Answer:
g(x) = x² - 5
Step-by-step explanation:
The vertex form of a parabola is:
→ y = (x - a)² + b
where (a, b) is the vertex of the parabola.
From the graph, we can identify that the vertex has been shifted down 5 units, and it has not been shifted horizontally. Therefore, we can assign the following a and b values:
Now, we can plug these into the vertexformequation to get the equation of the function g(x):
y = (x - 0)² + (-5)
This simplifies to:
y = x² - 5
The length of the deck will be equal to 15 feet.
A quadrilateral with four right angles is a rectangle. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal.
Since rectangles have two pairs of equal-length sides, for any rectangle with length L and width W,
its perimeter is always 2L + 2W (or 2(L + w), whichever you prefer). Here, we're told that the width is 4 feet less than the length.
Symbolically, we'd say that W = L - 4. This allows us to write the perimeter entirely in terms of length if we replace our W with the expression on the right side:
2L + 2W = 2l + 2(L - 4) = 2L +2L - 8 = 4L - 8
This expression to come out to 52, the equality 4L - 8 = 52 and solve for L to find what the length has to be:
Adding 8 to either side, the equality becomes 4L = 60. Diving either side by 4 gives us L = 15, which tells us that the length of the deck should be 15 feet.
Therefore, the length of the deck will be equal to 15 feet.
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Since rectangles have two pairs of equal-length sides, for any rectangle with length L and width W, its perimeter is always 2L + 2W (or 2(L + w), whichever you prefer). Here, we're told that the width is 4 feet less than the length. Symbolically, we'd say that W = L - 4. This allows us to write the perimeter entirely in terms of length if we replace our W with the expression on the right side:
2L + 2W = 2l + 2(L - 4) = 2L +2L - 8 = 4L - 8
Sam wants this expression to come out to 52, so we can set up the equality 4L - 8 = 52 and solve for L to find what the length has to be:
Adding 8 to either side, the equality becomes 4L = 60. Diving either side by 4 gives us L = 15, which tells us that the length of the deck should be 15 feet.
Answer:
26 ft height
Step-by-step explanation:
The distance between the streetlamp and the tip of his shadow is 9 + 13 = 22 ft.
A rectangle triangle is formed in which one side is 22 ft long and the other side is the streetlamp height. The angle between the 22 ft side and the hypotenuse is 50°. From tangent definition:
tan(50°) = (streetlamp height)/(22 ft)
tan(50°) * (22 ft) = streetlamp height
26 ft = streetlamp height
Answer:
1/9
Step-by-step explanation:
5a=45
divide it by 5 and a will =9
9b=1
divide 1 by 9
you get 1/9=b
therefore 9x1/9=1
Answer:
No. See explanation below.
Step-by-step explanation:
Since the cards are being selected without replacement, every time we select a card, the probability varies (since there is one less card) and therefore, the probability doesn't remain the same for every trial and therefore, the probability of success changes for every trial.
It is because of this that this probability experiment doesn't represent a binomial experiment.
Answer:
Step-by-step explanation:
Answer:
8/18, 12/27, 16/36, 20/45