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3 years ago

Determine whether the given binomial is a factor of the polynomial P(x).

1 answer:

7 0

No, it is not a factor of P(x)=5 $x^{3}$ + X^{2} -7 because when I used synthetic division, I got 37 as a remainder which means that (x-2) is not a factor. The remainder should be zero for it to be a factor.

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Two boats started to move towards each other from two docks, located 30 miles apart. One boat moved at a speed of 2.5 miles per

Vikki [24]

Answer:

They will meet after four hours

Step-by-step explanation:

The boat moving at 2.5 mph will have travelled 10 miles after 4 hrs, and the boat moving at 5 mph will have travelled 20 miles after 4 hrs

8 0

3 years ago

A large beach ball has a diameter of 4.14 feet. How much air can fill the ball?

aalyn [17]

The beach ball can hold 37.15 cubic feet of air

Solution:

Given that the beach ball has a diameter of 4.14 feet

We are asked to find how much air can fill the ball. This means that we have to find the volume of the ball

Finding volume of ball:

Given diameter = 4.14 feet

We know that radius is half of diameter

$radius = \frac{diameter}{2}$

$radius = \frac{4.14}{2} = 2.07$

Since ball is a sphere, Volume of sphere is given as:

$volume of sphere = \frac{4 \pi r^3}{3}$

By substituting the value of radius we get,

$v = \frac{4 \pi \times 2.07^3}{3}\\\\v = \frac{4 \times 3.14 \times 8.869743}{3}\\\\v = 37.15$

Hence the beach ball can hold 37.15 cubic feet of air

6 0

4 years ago

Which of the following shapes are rectangles ? Please choose 2 correct answers !!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!

timurjin [86]

Answer:

I think it is b and d .

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

How long will it take for an investment to triple, if interest is compounded continuously at 8%?

maw [93]

Answer:

It will take 14 years before the investment triples

Step-by-step explanation:

Continuous Compounding

Is the mathematical limit that compound interest can reach if it was calculated and reinvested into an account's balance over a theoretically infinite number of periods.

The formula for continuous compounding is derived from the formula for the future value of a compound interest investment:

$FV = PV\cdot e^{i.t}$

Where:

FV = Future value of the investment

PV = Present value of the investment

i = Interest rate

t = Time

It's required to find the time for an investment to triple, that is, FV = 3 PV, knowing the interest rate is i=8%=0.08.

Substituting the known values:

$3PV = PV\cdot e^{i.t}$

Dividing by PV:

$3 = e^{i.t}$

Taking logarithms:

$\ln 3=i.t$

Solving for t:

$\displaystyle t=\frac{\ln 3}{i}$

$\displaystyle t=\frac{\ln 3}{0.08}$

t = 13.7 years

Rounding up:

It will take 14 years before the investment triples

6 0

3 years ago

12x=76-20y 8x=84-20y

levacccp [35]

Answer:

Step-by-step explanation:

$\left\{\begin{array}{ccc}12x=76-20y&\text{change the signs}\\8x=84-20y\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}-12x=-76+20y\\8x=84-20y\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-4x=8\qquad\text{divide both sides by (-4)}\\.\qquad x=-2\\\\\text{put the value of x to the second equation}\\\\8(-2)=84-20y\\-16=84-20y\qquad\text{subtract 84 from both sides}\\-100=-20y\qquad\text{divide both sides by (-20)}\\5=y\to y=5$

4 0

4 years ago