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2 years ago

Simplify (3 + 2i)(7 − 5i).

2 answers:

8 0

Rule needed: i^2 = -1
Standard form a + bi

(3 + 2i)(7 - 5i) FOIL
3 * 7 = 21
3 * - 5i = - 15i
2i * 7 = 14i
2i * -5i = - 10i^2 = - 10 * -1 = 10
Putting it all back together.
31 - i

swat322 years ago

3 0

(3+2i)(7-5i) = 21 - 15i + 14i + 10 = 31 - i

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Answer:

angles 2 and 10 are corresponding Angles while angles 6 and 11 are alternate Angles

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When you receive a loan to make a purchase, you often must make a down payment in cash. The amount of the loan is the purchase c

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Summarizing the problem, there are three terms that you have to deal with: purchasing cost, down payment and loan. So, you would expect that the answer would contain these quantities. Among them, the unknown is the purchasing cost, therefore, we denote this as x.

Based on the statement, "The amount of the loan is the purchase cost minus the down payment", we can formulate an equation for this.

Amount of Loan = x - Down payment

This will be our working equation. Moving on, the down payment was mentioned to be equal to $1500. The lean received is equal to $2600. Substituting these values to the working equation, we can now determine the value of x.

2600 = x - 1500

Solving for x by transposing it to one side,

x = 2600-1500
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Therefore, the purchasing cost of the car is $1,100.

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3 years ago

Write a simplified polynomial expression in standard form to represent the area of the rectangle below.

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Answer:

$5x^{2} -18x-8$

Step-by-step explanation:

The formula for area of a rectange is lw, where l is length and w is width. Since x-4 and 5x+2 are the sides, we can multiply them together to give us the area. We do (x-4)(5x+2). We use the FOIL method (First Outside Inside Last) and get 5x^2-18x-8.

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2 years ago

A student's grade for the four quarters are 95, 83, 91, and 85. What does the student need to earn on the final exam to have an

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Answer:

The least score the student can get is 71 to get an overall B average at the end of the year.

Step-by-step explanation:

Let the score she needs to get be = x

We now have to take the mean of all the five subjects (including x) and equate it to the least score she can have to get a B grade.

Let us take the least score the student needs to get a B grade to be 85

Mean of all 5 scores =

$\frac{95+83+91+85+x}{5}=85$

$\frac{354+x}{5} =85$

$354+x = 425$

$x = 71$

The least score the student can get is 71 to get an overall B average at the end of the year.

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2 years ago

Mario claims that if the dinominator of a fraction is a prime number, then its decimal form is a repeting decimal. Do you agree?

vodomira [7]

Answer:

I do not agree because Mario's claim is not general.

Step-by-step explanation:

Prime numbers: These are a set of numbers that are divisible by 1 and itself only. Examples are: 2, 3, 5, 7. 11 etc.

And a denominator is the divisor in a given fraction.

Considering the following fractions whose denominators are prime numbers:

$\frac{2}{3}$ = 0.66666666...

$\frac{1}{7}$ = 0.142857142

$\frac{5}{11}$ = 0.45454545...

$\frac{3}{13}$ = 0.23076923

$\frac{1}{7}$ = 0.142857142

It could be observed that Mario's claim is not a general principle which is applicable to all fractions with a prime denominator. Thus, I do not agree with his claim.

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2 years ago