Answer:
- Sara is 10 and Laila is 8
Step-by-step explanation:
- Sara's age = s
- Laila's age = l
<u>The ratios:</u>
- (s + 2)/(l + 2) = 6/5 ⇒ 5(s + 2) = 6(l + 2) ⇒ 5s = 6l + 2
<u>Substitute s into the second equation and solve for l:</u>
- 5(5l/4) = 6l + 2
- 25l = 24l + 8
- l = 8
<u>Fins s:</u>
Answer:
F=90°
D=27°
Step-by-step explanation:
F is a right angle (90°)
90° + 63° = 153°
180°-153°=27°
Thought Process:
The solution to this can be found through plotting both of these functions and shading each region above or below the lines (as per the greater and less than signs given)
the region that overlaps both of the above shaded region is the solution set for all ordered pairs that satisfy the two inequalities.
Solution:
let's start by plotting
it's the same as plotting , but '>' sign suggests to shade everything above this line.
<u>side note:</u>
'' excludes every ordered pair in the line,
'' includes every ordered pair in the line,
coming back to our solution:
now let's plot the other equation
it's the same as plotting , but '<' sign suggests to shade the area below this line.
The solution set is the area that is overlapped by the two shaded regions.
So every ordered pair (or coordinate (x,y)) that lies within this overlapped shaded region, excluding the points that lie on the lines themselves, satisfy the given two inequalities
radius = 3 feet
rearrange the formula making r the subject
πr³ = V ( multiply both sides by 3 to eliminate fraction )
4πr³ = 3V ( divide both sides by 4π )
r³ = = ( 3 × 36π ) / 4π = 3 × 9 = 27
take the cube root of both sides
r = = 3
Answer:
2 imaginary roots
Step-by-step explanation:
The discriminate is the portion of the quadratic equation under the square root
D = b^2 - 4ac
D = 8^2 - 4(2)(16)
D = 64 - 128
D = -64
Since the discriminate is negative the square root will be imaginary
and there will be 2 of them
2 imaginary roots