The value of 5•10⁷ µs quantity in second is 50 .
The unitary methodology could be a methodology within which you discover the worth of a unit then the worth of a needed range of units.For simplification, invariably write the items to be calculated on the right-hand aspect and things illustrious on the left-hand aspect.In the unitary method, the value of many things is given and we need to either find the value of more or fewer things. In order to try to to that, we have a tendency to should initial realize the worth of 1 issue by division so realize the worth of additional or fewer things by multiplication.We know that 10⁶μs is equal to 1 second .
Using unitary method , we get
1 μs have = 10⁻⁶ second
5•10⁷ µs have = 5 × 10⁷ × 10⁻⁶
= 50 second
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I WILL MARK BRAINLIST!!! PLEASE HELP ITS MATH QUESTION Determine the approximate value of x using basic trigonometry.
Thank you so much for helping !
Step-by-step explanation:
I'm not sure but this is the solution hehe
A chemist is heating water so it can dissolve a larger amount of sodium chloride. The water's temperature increases 7°C each minute from an initial temperature of 21°C. How long will it take for the water to reach 49°C? Write and solve an equation to find the answer.
The time taken by the water to reach 49 degree Celsius is 4 minutes.
According to the question, larger amount of sodium chloride is dissolved in the heating water. And the given data states that the water temperature increases 7 degree Celsius every minute.
Initial temperature of water is 21 degree Celsius.
Let us assume, water reaches at 49° C after 'm' minutes.
As per question, every minute temperature increases as 7°C. So, the expression can be written as: (21 + 7m)°C
⇒ 21 + 7m = 49
⇒m = 4 minutes.
Hence, the time taken to reach 49° C is 4 minutes.
What is temperature?
Temperature defines the atmosphere hotness. And it is expressed in different scales as well as in different parameters like Celsius etc. It is measured through the device known as thermometer.
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You make $7.25/hr and your boss
promises at least 3 hours but no
more than 18 hours per week.
Payroll (FICA) taxes of 7.65% are
withheld from your paycheck.
Be sure to deduct your tax
Payroll (FICA) taxes of the question is 0.2295
According to the given data,
Payroll (FICA) taxes is 7.65%
boss promises at least 3 hours but no more than 18 hours per week.
then we get, 3 × 0.0765
= 0.2295
therefore, payroll taxes from your paycheck and to deduct tax
0.2295
SHARE
All About the FICA Tax
If you earn a wage or a salary, you’re likely subject to Federal Insurance Contributions Act taxes. Not to be confused with the federal income tax, FICA taxes fund the Social Security and Medicare programs. Also known as payroll taxes, FICA taxes are automatically deducted from your paycheck. Your company sends the money, along with its match (an additional 7.65% of your pay), to the government. In this article we’ll discuss what FICA taxes are, how they’re applied and who’s responsible for paying them.
Planning your finances goes beyond just taxes. Find a local financial advisor today.
FICA Taxes: The Basics
Every payday, a portion of your check is withheld by your employer. That money goes to the government in the form of payroll taxes. There are several different types of payroll taxes, including unemployment taxes, income taxes and FICA taxes. Two types of taxes fall under the category of FICA taxes: Medicare taxes and Social Security taxes.
Paying FICA taxes is mandatory for most employees and employers under the Federal Insurance Contributions Act. The funds are used to pay for both Social Security and Medicare.
If you own a business, you’re responsible for paying Social Security and Medicare taxes, too. For self-employed workers, they’re referred to as SECA taxes (or self-employment taxes) based on regulations included in the Self-Employed Contributions Act.
A wage base limit applies to employees who pay Social Security taxes. This means that gross income above a certain threshold is exempt from this tax. The wage limit changes almost every year based on inflation. In 2021, it was $142,800. For 2022, the limit rose to $147,000. This income ceiling is also the maximum amount of money that’s considered when calculating the size of Social Security benefits.
