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3 years ago

If g(x) = 2x2 + 6x + 5, use synthetic division to find g(-5).

Mathematics

1 answer:

diamong [38]3 years ago

6 0

<h3>Answer: 25</h3>

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Explanation:

Check out the image below. I've posted the synthetic division table. The value at the very end of the bottom row is the remainder. By the remainder theorem, this is exactly the value of g(-5).

Recall the remainder theorem says: If you divide p(x) by (x-k), then the remainder is p(k). In this case, k = -5 is our test root which is the value placed in the box on the left.

As a way to check the answer, we can say

g(x) = 2x^2 + 6x + 5

g(-5) = 2(-5)^2 + 6(-5) + 5

g(-5) = 25

So the answer is confirmed.

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In 2019, approximately 97.4% of all the runners who started the Boston Marathon (in Boston, Massachusetts, USA) were able to com

PtichkaEL [24]

Answer:

The probability that exactly 97 of them finished the marathon is 0.221.

Step-by-step explanation:

We are given that in 2019, approximately 97.4% of all the runners who started the Boston Marathon were able to complete the 42.2 km race.

100 runners are chosen at random.

The above situation can be represented through the binomial distribution;

$P(X = x) = \binom{n}{r} \times p^{r} \times (1-p)^{n-r};x = 0,1,2,3,......$

where, n = number of trials(or samples) taken = 100 runners

r = number of success = exactly 97

p = probability of success which in our question is the probability

that runners finished the marathon, i.e; p = 0.974

So, X ~ Binom(n = 100, p = 0.974)

Now, the probability that exactly 97 of them finished the marathon is given by = P(X = 97)

P(X = 97) = $\binom{100}{97} \times 0.974^{97} \times (1-0.974)^{100-97}$

= $161700 \times 0.974^{97} \times 0.026^{3}$

= 0.221

Hence, the required probability is 0.221.

6 0

3 years ago

Easy brainliest for correct answer 100%

Alik [6]

Answer:

It would be the last option.

8 0

3 years ago

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What is the difference of 73.9 and 8.801

user100 [1]

65.009 That’s the answer

7 0

2 years ago

A motorcycle daredevil is planning a stunt to perform at a county fair. A ramp must be built to give him a 20%

Shkiper50 [21]

Answer: 95 feet

Step-by-step explanation:

Let the length of the horizontal run be represented by x.

Slope Grade = (Rise/Run) × 100

20 = (19/x) × 100

20 = 1900/x

20x = 1900

x = 1900/20

x = 95

Therefore, the length of the horizontal run must be 95 feet

5 0

2 years ago

a mechanic worked 20 hours. another mechanic worked 15 hours. together they charged a total of $1950. what was the rate charged

Natasha_Volkova [10]

Answer: The mechanics both charged $70 and $45 per hour respectively

Step-by-step explanation: We shall start by calling the mechanics hourly rates x and y respectively. So if one worked for 20 hours and charged 20 times x dollars, and the other one worked for 15 hours and charged 15 times y dollars, totalling 1950 dollars, we can write the following expression,

20x + 15y = 1950

Also, if the sum of the two rates was 115 dollars, that means for working for an hour only, they both would earn

x + y = 115

We now have a pair of simultaneous equations

20x + 15y = 1950 --------(1)

x + y = 115 ------------------(2)

We shall use the substitution method for this problem.

From equation (2), make x the subject of the equation

x = 115 - y

Substitute for the value of x into equation (1)

20(115 - y) + 15y = 1950

2300 - 20y + 15y = 1950

By collecting like terms we now have

2300 - 1950 = 20y - 15y

(Note that when a negative value crosses to the other side of the equation, it becomes a positive value and vice versa)

350 = 5y

Divide both sides of the equation by 5

70 = y

We now substitute for the value of y into equation (2)

x + y = 115

x + 70 = 115

Subtract 70 from both sides of the equation

x = 45.

Therefore, the rate they charged per hour were $45 and $70 respectively.

7 0

3 years ago