Given: mTRV = 60° mTRS = (4x)° Prove: x = 30 What is the missing reason in step 3? substitution property of equality angle addition postulate subtraction property of equality addition property of equality
Answers
Answer: Angle addition postulate.
Explanation: If [tex]\angle TRV= 60^{\circ}[/tex] and [tex]\angle TRS=4x^{\circ}[/tex]
here, if we have to prove x=30
If there is a condition that TR is a line which meets with the line segment VS at point R then by the Angle addition postulate, we can say that [tex]\angle TRV+\angle TRS=180^{\circ}[/tex]⇒[tex]x=30^{\circ}[/tex]
But,
In option (1) substitution property of equality
If there is condition that [tex]\angle TRV=\angle TRS[/tex]
then we can use substitution property of equality,
And, in this case [tex]4x^{\circ}=60^{\circ}[/tex]⇒[tex]x=15^{\circ}[/tex]
which is wrong. So, we can not use this property here.
In option (3) subtraction property of equality
There is no use of this property to find the value x.
In option (4) addition property of equality
There is no use of this property to find the value x.
The omitted reason in step 3 should be the angle addition postulate.
According to the angle addition postulate , the value or measurement of an angle is the sum of all the angles which makes up that segment.From the diagram attached ;
mTRV = 60 ; ∠TRS = 4x
According to the addition postulate :
mTRV + ∠TRS = 180° (sum of linear pair of angles).
Though obtaining the value of the missing angle required substituting 30 for the value of x. However, it is because of the addition postulate which gives the sum of a linear pair of angles that we were able to establish that mTRV + ∠TRS = 180°.Hence, the missing reason for the third step is the angle addition postulate.
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The solution of expression is, x = 6
We have to give that,
An expression to simplify as,
⇒ 45 + 5/6x = 50
Now, Simplify the expression by combining like terms,
⇒ 45 + 5/6x = 50
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So, The solution is, x = 6
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Answer: Option 'B' is correct.
Step-by-step explanation:
Since we have given that
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Answers
Since you are given the x- and y-coordinates of both vectors a and b, we can apply the formula
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Therefore, substituting the known values: a⃗ ⋅b⃗ = (3 * -2) + (-8 * -6) = -6 + 48 = 42
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Answers
9x - 15 is equal to the angle 33° or 9x - 15 is equal to the other angle of the first triangle.
Let's probe with the first option:
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Now, let's probe the second option.
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F-j=jrt
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To solve the formula F=J+Jrt for 't', first, subtract 'J' from both sides to get F-J=Jrt. Then, divide both sides by 'Jr', for the final equation for 't' = (F-J)/Jr.
Explanation:This physics-related mathematics question is asking you to solve the given formula F=J+Jrt for 't'. To isolate 't', we first want to eliminate 'J' from the right side. We do this by subtracting 'J' from both sides of the equation. This gives us F-J=Jrt.
Then, we divide both sides by 'Jr'. When we do this, we are left with t=(F-J)/Jr as the rearranged formula with 't' as the subject. This results in 't' being isolated in the equation, which answers the student's question.
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A person who is 6ft tall walks away from a streetlight. When the person is 15 feet away from the light, the tip of his shadow is 5 feet in front of him. Find the height of the streetlight
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[tex]\frac{shadow}{actual}[/tex]
Since we know the ratio is going to stay constant at [tex]\frac{5}{6}[/tex], we can use this to find the height of the lamp along with the information that the total distance from the lamp to the tip of his shadow is 20:
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Complete each statement regarding an angle θ and its reference angle theta hat using radian measure. (Assume 0 ≤ θ < 2π. Give your answers in terms of θ.) (a) If θ is in QI, then theta hat = . (b) If θ is in QII, then theta hat = . (c) If θ is in QIII, then theta hat = . (d) If θ is in QIV, then theta hat = .
Answers
The reference angle is simply the acute angle between the terminal side and the x-axis
The terminal angles in the four quadrants are
[tex]\bar \theta = \theta[/tex].[tex]\bar \theta = \pi - \theta[/tex].[tex]\bar \theta = \theta - \pi[/tex].[tex]\bar \theta = 2\pi - \theta[/tex]The given parameters are:
[tex]\theta \to[/tex] reference angle
[tex]\bar \theta \to[/tex] terminal angle
(a) If the reference angle is in the first quadrant
In the first quadrant, the x-axis is at [tex]0\ rad[/tex]
So, the terminal angle is:
[tex]\bar \theta = \theta - 0[/tex]
[tex]\bar \theta = \theta[/tex]
(b) If the reference angle is in the second quadrant
In the second quadrant, the x-axis is at [tex]\pi \ rad[/tex],
While the reference angle is between [tex]\frac{\pi}{2}[/tex] and [tex]\pi \ rad[/tex]
It means that, we have to subtract the reference angle from the x-axis
So, the terminal angle is:
[tex]\bar \theta = \pi - \theta[/tex]
(c) If the reference angle is in the third quadrant
Here, the x-axis is still at [tex]\pi \ rad[/tex],
But the reference angle is between [tex]\pi \ rad[/tex] and [tex]\frac{3}{2}\pi[/tex]
It means that, we have to subtract the x-axis from the reference angle.
So, the terminal angle is:
[tex]\bar \theta = \theta - \pi[/tex]
(d) If the reference angle is in the fourth quadrant
Here, the x-axis is at [tex]2\pi \ rad[/tex]
And the reference angle is between [tex]\frac{3}{2}\pi[/tex] and [tex]2\pi \ rad[/tex]
It means that, we have to subtract the reference angle from the x-axis.
So, the terminal angle is:
[tex]\bar \theta = 2\pi - \theta[/tex]
See attachment for illustration of terminal angles
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Final answer:
When dealing with angles in radians and their reference angles, each quadrant has a specific relationship for determining the reference angle based on the given angle θ.
Explanation:
Radian Measure with Reference Angles:
If θ is in QI, then θ hat = θ
If θ is in QII, then θ hat = π - θ
If θ is in QIII, then θ hat = θ - π
If θ is in QIV, then θ hat = 2π - θ
Solve the absolute value equation. |x| = –45