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ycow [4]
3 years ago
12

Perform the indicated operations. Write the answer in standard form, a+bi. (5 + 6i)(5 - 6i)

Mathematics
2 answers:
lubasha [3.4K]3 years ago
5 0

\boxed{\underline{\bf \: ANSWER}}

\sf \: ( 5 + 6 i ) ( 5 - 6 i )

Multiply complex numbers 5+6i and 5-6i in the same way as you multiply binomials.

\dashrightarrow \sf 5\times 5+5\times \left(-6i\right)+6i\times 5+6\left(-6\right)i^{2}

By definition, i² is -1.

\dashrightarrow \sf 5\times 5+5\times \left(-6i\right)+6i\times 5+6\left(-6\right)\left(-1\right)

Do the multiplications.

\dashrightarrow \sf \: 25-30i+30i+36

Now cancel -30i & +30i

\dashrightarrow \sf \: 25 \:  \bcancel{- 30i}  \:  +  \: \bcancel{30i}+36

Now the equation becomes

\dashrightarrow \sf \: 25 \:  + 36 \\ \dashrightarrow  \boxed{\bf \: 61}

________

Hope it helps.

ŕάίήвόώşάĻţ2²2²

KIM [24]3 years ago
3 0

Answer:

61

Step-by-step explanation:

(5 + 6i)(5 - 6i)

FOIL

first: 5*5 =25

outer: 5 *-6i = -30i

inner: 6i *5 = 30i

last: 6i * -6i = -36 i^2 =-36 (-1) = 36

Add together

25 -30i+30i+36

61

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A can contained 5.5 ounces of tuna. Joey used 2.88 ounces of the tuna to make a sandwich. To find the amount of tuna remaining i
Veseljchak [2.6K]

Answer:

Yes

Step-by-step explanation:

A full can of tuna has a certain amount in it, if a portion is removed from the can it is therefore subtracted from the total amount. This means that Joey's work is correct and the tuna can would have

5.5 oz - 2.88 oz = 2.62 oz

The best way to tell if his work is correct would be to weigh the remaining tuna in the can and see if it matches Joey's answer.

7 0
2 years ago
What is the constant of variation for the quadratic variation? x 2 3 4 5 6 y 32 72 128 200 288
cluponka [151]
We use different models for different types of variation. For example, linear variation is associated with the formula y=ax, or the more familiar y=mx+b (the equation of a straight line). Cubic variation: y=a*x^3. In the present case we're discussing quadratic variation; perhaps that will ring a bell with you, reminding you that y=ax^2+bx+c is the general quadratic function. Now in y our math problem, we're told that this is a case of quadratic variation. Use the model y=a*x^2. For example, we know that if x=2, y =32. Mind substituting those two values into y=a*x^2 and solving for y? Then you could re-write y=a*x^2 substituting this value for a. Then check thisd value by substituting x=3, y=72, and see whether the resulting equation is true or not. If it is, your a value is correct. But overall I got 16!
7 0
3 years ago
7=8 + r/15 <br> Simplify, with steps pleaseee
Crazy boy [7]

Answer:

7 = 8 +  \frac{r}{15}  \\ 7 - 8 =  \frac{r}{15}  \\  - 1 = \frac{r}{15}  \\  \therefore \: r =  - 15

8 0
2 years ago
Read 2 more answers
Given various values of the linear functions f(x) and g(x) in the table, determine the y-intercept of (f- g)(x).
lisabon 2012 [21]

The y-intercept of linear function (f- g)(x) is (0,9)

<h3>How to determine the y-intercept?</h3>

The table of values is given as:

x   -6 -4 -1 3 4

f(x) 15 11 5 -3 -5

g(x) -36 -26 -11 9 14

The equations of the functions is calculated using:

y = \frac{y_2 -y_1}{x_2-x_1} * (x -x_1) + y_1

So, we have:

f(x) = \frac{11 -15}{-4 + 6} * (x + 6) + 15

Evaluate

f(x) = -2x + 3

Also, we have:

g(x) = \frac{-26 + 36}{-4 + 6} * (x + 6) - 36

Evaluate

g(x) = 5x - 6

Next, we calculate (f - g)(x) using:

(f - g)(x) = f(x) - g(x)

This gives

(f - g)(x) = -2x + 3 - 5x + 6

Substitute 0 for x

(f - g)(0) = -2(0) + 3 - 5(0) + 6

Evaluate

(f - g)(0) = 9

Hence, the y-intercept of (f- g)(x) is (0,9)

Read more about linear functions at:

brainly.com/question/24896196

#SPJ1

7 0
2 years ago
What is the solution set for the molar concentration of
malfutka [58]

Answer: B

Step-by-step explanation:

I got it right on Edge

4 0
3 years ago
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