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3 years ago

Explain how you can determine whether or not a number is rational

2 answers:

8 0

The easiest way to tell if a number is rational or not is to attempt to express it as a fraction. If you can, then the number is rational. If not, then the number is irrational. All integers are rational numbers, because they can be written as a fraction (for example, the integer 8 = 8/1). But numbers like pi or sqrt(2) cannot be written as a fraction and are not rational.

monitta3 years ago

6 0

Rational #s

(Terminating and repeating decimals)

Decimals
Fractions
Whole #s
Natural#s

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Jeanette can swim 45 meters in 30 seconds. How far can she probably swim in 90 seconds?

shtirl [24]

H. 135 meters

Work: 45 meters in 30 seconds 45/30= 1.5 so 90x1.5 = 135 meters

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3 years ago

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To solve the equation 5sin(2x)=3cosx, you should rewrite it as___.

galina1969 [7]

Answer:

Step-by-step explanation:

We want to solve the equation:

$5\sin(2x)=3\cos(x)$

To do so, we can rewrite the equation.

Recall the double-angle for sine:

$\sin(2x)=2\sin(x)\cos(x)$

By substitution:

$5\left(2\sin(x)\cos(x)\right)=3\cos(x)$

Distribute:

$10\sin(x)\cos(x)=3\cos(x)$

We can subtract 3cos(x) from both sides:

$10\sin(x)\cos(x)-3\cos(x)=0$

And factor:

$\cos(x)\left(10\sin(x)-3\right)=0$

Hence, our answer is A.

*It is important to note that we should not divide both sides by cos(x) to acquire 10sin(x) = 3. This is because we need to find the values of x, and one or more may result in cos(x) = 0, and we cannot divide by 0. Hence, we should subtract and then factor.

5 0

2 years ago

Read 2 more answers

Please find the exact length of the midsegment of trapezoid JKLM with vertices J(6, 10), K(10, 6), L(8, 2), and M(2, 2). Thank y

I am Lyosha [343]

Answer:

the exact length of the midsegment of trapezoid JKLM = $\mathbf{ = 3 \sqrt{5} }$ i.e 6.708 units on the graph

Step-by-step explanation:

From the diagram attached below; we can see a graphical representation showing the mid-segment of the trapezoid JKLM. The mid-segment is located at the line parallel to the sides of the trapezoid. However; these mid-segments are X and Y found on the line JK and LM respectively from the graph.

Using the expression for midpoints between two points to determine the exact length of the mid-segment ; we have:

$\mathbf{ YX = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} }$

$\mathbf{ YX = \sqrt{(8-5)^2+(8-2)^2} }$

$\mathbf{ YX = \sqrt{(3)^2+(6)^2} }$

$\mathbf{ YX = \sqrt{9+36} }$

$\mathbf{ YX = \sqrt{45} }$

$\mathbf{ YX = \sqrt{9*5} }$

$\mathbf{ YX = 3 \sqrt{5} }$

Thus; the exact length of the midsegment of trapezoid JKLM = $\mathbf{ = 3 \sqrt{5} }$ i.e 6.708 units on the graph

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3 years ago

The measure of a circumscribed angle is equal to 180° minus the measure of the __________

ss7ja [257]

I believe it is an inscribed angle but I am not positive

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3 years ago

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The table shows the height, in centimeters, that a weight bouncing from a spring would achieve if there were no friction, for a

Paha777 [63]

Hello! For ease of calculations, we can identify the time it took for the weight to bounce back to the other direction, then the other, and then back to its original position by looking at the time it took for the weight to change from 0 to 25 to 0 to -25 then back to 0. This is one whole cycle of the weight.

By the time the weight first reached zero, 1.5 seconds has passed. By the third time it got to zero again, 7.5 seconds has passed. Therefore, one whole cycle of the weight is 7.5-1.5 = 6.0 seconds.

ANSWER: One whole cycle of the weight took 6 seconds.

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3 years ago