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2 years ago

The equation 2x^2+12x=4 is written in the form of 2(x-p)^2+q=0. what is the value of q?

Mathematics

1 answer:

hram777 [196]2 years ago

7 0

1) Factor out the coefficient 2: 2x^2+12x=4 => 2(x^2 + 6x) = 4

2) Complete the square of x^2 + 6x: x^2 + 6x + 9 - 9. Then:

2(x^2 + 6x + 9 - 9) = 4

3) Rewrite the square as the square of a binomial:

2( [x+3]^2 - 9) = 4, or

2([x+3]^2) = 22, or

2( [x+3]^2 ) - 22 = 0

The value of q is -22.

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The sum of the first n consecutive even numbers can be found using S=n2+n, where n≥2. What is the value of n when the sum is 42?

lawyer [7]

Answer:

C. 6

Step-by-step explanation:

Given

S = n² + n
S = 42, n = ?

Substitute and solve for n:

42 = n² + n
n² + 2*1/2n + 1/4 = 42.25
(n + 0.5)² = 42.25
n + 0.5 = √42.25
n + 0.5 = 6.5
n = 6

Correct option is C

5 0

2 years ago

Read 2 more answers

Find x such that -1/3 = 7/x

Setler [38]

Answer:

x= -21

Step-by-step explanation:

-1/3=7/x

-1x=21

-1x/-1=21/-1

x= -21

7 0

2 years ago

Simplify x^2-9x-22/x-11

OleMash [197]

Answer:

x^2-11/-8x

Step-by-step explanation:

We can solve this equation easily by using PEMDAS, or order of operations.

Parenthesis

Exponents

Multiplication>Division (Depends on which comes first left to right)

Addition>Subtraction (See multiplication>division)

Now that we know the order of the operations, we can solve.

First, we cant solve for x^2 because we dont know the value of x, so well leave that alone. Same with 22/x. All we can do is use the commutative property.

So our equation is now x^2-11/-8x

Hope this helps!

6 0

2 years ago

[tex]cos {}^{4} α+sin {}^{4} α= \frac{1}{4} (3+cos4α) Prove:

asambeis [7]

Given:

$\cos^4 \alpha+\sin^4\alpha=\dfrac{1}{4}(3+\cos 4 \alpha)$

To prove:

The given statement.

Proof:

We have,

$\cos^4 \alpha+\sin^4\alpha=\dfrac{1}{4}(3+\cos 4 \alpha)$

$LHS=\cos^4 \alpha+\sin^4\alpha$

$LHS=(\cos^2 \alpha)^2+(\sin^2 \alpha)^2$

$LHS=(\cos^2 \alpha+\sin^2\alpha)^2-2\sin ^2\alpha\cos^2 \alpha$ $[\because a^2+b^2=(a+b)^2-2ab]$

$LHS=(1)^2-2(1-\cos^2 \alpha)\cos^2 \alpha$ $[\because \cos^2 \alpha+\sin^2\alpha=1]$

$LHS=1-2\cos^2 \alpha+2\cos^4 \alpha$

Now,

$RHS=\dfrac{1}{4}(3+\cos 4 \alpha)$

$RHS=\dfrac{1}{4}[3+(2\cos^2 2\alpha-1)]$ $[\because \cos 2\theta=2\cos^2\theta -1]$

$RHS=\dfrac{1}{4}[2+2\cos^2 2\alpha]$

$RHS=\dfrac{1}{4}[2+2(2\cos^2 \alpha-1)^2]$ $[\because \cos 2\theta=2\cos^2\theta -1]$

$RHS=\dfrac{1}{4}[2+2(4\cos^4 \alpha-4\cos \alpha+1)]$ $[\because (a-b)^2=a^2-2ab+b^2]$

$RHS=\dfrac{1}{4}[2+8\cos^4 \alpha-8\cos \alpha+2]$

$RHS=\dfrac{1}{4}[4+8\cos^4 \alpha-8\cos \alpha]$

$RHS=1+2\cos^4 \alpha-2\cos \alpha$

$RHS=1-2\cos^2 \alpha+2\cos^4 \alpha$

$LHS=RHS$

Hence proved.

8 0

2 years ago

Find the greatest common factor of 21 and 33

lions [1.4K]

Answer:

As you can see when you list out the factors of each number, 3 is the greatest number that 21 and 33 divides into.

Step-by-step explanation:

As you can see when you list out the factors of each number, 3 is the greatest number that 21 and 33 divides into.

5 0

2 years ago

Read 2 more answers