beth poured the same amount of juice into 10 glasses. she used 2quarts of juice. how much juice is in each glass
2 answers:
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Answer:
a = -1
b = -9
c = 9
d = 3
e = 3
f = 2
g = 3/2
Step-by-step explanation:
* Lets explain how to solve the problem
∵ are rational fractions
- To add or subtract the rational fractions they must have same
denominator
∵ 6 - 2x must be written 2x - 6, take (-1) as a common factor from 6 - 2x
∴ - 1(-6 + 2x) = - 1(2x - 6)
∴
∴ a = -1
∵ 9 ÷ -1 = -9
∴ =
∴ b = -9
∵ The denominators of the two fractions are 2x - 6
∴ We can add them by adding their numerator
∵ 3x + -9 = 3x - 9
∴ =
∴ c = 9
∵ 3x - 9 has a common factor 3
∴ 3x - 9 = 3(x - 3)
∵ 2x - 6 has common factor 2
∴ 2x - 6 = 2(x - 3)
∴ =
∴ d = 3 , e = 3 , f = 2
- The fraction has same factor (x - 3) up and down then we can cancel
them together
∴ =
∴ g = 3/2
Answer:
1)
2)
3)
4)
Step-by-step explanation:
1) Value of
since sin45° = 1/√2
Therefore
2).Value of
Since cos 30° = √3/2
Therefore
3). Value of
since tan 60° = √3
therefore
4). Value of
Since sin90°=1
Therefore
Answer:
(x + 5)² + (y + 7)² = 288
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
The radius is the distance from the centre (- 5, - 7) to the point on the circle (7, 5)
Use the distance formula to calculate r
r = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 5, - 7) and (x₂, y₂ ) = (7, 5)
r = =
=
Hence
(x - (- 5))² + (y - (- 7))² = ()², that is
(x + 5)² + (y + 7)² = 288