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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Related Questions
there are 3/4 of a pizza left over from last night how many 1/8 portions are there
Answers
3/4 = 6/8
There are 6 "1/8" portions left
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45+5/6x=50
need to find x and math for x
Answers
5/6x = 50 - 45
5/6x = 5
5x = 5 * 6
5x = 30
x = 6
hope that helps, God bless!
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
Subtract 45 on both sides,
⇒ 45 + 5/6x - 45 = 50 - 45
⇒ 5/6x = 5
Multiply by 6 on both sides,
⇒ 5x = 5 × 6
⇒ 5x = 30
Divide by 5 on both sides,
⇒ x = 30/5
⇒ x = 6
So, The solution is, x = 6
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Evaluate the dot product a⃗ ⋅b⃗ of a⃗ =3i^−8j^ and b⃗ =−2i^−6j^.
Answers
Since you are given the x- and y-coordinates of both vectors a and b, we can apply the formula
a dot b = ax*bx + ay*by, where ax=x-component of vector a, by=y comp of vector b, and so on.
So, for the problem at hand, ax * bx + ay * by becomes
3(-2) + (-8)(-6) = -6 + 48 = 42 (answer). Note that the dot product (or "scalar product" is itself a scalar.
The dot product of vectors a⃗ =3i^−8j^ and b⃗ =−2i^−6j^ is calculated by multiplying the corresponding components of the vectors and summing the results, giving a final dot product of 42.
Explanation:The dot product of two vectors a and b is calculated by multiplying the corresponding components of the vectors and summing the results. So, given the vectors a⃗ =3i^−8j^ and b⃗ =−2i^−6j^, the dot product can be found as follows:
a⃗ ⋅b⃗ = (a_x * b_x) + (a_y * b_y)
Therefore, substituting the known values: a⃗ ⋅b⃗ = (3 * -2) + (-8 * -6) = -6 + 48 = 42
So, the dot product a⃗ ⋅b⃗ for vectors a⃗ =3i^−8j^ and b⃗ =−2i^−6j^ is equal to 42.
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Solve the absolute value equation. |x| = –45
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"how many terms are there in the algebraic expression""
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What are the quotient and remainder when
a.19 is divided by 7?
b.−111 is divided by 11?
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the remainder = 5
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A section of a roller coaster track forms a parallelogram ABCD. If m∠ABC = 72°, what is m∠DAB? A) 72° B) 108° C) 144° D) 216°
Answers
Answer: Option 'B' is correct.
Step-by-step explanation:
Since we have given that
A section of a roller coaster track forms a parallelogram ABCD.
If m∠ABC = 72°
We need to find the m∠DAB,
Since ABCD is a parallelogram .
So, "Sum of interior angles on the same side is supplementary":
[tex]m\angle ABC+m\angle DAB=180\textdegree\\\\72\textdegree+m\angle DAB=180\textdegree\\\\m\angle DAB=180\textdegree-72\textdegree\\\\m\angle DAB=108\textdegree[/tex]
Hence, Option 'B' is correct.
anyone help me please!
A stereo listed for $350 is on sale for 20% off the list price. The sales tax is 6%. What total price does a customer pay for the stereo if she/he buys it on sale?
1 $324.00
2 $259.00
3 $262.20
4 $296.80
5 $301.00
Answers
then you need add 6% onto the price
Im not sure if youre supposed to calculate 6% of the original price or the price with 20% off
tax of normal price + discounted price= $301
tax of discounted price + discounted price= $296.60
Your answer should be E since $301 is an answer choice
[tex] \frac{dx}{dt} = \frac{t^{2}+3tx+ x^{2} }{ t^{2} } [/tex]
Answers
[tex]\dfrac{\mathrm dx}{\mathrm dt}=1+\dfrac{3x}t+\dfrac{x^2}{t^2}[/tex]
Let [tex]x(t)=ty(t)[/tex], so that [tex]\dfrac{\mathrm dx}{\mathrm dt}=t\dfrac{\mathrm dy}{\mathrm dt}+y[/tex].
[tex]t\dfrac{\mathrm dy}{\mathrm dt}+y=1+3y+y^2[/tex]
[tex]t\dfrac{\mathrm dy}{\mathrm dt}=1+2y+y^2=(1+y)^2[/tex]
[tex]\dfrac{\mathrm dy}{(1+y)^2}=\dfrac{\mathrm dt}t[/tex]
[tex]\implies-\dfrac1{1+y}=\ln|t|+C[/tex]
[tex]\implies y+1=-\dfrac1{\ln|t|+C}[/tex]
[tex]\implies yt=x=-t-\dfrac t{\ln|t|+C}[/tex]
a large bag of cashews weighs 8 1/3 pounds one serving is 1/3 pound how many servings are in the bag
Answers
one serving bag is 1/3
now, how many servings are in the bag?
