At a given time, the length, L, of the shadow of an object varies directlyas the height of the object, H. If the shadow is 27 ft when the height of
the object is 12 ft, what is the height of the object if the shadow is 18 ft?
Answers
Answer:
8 ft
Step-by-step explanation:
Use the direct variation equation, y = kx, where k is a constant.
Change the equation to fit the variables: L = kH
Plug in the given length of the shadow and the height of the object, then solve for k:
L = kH
27 = k(12)
2.25 = k
So, the equation is L = 2.25H
Then, plug in 18 as L, and solve for H:
L = 2.25H
18 = 2.25H
8 = H
So, when the shadow is 18 feet, the height of the object is 8 ft
Final answer:
Using the concept of direct variation, we find that the constant of variation is 2.25. Subsequent substitution in the equation reveals that the object's height when the shadow is 18ft is 8ft.
Explanation:
The question involves the concept of direct variation in mathematics. In direct variation, two quantities increase or decrease together to keep their ratio constant. This concept is given by the equation Y = kX, where Y and X are the quantities and k is a constant.
In our situation, the length of the shadow (L) varies directly with the object's height (H), i.e., L = kt. We are given that L=27ft when H=12ft, we can find the constant k by solving the equation 27ft = k * 12ft. This will get us k = 27ft/12ft = 2.25.
Now, we can determine the object's height if the shadow is 18ft. By substituting the values into the equation, we get 18ft = k * H. Substituting the value of k (2.25) will yield H = 18ft /2.25 = 8ft. Hence, the object's height when the shadow is 18ft is 8ft.
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Answers
Answer:
3, and -7
Step-by-step explanation:
First factor the trinomial
y=x2−4x−21
.
Find 2 numbers knowing sum (-4) and product (c = - 21). They are the numbers in the factor pair (3, -7).
y = (x + 3)(x - 7)
Solving the 2 binomials, we get:
x = -3 and x = 7
We want to solve the given quadratic inequality.
The correct option is the second one, counting from the top.
So we need to solve:
x^2 - 4x - 21 ≤ 0
Because we have the graph, we can avoid all the algebra.
Notice that the equation must be equal to or smaller than zero, then we just need to find the values of x such that the graph intersects the x-axis or is below it.
By looking at the given graph, we can see that the given range goes from -3 to 7
Then the solution is:
-3 ≤ x ≤ 7
This would be represented with a number line going from -8 to 8, two closed circles (because we use the symbols ≤ ≥) at negative 3 and 7, and the region between the circles is shaded.
The correct option is the second one.
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Answers
Answer:
slope - m= −0.2
F
Step-by-step explanation:
Answers
Answer:
I'm not sure
a)11:25 and 14:10
Answers
Answer:
14:10 is 24 hours clock which only come in after noon that is 12
11:25 is a normal clock with remains normal before 12:00
Answers
Answer:
551.25$
Step-by-step explanation:
u need to multiply the amount of money per a pound to the amount of pounds u have
Answers
Answer:
hope it helps mark as brainliest