Answer:
Step-by-step explanation:
- Rectangle has properties:
- Diagonals are congruent
- Opposite sides are congruent
- All angles are right
<h3>Given</h3>
- m∠ABD = 30°
- AC = 16 in
- BC = ?
<h3>Solution</h3>
<u>As per properties mentioned above we have:</u>
ΔABD is right triangle with ∠B - 30°, ∠A- 90°, ∠D - 60°
Side opposite to 30 is half of the length of the hypotenuse
<u>AD is opposite to ∠B and BD is the hypotenuse, then:</u>
- AD = 1/2*BD
- AD = 1/2(16)
- AD = 8 in
and
Answer:
Step-by-step explanation:
We want to find sin(θ) and cos(θ) given that tan(θ) = 1/4 and sin(θ) > 0.
First, since tan(θ) and sin(θ) are both positive, cos(θ) must be positive as well.
Recall that tangent is the ratio of the opposite side to the adjacent side.
Therefore, the hypotenuse is:
So, with respect to θ, the opposite side is 1, the adjacent is 4, and the hypotenuse is √17.
Then it follows that:
And that:
Answer:
Step-by-step explanation:
2x + 3y = 6
y = x/3 - 3
Since the second equation is already solved for y, we can easily use the substitution method.
Substitute y in the first equation with x/3 - 3
2x + 3(x/3 - 3) = 6
2x + x - 9 = 6
3x = 15
x = 5
Now use the second equation, and x = 5, to solve for y.
y = x/3 - 3
y = 5/3 - 3 = 5/3 - 9/3
y = -4/3
Answer: (5, -4/3)
Answer:
Equivalent Fractions with the LCD
7/8 = 231/264
10/11 = 240/264
2/3 = 176/264
Step-by-step explanation:
Solution:
Rewriting input as fractions if necessary:
7/8, 10/11, 2/3
For the denominators (8, 11, 3) the least common multiple (LCM) is 264.
LCM(8, 11, 3)
Therefore, the least common denominator (LCD) is 264.
Calculations to rewrite the original inputs as equivalent fractions with the LCD:
7/8 = 7/8 × 33/33 = 231/264
10/11 = 10/11 × 24/24 = 240/264
2/3 = 2/3 × 88/88 = 176/264
Answer:
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