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3 years ago

Factor `y=2x^2+11x+5`

Mathematics

1 answer:

mestny [16]3 years ago

5 0

Answer:

(2x + 1)(x + 5).

Step-by-step explanation:

`y=2x^2+11x+5`

2 * 5 = 10

1 * 10 = 10 and 1 + 10 = 11 so we write:

y = 2^2 + 10x + x + 5

y = 2x(x + 5) + 1(x + 5)

= (2x + 1)(x + 5).

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Bogdan [553]

Answer:

x = 16

Step-by-step explanation:

Δ AED and Δ ACB are similar thus the ratios of corresponding sides are equal, that is

$\frac{ED}{CB}$ = $\frac{AD}{AB}$ , substitute values

$\frac{11}{8}$ = $\frac{6+x}{x}$ ( cross- multiply )

11x = 8(6 + x) ← distribute

11x = 48 + 8x ( subtract 8x from both sides )

3x = 48 ( divide both sides by 3 )

x = 16

7 0

3 years ago

Please Answerrr! I need help ASAPP!

MArishka [77]

Step-by-step explanation:

5×6 = 30 and 30×8 = 240 divide that by three you get 80

6 0

3 years ago

Solve: 2cos(x)-square root 3=0 for 0 less than x less than 2 pi

Leona [35]

Answer:

The general solution of $cos x = cos(\frac{\pi }{6})$ is

x = 2nπ± $\frac{\pi }{6}$

The general solution values

$x = - \frac{\pi }{6} and x = \frac{\pi }{6}$

Step-by-step explanation:

Explanation:-

Given equation is

$2cosx-\sqrt{3} =0 for 0$

$2cosx =\sqrt{3}$

Dividing '2' on both sides, we get

$cos x =\frac{\sqrt{3} }{2}$

$cos x = cos(\frac{\pi }{6})$

General solution of cos θ = cos ∝ is θ = 2nπ±∝

Now The general solution of $cos x = cos(\frac{\pi }{6})$ is

x = 2nπ± $\frac{\pi }{6}$

put n=0

$x = - \frac{\pi }{6} and x = \frac{\pi }{6}$

Put n=1

$x = 2\pi +\frac{\pi }{6} = \frac{13\pi }{6}$

$x = 2\pi -\frac{\pi }{6} = \frac{11\pi }{6}$

put n=2

$x = 4\pi +\frac{\pi }{6} = \frac{25\pi }{6}$

$x = 4\pi -\frac{\pi }{6} = \frac{23\pi }{6}$

And so on

But given 0 < x< 2π

The general solution values

$x = - \frac{\pi }{6} and x = \frac{\pi }{6}$

6 0

3 years ago

Identify the diameter of the circular base created by folding the figure into a right cone. HELP ASAP PLEASE!!

Akimi4 [234]

let's notice something, we have a circle with a radius of 12 and one 90° sector is cut off, so only three 90° sectors of the circle are left shaded, so namely the cone will be using 3/4 of that circle.

think of it as, this shaded area is some piece of paper, and you need to pull it upwards and have the cutoff edges meet, and when that happens, you'll end up with a cone-shaped paper cup, and pour in some punch.

now, once we have pulled up the center of the circle to make our paper cup, there will be a circular base, its diameter not going to be 24, it'll be less, but whatever that base is, we know that is going to have the same circumference as those in the shaded area. Well, what is the circumference of that shaded area?

$\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=12 \end{cases}\implies C=2\pi 12\implies C=24\pi \implies \stackrel{\textit{three quarters of it}}{24\pi \cdot \cfrac{3}{4}} \\\\\\ 6\pi \cdot 3\implies 18\pi$

well then, the circumference of that circle at the bottom will be 18π, so, what is the diameter of a circle with a circumferenc of 18π?

$\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=18\pi \end{cases}\implies 18\pi =2\pi r\implies \cfrac{18\pi }{2\pi }=r\implies 9=r \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{\textit{diameter is twice the radius}}{d=18}~\hfill$

3 0

3 years ago

In a parking lot of 240 red and blue cars, the ratio of red cars to blue cars is 3 : 5.

irga5000 [103]

3+5 = 8

240/8 = 30

30*3 = 90 red cars

4 0

3 years ago