We are given : Cost of a gallon of milk = $2.50.
Cost of a cup of yogurt = $1.20.
Total money Monica has = $20.
Number of cups of yogurt Monica can buy = x.
And inequality made is also correct
1.20x + 2.5 ≤ 20.
Now, we need to solve it for x.
Subtracting 2.5 from both sides, we get
1.20x + 2.5 -2.5 ≤ 20 - 2.5.
1.20x ≤ 17.5
Dividing both sides by 1.20, we get
1.20x/1.20 ≤ 17.5/1.20.
x ≤ 14.5833...
Because it's less than 15, so final answer is : 14 is greatest number of cups of yogurt Monica can buy.
The question is find the height of the tree, given that at two points 65 feet apart on the same side of the tree and in line with it, the angles of elevaton of the top of the tree are 21° 19' and 16°20'.
1) Convert the angles to decimal form:
19' * 1°/60' = 0.32° => 21° 19' = 21.32°
20' * 1°/60' = 0.33° => 16° 20' = 16.33°
2) Deduce the trigonometric ratios from the verbal information.
You can form a triangle with
- horizontal leg x + 65 feet
- elevation angle 16.33°
- vertical leg height of the tree, h
=> trigonometric ratio: tan (16.33) = h /( x + 65) => h = (x+65) * tan(16.33)
You can form a second triangle with:
- horizontal leg x
- elevation angle 21.32°
- vertical leg height of the tree, h
=> trigonometric ratio: tan(21.32) = h / x => h = x * tan(21.32)
Now equal the two expressions for h:
(x+65)*tan(16.33) = x*tan(21.32)
=> x*tan(16.33) + 65*tan(16.33) = x*tan(21.32)
=> x*tan(21.32) - x*tan(16.33) = 65*tan(16.33)
=> x = 65*tan(16.33) / [ tan(21.32) - tan(16.33) ] = 195.73 feet
=> h = 195.73 * tan(21.32) = 76.39 feet.
Answer: 76.39 feet
5/6 of the paper is devoted to news and pictures
first I made the fraction have equal denominators which was 6 by doing that I multiplyed the numerator and the denominator
1/2
1×3=3
2×3=6
therefore 1/2 being equivalent to 3/6
1/3
1×2=2
3×2=6
therefore 1/3 being equivalent to 2/6
now you would be able to add the numerators, so 2+3=5
therefore being 5/6 of the paper is devoted to news and pictures
Answer:
a = 3
Step-by-step explanation:
Factor both expressions
x² - x - 6
Consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term (- 1)
The factors are - 3 and + 2 , since
- 3 × 2 = - 6 and - 3 + 2 = - 1 , thus
x² - x - 6 = (x - 3)(x + 2)
-----------------------------------
x² + 3x - 18
consider factors of constant term (- 18) which sum to give the coefficient of the x- term (+ 3)
The factors are + 6 and - 3 , since
6 × - 3 = - 18 and 6 - 3 = + 3 , thus
x² + 3x - 18 = (x + 6)(x - 3)
Both expressions have a common factor of (x - 3)
Compare with (x - a ), then a = 3
