Amy is 1 year older than Ben. The sum of their ages is greater than 33 and less than 45 Find all possible ages of Ben

−3 1/3 ÷ 9 pllllllllllllllllllllllllllllllllllllllllllllllllll

tia_tia [17]

$-\frac{10}{27}$ hope this helps :)

8 0

2 years ago

Which is a factor of the polynomial f(x) = 6x4 – 21x3 – 4x2 + 24x – 35?

QveST [7]

I note that this problem starts out with "Which is a factor of ... " This implies that you were given several answer choices. If that's the case, it's unfortunate that you haven't shared them.

I thought I'd try finding roots of this function using synthetic division. See below:

f(x) = 6x^4 – 21x^3 – 4x^2 + 24x – 35
Please use " ^ " to denote exponentiation. Thanks.

Possible zeros of this poly are factors of 35: plus or minus 1, plus or minus 5, plus or minus 7. Use synthetic division; determine whether or not there is a non-zero remainder in each case. If none of these work, form rational divisors from 35 and 6 and try them: 5/6, 7/6, 1/6, etc.

Provided that you have copied down the function
f(x) = 6x^4 – 21x^3 – 4x^2 + 24x – 35 properly, this approach will eventually turn up 1 or 2 zeros of this poly. Obviously it'd be much easier if you'd check out the possible answers given you with this problem.

By graphing this function, I found that the graph crosses the x-axis at 7/2. There is another root.

Using synth. div. to check whether or not 7/2 is a root:

___________________________
7/2 / 6 -21 -4 24 -35
21 0 -14 35
----------- ------------------------------
6 0 -4 10 0

Because the remainder is zero, 7/2 (or 3.5) is a root of the polynomial. Thus, (x-3.5), or (x-7/2), is a factor.

7 0

1 year ago

Read 2 more answers

A contractor has at most $42 to spend on nails for a project. Finishing nails cost $0.45 per pound and common nails cost $0.60 p

mojhsa [17]

Question:

A contractor has at most $42 to spend on nails for a project. Finishing nails cost $0.45 per pound and common nails cost $0.60 per pound. He would like to purchase at least 30 pounds of nails total. Write a system of linear inequalities

Answer:

The system of linear inequalities are:

$x + y\geq 30\\\\0.45x+0.60y\leq 42$

Solution:

Let "x" be the pounds of finishing nails

Let "y" be the pounds of common nails

Given that,

He would like to purchase at least 30 pounds of nails total.

"at least" means that he can purchase 30 pounds or more than 30 pounds also

So, we have to use "greater than or equal to" symbol

$x + y\geq 30$

From given,

Cost of 1 pound of finishing nail = $ 0.45

Cost of 1 pound of common nail = $ 0.60

A contractor has at most $42 to spend on nails for a project

"at most" means he can spend 42 or less than 42

So we have to use " less than or equal to" symbol

Thus we frame a inequality as:

$x \times 0.45 + y \times 0.60\leq 42\\\\0.45x + 0.60y\leq 42$

Thus the system of inequalities are:

$x + y\geq 30\\\\0.45x+0.60y\leq 42$

4 0

2 years ago

Investigate the following harvesting model both qualitatively and analytically. If a constant number h of fish are harvested fro

zalisa [80]

Answer:

a. The population does not become extinct in finite time.

Step-by-step explanation:

The model for the population of the fishery is

$dP/dt = P(a-bP)-h, P(0) = P_0$

If we rearrange and replace the constants we have:

$\frac{dP}{P(7-P)-49/4} =dt\\\\-4 (\frac{dP}{4(P-7)P+49}) =dt\\\\-4 \frac{dP}{(2P-7)^2} =dt\\\\-4 \int\frac{dP}{(2P-7)^2} =\int dt\\\\-4(-\frac{1}{2(2P-7)})=t+C\\\\\frac{2}{2P-7}=t+C\\\\ t=0 \,\,\, P(0)=P_0\\\\\frac{2}{2P_0-7}=0+C\\\\C=\frac{2}{2P_0-7}$

Now we can calculate if the population become 0 in any finite time

$\frac{2}{2P-7}=t+\frac{2}{2P_0-7}\\\\\frac{2}{2*0-7}=t+\frac{2}{2P_0-7}\\\\-\frac{2}{7}=t+\frac{2}{2P_0-7}\\\\$

To be a finite time, t>0

$t=-\frac{2}{7}-\frac{2}{2P_0-7}=0\\\\-\frac{2}{2P_0-7}=\frac{2}{7}\\\\7-2P_0=7\\\\P_0=0$

We can conclude that the only finite time in which P=0 is when the initial population is 0.

Because P0 is a positive constant, we can say that the population does not become extint in finite time.

5 0

2 years ago

Ms. Canciano was putting ribbon around a bulletim broard. She used 28 inches of ribbon to go all the way around and knew that th

Nadya [2.5K]

Answer:

48 sq inches

Step-by-step explanation:

Given that,

Ribbon used around a bulletin broard is 28 inches

The length of her board is 6 inches

Let B is breadth of her board. 28 inches is perimeter. The perimeter of rectangle is given by :

P = 2(L+B)

28=2(6+B)

14=6+B

B=8 inches

The area of a rectangle is given by :

A = L×B

A = 8×6

A=48 sq inches

So, the area of her board is 48 sq inches

5 0

2 years ago