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
Pavlova-9 [17]
3 years ago
11

The sum of the squares of three consecutive even integers is 980. Determine the integers.

Mathematics
2 answers:
olganol [36]3 years ago
4 0

Answer:

  16, 18, 20

Step-by-step explanation:

We can estimate that the square of the middle integer will be about 1/3 of 980. Then the middle integer is about ...

  √(980/3) ≈ 18.09

The integers are 16, 18, 20.

_____

<em>Check</em>

  16^2 +18^2 +20^2 = 256 +324 +400 = 980

viktelen [127]3 years ago
3 0

Answer:

16, 18, 20

Step-by-step explanation:

Let the three consecutive even integers be (x - 2), x, (x + 2)

\therefore \:  {(x -2 )}^{2}  +  {x}^{2}  + {(x + 2)}^{2}  = 980 \\  \therefore \:  {x}^{2}  - 4x + 4 +  {x}^{2}  + {x}^{2}   +  4x + 4  = 980 \\ \therefore \:  3{x}^{2}   + 8 = 980 \\ \therefore \:  3{x}^{2}  = 980 - 8 \\  \therefore \:  3{x}^{2}  = 972 \\  \\   \therefore \:  {x}^{2}  =  \frac{972}{3} \\  \\  \therefore \:  {x}^{2}  = 324 \\ \therefore \:   x =  \pm \sqrt{324}  \\  \therefore \:   x =  \pm \: 18 \\  \because \: x \: is \: even \: integer \\  \therefore \: x \neq  - 18 \\  \therefore \: x  =  18 \\  \\ x - 2 = 18 - 2 = 16 \\ x = 18 \\ x + 2 = 18 + 2 = 20 \\

Hence, three consecutive even integers are : 16, 18, 20.

You might be interested in
Write 4 with denominator 5
valkas [14]

Answer:

4/5

Step-by-step explanation:

I'm not exactly sure what this question is asking but I'm guessing it's asking to create a fraction with the numerator as 4 and denominator as 5.

4 0
3 years ago
​ △BCD ​ is a right triangle. The length of the hypotenuse is 19 centimeters. The length of one of the legs is 13 centimeters.
zheka24 [161]
<span>here we can use Pythogoras' theorem.
in right angled triangles the square of the hypotenuse is equal to the sum of the squares of the other 2 sides.
hypotenuse is 19 cm. One side is 13 cm and we need to find the length of the third side.
                                                                         
19</span>²<span> = 13</span>²<span> + X</span>²<span> 
X - length of the third side
                                                           
361 = 169 + X</span>²<span> 
X</span>²<span> = 361 - 169
                                                                     
X</span>²<span> = 192
                                                                             
X = 13.85 the length of third side rounded off to the nearest tenth is 13.9 cm</span>
3 0
3 years ago
Two trains are traveling at a constant rate. Which train has the greater speed?
natali 33 [55]
A point on the graph (for train b) that is exact is (2,250). From the origin, the rise is 250 and the run is 2. Rise/run would give us 250/2, which is 125. This means that train B travels 125mi every hour. For train A, we subtract the distance from hour 2 from hour 3 to get the miles per hour (because 3-2=1, subtracting the distance of hour 3 from 2 will give us the distance in 1 hour). 180-120= 60, meaning train A travels at 60mph. 60<125, meaning A
3 0
3 years ago
Heyy pls help! worth 20 points, and please only help if you know the answer. also no links those r kinda annoying lol
iragen [17]

Step 1: Find the slope:

    m= \dfrac{y_2-y_1}{x_2-x_1}= \dfrac{-2-7}{4-(-2)} =  \dfrac{-9}{6}= -\dfrac{3}{2}

This gives you y=-\dfrac{3}{2}x+b, but we need to find b.

To find b, substitute in one (x,y) pair and it doesn't matter which one.  I'll go with (4,-2):

    \begin{aligned}-2&=-\dfrac{3}{2}(4)+b\\[0.5em]-2&=-6+b\\[0.5em]4&=b\end{aligned}

Now take that b-value and plug in into the slope-intercept form:

     y=-\dfrac{3}{2}x+4

It's always a good idea to toss in the other x-value from the other point, to make sure it checks out.

7 0
3 years ago
Classify the polynomial.<br><br> 3r^5-2r^2+5r
ella [17]
Answer: 5th degree trinomial

The degree is 5 because its the largest exponent of the single variable polynomial.

It's a trinomial because there are 3 terms. The terms are separated by a plus or a minus.
7 0
3 years ago
Other questions:
  • The lines below are parallel. If the slope of the green line is -4, what is the slope of the red line?
    6·1 answer
  • The function of f(x) varies directly with x, and f(x)=48 when x=8.<br> Evaluate f(x) when x=2
    11·1 answer
  • What is a common factor of both x^2-9 and x^2+x-6
    8·1 answer
  • The area of a circle PQR with center O is 72cm. What is the area of sector POQ if angle POQ is 40
    7·1 answer
  • I need help on both of those 4 problems
    8·1 answer
  • Plz help <br> Draw the following triangle after a counterclockwise rotation about the origin.
    11·1 answer
  • 3−2=10<br><br><br> 1.k=4<br><br> 2.k=-4<br><br> 3.k=36<br><br> 4.k=-36
    11·1 answer
  • 1
    5·1 answer
  • Brainlest if correct
    15·2 answers
  • Question
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!