MATHEMATICS HIGH SCHOOL

Triangle PQR has vertices P(0, 0), Q(3, 4), and R(3, 0). If triangle PQR is rotated 180° about the origin, what is the length of side P'Q'?

Answers

Answer 1

Answer:

Answer:

The length of P'Q' is 4 units

The length of P'R' is 3 units

Step-by-step explanation:

If you rotate the figure 180° then the vertex would be R, and from P to Q is 3 units left and 4 units down

Answer 2

Answer:

Final answer:

To find the length of side P'Q' after rotating triangle PQR 180° about the origin, we need to find the distance between the points P'(0,0) and Q'. When you rotate a point (x, y) 180° about the origin, the new coordinates are (-x, -y). Using the distance formula, we can find the length of side P'Q': d = sqrt((-3-0)^2 + (-4-0)^2) = sqrt(9 + 16) = sqrt(25) = 5. Therefore, the length of side P'Q' is 5 units.

Explanation:

To find the length of side P'Q' after rotating triangle PQR 180° about the origin, we need to find the distance between the points P'(0,0) and Q'.

When you rotate a point (x, y) 180° about the origin, the new coordinates are (-x, -y).

So, the coordinates of point Q' would be (3, 4) rotated 180°, which is (-3, -4).

Using the distance formula, we can find the length of side P'Q':

d = sqrt((-3-0)^2 + (-4-0)^2) = sqrt(9 + 16) = sqrt(25) = 5.

Therefore, the length of side P'Q' is 5 units.

Learn more about rotating triangles here:

brainly.com/question/16631420

#SPJ2

Related Questions

Katie spent $465 on DVDs and CDs. The CDs cost $15 each, and the DVDs cost $19 each. A total of 27 CDs and DVDs were purchased. How many of each did she buy?(solve by substitution or elimination methods only)
What is the graph line for this problem? x+3y=9
You purchase a computer for $875.00 plus 5% sales tax. You decide to finance it through the store's 0% program for 12 months. The terms state that you must pay $100.00/month and that if you miss a payment, you will be assessed a late fee of $39.00 plus the interest accrued to that point at a 14.25% APR. If you miss a payment in the eighth month, how much interest will you be charged?. A. $83.13. B. $16.63. C. $87.28. D. $20.78
Joe paid $14.00 for a board game this is 70% of the original price what was the original price
Find slope of a line (1,7) (3,6)

Multiply. Check picture.

Answers

The answer is $3x^4-13x^3-x^2-11x+6$ .

Solution:

Use algebraic identity: $a^m* a^n=a^(m+n)$

For example: $x^2* x=x^(2+1)=x^3$

Given expression $(x^2-5x+2)$ and $(3x^2+2x+3)$ .

To multiply these equations.

$(x^2-5x+2)*(3x^2+2x+3)$

$=x^2(3x^2+2x+3)-5x(3x^2+2x+3)+2(3x^2+2x+3)$

$=(3x^4+2x^3+3x^2)+(-15x^3-10x^2-15x)+(6x^2+4x+6)$

$=3x^4+2x^3+3x^2-15x^3-10x^2-15x+6x^2+4x+6$

Combine like terms together.

$=3x^4+(2x^3-15x^3)+(3x^2-10x^2+6x^2)-15x+4x+6$

$=3x^4-13x^3-x^2-11x+6$

$(x^2-5x+2)*(3x^2+2x+3)=3x^4-13x^3-x^2-11x+6$

Hence the answer is $3x^4-13x^3-x^2-11x+6$ .

What annual simple interest rate will increase Jacob Davidson’s initial investment of $5,000 to $6,000 in two years?multiple choice
A)10%

B)5%

C)4%

D)6%

Answers

Answer:

Hence, the annual simple interest rate is:

10%

Step-by-step explanation:

The initial investment(I) of Jacob Davidson=$ 5000.

Time(T)=2 year.

Interest(I') earned by him=His income after investment-His initial investment.

= $ (6000-5000)

= $ 1000.

Now, the rate of interest(R) is given by :

$I'=(I* R* T)/(100)\n\n\n1000=(5000* R* 2)/(100)\n\n1000=100R\n\nR=10\%$

Hence, the annual simple interest rate is:

10%

a its 10 percent because of the amount of money he has in his account

IF the navy pier ferris wheel in chicago has a circumference that is 56% of the circunference of the first ferris wheel built in 1893. a. What is the radius of the navy pier wheel?
b. what was the radius of the first ferris wheel?
c. The first ferri wheel took nine minutes to make a complete revolution. how fast was the wheel moving?