Medicare taxes, on the other hand, don’t have a wage limit. But there’s an Additional Medicare Tax that high-income individuals must pay. That has been the case since January 1, 2013.
The Additional Medicare Tax rate is 0.90% and it applies to employees’ (and self-employed workers’) wages, salaries and tips. So any part of your income that exceeds a certain amount gets taxed for Medicare at a total rate of 2.35% (1.45% + 0.90%). That income ceiling for 2021 and 2022 is $200,000 for single filers, qualifying widows and anyone with the head of household filing status; $250,000 for married couples filing joint tax returns and $125,000 for couples filing separate tax returns. You can calculate how much you owe using Form 8959.
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203X12 estimate to check for reasonableness
2436 ≈ 2400 is the estimate products of 203X12 .
What is estimate products?
Round the numbers to some nearby figures that you can mentally multiply to estimate the product of multiplication. Rounding all variables to the biggest digit (place value) they have is one way to estimate values.Example -Estimation is frequently accomplished through sampling, which involves counting a small sample of a given thing and extrapolating that number to a wider population. Calculating how many sweets of a certain size are contained in a glass jar is an example of estimation.203X12
= 2436
We can take compatible numbers
200 × 12
2400
So, 2436 ≈ 2400
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Porfabor ayuda con esto de matemáticas
Answer: A; $9; B; D
Step-by-step explanation:
1. 480➗6 = 80%
2. 36➗4= $9
3. 0.85 x 20= 17
4. 28➗2 = 14
14 x 6= 84
i need help please
Y=CD-8 for C
Answer:
c = (y+8)/d
Step-by-step explanation:
PLS PLS HELP ME THIS
Answer:
Yes
Step-by-step explanation:
Points D and E are on plane F.
What is f(-3) for the function f(x)=-3 x+6 ?
The value of f(-3) is 15.
The given function is f(x) = -3x+6. Now, f(-3) = x = -3
Substituting and Evaluating the value of x in the equation f(x) = -3x+6, we get
f(-3) = -3(-3)+6f(−3)=−3(−3)+6
f(-3) = 9+6f(−3)=9+6
f(-3) = 15f(−3)=15
∴ The value of f(-3) for the function f(x) = -3x+6 is equal to 15.
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Peter bought three items at a store. Here are their prices (in dollars):
18.23, 6.39, and 15
What is the total amount Peter paid at the store? Do not round your answer.
$____
Type your numerical answer below.
-
Answer: $39.62
Step-by-step explanation: To get the answer to the cost of Peter's three items, I took the prices of the three and added them together. This amount would be the amount he paid WITHOUT TAX.
20 POINTS
If f(x) = x - 5, what is the value of x when f(x) = 15?
10
20
5
0
Answer: The value of x is 20.
Algebraic function :
Given function is,
We have to find the value of x when
The value of x is 20.
Step-by-step explanation: hope this helps
A is between points B and C. AB = 2x - 3, BC = 7x - 10, and AC = 32.
What is the value of x?
The value of the x in a linear equation is 7.8.
According to the statement
We have to find that the value of x.
So, For this purpose, we know that the
A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
From the given information:
A is between points B and C. AB = 2x - 3, BC = 7x - 10, and AC = 32.
It means
BC = BA + AC
Then we have to substitute the values in it
Then
BC = BA + AC
7x - 10 = 2x - 3 + 32
7x - 2x = -3 +32+10
5x = 39
here the values of the x is a
x = 39/5.
x = 7.8
So, The value of the x in a linear equation is 7.8.
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find the volume of the object.
please HURRY
Answer: Total volume= 71.21 in^3
Step-by-step explanation:
The volume of the sphere= (4/3)*π*(2^3) = 33.51 in^3
The volume of the cylinder= π*(2^2)*3 = 37.7 in^3
Total volume= 71.21 in^3
This question is incomplete
5. A city has a population of 350,000.
The
population has decreased by 30% in the past
ten years. What was the population of the city
ten years ago?
