There are 600 students at a middle school. If 60% of the students are girls, how many students at the middle school are girls?

OOF I need help-

Answer:

A

Step-by-step explanation:

Not much of a reason but thats what i g ot

Answer:

a

Step-by-step explanation:

Answer:

m∠ABG = 20 degrees

m∠BCA = 22 degrees

m∠BAC = 118 degrees

m∠BAG = 59 degrees

DG = 4

BE = 12.4

BG = 11.7

GC = 20.4

Step-by-step explanation:

The given parameters are;

m∠CBG = 20°, m∠BCG = 11°

The incenter of a triangle is the point where the three bisectors of ΔABC meets

m∠ABG = m∠CBG = 20° by definition of angle bisector

m∠ABG = 20°

m∠ACG = m∠BCG = 11° by definition of angle bisector

m∠BCA = m∠ACG + m∠BCG = 11° + 11° = 22°

m∠ABC = m∠ABG + m∠CBG = 20° + 20° = 40°

m∠BAC = 180° - (m∠BCA+m∠ABC) = 180° - (40° + 22°) = 118°

m∠BAG = m∠CAG by definition of angle bisector

m∠BAC = 118° = m∠BAG + m∠CAG = m∠BAG + m∠BAG = 2 × m∠BAG

2 × mBAG = 118°

m∠BAG = 118°/2 = 59°

m∠BAG = 59°

Given that "G" is the incenter of the triangle ABC, we have;

GF = GE = DG = The radius of the incircle of the triangle = 4

Therefore, by Pythagoras' theorem, we have;

BG = √(11² + 4²) = √137 ≈ 11.7

BE = √((BG)² + 4²) = √(137 + 4²) = √153 ≈ 12.4

GC = √(20² + 4²) = √416= 4·√26 ≈ 20.4

Applying the definition of the incenter of a triangle, the measures in triangle ABC where G is the incenter are:

Recall the following facts about the incenter of a triangle:

The incenter of a triangle is the point where the three angle bisectors that divides each angle vertex into two intersect each other.

The incenter also, is a point equidistant to all three sides of the triangle at right angle.

Applying the properties above, the measures in the image can be calculated as shown below.

[tex]m \angle EBG = 20^{\circ}\\\\m \angle ECG = 11^{\circ}\\\\CF = 20\\\\EG = 4\\\\BD = 11[/tex]

Find [tex]m \angle ABG[/tex]:

[tex]m \angle ABG = m \angle EBG[/tex] (angle bisector definition)

[tex]\mathbf{m \angle ABG = 20^{\circ}}[/tex]

Find [tex]m \angle BCA[/tex]:

[tex]m \angle BCA = 2(m \angle ECG)[/tex] (angle bisector definition)

[tex]m \angle BCA = 2(11)\\\\\mathbf{m \angle BCA = 22^{\circ}}[/tex]

Find [tex]m \angle BAC[/tex]:

[tex]m \angle BAC = 180 - (m \angle CBA + m \angle BCA)[/tex] (sum of triangle definition)

[tex]m \angle BAC = 180 - (40 + 22)\\\\\mathbf{m \angle BAC = 118^{\circ}}[/tex]

Find [tex]m \angle BAG[/tex]:

[tex]m \angle BAG = \frac{1}{2} (m \angle BAC)[/tex] (angle bisector definition)

[tex]m \angle BAG = \frac{1}{2} (118)\\\\\mathbf{m \angle BAG = 59^{\circ}}[/tex]

Find DG:

[tex]DG = EG[/tex] (Perpendicular bisectors of the sides of a the triangle are equal in length from the incenter of a triangle)

[tex]\mathbf{DG = 4}[/tex]

Find BG:

[tex]BG = \sqrt{BD^2 + DG^2}[/tex] (Pythagorean Theorem)

[tex]BG = \sqrt{11^2 + 4^2} \\\\BG = \sqrt{137} \\\\\mathbf{BG = 11.7}[/tex]

Find BE:

[tex]BE = \sqrt{BG^2 - EG^2}[/tex] (Pythagorean Theorem)

[tex]BE = \sqrt{11.7^2 - 4^2} \\\\BE = \sqrt{120.89} \\\\\mathbf{BE = 10.99}[/tex]

Find GC:

[tex]GC = \sqrt{CF^2 + FG^2}[/tex] (Pythagorean Theorem)

[tex]GC = \sqrt{20^2 + 4^2} \\\\GC = \sqrt{416} \\\\\mathbf{GC = 20.4}[/tex]

In summary, applying the definition of the incenter of a triangle, the measures in triangle ABC where G is the incenter are:

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Answer:

I think answer is

D. X=4

:-))

It is a right triangle. The distance is the hypotenuse of the triangle.

Use the Pythagorean theorem:

Distance = sqrt(3^2 + 2^2)

Distance = sqrt( 9 + 4)

Distance = sqrt(13) (exact distance)

As a decimal sqrt(13) = 3.60555

Answer:

I think it is 10 km/hr

Step-by-step explanation:

5 hrs = 40 more with 2 km/hr current

2 hrs= less 40 no current

40-2x5=30

30 without current for three hours

30/3=10 km/hr no current

CHECK

10x2=20

10x5=50+2x5=60

The speed of the motorboat in still water is 10 km/hr

A motorboat travels downstream on a river for 5 hours.      

The speed of the current = 2 km/h

The river flows into a still lake and the motorboat continues for two more hours.

The distance covered by the boat on the river was 40 km more than the distance that was covered on the lake.

