<span>1) The problem says that the quilt squares are cut on the diagonal to form triangular quilt pieces. Then, the triangle pieces have angles of 45°, and the legs have the same lenght. So, you can solve the exercise by applying </span><span>the Pythagorean Theorem:
</span>
h²:s²+s²
h²=2s²
h²/2=s²
s=√(h²/2)
"h" is the hypotenuse (h=10 inches) and "s" is the length of the sides.
When you substitute the value of the hypotenuse into the formula s=√(h²/2), you obtain the sides length:
s=√(h²/2)
s=√(10²/2)
s=5√2
What is the side length of each piece?
The answer is: 5√2
2)Tan(α)=Opposite/Adjacent
α=30°
Opposite=17
Adjacent=x
When you substitute these values into Tan(α)=Opposite/Adjacent, you obtain:
Tan(α)=Opposite/Adjacent
Tan(30°)=17/x
x=17/Tan(30°)
x=17√3
Sin(α)=Opposite/Hypotenuse
α=30°
Opposite=17
Hypotenuse=y
Then, you have:
Sin(30°)=17/y
ySin(30°)=17
y=17/Sin(30°)
y=34
There is 4.88% decrease in Olivia's score.
Step-by-step explanation:
Given,
Score on first math test = Old value = 82 points
Score on second math test = New value = 78 points
Change = New value - Old value
Change = 78 - 82 = -4
The negative sign indicates the decrease.
Decrease percent = 
Decrease percent = 
Decrease percent = 4.88%
There is 4.88% decrease in Olivia's score.
Keywords: percentage, difference
Learn more about percentage at:
#LearnwithBrainly
Answer:
97.7 %
Step-by-step explanation:
TWO standard deviations above the mean
z - score = 2 corresponds to .9772 97.7 %
So with 1 cup of sugar u could have 18 servings. divide that by 2 equals 9 which is how many servings you need. divide 1 by 2 and get 1/2. she would use 1/2 cups of sugar.
