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Mariana [72]
2 years ago
8

So, I need someone to help show me the steps for solving the equation after equal sign. It is supposed to = 729, and I am pretty

sure it does and it's true, but everytime I try to prove it I must be doing something wrong because I get insane answers instead.. Can someone help me and show the steps to getting 729 for this polynomial? Thanks!
(4+5)(4+5)(4+5) = 4^3+3(4)^2(5)+3(4)(5)^2+(5)^3
Mathematics
1 answer:
meriva2 years ago
3 0
<span>4^3+3(4)^2(5)+3(4)(5)^2+(5)^3
64 + 3*16*5 + 12*25 + 125
64 + 240 + 300 + 125
729
</span>
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The length of the longer leg of a right triangle is 4 inches more than twice the length of the shorter leg. the length of the hy
Serjik [45]

The Pythagorean's Theorem for our situation would look like this:

shortleg^2+longleg^2=hypotenuse^2

So let's call the short leg s, the long leg l and the hypotenuse h. It appears that all our measurements are based on the measurement of the short leg. The long leg is 4 more than twice the short leg, so that expression is l=2s+4; the hypotenuse measure is 6 more than twice the short leg, so that expression is h=2s+6. And the short leg is just s. Now we can rewrite our formula accordingly:

s^2+(2s+4)^2=(2s+6)^2

And of course we have to expand. Doing that will leave us with

s^2+4s^2+8s+8s+16=4s^2+12s+12s+36

Combining like terms we have

5s^2+16s+16=4s^2+24s+36

Our job now is to get everything on one side of the equals sign and solve for s

s^2-8s-20=0

That is now a second degree polynomial, a quadratic to be exact, and it can be factored several different ways. The easiest is to figure what 2 numbers add to be -8 and multiply to be -20. Those numbers would be 10 and -2. Since we are figuring out the length of the sides, AND we know that the two things in math that will never EVER be negative are time and distance/length, -2 is not an option. That means that the short side, s, measures 10. The longer side, 2s+4, measures 2(10)+4 which is 24, and the hypotenuse, 2s+6, measures 2(10)+6 which is 26. So there you go!

6 0
3 years ago
You have $75.00 to spend at the mall. You want to buy a hoodie that costs $80.00. The store is having a 20%-off sale. (There is
lesya692 [45]
Ok so find 20% off and see if less tha 75
percent means parts out of 100
20% means 20/100=1/5

'of' means multiply

20% of 80=1/5 times 80=16

off means subtract
disctoun tof 16 is 80-16=64
64<75

how much left over
75-spent=left over
75-64=11


anwwer is $11 left over and enough money to buy
6 0
2 years ago
Read 2 more answers
The table represents an exponential function. What is the multiplicative rate of change of the function? X, 1,2,3,4 Y, 6,4,8/3,1
Vsevolod [243]
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6 0
3 years ago
7 + 2y = 8x 3x - 2y = 0 Solve the system of equations by substitution. (70/3, 140/9) (7/5, 21/10) no solution coincident
Wittaler [7]
So we have the system of equations:
7+2y=8x equation (1)
3x-2y=0 equation (2)

To use substitution, we are going to solve for one variable in one of our equations, and then we are going to replace that value in the other equation:
Solving for x in equation (2):
3x-2y=0
3x=2y
x= \frac{2}{3}y equation (3)

Replacing equation (3) in equation (1):
7+2y=8x
7+2y=8( \frac{2}{3} y)
7+2y= \frac{16}{3} y
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y= \frac{7}{ \frac{10}{3} }
y= \frac{21}{10} equation (4)

Replacing equation (4) in equation (3):
x= \frac{2}{3}y
x=( \frac{2}{3} )( \frac{21}{10} )
x= \frac{7}{5}

We can conclude that the solution of our system of equations is <span>(7/5, 21/10)</span>
5 0
3 years ago
What is (14,-8)and (7,-6) slope?
bonufazy [111]

Answer:

2/-7

Step-by-step explanation:

Formula for slope given two points is attached.

1) Plug the points into the slope formula:

(-6+8)/(7-14)

2) Simplify:

2/-7

8 0
3 years ago
Read 2 more answers
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