what rational function is represented by g(x)?

Answer:

AC = 12

Step-by-step explanation:

If BC is parallel to DE then ∠D ≅ ∠B and ∠E ≅ ∠C. Therefore

ΔABC is similar to ΔADE.

The sides of smaller triangle are in proportion with sides of bigger triangle.

Therefore we have the equation:

AC/AE = AB/AD

Substitute the given numbers:

x/x+15 =8/18

18x= 8(x+15)

18x = 8x+120

10x = 120

x = 12

AC=12

To find the surface area of a cylinder, the formula is.

Where diameter, d, and height, h, is given below as,

Where radius, r, is half of the diameter,

Substituting for r and h into the surface area formula above,

Hence, the surface area of the cylinder is 979.68m²

Answer: 7

Step-by-step explanation:

3 x 3 = 9 - 2(3)+4

9-6+4

=7

Answer:

10.7 miles/hour

Step-by-step explanation:

So let's first write all the known for the question

total race = 5 mile

Rafe time 3:30~4:00pm

Sebastian time 4:25~4:53 pm

Then let's find out how much time rafe and sebastian took for races in hours and who took less time(who's faster)

Rafe time 30 min = 0.5 hours

Sebastian time 28 min = 0.467 hours

0.467 < 0.5 hours

-Hence Sebastian had faster speed.

Now let's calculate the speed of Sebastian

5 mile/0.467 hours= 10.714

Round to nearest tenth

10.7 miles/hour

Answer:

look at the explanation

Step-by-step explanation:

for f(x) and g(x) to be inverse,

f(g(x))=g(f(x))=x

The side lengths from least to greatest as follows:

IK < KL < IJ < IL < LJ

To order the side lengths IK, KL, IJ, IL, and LJ from least to greatest, we can analyze the given figure.

Since the figure is not drawn to scale, we cannot determine the exact lengths of the sides. However, we can make some observations based on the given angles.

Let's analyze the angles:

Angle L: Since angle L is marked as 47°, we know that side KL is the shortest side, as it is opposite to the smallest angle in a triangle.

Angle I: Since angle I is marked as 20°, we can infer that side IJ is longer than side IK, as it is opposite to a larger angle.

Angle LJ: Since angle LJ is marked as 89°, we can conclude that side LJ is the longest side, as it is opposite to the largest angle in the triangle.

Based on these observations, we can order the side lengths from least to greatest as follows:

IK < KL < IJ < IL < LJ

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Answer:

12 with a remainder of 3

Step-by-step explanation:

hope this helps

Answer:

x = 41.05

Step-by-step explanation:

Given that,

In a right angles triangle,

Perpendicular height, P = 228

Angle 1 = 90°

Angle 2 = 47°

Angle 3 = 180-(90+47) = 43°

Using trigonometry to find x.

\(\sin\theta=\dfrac{P}{x}\\\\x=\dfrac{P}{\sin\theta}\\\\x=\dfrac{28}{\sin(43)}\\\\x=41.05\)

So, the value of x is equal to 41.05.

The area of the shaded region is 0.725746882.

The probability distribution of random variables is described using the cumulative distribution function. The probability for a discrete, continuous, or mixed variable may be described using it. The cumulative probability for a random variable is calculated by adding the probability density function.

Given:

The graph depicts the IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. 91.

From the diagram,

the critical value is 91.

The formula to calculate the z-score is,

z = (x - u) / s,

Substituting the given values to the formula,

the given values are;

x = critical value = 91

u = mean = 100

s = standard deviation = 15

Thus,

z = (x - u) / s

z = -0.6

P(z > -0.6 ) = 0.725746882

Therefore, the area is 0.725746882.

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Answer:

6^7

Step-by-step explanation:

So, there are 5 widowed people (3+2) and there are 3 females in the widowed category. So:-

3/5*100 = 60%

After 2 hours, Zoe and Wanda will complete the same total number of shirts.

Each tailor will finish 18 shirts.

What is linear equation?

An algebraic equation of the form y=mx+b is referred to as a linear equation. m is the slope, and b is the y-intercept, and all that is involved is a constant and a first-order (linear) term. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Given that,

Zoe can embroider 2 shirts per hour, and Wanda can get through 6 shirts per hour. Zoe has already completed 14 shirts, and Wanda has completed 6 shirts.

Assume that after x hours they have finished the same total number of shirts.

The number of shirts that Zoe finished is

Z(x) = 14 + 2x ....(i)

The number of shirts that Wanda finished is

W(x) = 6 + 6x ...(ii)

When they make same number of shirts, then Z(x) = W(x)

14 + 2x = 6 + 6x

6 + 6x = 14 + 2x

Subtract 2x from both sides:

6x - 2x = 14 - 6

4x = 8

Divide both sides by 4

x = 8/4

x = 2.

Putting x = 2 in Z(x) = 14 + 2x:

Z(2) = 14 + (2×2)

Z(2) = 18

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Answer:

-2x + 10

Step-by-step explanation:

3 - x + 4 - (x - 3)

1. Combine like terms:

-x + 7 - (x - 3)

2. Apply the distributive law - (a - b) = -a + b :

-x + 7 -x + 3

3. Combine like terms:

-2x + 10

hope this helps!

