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maks197457 [2]
2 years ago
8

(3-4i)(6i+7)-(2-3i)

Mathematics
1 answer:
Sergeu [11.5K]2 years ago
5 0

Answer:

43-7i

Step-by-step explanation:

We are given the expression:

\displaystyle \large{(3 - 4i)(6i + 7) - (2 - 3i)}

First, expand 3-4i in 6i+7. To expand binomial with binomial, first we expand 3 in 6i+7 then expand -4i in 6i+7.

\displaystyle \large{[(3 \cdot 6i) + (3 \cdot 7) + ( - 4i \cdot 6i) + ( - 4i \cdot 7)]- (2 - 3i)}  \\  \displaystyle \large{[18i + 21  - 24 {i}^{2}  - 28i]- (2 - 3i)}

Now combine like terms.

\displaystyle \large{[ - 10i+ 21  - 24 {i}^{2} ]- (2 - 3i)}

<u>I</u><u>m</u><u>a</u><u>g</u><u>i</u><u>n</u><u>a</u><u>r</u><u>y</u><u> </u><u>U</u><u>n</u><u>i</u><u>t</u>

\displaystyle \large{i =   \sqrt{ - 1} } \\ \displaystyle \large{ {i}^{2}  =   - 1 }

Therefore:-

\displaystyle \large{[ - 10i+ 21  - 24  ( - 1) ]- (2 - 3i)}  \\   \displaystyle \large{[ - 10i+ 21   + 24]- (2 - 3i)}  \\   \displaystyle \large{[ - 10i+ 45]- (2 - 3i)}

Then expand negative sign in 2-3i; remember that negative times negative is positive and negative times positive is negative.

\displaystyle \large{- 10i+ 45 -  (2 - 3i)}  \\   \displaystyle \large{- 10i+ 45 -  2 + 3i}

Combine like terms.

\displaystyle \large{43 - 7i}

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8÷(7-3)x(4+6)

8÷4x10

2x10

<u>20</u>

3 0
3 years ago
Please help, I need input on if I did this correctly and you just substitute.
kow [346]

The value of h(t) when t=\frac{15}{32} is 10.02.

Solution:

Given function h(t)=-16t^2+15t+6.5

To find the value of h(t) when t=\frac{15}{32}:

h(t)=-16t^2+15t+6.5

Substitute t=\frac{15}{32} in the given function.

$h\left(\frac{15}{32} \right)=-16\left(\frac{15}{32} \right)^2+15\left(\frac{15}{32} \right)+6.5

            $=-16\left(\frac{225}{1024} \right)+15\left(\frac{15}{32} \right)+6.5

Now multiply the common terms into inside the bracket.

           $=-\left(\frac{3600}{1024} \right)+\left(\frac{225}{32} \right)+6.5

Now, in the first term, the numerator and denominator both have common factor 16. So reduce the first term into the lowest term.

          $=-\left(\frac{225}{64} \right)+\left(\frac{225}{32} \right)+6.5

To make the denominator same, take LCM of the denominators.

LCM of 64 and 32 = 64

        $=-\left(\frac{225}{64} \right)+\left(\frac{225\times2}{32\times2} \right)+6.5\times\frac{64}{64}

        $=-\frac{225}{64} +\frac{450}{64}+\frac{416}{64}

        $=\frac{-225+450+416}{64}

       $=\frac{641}{64}

       = 10.02

$h\left(\frac{15}{32} \right)=10.02

Hence the value of h(t) when t=\frac{15}{32} is 10.02.

8 0
3 years ago
Can someone please help me like I really need help this problem has to have more than one step to be solved I really need help a
kumpel [21]

Answer:

85°

Step-by-step explanation:

Please follow along with these directions on the attached picture so that this makes sense.  I have labeled the picture with the variables I used and the angles I figured out.

Let's start in the top left corner. Remember: triangles always have 180°, and straight lines always have 180°.

180-115 = 65

65+85+x = 180, so x = 30

30+90+y = 180, so y = 60

180-155 = 25

25+60+z = 180, so z = 95

180-95 = 85°

8 0
3 years ago
What is the value of x makes this equation true? -6x+3=45
Oduvanchick [21]

Answer:

x=-7

Step-by-step explanation:

subtract 3 from both sides

-6x=45-3

-6x=42

divide each term by 6

\frac{-6x}{-6} =\frac{42}{-6}

x=\frac{42}{-6}

simplify

x=-7

3 0
3 years ago
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Write 0.70 to 0.14 as a fraction in simplest form
Delvig [45]
\cfrac{0.70}{0.14}=  \cfrac{70}{14}= \cfrac{35}{7}= \cfrac{5}{1}
3 0
3 years ago
Read 2 more answers
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