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3 years ago

Simpilify the expresssion 2+3i/4+3i

1 answer:

3 0

Multiply the numerator and denominator by 4+5i
=[(2+3i)(4+5i)]/[(4-5i)(4+5i)]
=[(8-15)+(12+10)i] / [16+25] <span>= [ -7 + 22i ] / [41]
= (-7/41) + (22/41)i </span>

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Find the length of both of the unknown sides in the triangle shown here.

icang [17]

Answer:

$(x+11)^2 = (x+3)^2 +16^2$

And if we solve this equation for x we got:

$x^2 +22x +121 = x^2 +6x +9 +256$

We can cancel $x^2$ in both sides and we have this:

$22x -6x= 256+9-121 =144$

And then we got:

$16 x= 144$

$x =\frac{144}{16}= 9$

And then the length of the sides are 9+11= 20 m for the hypothenuse, 16 for the adjacent side and 9+3 = 12m for the last side.

Lenght of the smaller unknown side: 12m

Lenght of the larger unknown side: 20m

Step-by-step explanation:

For this case we have a right triangle and we can use the Pythagoras Theorem and using the info given by the triangle we can set up the following equation:

$(x+11)^2 = (x+3)^2 +16^2$

And if we solve this equation for x we got:

$x^2 +22x +121 = x^2 +6x +9 +256$

We can cancel $x^2$ in both sides and we have this:

$22x -6x= 256+9-121 =144$

And then we got:

$16 x= 144$

$x =\frac{144}{16}= 9$

And then the length of the sides are 9+11= 20 m for the hypothenuse, 16 for the adjacent side and 9+3 = 12m for the last side side.

Lenght of the smaller unknown side: 12m

Lenght of the larger unknown side: 20m

8 0

3 years ago

Which expressions are a factor of -48xyz -24xy +40xyz?

Paha777 [63]

A. 4 (is the only factor for expression -48xyz -24xy +40)

6 0

3 years ago

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I need the answer <br><br> Ushshsbshfhd

stealth61 [152]

Answer:

Step-by-step explanation:

Its the only one that makes sense

5 0

3 years ago

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There are 72 students in the gym. 45 students are girls. The rest are boys. What is the ratio of boys to girls?

PIT_PIT [208]

Answer:

3 to 5

Step-by-step explanation:

To find the number of boys, take the total students and subtract the girls

72 -45 =27

We want the ratio of boys:girls

boys:girls

27:45

Divide each number by 9

27/9:45/9

3 : 5

3 0

3 years ago

Kyle drew three line segments with lengths: 2/4 inch 2/3inch, and 2/6 inch list the fractions in order from least to greatest

Sati [7]

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Method 1
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Since the numerators are the same, the smaller the denominators, the greater the fraction is.

Arranging from the least to the greatest
$\dfrac{2}{6} \ , \ \dfrac{2}{4} \ , \ \dfrac{2}{3}$

----------------------------------------------------------------
Method 2
----------------------------------------------------------------
Lets change all to the same denominators

$\dfrac{2}{4} = \dfrac{2 \times 3}{4 \times 3} = \dfrac{6}{12}$

$\dfrac{2}{3} = \dfrac{2 \times 4}{3 \times 4} = \dfrac{8}{12}$

$\dfrac{2}{6} = \dfrac{2 \times 2}{6 \times 2} = \dfrac{4}{12}$

Now that all the denominators are the same, we can arrange the fractions by comparing the numerators. The bigger the numerators, the greater the fraction.

Arranging from the least to the greatest
$\dfrac{2}{6} \ , \ \dfrac{2}{4} \ , \ \dfrac{2}{3}$

3 0

3 years ago

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