Answer:
The three numbers are 7 8 and 9
Step-by-step explanation:
Givens
- Let the first number be n - 1
- Let the second number be n
- Let the third number = n + 1
Equation
(n - 1)(n)(n + 1) - (n-1 + n + n+1) = 480
Solution
Multiply (n - 1) and (n + 1) = (n - 1)*(n + 1) = n^2 - 1
Multiply the second integer by the result of the first and third: n (n^2 - 1)
Add the three integers together: (x - 1) + (n - 1) + n = 3n Combine these 2 steps
n(n^2 - 1) - 3n = 480 Remove the brackets
n^3 - n - 3n = 480
n^3 - 4n = 480
n^3 - 4n - 480 = 0
Graph
The graph shows that the intercept point is n =8. This is the only way I can see to solve this cubic. There are no other real roots.
Answer
n - 1 = 7
n = 8
n + 1 = 9
Check
Product 7*8*9 = 504
Sum = 7 + 8 + 9 = 24
504 - 24 = 480 Which checks.
Answer:
hypotenuse = 10
Step-by-step explanation:
If you can tell at first glance it is a 3,4,5 triangle (6,8,10)/2=(3,4,5). Then you know that c has to equal 5.
If not,
a^2+b^2=c^2
6^2+8^2=c^2
36+64=c^2
100=c^2
10=c
Hello!
It is given information that this triangle is a right triangle, meaning that the Pythagorean Theorem can apply here.

We can set the length of a leg as an unknown variable
.

Remember that it is the whole
term being squared, meaning that it'll simplify to
, not
.




This means we can plug back in to find the sides.
The hypotenuse would be
, or 4.2.
And the legs would be 1.4 and 4, respectively.
Hope this helps!
Answer:
y = 2/7x + 7
Step-by-step explanation:
We start off by putting the original equation into slope-intercept form. Subtract 7x from both sides, then divide both sides by -2. Your new equation should be y = -7/2x - 8. It's important to know that when two lines are perpendicular, their slopes (m) are opposite reciprocals of each other. So -7/2 becomes 2/7. The first part of your final equation is y = 2/7x + b.
Next, we need to find the y intercept (b). You need to plug the x and y values from the given coordinate point (-7,5) into your final equation. You should end up with: 5 = 2/7(-7) + b. Then, solve for b.
5 = -14/7 + b
5 = -2 + b
7 = b
Finally, plug the b value into your final equation and you will have your answer.