The values of x and y are ⇒ x = 4 and y = 9
Step-by-step explanation:
In a parallelogram
1. Each two opposite sides are equal and parallel
2. Each two opposite angles are equal
3. Its two diagonals bisect each other
In parallelogram ABCD
∵ Its diagonal AC and BD intersect each other at point E
∵ AC and DE bisect each other at E
∴ E is the mid-point of AC
∴ AE = EC
∴ E is the mid-point of BD
∴ DE = EB
∵ AE = x + 5
∵ EC = y
∵ AE = EC
∴ x + 5 = y ⇒ (1)
∵ DE = 2x + 3
∵ EB = y + 2
∵ DE = EB
∴ 2x + 3 = y + 2
- Subtract 2 from both sides
∴ 2x + 1 = y ⇒ (2)
Substitute y in equation (2) by equation (1)
∵ 2x + 1 = x + 5
- Subtract x from both sides
∴ x + 1 = 5
- Subtract 1 from both sides
∴ x = 4
Substitute the value of x in equation (1) to find y
∵ x + 5 = y
∵ x = 4
∴ 4 + 5 = y
∴ y = 9
The values of x and y are ⇒ x = 4 and y = 9
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Answer:
an = 4/3n - 13/3.
Step-by-step explanation:
The first term is a1,
a24 = a1 + 23d
83/3 = a1 + 4/3* 23
a1 = 83/3 - 92/3
a1 = -9/3 = -3.
So the nth term an = -3 + 4/3(n - 1)
an = -3 + 4/3 n - 4/3
an = 4/3n - 13/3
To find f(4), you want to substitute x for 4 in the equation. It would look like:
f(4) = 3(4) - 6
Then, just do the math:
f(4) = 12 - 6
f(4) = 6
Hope this helps! :)
Answer:
The correct value of the h function is; h= -9.8t² + 45t + 1
Using the discriminant, no real solution exists and the baseball will not hit the roof
.Step-by-step explanation:
h= -9.8t² + 45t + 1
Astrodome has a maximum height of 63.4 m
find out if the baseball hit at a velocity of 45 m/s will hit the roof, we'll replace h with 63.4m.
Thus;
63.4 = -9.8t² + 45t + 1
Subtract 63.4 from both sides to give;
-9.8t² + 45t + 1 - 63.4 = 0
-9.8t² + 45t - 62.4 = 0
Using quadratic formula, we have;
t = -45 ± √{(45² - (4 * (-9.8) * (-62.4)}
t = -45 ± √(2025 - 2446.08)
t = -45 ± √(-421.08)
The discriminant is -421.08
This value is less than 0.
Thus, no real solution exists and the baseball will not hit the roof.
Answer:
The answer is 90 songs.
Step-by-step explanation:
Let x be the number she has to transfer, then:
x + 150 =2(210 - x)
x + 150 = 420 - 2x
3x = 420 - 150
3x = 270
x = 90