The population of city 10 years ago before 30% decrease in population was 500,000
In the given statement is :
A city has a population of 350,000.The population has decreased by 30% in the past ten years.
The formula for calculating the percent change between two values over the time is given by:
[tex]p=\frac{A-B}{B}[/tex]×[tex]100[/tex]
where,
'p' represents the percent change
'A' represents the New value
'B' represents the Old value
Since, p is the percent (decreased) = -30
Substitute the given values and solve for B;
then;
[tex]-30=\frac{350,000-B}{B}[/tex] × 100
Divide both sides by 100 we get;
[tex]-0.3=[/tex] [tex]\frac{350,000-B}{B}[/tex]
By cross multiply we get;
-0.3B = 350,000 - B
Add both sides B, we get
-0.3B + B = 350,000
0.7B = 350,000
Divide both sides by 0.7 we get;
B = 500,000
Therefore, The population of city 10 years ago before 30% decrease in population was 500,000
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If the measure of angle 1 = (7x-19), and the measure of angle 2 = (x+5) find the measure of angle 2
We can say that if the measure of angle 1 = (7x-19), and the measure of angle 2 = (x+5), then the measure of angle 2 is 18°.
Define supplementary angle.
Supplementary angles are those two angles whose sum is always equal to 180 degrees.
Mathematically, a supplementary angle is calculated as follows:
Q + R = 180
Since the angles on this line segment are supplementary angles, we have:
Angle (1) + Angle (2) = 180° - Angle 3
Substituting the given values into the formula, we get;
7x - 19 + x + 5 = 180 - 90
8x - 14 = 90
8x = 90 + 14
8x = 104
x = 104/8
x = 13
Now, we can calculate the length of angle 2 by putting the 'x' value:
Angle 2 = x + 5
Angle 2 = 13 + 5
Angle 2 = 18°
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Find 1, 305 x 81. Then estimate to check your answer.
A. 1, 305 x 81 = 85, 705 Check: 1,000 × 8 = 80,000
B. 1, 305 x 81 = 105, 705. Check: 1,400 x 90 = 12, 600 :
C. 1,305 x 81 = 105, 705 Check: 1, 200 × 80 = 96,000
D. 1, 305 x 81 105, 705 Check: 1,300 x 80 = 104, 000
the estimate of the product is reasonable and the values are Estimate: 1,305 × 81 ≈ 104,000 and Actual 1,305 × 81 = 105,706
The correct option is D.
In the given statement is:
Find 1, 305 x 81. Then estimate to check your answer.
The estimate of the product is reasonable and the values are Estimate: 1,305 × 81 ≈ 104000 and Actual 1,305 × 81 = 105706
How to estimate and then compute the product check that your answer is reasonable?
The product expression is given as
1,305 × 81
As an estimate, we have
1305 = 1300
81 = 80
So, we have:
1,305 × 81 ≈ 1300 * 80
Evaluate the product
1,305 × 81 ≈ 104000
For the actual product, we have
The estimate and the actual product both approximate to 100000
Hence, the estimate of the product is reasonable and the values are Estimate: 1,305 × 81 ≈ 104,000 and Actual 1,305 × 81 = 105,706
The correct option is D.
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If f + j = 115 and j+k= 103 what is the value of j
The value of j is j = 103 - k = 115 - f.
A collection of equations for which we searched for common solutions is referred to in mathematics as a system of equations, sometimes known as a set of simultaneous equations or an equation system. Similar to single equations, a system of equations can be categorized. In everyday life, systems of equations are used to model problems when the unknown values can be represented by variables.
Consider the two equations,
f + j = 115 ----------------------(1)
j + k = 103 ----------------------(2)
Consider equation (2),
j + k = 103
Subtracting k from each side of the equation.
j + k - k = 103 - k
j = 103 - k
Consider equation (1),
f + j = 115
Subtraction f from each side of the equation,
f + j - f = 115 - f
j = 115 - f
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(PLEASE HELP!!)
