Vertex of y=-2(x-3)^2+2
Answers
Answer:
vertex = (3, 2 )
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
y = 2(x - 3)² + 2 ← is in vertex form
with vertex = (3, 2 )
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a teacher needs 70 lengths of string cut to 40 cm each. If balls of string are 10 m long how many balls will be needed
Answers
Answer:
The gain on retirement is $5,000
Step-by-step explanation:
In this question, we are asked to calculate the gain or loss on retirement if a company calls some bonds at a particular price.
From the question, we can identify the following needed parameters to solve the question;
The carrying value of bonds = $221,000
Call price of bonds = $216,000
Mathematically, the gain on retirement can be calculated as follows;
Gain on retirement = carrying value - call price
= $221,000 - $216,000 = $5,000
Hence , the gain on retirement is $5,000
2.) Allison buys a Greek Treasury bond. The Greek government announces that it is defaulting on its debt. What options does Allison have to recover her money?
3.) Why are municipal bonds less attractive to foreign bondholders?
4.) Why does building a ladder of bonds protect against changes in interest rates?
Answers
2) Defaulting means being unable to pay for the debt in time. They will pay for the debt when they have the available funds to do so. Allison will just have to wait until the Greek government has enough money to cover their debts.
b. 70 <= 82 + 88 + n / 3 <= 85; 80 <= n <= 85
c. 80 <= 82 + 88 + n / 3 < 85; 70 < n < 85
d. 82 <= 80 + 85 + n / 3 <= 88; 70 <= n <= 85
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Answer : option A
Jackie scored 82 and 88 on her first two quizzes
Let n be the score of third quiz
Average of 3 quiz =
average between 80 and 85, inclusive.
so average lies between 80 and 85
Question says 80 and 85 inclusive. so we use <= or >= symbol
So inequality becomes
( multiply all sides by 3)
(subtract all sides by 170)
so option A is correct
i hope this is helpful
Answers
Answer:
61.5
Step-by-step explanation:
In this case to calculate the height, we do the following:
The first is the graphic, attached image.
Then the calculations.
b / d = tan (42 °) = 0.9
d = b / 0.9
Then we have to:
(40 + b) / d = tan (56 °) = 1.48
(40 + b) = d * 1.48
Replacing we have:
(40 + b) = (b / 0.9) * 1.48
40 + b = 1.65 * b
1.65 * b - b = 40
b = 40 / 0.65
b = 61.5
Therefore the height is approximately 61.5
Final answer:
Using the tangent function of trigonometry for the two given angles, we can set up two equations. We solve these equations by substituting the fabricate distance from one into the other, providing the height of the building.
Explanation:
To find the height of the building, we'll use the tangent function of trigonometry. In this case, the tangent of an angle in a right triangle is defined as the opposite side divided by the adjacent side. Therefore, we create two equations using the two provided angles and the respective opposite sides (antenna and building + antenna), as we know the distances are proportional to the tangent of their angles when the adjacent side (distance from the point on the ground to the building) is the same.
- For the entire structure (building + antenna): tan(56 degrees) = (Height of building + 40 feet) / Distance from the building.
- For the antenna only: tan(42 degrees) = 40 feet / Distance from the building.
We can solve this system of equations by substitution. Since tan(42 degrees) = 40 feet / Distance from the building, it means the Distance from the building = 40 feet / tan(42 degrees). Plugging the Distance into equation 1 and solving for Height of building, we get: Height of building = tan(56 degrees) * Distance from building - 40 feet = tan(56 degrees) * (40 feet / tan(42 degrees)) - 40 feet. This gives us the height of the building.
Learn more about Trigonometry here:
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