=> 25/3 ÷ 1/3
=> 25/3 X 3/1 (changing division into multiplication form)
=> 25, bag are in serving .
A car is driving at the speed of 58 km/h.How much time will it take to drive for distance 32 miles?
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Michael sold his house for $548,900, which was 160% of the amount he paid for it. Calculate the amount he paid for the property.
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F=J+Jrt solve following formula for t
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F-j=jrt
t=(F-j)/jr
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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How much greater is the area of a square with a side length of 9 inches than the area of a circle with a radius of 3 inches?
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Subtract: 81 sq in - 28.27 sq in = approx. 52.73 sq in.
The difference is 52.73 sq in; the square is larger, the circle smaller.
Reina and Sam are multiplying (84)5 (73)9. Reina's Work Sam's Work (84)5 (73)9 = 84 + 573 + 9 = 89712 (84)5 (73)9 = 84⋅573⋅9 = 820727 Is either of them correct? Explain your reasoning.
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Find the ratio and simplify. In this triangle, find the ratio of the shortest side to the longest. A triangle has three sides with lengths 15.2, 5.6, 14.1
Answers
let's check the ratio from shortest to longest.
[tex]\bf 14.1\implies \cfrac{141}{10}\qquad \qquad\qquad 15.2\implies \cfrac{152}{10} \\\\\\ \cfrac{shortest}{longest}\qquad 14.1:15.2\qquad \cfrac{14.1}{15.2}\implies \cfrac{\quad \frac{141}{10}\quad }{\frac{152}{10}}\implies \cfrac{141}{10}\cdot \cfrac{10}{152} \\\\\\ \cfrac{141}{152}[/tex]
Caroline bought 20 shares of stock at 10 ½, and after 10 months the value of the stocks was 11 ¼. If Caroline were to sell all her shares of this stock, how much profit would she make? A. $210 B. $10 C. $15 D. $225
Answers
20 shares at 11 1/4 (or 11.25) = 20 * 11.25 = 225
so the profit made would be : 225 - 210 = $ 15 <==
A scuba diver swimming at the Deppe shown, and then swim 0.5 feet toward the surface every three seconds. What is the location of the scuba diver, relative to the surface, after 15 seconds?
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after 15 seconds = your answer
3 x 5 = 15
0.5 x 5 = your answer
your answer = 2.5
2.5 is your answer
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y=-2/5x+4 in standard form
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2、 4
4、 Y=-2/5x+4
on a certain day the temperature in Seattle was -1 degrees C and the temperature in the Hudson was 18 degrees C is how many degrees lower was the temperature in Seattle
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The temperature in Seattle was 19 degrees lower than in the Hudson.
we subtract the temperature of Seattle from the temperature of the Hudson:
18°C - (-1°C) = 19°C
Therefore, the temperature in Seattle was 19 degrees lower than the temperature in the Hudson.
What percent is 6 out of 30? 2% 6% 20% 30%
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Two right triangles are congruent. Find the value of x.
right triangle with angle of 33 degrees, right triangle with angle of 9 x minus 15 degrees
Select one:
a. 5
b. 6
c. 8
d. 12
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:
9x - 15 = 33 => 9x = 33 + 15 = 48
=> x = 48 / 9 = 5,33, which is no in the list of options.
Now, let's probe the second option.
The other angle of the first right triangle is 90° - 33° = 57°
Then, 9x - 15 = 57
=> 9x = 57 + 15 = 72
=> x = 72 / 9 = 8
Which is the option c. 8.
So, I am sure that if you have a figure it will be compatible with that answer, else yet the procedure to find the answer is what I have used here.
Answer: option c. 8
Outlet malls sell goods _____
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1. at a discount
2. add all the items together at their sales cost then add salves tax
3. $26.75
4. $66.23
how many times can 36 go into 300
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What is 129,543 rounded to the nearest ten thousand
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hope this helps
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
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
Answers
[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:
[tex]\frac{5}{6}=\frac{20}{h}[/tex]
[tex]5h=120[/tex]
[tex]h=24[/tex]
Algebra help me please ILL MARK BRAINIEST
Answers
0 4
- 6 1
3 -4
Rember row times columns.
=>
a11 = 4*0 + 0*(-3) = 0
a12 = 4*1 + 0*1 = 4 + 0 = 4
a21 = -1*0 + 2*(-3) = 0 - 6 = -6
a22 = -1*1 + 2*1 = -1 + 2 = 1
a31 = -3*0 + (-1)*(-3) = 0 + 3 = 3
a32 = -3*1 + (-1)*1 = -3 - 1 = -4
family drinks 1 3/4 gallons of milk every 4 1/2 days what is the unit rate of milk per day
Answers
which gives us a quotient of about 0.39 gallons of milk for one day.
A driveway is 40 yards long. About how many meters long is it? Round to the nearest hundredth