Answer:

yo- ehm I think itssss 2 > -4

Step-by-step explanation:

Answer:

The percentage Jamie ate is 20%.

Step-by-step explanation:

To find our answer we will first divide 100 by 15 and we get 6.666666666666667.  Now multiply it by it by 3 and we get 20%.  Therefore, 20% is our answer.

Answer:

4 m

Step-by-step explanation:

Answer:

4m

Step-by-step explanation:

Answer:

In the beginning, there is 60 L of water in the bathtub. The water drains out from the bathtub at 2.5 L per minute. How many minutes does it take until all of the water is drained out?

Zero of the function: (24, 0)

The value 24 min represents the number of minutes it takes for the water to completely drain out from the bathtub.

Step-by-step explanation:

Zero of the function is when y=0

0 = 60 -2.5 x

x = 24

Answer:

The mathematical expectation of a student who purchases 10 tickets is -$39.65.

Step-by-step explanation:

A student that purchases 10 tickets out of 2900 has a probability of winning the cruise that can be calculated as:

\(p=10/2900\approx0.00345\)

Each ticket cost $5, so he has spent $50 for the 10 tickets.

Then, the expected value of this operation is equal to the expected value of the earnings (probability of winning the prize multiplied by the value of the prize), minus the costs:

\(E(X)=p\cdot R-C\\\\E(X)=0.00345\cdot3000-50=10.35-50=-39.65\)

The mathematical expectation of a student who purchases 10 tickets is -$39.65.

The image coordinates of K′ if the preimage is reflected across y = −7 is (-4, -8)

Based on the given question, we have certain variables that can be utilized for our calculations.

K = (-4, -6)

First, find the equation of the reflection line

The reflection line is y = -7.

This can be expressed as

y = a = -7

The image of the reflection is then calculated as

K' = (x, -(y + 2|a|))

Replace the given or established values in the equation mentioned earlier, resulting in the following expression

K' = (-4, -(-6 + 2 * 7))

Evaluate

K' = (-4, -8)

Hence, the image coordinates of K′ are (-4, -8).

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The area of the rectangular figure with two semicircles on the opposite side is  36.56 sq cm.

The circumference of a circle is the distance around the circle which is 2πr.

The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.

Given, A rectangle with two semicircles on two opposite sides.

The length of the rectangle is 6cm and the width of the rectangle is 4cm.

The two given semicircles have a diameter of 4cm seems obvious.

∴ The area of the total figure is an area of the rectangle added to the area of 2 semicircles which makes up to a circle with a radius 2 cm.

∴ (4×6) + π(2)² sq cm.

= 24 + 4π sq cm.

= 24 + 12.56 sq cm.

= 36.56 sq cm.

The area which is not taken up in the rectangle and two circle questions are

(area of the rectangle - 2 times the area of a circle).

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Answer:

x = 16°

Step-by-step explanation:

What we know:

∠JML = 47°

∠JKL = (7x + 21)°

∠JML is an inscribed angle

∠JKL is an inscribed angle

Inscribed angles are half of the value of their intercepted arc

So if m∠JML = 47° then mArc JL is double that or 94°

And ∠JKL is intercepted by Arc JML which is the rest of the circle not intercepted by ∠JML so

mArc JL + Arc JML = 360°

94 + Arc JML = 360

Subtract 94 from both sides to isolate Arc JML

Arc JML = 266°

So if Arc JML = 266° then it's intercepted inscribed angle is half of that.

Arc JML ÷ 2 = ∠JKL

266 ÷ 2 = ∠JKL

133 °= ∠JKL

Now we can use this value and set it equal to the expression to find the value of x

(7x + 21) = 133

Subtract 21 from both sides to isolate the x

7x = 112

Divide both sides by 7

x = 16

Answer:

D. \sqrt(384)

Step-by-step explanation:

All you have to do is to expand the root the way I have done. I hope you understand and rate this answer well.

Don't forget 8 is the same as root(8) * root(8) which will give root(64) and the square root of 64 is 8.

Answer:

The scale ratio of 1:87.1 means that for every 1 unit of measurement on the model (in this case, inches), there are 87.1 units of measurement on the actual railroad car. This means that the actual railroad car is 87.1 times larger than the model in every dimension. If the model is 1.4 inches tall, the actual railroad car would be 1.4 x 87.1 = <<1.4*87.1=122.54>>122.54 inches tall.

Answer:

6

Step-by-step explanation:

1/3 times 6 = 2

2 +  6 = 6

Answer:

53 degrees

Step-by-step explanation:

Answer:

53

Step-by-step explanation:

Angle D = Angle F as they are vertical angles :)))

Answer:

Step-by-step explanation:

We have the equation:

11 ÷ 132 = 0.083333

Calculated to 6 decimal places.

     0 0. 0 8 3 3 3 3

1 3 2 1 1. 0 0 0 0 0 0

   − 0              

     1 1            

   −   0            

     1 1 0          

   −     0          

     1 1 0 0        

   − 1 0 5 6        

         4 4 0      

       − 3 9 6      

           4 4 0    

         − 3 9 6    

             4 4 0  

           − 3 9 6  

               4 4 0

             − 3 9 6

                 4 4

Answer:50000000000000000000000000000000000000000000000000000