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DerKrebs [107]
4 years ago
14

Solve the following quadratic equation for x by completing the square and solve x^2-8x=-65​

Mathematics
1 answer:
Licemer1 [7]4 years ago
7 0

Answer:

x= 4-7i  x= 4+ 7i

Step-by-step explanation:

step 1 : make equation = 0

x^{2} - 8x + 65 = 0

step 2 : solve for x [ using the quadratic equation]

ie :     x = -b ± \sqrt{b^{2}-4ac} / 2a

so it will look like this

x= -(-8) ± \sqrt{(-8)^{2} - 4(1)(65)} /2(1)

when you simplify you wont be able to root the -196 so you will have to separate the roots

x = 8 ±( \sqrt{-1} )( \sqrt{196}) / 2

now there is a rule for negative roots whereby  \sqrt{-1} is equivalent to i so now you will change \sqrt{-1} into i

Simplify \sqrt{196}

which will give you 14

now place all the new values into the formula

8 ± 14i /2

you can then further simplify to  

4 ± 7i

step 3 : separate

this will give you the final answer of

x= 4 + 7i   x= 4- 7i

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Maddy Evans drove 200 miles in the same amount of time that it took a turbo plane to travel 1200 miles at the speed of the plane
Romashka [77]
Maddy Evans:

D = rt

200 = xt

Turbo Plane:

D = rt

1200 = (200 + x)t

This is all that can be done with the information you provided. There is missing information here.
6 0
4 years ago
The first term in a geometric sequence is 54, and the 5th term is 2 / 3. Find an explicit form for the geometric sequence.
quester [9]

Answer:  ar^{n-1}=54(\dfrac{1}{3})^{n-1}

Step-by-step explanation:

The nth term for a geometric sequence is given by :-

a_n=ar^{n-1}    (1)

We are given that The first term in a geometric sequence is 54. i.e. a=54

5th term=\dfrac{2}{3}   (2)

Put n=5 and a= 54 in (1), we get

a_5=(54)r^{4}=     (3)

From (2) and (3), we have

\Rightarrow(54)r^{4}=\dfrac{2}{3}\\\\\Rightarrow r^4=\dfrac{2}{3}\times\dfrac{1}{54}=\dfrac{1}{3\times27}=\dfrac{1}{81}\\\\\Rightarrow\ r=(\dfrac{1}{81})^{\frac{1}{4}}=\dfrac{1}{3}

Explicit form for the geometric sequence: ar^{n-1}=54(\dfrac{1}{3})^{n-1}

3 0
4 years ago
19 POINT QUESTION PLZ HELP
Tpy6a [65]
When you need to identify elements in an informative manner. It also provides the essential information needed to balance chemical equations.
7 0
3 years ago
.0000458 put this in scientific notation
amm1812


4.58 x 10^-5



hope I helped
3 0
3 years ago
Matsu wants to measure the dimensions of her vegetable garden. Which unit of measurement should she use to eliminate the need to
Sati [7]
The complete question is
<span>Matsu wants to measure the dimensions of her vegetable garden. Which unit of measurement should she use to eliminate the need to write the values in scientific notation?
inches
feet
cups
tons

we know that

case a) inches
</span><span>is a measure of length used for small dimensions
</span><span>
case b) feet
</span>is a measure of length commonly used for dimensions of land, rooms, houses, etc.<span>

case c) cups
is not a measure of length

case d) tons
</span>is not a measure of length
<span>
therefore

the answer is the option
feet


</span>
6 0
3 years ago
Read 2 more answers
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