Simplify 1/3 (9a+b)-1/2 (4a+2b)

If I am understanding you correctly,  first solve for the whole sector, which you can use this formula. 

[tex] \frac{\Theta}{360} \pi r^2[/tex] 

Once you find the area of the sector, all you have to do is get the area of the triangle and then subtract the area of the triangle from the sector and that will tell you the area of CFD and CED and let you know which one is greater.

For instance, Lets find A

sector area = [tex] \frac{90}{360} \pi 10^2 = 25\pi [/tex] 

Now lets get the area of the triangle, which is 

area triangle = [tex] \frac{1}{2} bh\sin C[/tex]

area triangle = [tex] \frac{1}{2} \times 10 \times 10 \times sin 90 = 50m^2[/tex]

CED =  sector area - area of triangle = [tex] 25\pi - 50 = 28.53m^2[/tex]

Now lets find B

sector area = [tex] \frac{60}{360} \pi 12^2 = 24\pi [/tex] 

Now lets get the area of the triangle, which is 

area triangle = [tex] \frac{1}{2} bh\sin C[/tex]

area triangle = [tex] \frac{1}{2} \times 12 \times 12 \times \sin 60 = 36\sqrt(3)[/tex]

CFD = sector area - area of triangle = [tex] 24\pi - 36\sqrt(3) = 13.04m^2[/tex]

So A has the greater area base.

x+y =44

x-y=22

x = 22+y

22+y +y =44

22+2y =44

2y=22

y=11

x=22+11=33

check:

11 +33 = 44

33-11=22

 so the numbers are 11 and 33

Answer: B.  ΔMLZ

D.  ΔLMZ

E. ΔZML

Step-by-step explanation:

In the given picture we have one triangle with three vertices as

Vertex L

Vertex M

Vertex Z

To name a triangle we use the labels of the vertices of the triangle, which are commonly written in capital letters.

When we name a triangle, we can start with any vertex but we need to keep the letters in order as you go around the triangle.

Therefore, the possible names of the triangle are :-

ΔLMZ   Δ LZM    ΔMLZ    ΔMZL   ΔZLM    ΔZML

To solve this problem, let us first remember that probability is:

Probability = number of successful events / number of total events

Now, let us first calculate the probability of getting a blue marble. There are 20 blue marbles out of 50 total marbles, therefore the probability is:

P (blue marble) = 20 / 50 = 0.4

Next, let us calculate for the probability of landing tails up. There are 22 tails success out of 50 times the coin was tossed, therefore the probability is:

P (tails) = 22 / 50 = 0.44

Finally, since we want to find the Probability of getting blue and Probability of landing tails, we multiply the two:

P (blue and tails) = 0.4 * 0.44

P (blue and tails) = 0.176               (ANSWER)

Now if the choices are in fraction:

P (blue and tails) = (20 / 50) (22 / 50) = 440 / 2500

Answer:

The answer is 440/2500

Step-by-step explanation:

3) area = pi x r^2

113 = 3.14 x r^2

r^2 =113/3.14 = 35.98726

r = sqrt(35.98726) = 5.9989 round to 6 inches

answer is C 6 inches

4) G = 2.5 times smaller than 18.04

18.04/2.5 = 7.216

 answer is B0 7.216 cm

Answer: 0.1

Step-by-step explanation:

Given : The number of Democrats : 4

The number of Republicans : 6

The total number of group members =[tex]4+6+6=16[/tex]

The probability that the first member selected is Democrat :-

[tex]\dfrac{4}{16}=\dfrac{1}{4}[/tex]

Now, the total number of group members left = 15

The probability that the second member selected is Republican  :-

[tex]\dfrac{6}{15}=\dfrac{2}{5}[/tex]

Now, the required probability will be :_

[tex]\dfrac{1}{4}\times\dfrac{2}{5}=\dfrac{1}{10}=0.1[/tex]

Jacqueline's car gets 12 km per liter of gasoline. Therefore, on a full 50 L tank, she would be able to drive 600 km.

To solve this problem, we need to determine Jacqueline's rate of distance traveled per liter of fuel consumed, then scale this up to find out how far she could theoretically drive on a full tank of 50 liters of gasoline. Jacqueline drove 72 km on 6 L of gasoline, so she is driving at a rate of 72 km / 6 L = 12 km/L.

