1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
LenaWriter [7]
3 years ago
12

The sum of four consecutive even integers is 256. what are the numbers?

Mathematics
1 answer:
Naily [24]3 years ago
7 0

Answer:

61 , 63 , 65 , 67

Step-by-step explanation:

Let the least even number be denoted by x. The sum of the four consecutive even numbers would be:

(x) + (x + 2) + (x + 4) (x + 6) = 256

First, simplify. Combine all like terms:

x + x + x + x + 2 + 4 + 6 = 256

4x + 12 = 256

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

First, subtract 12 from both sides of the equation:

4x + 12 (-12) = 256 (-12)

4x = 256 - 12

4x = 144

Next, divide 4 from both sides of the equation:

(4x)/4 = (144)/4

x = 144/4

x = 61

61 is your first number. Find the next 3 consecutive numbers:

x = 61

x + 2 = 63

x + 4 = 65

x + 6 = 67

Check:

61 + 63 + 65 + 67 = 256

256 = 256

~

You might be interested in
Make A the subject of the formula <br><br>r=<br><img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B%20%5Cfrac%7Ba%7D%7B3%7D%20%7D%20
DaniilM [7]

Answer:

Huh

Step-by-step explanation:

<h2>3-4=8+7-87+2Kknn<em><u>j</u></em><em><u>a</u></em><em><u>j</u></em><em><u>a</u></em><em><u>j</u></em><em><u>a</u></em><em><u>a</u></em><em><u>a</u></em></h2>

<em><u>T</u></em><em><u>H</u></em><em><u>A</u></em><em><u>N</u></em><em><u>G</u></em><em><u>I</u></em><em><u>N</u></em><em><u>A</u></em><em><u> </u></em><em><u>M</u></em><em><u>O</u></em><em><u> </u></em><em><u>T</u></em><em><u>A</u></em><em><u>N</u></em><em><u>O</u></em><em><u>N</u></em><em><u>G</u></em><em><u> </u></em><em><u>M</u></em><em><u>O</u></em><em><u> </u></em><em><u>S</u></em><em><u>A</u></em><em><u> </u></em><em><u>P</u></em><em><u>A</u></em><em><u>G</u></em><em><u>O</u></em><em><u>N</u></em><em><u>G</u></em><em><u> </u></em><em><u>V</u></em><em><u>O</u></em><em><u>V</u></em><em><u>O</u></em><em><u> </u></em><em><u>M</u></em><em><u>O</u></em><em><u> </u></em><em><u>V</u></em><em><u>O</u></em><em><u>V</u></em><em><u>O</u></em><em><u> </u></em><em><u>T</u></em><em><u>A</u></em><em><u>L</u></em><em><u>A</u></em><em><u>G</u></em><em><u>A</u></em><em><u> </u></em><em><u>1</u></em><em><u>V</u></em><em><u>1</u></em><em><u> </u></em><em><u>M</u></em><em><u>L</u></em>

3 0
2 years ago
You want to buy a tent in the shape of a pyramid. The rectangular base is 35 square feet, with a height of 4 feet. What is the v
GenaCL600 [577]
The volume of a pyramid is
V=(l*w*h)/3=(35*4)/3=140/3=46.67 cubic feet , choice C
3 0
3 years ago
Reas the above and answer​
sergeinik [125]

Answer:

48cm^2

Step-by-step explanation:

You first find the area (l * w) of the first rectangle on the top.

4 * 2 is 8

Then you find the area of the rectangle on the bottom.

5 * 8 is 40

Finally you add the area's together.

48

6 0
3 years ago
Square root of 2tanxcosx-tanx=0
kobusy [5.1K]
If you're using the app, try seeing this answer through your browser:  brainly.com/question/3242555

——————————

Solve the trigonometric equation:

\mathsf{\sqrt{2\,tan\,x\,cos\,x}-tan\,x=0}\\\\ \mathsf{\sqrt{2\cdot \dfrac{sin\,x}{cos\,x}\cdot cos\,x}-tan\,x=0}\\\\\\ \mathsf{\sqrt{2\cdot sin\,x}=tan\,x\qquad\quad(i)}


Restriction for the solution:

\left\{ \begin{array}{l} \mathsf{sin\,x\ge 0}\\\\ \mathsf{tan\,x\ge 0} \end{array} \right.


