Answer:
360
Step-by-step explanation:
We need to find the LCM of 18,90 and 24.
The prime factorization of 18 = 2 × 3 × 3
The prime factorization of 90 = 2 × 5×3×3
The prime factorization of 24 = 2 × 3×2×2
LCM is least common multiple.
LCM = 2 x 2 x 2 x 3 x 3 x 5
= 360
Hence, the LCM of 18,90 and 24 is 360.
Answer:
B and C
Step-by-step explanation:
Required
Select graphs that are dilated by a scale factor greater than 1
For graph A:
Graph A is smaller than the original graph. This indicates dilation with a scale factor less than 1
For graph B:
Graph B is bigger than the original graph and is dilated over (0,0). This indicates dilation with a scale factor greater than 1
For graph C:
Graph C is bigger than the original graph; however, it is not dilated over (0,0). This indicates dilation with a scale factor greater than 1
For graph D:
Graph D is bigger than the original graph; however, it is not only dilated but also flipped over (i.e. rotated).
<em>Hence, b and c is true</em>
Answer:
22.9 yards
Step-by-step explanation:
Since b² = a² - c² where a = vertex of major axis, 2a = 50 yards the length of the major axis. So , a = 50/2 = 25 yards. c = focus of chamber = 10 yards from center and b = vertex of minor axis.
So, b = ±√(a² - c²)
= ±√(25² - 10²)
= ±√(625 - 100)
= ±√525
= ±22.91 yards
≅ ± 22.9 yards
Since b = length of minor axis from center of chamber = 22.91 yards. So, he should build the whisper chamber 22.9 yards out from the center of the chamber.
Answer:
1000%
Step-by-step explanation:
c=10d,
3c will become 3*10d=30d
d is 10 times to c which converts to 1000%
Answer: Rate of change of Area of the triangle = 2.75cm~/min
Step-by-step explanation:
If the present height of the triangle is 22cm and the height increases by 5cm/min. It means the height was 2cm four minutes earlier: 5cm for 1st min + 5cm for 2nd min + 5cm for 3rd min + 5cm for 4th min = 20cm after 4min.
Therefore height equals 22 - 20 = 2cm four minutes earlier.
Using the same four minutes for the base. Since the base shrinks at 1cm/min, for the base to shrink to 10cm it means it was 14cm four minutes earlier.
The Area of a triangle is given by
A = 1/2 × base × height
Therefore Area= 1/2× 10×22 = 110cm~
Since it took four minutes to get to this area, the rate of change of the area will be 110÷4 = 2.75cm~/min