Complex numbers are used to describe current. I voltage, E, and impedance, Z. These three quantities are related by the equation E = IZ. Given two ofthese quantities, solve the equation E = IZ for the missing variable.I = 4 + 4i, Z= 7+3iE=(Simplify your answer. Type your answer in the form a+b/. Use integers or fractions for any numbers in the expression.)

Given that,

The perimeter of a rectangle is 60.

The perimeter is generally defined as the length of the outline of the shape.

So, in rectangle having four sides, the perimeter would be sum of all the sides.

Length1 + length2 + length3 + length4 = perimeter

Here, length1 and length3 are equal, that are the lengths (y),

Similarly,

Length2 and length4 are equal, that is width (x).

Hence, the equation becomes,

x + y + x + y = perimeter

or

2x + 2y = 60

or

2 (x + y) = 60

Hence, the first two options are correct.

The Solution:

The value of the house in 13 years time can be calculated using the formula below:

In this case,

Substituting these values in the formula above, we get

Thus, the value of the house in 13 years is $911820 (to the nearest dollars)

A. We must divide the distance between the number of divisions

from 0 to 1 we have a distance of 1 and count 8 divisions

so

so the length of each segment is 1/8 or 0.125

B.

Two functions are called cofunctions if they are equal on complementary angles

Since

Substitute it in the rule above

The cofunction is sec(pi/4)

Solution

For this case we know that the total of students are 396 so we can do this:

x + y = 396

Where:

x= number of girls

y = number of boys

Then we have the following condition:

4x = 7y

Then solving for x we got:

x = 7/4 y

Replacing in the first equation we got:

7/4 y + y = 396

11/4 y= 396

y= 396*4/11 = 144

And x= 7/4 * 144 = 252

Then the answer would be:

252 girls and 144 boys

t = n(p-c)

t=100(11.75 - 1.75)

t = 100(10)

t=$1000

total profit received = $1000

We have to solve the expression:

We have to find a common denominator for the fractions and then solve it.

We can start by simplifying the fractions that can be simplified, like 2/6.

Then, the common denominator between 14 and 3 is 14*3=42, so we end with:

Answer: 41/42

In order to find Lorenzo's speed in miles per hour, we need to convert from yard to mile and from second to hour. The rates are:

1 yard = 1/1760 miles

1 second = 1/3600 hours

So we have that:

Lorenzo can ride 10.227 miler per hour.

To make the graph we need to make a table with different pairs of angles and radius.

We can start with θ = 0, and calculate the radius for different values of θ. (π/6, π/3, π/4 and so on. Then, you can join the points.

The equation for radius will be:

Then, in the line of θ = 0, you draw a point in the fourth circle.

Then, we get the following table of values:

θ r

04.00

π/63.72

π/43.36

π/32.83

π/20.00

Note that we can't evaluate angles whose cosine is negative (angles in quadrants 2 and 3) since we would be trying to calculate the square root of a negative number, which does not exist among real numbers. Then, we will evaluate angles in the first quadrant (already done) and the 4th quadrant.

θ r

-π/63.72

-π/43.36

-π/32.83

-π/20.00

In the last table we use negative angles, they can be "translated" to positive:

-π/6= π/6

-π/4= 7π/4

-π/3= 5π/3

-π/2= 3π/2

Now, we can draw the points:

Joining the points:

78 divide by 14

First, divide the numbers

78/14 = 5.57

5.57 lies between 5 and 6

We have a quadrilateral ABCD, where we know that AB || DC.

The other condition for the quadrilateral to be a parallelogram is that the other 2 sides of the parallelogram are congruent.

The other two sides are AC and BD, so the other condition needed is that AC and BD are congruent.

Answer: AC and BD are congruent.

Given the equation;

You are to calculate the value of y. This is as shown below;

First collect the like terms;

Evaaluate the expression an find y;

Divide both sides by -6;

Hence the value of y is -5

Analysing the letter D, we can find the following symmetry (in red):

There is no point of symmetry. Therefore, the correct option is B.

The best cluster is Las Vegas, which has a percentage of 78% that is linearly close to 77%, the percentage of the whole population of the United States.

Las Vegas

we get that:

its current value is $11091.25

Equations:

Sum (1)+ (2):

x=2

Now, we are going to sum (3)*2+(2).

y=2.

Replacing y and x in (4) and (3):

Isolating w in (5) ans replacing in (6):

Answer: z=35.

ANSWER

Not a right triangle

EXPLANATION

In a right triangle, the hypotenuse is always the longest side. If these are the side lengths of a right triangle, the sides would be,

The Pythagorean theorem must be true for any right triangle,

Let's see if it is indeed true,

If the Pytagorean theorem is nort true, then this is not a right triangle

1/3 is a rational number, which written as a decimal is an infinite period decimal.

Answer:

Choice B.

Explanation:

The equation can be rewritten as

Now since

and

the expression becomes

Hence, choice B is the correct answer since it matches the answer we got above.

Answer

The x-intercept of a line is the x-coordinate of the point where the line crosses the x-axis. It occurs when y = 0.​

Hope this Helps!!!

We will solve as follows:

So, the solution is x < -3.

***Breakdown:

*After we obtain:

We operate like terms, that is we separate the variables and integers in the different side [Operating as if it were a normal equation]:

After this, we know that by dividing and/or multiplying by negative values in the inequality the orientation of the inequality will shift [That is if it was "<" then it will become ">" and viceversa], that is:

y = 2

The given equation is 4y

Divide both sides of the equation by 4

y = 2

Also, since we are asked to use our number sense, we can find what we will multiply by 4 to give 8

Since 4 x 2 = 8, then y = 2

The given expression is

First, we add 16 on each side

Then, we apply a square root on each side

Now, we subtract 6 from each side

We are asked to correct the following statements:

A. "The hypotenuse is the longest side of the right triangle" The statement is true.

B. "The Pythagorean theorem applies to all triangles". The statement is false. The Pythagorean theorem applies to RIGHT triangles.

C. "The hypotenuse is always adjacent to the 90° angle". The statement is false. The hypotenuse is opposite to the 90° angle.

D. "The Pythagorean theorem states that 2a + 2b - 2c". The statement is false. The Pythagorean theorem states that:

E. "The logs, a and b, will always be adjacent to the 90° angle". The statement is true, since a and b represent the adjacent sides of the 90 degrees angle.

F.

ANSWER:

$ 117.51

STEP-BY-STEP EXPLANATION:

The commissions are divided into two payments, the first payment of the first $ 1500 with a commission of 3.16% and a second payment with a commission of 11% of all the remaining money of the first $ 1500.

Therefore, we calculate it as follows:

The total commission is $ 117.51

You have the following equation:

M = 2rt³ - 3rx

In order to solve the previous equation for x, proceed as follow:

M = 2rt³ - 3rx subtract 2rt³ both sides

M - 2rt³ = -3rx divide by -3r both sides

(M - 2rt³)/(-3r) = x simplify left side

-M/3r + 2/3 t³ = x

We will have the following:

First, we construct the exponential decay function, that is:

Now, we will determine the population after 6 years:

So, the population after 6 years will be of approximately 37491 people-

x = -43/4

Given:

To find:

the value of x

Given:

A rectangular pool with the following measures,

Perimeter

Length = x + 8

Width = x

Let's determine the measure of its dimensions:

Let's now determine its dimensions,

Length = x + 8 = 7 + 8 = 15 ft.

Width = x = 7 ft.

Therefore, the dimension of the rectangular pool is Length = 15 ft. and Width =7 ft.