Answer:
525 meters
Step-by-step explanation:
Answer:
∠1 is 33°
∠2 is 57°
∠3 is 57°
∠4 is 33°
Step-by-step explanation:
First off, we already know that ∠2 is 57° because of alternate interior angles.
Second, it's important to know that rhombus' diagonals bisect each other; meaning they form 90° angles in the intersection. Another cool thing is that the diagonals bisect the existing angles in the rhombus. Therefore, 57° is just half of something.
Then, you basically just do some other pain-in-the-butt things after.
Since that ∠2 is just the bisected half from one existing angle, that means that ∠3 is just the other half; meaning that ∠3 is 57°, as well.
Next is to just find the missing angle ∠1. Since we already know ∠3 is 57°, we can just add that to the 90° that the diagonals formed at the intersection.
57° + 90° = 147°
180° - 147° = 33°
∠1 is 33°
Finally, since that ∠4 is just an alternate interior angle of ∠1, ∠4 is 33°, too.
Answer:
x + y = 60 and 1.55x + 1.4y = 88.20 and the solution is x = 32 and y = 28.
Mr. Sanchez’s class earned more money by $10.4.
Step-by-step explanation:
Mr. Sanchez’s class sold fruit pies for $1.55 each and Mr. Kelly’s class sold bottles of fruit juice for $1.40 each.
Let the number of sold fruit pies is x and bottles of fruit juice is y.
So, from the given condition we can write
x + y = 60 ........ (1)
⇒ 1.4x + 1.4y = 84 ....... (2) and
1.55x + 1.4y = 88.20 ........ (3)
Now, solving equations (2) and (3) we get (1.55 - 1.4)y = (88.2 - 84)
⇒ y = 28
And from equation (1) we get x = 60 - 28 = 32.
Therefore, Mr. Sanchez’s class earned more money. (Answer)
Now, this class have earned $(32 × 1.55 - 28 × 1.4) = $10.4 more. (Answer)
Answer:
k > 7
Step-by-step explanation:
Given the inequality statement: 4k - (5 + 3k) > 2
Distribute -1 into (5 + 3k):
4k -5 - 3k > 2
Next, add like terms:
k - 5 > 2
Add 5 to both sides of the inequality:
k - 5 + 5 > 2 + 5
k > 7
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Price of one citron = 5 units
Price of one fragrant = 5/7 units = 0.71 units
Further explanation:
Let x be the price of one citron and
y be the price of one fragrant
Then according to given statement
10x+7y = 55 Eqn 1
7x+10y = 64 Eqn 2
Multiplying equation 1 by 7
This will be equation 3.
Multiplying equation 2 by 10
This will be equation 4.
Subtracting equation 3 from equation 4
So,
Price of one citron = 5 units
Price of one fragrant = 5/7 units = 0.71 units
Keywords: Linear Equations, Solving system of linear equations
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