Which expression shows (3-4i)+(-7-8i) in simplest form?

What is the volume of the rectangular prism

-Dominant- [34]

Answer:

D

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Please help

Harrizon [31]

Answer:

(-1/2, 3/4)

Step-by-step explanation:

Let's use the elimination by adding or subtracting method. Note that we have 8y in the first equation, and that we could obtain -8y in the second equation by multiplying the second equation by 2:

2(24x - 4y = -15) => 48x - 8y = -30

Now combine this result (this equation) with the first equation:

2x + 8y = 5

+48x -8y = -30

---------------------

50x = - 25

Dividing both sides by 50, to isolate x, we get

x = -25/50 = -1/2.

Now substitute -1/2 for x in the first equation and solve the resulting equation for y:

2x + 8y = 5

2(-1/2) + 8y = 5, or -1 + 8y = 5, or 8y = 6 (after having added 1 to both sides)

Dividing both sides of 8y = 6 by 8 leads to determining the value of y:

y = 6/8 = 3/4

The solution is (-1/2, 3/4).

3 0

3 years ago

Fred flips a coin, spins the spinner, and rolls a standard number cube. Find the probability that the coin will show tails, the

Inessa05 [86]

Answer:

The probability that the coin will show tails, the spinner will land on yellow or green (out of yellow, green, blue), and the cube will show a three is $\frac{4}{3}$

Step-by-step explanation:

Given : Fred flips a coin, spins the spinner, and rolls a standard number cube.

To find : The probability that the coin will show tails, the spinner will land on yellow or green (out of yellow, green, blue), and the cube will show a three ?

Solution :

First we find probability one by one,

1) Flips a coin - Head, Tail

Total number of outcome = 2

Favorable outcome (getting a tail) = 1

Probability that the coin will show tails is $P(T)=\frac{1}{2}$

2) Spins the spinner - yellow, green, blue

Total number of outcome = 3

Favorable outcome (land on yellow or green) = 2

Probability that the spinner will land on yellow or green $P(S)=\frac{2}{3}$

3) Rolls a standard number cube - 1,2,3,4,5,6

Total number of outcome = 6

Favorable outcome (show a three) = 1

Probability that the cube will show a three $P(C)=\frac{1}{6}$

The probability that the coin will show tails, the spinner will land on yellow or green (out of yellow, green, blue), and the cube will show a three is

$P=P(T)+P(S)+P(C)$

$P=\frac{1}{2}+\frac{2}{3}+\frac{1}{6}$

$P=\frac{3+4+1}{6}$

$P=\frac{8}{6}$

$P=\frac{4}{3}$

Therefore, The probability that the coin will show tails, the spinner will land on yellow or green (out of yellow, green, blue), and the cube will show a three is $\frac{4}{3}$

5 0

3 years ago

Some one factor 3x^2+7x-20

mylen [45]

Split it up
3x^2+12x-5x-20
group
(3x^2+12x)+(-5x-20)
factor
(3x)(x+4)+(-5)(x+4)
undistribute (x+4) like ab+ac=a(b+c)
(3x-5)(x+4)

6 0

3 years ago

This is finding exact values of sin theta/2 and tan theta/2. I’m really confused and now don’t have a clue on how to do this, pl

Lostsunrise [7]

First,

tan(θ) = sin(θ) / cos(θ)

and given that 90° < θ < 180°, meaning θ lies in the second quadrant, we know that cos(θ) < 0. (We also then know the sign of sin(θ), but that won't be important.)

Dividing each part of the inequality by 2 tells us that 45° < θ/2 < 90°, so the half-angle falls in the first quadrant, which means both cos(θ/2) > 0 and sin(θ/2) > 0.

Now recall the half-angle identities,

cos²(θ/2) = (1 + cos(θ)) / 2

sin²(θ/2) = (1 - cos(θ)) / 2

and taking the positive square roots, we have

cos(θ/2) = √[(1 + cos(θ)) / 2]

sin(θ/2) = √[(1 - cos(θ)) / 2]

Then

tan(θ/2) = sin(θ/2) / cos(θ/2) = √[(1 - cos(θ)) / (1 + cos(θ))]

Notice how we don't need sin(θ) ?

Now, recall the Pythagorean identity:

cos²(θ) + sin²(θ) = 1

Dividing both sides by cos²(θ) gives

1 + tan²(θ) = 1/cos²(θ)

We know cos(θ) is negative, so solve for cos²(θ) and take the negative square root.

cos²(θ) = 1/(1 + tan²(θ))

cos(θ) = - 1/√[1 + tan²(θ)]

Plug in tan(θ) = - 12/5 and solve for cos(θ) :

cos(θ) = - 1/√[1 + (-12/5)²] = - 5/13

Finally, solve for sin(θ/2) and tan(θ/2) :

sin(θ/2) = √[(1 - (- 5/13)) / 2] = 3/√(13)

tan(θ/2) = √[(1 - (- 5/13)) / (1 + (- 5/13))] = 3/2

3 0

3 years ago