Is the following expression true or false? Show your work.

Mathematics

1 answer:

Paul [167]3 years ago

3 0

Answer: True

Solution:

Rearrange the equation to the LHS:

[x^2 + 8x + 16] · [x^2 – 8x + 16] - (x^2 – 16)^2 = 0

Factoring x^2+8x+16

x^2 - 4x - 4x - 16

= (x-4) • (x-4)

= = (x+4)2

So now we have an equation

(x + 4)^2 • (x - 4)^2 - (x^2 - 16)^2 = 0

Step 2: Evaluate the following:

(x+4)2 = x^2+8x+16

(x-4)2 = x^2-8x+16

(x^2-16)2 = x^4-32x^2+256

(x^2+8x+16) (x^2-8x+16 ) - (x^4-32x^2+256 )

0 = 0

Hence True

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At Katya’s fruit stand, a basket of strawberries costs $4 and a basket of raspberries costs $9. In one morning, Katya sells 96 b

Tcecarenko [31]

Answer:

The number of strawberry baskets sold was 44

Step-by-step explanation:

Let

x ----> the number of strawberry baskets sold

y ---> the number of raspberries baskets sold

we know that

In one morning, Katya sells 96 baskets for $644

$x+y=96$ ----> equation A

$4x+9y=644$ ---> equation B

Solve the system by graphing

Remember that the solution is the intersection point both graphs

using a graphing tool

The solution is the point (44.52)

see the attached figure

therefore

The number of strawberry baskets sold was 44 and the number of raspberries baskets sold was 52

4 0

3 years ago

Two balls are drawn in succession out of a box containing 5 red and 5 white balls. Find the probability that at least 1 ball was

Lera25 [3.4K]

Check the tree diagram of the problem:

The first ball can be either Red or Blue, the second ball can either be Red or Blue.

The branches represent all possible scenarios.

For example, consider the upper branch, the case when both balls are blue:

The first ball is Blue, probability 5/10, the second ball is Blue, probability 4/9 because now there are 4 left blue balls, and 9 balls in total, after we picked the first blue.

The other branches have the same logic.

The question is not completed so we have 2 cases:

"Find the probability that at least 1 ball was red, given that the first ball was red"

here we add the separate probabilities of (R, R) and (R, B)

P(R,R)+P(R,B)=2/9 + 5/18 = 4/18 +5/18= 9/18=0.5

"Find the probability that at least 1 ball was red, given that the first ball was blue"

probability is P(B, R)=5/18=0.28