Flat rate 8

b  slope is 4

c  3.5 hours

Step-by-step explanation:

The y intercept is where it crosses the y axis, which is (0,8)

The flat rate is the y intercept which is 8

The rate per hour is the slope

m = ( y2-y1)/(x2 -x1)

Using 2 point ( 1,12) and ( 2,16)

    = (16 -12)/(2-1)

     = 4/1

    = 4

The equation is

y = mx+b

y = 4x+8

Let y = 22

22 = 4x+8

Subtract 8 from each side

22-8 = 4x+8-8

14 = 4x

Divide by 4

14/4 = 4x/4

3.5 = x

3.5 hours

(0,8) is the y intercept because it crosses the y axis.

We can see that the flat rate is 8, which is the y intercept.

[tex] \quad\quad\quad\boxed{ \tt{m = \frac{rise}{run} = \frac{ y \tiny{2} \: \small{ - } \: y \tiny{1}}{x \tiny{2} \: \small{ - } \: x \tiny{1}} }}[/tex]

[tex]\quad\quad\quad\boxed{ \tt{m = \frac{16 - 12}{2 - 1} }}[/tex]

[tex]\quad\quad\quad\boxed{ \tt{m = \frac{4}{1} }}[/tex]

[tex] \quad\quad\quad\boxed{ \color{green}\tt{m = 4}}[/tex]

[tex] \quad \quad \quad \boxed{ \tt{y = mx + b}}[/tex]

[tex] \quad \quad \quad \boxed{ \tt{y = mx + b}}[/tex]

[tex] \quad \quad \quad \boxed{ \tt{22 =4x + 8}}[/tex]

[tex] \quad \quad \quad \boxed{ \tt{22 - 8 = 4x + 8 - 8}}[/tex]

[tex] \quad \quad \quad \boxed{ \tt{14 = 4x \: \:\cancel{ \color{red}+ 8 - 8}}}[/tex]

[tex]\quad \quad \quad \boxed{ \tt{ \frac{14 = \cancel4x}{ \cancel{4} }}}[/tex]

[tex]\quad \quad \quad \boxed{ \color{green} \tt{3.5 = x}}[/tex]

_________

#LetsStudy

#HikariSquad

Answer:

y = -2x+7

Step-by-step explanation:

Parallel lines have the same slope

y = 1-2x has a slope of -2

So the new line has a slope of -2

We have a slope of -2 and a point of (3,1)

y = mx+c

1 = -2(3)+c

1 = -6+c

Add 6 to each side

1+6 =c

7 =c

y = -2x+7

Answer:

2/11

Step-by-step explanation:

12-4-5=3

So now we know that we have:

4 pairs of polo socks

5 pairs of plain white socks

3 pairs of grey socks

To pull a grey sock one time is 3/12 since there are 12 total socks and 3 pairs of grey socks but since we remove a sock, in the second time, the probability would be 2/11.

Hope this helps! Brainliest?

Answer:

x = 6

Step-by-step explanation:

The sum of the angles of a quadrilateral is 360

69+111+12x-3 +111 = 360

Combine like terms

12x+288=360

Subtract 288 from each side

12x+288-288 = 360-288

12x = 72

Divide by 12

12x/12 = 72/12

x = 6

Answer:

x = 6

Step-by-step explanation:

All angles together equal 360

Us this to set up your formula

360 = 111 + 111 + 69 + 12x-3

360 = 288 + 12 x

360 - 288 = 12x

72 = 12x

72/12 = x

6 = x

You could also use the fact that angle t and r are equal to set your formula up as

69 = 12x-3

69+3=12x

72=12x

72/12=x

6=x

Answer:

x = 45

Step-by-step explanation:

x = 20 + 25

as x is vertically opposite to GED

and vertically opposite angles are equal

Answer:

The author sold a total of 30240 books following this trend.

Step-by-step explanation:

Let's find 5% of 14400 first;

14400 * 5%

14400 * 5/100

144 * 5

720 (So now we know that they are decreasing by 720 each month; therefore thats the constant)

=> aₙ = a₁ + r(n - 1)

=> a₂₃ = 14400 + 720(23 - 1)

=> a₂₃ = 14400 + 720(22)

=> a₂₃ = 14400 + 15840

=> a₂₃ = 30240

Hope this helps!

The author sold a total of 30240 books following this trend.

Let's find 5% of 14400 first;

[tex]14400 * 5\%\\14400 * 5/100\\144 * 5=720[/tex]

A, is a type of numerical sequence studied by Mathematics, where each term or element counting from the second is equal to the sum of the previous term with a constant.

