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3 years ago

- x is less than or equal to 5

Mathematics

1 answer:

Bad White [126]3 years ago

8 0

Answer:

equal

Step-by-step explanation:

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There are 90 people in the cafeteria. 50 are wearing red shirts, 15 are wearing green shirts, and the rest are wearing blue shir

Rainbow [258]

First we need to calculate the number of people wearing a blue shirt,
90 - 50 - 15 = 25
the ratio is actually just like division, like the way you wrote fractions. the number on top will be the number of people who wears blue, and the number at the bottom will be the total number of people
25/90
but we need to simplify that.
5/18
therefore the ratio will be 5:18

7 0

3 years ago

Simplify the complex numbers using de Moivre's Theorem and match them with their solutions.

alexandr1967 [171]

For the numbers in $a+bi$ form, convert to polar form:

$1+i=\sqrt2\dfrac{1+i}{\sqrt2}=\sqrt2\left(\cos\dfrac\pi4+i\sin\dfrac\pi4\right)$

By DeMoivre's theorem,

$(1+i)^5=(\sqrt2)^5\left(\cos\dfrac{5\pi}4+i\sin\dfrac{5\pi}4\right)=4\sqrt2\dfrac{-1-i}{\sqrt2}=-4-4i$

$-1+i=\sqrt2\dfrac{-1+i}{\sqrt2}=\sqrt2\left(\cos\dfrac{3\pi}4+i\sin\dfrac{3\pi}4}\right)$

$\implies(-1+i)^6=(\sqrt2)^6\left(\cos\dfrac{18\pi}4+i\sin\dfrac{18\pi}4\right)=8i$

$\sqrt3+i=2\dfrac{\sqrt3+i}2=2\left(\cos\dfrac\pi6+i\sin\dfrac\pi6\right)$

$\implies2(\sqrt3+i)^{10}=2^{11}\left(\cos\dfrac{10\pi}6+i\sin\dfrac{10\pi}6\right)=2^{11}\dfrac{1-i\sqrt3}2=2^{10}(1-i\sqrt3)$

For the numbers already in polar form, DeMoivre's theorem can be applied directly:

$2\left(\cos20^\circ+i\sin20^\circ\right)^3=2\left(\cos60^\circ+i\sin60^\circ\right)=2\dfrac{1+i\sqrt3}2=1+i\sqrt3$

$2\left(\cos\dfrac\pi4+i\sin\dfrac\pi4\right)^4=2(\cos\pi+i\sin\pi)=-2$

At second glance, I think the 2s in the last two numbers should also be getting raised to the 3rd and 4th powers:

$\left(2(\cos20^\circ+i\sin20^\circ)\right)^3=8\left(\cos60^\circ+i\sin60^\circ\right)=4+4\sqrt3$

$\left(2\left(\cos\dfrac\pi4+i\sin\dfrac\pi4\right)\right)^4=16(\cos\pi+i\sin\pi)=-16$

4 0

3 years ago

How do you do long divison with 2 digits?

Anastaziya [24]

By 2 digits if you mean there is a digit on each side of a division symbol you will solve what you have there and then add a decimal point to the answer and then add zeros to bring down. Then you can repeat the long division process and will have an answer.

6 0

3 years ago

If 2k - 3 = 9 (k+7)-3 then k is ????

m_a_m_a [10]

Answer:

k= -9

Step-by-step explanation:

2k-3=9k+63-3 [expand the 9(k+7) first]

2k-9k=63-3+3 [put the like terms together]

-7k=63 [do the simple math]

k= 63 ÷ by -7

k=-9

4 0

3 years ago

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Solve the inequality 7x - 35 < 2 [x - 5]

Daniel [21]

Answer:

x < 5

Step-by-step explanation:

Step 1: Simplify

7x−35<2x−10

Step 2: Substract 2x from both sides

7x−35−2x<2x−10−2x

5x−35<−10

Step 3: Add 35 to both sides

5x−35+35<−10+35

5x<25

Step 4: Divide by 5

5x/5 × 25/5

x < 5

8 0

3 years ago

Read 2 more answers