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3 years ago

X^2-14x-4=0, solve by completing the square

2 answers:

4 0

The answer is: x = 7 - √53 or x = 7 + √53

The general quadratic equation is: ax² + bx + c = 0.
But, by completing the square we turn it into: a(x + d)² + e = 0, where:
d = b/2a
e = c - b²/4a
Our quadratic equation is x² - 14x -4 = 0, which is after rearrangement:
So, a = 1, b = -14, c = -4
Let's first calculate d and e:
d = b/2a = -14/2*1 = -14/2 = -7
e = c - b²/4a = -4 - (-14)²/4*1 = -4 - 196/4 = -4 - 49 = -53
By completing the square we have:
a(x + d)² + e = 0

1(x + (-7))² + (-53) = 0
(x - 7)² - 53 = 0
(x - 7)² = 53
x - 7 = +/-√53
x = 7 +/- √53

Therefore, the solutions are:
x = 7 - √53
or
x = 7 + √53

devlian [24]3 years ago

4 0

×^2-14×+49-49-4=0
(×-7)^2-53=0
(×-7-7.3)(×-7+7.3)
(×-14.3)(×+0.3)=0

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Mike wants to fence in part of his backyard. He wants the length of the fenced-in area to be at least 20 feet long, l ≥ 20. He h

zhuklara [117]

I added a screenshot of the complete question along with the given choices.

Answers:

w = 10 ft and l = 50 ft ................> second option

w = 20 ft and l = 60 ft ...............> third option

w = 50 ft and l = 40 ft ...............> fifth option

Explanation:

We are given that:

length should be at least 20 ...........> length ≥ 20

equation for perimeter is : 2l + 2w ≤ 200

We will check each option as follows:

Option 1:

w = 50 ft and l = 10 ft

This option is incorrect as the proposed length is less than 20.

Option 2:

w = 10 ft and l = 50 ft

Since the length is greater than 20, the first condition is satisfied.

Now, we check the second condition:

2l + 2w = 2(50) + 2(10) = 100 + 20 = 120 ≤ 200

The second condition is also satisfied.

This option is correct

Option 3:

w = 20 ft and l = 60 ft

Since the length is greater than 20, the first condition is satisfied.

Now, we check the second condition:

2l + 2w = 2(60) + 2(20) = 120 + 40 = 160 ≤ 200

The second condition is also satisfied.

This option is correct

Option 4:

w = 90 ft and l = 30 ft

Since the length is greater than 20, the first condition is satisfied.

Now, we check the second condition:

2l + 2w = 2(30) + 2(90) = 60 + 180 = 240 > 200

The second condition is not satisfied.

This option is incorrect

Option 5:

w = 50 ft and l = 40 ft

Since the length is greater than 20, the first condition is satisfied.

Now, we check the second condition:

2l + 2w = 2(50) + 2(40) = 100 + 80 = 180 ≤ 200

The second condition is also satisfied.

This option is correct

Hope this helps :)

8 0

3 years ago

Read 2 more answers

In the diagram below, ST is parallel to PQ. If ST is 4 more than PS,SR = 12, and PQ = 15, find the length of PS. Figures are not

Tpy6a [65]

Since segments ST and PQ are parallel, triangles SRT and PRQ are similar due to the AAA postulate. In general, the ratio between the corresponding sides of two similar triangles is constant; therefore,

$\frac{SR}{PR}=\frac{RT}{RQ}=\frac{TS}{QP}$

Furthermore,

$PS=PR-RS$

Finding PR and RS,

$\begin{gathered} ST=4+PS \\ SR=12 \\ PQ=15 \end{gathered}$

Then,

$\frac{12}{PR}=\frac{TS}{15}$ $\begin{gathered} \Rightarrow\frac{12}{PR}=\frac{4+PS}{15} \\ \Rightarrow\frac{12}{PS+12}=\frac{4+PS}{15} \end{gathered}$

Solving for PS,

$\begin{gathered} 12\cdot15=(PS+12)(PS+4) \\ \Rightarrow180=PS^2+16PS+48 \end{gathered}$

Solve the quadratic equation in terms of PS, as shown below

$\begin{gathered} \Rightarrow PS^2+16PS-132=0 \\ \Rightarrow PS=\frac{-16\pm\sqrt[]{16^2-4(-132)}}{2}=\frac{-16\pm28}{2} \\ \Rightarrow PS=-22,6 \end{gathered}$

And PS is a segment; therefore, it has to be positive.

Hence, the answer is PS=6

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1 year ago

Which of the following is most likely the next step in the series?

Nostrana [21]

Answer:

A is most likely the next step in the series

Step-by-step explanation:

Each step, the number of sides is increasing by 1.

4,5,6 means that the next number of sides would be 7. Option A has 7 sides.

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3 years ago

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2 years ago

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Paraphin [41]

Answer:

Step-by-step explanation:

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2 years ago

Read 2 more answers