So using the arithmetic progression we have:

[tex]a_n = a_1 + r(n - 1)\\a_{23} = 14400 + 720(23 - 1)\\ a_{23} = 14400 + 720(22)\\ a_{23} = 14400 + 15840\\a_{23} = 30240[/tex]

See more about arithmetic progression at brainly.com/question/20385181

Answer:

A. Conditional Statement

Step-by-step explanation:

In a conditional statement, A would be the premise, and B would be the conclusion.

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Have a great summer :)

Answer:  The total number of colored papers is 18.

Step-by-step explanation:

Given: The ratio of coloured papers to wight papers is 3:8.

Let total number of colored papers = 3x

and total number of wight papers = 8x

Since, there are 48 wight papers , then

[tex]8x=48[/tex]

[tex]\Rightarrow\ x=6[/tex]

Now , number of colored papers = 3(6)=18

Hence, the total number of colored papers is 18.

Answer:

By distributing the parenthesis

Step-by-step explanation:

Given

5(3x - 6) ← multiply each term in the parenthesis by 5

= 15x - 30 ← as required

Answer:

I think it's 9/22

Step-by-step explanation:

Probability of A given B = (probability of A and B)/probability of B

[tex]\frac{(14/22)(9/22)}{14/22} \\=\frac{9}{22}[/tex]

P(B) = P(1 checked bag) = 14/22

P(A) = P(silver status) = 9/22

P(A ∩ B) = (14/22)(9/22)

Answer:

4 minutes

Step-by-step explanation:

Let the time taken for them to have the same number of strawberries be x minutes.

Initially

Ruby: 10 strawberries

Sapphire: 30 strawberries

After x minutes

Ruby: (10 +3x) strawberries

Sapphire: (30 -2x) strawberries

Since we let x minutes be the amount of time that has passed when they have the same amount of strawberries,

10 +3x= 30 -2x

Bring all x terms to one side, constant to the other:

3x +2x= 30 -10

Simplify:

5x= 20

Divide both sides by 5:

x= 20 ÷5

x= 4

∴ It will take 4 minutes.

Answer:

c

Step-by-step explanation:

If he could clean the house alone in one hour, then it wouldve taken him and his sister less than that. if he could clean it in 3 hours, it wouldve tkane him and his sister 1.5 hours.

Answer:

Step-by-step explanation:

c. 6 hours

Answer:

I don't see an O in the picture at all.

but here's how you solve it: just count the nodes between the species, the fewer the closer

I would go for E and I, only one step between them

Answer:

[tex]y = 16 + 0.2t[/tex] --- the equation of SaveMore company

Step-by-step explanation:

Given

SaveMore

[tex]Initial = 16[/tex]

[tex]Additional\ Rate = 0.20[/tex]

Required

Determine the equation

Let

[tex]y \to cost[/tex]

[tex]t \to texts[/tex]

So, we have:

[tex]y = Initial + Additional\ Rate * t[/tex]

[tex]y = 16 + 0.20 * t[/tex]

[tex]y = 16 + 0.2t[/tex]

The equation for the second company is not given. So, the (b) part cannot be correctly answered.

A general solution to the (b) part is:

Assume the equation is:

[tex]y = 10 + 0.4t[/tex]

Next, we equate both

i.e.

[tex]y = y[/tex]

This gives:

[tex]16 + 0.2t = 10 + 0.4t[/tex]

Collect like terms

[tex]0.4t - 0.2t = 16 - 10[/tex]

[tex]0.2t = 6[/tex]

Divide by 0.2

[tex]t = 30[/tex]

Hence, the charges will be the same after 30 texts

Step-by-step explanation:

hear is your both answer

Answer:

$74.36 sorry all i got

Step-by-step explanation:

First, we need to determine the sales price of the skateboard. The formula for find the discounted prices is:

Where:

is the sales price of the item: what we are solving for in this part of the problem.

is the regular price of the item: $79.16 for this problem.

is the discount rate: 12% for this problem. "Percent" or "%" means "out of 100" or "per 100", Therefore 12% can be written as  

12

100

Substituting and calculating  

gives

79.16

79.16

12

100

79.16

949.92

100

79.16

9.4992

69.6608

69.66

rounded to the nearest cent.

Now we can find the total price of the item with tax included. The formula for this is

#t = p + (p * r)

Where, this time:

is the total price: what we are solving for in this problem.

is the price of the item: it is the sales price of the item for this problem which is $69.66

is the tax rate: 6.75% or, using the same rule as in the formula above:  

6.75

100

Substituting and calculating  

gives:

69.66

69.66

6.75

100

69.66

470.205

100

69.66

4.70205

74.36205

74.36

rounded to the nearest cent.

Noah would pay a total cost (with the discount and after tax) of $74.36

Answer:

8

Step-by-step explanation:

7 x 8 = 56 56 - 4 = 52.

3 x 8 = 24 24 + 28 = 52