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3 years ago

What is the solution of −81=b6 ? A. b = −486 B. b = −75 C. b = 13.5 D. b = 486

1 answer:

7 0

We have to isolate b to be alone.
Soooo first we divide both sides by 6

-81 = b6
÷6 = ÷6 The right side cancels out and gets the b alone. While we solve the right side of the equal sign.
-81 ÷ 6 = -13.5
So this means we isolated b alone!
b = -13.5

Our final answer is..
b = -13.5

:)

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3 years ago

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Vlad1618 [11]

Answer:

$4.171\times10^6$

Step-by-step explanation:

Given:

First Number = 97

Second Number = $4.3\times10^4$

We need to find the product of two numbers in Scientific notation.

Product of two numbers means we need to multiply two number.

Also The proper format for scientific notation is a x 10^b where a is a number or decimal number such that the absolute value of a is less than ten and is greater than or equal to one or, 1 ≤ |a| < 10. b is the power of 10 such that the scientific notation is mathematically equivalent to the original number.

Decimal points are moved until there is only one non-zero digit to the left of the decimal point. The decimal number results as a.

Number of decimal point moved needs to be counted. This number is b.

If decimal are moved to the left b is positive.

If decimal are moved to the right b is negative.

If decimal are not moved b = 0.

scientific notation of a number can be written as a x 10^b and read it as "a times 10 to the power of b."

Hence the product is;

$97\times4.3\times 10^4 = 417.1 \times 10^4$

Expressing in Scientific Notation form we get

$4.171 \times 10^6$

Hence the Answer is $4.171 \times 10^6$ .

3 0

3 years ago

Complete the factorization of 3x ^ 2 - 10x + 8 3x^ 2 -10x+8=(x- Box x-4)

aniked [119]

Answer:

$3x^2-10x+8=(x-x_1)(x-x_2)=(x-2)(x-\frac{4}{3})$

Step-by-step explanation:

The general form of a quadratic polynomial is given by:

$ax^2+bx+c$ (1)

You have the following polynomial:

$3x^2-10x+8$ (2)

In order to complete the factorization you can use the quadratic formula, to obtain the roost of the polynomial. The quadratic formula is given by:

$x_{1,2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ (3)

By comparing the equation (1) with the equation (2) you obtain:

a = 3

b = -10

c = 8

Then, you replace these values in the equation (3):

$x_{1,2}=\frac{-(-10)\pm \sqrt{(-10)^2-4(3)(8)}}{2(3)}\\\\x_{1,2}=\frac{10\pm2}{6}\\\\x_1=2\\\\x_2=\frac{4}{3}$

Then, the factorization of the polynomial is:

$3x^2-10x+8=(x-x_1)(x-x_2)=(x-2)(x-\frac{4}{3})$

5 0

2 years ago

The rabbit population of Springfield, Ohio was 144,000 in 2016. It is expected to decrease by about 7.2% per year. Use an expone

ehidna [41]

Answer:

The estimated Rabbit population by the year 2036 is 32,309 rabbits

Step-by-step explanation:

In this question, we are expected to use the exponential decay function to estimate population of rabbits in a certain year.

An exponential decay function refers to an equation that estimates the value of a parameter(dependent parameter) at a certain value of the independent parameter given that the independent parameter decreases at a certain constant rate.

Firstly, what we need to do is to write the decay function. To do this, we shall be representing the population by variable P, the rate by r , the number of years by t and the initial population by I

Mathematically, we have the decay function as;

P = I(1-r)^t

From the question, we identify these values as;

P = 144,000 : r = 7.2% = 7.2/100 = 0.072, I = 144,00 and t = 2036-2016 = 20 years

Let's plug these values;

P = 144,000(1-0.072)^20

P = 144,000(0.928)^20

P= 32,309

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3 years ago