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d1i1m1o1n [39]
3 years ago
15

8

Mathematics
1 answer:
tia_tia [17]3 years ago
6 0

Answer:

8-6i

Step-by-step explanation:

Multiply out (3-i)^2 in order to find out which expression it is equivalent to.

1) Since the whole quantity is squared, write it out as (3-i)(3-i).

(3-i)^2\\(3-i)(3-i)

2) Multiply binomials by using the FOIL method. Multiply the terms that are listed first in each binomial, then the ones that are listed outermost when looking at both binomials, then innermost, and finally the last terms listed in each binomial. Simplify and combine like terms.

(3-i)(3-i)\\9 - 3i - 3i + i^2

9 - 6i + i^2

3)  i = \sqrt{-1}, so i ^2 must be (\sqrt{-1} )(\sqrt{-1}). Thus, i^2 is equivalent to -1. Knowing this, simplify and combine like terms.

9 - 6i + ((-\sqrt{1} )(\sqrt{-1} ))

9 - 6i -1\\8 - 6i

Thus, it is equivalent to  8 - 6i .

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1/2 times ? Equals 3 1/2
stepan [7]

Answer:

7

Step-by-step explanation:

1/2(x)=7/2

divide both sides by 1/2

x=\frac{7}{2}÷\frac{1}{2}

x=\frac{7}{2}·\frac{2}{1}

x=14/2=7

4 0
2 years ago
Write an equation for a line parallel to y=2x-2 and passing through the point (1,1) Y=???? PLEASE HELP ANYONE
Rufina [12.5K]
The general equation for slope-intercept form is y = mx + b, where m = the slope of the equation, b = the y intercept, and x and y are your variables (and the coordinate points on the graph). 

Remember that for parallel lines, the slope, m, is the same for both equations. The equation you're given, y = 2x - 2, is already in slope-intercept form and the 2 in front of x is m, your slope. That means for whatever equation we come up with, m has to be 2. 

So far we know the equation for our parallel line is y = 2x + b. How do we figure out b? Plug in the (x, y) coordinate you're given, (1, 1) and solve for b:
y = 2x + b\\
1 = 2(1) + b\\
1 = 2 + b\\
b = -1

Now we know b = -1. Put that into our y = 2x + b equation to get the final equation of your parallel line: 
Your final answer is y = 2x - 1.

5 0
3 years ago
MZJ and m M are base angles of isosceles trapezoid JKLM. If mZJ = 18x + 8 and m_M=11x + 15 find m2K.
maxonik [38]

The question is incomplete. Here is the complete question.

m∠J and m∠Kare base angles of an isosceles trapezoid JKLM.

If m∠J = 18x + 8, and m∠M = 11x + 15 , find m∠K.

A. 1

B. 154

C. 77

D. 26

Answer: B. m∠K = 154

Step-by-step explanation: <u>Isosceles</u> <u>trapezoid</u> is a parallelogram with two parallel sides, called Base, and two non-parallel sides that have the same measure.

Related to internal angles, angles of the base are equal and opposite angles are supplementary.

In trapezoid JKLM, m∠J and m∠M are base angles, so they are equal:

18x + 8 = 11x + 15

7x = 7

x = 1

Now, m∠K is opposite so, they are supplementary, which means their sum results in 180°:

m∠J = 18(1) + 8

m∠J = 26

m∠K + m∠J = 180

m∠K + 26 = 180

m∠K = 154

The angle m∠K is 154°

7 0
3 years ago
Solve for angle B in right triangle ABC. <br><br> I got 53, is it right?
lara31 [8.8K]
Yup its 53 Degrees you got it right :)

8 0
3 years ago
Solve the system y = -x + 7 and y = -0.5(x - 3)^2 + 8.
AlladinOne [14]

Answer:

(1,6) & (7,0)

Step-by-step explanation:

y = -x + 7

y = -0.5(x - 3)² + 8

To solve the system, solve these two equations simultaneously

-x + 7 = -0.5(x - 3)² + 8

-x + 7 = -0.5(x² - 6x + 9) + 8

-x + 7 = -0.5x² + 3x - 4.5 + 8

0.5x² - 4x + 3.5 = 0

x² - 8x + 7 = 0

x² - 7x - x + 7 = 0

x(x - 7) - (x - 7) = 0

(x - 1)(x - 7) = 0

x = 1, 7

y = -1 + 7 = 6

y = -7 + 7 = 0

(1,6) (7,0)

Since the system has two distinct solutions, the line and the curve meet at two distinct poibts9: (1,6) & (7,0)

8 0
3 years ago
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