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Reil [10]
2 years ago
8

Find the solution to the following equation by transforming it into a perfect square trinomial.* x2 + 2x = 8

Mathematics
2 answers:
andriy [413]2 years ago
6 0
x^{2} +2x=8 \ add \ 1 \ to \ both \ sides\\
\\
 x^{2} +x+8+1 \ in \ the \ left \ side \ you \ find \ a perfect \ square \ trinomial\\
\\
(x+1)^2=9\\
\\
So:\\
\\
x+1=\pm  \sqrt{9}\\
\\
x+1=\pm 3\\
\\
 x+1=3 \rightarrow x=2\\
\\
x+1=-3 \rightarrow \x=-4
aleksklad [387]2 years ago
6 0
X2+2x-8 =0
x2 + 4x - 2x - 8 = 0
x(x+4) - 2(x+4) = 0
(x-2)(x+4) = 0
let x- 2 = 0
x = 2
let x+4 = 0
x= -4
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NO LINKS!!
dexar [7]

Answer: Anything between 0 and 10, excluding both endpoints.

In terms of symbols we can say 0 < w < 10 where w is the width.

===================================================

Explanation:

You could do this with two variables, but I think it's easier to instead use one variable only. This is because the length is dependent on what you pick for the width.

w = width

2w = twice the width

2w-5 = five less than twice the width = length

So,

  • width = w
  • length = 2w-5

which lead to

area = length*width

area = (2w-5)*w

area = 2w^2-5w

area < 150

2w^2 - 5w < 150

2w^2 - 5w - 150 < 0

To solve this inequality, we will solve the equation 2w^2-5w-150 = 0

Use the quadratic formula. Plug in a = 2, b = -5, c = -150

w = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\w = \frac{-(-5)\pm\sqrt{(-5)^2-4(2)(-150)}}{2(2)}\\\\w = \frac{5\pm\sqrt{1225}}{4}\\\\w = \frac{5\pm35}{4}\\\\w = \frac{5+35}{4} \ \text{ or } \ w = \frac{5-35}{4}\\\\w = \frac{40}{4} \ \text{ or } \ w = \frac{-30}{4}\\\\w = 10 \ \text{ or } \ w = -7.5\\\\

Ignore the negative solution as it makes no sense to have a negative width.

The only practical root is w = 10.

If w = 10 feet, then the area = 2w^2-5w results in 150 square feet.

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

Based on that root, we need to try a sample value that is to the left of it.

Let's say we try w = 5.

2w^2 - 5w < 150

2*5^2 - 5*5 < 150

25 < 150 ... which is true

This shows that if 0 < w < 10, then 2w^2-5w < 150 is true.

Now try something to the right of 10. I'll pick w = 15

2w^2 - 5w < 150

2*15^2 - 5*15 < 150

375 < 150 ... which is false

It means w > 10 leads to 2w^2-5w < 150  being false.

Therefore w > 10 isn't allowed if we want 2w^2-5w < 150 to be true.

4 0
2 years ago
For a class trip, there are two adults for every 15 students. There are 238 people (adults and students) on the trip. How many s
-Dominant- [34]

Answer:

210

Step-by-step explanation:

x = num of adults

x + 7.5x = 238

8.5x = 238

x = 28

#students = 238-x

                 = 210

8 0
2 years ago
Let f (x) = 3x − 1 and ε &gt; 0. Find a δ &gt; 0 such that 0 &lt; ∣x − 5∣ &lt; δ implies ∣f (x) − 14∣ &lt; ε. (Find the largest
s344n2d4d5 [400]

Answer:

This proves that f is continous at x=5.

Step-by-step explanation:

Taking f(x) = 3x-1 and \varepsilon>0, we want to find a \delta such that |f(x)-14|

At first, we will assume that this delta exists and we will try to figure out its value.

Suppose that |x-5|. Then

|f(x)-14| = |3x-1-14| = |3x-15|=|3(x-5)| = 3|x-5|< 3\delta.

Then, if |x-5|, then |f(x)-14|. So, in this case, if 3\delta \leq \varepsilon we get that |f(x)-14|. The maximum value of delta is \frac{\varepsilon}{3}.

By definition, this procedure proves that \lim_{x\to 5}f(x) = 14. Note that f(5)=14, so this proves that f is continous at x=5.

3 0
2 years ago
What is the solution of the equation x^2 = 64?
timurjin [86]

Answer:

the answer is the First option.

7 0
2 years ago
How do I do this? Help????!!!
mylen [45]
A = 9 because 11.2-2.2=9
B= 2.2 because 9+2.2=11.2
C=2.2 because 11.2-9=2.2
D=9.2 because 11.2-2=9


E=4.5 because 9.5-5=4.5
F= 5 because 9.5-4.5=5
G=4.5 because 9.5-5=4.5
H=5 because 9.5-4.5=5

I= x=11 because 99 divided by 9 = 11
J= x=9 because 99 divided by 11 = 9
K= 9 because 99 divided by 11 =9
L= 11 because 99 divided by 9=11

M=2 because 4 divided by 2 =2
N=4 because 2 times 2 =4
O=2 because 4 divided by 2 =2
P=2 because 4 divided by 2=2


hope this helps:)
4 0
3 years ago
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