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Setler79 [48]
2 years ago
8

"What is the name of the relationship between angle 1, and angle 4?

Mathematics
2 answers:
zvonat [6]2 years ago
7 0
1 and 4,2 and 3 are the alternate interior angles
AfilCa [17]2 years ago
7 0
Alternate interior angles
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Find the longer leg of the triangle.
Paha777 [63]

Answer:

Choice A. 3.

Step-by-step explanation:

The triangle in question is a right triangle.

  • The length of the hypotenuse (the side opposite to the right angle) is given.
  • The measure of one of the acute angle is also given.

As a result, the length of both legs can be found directly using the sine function and the cosine function.

Let \text{Opposite} denotes the length of the side opposite to the 30^{\circ} acute angle, and \text{Adjacent} be the length of the side next to this 30^{\circ} acute angle.

\displaystyle \begin{aligned}\text{Opposite} &= \text{Hypotenuse} \times \sin{30^{\circ}}\\ &=2\sqrt{3}\times \frac{1}{2} \\&= \sqrt{3}\end{aligned}.

Similarly,

\displaystyle \begin{aligned}\text{Adjacent} &= \text{Hypotenuse} \times \cos{30^{\circ}}\\ &=2\sqrt{3}\times \frac{\sqrt{3}}{2} \\&= 3\end{aligned}.

The longer leg in this case is the one adjacent to the 30^{\circ} acute angle. The answer will be 3.

There's a shortcut to the answer. Notice that \sin{30^{\circ}} < \cos{30^{\circ}}. The cosine of an acute angle is directly related to the adjacent leg. In other words, the leg adjacent to the 30^{\circ} angle will be the longer leg. There will be no need to find the length of the opposite leg.

Does this relationship \sin{\theta} < \cos{\theta} holds for all acute angles? (That is, 0^{\circ} < \theta?) It turns out that:

  • \sin{\theta} < \cos{\theta} if 0^{\circ} < \theta;
  • \sin{\theta} > \cos{\theta} if 45^{\circ} < \theta;
  • \sin{\theta} = \cos{\theta} if \theta = 45^{\circ}.

4 0
2 years ago
Read 2 more answers
What are the intercepts of the line?
Schach [20]
To solve your X int you substitute 0 for y.

X int-
-5x+9(0)=-18
-5x=-18
X= 18/5 and the coordínate is (18/5,0)

Then to solve for y int you substitute 0 for x.

-5(0)+9y=-18
9y=-18
Y= -2 and the coordinate is (0,-2)
3 0
2 years ago
What is the mean of 68,75,72,90,80
andriy [413]

Answer: 77

Step-by-step explanation:

5 0
3 years ago
If you need 2 liters of soda for every 12 students at the school dance, and you sold 360 student tickets to the dance. About how
GalinKa [24]

Answer:

60 liters

Step-by-step explanation:

360/12=30

30x2=60 liters

Hope this helps! :)

4 0
2 years ago
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Match the equation with its graph. -2/3x - -1/4y=1/3
Volgvan
If the equation is -(2/3) x - (1/4) y = 1/3, it is a straight line, so you can use some special points to identify the graph.

It is easier is you solve the equation for y:

(1/4)y = - 1/3 - (2/3) x

y = (-4/3) - (8/3)x

That is the slope -y-intercept form of the equation.

That means that the slope is -8/3, and the y-intercept is -4/3.

Use this points to identify the graph:

x = 0 => y = - 4/3 ---> (0, - 4/3)

y = 0 => x = - 1/2 -----> (-1/2, 0)

Now you can punt those two points on the graph and draw the line that joins them.

With this procedure you can find the graph of any straight line.
4 0
2 years ago
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