Answer:
7 units
Step-by-step explanation:
In an isosceles right triangle, the hypotenuse is √2 times the leg length. Then ...
... 7√2 = leg·√2
... 7 = leg . . . . . . . divide both sides by √2
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<em>Comment on isosceles right triangle</em>
If the legs are both length 1, the Pythagorean theorem tells us ...
... hypotenuse² = 1² +1² = 2
... hypotenuse = √2 . . . . . . . . . square root both sides of the equation
This result can be scaled by any multiplier you like. In this problem, the scale factor is 7, making the legs 7 and the hypotenuse 7√2.
Sin 2x - sin x=0
Using the trigonometric identity: sin 2x=2 sinx cosx
2 sinx cosx - sinx =0
Common factor sinx
sinx ( 2 cosx -1)=0
Two options:
1) sinx=0
on the interval [0,2π), the sinx=0 for x=0 and x=<span>π=3.1416→x=3.14
2) 2 cosx - 1=0
Solving for cosx
2 cosx-1+1=0+1
2 cosx = 1
Dividing by 2 both sides of the equation:
(2 cosx)/2=1/2
cosx=1/2
cosx is positive in first and fourth quadrant:
First quadrant cosx=1/2→x=cos^(-1) (1/2)→x=</span><span>π/3=3.1416/3→x=1.05
Fourth quadrant: x=</span>2π-π/3=(6π-π)/3→x=5<span>π/3=5(3.1416)/3→x=5.24
Answer: Solutions: x=0, 1.05, 3.14, and 5.24</span>
Tammy's recipe makes a sweeter fruit punch. This is because 3/4 (Kim's recipe) equals 18/24 (Tammy's recipe) and 5/6 equals 20/24 and since 20/24 is the bigger ratio, Tammy's recipe will make a sweeter fruit punch. I hope this helps. (:
Correct option would be B.
Explanation: A rational number is any integer, fraction, terminating decimal, or repeating decimal. Option B is a repeating decimal hence the .... at the end of the number.
(I think let me know if I’m wrong)
Answer:
Probability of choosing a penny at random is 1/5 or 0.2
Step-by-step explanation:
For many probabilities like this one, you have to add the total of materials or items together, even if they are different colors, shape, coin type, etc.
you have 12 pennies, 19 nickles, 14 dimes, and 15 quarters. This adds up to a total of 60 coins. Twelve of those are pennies.
You have twelve possible pennies to choose at random from a total of 60 in a bag.
So 12/60/ This simplifies to a probability of 1/5. If you divide 1 by 5 than it would be 0.2
The probability of choosing a penny from a bag of coins is 1/5, or 0.2.
Hope this helps