Solve the following system of equations using either Gaussian elimination or a matrix. Write your answer as a point and explain how you would check your work:
2xy + 4z = 33
x + 2y - 3z = -26
-5x - 3y + 5z = 23
Using Gaussian elimination, the solution to the given system of equations is given as follows:
x = 5, y = -11, z = 3.
What is a system of equations?A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem.
For this problem, the equations are given as follows:
2x - y + 4z = 33.x + 2y - 3z = -26.-5x - 3y + 5z = 23.(I suppose there was a typing mistake on the first equation, as Gaussian elimination can only be applied to solve linear systems).
For Gaussian elimination, the first step is building the matrix of the system, in which:
The first three columns contain the coefficients of x, y and z, respectively.The last column contains the results of the operations.Hence, the matrix of the system is given as follows:
[tex]\left[\begin{array}{cccc}2&-1&4&33\\1&2&-3&-26\\-5&-3&5&23\end{array}\right][/tex]
Then, we need to make the coefficient of x zero in the second and third rows, hence:
R2 -> 2R2 - R1.R3 -> 5R1 + 2R3.Then the matrix will be given by:
[tex]\left[\begin{array}{cccc}2&-1&4&33\\0&5&-10&-85\\0&-11&30&211\end{array}\right][/tex]
Now we need to make the coefficient of y on the third row zero, hence:
R3 -> 11R2 + 5R3.
Then:
[tex]\left[\begin{array}{cccc}2&-1&4&33\\0&5&-10&-85\\0&0&40&120\end{array}\right][/tex]
From the third row, we have that:
40z = 120
z = 120/40
z = 3.
From the second row, we have that:
5y - 10z = -85
5y - 30 = -85
5y = -55
y = -11.
From the first row, we have that:
2x - y + 4z = 33
2x + 11 + 12 = 33
2x = 10
x = 5.
Hence the solution of the system is given by:
x = 5, y = -11, z = 3.
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5x-48=-3x+8 solve for x
Answer:
[tex]x = 7[/tex]
Step-by-step explanation:
[tex]5x + 3x = 8 +48[/tex]
⬇️
8x = 8 + 48
⬇️
8x = 56
Divide both sides of the equation by the coefficient of the variable;
[tex]x = \frac{56}{8}[/tex]
Cross out common factors;
[tex]x=7[/tex]
The radius, diameter, or circumference of a circle is given. Find the missing measure to the nearest hundredth.
r = x/8,d= ___, C=?
A circle is a curve sketched out by a point moving in a plane. The diameter and circumference of the circle are (x/4) units and (x/4)π units, respectively.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.
Given that radius of the circle is x/8 units. Therefore, the diameter and the circumference of the circle can be written as,
Diameter of circle = 2 × (Radius of the circle)
= 2 × (x/8) units
= x/4 units
Circumference of circle = 2 × π × (Radius of the circle)
= 2 × π × (x/8) units
= (x/4)π units
Hence, the diameter and circumference of the circle are (x/4) units and (x/4)π units, respectively.
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Find the coordinates of the midpoint of the segment with the endpoints (5, 24) and
(-1, 10).
Coordinates of the y- intercept
Answer:
(0, - 9 )
Step-by-step explanation:
the y- intercept is where the line crosses the y- axis
the line crosses the y- axis at (0, - 9 ) and is the y- intercept
PLEASE HELP ME!!! THIS IS TOO HARD!!! Emily runs 2,000 feet away from her house, and she ran back. How many miles did she run in total.
Answer: 4000
Step-by-step explanation: 2000 there and 2000 back. 2000+2000=4000
Hope this helps!
