The vertices of PQR are P(6, 1), Q(3,5), and R(11, 11). The length of segment PR is √125 units. Use the coordinates and geometric reasoning to show that PQR is a right triangle.Explain your reasoning and show your work
Answers
Check the picture below, so hmm we know that much, and we can also more or less see that PR is the longest side, let's check the length of the other two sides
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P(\stackrel{x_1}{6}~,~\stackrel{y_1}{1})\qquad Q(\stackrel{x_2}{3}~,~\stackrel{y_2}{5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ PQ=\sqrt{[3 - 6]^2 + [5 - 1]^2}\implies PQ=\sqrt{(-3)^2+4^2}\implies \boxed{PQ=5} \\\\[-0.35em] ~\dotfill\\\\ Q(\stackrel{x_1}{3}~,~\stackrel{y_1}{5})\qquad R(\stackrel{x_2}{11}~,~\stackrel{y_2}{11})~\hfill QR=\sqrt{[11 - 3]^2 + [11 - 5]^2} \\\\\\ QR=\sqrt{8^2+6^2}\implies \boxed{QR=10}[/tex]
if that's true, the triangle is indeed a right-triangle, then hmmmm most likely using the pythagorean theorem PR² = PQ² + QR², let's check
[tex](\sqrt{125})^2~~ = ~~5^2~~ + ~~10^2\implies 125=25+100\implies 125=125~~\textit{\Large \checkmark}[/tex]
Related Questions
calculate the equation of straight line passing through (5,-10) and making equal but opposite intercept.
Answers
The equation of the straight line passing through (5,-10) and making equal but opposite intercept is y = -4x + 10.
To solve the problem, we need to know the equation of a straight line
Equation of a straight line in slope intercept formThe equation of a straight line in slope intercept form is given by y = mx + c where
m = slope and c = y- intercept.Given that the straight line passes through the point (5, -10) and making equal but opposite intercept, its intercept is at (-5, 10)
The gradient of the lineWe need to find the gradient, m by making m subject of the formula in y.
So, m = (y - c)/x
With
x = 5, y = -10 and c = 10, we havem = (y - c)/x
m = (-10 - 10)/5
m = -20/5
m = -4
Substiting m and c into y, we have
y = mx + c
y = -4x + 10
So, the equation of the straight line passing through (5,-10) and making equal but opposite intercept is y = -4x + 10.
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On a test that has a normal distribution, a score of 25 falls three standard deviations
below the mean, and a score of 35 falls two standard deviations above the mean.
Determine the mean of this test.
Answers
Answer: 31
Step-by-step explanation: 25 and 35 are 5 standard deviations apart
35-25/5 =10/15 =2
Add/ Subtract 2 each time
how do you graph y=4-4x
Answers
Answer:
Break it into 2 parts.
Explanation:
Y=4x
Firstly draw the graph of y=4x , then light it up the y-axis by 4 units.
Or you can do it by plotting points; say x=0, x=1, x=2 and so on.
Step-by-step explanation:
Simplify this equation...
Answers
(It would be option 1) x - 2/2
6÷2(1+2)=???
I can't figure it out :(
very much appreciated!!!!
Answers
9
using Bodmas rule
[tex]\sf B - brackets, \ O - order, \ D - division, \ M - multiplication, \ A - addtion, \ S - subtraction[/tex]
⟼ ⟼ ⟼ ⟼ ⟼ ⟼
Solve:
6 ÷ 2(1+2) [simplify the following inside brackets]
6 ÷ 2(3) [divide]
(3)(3) [multiply]
9 [final answer]
Hey there!
6 ÷ 2(1 + 2)
= 6 ÷ 2(3)
= 3(3)
= 9
Therefore, your answer should be:
9
Good luck on your assignment & enjoy your day!
