All categories

2 years ago

Find the quotient. (6x 2 + 23x + 20) ÷ (5 + 2x)

Mathematics

2 answers:

arsen [322]2 years ago

8 0

Answer:

The quotient is 3x+4

Step-by-step explanation:

Given the dividend and divisor i.e we have to find the quotient if $6x^2+23x+20$ is divided by 5+2x

Given dividend is

$6x^2+23x+20$

⇒ $6x^2+15x+8x+20$

⇒ $3x(2x+5)+4(2x+5)$

⇒ $(3x+4)(2x+5)$

Hence, the given dividend can written in two factors.

Now, $\frac{6x^2+23x+20}{5+2x}=\frac{(3x+4)(2x+5)}{2x+5}=3x+4$

Hence, the quotient is 3x+4

tekilochka [14]2 years ago

4 0

<span>(3x -4)(2x-5) as this it is divided </span>

You might be interested in

a container with a square bottom, rectangular sides and no top is to e constructed to have a volume of 5 m^3. material for the b

VLD [36.1K]

Answer:

$2m\times 2m\times \frac{5}{4}m$

Step-by-step explanation:

We are given that a container with square bottom.

Let side of square=x

Height of container=h

Volume of container= $5m^3$

Cost of 1 square meter of material for the bottom=$10

Cost of 1 square meter of material for side=$8

We have to find the dimension of least expensive container.

Volume of container= $x^2h$

$x^2h=5$

$h=\frac{5}{x^2}$

Surface area of container= $x^2+2(x+x)h=x^2+4xh$

Cost= $C(x)=10x^2+8(4xh)=10x^2+32x(\frac{5}{x^2})=10x^2+\frac{160}{x}$

$C(x)=10x^2+\frac{160}{x}$

Differentiate w.r.t x

$\frac{dC}{dx}=20x-\frac{160}{x^2}$

$\frac{dC}{dx}=0$

$20x-\frac{160}{x^2}=0$

$\frac{160}{x^2}=20x$

$x^3=\frac{160}{20}=8$

$x=\sqrt[3]{8}=2$

Because side of container is always positive.

Again differentiate w.r.t x

$\frac{d^2C}{dx^2}=20+\frac{320}{x^3}$

Substitute x=2

$\frac{d^2C}{dx^2}=20+\frac{320}{2^3}=60>0$

Hence, the cost is minimum at x=2

Substitute the value of x

$h=\frac{5}{2^2}=\frac{5}{4}$ m

Hence, the dimensions of the least expensive container are

$2m\times 2m\times \frac{5}{4}m$

7 0

3 years ago

Read 2 more answers

How do you solve 2,631×83

Aneli [31]

Its 218373 sjwbushwhdvd

3 0

3 years ago

Read 2 more answers

(-3)(5)(-5)(-4) thank you

lesya [120]

The answer is -300

Hope this helped <3 .

5 0

3 years ago

Read 2 more answers

About how many students do not prefer non- fiction?

slamgirl [31]

Answer:

B. 75%

Step-by-step explanation:

If about a quarter ( 25% ) do like non-fiction, then we know that the rest do not prefer it ( 75% )

75 + 25 = 100

8 0

1 year ago

Write an equation for the line that has a slope of -4 and passes through the point (2,-3)

faltersainse [42]

Answer:

y = -4x + 5

Step-by-step explanation:

y = -4x + b

-3 = -4(2) + b

-3 = -8 + b

5 = b

4 0

3 years ago