Answer:
26 - 7 i. hopefully this helps!
In this diagram we see that 80 and 3x+4y are both vertical angles and vertical angles are congruent or always equal so we can set those two equations equal to each other then we can see that a line splits two angles making them supplementary (they equal 180 degrees) So we can have another equation, the two equations are:
3x+4y=80 and 3x+4y+7x-8y=180 (add like terms to simplify and get 10x-4y=180
Then use elimination to get rid of the y variables
10x-4y=180 (plus)
+3x+4y=80 (the negative 4 and positive 4 cancels each other out so you are left with:)
13x=160 (divide by x)
x=12.30769 which can be rounded to x=12.31
Then we have to plug in x into the first equation:
3(12.31) + 4y = 80
36.93 + 4y = 80 (subtract 36.93 from 80)
4y = 43.07 (divide)
y=10.7675 or rounded to 10.77
so x=12.31 and y=10.77
We have given
hypotenuse=<span>6√2
let us suppose leg =a
using Pythagorean theorem
a^2+a^2=(</span><span>6√2)^2
</span>2a^2=36*2
diving by 2 on both sides
a^2=36
taking square root on both sides
√a^2 =<span>√36
a=6
therefore
</span><span>the leg of each isosceles right triangle is 6</span>
27.8 x 9.6 is 266.88 so 280
Step-by-step answer:
Since the question can be solved easily with a calculator, it is assumed that no calculators are allowed.
13*379 is the same as (10+3)*379
Applying distributive law, we then solve
10*379 = 3790
3*379 = 1137
Adding the two, we get
4927
Alternatively, we can calculate the product by long multiplication to get also 4927.
To check for mistakes, we use casting out nines
13 * 379 (add the digits, 1+3, 3+7+9)
4 * 19 (add the digits)
4*10 (multiply)
40 (add digits)
4
Add digits of 4927
4+9+2+7 = 22
add digits again
2+2 =4
the two match, so the likelihood of make arithmetic error is very low.
Note: using a calculator, the value is indeed 4927.
