All categories

3 years ago

find three consecutive even integers so that the twice the sum of the second and third is twelve less than six times the first

Mathematics

1 answer:

zysi [14]3 years ago

4 0

n, n + 2, n + 4 - three consecutive even integers

the twice the sum of the second and third: 2[(n + 2) + (n + 4)]

twelve less than six times the first: 6n - 12

The equation:

2[(n + 2) + (n + 4)] = 6n - 12

2(n + 2 + n + 4) = 6n - 12

2(2n + 6) = 6n - 12 <em>use distributive property</em>

(2)(2n) + (2)(6) = 6n - 12

4n + 12 = 6n - 12 <em>subtract 12 from both sides</em>

4n = 6n - 24 <em>subtract 6n from both sides</em>

-2n = -24 <em>divide both sides by (-2)</em>

n = 12

n + 2 = 12 + 2 = 14

n + 4 = 12 + 4 = 16

<h3>Answer: 12, 14, 16</h3>

You might be interested in

Help me please!!

Mice21 [21]

Answer:

1.) - 1/2

2.) the slope is 0 which means it is a vertical line

Step-by-step explanation:

In order to solve this you take the formula

y-y / x-x

and put they y value and x value of each equation in

7 0

3 years ago

What is the solution to the system of equations y=-5x+3

Nimfa-mama [501]

Hola User______

Here is Your Answer...!!!!

_________________

thus the given equation is a linear equation in two variables ...

thus ploting a table we get as ...

y = -5x + 3

there fore

1) at y=0 , x = 3/5 .... 0 = -5x +3

= -5x = -3 ..thus X = 3/5

2) at x=0 , y= 3 ...

y = -5 (0) + 3 = 3

3) at X =1 , y = -2

4) at y=1 , x = 2/5

8 0

4 years ago

Use the given information to find the exact value of the trigonometric function

eimsori [14]

$\begin{gathered} \csc \theta=-\frac{6}{5} \\ \tan \theta>0 \\ \cos \frac{\theta}{2}=\text{?} \end{gathered}$

Half Angle Formula

$\cos \frac{\theta}{2}=\pm\sqrt[\square]{\frac{1+\cos\theta}{2}}$ $\tan \theta>0\text{ and csc}\theta\text{ is negative in the third quadrant}$ $\begin{gathered} \csc \theta=-\frac{6}{5}=\frac{r}{y} \\ x^2+y^2=r^2 \\ x=\pm\sqrt[\square]{r^2-y^2} \\ x=\pm\sqrt[\square]{6^2-(-5)^2} \\ x=\pm\sqrt[\square]{36-25} \\ x=\pm\sqrt[\square]{11} \\ \text{x is negative since the angle is on the 3rd quadrant} \end{gathered}$ $\begin{gathered} \cos \theta=\frac{x}{r}=\frac{-\sqrt[\square]{11}}{6} \\ \cos \frac{\theta}{2}=\pm\sqrt[\square]{\frac{1+\cos\theta}{2}} \\ \cos \frac{\theta}{2}is\text{ also negative in the 3rd quadrant} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{1+\frac{-\sqrt[\square]{11}}{6}}{2}} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{\frac{6-\sqrt[\square]{11}}{6}}{2}} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}} \\ \\ \end{gathered}$

Answer:

$\cos \frac{\theta}{2}=-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}}$

Checking:

$\begin{gathered} \frac{\theta}{2}=\cos ^{-1}(-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}}) \\ \frac{\theta}{2}=118.22^{\circ} \\ \theta=236.44^{\circ}\text{ (3rd quadrant)} \end{gathered}$

Also,

$\csc \theta=\frac{1}{\sin\theta}=\frac{1}{\sin (236.44)}=-\frac{6}{5}\text{ QED}$

The answer is none of the choices

7 0

1 year ago

Jimmy is working at a factory where they make cars and trucks in the ratio five to four if the factory makes 100 trucks how many

-BARSIC- [3]

Answer:

125

Step-by-step explanation:

5/4=x/100

x=500/4

x=125

4 0

2 years ago

How to Divide 986 by 26 by using partial quotients

Debora [2.8K]

Wouldnt be 36.7 or no i underlined 7 because it never ends
_

3 0

3 years ago

Read 2 more answers