Evaluate each expression if x=9 and y= 3.<br><br> please help

Apply division algorithm to find the quotient and remainder on dividing the polynomial 3 x^ + 4 x^ square + 6 x + 9 by x^ + 3x +

Ulleksa [173]

I suppose you mean

$\dfrac{3x^3+4x^2+6x+9}{x^2+3x+7}$

$3x^3=3x\cdot x^2$ , and if we multiply $x^2+3x+7$ by $3x$ we get $3x^3+9x^2+21x$ . Subtracting this from the numerator gives a remainder of $-5x^2-15x+9$ .

$-5x^2=-5\cdot x^2$ , and multiplying $x^2+3x+7$ by $-5$ gives $-5x^2-15x-35$ . Subtracting this from the previous remainder gives a new remainder of $44$ .

$44$ has no remaining factors of $x^2$ in it, so we're done, and

$\dfrac{3x^3+4x^2+6x+9}{x^2+3x+7}=\underbrace{3x-5}_{\rm quotient}+\dfrac{\overbrace{44}^{\rm remainder}}{x^2+3x+7}$

4 0

3 years ago

A shipping crate holds 14 books. The dimensions of each book are 4 inches by 11 by 14 inches. For A-C, select Yes or No to indic

Inga [223]

Answer:

A. No

B. Yes

C. No

Step-by-step explanation:

Dimensions of each book are 4 inches by 11 by 14 inches.

A. Each book has a volume of 29 cubic inches.

Volume of each book = length × width × height

= 4 × 11 × 14

= 616 cubic inches

No

B. If the crate could hold 18 books the volume of the crate would be 11,088.

Volume of each book = 616 cubic inches

Volume of the crate = volume of each book × number of books

= 616 × 18

= 11,088 cubic inches

Yes

C. Each crate has a volume of about 8,524 cubic inches

If the crate holds 14 books,

Volume of the crate = volume of each book × number of books

= 616 × 14

= 8,624 cubic inches

No

5 0

2 years ago

30 pointss!HELP! Two students get into an argument about the correct answer.

Mamont248 [21]

Both Rhianna and Christopher were correct as they took different reference angles.

Step-by-step explanation:

Step 1:

$tan \theta = \frac{opposite side}{adjacentside} .$

The value of the tan of a reference angle is calculated using the above formula.

The hypotenuse is the longest side of the triangle is always opposite the right angle of the triangle.

In this triangle, the hypotenuse is the side measuring 5 units.

Step 2:

When the reference angle is A, the opposite side measures 3 units and the adjacent side measures 4 units.

So $tan A = \frac{3}{4} .$

When the reference angle is C, the opposite side measures 4 units and the adjacent side measures 3 units.

So $tan C = \frac{4}{3} .$

So both Rhianna and Christopher were right as they took different reference angles i.e. A and C.

7 0

2 years ago

Olive reads 4 books every month for school. How many books does she read in 8 months?

Novosadov [1.4K]

Answer:

32 books.

Step-by-step explanation:

What do we know?

As Olive continues this pattern, this will involve multiplication.

4 books per month and 8 months.

4*8=32 books.

So, Olive will read 32 books within 8 months.

6 0

2 years ago

A rumor spreads through a small town. Let y ( t ) be the fraction of the population that has heard the rumor at time t and assum

Ivan

Answer:

Differential equation

$\frac{dy}{dt} =ky(1-y)$

Solution

$y=\frac{1}{1+4e^{-0.327t}}$

Value of constant k=0.327 days^(-1)

The rumor reaches 80% at 8.48 days.

Step-by-step explanation:

We know

y(t): proportion of people that heard the rumor

y'(t)=ky(1-y), rate of spread of the rumor

Differential equation

$\frac{dy}{dt} =ky(1-y)$

Solving the differential equation

$\frac{dy}{y(1-y)}=k\cdot dt \\\\\int \frac{dx}{y(1-y)} =k \int dt \\\\-ln(1-\frac{1}{y} )+C_0=kt\\\\1-\frac{1}{y} =Ce^{-kt}\\\\\frac{1}{y} =1-Ce^{-kt}\\\\y=\frac{1}{1-Ce^{-kt}}$

Initial conditions:

$y(0)=0.2\\y(3)=0.4\\\\y(0)=0.2=\frac{1}{1-Ce^0}\\\\1-C=1/0.2\\\\C=1-1/0.2= -4\\\\\\y(3)=0.4=\frac{1}{1+4e^{-3k}} \\\\1+4e^{-3k}=1/0.4\\\\e^{-3k}=(2.5-1)/4=0.375\\\\k=ln(0.375)/(-3)=0.327\\\\\\y=\frac{1}{1+4e^{-0.327t}}$

Value of constant k=0.327 days^(-1)

At what time the rumor reaches 80%?

$y(t)=0.8=\frac{1}{1+4e^{-0.327t}} \\\\1+4e^{-0.327t}=1/0.8=1.25\\\\e^{-0.327t}=(1.25-1)/4=0.0625\\\\t=ln(0.0625)/(-0.327)=8.48$

The rumor reaches 80% at 8.48 days.

8 0

2 years ago

Evaluate each expression if x=9 and y= 3. please help