Fyodor and his three sons, Ivan, Dmitri and Alyosha, are standing exactly on the corners of a rectangular room. Fyodor is $3$ meters from Dmitri and $5$ meters from Ivan. What is the minimum possible distance that Fyodor could be from Alyosha, in meters
Answers
The minimum possible distance that Fyodor could be from Alyosha is 4 meters.
Given Information and Deduction
It is given that Fyodor is 3 meters in distance away from Dmitri and 5 meters from Ivan.
Now, since we know that the longest side of a right angle triangle formed by the dividing the rectangular room into two parts using a diagonal is the hypotenuse. Thus, if we want to find the minimum possible distance between Fyodor and Alyosha, we will have to assume that Ivan is standing diagonally opposite to Fyodor, as shown in the figure below.
Calculating the Minimum Distance
According to Pythagoras Theorem,
(hypotenuse)² = (base)² + (perpendicular)²
Here, the hypotenuse is the distance between Fyodor and Ivan.
Perpendicular and the base are the distances between Fyodor and Dmitri, and Fyodor and Alyosha respectively.
⇒ base = √(hypotenuse)² -(perpendicular)²
⇒ base = √(5)²-(3)²
⇒ base = √(25-9)
⇒ base = √16
⇒ base = 4 meters
Therefore, the minimum possible distance between Fyodor and Alyosha is 4 meters.
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Answer:
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Step-by-step explanation:
by using SOHCAHTOA
hypotenus = 8
adjacent = x
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Answers
Answer:
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Answer:
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Step-by-step explanation:
Answer:
Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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3x + 4y = -2
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Answers
Answer:
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Answers
Given:
The bases of a trapezoid lie on the lines
[tex]y=2x+7[/tex]
[tex]y=2x-5[/tex]
To find:
The equation that contains the midsegment of the trapezoid.
Solution:
The slope intercept form of a line is
[tex]y=mx+b[/tex]
Where, m is slope and b is y-intercept.
On comparing [tex]y=2x+7[/tex] with slope intercept form, we get
[tex]m_1=2,b_1=7[/tex]
On comparing [tex]y=2x-5[/tex] with slope intercept form, we get
[tex]m_2=2,b_2=-5[/tex]
The slope of parallel lines are equal and midsegment of a trapezoid is parallel to the bases. So, the slope of the bases line and the midsegment line are equal.
[tex]m=m_1=m_2=2[/tex]
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[tex]b=\dfrac{b_1+b_2}{2}[/tex]
[tex]b=\dfrac{7-5}{2}[/tex]
[tex]b=\dfrac{2}{2}[/tex]
[tex]b=1[/tex]
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[tex]y=2x+1[/tex]
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Answers
Answer:
Step-by-step explanation:
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it crosses the y axis at (0,4)
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Answers
Answer:
C
Step-by-step explanation:
Remark
There are probably a couple of ways that you could do this. I'm going to pick the most obvious way.
Givens.
KN = 2.5
NO = 10
LM = 3
MP = x
Equation
NO/KN = PM / LM
Solution
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2.5x = 10 * 3 Combine
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x = 30/2.5
x = 12
That looks like it should be the answer, and it almost is, but you are asked for LP.
LP = LM + MP
LP = 3 + 12
LP = 15
The answer is 15
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Answers
Answer:
45 square centimeters.
Step-by-step explanation:
Length(L) = 9 cm
breadth (b) = 5 cm
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= L * b
= 9 * 5
= 45 cm²
Hope it will help :)
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Answers
Answer:
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Step-by-step explanation:
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Answers
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Answers
Answer:
only x+1 , x+3 COULD represent consecutive even integers
Step-by-step explanation:
only x+1 , x+3 COULD represent consecutive even integers
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What is the slope of a line perpendicular to this line?
Answers
And the slope of a line perpendicular is 3/4
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Enter your answer and show all the steps that you use to solve this problem in the space provided.
Multiply and simplify if possible.
√7x(√x−7√7)
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Answers
Step-by-step explanation:
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what is the area of a rectangle when the two sides are 4200 and 4500 in meters squared
Answers
Answer 17400
Step-by-step explanation:
Answer:
A=1.89×10 7 (7 as the exponent)
Explanation: