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3 years ago

Which of the following statements have the same result? Explain each step in solving each one.

1 answer:

6 0

$f(x) = 5x + 1\\\\subtitute\ x = 1\ to\ the\ equation\\\\f(1) = 5\cdot1 + 1 = 5 + 1 = 6\\----------------------\\f(x)=\dfrac{2x+3}{5}\to y=\dfrac{2x+3}{5}\ \ \ \ |multiply\ both\ sides\ by\ 5\\\\5y=2x+3\ \ \ \ |subtract\ 3\ from\ both\ sides\\\\2x=5y-3\ \ \ \ \ |divide\ both\ sides\ by\ 2\\\\x=\dfrac{5y-3}{2}\\\\f^{-1}(x)=\dfrac{5\cdot(-1)-3}{2}=\dfrac{-5-3}{2}=\dfrac{-8}{2}=-4\\---------------------\\3y-7=y+5\ \ \ |add\ 7\ to\ both\ sides\\3y=y+12\ \ \ \ |subtract\ y\ from\ both\ sides\\2y=12\ \ \ \ |divide\ both\ sides\ by\ 2\\y=6$

Answer: f(1) when f(x) = 5x + 1 and 3y - 7 = y + 5

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3 years ago

Read 2 more answers

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Answer:

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Step-by-step explanation:

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No sé si es del todo correcto, ¡pero que tengas un buen día!

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3 years ago

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taurus [48]

Answer:

-0.45 or 9/20

Step-by-step explanation:

6 0

3 years ago

Write the prime factorization for 65,169

posledela

Let's try to find some primes that divide this number.

The number is not divisible by 2, because it is odd.

The number is divisible by 3 though, because the sum of its digits is:

$6+5+1+6+9=27=3\cdot 9$

So, we can divide the number by 3 and keep going with the factorization:

$65169\div 3 = 21723$

This number is again divisible by 3, because

$2+1+7+2+3 = 15 = 3\cdot 5$

We have

$21723\div 3 = 7241$

This number is no longer divisible by 3. Let's go on looking for primes that divide it: 5 doesn't because the number doesn't end in 0 nor 5. This number is not divisible by 7 or 11 either (just try). It is divisible by 13 though: we have

$7241\div 13 = 557$

And 557 is prime, so we're done. This means that the prime factorization of 65169 is

$3^2\cdot 13 \cdot 557$

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3 years ago

Abel Alonzo, Director of Human Resources, is exploring employee absenteeism at the Plano Power Plant. Ten percent of all plant e

Alex17521 [72]

Answer: 0.23

Step-by-step explanation:

Given : F is the event "works in the finishing department;"

and A is the event "is absent excessively."

Given : 10% of all plant employees work in the finishing department; 20% of all plant employees are absent excessively; and 7% of all plant employees work in the finishing department and are absent excessively.

i.e. P(A)= 0.20 ; P(F)=0.10 ; P(A ∩ F) = 0.07

We know that $P(X\cup Y)=P(X)+P(Y)-P(X\cap Y)$

Then,

$P(A\cup F)=P(A)+P(F)-P(A\cap F)\\\\\Rightarrow\ P(A\cup F)=0.20+0.10-0.07=0.23$

Hence, the required answer is $P(A\cup F)=0.23$

5 0

3 years ago