Square both sides of  (i):

\mathsf{(\sqrt{2\cdot sin\,x})^2=(tan\,x)^2}\\\\ \mathsf{2\cdot sin\,x=tan^2\,x}\\\\ \mathsf{2\cdot sin\,x-tan^2\,x=0}\\\\ \mathsf{\dfrac{2\cdot sin\,x\cdot cos^2\,x}{cos^2\,x}-\dfrac{sin^2\,x}{cos^2\,x}=0}\\\\\\ \mathsf{\dfrac{sin\,x}{cos^2\,x}\cdot \left(2\,cos^2\,x-sin\,x \right )=0\qquad\quad but~~cos^2 x=1-sin^2 x}

\mathsf{\dfrac{sin\,x}{cos^2\,x}\cdot \left[2\cdot (1-sin^2\,x)-sin\,x \right]=0}\\\\\\ \mathsf{\dfrac{sin\,x}{cos^2\,x}\cdot \left[2-2\,sin^2\,x-sin\,x \right]=0}\\\\\\ \mathsf{-\,\dfrac{sin\,x}{cos^2\,x}\cdot \left[2\,sin^2\,x+sin\,x-2 \right]=0}\\\\\\ \mathsf{sin\,x\cdot \left[2\,sin^2\,x+sin\,x-2 \right]=0}


Let

\mathsf{sin\,x=t\qquad (0\le t


So the equation becomes

\mathsf{t\cdot (2t^2+t-2)=0\qquad\quad (ii)}\\\\ \begin{array}{rcl} \mathsf{t=0}&\textsf{ or }&\mathsf{2t^2+t-2=0} \end{array}


Solving the quadratic equation:

\mathsf{2t^2+t-2=0}\quad\longrightarrow\quad\left\{ \begin{array}{l} \mathsf{a=2}\\ \mathsf{b=1}\\ \mathsf{c=-2} \end{array} \right.


\mathsf{\Delta=b^2-4ac}\\\\ \mathsf{\Delta=1^2-4\cdot 2\cdot (-2)}\\\\ \mathsf{\Delta=1+16}\\\\ \mathsf{\Delta=17}


\mathsf{t=\dfrac{-b\pm\sqrt{\Delta}}{2a}}\\\\\\ \mathsf{t=\dfrac{-1\pm\sqrt{17}}{2\cdot 2}}\\\\\\ \mathsf{t=\dfrac{-1\pm\sqrt{17}}{4}}\\\\\\ \begin{array}{rcl} \mathsf{t=\dfrac{-1+\sqrt{17}}{4}}&\textsf{ or }&\mathsf{t=\dfrac{-1-\sqrt{17}}{4}} \end{array}


You can discard the negative value for  t. So the solution for  (ii)  is

\begin{array}{rcl} \mathsf{t=0}&\textsf{ or }&\mathsf{t=\dfrac{\sqrt{17}-1}{4}} \end{array}


Substitute back for  t = sin x.  Remember the restriction for  x:

\begin{array}{rcl} \mathsf{sin\,x=0}&\textsf{ or }&\mathsf{sin\,x=\dfrac{\sqrt{17}-1}{4}}\\\\ \mathsf{x=0+k\cdot 180^\circ}&\textsf{ or }&\mathsf{x=arcsin\bigg(\dfrac{\sqrt{17}-1}{4}\bigg)+k\cdot 360^\circ}\\\\\\ \mathsf{x=k\cdot 180^\circ}&\textsf{ or }&\mathsf{x=51.33^\circ +k\cdot 360^\circ}\quad\longleftarrow\quad\textsf{solution.} \end{array}

where  k  is an integer.


I hope this helps. =)

3 0
3 years ago
How do you know that these mixtures would make the same shade of light blue paint
andre [41]

Answer:

you don't you just try it numnut

Step-by-step explanation:

6 0
2 years ago
Other questions:
  • What is 72/63 in simplest form?
    10·2 answers
  • What's the algebraic expression for n cubed increased by 5??
    10·1 answer
  • 4/9 is it equivalent to 20/36
    12·2 answers
  • A scientist mixes water (containing no salt) with a solution that contains 35% salt. She wants to obtain245 ounces of a mixture
    10·1 answer
  • If sales tax is 7%, what would the tax on. $7.99 meal be? What would the meal cost after tax?
    5·2 answers
  • What is the y intercept of the line with the equation y=2x+8
    7·2 answers
  • Apply the distributive property to factor out the greatest common factor. <br> 60 - 40y =
    12·1 answer
  • Find the hypotenuse of each isosceles right triangle when the legs are of the given measure.
    5·1 answer
  • Please help i can't figure this problem out​
    11·1 answer
  • Help its math again i forgot how to do it theres 2​
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!