Find the sum of each finite series. Σ¹° n = 5 (20-n)
The sum of the given finite series is 75
The given series is:
[tex]\sum\limits^{10}_{n=5} {(20-n)}}[/tex]
To find the sum of this series,
Expand the summation notation by using the properties of sum operator:
Σ(a+b) = Σa + Σb
Hence,
[tex]\sum\limits^{10}_{n=5} {(20-n)}=\sum\limits^{10}_{n=5} {20}-\sum\limits^{10}_{n=5} {n}[/tex]
If a is a constant, then Σa = k. a, where k is the number of terms = upper limit - lower limit + 1
Using this property:
[tex]\sum\limits^{10}_{n=5} {20} = (10 - 5+1)\times20=6\times20=120[/tex]
Expand
[tex]\sum\limits^{10}_{n=5} {n}=5+6+7+8+9+10=45[/tex]
Hence,
[tex]\sum\limits^{10}_{n=5} {(20-n)}=\sum\limits^{10}_{n=5} {20}-\sum\limits^{10}_{n=5} {n}[/tex]
= 120 - 45 = 75
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please answer correctly and ignore the bottom ill do that part just the top for you guys and gals please!
Answer:
7) x ≥ -3
8) x < -8
Explanation:
[tex]\sf If \ u^n < a, \ then -\sqrt[n]{a} < u < \sqrt[n]{a}[/tex][tex]\sf If \ u^n > a, \ then \ u < -\sqrt[n]{a} \ \ or \ \ u > \sqrt[n]{a}[/tex]7.[tex]\sf -3(2x-7) \leq 39[/tex]
distribute
[tex]\sf -6x + 21 \leq 39[/tex]
relocate variables
[tex]\sf -6x \leq 39-21[/tex]
simplify
[tex]\sf -6x \leq 18[/tex]
dividing both sides by (-), changes the inequality sign
[tex]\sf x \geq -3[/tex]
8.[tex]\sf 4x + 9 < x - 15[/tex]
collect like terms
[tex]\sf 4x -x < - 15-9[/tex]
simplify
[tex]\sf 3x < - 24[/tex]
divide both sides by (+)3
[tex]\sf x < -8[/tex]
Please help (show steps too)
Answer:
5
Step-by-step explanation:
[tex]d=\frac{|-3(5)-4(5)+10|}{\sqrt{(-3)^2+(-4)^2}}=5[/tex]
Amy is paddling her canoe across a lake at a speed of 10 feet per second headed due north. The wind is blowing 40°C east of north with a velocity of 2.8 feet, per second. What is Amy's resultant velocity? Express your answer as a vector. Show your work.
The resultant velocity is about 12.3 feet per second at a heading of 8.4°east of north, <1.8, 12.14>
In this question,
Amy is paddling her canoe across a lake at a speed of 10 feet per second headed due north.
The wind is blowing 40°C east of north with a velocity of 2.8 feet, per second.
We need to find Amy's resultant velocity.
We write the direction vector for Amy in component form.
Due north is equivalent to 90° from the horizontal.
x-component:
x = 10 cos(90°)
x = 0
And y-component:
y = 10 sin(90°)
y = 10
The component form for Amy’s vector is <0, 10>.
Now we write the direction vector for wind in component form.
40 east of north is equivalent to 50° from the horizontal.
x-component:
x = 2.8 cos(50°)
x = 1.8
And y-component:
y = 2.8 sin(50°)
y = 2.14
The component form for the wind’s vector is <1.8, 2.14>
Add the vectors for Amy and the wind.
<0, 10> + <1.8, 2.14> = <1.8, 12.14>
Now, we determine the vector's magnitude by using Pythagoras theorem.
Let v be the velocity of Amy.
Let θ be the angle made by Amy with the horizontal
⇒ tan(θ) = |y/x|
⇒ tan(θ) = |12.14 / 1.8|
⇒ θ = 81.6°
81.6° with the horizontal is equivalent to 8.4° east of north.
Therefore, the resultant velocity is about 12.3 feet per second at a heading of 8.4°east of north, <1.8, 12.14>
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Identify the property illustrated by the equation.
5+(-5)=0
Identify the property illustrated by the equation.5+(-5)=0 Additive Inverse
What is an additive Inverse ?