~Amphitrute1040:)
im going to a behavior health hospital (mental hospital) in a few hours but they cant fint a bed so ill be at the reg hospital for a while wish me luck yall :)
Answers
Answer:
good luck bestie
sending best of luck~♡
By visual inspection,determine the best fitting regression model for the scatter plot
Answers
Answer:
The answer is quadratic
Step-by-step explanation:
I just took the quiz and got this question correct, also it cant be linear because if it were linear, it would be more of a straight shape, but this is more of a u shape, if it were exponential, it would look more drawn out to the sides i believe, and if it were no pattern, there would just be dot points threwn at random spots. Therefore, the answer is Quadratic.
Are solar systems unique to just our sun? Explain.
Answers
please help, thank you if you do!
Answers
Answer:
The constant ratio is 2.
Explanation:
Everything is multiplied by 2.
I hope this helps. :)
Question 2 You have to make a model of the Great Pyramid at Giza, painted to look as close to identical as possible. Which term best describes the part that you must cover?
Volume
Area
Surface Area
Lateral Area
Answers
The term that describes the part of the model of the Great Pyramid to be painted is called the: lateral area.
What is the Lateral Area of a Pyramid?The lateral area of any pyramid is the area covered by the slant lateral faces of the pyramid. This excludes the base area of the pyramid.
The best term that describes the part of the Great Pyramid to be covered is therefore known as: lateral area.
Learn more about lateral area on:
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Which is different?
How much does it take to fill the cylinder?
What is the capacity of the cylinder?
How much does it take to cover the cylinder?
How much does the cylinder contain?
Answers
Answer:
Step-by-step explanation:
Remark
A B and D refer to what the cylinder can contain. They all refer to the hollowed out part of the cylinder.
C is the only one that talks about what you need to cover the cylinder with (say) paper or cloth. C is external to the surface of the cylinder.
Answer: C
What is the answer? Please
NO LINKS!!!
Answers
Answer:
3 If they all have to be different
Step-by-step explanation:
small
medium
large
medium
large
small
large
medium
small
Inali ate 3/8 of a pizza. His friend ate 1/4 of the
pizza. How much did they eat all together.
Answers
Answer:
5/8
Step-by-Step Explanation:
Inali - ate 3/8
His Friend - ate 1/4, but you need it with denominator of 8 so you can do 1/4=x/8 and x=2
Now, you have to add 3/8 plus 2/8 and you get 5/8.
3. What is the surface area of this composite solid? Show your work.
5 ft
5 ft
3 ft
4 ft
10 ft
8 ft
Answers
Hope this helps!
You decide to bake a pizza. The pizza crust that you purchase has a diameter of 14 inches.
If you decide to do stuffed crust, you need to put cheese around the outer edge. How many inches of cheese do you need?
How much space do you have to cover with sauce, cheese, and toppings?
Answers
Using the circumference of the pizza, it is found that you have 44 inches to cover the pizza.
What is the circumference of a circle?
The circumference of a circle is the length of it's outer edge, and considering a diameter d, is given by:
[tex]C = \pi d[/tex]
In this problem, the diameter is of 14 inches, hence the circumference is given by:
C = 14pi = 44 inches.
You have 44 inches to cover the pizza.
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Quadrilateral JKLM is inscribed in circle R.
68
What is m L?
Enter your answer in the box.
105
XK
•R
L
M
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
As we know, opposite sides of a cyclic quadrilateral add up to 180°, let's use this property to find Angle L
[tex]\qquad \tt \dashrightarrow \: \angle L + 68 = 180[/tex]
[tex]\qquad \tt \dashrightarrow \: \angle L = 180 - 68[/tex]
[tex]\qquad \tt \dashrightarrow \: \angle L = 112 \degree[/tex]
So, measure of Angle L is 112°
why is math so hard :(
Answers
Step-by-step explanation:
Check out the attached photo
25 points
Find Y. Assume that segments that appear to be tangent are tangent. Around to the nearest tenth if necessary.
