Which equation is equivalent to f(x) =-4(x+7)^2-6
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Answer:
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Answer:
Distance = 5 units
Step-by-step explanation:
The given problem asks us to determine the distance between two points, (1, 5) and (5, 2).
<h2>Solution:</h2>In order to find the distance between two points, we can use the following distance formula:
Let (x₁, y₁) = (1, 5)
(x₂, y₂) = (5, 2)
Step 1: Substitute points into the formula:
Step 2: Subtract the integers in each of the parenthesis under the radical:
Step 3: Evaluate the powers (exponents):
Step 4: Add 16 and 9:
Step 5: Take the square root of 25:
⇒ Distance (D) = 5 units.
<h2>Final Answer:</h2>Therefore, the distance between points (1, 5) and (5, 2) is <u>5 units</u>.
<h3>________________________</h3><u><em>Keywords:</em></u>
Distance formula
Two points
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Answer:
Step-by-step explanation:
Assuming the tree is perpendicular to the ground, we can use the right triangle trigonometric ratios to find the tree's height.
- sin(θ)= opposite/hypotenuse
- cos(θ)= adjacent/hypotenuse
- tan(θ)= opposite/adjacent
Now, let's draw a diagram. We know Aiko is 5 meters from the base of the tree. From there, the angle to the top of the tree is 80 degrees. We are looking for x, the tree's height. The diagram attached is not to scale.
We base the sides off of the angle. x is opposite of 80 degrees and 5 is adjacent. Therefore we must use tangent.
- opposite=x
- adjacent=5 m
- θ=80
Substitute in the known variables.
We want to find x, the height of the tree. Therefore we need to isolate that variable.
x is being divided and the inverse operation is multiplication. Multiply both sides of the equation by 5 meters.
The question asks for an approximation, so let's round to the nearest hundredth.
The 6 in the thousandth place tells us to round the 5 to a 6.
The tree is about <u>28.36 meters tall.</u>