The number that produces zero when added by -a is known as the additive inverse of a number, or a, in mathematics. The opposite, a shift in the sign, and negation are other names for this number.The definition of the additive inverse, which permits a wide application to mathematical objects other than numbers, is its inverse element under the binary operation of addition.Double additive inverse has no net effect, as with any inverse operation: −(−x) = x.To learn more about additive inverse, refer:
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How do you solve 9=x+3/5 when the x and 3 are together above the five?
Answer:
x = 42
Step-by-step explanation:
9*5 = x+3/5*5
45 - 3= x+3 - 3
42 = x
UR WELCOME
Which is the first step in simplifying the expression 2(x 3) 5? 2x 2(3) 5 2x 3 5 2 x 3 5 2(5) x 3
The first step in simplifying the expression 2(x+3)+5 = 2x+2(3)+5.
Given expression in 'x' is 2(x+3)+5.
In order to simplify this expression, we need to expand it by opening the parenthesis. That is, we need to distribute 2 over (x+3) first. For this we multiply 2 into (x+3) and then only we can add 5 to it.
So, 2(x+3) +5 = 2x + 2(3) +5
= 2x +6 +5
= 2x+11
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Write a coordinate proof to prove the Centroid Theorem.
Given: Δ A B C , medians AR, BS , and CQ
Prove: The medians intersect at point P and P is two thirds of the distance from each vertex to the midpoint of the opposite side.
If Δ ABC , medians AR, BS , and CQ then the value of AP = 2/3 AR,
BP = 2/3 BS, and CP = 2/3 CQ.
What is meant by Centroid Theorem?The triangle's centroid is the point where the three medians intersect. According to the centroid theorem, the centroid is 23 times the distance from each vertex to the midpoint of the opposite side.
Given: ΔABC, medians AR, BS, and CQ
AP = 2/3 AR, BP = 2/3 BS, and CP = 2/3 CQ.
Slope of [tex]$\overline{A R}=\frac{3 c}{3 b+3 a}=\frac{c}{b+a}$[/tex]
Slope of [tex]$\overline{B S}=\frac{6 c}{6 b-3 a}=\frac{2 c}{2 b-a}$[/tex]
Slope of [tex]$\overline{C Q}=\frac{3 c}{3 b-6 a}=\frac{c}{b-2 a}$[/tex]
AR contained in the line [tex]$y=\left(\frac{c}{b+a}\right) x[/tex], BS contained in the line [tex]$y=\left(\frac{2 c}{2 b+a}\right)(x-3 a)[/tex], CQ contained in the line [tex]$y=\left(\frac{c}{b-2 a}\right)(x-6 a)$[/tex]
To find the coordinates of P, find the intersection point of two medians, BS and CQ.
[tex]$y=\left(\frac{2 c}{2 b-a}\right)(x-3 a) \text[/tex] and [tex]$y=\left(\frac{c}{b-2 a}\right)(x-6 a)[/tex]
[tex]$\frac{2 c}{2 b-a}(x-3 a) &=\frac{c}{b-2 a}(x-6 a) \\[/tex]
simplifying the above equation, we get
[tex]2 c(x-3 a)(b-2 a) &=c(x-6 a)(2 b-a) \\[/tex]
[tex]2 c\left(b x-2 a x-3 a b+6 a^2\right) &=c\left(2 b x-a x-12 a b+6 a^2\right)[/tex]
[tex]2 b c x-4 a c x-6 a b c+12 a^2 c &=2 b c x-a c x-12 a b c+6 a^2 c \\[/tex]
[tex]-3 a c x &=-6 a b c-6 a^2 c \\[/tex]
x = 2b + 2a
To find the value of y,
[tex]$y=\frac{2 c}{2 b-a}(x-3 a)[/tex]
simplifying the above equation, we get
[tex]$=\frac{2 c}{2 b-a}(2 b+2 a-3 a)[/tex]
[tex]$=\frac{2 c(2 b-a)}{2 b-a}=2 c$$[/tex]
So the coordinates of P are (2b + 2a, 2c).
