Use the distributive property to write an expression equivalent to 5 times(3 plus 4)

Mathematics

1 answer:

Sergeeva-Olga [200]3 years ago

6 0

5x(3+4) = (5x3)+(5x4)

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Five million bacteria live in an organism. The doubling period is 1.5 hours. How many will there be after:

finlep [7]

We write the generic exponential equation:
y = A (b) ^ t
Where,
A: initial population
B: growth rate
t: time in hours.
Substituting values we have:
y = 5 (2) ^ ((1 / 1.5) * t)
For t = 9 hours we have:
y = 5 (2) ^ ((1 / 1.5) * 9)
y = 320 million
For t = 24 hours (one day) we have:
y = 5 (2) ^ ((1 / 1.5) * 24)
y = 327680 million
For t = 2 hours we have:
y = 5 (2) ^ ((1 / 1.5) * 2)
y = 12.5992105 million
Answer:
a) t hours?
y = 5 (2) ^ ((1 / 1.5) * t)
b) 9 hours?
y = 320 million
c) 1 day?
y = 327680 million
d) 2 hours?
y = 12.5992105 million

8 0

3 years ago

There were 18 balls in a bucket. Oliver removed 1/2 of the balls, in a bucket and then removed another 2/3 of those that were le

deff fn [24]

Answer:

there is only 3 left

Step-by-step explanation:

18 divided by 1/2 is 9 then 2/3 is 6 so you would subtract 6 from 9 and get 3

6 0

4 years ago

Prove: If a chord of a circle makes an angle of 30° with a diameter, prove that the distance from the center to the chord is one

Svet_ta [14]

Answer:

See explanation.

Step-by-step explanation:

Let BC be the diameter of the circle with center at point O, AB be the chord and ∠ABC=30°. OD is the distance from the center to the chord.

Consider triangle BDO. This triangle is special 30°-60°-90° right triangle. The leg OD is opposite to the angle of 30° and is half of the hypotenuse. The hypotenuse of the triangle BDO is BO. BO is the radius of the circle and is equal to half of the diameter AB. Thus,

$OD=\dfrac{1}{2}BO=\dfrac{1}{2}\cdot \dfrac{1}{2}AB=\dfrac{1}{4}AB.$