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3 years ago

Identify the "c" value of the following quadratic equation given below. -8 = 2(x + 9)^2

1 answer:

3 0

$\bf -8=2(x+9)^2\implies -8=2(\stackrel{\mathbb{F~O~I~L}}{x^2+18x+81})\implies \cfrac{-8}{2}=x^2+18x+81 \\\\\\ -4=x^2+18x+81\implies 0=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+18}x\stackrel{\stackrel{c}{\downarrow }}{\boxed{+85}}$

You might be interested in

If $500 is invested at 8% annual interest, how much will be in the account after 3 years if it's compounded quarterly?

Alchen [17]

Answer:

FV= $634.12

Step-by-step explanation:

Giving the following formula:

Initial investment (PV)= $500

Number of periods (n)= 3*4= 12 quarters

Interest rate (i)= 0.08/4= 0.02

<u>To calculate the future value, we need to use the following formula:</u>

<u></u>

FV= PV* (1 + i)^n

FV= 500*(1.02^12)

FV= $634.12

8 0

3 years ago

Two squares are similar. The ratio of the length of square A to the length of square B is 3:5. If the length of square A is 18 m

Firlakuza [10]

Answer:

120 meters

Step-by-step explanation:

18 ÷ 3 = 6

5 x 6 = 30

30 x 4 = 120

7 0

3 years ago

How to solve this problem

Agata [3.3K]

So first, you have to get two of the same variables to cancel out. Let's do this for x. In order for the x's to cancel out, we could multiply the bottom problem by 2.
(2) 3x-6y=24
After multiplying all the numbers by 2, you get the equation 6x-12y=48
The set of equations is now
-6x+2y=12
6x-12y=48
Now you can add them. The x variables cancel out, so you are left with the y variable.
2y+-12y=-10y and 12+48=60
Then you would divide 60 by -10 to get y=-6.
You would plug the answer for y into one of the original equations, lets do the top one. -6x+2y=12 becomes -6x+2(-6)=12
You'd multiply the 2 and -6 to get -12 so the equation is
-6x-12=12
The negative 12 turn positive and you add to both sides to get the -6x alone.
-6x-12=12
+12=12
-6x=24
Then divide 24 by -6
X=4

(-4,-6) is your final answer.

7 0

3 years ago

At a school, 129 students play at least one sport. This is 30% of the students at the school. How many students are at the sc

kkurt [141]

129/x=30/100
30x=12900
x=430
430 students

3 0

4 years ago

The average maximum monthly temperature in Campinas, Brazil is 29.9 degrees Celsius. The standard deviation in maximum monthly t

kvv77 [185]

Answer:

$P(X>32)=P(\frac{X-\mu}{\sigma}>\frac{32-\mu}{\sigma})=P(Z>\frac{32-29.9}{2.31})=P(z>0.909)$

And we can find this probability with the complement rule and using the normal standard distributon table or excel we got:

$P(z>0.909)=1-P(z$

And if we convert this to a % we got 18.2 % of maximum temperatures higher or equal than 32 C

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the maximum monthly temperature of a population, and for this case we know the distribution for X is given by:

$X \sim N(29.9,2.31)$

Where $\mu=29.9$ and $\sigma=2.31$

We are interested on this probability

$P(X>32)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X>32)=P(\frac{X-\mu}{\sigma}>\frac{32-\mu}{\sigma})=P(Z>\frac{32-29.9}{2.31})=P(z>0.909)$

And we can find this probability with the complement rule and using the normal standard distributon table or excel we got:

$P(z>0.909)=1-P(z$

And if we convert this to a % we got 18.2 % of maximum temperatures higher or equal than 32 C

8 0

3 years ago