1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Sauron [17]
3 years ago
6

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

Mathematics
2 answers:
Slav-nsk [51]3 years ago
6 0

Answer:

(x + 1 + i)(x + 1 - i) ↔ x²+2x+2; (x+2i)(x-2i) ↔ x²+4; (x-2i-2)(x+2i-2) ↔ x²-4x+8

Explanation:

For the first expression, use the distributive property to multiply.  First multiply all terms of the second trinomial by x:

x(x)+x(1)-x(i) = x²+x-xi

Next multiply all terms of the second trinomial by 1:

1(x)+1(1)-1(i) = x+1-i

Next multiply all terms of the second trinomial by i:

i(x)+i(1)-i(i) = xi+i-i²

Combining all terms,

x²+x-xi+x+1-i+xi+i-i²

Combining like terms, we have

x²+(x+x)+(-xi+xi)+(-i+i)+1-i² = x²+2x+1-i² = x²+2x+1-(-1) = x²+2x+2

For the second expression, use the acronym FOIL (First, Outer, Inner, Last):

x(x) = x²

x(-2i) = -2xi

2i(x) = 2xi

2i(-2i) = -4i² = -4(-1) = 4

This gives us x² - 2xi + 2xi + 4, which simplifies to x²+4.

For the third expression, use the distributive property.  Multiply everything in the second trinomial by x:

x(x)+x(2i)+x(-2) = x²+2xi-2x

Multiply everything in the second trinomial by -2i:

-2i(x)+-2i(2i)+-2i(-2) = -2xi-4i²+4i = -2xi-4(-1)+4i = -2xi+4+4i

Multiply everything in the third trinomial by -2:

-2(x)+-2(2i)+-2(-2) = -2x-4i+4

Combining all, we have

x²+2xi-2x+-2xi+4+4i+-2x-4i+4

Combining like terms gives us

x²+(2xi+-2xi)+(-2x+-2x)+(4+4)+(4i-4i) = x²-4x+8

Tems11 [23]3 years ago
5 0
The first one is x^2+2x+2
the second one is x^2+4
the last one is x^2-4x+8

You might be interested in
Consider function f.
tekilochka [14]

Given:

The function is:

f(x)=\sqrt{7x-21}

To find:

The steps of finding the inverse function f^{-1}(x).

Solution:

We have,

f(x)=\sqrt{7x-21}

The steps of finding the inverse function are:

Step 1: Substitute f(x)=y.

y=\sqrt{7x-21}

Step 2: Interchange x and y.

x=\sqrt{7y-21}

Step 3: Taking square on both sides, we get

x^2=7y-21

Step 4: Adding 21 on both sides, we get

x^2+21=7y

Step 5: Divide both sides by 7.

\dfrac{1}{7}x^2+3=y

Step 6: Substitute y=f^{-1}(x).

\dfrac{1}{7}x^2+3=f^{-1}(x), where x\geq 0.

Therefore, the inverse of the given function is f^{-1}(x)=\dfrac{1}{7}x^2+3 and the arrangement of steps is shown above.

7 0
3 years ago
A square has an area of 289 sq cm. what is the length of one side
MatroZZZ [7]
For this problem you can do it one of two ways. The first way would be simply take the square root because the area of a square is one side squared. The other way using the same rule would be to go up from a reasonable number and square it, if that is not the number you are looking for add 1 to the original number and square it again. if you cannot square and square root in your head, you should be allowed to use a calculator to get the answer or 17 as the length of a side.
5 0
3 years ago
When 10 b = 5 (StartRoot c EndRoot + 2) is solved for c, one equation is c = (2b minus 2) squared Which of the following is an e
Burka [1]

Answer:

I will show all the steps to lead to the solution.

1) 10b = 5 (√c + 2)  <---- starting equation

2) divide by 5 => 2 b = √c + 2

3) subtract 2 => 2b - 2 = √c

4) raise to the power 2 => (2b - 2)^2 = c, which is the expression given.

Now these are two equivalent forms:

1) extract 2 from the parentheses: c = 4 (b -1)^2

2) expand the parentheses: c = 4b^2 - 8b + 4)

Step-by-step explanation:

Choice D

8 0
2 years ago
Four friends own a carwash, the first total profit in the first month was 438 and two months each other friends had made a profi
harkovskaia [24]

Answer:

298

Step-by-step explanation:

given data

total friend = 4

total profit in the first month = 438

two months each friend profit = 184

solution

we consider here total profit second month is = x

so

profit second month = 184 × 4 - 438

x = 736 - 438

x = 298

so that here profit that car wash making the second month is 298

4 0
2 years ago
Find the y and x-intercept for <br> -x+3y+3
Darya [45]
-x+3y+3=0 <-- This puts the expression into an equation to make it solvable.
3y+3=x  <-- Use Addition Property of Exponents to move the (x) to the right
3y=x-3 <-- Use Subtraction Property of Exponents to move the (3) to the right
y=\frac{1}{3}-1 <-- Use Division Property of Exponents to remove the 3 from y
y=\frac{1}{3}-1 < This is the equation for the y-intercept

-x+3y+3=0 <-- Same as above, makes it so the expression is an equation to solve
-x+3=-3y <-- Use Subtraction Property of Exponents to move the 3y to the right
-x=-3y-3 <-- Use Subtraction Property of Exponents to move the 3 to the right
x=3y+3 <--Use Divison Property of Exponents to remove the -1 from x
x=3y+3 <-- This is the equation for the x-intercept

Hope this helped!


6 0
2 years ago
Read 2 more answers
Other questions:
  • I rlly need to know this asap thanks
    10·2 answers
  • Do you tailgate the car in front of you? About 35% of all drivers will tailgate before passing, thinking they can make the car i
    9·1 answer
  • mike constructed a closed box that measures 2.5 feet long by 3 feet wide by 1.5 feet high. what is the total area of the materia
    8·1 answer
  • For every dollar increase in the price of music CDs sold by a record label, the demand for the CDs drops by 100. However, 4,000
    12·1 answer
  • Use the calculator to find the following to the nearest thousandth.
    14·2 answers
  • Find the GCF of the following literal terms.<br><br> m^7n^4p^3 and mn^12p^5
    6·2 answers
  • You have a new mobile phone .The phone costed ?140 and then you pay for one year contract at ?15 per month .How much do you pay
    7·1 answer
  • Linear or nonlinear!?
    6·2 answers
  • In the diagram below, which line has a positive slope? AB AD AC DB
    12·1 answer
  • URGENT!!!!!!!! PLEASE HELP ASAP TIMED!!!!!!!!!!!!!!!
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!