Answer:
AECG
Step-by-step explanation:
1
sqrt(49) = 7
sqrt(a^2) = a
sqrt(b^2) = b
For every two variables you can take one out from under the root sign and thorough the other one away.
Answer: E
2
sqrt(36) = 6
sqrt(a^2) = a See comment for 1.
b must be left where it is. There is only 1 of them.
6asqrt(b)
Answer: A
3. sqrt(25) = 5
sqrt(b^2) = b
a must be left alone. There's only 1 of them.
5b sqrt(a)
answer: C
4
sqrt(81 a b)
sqrt(81) = 9
The variables must be left alone. There's only1 of them
9 sqrt(ab)
Answer G
Answer:
x=4.875
y=-0.25
Step-by-step explanation:
4x – 2y = 10
2x-y=10
y=2x-10
4x + 6y = 18
2x+3(2x-10)=9
8x=39
x=4.875
y=2(4.875)-10
y=-0.25
Answer: 4.5 miles
Explanation:
When you draw the situation you find two triangles.
1) Triangle to the east of the helicopter
a) elevation angle from the high school to the helicopter = depression angle from the helicopter to the high school = 20°
b) hypotensue = distance between the high school and the helicopter
c) opposite-leg to angle 20° = heigth of the helicopter
d) adyacent leg to the angle 20° = horizontal distance between the high school and the helicopter = x
2) triangle to the west of the helicopter
a) elevation angle from elementary school to the helicopter = depression angle from helicopter to the elementary school = 62°
b) distance between the helicopter and the elementary school = hypotenuse
c) opposite-leg to angle 62° = height of the helicopter
d) adyacent-leg to angle 62° = horizontal distance between the elementary school and the helicopter = 5 - x
3) tangent ratios
a) triangle with the helicpoter and the high school
tan 20° = Height / x ⇒ height = x tan 20°
b) triangle with the helicopter and the elementary school
tan 62° = Height / (5 - x) ⇒ height = (5 - x) tan 62°
c) equal the height from both triangles:
x tan 20° = (5 - x) tan 62°
x tan 20° = 5 tan 62° - x tan 62°
x tan 20° + x tan 62° = 5 tan 62°
x (tan 20° + tan 62°) = 5 tan 62°
⇒ x = 5 tant 62° / ( tan 20° + tan 62°)
⇒ x = 4,19 miles
=> height = x tan 20° = 4,19 tan 20° = 1,525 miles
4) Calculate the hypotenuse of this triangle:
hipotenuese ² = x² + height ² = (4.19)² + (1.525)² = 19.88 miles²
hipotenuse = 4.46 miles
Rounded to the nearest tenth = 4.5 miles
That is the distance between the helicopter and the high school.
Fraction wise: 19/225
decimal wise: 0.084444444
The probability that a vowel will land face up on the cube would be 1/2. This is because there are six total letters; three vowels and three consonants, so there is a 3/6 chance of it being a vowel and you simplify it down to 1/2. I hope this helped :)
