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vagabundo [1.1K]
3 years ago
5

What is the range of the function graphed below? ​

Mathematics
1 answer:
Naddik [55]3 years ago
6 0
I believe it is the second on, as the range will always be Y
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Given: △ABC, AB=5sqrt2 <br> m∠A=45°, m∠C=30°<br> Find: BC and AC
Marysya12 [62]

BC is 10 units and AC is 5+5\sqrt{3} units

Step-by-step explanation:

Let us revise the sine rule

In ΔABC:

  • \frac{AB}{sin(C)}=\frac{BC}{sin(A)}=\frac{AC}{sin(B)}
  • AB is opposite to ∠C
  • BC is opposite to ∠A
  • AC is opposite to ∠B

Let us use this rule to solve the problem

In ΔABC:

∵ m∠A = 45°

∵ m∠C = 30°

- The sum of measures of the interior angles of a triangle is 180°

∵ m∠A + m∠B + m∠C = 180

∴ 45 + m∠B + 30 = 180

- Add the like terms

∴ m∠B + 75 = 180

- Subtract 75 from both sides

∴ m∠B = 105°

∵ \frac{AB}{sin(C)}=\frac{BC}{sin(A)}

∵ AB = 5\sqrt{2}

- Substitute AB and the 3 angles in the rule above

∴ \frac{5\sqrt{2}}{sin(30)}=\frac{BC}{sin(45)}

- By using cross multiplication

∴ (BC) × sin(30) = 5\sqrt{2} × sin(45)

∵ sin(30) = 0.5 and sin(45) = \frac{1}{\sqrt{2}}

∴ 0.5 (BC) = 5

- Divide both sides by 0.5

∴ BC = 10 units

∵ \frac{AB}{sin(C)}=\frac{AC}{sin(B)}

- Substitute AB and the 3 angles in the rule above

∴ \frac{5\sqrt{2}}{sin(30)}=\frac{AC}{sin(105)}

- By using cross multiplication

∴ (AC) × sin(30) = 5\sqrt{2} × sin(105)

∵ sin(105) = \frac{\sqrt{6}+\sqrt{2}}{4}

∴ 0.5 (AC) = \frac{5+5\sqrt{3}}{2}

- Divide both sides by 0.5

∴ AC = 5+5\sqrt{3} units

BC is 10 units and AC is 5+5\sqrt{3} units

Learn more:

You can learn more about the sine rule in brainly.com/question/12985572

#LearnwithBrainly

6 0
3 years ago
Find the image of triangle GHJ under the translation of (X,Y) ——&gt; ( x-1, y-8)
MAVERICK [17]

Answer:

triangle KLM

Step-by-step explanation:

Take one point on the initial triangle and move it according to the given translation to locate the image. I used point G. Its coordinate plot is at

(2,3). I perform the operation of the given translation to this. (X1-X2, y1-y2).

So, (2-1, 3-8). The new coordinates will be (1,-5) and the only triangle with these coordinates is triangle KLM.

8 0
3 years ago
Read 2 more answers
What is the value of 7 over 3 divided by 5 over 6
rodikova [14]

Answer:

7/3/5/6= 2.8

Step-by-step explanation:

7 0
3 years ago
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What value is equivalent to 4 + 3(10 − 2 3)? 3 means the third power.
katrin [286]

Answer: 10

Step-by-step explanation:

4+ 3x (10 - 2^3)

4+ 3x (10 - 8)

4+ 3x 2

4 +6 = 10

5 0
3 years ago
Read 2 more answers
I how to solve this problem
Mrac [35]
Look at the picture.<span>
</span>

5 0
3 years ago
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