To find out how far she could drive on a full tank of 50 L of gasoline, we can multiply this rate (12 km/L) by the total volume of the tank. This gives us 12 km/L * 50 L = 600 km.

So using this rate, Jacqueline would be able to drive 600 km on a full 50 L tank of gasoline, assuming that her car’s fuel efficiency stays consistent.

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Jacqueline can travel 600 km on a full tank of 50 L.

First, set up the proportion based on the given information,

Distance travelled / Gasoline used = Unknown distance / Full tank

This gives us:

72 km / 6 L = X km / 50 L

Now, solve for X by cross-multiplying and then dividing,

72 km * 50 L = 6 L * X km

3600 kmL = 6X kmL

3600 kmL / 6 = X km

X = 600 km

Therefore, Jacqueline can travel 600 km on a full tank of 50 L of gasoline.

Final answer:

To solve 3/4x = 1/5, cross multiply and simplify to get 15 = 4x. Divide both sides by 4 to find x = 3.75 or 15/4.

Explanation:

To solve the equation 3/4x = 1/5, we need to find the value of x that makes the equation true. First, we will cross multiply to get rid of the fractions. We multiply both sides of the equation by 4x and by 5, resulting in 5 × 3 = 4x × 1, which simplifies to 15 = 4x.

To find the value of x, we then divide both sides of the equation by 4, yielding x = 15/4. Therefore, the solution to x is 3.75 or ⅔.

Angle L in triangle JKL is [tex]\( 180^\circ - (72^\circ + 36^\circ) = 72^\circ \)[/tex]. Therefore, angle L measures [tex]\( 72^\circ \).[/tex]

1. Start with the fact that triangle JKL is isosceles, which means that angles J and K are congruent.

2. Given that angle J measures [tex]\( 72^\circ \)[/tex] and angle K measures \( 36^\circ \), the sum of angles J and K is [tex]\( 72^\circ + 36^\circ = 108^\circ \).[/tex]

3. Since the triangle is isosceles, the base angles (angles J and K) are congruent, so each measures half of the sum of angles J and K, which is [tex]\( \frac{108^\circ}{2} = 54^\circ \).[/tex]

4. Since angle L is the remaining angle in the triangle and the sum of the angles in a triangle is \( 180^\circ \), we subtract the sum of angles J and K from [tex]\( 180^\circ \)[/tex] to find the measure of angle L: [tex]\( 180^\circ - 108^\circ = 72^\circ \)[/tex].

5. Therefore, angle L measures [tex]\( 72^\circ \)[/tex].

he needs  1/4 gallon total

4 walls so need to divide 1/4 x 4

1/4 / 4/1 = 1/4 * 1/4 = 1/16 gallon on each wall

Answer:

He needs [tex]\frac{1}{16}[/tex] of gallon to paint each wall.

Step-by-step explanation:

Given :  He needs 1/4 of a gallon to paint all four walls .

To Find : How much paint will he need for each of his 4 walls if he uses the same amount of paint on each .

Solution:

He needs 1/4 of a gallon to paint all four walls .

He need paint to color 1 wall = [tex]\frac{\frac{1}{4}}{4}[/tex]

                                               = [tex]\frac{1}{16}[/tex]

Hence he needs [tex]\frac{1}{16}[/tex] of gallon to paint each wall.

Answer:9953.46M squared

Step-by-step explanation:

The probability of getting the desired outcome is 5/12.

Like "point" and "time," the concept of "the likelihood of anything" is one of those concepts that we can't precisely describe but that are nevertheless helpful. The four most popular approaches to probability are classical, empirical, subjective, and axiomatic.

Given flip a coin and roll a 6-sided die. to find the probability that you will flip a head and roll less than a 6. since there are two events that are separated from each other hence we need to find out the probability of both P(a∪b). hence,

probability of getting head on a coin flip P(a) = 1/2

probability of getting less than 6 on dice roll P(b) = 5/6

Probability of getting both the vent simultaneously = P(a) * P(b)

Therefore, the Probability of getting flipped a head and rolling less than a 6 is 5/12.

Learn more about probability here:

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