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2 years ago

Which properties are used to add these complex numbers? Choose all that apply.

Mathematics

2 answers:

mario62 [17]2 years ago

5 0

B. Associative Property , you're working out the numbers in the parentheses before anything else.

Dennis_Churaev [7]2 years ago

3 0

Answer:

Properties used here are:

A. Commutative property.

C. Associative property

Step-by-step explanation:

Given the expression:

(7+2i) + (4+3i)

(7+ 2i) + 4 + 3i

According to associative property:

a + (b + c) = (a + b) + c

7 + (2i + 4) + 3i

Using commutative property:

a + b = b + a

7 + (4 + 2i) + 3i

(7 + 4) + (2i + 3i)

Simplify:

11 + 5i

So, we use Commutative & Associative Property.

That's the final answer.

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A kite has a perimeter of 70 centimeters. One of the shorter sides measures 16 centimeters. What are the lengths of the other th

kari74 [83]

Answer:

a kite has 2 short sides and 2 long sides. The 2 short sides are equal. The 2 long sides are also equal. This means that the other short side is 16cm. And the remaining longer sides can be found like this:

let's pretend *y* is the long side

2*y = 70 - 16 - 16. (two of the long sides = 70 - short side - another short side)

so use algebra to find y.

2*y = 38

y = 19 so the long sides are both 19cm each

Your final answer: 16cm, 19cm, 19cm

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2 years ago

Read 2 more answers

Suppose y varies directly with x. If y = –4 when x = 8, what is the equation of direct variation? Complete the steps to write th

Sauron [17]

Answer:

y = -1/2 x

Step-by-step explanation:

Follow the directions "Complete the steps to write the equation of direct variation. Start with the equation of direct variation y = kx. Substitute in the given values for x and y to get . Solve for k to get . Write the direct variation equation with the value found for k."

y = kx substitute y = -4 and x = 8.

-4 = k*8

-4/8 = k

-1/2 = k

So the equation is y = -1/2(x).

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2 years ago

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Which of the following are necessary when proving that the opposite angles of a parallelogram are congruent? A. Opposite sides a

Misha Larkins [42]

Answer:

C and B

Step-by-step explanation:

The correct option is option B and C. The necessary condition to prove that the opposite angles of a parallelogram are congruent:

C. Angle Addition Postulate.

B. Opposite sides are congruent

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2 years ago

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Peyton plans to deposit her next paycheck into her savings account.she makes $12.50 per hour and her next paycheck will be h hou

Snowcat [4.5K]

Answer: Current savings account balance

Step-by-step explanation:

since the equation is y = mx + b

mx would be the starting point so she earns 12.50 per hour so it's the current amount she has is 12.50.

Sorry if it dosen't make sense.

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2 years ago

Steve likes to entertain friends at parties with "wire tricks." Suppose he takes a piece of wire 60 inches long and cuts it into

Alex_Xolod [135]

Answer:

a) the length of the wire for the circle = $(\frac{60\pi }{\pi+4}) in$

b)the length of the wire for the square = $(\frac{240}{\pi+4}) in$

c) the smallest possible area = 126.02 in² into two decimal places

Step-by-step explanation:

If one piece of wire for the square is y; and another piece of wire for circle is (60-y).

Then; we can say; let the side of the square be b

so 4(b)=y

b= $\frac{y}{4}$

Area of the square which is L² can now be said to be;

$A_S=(\frac{y}{4})^2 = \frac{y^2}{16}$

On the otherhand; let the radius (r) of the circle be;

2πr = 60-y

$r = \frac{60-y}{2\pi }$

Area of the circle which is πr² can now be;

$A_C= \pi (\frac{60-y}{2\pi } )^2$

$=( \frac{60-y}{4\pi } )^2$

Total Area (A);

A = $A_S+A_C$

= $\frac{y^2}{16} +(\frac{60-y}{4\pi } )^2$

For the smallest possible area; $\frac{dA}{dy}=0$

∴ $\frac{2y}{16}+\frac{2(60-y)(-1)}{4\pi}=0$

If we divide through with (2) and each entity move to the opposite side; we have:

$\frac{y}{18}=\frac{(60-y)}{2\pi}$

By cross multiplying; we have:

2πy = 480 - 8y

collect like terms

(2π + 8) y = 480

which can be reduced to (π + 4)y = 240 by dividing through with 2

$y= \frac{240}{\pi+4}$

∴ since $y= \frac{240}{\pi+4}$ , we can determine for the length of the circle ;

60-y can now be;

= $60-\frac{240}{\pi+4}$

= $\frac{(\pi+4)*60-240}{\pi+40}$

= $\frac{60\pi+240-240}{\pi+4}$

= $(\frac{60\pi}{\pi+4})in$

also, the length of wire for the square (y) ; $y= (\frac{240}{\pi+4})in$

The smallest possible area (A) = $\frac{1}{16} (\frac{240}{\pi+4})^2+(\frac{60\pi}{\pi+y})^2(\frac{1}{4\pi})$

= 126.0223095 in²

≅ 126.02 in² ( to two decimal places)

4 0

2 years ago