Omar can make 14 whole dumplings. You change 2 3/4 cups to an improper fraction ( multiply the denominator and add the numerator ) and you get 11/4. Since you need 3/16 cups for one dumpling you have to find the greatest common denominator which is 16. You multiply 4 by 11 to get the numerator and end up with 44/16. Since you need 3/16 for one whole dumping you divide 44 by 3 and get 14.6 repeating. You cannot have a fraction of a dumpling so you round down and get the answer 14.
Answer:
1=c
2=b
3= -2
4= (1,10)
Step-by-step explanation:
Answer:
(- 2, 3 )
Step-by-step explanation:
Given the 2 equations
4x + 3y = 1 → (1)
x - 3y = - 11 → (2)
Adding the 2 equations term by term will eliminate the y- term
5x + 0 = - 10
5x = - 10 ( divide both sides by 5 )
x = - 2
Substitute x = - 2 into either of the 2 equations and solve for y
Substituting into (1)
4(- 2) + 3y = 1
- 8 + 3y = 1 ( add 8 to both sides )
3y = 9 ( divide both sides by 3 )
y = 3
solution is (2, - 3 )
The question is asking us to find the dimensions of the rectangle, which would be the length and width. So, to find this, we must first state our givens, as it is Geometry.
Given: Length of rectangle = 59 + twice the width, diagonal = 2 inches longer than the width
Let's first translate all our givens to numbers. We'll start off by assigning variables that are easy to work with (x, y and z).
x = width
y = length
z = diagonal
Now that we have done that, we need to translate all our givens into numbers. Here is how that would look like:
y = 2x + 59 ←59 plus twice the width (x)
z = y + 2 ←Diagonal = 2 inches more than width
If we draw a diagram, we can see that the diagonal, length, and width all create a right triangle, which means that we can use the Pythagorean Theorem. By using right triangle postulates and theorems, we can deduce that the diagonal is the hypotenuse. Here is what our setup looks like:
x² + y² = z²
<em />Now, all we need to do is plug in the expressions we created for y and z:
x² + (2x + 59)² = [2 + (2x + 59)²]
When we solve for x, we get x = 20. Now, we just plug the x value back into the y equation to get 99. Therefore, the length equals 99 inches and the width equals 20 inches. Hope this helps and have a great day!
