ABCD~EFGH. identify the pairs of congruent angles and the corresponding sides.

Which of the following is equivalent to the complex number -8(7i - 3i^2)

Leni [432]

Answer: B) -56i - 24

This is the same as -24 - 56i

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Explanation:

The 'i' refers to the imaginary number $\sqrt{-1}$

In other words, $i = \sqrt{-1}$

Squaring both sides gets us $i^2 = -1$

So,

$x = -8(7i - 3i^2)\\\\x = -8(7i - 3(-1))\\\\x = -8(7i + 3)\\\\x = -8(7i) -8(3)\\\\x = -56i -24 \ \ \text{ .... Answer: Choice B}\\\\x = -24 - 56i\\\\$

The result is in the form a+bi where a = -24 is the real part and b = -56 is the imaginary part.

7 0

3 years ago

PLEASE HELP

sweet [91]

To model and solve our situation we are going to use the equation: $s= \frac{d}{t}$
where
$s$ is speed
$d$ is distance
$t$ is time

1. We know that the distance between the cities is 2400 miles, so $d=2400$ . We also know that the speed of the plane is 450 mi/h. Since we don't know the speed of the air, $S_{a}=?$ . We don't know how much the westward trip takes, so $t_{w}=?$ , and we also don't know how much the eastward trip takes, so $t_{e}=?$ .

Going westward. Here the plane is flying against the air, so we need to subtract the speed of the air from the speed of the plane:
$450-S_{a}= \frac{2400}{t_{w} }$
Going eastward. Here the plane is flying with the the air, so we need to add the speed of the air to the speed of the plane:
$450+S_{a}= \frac{2400}{t_{e} }$

2. We know for our problem that the round trip takes 11 hours; so the total time of the trip is 11, $t_{t}=11$ . Notice that we also know that the total time of the trip equals time of the tip going westward plus time of the trip going eastward, so $t_{t}=t_{w}+t_{e}$ . Since we know that the total trip takes 11 hours, we can replace that value in our total time equation and solve for $t_{w}$ :
$11=t_{w}+t_{e}$
$t_{w}=11-t_{e}$

Now we can replace $t_{w}$ in our going westward equation to model our round trip with a system of equations:
$450-S_{a}= \frac{2400}{t_{w}}$
$450-S_{a}= \frac{2400}{11-t_{e} }$ equation (1)
$450+S_{a}= \frac{2400}{t_{e}}$ equation (2)

3. To solve our system of equations, we are going to solve for $t_{e}$ in equations (1) (2):

From equation (1)
$450-S_{a}= \frac{2400}{11-t_{e} }$
$11-t_{e}= \frac{2400}{450-S_{a} }$
$-t_{e}= \frac{2400}{450-S_{a} } -11$
$t_{e}=11- \frac{2400}{450-S_{a} }$
$t_{e}= \frac{4950-11S_{a} -2400}{450-S_{a} }$
$t_{e}= \frac{2550-11S_{a} }{450-S_{a} }$ equation (3)

From equation (2):
$450+S_{a}= \frac{2400}{t_{e} }$
$t_{e}= \frac{2400}{450+S_{a} }$ equation (4)

Replacing (4) in (3)
$\frac{2400}{450+S_{a}} = \frac{2550-11S_{a}}{450-S_{a} }$
Now, we can solve for $S_{a}$ to find the speed of the wind:
$2400(450-S_{a})=(450+S_{a})(2550-11S_{a})$
$1080000-2400S_{a}=1147500-4950S_{a}+2550S_{a}-11(S_{a})^{2}$
$11(S_{a})^{2}-67500=0$
$11(S_{a})^{2}=67500$
$(S_{a})^{2}= \frac{67500}{11}$
$S_{a}=+/- \sqrt{ \frac{67500}{11} }$
Since speed cannot be negative, the solution of our equation is:
$S_{a}= \sqrt{ \frac{67500}{11} }$
$S_{a}=78.33$

We can conclude that the speed of the wind is 78 mph.

3 0

4 years ago

What are the steps and properties to this problem

lawyer [7]

3(2m+12) -4m = 20 -3(3m+5)

Step 1. Distribute 3 to (2m+12) and -3 to (3m+5)

Distribution property:
When you are distributing, you multiply the outside number by the numbers inside. For example,
-1(4-2)
-1 times 4, -1 times -2
-4, 2 (negative times negative =positive)
Then you would get
-4+2. You do not distribute with multiplication and division. So then we would do this with our numbers.

6m+36 -4m = 20 -9m-15
______
Step 2. Simplify by adding like terms.

Like terms:
Terms are separated by operation symbols (+,-,*,➗). Like terms are terms with the same variable next to it. 5a and 6a are like terms. Terms with no variables at all are also like terms. 5 and 6 are like terms. 8a and 7 are not like terms. 9a and 9b are not like terms.

6m+-4m= 2m. 20+(-15)=5
_____
2m+36=5-9m

Step 3. Add 9m to both sides
11m+36=5
____
Step 4. Subtract 36 from both sides
11m=-31
____
Step 5. Divide by 11
m=-31/11

If you can please provide brainliest. I took 30 minutes doing this.