Given g(x) = -2x + 3, solve for x when g(x) = -3.

If the modulus is 4 and the real part is –2.0, what is the imaginary part?

faltersainse [42]

Answer:

3.5

Step-by-step explanation:

edgenuity2020

3 0

4 years ago

Three airports have a total of

eimsori [14]

Answer:

76.7 million
89.1 million
75 million

Step-by-step explanation:

Let x represent the arrivals and departures at the third airport. Then the number at the first airport is x+1.7, and the number at the second airport is x+14.1. The total is ...

(x+1.7) + (x+14.1) + (x) = 240.8

3x +15.8 = 240.8

3x = 225

x = 75

x+1.7 = 76.7

x+14.1 = 89.1

The first airport has 76.7 million arrivals.

The second airport has 89.1 million arrivals.

The third airport has 75 million arrivals.

8 0

3 years ago

A gallon jug of milk is 5/6 full. After breakfast the jug is 1/12 full. Find the difference of the amounts before breakfast and

Oxana [17]

5/6=10/12

So 9/12 is the differemce

6 0

3 years ago

Read 2 more answers

If

Daniel [21]

Answer:

$x=\sqrt{\frac{7(4+\sqrt{15})}{2}}$

Step-by-step explanation:

From the way it is written, the $x$ is outside the square root. I will rewrite it as:

$x\sqrt{5} =x\sqrt{3} +\sqrt{7}$

$x\sqrt{5}-x\sqrt{3}=\sqrt{7}$

$x(\sqrt{5} - \sqrt{3} )=\sqrt{7}$

$x= \frac{\sqrt{7} }{\sqrt{5} - \sqrt{3}} \implies \frac{\sqrt{7}(\sqrt{5} + \sqrt{3}) }{2}$

$x=\frac{1}{2} \sqrt{7} (\sqrt{5} + \sqrt{3} )$

$x=\frac{\sqrt{35}}{2} +\frac{ \sqrt{21}}{2}$

$x=\frac{\sqrt{35}+\sqrt{21}}{2}$

Multiply denominator and numerator by 3

$x=\frac{3\sqrt{35}+3 \sqrt{21}}{6}$

Factor $\sqrt{3}$

$\sqrt{3} (\sqrt{105}+3 \sqrt{7})$

$x=\frac{\sqrt{3} (\sqrt{105}+3 \sqrt{7})}{6}$

Divide denominator and numerator by $\sqrt{3}$

$x=\frac{\sqrt{105}+3 \sqrt{7}}{2\sqrt{3} }$

Let's rewrite it again

$x=\frac{\sqrt{ (\sqrt{105}+3 \sqrt{7})^2}}{\sqrt{12} }$

$x=\sqrt{ \frac{1}{12} \cdot (\sqrt{105}+3 \sqrt{7})^2}$

It is already in the form $\sqrt{\frac{a}{b} }$

Expanding the perfect square, we have

$63+42\sqrt{15}+105$

$\frac{63}{12} +\frac{42\sqrt{15}}{12} +\frac{105}{12}$

$\frac{21}{4} +\frac{7\sqrt{15}}{2} +\frac{35}{4}$

Factor $\frac{7}{2}$

$\frac{7}{2} (4+\sqrt{15} )$

Therefore,

$x=\sqrt{\frac{7}{2} \left(4+\sqrt{15} \right)}$

$x=\sqrt{\frac{7(4+\sqrt{15})}{2}}$

7 0

3 years ago

Read 2 more answers

Help with these 3 I did all the other questions of the assignment, these are confusing ASAP

Gnom [1K]

Answers:

Problem 7) 25.2 feet
Problem 8) Angle = 52 degrees; Distance = 14.3 feet
Problem 9) DE = 22, EC = 10, BC = 20

=====================================================

Explanation:

The diagrams for problems 7 and 8 are shown below.

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Problem 7

Apply the tangent ratio to find that...

tan(angle) = opposite/adjacent

tan(42) = x/28

28*tan(42) = x

x = 28*tan(42)

x = 25.2113132403396

x = 25.2

Make sure your calculator is in degree mode. One way to check is to type in tan(45) and you should get 1 as a result.

------------------------------------

Problem 8, part 1

To find the angle y, we must use the sine ratio

sin(angle) = opposite/hypotenuse

sin(y) = 18/23

y = arcsin(18/23)

y = 51.5000495907521

y = 52 degrees approximately

------------------------------------

Problem 8, part 2

We can use the pythagorean theorem to find the missing side x

a^2+b^2 = c^2

18^2+x^2 = 23^2

324+x^2 = 529

x^2 = 529-324

x^2 = 205

x = sqrt(205)

x = 14.3178210632763

x = 14.3

Or alternatively, we can apply the tangent ratio on the angle y we found earlier to help find x

tan(angle) = opposite/adjacent

tan(y) = 18/x

tan(51.50004959) = 18/x

x*tan(51.50004959) = 18

x = 18/tan(51.50004959)

x = 14.3178210636621

x = 14.3

------------------------------------

Problem 9

The double tickmarks show that BE = EC = 10. That means BC = BE+EC = 10+10 = 20.

Since we have similar triangles, we can solve for x like so

DE/AC = BE/BC

x/44 = 10/20

20x = 44*10

20x = 440

x = 440/20

x = 22

So DE is 22 units long. Note how this is half as long as the side AC = 44.

4 0

3 years ago