Answer:
x = 5
, y = 0
Step-by-step explanation by elimination:
Solve the following system:
{-6 x - 8 y = -30 | (equation 1)
4 x + 2 y = 20 | (equation 2)
Add 2/3 × (equation 1) to equation 2:
{-(6 x) - 8 y = -30 | (equation 1)
0 x - (10 y)/3 = 0 | (equation 2)
Divide equation 1 by -2:
{3 x + 4 y = 15 | (equation 1)
0 x - (10 y)/3 = 0 | (equation 2)
Multiply equation 2 by 3/10:
{3 x + 4 y = 15 | (equation 1)
0 x - y = 0 | (equation 2)
Multiply equation 2 by -1:
{3 x + 4 y = 15 | (equation 1)
0 x+y = 0 | (equation 2)
Subtract 4 × (equation 2) from equation 1:
{3 x+0 y = 15 | (equation 1)
0 x+y = 0 | (equation 2)
Divide equation 1 by 3:
{x+0 y = 5 | (equation 1)
0 x+y = 0 | (equation 2)
Collect results:
Answer: {x = 5
, y = 0
Answer:
15h² - 4h
Step-by-step explanation:
-3(2h + -5h²) + 2h
-3(2h - 5h²) + 2h
(-3*2h -3*-5h²) + 2h
-6h + 15h² + 2h
-4h + 15h²
-6h
Answer:
A
Step-by-step explanation:
It's hard to see but when x is 6, y is 4.5. Just plug that into each equation and see which one is correct.
First, let's label our decimal places from the ones to the millions.
A number to the left of a decimal is labeled as the 'ones' place.
For example;
9,864,571.23
"9" is in the millions place (the number seven places to the left of a decimal).
"8" is in the hundred-thousands place (the number six places to the left of a decimal).
"6" is in the ten thousands place (the number five places to the left of a decimal).
"4" is in the thousands place (the number four places to the left of a decimal).
"5" is in the hundreds place (the number three places to the left of a decimal).
"7" is in the tens place (the number two places to the left of a decimal).
"1" is in the ones place (the number one place to the right of a decimal).
"2" is in the tenths place (i.e "one tenth").
"3" is in the hundredths place (i.e "one hundredth", or one-out-of-one-hundred).
Our number is
8,765,432.00 (the decimal place is just additional information to assist us in understanding)
Let's look for the number in the tens place.
Remember, the 'tens' place is the number two places to the left of a decimal.
"3" is the number in the tens place.
Your answer for A.) is 3.
Now, let's look for the number in the hundred thousand place.
Remember, the hundred thousands place is six places to the left of a decimal.
"7" is the number in the hundred thousands place.
Your answer for B.) is 7.
Your answers are:
A.) 3
B.) 7
I hope this helps!
Answer:
Step-by-step explanation:
The area left over for scrap is the area of the circle minus the area of the hexagon.
1. Area of circle
The formula for the area of a circle is
A = πr²
A = π(6)² = 36π = 113.1 in²
2. Area of hexagon
A hexagon consists of six equilateral triangles, each of side a, and we can divide each of them into two right triangles.
So, we can calculate the area of one right triangle and multiply by 12.
The formula for the area of one triangle is
A = ½bh
(a) Height of a small triangle
Per the Pythagorean Theorem,
(b) Area of a small triangle
A = ½ bh = ½ × 3 × 3√3 = 4.5√3 in²
(c) Area of the hexagon
The hexagon contains 12 small triangles.
A = 12 × 4.5√ 3 = 54√3 ≈ 93.53 in²
3. Area of scrap
A ≈ 113.1 in² - 93.53 in² = 19.6 in²