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2 years ago

29. Which of the following expressions will result in a real answer after being simplified? Select all that apply.

Mathematics

1 answer:

nexus9112 [7]2 years ago

5 0

Answer: A, B, C, and E

Step-by-step explanation:

If both sides are real numbers, then the product will be a real number.

If in at least one of the sides we have a complex number, then the product will be real if:

The other number is zero.

The other number is the conjugate of the first.

This is when:

Suppose we have a number:

z = a + b*i

The conjugate will be:

w = a - b*i

And the product between them is:

(a + b*i)*(a - b*i) = a^2 + a*b*i - a*b*i + b^2 = a^2 + b^2

Then the options that will have a real answer are:

A. (4+5i)(4-5i) = 4^2 + 5^2 = 16 + 25 = 41

B. (4 + 91)*(41 - 9) = 3040

C. (3 + 2*i)*(3 -2*i) = 3^2 + 2^2 = 9 + 4 = 13

E. (312 + 7i)*(312 - 7i) = 312^2 + 7^2 = 97,393

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solniwko [45]

Answer:

B) 38.4

Step-by-step explanation:

5 0

3 years ago

Help me with A and B please

g100num [7]

Part A.

Ashwin had a 4-cm cube.

volume of cube = side^3

volume = (4 cm)^3 = 64 cm^3

Ashwin has 64 small cubes.

We need to find the volumes of all prisms in Part A. Only prisms with at most 64 cm^3 volume can be the answer.

A. v = 2 * 4 * 7 = 28

B. v = 4 * 5 * 6 = 120

C. v = 5 * 5 * 4 = 100

D. v = 4 * 7 * 5 = 140

E. v = 3 * 5 * 4 = 60

Part A. answer: A, E

Part B.

Dora had a 5-cm cube.

volume of cube = side^3

volume = (5 cm)^3 = 125 cm^3

Dora has 125 small cubes.

We need to find the volumes of all prisms in Part B. Only prisms with at most 125 cm^3 volume can be the answer.

A. v = 3 * 3 * 8 = 72

B. v = 3 * 4 * 5 = 60

C. v = 6 * 6 * 4 = 144

D. v = 5 * 8 * 4 = 160

E. v = 3 * 5 * 4 = 60

Part B. answer: A, B, E

6 0

3 years ago

Kristian buys a meal for $8.40 calculate the fraction of the $72 after buying the computer game which costed $32.40 and the meal

brilliants [131]

Answer:

After buying the meal and the computer game, Kristian has 43.33% of his money left.

Step-by-step explanation:

Given that Kristian buys a meal for $ 8.40, to calculate the fraction of the $ 72 after buying the computer game which cost $ 32.40 and the meal, the following calculation must be performed:

72 = 100

8.40 + 32.40 = X

72 = 100

40.80 = X

40.80 x 100/72 = X

4,080 / 72 = X

56.66 = X

100 - 56.66 = 43,333

Therefore, after buying the meal and the computer game, Kristian has 43.33% of his money left.

7 0

3 years ago

<img src="https://tex.z-dn.net/?f=%5Cfrac%7B3%2F7%7D%7B7%5Csqrt%7B10%7D%2F2%20%7D" id="TexFormula1" title="\frac{3/7}{7\sqrt{10}

VashaNatasha [74]

Multiply the numerator and denominator by 7×2 = 14 to eliminate the denominators of those fractions:

$\dfrac{\dfrac37}{\dfrac{7\sqrt{10}}2}\times\dfrac{14}{14}=\dfrac{3\times2}{7\sqrt{10}\times7}=\dfrac6{49\sqrt{10}}$

Rationalize the denominator by multiplying both numerator and denominator by √10:

$\dfrac6{49\sqrt{10}}\times\dfrac{\sqrt{10}}{\sqrt{10}}=\dfrac{6\sqrt{10}}{49(\sqrt{10})^2}=\dfrac{6\sqrt{10}}{49\times10}=\dfrac{6\sqrt{10}}{490}$

Lastly, cancel the common factor of 2 in both the numerator and denominator (which comes from 6 = 2×3 and 490 = 2×245):

$\dfrac{6\sqrt{10}}{490}=\dfrac{3\sqrt{10}}{245}}$

8 0

2 years ago

There were 75 roasted turkeys at Ally's Eats. Bob's Goods had 4/5 as many roasted turkeys as Ally's Eats. If Ally's Eats had 5/6

Vilka [71]

Answer:

Step-by-step explanation:

Roasted turkey in Ally's Eats = 75

Roasted turkey in Bob's goods = 4 / 5 x Ally's Eats

= (4 / 5) x 75

= 60

Roasted turkey in Charlotte's Market = N ( let )

Given

5/6 N = 75

N = 6 / 5 x 75

= 90

Roasted turkey in Charlotte's Market = 90 .

8 0

3 years ago