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3 years ago

Mary draws the number line below to repersent the solution set of the inequality 50-8t<90

Mathematics

1 answer:

marta [7]3 years ago

4 0

<span>50-8t<90
50-90<8t
-40<8t
8t>-40
t>-5
Solutions should go to the right.
Mary probably was solving it as following
</span>50-8t<90
<span>-8t<90-50
-8t<40 (here, when she divided both sides by -8, she had to change sign < to the sign >)
But she did not change the sign, and got
t<-5

</span>

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The ratio of the circumference of two circles is 3:2.What is the ratio of their area

Nezavi [6.7K]

The ratio of their area is 9/4

<h2>Explanation:</h2>

We use ratios to compares values. In this exercise, we are comparing the circumference of two circles, which is:

$3:2$

and we want to know what is the ratio of their area. Recall that the circumference of a circle is given by:

$C=2\pi r \\ \\ \\ Where: \\ \\ C:Circumference \\ \\ r:Radius \ of \ the \ circle$

If we define:

$C_{1}: \ Circumference \ of \ circle \ 1 \\ \\ C_{2}: \ Circumference \ of \ circle \ 2 \\ \\ r_{1}: \ Radius \ of \ circle \ 1 \\ \\ r_{2}: \ Radius \ of \ circle \ 2$

Then, the ratio of the circumference of two circles is 3:2 is:

$\frac{C_{1}}{C_{2}}=\frac{2\pi r_{1}}{2\pi r_{2}}=\frac{3}{2} \\ \\ \therefore \frac{r_{1}}{r_{2}}=\frac{3}{2}$

The area of a circle is given by:

$A=\pi r^2 \\ \\ A:Area \\ \\ r:Radius$

So the ratio of their area can be found as:

$\frac{A_{1}}{A_{2}}=\frac{\pi r_{1}^2}{\pi r_{2}^2} \\ \\ \\ A_{1}:Area \ of \ circle \ 1 \\ \\ A_{2}:Area \ of \ circle \ 2$

So:

$\frac{A_{1}}{A_{2}}=\frac{r_{1}^2}{r_{2}^2}=\left( \frac{r_{1}}{r_{2}} \right)^2 \\ \\ \frac{A_{1}}{A_{2}}=\left(\frac{3}{2}\right)^2 \\ \\ \boxed{\frac{A_{1}}{A_{2}}=\frac{9}{4}}$

<h2>Learn more:</h2>

Unit rate: brainly.com/question/13771948#

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3 years ago

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Alexus [3.1K]

Answer:

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Step-by-step explanation:

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julsineya [31]

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Step-by-step explanation:

You can use law of sines to answer. Law of Sines states that $\frac{sin(a)}{A} =\frac{sin(b)}{B}$ . That means that $\frac{sin(60)}{4\sqrt{6} }=\frac{sin(b)}{8}$ . Multiplying 8 to both sides gives us $\frac{8sin(60)}{4\sqrt{6} }=sin(b)$ . By using inverse of sin, we get $b = sin^{-1} (\frac{8sin(60)}{4\sqrt{6} } )$ . Plugging that into a calculator gives us b=45 degrees.

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Step-by-step explanation:

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Which of the following is equivalent to <br><br> 3x−4y=18?

sammy [17]

The equation which is equivalent to the equation as given in the task content is; 6x -8y = 36.

<h3>Which equation is equivalent to the equation as given in the task content?</h3>

According to the task content, it follows that the equation which is given in the task content is;

3x -4y = 18.

Hence, upon multiplication of the whole equation by 2; the resulting equation from the multiplication is;

6x -8y = 36

Ultimately, the equivalent equation is; 6x -8y = 36.