If the graph of the function g defined by g(x)=-2x^2+9. Is translated vertically downward by 8 units, it becomes the graph of a function f. Find the expression for f(x)

Answers

Answer 1

Answer: g ( x ) = - 2 x² + 9
If this function is translated vertically downward by 8 units it becomes:
f ( x ) = g ( x ) - 8
f ( x ) = - 2 x² + 9 - 8
Answer:
f ( x ) = - 2 x² + 1

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A bag contains 8 red marbles, 4 white marbles, and 5 blue marbles. You draw one marble at random. Find P(red and blue) A. 40/17. B. 0. C. 12/17. D. 13/16.

Answers

Sum of all marbles in the bag is 8+4+5 = 17.
Sum of red and blue marbles is 8+5 = 13.

Now, because you are picking only 1 marble it is impossible for it to be both red and blue. You would need to pick at least 2 marbles to have a chance that one is red and one is blue.

The answer is B. 0

If you are drawing only one marble then the probability of getting red and blue simultaneously is zero.

What is probability?

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

The Sum of all marbles in the bag is

8 + 4 + 5 = 17.

The Sum of red and blue marbles is

8 + 5 = 13.

Now, because you are picking only 1 marble it is impossible for it to be both red and blue. You would need to pick at least 2 marbles to have a chance that one is red and one is blue.

Therefore If you are drawing only one marble then the probability of getting red and blue simultaneously is zero.

To know more about probabilityfollow

brainly.com/question/24756209

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Connor went to New York for vacation. He spent 3 nights at a hotel and rented a car for 4 days. Jillian stayed at the same hotel, but spent 4 nights and rented a car for 5 days from the same company. If Connor paid $675 and Jillian paid $875, how much did one night at the hotel cost?

Answers

The answer for the question in problem would be $125 is the price of hotel per night. This is computed by establishing the equations from the given statements, 3x + 4y = 625 and 4x +5y = 875. And by substitution you would get the answer of 125 as the price per night n the hotel and 75 per day for the rental of car.

Answer:

The cost of one night at the hotel is $125

Step-by-step explanation:

Let the cost of each night spend in hotel is = $x

Let the cost of each day of car rented = $y

Cannor spent 3 nights at a hotel and rented a car for 4 days paid $675.

$\Rightarrow3x+4y=675$ ......(1)

Jillian also spent 4 nights in same hotel and rented a car for 5 days paid $875.

$\Rightarrow4x+5y=875$ .......(2)

Now, we solve equation (1) and (2) by substitution method

From (1) take the value of x, $x=(675-4y)/(3)$

then put in equation (2) $4*(675-4y)/(3)+5y=875$

solve,

$\Rightarrow 4*(675-4y)+5y*3=875*3$ (Taking LCM)

$\Rightarrow2700-16y+15y=2625$

$\Rightarrow y=2700-2625=75$

Now, put value of $y=75$ in value of $x=(675-4y)/(3)$

$\Rightarrow x=(675-4(75))/(3)$

$\Rightarrow x=(675-300)/(3)$

$\Rightarrow x=(375)/(3)$

$\Rightarrow x=125$

Therefore, the cost of one night at the hotel is $125

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Answers

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Answers

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Answers

The numbers represent an arithmetic progression. The difference between terms is d=7. S=a1+a2+...+an, a1=3 and an=a1+(n-1)×d=3+17×7=122 S=(a1+an)n/2=(3+122)×18/2=125×9=1125

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Answers

$3^(x+1)+3^x=324\n\n3\cdot3^x+3^x=324\n\n3^x\cdot(3+1)=324\n\n4\cdot3^x=324\ \ \ /:4\n\n3^x=81\n\n3^x=3^4\iff x=4$

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