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2 years ago

Evaluate the expression (-4+4i)(1+4i)(1+4i) and write the result in the form a+bi

Mathematics

1 answer:

allsm [11]2 years ago

8 0

Answer:

Step-by-step explanation:

Since 2 of the 3 binomials are identical I would start the distribution there.

(1 + 4i)(1 + 4i) = $1+8i+16i^2$

I'm sure you have learned in class by now that i-squared is = to -1, so we can make that substitution:

1 + 8i + 16(-1) which simpifies to

1 + 8i - 16 which simplifies further to

-15 + 8i. Now we need to FOIL in the last binomial:

(-15 + 8i)(-4 + 4i) = $60-60i-32i+32i^2$

Combine like terms to get

$60-92i+32i^2$

Again make the substitution of i-squared = -1:

60 - 92i + 32(-1) which simplifies to

60 - 92i - 32 which simpifies, finally, to a solution of:

28 - 92i

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Please help! It’s urgent!

Gre4nikov [31]

Answer:

9/35

all the boxes in one row are 7 and the number of rows are 5 .. so 7x5=35 and the number of boxes shaded are 9

5 0

1 year ago

Trina planted plants in her garden last week. She planted twice as many cucumbers as zucchini and eight more tomatoes than cucum

maxonik [38]

Answer:

7 Zuchini, 14 Cucumbers and 22 Tomatoes plants.

Step-by-step explanation:

Let the number of tomatoes=t
Let the number of cucumber planted=c
Let the number of zucchini planted=z
Total Number of Plants=43

She planted twice as many cucumbers as zucchini, this is written as:

c=2z

She also planted eight more tomatoes than cucumbers, this is written as:

t=c+8=2z+8

In total, she planted 43 plants

Therefore:

z+(2z)+(2z+8)=43

5z+8=43

5z=43-8

5z=35

Divide both sides by 5

z=7

Number of Cucumbers, c=2z=2 X 7 =14

Number of Tomatoes, t=c+8=14+8=22

Therefore, she planted 7 Zuchini, 14 Cucumbers and 22 Tomatoes plants.

3 0

2 years ago

What values of c and d make the equation true?

saul85 [17]

Answer:

Third option.

Step-by-step explanation:

You need to cube both sides of the equation. Remember the Power of a power property:

$(a^m)^n=a^{mn$

$\sqrt[3]{162x^cy^5}=3x^2y(\sqrt[3]{6y^d})\\\\(\sqrt[3]{162x^cy^5})^3=(3x^2y(\sqrt[3]{6y^d}))^3\\\\162x^cy^5=27x^6y^36y^d$

According to the Product of powers property:

$(a^m)(a^n)=a^{(m+n)$

Then. simplifying you get:

$162x^cy^5=162x^6y^{(3+d)}$

Now you need to compare the exponents. You can observe that the exponent of "x" on the right side is 6, then the exponent of "x" on the left side must be 6. Therefore:

$c=6$

You can notice that the exponent of "y" on the left side is 5, then the exponent of "x" on the left side must be 5 too. Therefore "d" is:

$3+d=5\\d=5-3\\d=2$

4 0

3 years ago

How much faster does Student B read than Student A?

Romashka-Z-Leto [24]

Answer:

He reads faster by 8 pages.

3 0

2 years ago

Pleaseeeeeeeeeeeeee hellllppppppp me urgentttt

Rufina [12.5K]

Answer:

Step-by-step explanation:

each box has 12 melon for 15 dollars:

the price of one melon : 15/12=1.25 dollar each

he bought 12 boxes of melon and paid 15 dollars for each :

12*15=180 dollars

total melon is : 12*12=144 dollars

he sold 3/4 of a melon : 3/4 *144=108

the cost of 108 : 108*1.25= 135 dollars

at a price of $ 1.6 = 108*1.6= 172.8

the rest of the melon sold at reduce price=

144-108= 36

over all profit = 15 %

180*(1+0.15)=207 dollars profit

selling 108 melons : $172.8

overall profit - profit from selling 108 melons: 207-172.8=$34.2

<h2>reduced price = 34.2/36=0.95 dollars</h2>

5 0

2 years ago