15 = 5 x 3 = 5 x √3 x √<span>3
so
15 / (5</span><span> √</span>3)
= (5 x √3 x √3)/ (5 x √3) ............( 5 x √3 are canceled out)
= √3
or
= 1.73
Answer:
a) nearest jump is JL = 1380 inches = 115ft
b) number of jumps in 1 mile N= 46 jumps
Step-by-step explanation:
Given that the jump length is proportional to the body length.
If 2 inch grasshopper can jump 40 inches.
JL = k(BL)
k = JL/BL
where JL = jump length = 40 inches
BL = Body length = 2 inches.
k = 40/2 = 20
The constant of proportionality is 20.
For the athlete :
BL = 5ft 9 inches = 5(12)+9 = 69 inches.
The jump length of the athlete is:
JL = k(BL) = 20(69)
JL = 1380 inches. = 115ft
The number of jumps in 1 mile is
1 mile = 63360 inches
N = 63360/1380
N = 45.9 = 46
N= 46
Therefore, 46 jumps would be needed.
Let the hamburgers be x and cheese burgers be y.
x + y = 24
3x + 3.5 y = 79
x = 24 - y.
Substituting the value of x,
3( 24 - y) + 3.5 y = 79
72- 3y + 3.5 y = 79
72 + 0.5 y = 79
0.5y = 79 - 72 = 7
1/2 y = 7
thus, y = 7 * 2 = 14
Substituting the value for x,
x + y = 24
x + 14 = 24
x = 24-14 = 10
Thus, x = 10.
Thus, she sold 10 hamburgers and 14 cheeseburgers
The definition of similar triangles says that 2 triangles are similar if they have the same shape but different size. There are two criteria to check for this:
1) If all angles in one triangle are equal to the angles in another one, then the 2 are equal.
2) If the sides have the same proportions, then the 2 triangles are similar.
1) We have that all the angles of the 2 triangles have an equal angle in the other triangle. In specific, Q is matched to B, P to A and R to C. Hence, since corresponding angles are congruent, the two triangles are similar.
2) Here we are given information about the sides of the triangles, so we will check the second criterion. We form the ratio of the largest sides of each trangle and the shortest sides. 30/5=6. For the shortest sides, 18/3=6. Finally for the middle sides, 24/4=6. Hence, we have that the triangles are similar since the ratios are equal. (it doesn't matter whether we take the bigger or the smaller side as a numerator, as long as we are consistent).
