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Novay_Z [31]
4 years ago
8

Simplify the expression 2√ 20 − 3√ 7 − 2√ 5 + 4√ 63 .

Mathematics
1 answer:
Kisachek [45]4 years ago
3 0

Simplify √20 to 2√5

2 * 2√5 - 3√7 - 2√5 + 4√63

Simplify √63 to 3√7

2 * 2√5 - 3√7 - 2√5 + 4 * 3√7

Simplify 2 * 2√5 to 4√5

4√5 - 3√7 - 2√5 + 4 * 3√7

Simplify 4 * 3 √7 to 12√7

Collect like terms

(4√5 - 2√5) + (-3√7 + 12√7)

Simplify

2√5 + 9√7

Answer: B

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What does the coefficient of the expression represent? 2+0.25x
IrinaVladis [17]

Answer:

The coefficient in the equation is 0.25.

It represents the rate of change (decrease factor) or the slope.

Depending on the context, it can have different representations.

8 0
4 years ago
William invested $12,000 in a bank account that pays 9 percent simple interest. His friend invested the same amount at another b
yarga [219]
<h3>Answer: B) 1.0 year</h3>

===========================================================

Explanation:

We have these two functions

  • f(t) = 12(1.02)^(4t)
  • g(t) = 12(1.09)t

which represent the amounts for his friend and William in that order. Strangely your teacher mentions William first, but then swaps the order when listing the exponential function as the first. This might be slightly confusing.

The table of values is shown below. We have t represent the number of years and t starts at 0.5. It increments by 0.1

The f(t) and g(t) columns represent the outputs for those mentioned values of t. For example, if t = 0.5 years (aka 6 months) then f(t) = 12.48 and that indicates his friend has 12,480 dollars in the account.

I've added a fourth column labeled |f - g| which represents the absolute value of the difference of the f and g columns. If f = g, then f-g = 0. The goal is to see if we get 0 in this column or try to get as close as possible. This occurs when we get 0.09 when t = 1.0

So we don't exactly get f(t) and g(t) perfectly equal, but they get very close when t = 1.0

It turns out that the more accurate solution is roughly t = 0.9925 which is close enough. I used a graphing calculator to find this approximate solution.

It takes about a year for the two accounts to have the same approximate amount of money.

4 0
4 years ago
3 x 10^2 and 7 x 10^33 which is faster
Radda [10]

Answer:

first one

Step-by-step explanation:

3 0
3 years ago
A rectangular garden is to be constructed using a rock wall as one side of the garden and wire fencing for the other three sides
givi [52]

Answer:

x  =  28 m

y  =  14  m

A(max)  =  392 m²

Step-by-step explanation:

Rectangular garden    A (r ) =  x * y

Let´s call x the side of the rectangle to be constructed with a rock wall, then only one x side of the rectangle will be fencing with wire.

the perimeter of the rectangle is  p  =  2*x  +  2*y    ( but in this particular case only one side x will be fencing with wire

56   =   x    +  2*y      56   -  2*y  =  x

A(r)   =  ( 56  -  2*y ) * y

A(y ) =  56*y  -  2*y²

Tacking derivatives on both sides of the equation we get:

A´(y )  =  56  - 4 * y        A´(y) = 0     56  -  4*y  =  0    4*y  =  56

y =  14 m

and x  =  56  - 2*y    =  56 - 28  = 28 m

Then dimensions of the garden:

x  =  28 m

y  =  14  m

A(max)  =  392 m²

How do we know that the area we found is a local maximum??

We find the second derivative

A´´(y)  = - 4     A´´(y)  <  0   then the function A(y) has a local maximum at y = 14 m

4 0
3 years ago
The sum of a certain quantity "P" together with its two-third, and it's half becomes 234
kykrilka [37]
You need to form an equation:
P+2/3P+1/2P=234
P+4/6P+3/6P=234
P+7/6P=234
13/6P=234
P=234/(13/6)
P=108

8 0
3 years ago
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