Answer:
x = 7/
or 4.949747468
Step-by-step explanation:
45-45-90 triangles have a specific pattern.
The smaller sides are x, & the hypotenuse is 
With this knowledge, we know we have to divide the hypotenuse by to get the smaller sides, so we divide 7 by the to find x.
Answer:
13.
Let us say
first angle be = 4x -10
second angle = x
now add them to 90 as complementary angles add up to 90
4x - 10 + x = 90
5x - 10 = 90
5x = 90+10
5x = 100
x = 100/5
x = 20
the first angle = 4x -10
= 4(20) -10
= 80 -10
= 70
the second angle = x
= 20
the angles are 70 and 20
Check the picture below.
as you can see, the graph of the volume function comes from below goes up up up, reaches a U-turn then goes down down, U-turns again then back up to infinity.
the maximum is reached at the close up you see in the picture on the right-side.
Why we don't use a higher value from the graph since it's going to infinity?
well, "x" is constrained by the lengths of the box, specifically by the length of the smaller side, namely 5 - 2x, so whatever "x" is, it can't never zero out the smaller side, and that'd happen when x = 2.5, how so? well 5 - 2(2.5) = 0, so "x" whatever value is may be, must be less than 2.5, but more than 0, and within those constraints the maximum you see in the picture is obtained.
You can use systems of equations for this one.
We are going to use 'q' as the number of quarters Rafael had,
and 'n' as the number of nickels Rafael had.
You can write the first equation like this:
3.50=0.05n+0.25q
This says that however many 5 cent nickels he had, and however many
25 cent quarters he had, all added up to value $3.50.
Our second equation is this:
q=n+8
This says that Rafael had 8 more nickels that he had quarters.
We can now use substitution to solve our system.
We can rewrite our first equation from:
3.50=0.05n+0.25q
to:
3.50=0.05n+0.25(n+8)
From here, simply solve using PEMDAS.
3.50=0.05n+0.25(n+8) --Distribute 0.25 to the n and the 8
3.50=0.05n+0.25n+2 --Subtract 2 from both sides
1.50=0.05n+0.25n --Combine like terms
1.50=0.30n --Divide both sides by 0.30
5=n --This is how many NICKELS Rafael has.
We now know how many nickels he has, but the question is asking us
how many quarters he has.
Simply substitute our now-known value of n into either of our previous
equations (3.50=0.05n+0.25q or q=n+8) and solve.
We now know that Rafael had 13 quarters.
To check, just substitute our known values for our variables and solve.
If both sides of our equations are equal, then you know that you have
yourself a correct answer.
Happy math-ing :)
