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MissTica
2 years ago
13

Solve x2 + 6x = 7 by completing the square. Which is the solution set of the equation?

Mathematics
2 answers:
Doss [256]2 years ago
8 0

Answer:

x = 1; x = -7

Step-by-step explanation:

Given  

x^2 + 6x = 7  

we want to complete the square. If we have (x + a)^2 and expand it we get: x^2 + 2ax + a^2. The second term in the equation suggest that 2ax = 6x or a = 3. Then, adding 3^2 at both sides of the equation of the problem:

x^2 + 6x + 3^2 = 7 + 3^2

(x + 3)^2 = 16

x + 3 = sqrt(16)

That gives us two  options

x + 3 = 4

x = 1

or

x + 3 = -4

x = -7

Ber [7]2 years ago
7 0
So first you have to find the perfect square that matches up with x^2 + 6x

so half of 6, and square it. your perfect square is 9

x^2 + 6x + 9 = 7 + 9

then, condense the left side of the equation into a squared binomial:

(x + 3)^2 = 16

take the square root of both sides:

x + 3 = ± √16

therefore:

x + 3 = ± 4

x = - 3 ± 4

so your solution set is:

x = 1, -7
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Use Pythagorean identities to prove whether ΔLMN is a right, acute, or obtuse triangle. Show all work for full credit.
liq [111]
Using Pythagorean identities:
 
If the sum of the height and base squared is greater than the hypotenuse squared, it would be an acute triangle.

If the sum of the height and base squared is less than the hypotenuse squared, it would be an obtuse triangle.

If the sum of the height and base squared is equal to the hypotenuse squared, it would be a right triangle.

The height = 10
The base = 24

10^2 + 24^2 = 100 + 576 = 676

The hypotenuse = 27 = 27^2 = 729

Because the sum of the height and base squared (676) is smaller than the hypotenuse squared (729) the triangle  is an obtuse triangle.


5 0
2 years ago
Read 2 more answers
The failure rate for a guided missile control system is 1 in 1,000. Suppose that a duplicate but completely independent control
olga_2 [115]

Answer:

<h2>The reliability is 0.999999.</h2>

Step-by-step explanation:

The failure rate for a guided missile control system is 1 in 1,000.

Hence, the probability that the missile will not fail is \frac{1000 - 1}{1000} = \frac{999}{1000}.

According to the new system, if the first fails, the second can take over.

There are two possibilities, either the first one will be fail or not.

If the first one will not fail, then the probability will be \frac{999}{1000} = 0.999.

If the first one will fail, then the probability will be \frac{999}{1000} \times\frac{1}{1000} = 0.000999.

The reliability of the modified missile is 0.999 + 0.000999 = 0.999999.

6 0
2 years ago
The sum of the first n consecutive even numbers can be found using S = n2 + n, where n ≥ 2.
viktelen [127]
The following are the choices on this question:
 A.6
 B. 39
 C. 26
 D. 12   
The answer is option D. 12.

Check this out:
S=n² + n
S= 12² + 12
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2 years ago
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A water tank is a cylinder with radius 40 cm and depth 150 m
djverab [1.8K]

3.142×40^2×150=753,982.237

if1sec =0.2litres

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753.982×1/0.2

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2 years ago
A dog groomer is offering 20% off a full groom for one dog, and 15% off for each additional dog. You decide to take your two fur
jarptica [38.1K]

Answer:the total discounted price for two dogs to be groomed is 22.75

Step-by-step explanation:

A dog groomer is offering 20% off a full groom for one dog, and 15% off for each additional dog. Normally, a full groom costs $65 for each dog.

If you decide to take your two furry friends to be groomed,

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the discount on the second one would be

10/100 × 65 = 0.15 × 65 = 9.75

the total discounted price for two dogs to be groomed would be

13 + 9.75 = 22.75

3 0
2 years ago
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