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stiks02 [169]
3 years ago
8

If f(x)= x^2 + 5 and g(x) =5x+4, what is[f o g(6)

Mathematics
1 answer:
natulia [17]3 years ago
7 0
You can do this a couple ways: either find g(6), then find f(x) of whatever that gives you (a 2-step process), or come up with a new expression to represent f(g(x)) and sub 6 into that (a 1-step process). I like the 1-step process more.

g(x) = 5x + 4; We want to sub this expression into every x in f(x) to get f(g(x)). If f(x) = x^2 + 5, then f(g(x)) = g(x)^2 + 5 = (5x + 4)^2 + 5. Now you can sub 6 into this equation and solve: f(g(6)) = (5(6) + 4)^2 + 5 = 1161.
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A car travels 312 miles in the same time that a motorcycle traveled 272. If the cars speed is 10mph more than the motorcycles, f
dimaraw [331]

Answer: speed of the car is 88 miles per hour

the speed of the motorcycle is 78 miles per hour

Step-by-step explanation:

Number of miles travelled by car = 312

Number of miles travelled by motorcycle = 272

Let x = speed of the car

Let y = speed of the motorcycle

If the car's speed is 10mph more than the motorcycle's, it means

x = y + 10 - - -- - - 1

Time taken for car to travel 312 miles is distance /speed = 312/x

Time taken for motorcycle to travel 272 miles is distance /speed = 272/y

The car travels 312 miles in the same time that a motorcycle traveled 272.

This means

312/x = 272/y

312y = 272x

y = 272x/312

Substituting y = 272x/312 into equation 1, it becomes

x = 272x/312 + 10

312x = 272x + 3120

312x-272x = 3120

40x = 3120

x = 3120/40 = 78 miles per hour

x = y + 10 = y + 78

x = 88 miles per hour

3 0
2 years ago
The sum of two consecutive integers is at most 3. what is the greatest possible value for the greater integer?
Rudik [331]
2 consecutive integers...x and x + 1

x + x + 1 < = 3
2x + 1 < = 3
2x < = 3 - 1
2x < = 2
x < = 1

x + 1 = 1 + 1 = 2.......the greatest possible value for the greatest integer is 2
8 0
2 years ago
A contractor claims that she finishes a job on time 90%
Elina [12.6K]

Answer:

yesssiriytrewqsdfgh

Step-by-step explanation:

(1, 2), (2, 4), (3, 8), (4, 16)

Use a recursive formula to determine the time she will complete station 5. Show your work.

Geometric Recursive Formula

f(n) = f(n − 1) • r

7 0
2 years ago
Please help i need to turn it in
larisa [96]

Answer:

978 in

Step-by-step explanation:

(9x6)+(18x18)+(25x24)=978

4 0
3 years ago
Read 2 more answers
Two telephone calls come into a switchboard at random times in a fixed one-hour period. Assume that the calls are made independe
svp [43]

Answer:

0.25

Step-by-step explanation:

From the given information:

Since the times are uniform distributed over the one hour period (0,1):

Then;

f_1(y_1) = 1

f_2(y_2) = 1

So, Y_1 and Y_2 are independent; then:

f(y_1|y_2) = f_1(y_1)f_2(y_2)  \\ \\ = 1(1) = 1

P(Y_1\le 0.5 Y_2 \le 0.5) = \int ^{0.5}_{0} \int ^{0.5}_{0} f(y_1,y_2) dy_{2}dy_{1}

\implies  \int ^{0.5}_{0} \int ^{0.5}_{0} (1)  dy_{2}dy_{1}

= \dfrac{1}{4}

= 0.25

3 0
2 years ago
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