1.) Solve for x. 2x(x - 12) = -40
2.) Solve for x. 3x2 + 2x = 12 - 7x
3.) Simplify the expression. 8sqrt[-63]
4.) Find the absolute value of the complex number. Abs Val [7 + 24i]
5.) Simplify the expression. [4 - 7i] + [2 + 3i]
Thank you so much!! :)
3x2 + 2x = 12 - 7x
3 x^2 + 9 x - 12 = 0
x^2 + 3 x - 4 = 0
(x+4)(x-1) = 0
x = 1
or
x = -4
8sqrt[-63]
not much I can do but put an i in
8 i sqrt 63
7 + 24i
r = sqrt (49 + 576) = 25
[4 - 7i] + [2 + 3i]
just add
6 -4i
1.) Solve for x: 2x(x - 12) = -40
To solve this equation, we can start by distributing 2x to both terms inside the parentheses:
2x(x - 12) = -40
2x^2 - 24x = -40
Next, we can move all the terms to one side of the equation to set it equal to zero:
2x^2 - 24x + 40 = 0
Now, we can try factoring the quadratic equation:
2(x^2 - 12x + 20) = 0
The factors of 20 that add up to -12 are -2 and -10, so we can rewrite the equation as:
2(x - 2)(x - 10) = 0
Now, we can set each factor equal to zero and solve for x:
x - 2 = 0 or x - 10 = 0
Solving each equation separately, we get:
x = 2 or x = 10
Therefore, the solutions for x are x = 2 and x = 10.
2.) Solve for x: 3x^2 + 2x = 12 - 7x
To solve this equation, we want to make sure all the terms are on one side, so let's move the -7x term to the left side:
3x^2 + 2x + 7x = 12
Combining like terms gives us:
3x^2 + 9x = 12
Now, let's subtract 12 from both sides to set the equation equal to zero:
3x^2 + 9x - 12 = 0
To solve this quadratic equation, we can try factoring:
3(x^2 + 3x - 4) = 0
The factors of -4 that add up to 3 are 4 and -1, so we can rewrite the equation as:
3(x + 4)(x - 1) = 0
Now, we can set each factor equal to zero and solve for x:
x + 4 = 0 or x - 1 = 0
Solving each equation separately, we get:
x = -4 or x = 1
Therefore, the solutions for x are x = -4 and x = 1.
3.) Simplify the expression: 8sqrt[-63]
To simplify this expression, we can first simplify the square root of -63. Recall that the square root of a negative number is not a real number, so we need to express it in terms of the imaginary unit, i.
We can rewrite -63 as -1 * 9 * 7, and the square root of -1 can be represented as i. Thus, we have:
8sqrt[-63] = 8sqrt[-1 * 9 * 7]
= 8sqrt[-1] * sqrt[9] * sqrt[7]
= 8i * 3 * sqrt[7]
= 24i * sqrt[7]
Therefore, the simplified expression is 24i * sqrt[7].
4.) Find the absolute value of the complex number: Abs Val [7 + 24i]
To find the absolute value of a complex number, we use the formula: √(a^2 + b^2), where a and b are the real and imaginary parts of the complex number.
In this case, the real part is 7 and the imaginary part is 24. So we have:
Abs Val [7 + 24i] = √(7^2 + 24^2)
= √(49 + 576)
= √625
= 25
Therefore, the absolute value of the complex number 7 + 24i is 25.
5.) Simplify the expression: [4 - 7i] + [2 + 3i]
To simplify this expression, we can combine the real parts and imaginary parts separately:
Real part: 4 + 2 = 6
Imaginary part: -7 + 3 = -4
Combine the real and imaginary parts to get the simplified expression:
[4 - 7i] + [2 + 3i] = 6 - 4i
Therefore, the simplified expression is 6 - 4i.
1)
2x^2 -24 x + 40 = 0
x^2 - 12 x + 20 = 0
(x-2)(x-10) = 0
x = 2
or
x = 10