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NemiM [27]
3 years ago
8

Use the following function to find the value of each operation.

Mathematics
1 answer:
Murljashka [212]3 years ago
8 0
<h2>Evaluating Composite Functions</h2><h3>Answer:</h3>

w(f(m(2))) = 593

<h3>Step-by-step explanation:</h3>

We can write how w(f(m(x))) will be defined but that's too much work and it's only useful when we are evaluating w(f(m(x))) with many inputs.

First let's solve for m(2) first. As you read through this answer, you'll get the idea of what I'm doing.

Given:

m(x) = -4x +1

Solving for m(2):

m(2) = -4(2) +1 \\ m(2) = -8 +1 \\ m(2) = -7

Now we can solve for f(m(2)), since m(2) = -7, f(m(2)) = f(-7).

Given:

f(x)=3x-1

Solving for f(-7):

f(-7)=3(-7)-1 \\ f(-7) = -21 -1 \\ f(-7) = -22

Now we are can solve for w(-22). By now you should get the idea why w(f(m(2))) = w(-22).

Given:

w(x) = x^2 -5x -1

Solving for w(-22):

w(-22) = (-22)^2 -5(-22) -1 \\ w(-22) = 484 -5(-22) -1 \\ w(-22) = 484 +110 -1 \\ w(-22) = 593

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Sonali invests 15% of her monthly salary in insurance policies.
strojnjashka [21]

Answer:

₹42,500

Step-by-step explanation:

Let Sonali's monthly income be ₹x

<h2>According to the question </h2>

15\% \:ofx + 55\% \: of \: x + 12750 = x

=  >  \frac{15}{100} x +  \frac{55}{100} x + 12750 = x

=  >  \frac{70}{100} x + 12750 = x

=  > 12750 = (1 -  \frac{70}{100} )x

=  > 12750 = 30x

=  > x =  \frac{12750 \times 10}{3}

=  > 42500

So your answer will be ₹42,500.

3 0
2 years ago
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A safe has a 4- digit code and no digit can be repeated what is the probability that the code has all even digits
n200080 [17]

Answer:

Step-by-step explanation:

5 0
3 years ago
Angle Q measures 30 degrees. If angle Q is rotated 15 degrees, what is the measure of angle Q'? 30 degrees 45 degrees 150 degree
scoray [572]
The correct answer is 30 degrees
8 0
3 years ago
Read 2 more answers
What’s the equation in vertex form?
pshichka [43]

Answer:

\large\boxed{y=(x+5)^2-64}

Step-by-step explanation:

\text{The vertex form of equation}\ y=ax^2+bx+c:\\\\y=a(x-h)^2+k\\\\h=\dfrac{-b}{2a},\ k=f(h)\\\\\text{We have the equation:}\ y=x^2+10x-39\to x=1,\ b=10,\ c=-39.\\\\\text{Substitute:}\\\\h=\dfrac{-10}{2(1)}=\dfrac{-10}{2}=-5\\\\k=f(-5)=(-5)^2+10(-5)-39=25-50-39=-64\\\\\text{Finally:}\\\\y=1(x-(-5))^2-64=(x+5)^2-64

8 0
3 years ago
Volume of cylinder in terms of pi
amid [387]

The formula to calculate the volume of a cylinder is: V = Π h r², that is, Pi per height per radius squared Steps to follow: one When calculating the volume of a cylinder, you will need to measure the height (h) of the cylinder, a value that sometimes also receives the name of length. Let's give a concrete example to be able to apply the formula and that way you understand better how to carry out the operations. In this way, we will assume that the height or length of the cylinder is 10 cm. two On the other hand, you must also have the measure of the radius (r) of the cylinder, that is, the distance from the outer edge to the center of the circle that serves as the base of this polyhedral figure. Make sure you use the same unit of measure for each dimension, if they are expressed in different units, you must do the conversion to obtain the equivalence. Following the example, let's give the radio a value of 3 cm 3 So, knowing that the formula to calculate the volume of a cylinder is: V = Π h r² We just need to know how much pi is worth, remember? Yes, we can round it to 3.14 and, therefore, we will only need to substitute each value in the formula. Next, you must calculate the square of the radius (r²), multiplying the value by itself and then multiply the result of the height by Pi, by the result of the radius squared. V = 3.14 x 10 x 3² = 3.14 x 10 x 9 = 282.6 cm³ Remember to write the answer in the appropriate cubic unit of measure. So you can understand where you get the formula to calculate the volume of a cylinder: If you disarm a cylinder in your hands you will have two equal circles and a rectangle, right? First you must use the formula to take out the area of ​​a circle that is: A = (Π) (r²) When you get the area of ​​the circle you multiply it by the height of the cylinder and the result is the volume of the cylinder. Always remember to be careful with the units of measurement you use in calculations.

6 0
3 years ago
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