Now, show that P is on AR.
[tex]$&y=\left(\frac{c}{b+a}\right)(2 b+2 a)=\frac{2 c(b+a)}{b+a}=2 c[/tex]
Thus, the three medians intersect at the same point.
To find the lengths of AR, AP, BS, BP, CQ, and CP
Using the Distance Formula.
[tex]A R &=\sqrt{\left((3 b+3 a)-0^2\right)+(3 c-0)^2} \\[/tex]
simplifying the above equation, we get
[tex]&=\sqrt{(3(b+a))^2+(3 c)^2} \\[/tex]
[tex]&=\sqrt{9\left((b+a)^2+c^2\right)} \\[/tex]
[tex]&=3 \sqrt{(b+a)^2+c^2} \\[/tex]
[tex]A P &=\sqrt{\left((2 b+2 a)-0^2\right)+(2 c-0)^2} \\[/tex]
[tex]&=\sqrt{(2(b+a))^2+\left(2 c^2\right)} \\[/tex]
[tex]&=\sqrt{4\left((b+a)^2+c^2\right)} \\[/tex]
[tex]&=2 \sqrt{(b+a)^2+c^2}[/tex]
[tex]B S &=\sqrt{(6 b-3 a)^2+(6 c-0)^2} \\[/tex]
[tex]&=\sqrt{(3(2 b-a))^2+(3(2 c))^2} \\[/tex]
[tex]&=\sqrt{9(2 b-a)^2+9(2 c)^2} \\[/tex]
[tex]&=3 \sqrt{(2 b-a)^2+4 c^2}[/tex]
[tex]B P &=\sqrt{(6 b-(2 b+2 a))^2+(6 c-2 c)^2} \\[/tex]
[tex]&=\sqrt{(4 b-2 a)^2+(4 c)^2} \\[/tex]
[tex]&=\sqrt{(2(2 b-a))^2+(2(2 c))^2} \\[/tex]
[tex]&=2 \sqrt{(2 b-a)^2+4 c^2} \\[/tex]
[tex]C Q &=\sqrt{(6 a-3 b)^2+(0-3 c)^2} \\[/tex]
[tex]&=\sqrt{(3(2 a-b))^2+(-3 c)^2} \\[/tex]
[tex]&=\sqrt{9\left((2 a-b)+c^2\right)} \\[/tex]
[tex]&=3 \sqrt{(2 a-b)^2+c^2} \\[/tex]
[tex]C P &=\sqrt{(6 a-(2 b+2 a))+(0-2 c)^2} \\[/tex]
[tex]&=\sqrt{(4 a-2 b)^2+(-2 c)^2} \\[/tex]
[tex]&=\sqrt{(2(2 a-b))^2+4 c^2} \\[/tex]
[tex]&=\sqrt{4(2 a-b)^2+4 c^2}[/tex]
Show that the P is two thirds of the distance from the vertices to the midpoints.
[tex]$\frac{2}{3} A R &=\frac{2}{3}\left(3 \sqrt{(b+a)^2+c^2}\right) \\[/tex]
[tex]&=2 \sqrt{(b+a)^2+c^2} \\[/tex] = A P
[tex]$\frac{2}{3} B S &=\frac{2}{3}\left(3 \sqrt{(2 b-a)^2+4 c^2}\right) \\[/tex]
[tex]$&=2 \sqrt{(2 b-a)^2+4 c^2} \\[/tex] = B P
[tex]$\frac{2}{3} C Q &=\frac{2}{3}\left(3 \sqrt{(2 a-b)^2+c^2}\right) \\[/tex]
[tex]&=2 \sqrt{(2 a-b)^2+c^2} \\[/tex] = C P
Therefore, AP = 2/3 AR, BP = 2/3 BS, and CP = 2/3 CQ.
To learn more about Centroid Theorem refer to:
brainly.com/question/24246680
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