Which expressions are equivalent to log4(1/4x^2)

Mathematics

1 answer:

natulia [17]2 years ago

8 0

answer:

simplify:

log 4 ( x 2 ) − 1

evaluate:

log(x^2)/log(4)-1

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All the dimensions of a triangle were multiplied by the same factor. If the base of the triangle went from 1 centimeter to 3 cen

timama [110]

The answer is 9.

To calculate this, we will use Galileo's square cube law, used to describe the change of the area or the volume of the shape, when their dimensions increase or decrease. The formula used for change of the area is
$A_2= A_1 (\frac{l_2}{l_1} )^{2}$
A₂ - the area after the change,
A₁ - the area before the change,
l₂ - the dimension after the change,
l₁ - the dimension before the change.

It is given:
l₁ = 1 cm
l₂ = 3 cm

Let's use this formula for the mentioned triangle:
$A_2=A_1( \frac{l_2}{l_1}) ^{2} =A_1( \frac{3}{1})^{2} =A_1*3 ^{2} =9A_1$

Therefore, the area of the triangle was multiplied by 9.

8 0

3 years ago

10 coupons are given to 20 shoppers in a store. Each shopper can receive at most one coupon. 5 of the shoppers are women and 15

zmey [24]

Answer:

$\, {20 \choose 10} - {15 \choose 10}$

Step-by-step explanation:

We can find the total amount of ways at least a woman receives a coupon by calculating the total amount of possibilities ot distribute the coupon and substract it to the total amount of possibilities to distribute 10 coupons to the 15 men (this is the complementary case that at least a woman receives a cupon).

- The total amount of possibilities to distribute the coupons among the 20 shoppers is equivalent to the total amount of ways to pick a subset of 10 elements from a set of 20. This is the combinatiorial number of 20 with 10, in other words, $\, {20 \choose 10} = \frac{20!}{10!10!} .$

- To calculate the total amount of possibilities to distribute the coupons among the 15 men, we need to make the same computation we made above but with a set of 15 elements instead of 20. This gives us $\, {15 \choose 10} = \frac{15!}{10!5!}$ possibilities.