Express the following in simplest a + bi form.
root 9+ root -36
A. -9i
B. 3-6i
C. 3+6i
D. 9i

ANSWER C

Answer:

it is the frst tow numbrs 41

Step-by-step explanation:

Answer:

14.2

Step-by-step explanation:

The ladder forms a right angles triangle,

We have,

h=20

p=16

b=x

Using pythogorean theorem,

b=√(20^2-16^2)

√144

b=12

Now,

Since, she pulls it 2 cm,

b=x+2

b=14

p=?

Using pythogorean theorem,

p=√(20^2-14^2)

√204

p=14.2828568571

Rounding  to the nearest tenth,

p=14.2

The side of the ladder will reach up is 14.3 feet.

"Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. It is with respect to any of its acute angles are known as the trigonometric ratios of that particular angle".

For the given situation,

Hypotenuse, h = 20 feet

Perpendicular, p = 16 feet

Base = b

By Pythagoras theorem,

[tex]h^{2} = p^{2} + b^{2}[/tex]

⇒[tex]20^{2} = 16^{2}+b^{2}[/tex]

⇒[tex]b^{2} = 400-256[/tex]

⇒[tex]b^{2}=144[/tex]

⇒[tex]b=\sqrt{144}[/tex]

⇒[tex]b=12[/tex]

The ladder at the house is pulled 2 feet farther.

So, base = [tex]12+2[/tex]

⇒[tex]b=14[/tex]

Now, the side of the ladder will reach up

[tex]p^{2} = h^{2}-b^{2} \\[/tex]

⇒[tex]p^{2}=20^{2}-14^{2} \\[/tex]

⇒[tex]p^{2}=400-196[/tex]

⇒[tex]p^{2}=204[/tex]

⇒[tex]p=\sqrt{204}[/tex]

⇒[tex]p=14.28[/tex]

⇒[tex]p=14.3[/tex] (rounded off to nearest tenth)

Hence we can conclude that the side of the ladder will reach up is      14.3 feet.

Learn more about trigonometric ratios here

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Answer:

[tex]48 cm^2[/tex]

Step-by-step explanation:

Each of the small triangles are right, so we can add up all the small triangle's areas to find the total area.

The 4-by-10 triangle: The area is [tex]4*10/2=40/2=20[/tex].

The other 4-by-10 triangle has the same side lengths and hence the same area, so the area is [tex]20[/tex].

The 4-by-4 triangle: The area is [tex]4*4/2=8/2=4[/tex].

The other 4-by-4 triangle has the same area, [tex]4[/tex].

The total area is [tex]20+20+4+4=\boxed{48} cm^2[/tex].

Answer:

B. 7

Step-by-step explanation:

[tex] \frac{1}{2} \times 4 + 5 = 7 \\ sub \: in \: 4 \: into \: the \: equation[/tex]

Answer: 12

Step-by-step explanation:

I will assume those are coordinates.

The distance between 2 points is given by  √ (x2 − x1)^2 + (y2 − y1)^2.

Replacing the values, we get  √ (5 − 5)^2 + (6 − -6)^2 =  √0+144 = 12

Answer:

150 cm2

Step-by-step explanation:

double of triangle abc is 200

this is in middle of both

Answer:

This graph does represent a function because when you do the vertical line test, none of the x-values intercept more than once.

Step-by-step explanation:

Hope this helps!

Answer:

Yup looks correct

Step-by-step explanation:

Lol I verified using the calculator :)

Answer:

v = 5

Step-by-step explanation:

Distribute on the left:

5 ( v + 7 )

( 5 x v ) + ( 5 x 7 )

5v + 35

7v + 25 = 5v + 35

Subtract 5v from each side:

2v + 25 = 35

subtract 25 from each side:

2v = 10

Divide each side by 2:

v = 5

Answer:

-8

Step-by-step explanation:

Start by putting a dot on the number line at -3.  As we are to subtract 6, start at -3 and move 6 units to the left, arriving at -9.  Finally, recognizing that -(-1) = +1, move 1 unit to the right from -9, ending up at -8.

Answer:

c

Step-by-step explanation:

Answer:

b<-21

Step-by-step explanation:

1/3b+1<-6

1/3b<-7

*3     *3

b<-21

Answer:

b <  - 21

Step-by-step explanation:

[tex]\frac{1}{3}[/tex] b + 1 < - 6 ( subtract 1 from both sides )

[tex]\frac{1}{3}[/tex] b < - 7 ( multiply both sides by 3 to clear the fraction )

b < - 21

Answer:

x=-2,y=-2

Step-by-step explanation:

x+y=-4

x=-4-y--(3)

substitute (3) in (1)

5(-4-y) -3y=-4

-20-5y-3y=-4

-8y=16

y=16/-8

y=-2

substitute y in (3)

x=-4-(-2)

x=-2

Answer:

y = x + -2.3

x = -y - 2.3 (but why would one need this?...)

Step-by-step explanation:

(6.1 - (-9.7))/(8.4 - (-7.4)) = 15.8/15.8 = 1

6.1 = 8.4 + b

b = -2.3

Answer:

2a

Step-by-step explanation:

a+1a is the same as a+a=2a

Answer:

13/6

Step-by-step explanation:

Answer: 33/16

Step-by-step explanation:  2*16 = 32...      32+1= 33

Answer: 108

Step-by-step explanation:

If 90% are female, that means that female = 90% of 120, or 90/100 x 120

90/100 x 120 = 108, meaning that there are 108 female cows.

Answer:

10 dollars

Step-by-step explanation:

Answer:

Inequality: 20.50x + $17.75 ≤ $110

Solve: 4 people can go to the amusement park

Explaination:

Inequality:

$110 = Amount of money they have

$17.75 = Parking Cost

$20.50 = Cost of tickets per person

Because they only have $110, they can't spend more than that amount.

Therefore, the inequality would be the ticket cost per person, times the amount of people being payed for (aka x) plus the parking cost is less than or equal to the amount of money they have to spend. Hence the inequality:

20.50x + $17.75 ≤ $110

Solve:

$110 - $17.75 = $92.25 (92.25 is how much is left for tickets after subtracting the parking cost)

$20.50 x 4 = $82 (4 tickets can be bought for the price of $20.50)

$92.25 - $82 = $10.25 (10.25 isn't enough for another person)

So, the solution to the inequality is 4 people can go to the amusement park.

Answer:

very easy just follow instruction

Answer:

For #1 add up all males and females and then create a chart of how many bars males and females ate

Answer: No, it is not a unit rate

Explanation:

A unit rate is when the time value in the denominator is 1. So it would need to be "1 day" instead of "5 days" for it to be a unit rate. The term "unit" means "one".

To convert to a unit rate, we simply compute 1/5 = 0.20 to see that the unit rate is 0.20 books per day. This is the same as saying "0.20 books every 1 day", but I think the phrasing "books per day" is more common.

Answer:

1.Train b travels 125 miles in four hours.

2. Train A's speed is 50 mph and train b's speed is 31.25 mph

srry about the last one but i don't know what the answer is since i don't know the choices for it

Answer: it would be 7

Step-by-step explanation:

Because 35 divided by 5 is 7