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mestny [16]
3 years ago
15

Which are the roots of the quadratic function f(b) = 62 – 75? Select two options.

Mathematics
1 answer:
elena55 [62]3 years ago
4 0

Answer:

b = 5 \sqrt{3} \ or\ b = -5 \sqrt{3}

Step-by-step explanation:

Given

f(b) = b^2 - 75

Required

Determine the roots

To get the root of the function, then f(b) must be 0;

i.e. f(b) = 0

So, the expression becomes

0 = b^2 - 75

Add 75 to both sides

75 + 0 = b^2 - 75 + 75

75 = b^2

Take square roots of both sides

\sqrt{75} = \sqrt{b^2}

\sqrt{75} = b

Reorder

b = \sqrt{75}

Expand 75 as a product of 25 and 3

b = \sqrt{25*3}

Split the expression

b = \sqrt{25} *\sqrt{3}

b = \±5 *\sqrt{3}

b = \±5 \sqrt{3}

b = 5 \sqrt{3} \ or\ b = -5 \sqrt{3}

The options are not clear enough; however the roots of the equation are b = 5 \sqrt{3} \ or\ b = -5 \sqrt{3}

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Dimas [21]
Hello,

6b) (i) As you can see, in the first year the price drops from 27,000 to 17,000. (Look at year 0-1 on the x axis). To find the percentage drop, find the difference between the two values and divide it over the initial value of 27,000.

So, the percentage drop in the first year is:
(27000-17000) / (27000) = 0.37, or a 37% drop

The answer is 37%.

(ii) For this question, we basically have the same process as the previous question except for the second year.

From year 1 to year 2, the value starts at 17,000 and ends at 15,000.
To find the percentage drop, we do:
(17000 - 15000) / (17000) = 0.118 ≈ 0.12, or a 12% drop

The answer is 12%.

6c) To find the percentage depreciation over the first 5 years, we look at the initial value (x = 0) and the value after 5 years (x = 5), and use these values in the same percentage formula we have been using.

The initial value of the car is 27,000, and after 5 years the value is 8,000. 
This is a percentage drop of (27000 - 8000) / (27000) = 0.70, or a 70% drop.

The answer is 70%.

Hope this helps!


7 0
3 years ago
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Robert accepted a new job at a company with a contract guaranteeing annual raises. Let S represent Robert's salary after working
vesna_86 [32]

Answer:

74,000

Step-by-step explanation:

In the year where he got 104,000 the year before he got 6,000 less. The year before 98,000 he got 12,000 less which means that now it would just be 86,000-12,000=74,000

I think this is right but you can double check on a calculator

Hope this helped!

6 0
2 years ago
A gas pump fills 2^-2 gallon of gasoline per second. how many gallons does the pump fill in one minute?
astraxan [27]

Answer:

The gas pump filling the gallons in 1 minute will be: 15

Step-by-step explanation:

  • Given that a gas pump fills 2^-2 gallon of gasoline per second.

As there are 60 seconds in 1 minute.

Thus,

Gas pump filling the gallons in 1 minute will be:

60\:\times 2^{-2}

=60\times \frac{1}{2^2}             ∵ a^{-b}=\frac{1}{a^b}

\mathrm{Multiply\:fractions}:\quad \:a\times \frac{b}{c}=\frac{a\:\times \:b}{c}

=\frac{1\times \:60}{2^2}

=\frac{60}{2^2}

=\frac{2^2\times \:3\times \:5}{2^2}

=3\times \:5

=15 gallons in one minute

Therefore, the gas pump filling the gallons in 1 minute will be: 15

6 0
3 years ago
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