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Oksi-84 [34.3K]
3 years ago
6

Complete the square for 5x^2+10x-16.

Mathematics
1 answer:
Lelechka [254]3 years ago
7 0
Answer = 5(x+1)^2 -21

5 {x^2 + 2x } - 16

5 {(x+1)^2 -1 } - 16
5(x+1)^2 -5 - 16

5(x+1)^2 -21
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Select the correct answer from each drop-down menu. A system of equations and its solution are given system A x-y=7 -3x+9y=-39 s
galina1969 [7]

Answer:

Step-by-step explanation:

x-y=7

-3x+9y=-39

Divide the second equation by 3

-x +3y = -13

Add this to the first equation

x-y=7

-x +3y = -13

----------------------

0x +2y = -6

Divide by 2

2y/2 = -6/2

y = -3

Now find x

x-y = 7

x -(-3) = 7

x+3 = 7

Subtract 3 from each side

x = 4

(4,-3)

Or by substitution

x-y=7  

solve for x

x = 7+y

-3x+9y=-39

Substitute y+7 in for x

-3(7+y) +9y = -39

Distribute

-21 -3y +9y = -39

Combine like terms

-21 +6y = -39

Add 21 to each side

6y = -18

4 0
3 years ago
The projected rate of increase in enrollment at a new branch of the UT-system is estimated by E ′ (t) = 12000(t + 9)−3/2 where E
nexus9112 [7]

Answer:

The projected enrollment is \lim_{t \to \infty} E(t)=10,000

Step-by-step explanation:

Consider the provided projected rate.

E'(t) = 12000(t + 9)^{\frac{-3}{2}}

Integrate the above function.

E(t) =\int 12000(t + 9)^{\frac{-3}{2}}dt

E(t) =-\frac{24000}{\left(t+9\right)^{\frac{1}{2}}}+c

The initial enrollment is 2000, that means at t=0 the value of E(t)=2000.

2000=-\frac{24000}{\left(0+9\right)^{\frac{1}{2}}}+c

2000=-\frac{24000}{3}+c

2000=-8000+c

c=10,000

Therefore, E(t) =-\frac{24000}{\left(t+9\right)^{\frac{1}{2}}}+10,000

Now we need to find \lim_{t \to \infty} E(t)

\lim_{t \to \infty} E(t)=-\frac{24000}{\left(t+9\right)^{\frac{1}{2}}}+10,000

\lim_{t \to \infty} E(t)=10,000

Hence, the projected enrollment is \lim_{t \to \infty} E(t)=10,000

8 0
3 years ago
If 35% of a number is 21 and 90% of the same number is 54, find 55% of that number.
inn [45]

Answer:

Step-by-step explanation:

The number is 60:

Divide the amount and decimal of the percentage to be extracted

Case 1

\frac{21}{0.35} =60

Case 2

\frac{54}{0.9} =60

Now the 55% of this number is:

60(0.55)=33

Hope this helps

4 0
2 years ago
Convert 3 quarts to pints
ss7ja [257]

Answer:

6 pints

Step-by-step explanation:

There are two pints in a quart, so there are 2 times 3 pints in three quarts.

Hope this helps!

4 0
3 years ago
Read 2 more answers
In a particular course, it was determined that only 70% of the students attend class on Fridays. From past data it was noted tha
siniylev [52]

Answer: Probability that students who did not attend the class on Fridays given that they passed the course is 0.043.

Step-by-step explanation:

Since we have given that

Probability that students attend class on Fridays = 70% = 0.7

Probability that who went to class on Fridays would pass the course = 95% = 0.95

Probability that who did not go to class on Fridays would passed the course = 10% = 0.10

Let A be the event students passed the course.

Let E be the event that students attend the class on Fridays.

Let F be the event that students who did not attend the class on Fridays.

Here, P(E) = 0.70 and P(F) = 1-0.70 = 0.30

P(A|E) = 0.95,  P(A|F) = 0.10

We need to find the probability that they did not attend on Fridays.

We would use "Bayes theorem":

P(F\mid A)=\dfrac{P(F).P(A\mid F)}{P(E).P(A\mid E)+P(F).P(A\mid F)}\\\\P(F\mid A)=\dfrac{0.30\times 0.10}{0.70\times 0.95+0.30\times 0.10}\\\\P(F\mid A)=\dfrac{0.03}{0.695}=0.043

Hence, probability that students who did not attend the class on Fridays given that they passed the course is 0.043.

8 0
3 years ago
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