They give us 2 pieces to the puzzle. Both are positive numbers...x and y.
1.) 1 number is 1 less than twice another number. (x = 2y -1)...and
2.) the sum of their squares is 106. (x^2 + y^2 = 106).
substitute the value for x into the second equation.
(2y-1)^2 + y^2 = 106
(2y-1) (2y-1) + y^2 = 106 (use distributive property)
4y^2 - 2y - 2y + 1 + y^2 = 106 (subtract 106 from both sides)
4y^2 - 2y - 2y + 1 + y^2 - 106 = 106 - 106 (combine like terms)
5y^2 - 4y - 105 = 0 (factor)
(y-5) (5y-21) = 0 (set to 0)
y - 5 = 0
y = 5
substitute the 5 into the equation for y (x = 2(5) - 1)
x = 9 if we square 9, we get 81.
subtracted from 106 we have 25...the square root of 25 is 5.
our answers are 5 and 9.
Answer: it will be 6 ounces of frozen yogurt and 10 ounces of orange juice.
Step-by-step explanation:
3 parts frozen yogurt
5 parts orange juice For a total of 8 parts divided by 16 ounces = 2 Multiply 3 fy x 2= 6 ounces And multiply 5 oj x 2= 10 ounces
She will need 1/3 cup because she has already covered 3/4
Answer: The length is 510 and the width is 110.
Step-by-step explanation:
To find the area of a rectangle, you will have to add the 2 times the length plus 2 times the width because a rectangle have 4 sides. Two widths and two lengths.
You can now use the formula P= 2l + 2w
were P is the perimeter , l is the length, and w is the width.
the length is 400 more than the width, so we can represent that by the equation, l = w + 400
And now we know that the width is w.
So now we will input the perimeter, length, and into the formula to solve for w.
1240 = 2(w + 400) + 2w
1240 = 2w + 800 + 2w
1240 = 4w + 800
-800 -800
440 = 4w
w = 110
L= 110 + 400
L = 510
Check :
1240 = 2(510) + 2(110)
1240 = 1020 + 220
1240 = 1240
Answer:
Your answer is 120 degrees.
Step-by-step explanation: