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2 years ago

latoya is going for a run. she runs at a speed of 6 miles per hour for 9.6 miles. for how many hours does she run?

1 answer:

7 0

$\begin{array}{ccc}6mi&-&1h\\9.6mi&-&xh\end{array}\ \ |cross\ multiply\\\\6x=1\cdot9.6\\\\6x=9.6\ \ \ |divide\ both\ sides\ by\ 6\\\\\boxed{x=1.6\ (h)}$

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What is the reciprocal of -2/3

ryzh [129]

3/-2

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3 years ago

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Which of the following is equivalent to the complex number -8(7i - 3i^2)

Leni [432]

Answer: B) -56i - 24

This is the same as -24 - 56i

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

Explanation:

The 'i' refers to the imaginary number $\sqrt{-1}$

In other words, $i = \sqrt{-1}$

Squaring both sides gets us $i^2 = -1$

So,

$x = -8(7i - 3i^2)\\\\x = -8(7i - 3(-1))\\\\x = -8(7i + 3)\\\\x = -8(7i) -8(3)\\\\x = -56i -24 \ \ \text{ .... Answer: Choice B}\\\\x = -24 - 56i\\\\$

The result is in the form a+bi where a = -24 is the real part and b = -56 is the imaginary part.

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2 years ago

I think of a number, multiply it by three, and add four. I get twenty two.

melomori [17]

Step-by-step explanation:

3x+4=22

3x=22-4

3x=18

x=18/3

x=6

3 0

2 years ago

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The angle θ 1 is located in Quadrant IV, and cos ⁡ ( θ 1 ) = 9/ 19 , theta, start subscript, 1, end subscript, right parenthesis

Firdavs [7]

Answer:

$sin\theta_1 = - \frac{2\sqrt{70}}{19}$

Step-by-step explanation:

We are given that $\theta_1$ is in fourth quadrant.

$cos\theta_1$ is always positive in 4th quadrant and

$sin\theta_1$ is always negative in 4th quadrant.

Also, we know the following identity about $sin\theta$ and $cos\theta$ :

$sin^2\theta + cos^2\theta = 1$

Using \theta_1 in place of \theta:

$sin^2\theta_1 + cos^2\theta_1 = 1$

We are given that $cos\theta_1 = \frac{9}{19}$

$\Rightarrow sin^2\theta_1 + \dfrac{9^2}{19^2} = 1\\\Rightarrow sin^2\theta_1 = 1 - \dfrac{81}{361}\\\Rightarrow sin^2\theta_1 = \dfrac{361-81}{361}\\\Rightarrow sin^2\theta_1 = \dfrac{280}{361}\\\Rightarrow sin\theta_1 = \sqrt{\dfrac{280}{361}}\\\Rightarrow sin\theta_1 = +\dfrac{2\sqrt{70}}{19}, -\dfrac{2\sqrt{70}}{19}$

$\theta_1$ is in 4th quadrant so $sin\theta_1$ is negative.

So, value of $sin\theta_1 = - \frac{2\sqrt{70}}{19}$

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2 years ago

The local county officials need to calculate the capacity of a large hole for the garbage refuse dump. The dump hole is 250 ft l

stepan [7]

Multiply 250 by 120 and the answer is 300,000ft2

4 0

3 years ago

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