Answers

Answer:

a. The radius of the navy pier wheel is 56% of the radius of the first ferris wheel

b. The radius of the first ferris wheel was 179% of the radius of the navy pier ferris wheel

c. The wheel was moving at 0.70 $(rad)/(min)$

Step-by-step explanation:

Navy pier wheel circumference = Cn

First ferris wheel circumference = Cf

Cn = 0.56*Cf

Circumference Perimeter = 2*π*Radius

Navy pier wheel radius = Rn

First ferris wheel radius = Rf

Cn = 0.56*Cf

2*π*Rn = 0,56*2*π*Rf (equation 1)

dividing both sides by 2π

Rn = 0,56*Rf

From equation 1

2*π*Rn = 0,56*2*π*Rf

dividing both sides by 2π

Rn = 0.56*Rf

dividing both sides by 0.56

Rf = $(1)/(0.56)$ *Rn

Rf = 1.79*Rn

9 minutes / revolution

1 revolution = 2π radians

The wheel makes 2π radians in 9 minutes

Wheel velocity = $(2\pi )/(9) (rad)/(min)$

Wheel velocity = 0.70 $(rad)/(min)$

Meg started her trip with 11 1/2 gallons of gas in her car's tank. She bought an additional 6 4/5 gallons on her trip and arrived back home with 3 3/10 gallons left. How much gas did she use on the trip?

Answers

Answer:

Hence, the amount of gas she used on the trip is:

15 gallons.

Step-by-step explanation:

Meg started her trip with 11 1/2 gallons of gas in her car's tank.

i.e. we can represent the mixed fraction 11 1/2 in fraction as:

$11(1)/(2)=(23)/(2)gallons$

She bought an additional 6 4/5 gallons on her trip.

i.e. we can represent the mixed fraction 6 4/5 in fraction as:

$6(4)/(5)=(34)/(5)gallons$

Hence, the amount of gas filled in tank:

$=(23)/(2)+(34)/(5)\n\n=(23* 5+34* 2)/(10)\n\n=(115+68)/(10)\n\n=(183)/(10)gallons$

now after coming back home the amount of gas left in the car tank is:

3 3/10 gallons ; which could be represented in fraction as:

$3(3)/(10)=(33)/(10)$

Amount of gas used in the trip is:

=Amount of gas filled-gas remaining

$=(183)/(10)-(33)/(10)\n\n=(183-33)/(10)\n\n=(150)/(10)\n\n=15gallons$

Hence, the amount of gas she used on the trip is:

15 gallons.

Meg used 15 gallons. First you find the lowest common denominator to add 11 1/2 and 6 4/5, which is 10. What you do to the bottom you have to do to the top. You multiply 2 and 5, which gives you 10. 1 times 5 is 5... 11 5/10. 2 times 5 is 10, 4 times 2 is 8... 6 8/10. Add 11 5/10 and 6 8/10 and it gives you 18 3/10. To find out how much she used subtract the total amount she bought and how much she returned home with. The fractions cancel out since 3/10 minus 3/10 equals 0. You're just left with 18 minus 3, which is 15.

If you rent a car for one day and drive it for 100 miles, the cost is $40.00. If you drive it 220 miles, the cost is $46.00. What are the data points given?

Answers

The given data points are (100, 40) and (220, 46).

The results of a survey indicate that between 76% and 84% of the season ticket holders are satisfied with their seat locations.What is the survey’s margin of error?

Answers

The margin of error is a statistic that expresses how much random sampling error there is in a survey's results. The margin of error of the survey will be ±4%.

What is the margin of error?

The margin of error is a statistic that expresses how much random sampling error there is in a survey's results. The wider the margin of error, the less confident one should be that a poll result reflects the outcome of a population-wide survey.

The results of a survey indicate that between 76% and 84% of the season ticket holders are satisfied with their seat locations. Therefore, the margin of error can be written as,

Margin of Error = (84%-76%)/2 = 8%/2 = ±4%

Hence, the margin of error of the survey will be ±4%.

Learn more about Margin of Error:

brainly.com/question/13990500

#SPJ2

Answer:

±4

Step-by-step explanation:

The margin of error in a confidence interval is half the range:

(84 - 76) / 2 = 4

So the margin of error is ±4.

Other Questions

The graphs of the equations y=2x-7 and y-kx=7 are parallel when k equals

Rs+h²=1 solve for h

Find the measure of each exterior angle for a regular hexagon. Round to the nearest tenth if necessary.

The current winning teams final score is 52.08 ft. miguel's teammates threw 12.26 ft, 12.82 ft, 13.75 ft. what does miguel need to score to tie?