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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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Step-by-step explanation:

7 0
2 years ago
Country A has a growth rate of 4.9​% per year. The population is currently 4 comma 151​,000, and the land area of Country A is 1
kvv77 [185]

Answer:

There will be one person on 1 square yard of land after 1,892,147.588 years.

Step-by-step explanation:

Continuous exponential growth formula:

P(t)=Pe^{rt}

P(t)= Population after t years.

P= Initial population

r=rate of growth.

t= time in year

Given that,

Growth rate of country A (r)= 4.9% per year=0.049 per year.

Initial population (P)= 151,000.

Land area of country area= 14,000,000,000 square yards.

There will be one person on one  square yard of land.

So, there will be 14,000,000,000  person for 14,000,000,000 square yard of land in country A.

P(t)=14,000,000,000 person

\therefore 14,000,000,000= 151,000 e^{0.049t}

\Rightarrow e^{0.049t}=\frac{ 14,000,000,000}{ 151,000}

Taking ln both sides

\Rightarrow ln|e^{0.049t}|=ln|\frac{ 14,000,000,000}{ 151,000}|

\Rightarrow {0.049t}=ln|\frac{ 14,000,000,000}{ 151,000}|

\Rightarrow t}=\frac{ln|\frac{ 14,000,000,000}{ 151,000}|}{0.049}

\Rightarrow t}=1,892,147.588 years

There will be one person for every square yard of land after 1,892,147.588 years.

7 0
3 years ago
It is computed that when a basketball player shoots a free throw the odds in favor of his making our 23 to 3 find the probabilit
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Answer:

Step-by-step explanation:

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4 0
2 years ago
Find a, for the sequence 0.5, 3.5, 24.5,<br> 171.5.
antiseptic1488 [7]
The numbers are being multiplied by 7

.5 • 7 = 3.5
3.5 • 7 = 24.5
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etc
8 0
2 years ago
Carson needs to lease out a music studio to record his new album. The studio charges an initial studio-use fee plus an hourly fe
Naily [24]

Answer:

The y-intercept of the equation is 100 and represents the initial studio-use fee.

Step-by-step explanation:

In this equation, our t variable (time) is the equivalent of the x-variable on a graph. This is because it is the variable that we 'change' to see its impact on y. We see how the amount of hours affects the price. So our P variable (price) is the equivalent of y on a graph. The y-intercept is where the line crosses the y-axis on a graph. At this point, x=0.

Since P is our y, and t is our x, to find the y-intercept, we simply need to make t = 0.

P = 50(0) + 100

P = 100

Therefore the y-intercept is 100.

In this context, t represents time, so even though the studio has been used for 0 hours, the price is still 100. This is because the 100 represents the initial studio-use fee, and using it for certain amounts of time adds onto the initial fee of $100. The hourly fee is represented by 50t so it costs $50 more for each hour of use.

Hope this helped!

5 0
3 years ago
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