Factors and multiples Q&A: Get Expert Help and Learn from Real-World Examples

To simplify the expression, ${\displaystyle \sqrt{19}}$.

What are the factors of 6?

Find the outcome.
${\displaystyle \frac{3+2\times 5-4}{\frac{8}{4}+1}}$

A vihacle valued at $35,795 originally, depreciates at a rate of 17%/year. The equation ${\displaystyle y=35795{\left(0.83\right)}^x}$ represents the vehicle's value. x is time passed since purchase (in years) and y is the woth (in dollars). How much will the car be worth ten years after the purchase?

Write expression as a sum and/or difference or logarithms, express powers as factors:
${\displaystyle {\log }_3(\frac{x^4}{2}-x)}$

Let M,N and K be matrices of type ${\displaystyle 3\times 2,2\times 3}$ and ${\displaystyle 3\times 3}$ respectively, such that det (MN) ${\displaystyle =2}$ and ${\displaystyle det\left(K\right)=6}$. Then which of the following is the value of the det ${\displaystyle {\left[{(-3MN)}^T{K}^{-1}\right]}^{-1}}$?
a) ${\displaystyle -3^2.2}$ b)${\displaystyle \frac{-1}{3^3.2}}$ c) ${\displaystyle \frac{2}{3^2}}$ d)${\displaystyle \frac{-3^2}{4}}$ e) ${\displaystyle \frac{-1}{3^2}}$

A ball is tossed upward from the ground. Its height in feet above ground after t seconds is given by the function ${\displaystyle h\left(t\right)=-16t^2+24t}$. Find the maximum height of the ball and the number of seconds it took for the ball to reach the maximum height.

add or subtract as indicated, and express answers in lowest terms. ${\displaystyle \frac{1}{6}+\frac{1}{8}}$.

A polynomial P is given. (a) Factor P into linear and irreducible quadratic factors with real coefficients. (b) Factor P completely into linear factors with complex coefficients.
${\displaystyle P\left(x\right)=x^4+8x^2-9}$

According to one source, the amount of data passing through mobile phone networks doubles each year.
Explain why the amount of data passing through mobile phone networks is an exponential function of time. The amount of data grows by a factor of_________________ each year, this is an exponential function because the amount is growing by _____________________ multiples.
Use ${\displaystyle D_o}$ for the initial amount of data and find a formula that gives the data D as an exponential function of the time t in years.
If this trend continues, how long will it be before the amount of data is 100 times its initial value? Round to three decimal places.

Using Sum-to-Product Formulas Solve the equation by first using a Sum-to-Product Formula.
${\displaystyle \sin \theta +\sin 3\theta =0}$

In the following exercises, use the divisibility tests to determine whether each number is divisible by 2,3,4,5,6 and 10.
800

To solve the given equation for x.
Given equation: ${\displaystyle {\log }_3(x^2-x-6)-{\log }_3(x-3)=1}$

Given ${\displaystyle P\left(x\right)=x^3+5x^2+25x+125}$, find the zeros, real and non-real of P.
The zeros are 5.
Write P in factored form (as a product of linear factors). Be sure to write the full equation, including ${\displaystyle P\left(x\right)=}$.

Write the exprissuon as a sum and/or difference of logarithms.
${\displaystyle \log \left(\frac{7\sqrt{x+3}}{x^4{(x-5)}^2}\right)x>5}$

The number 6 has exactly four different factors: 1,2,3, and 6. How many different factors does the number 36 have?

One of the wagers in roulette is to bet that the ball will stop on a number that a multiple of 3. (The roulette wheel Includes the numbers 0,00and 1 - 36 . and 00 are not considered multiples of 3.) If the ball stops on such a number, the player wins double the amount bet. What is the probability of winning this bet? (Write your answer as a fraction.)

To calculate: The simplified expression for the expression ${\displaystyle i^{1000}+i^{1002}}$

Find the least common multiple by listing multiples: 18 and 24.

What is the difference between gcf and lcm