We have to determine the speed of the motorboat in still water

Let the speed of motorboat in still water = m km/h

Given that

The speed of river current = 2 km/hr

The river runs into a still lake

The motorboat continues to travel for 2  more hours

The distance traveled by the motorboat in two more hours in the lake  = 2m km

The distance covered by the boat in the river = (40 +2m)   km

Net speed of the boat in the river = (m +2 ) km/hr

Let t  be the time spent by motorboat into the river.

[tex]\rm Time = \dfrac{Distance}{Speed}[/tex]

[tex]\rm t = \dfrac{40+2m }{m +2}..........(1)[/tex]

Given that the motorboat travels downstream of the river for 5 hrs

so on putting t = 5 in equation (1).

[tex]\rm 5 = \dfrac{40 +2m }{m+2}\\\\5m +10 = 40 +2m\\5m -2m = 40-10\\3m = 30\\m = 10 km/h[/tex]

So the speed of the motorboat in still water is 10 km/hr

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Answer:

Step-by-step explanation:

we know that the interior angles are supplementary,

(2x-10)+(4x+16)=180

2x-10+4x+16=180

6x=180+6

6x=186

x=31

Answer:

your answer,

you can answer 15 math problems in 12 minutes

Answer:

45

Step-by-step explanation:

Answer:

125 times out of 200 spins or 125/200

Step-by-step explanation:

Set up your equation:

5/8 = x/200

Cross Multiply:

1000 = 8x

x = 125

Answer:

(1, 6)

Step-by-step explanation:

Use elimination or substitution (elimination is easier)

Answer:

22.5% increase.

Step-by-step explanation:

Because her collection grows by 9, that means it increases by 9/40 total. As a decimal, this would be 0.225. Then, as a percent you multiply that by 100 to get 22.5%. Pilar's collection increased by 22.5%

Answer:

hahaha is

easy hmm..........

Answer:

15.83 servings

Answer:

1/5. d

Step-by-step explanation:

sorry if I'm wrong

Answer: 3

Step-by-step explanation:

From the question, we are informed that Johnny has 30 marbles while Mark has m marbles.

Since Johnny has 10 times as many marbles as Mark, it means that Johnny has: = 10 × m = 10m

Therefore, 10m = 30

m = 30/10

m = 3

Mark has 3 marbles

Answer:

What is the LCM of 60 and 108? The LCM of 60 and 108 is 540.

Step-by-step explanation:

What is the LCM of 60 and 108? The LCM of 60 and 108 is 540.

The HCF of 60 and 108 is 540.

For given question,

We have been given the HCF of 60 and 108 is 12.

We know, the product of LCM and HCF of numbers is equivalent to the product of the given numbers.

⇒ LCM × 12 = 60 × 108

⇒ LCM = 540

Therefore, the HCF of 60 and 108 is 540.

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Answer: She should sell her artwork for $39.60 or almost $40.

Step-by-step explanation:

First you need to find out what 80% of 22 is, which is 17.6, then you add that price to the price of her supplies.

22+17.6=$39.60

Answer:

y= -2x +13

Step-by-step explanation:

The total amount of income Xander earns from selling y books algebraically is C = 25000 + xy + 0.08y.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenarios.

In this situation, Xander writes math textbooks that sell x dollars each, he received a bonus of $25,000 for signing a contract, and he receives 8% commission on each book sale.

c = total amount

y = number of books.

The total amount of income will be:

= 25000 + (x × y) + (8% × y)

= 25000 + xy + (0.08 × y)

C = 25000 + xy + 0.08y

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Answer:

40

Step-by-step explanation:

I hope this helps!

Answer:

40

Explanation:

Multiply -4 by 5

Then, Multiply -20 by -2

Which equals 40

Hope this helps:)

Answer:

24/30-5/30=19/30

this is the answer

Answer:

It's 24/30 and 5/30 and it's 19/30

Step-by-step explanation:

Answer:

Step-by-step explanation:

16 divided by $3.50 = 4.5

Answer:

0.286 pounds

Step-by-step explanation:

one pound=$3.50

x pounds=$1.00

then

1/3.5=0.286 pounds

check:

0.285 pounds per dollar x $3.50=1 pound

Answer:

11

Step-by-step explanation:

90-35=55

55=5x

x=11

good luck

Given:

m || QR

To find:

The measure of ∠QPR.

Solution:

Since m || QR and a transversal line intersect them, therefore the alternate interior angles are equal.

Let points S and T lie on the line m. S is on the right and T is on the left side of point P.

[tex]m\angle RPS=m\angle PRQ[/tex]

[tex]m\angle RPS=45^\circ[/tex]

Now, angles TPQ, QPR and RPS lie on the one side of a straight line. It means, their sum is 180 degrees.

[tex]m\angle TPQ+m\angle QPR+m\angle RPS=180^\circ[/tex]

[tex]50^\circ+m\angle QPR+45^\circ=180^\circ[/tex]

[tex]m\angle QPR+95^\circ=180^\circ[/tex]

[tex]m\angle QPR=180^\circ-95^\circ[/tex]

[tex]m\angle QPR=85^\circ[/tex]

Therefore, the measure of angle QPR is 85 degrees.

Answer:

9q^3+293

Step-by-step explanation:

Answer:

2 lbs

Step-by-step explanation:

it's kind of just a guess, the question is not that clear.

Answer:

Yes, it is

Step-by-step explanation:

For the first part is 10 per people = y = 10x

And the second part is 2 per people = y = 2x

So the two equations are

y = 10x

and

y = 2x

Hope this helped!

Have a supercalifragilisticexpialidocious day!

Answer:

this is an iscoceles triangle.

I know this because 2 of the sides are equal in length

Therefore,

AB=AC

3x-5=-2x+15

x-5=15

x=20

if x=20 then BC=2(20)

BC=40

Step-by-step explanation: