<span>The line of symmetry of the triangle bisects the right angle and the diagonal of the square.
The line is 1/2 the length of the square's diagonal :
(1/2)(10√2) = 5√2.
</span>Let CG be a distance x from the vertex of the right angle in the triangle.
Remaining distance = 5√2 - x.
<span>
(1)(x) = (2)(5√2 - x)</span>
x = 10√2 - 2x
<span>3x = 10√2 </span>
<span>x = (10/3)√2.
</span>
Using Pythagorean theorem,
x^2 + y^2 = c^2
<span>c = (10/3)√2,
and x = y,
so 2x^2 = 200/9
x = √(100/9) = 10/3 = y.
</span>
<span>x = y = 3.333</span>
3) It's basically asking how many 7 ounce servings can be made out of a 64 ounce container. Divide 64 by 7 and you will get a decimal but their asking for full servings so round down to the closest whole number
Answer:
see explanation
Step-by-step explanation:
(3)
Given cosΘ = - 
Then by Pythagoras' theorem the third side is 3 ( 3,4, 5 triangle )
Since Θ in second quadrant then sinΘ > 0
sinΘ = 
Using the trigonometric identity
sin2Θ = 2sinΘcosΘ, then
sin2Θ = 2 ×
× -
= - 
(4)
Using the trigonometric identity
cos(x - y) = cosxcosy + sinxsiny
note cos15° = cos(45 - 30)°
cos(45 - 30) = cos45cos30 + sin45sin30
= (
×
) + (
×
)
= 
7.41% as a decimal is 0.0741. :)
Answer:
For both sets of data, the median is equal to the mean.
The interquartile range (IQR) is greater for M's classes than J's classes.
Step-by-step explanation:
<u>J's Classes:</u>
23, 25, 27, 28, 32
Median: 27
Mean: 27
Mean Absolute Deviation: 2.4
Interquartile Range: 3
<u>M's Classes:</u>
20, 24, 26, 29, 31
Median: 26
Mean: 26
Mean Absolute Deviation: 3.2
Interquartile Range: 5