Answers
Answer:
y ≈ 12.6
Step-by-step explanation:
the angle between a tangent and the radius of the circle at the point of contact is 90°
then the triangle with y as a leg is right.
using Pythagoras' identity in the right triangle.
y² + 39² = 41²
y² + 1521 = 1681 ( subtract 1521 from both sides )
y² = 160 ( take square root of both sides )
y = [tex]\sqrt{160}[/tex] ≈ 12.6 ( to the nearest tenth )
22 23
22 - 26
m27 +mZ8 = 180°
mZ3 +mZ5 = 90°
Answers
Answer:
i believe it would be 22-26 but i am not sure
Using the information in the Venn diagram below, how many people play basketball? A. 5 B. 9 C. 12 D. 17 4 D. 5
Answers
Answer:
52 people
Step-by-step explanation:
add 5 9 12 17 4 5 and youlk get 52 people.
Answer:
its 5
Step-by-step explanation:
PLEASE ANSWER ASAP AND LMK HOW U GOT UR ANSWER ‼️
Answers
Answer:
π/4 radiansπ/4 radiansStep-by-step explanation:
The relationship between angle measures in degrees and angle measures in radians does not depend on the radius of the circle. It is always ...
180° = π radians
__
Then an angle of 45° will be ...
45° × (π radians)/(180°) = π/4 radians
This value is the same for a radius of 5 cm or of 1 cm.
_____
Additional comment
We have made the conversion from degrees to radians using a conversion factor that has radians in the numerator and degrees in the denominator. When we mutiply by this factor, the units of degrees cancel, leaving units of radians. We use a conversion factor that has the same angle value in numerator and denominator, so it doesn't change the angle we're multiplying. It only changes the units.
The same relation can be expressed as a proportion:
(π radians)/180° = (x radians)/(45°)
When you multiply this equation by 45° on both sides, you get the equation we used above.
Complete The Table
Original Price ( )
Percent Of Discount 25%
Sale Price $40
What is the original price?
Answers
Answer:
$ 53.33
Step-by-step explanation:
x = original price
.75 * x = 40
x = 40 / .75 = 53.33
Let original price be x
Discount=25%Hence
x-0.25x=40(1-0.25)x=400.75x=40x=40/0.75x=40/(3/4)x=53.34$find the value of x when 6-2x= 5x-9x+18
Answers
Answer:
x = 6
Step-by-step explanation:
6 - 2x = (5-9)x +18
6 - 2x = -4x +18
2x = 12
x = 6
Find the circumference of the circle
12m
Answers
Answer:
The answer would be 75.4 (rounded to nearest 10th)
Step-by-step explanation:
Step 1. Multiply the radius (12) by 2 to get 24.
Step 2. Do 24π
Step 3. Get the answer of 75.3982236862
Step 4. Round to 75.4
Hope this helps! :)
Answer:
C ≈ 75.4 m
Step-by-step explanation:
using the formula C = 2πr , then
C = 2π × 12 = 24π ≈ 75.4 m ( to 1 dec. place )
What the location of point A?
Will mark brainlyest!!
Answers
Answer:
C) (-5,8)
Step-by-step explanation:
The format for point is (x,y)
X is the horzontal (left or right)
Y is verticle (Up or down)
Remember that left and down are negatives
So you move 5 times to the left, thus -5
You move 8 upwards, thus 8
The answer is (-5,8)
Hope this helps!
What is 527 x 36 with an area model???
Answers
Answer:
18972
Step-by-step explanation:
With an area model, the model will have dimensions of 576 and 36. The product of the units will be within the model.
The value of the equation is A = 18,972
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the first number be p = 527
Let the second number be q = 36
Now , the equation will be
A = p x q
Substituting the values in the equation , we get
A = 527 x 36
On simplifying the equation , we get
A = 18,972
Hence , the equation is A = 18,972
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i think this should be pretty easy, just not for me lol. please help!
Answers
Answer:
(1) False. (2) True. (3) True. (4) True. (5) True
Step-by-step explanation:
This is really easy :)
The diameter of a circle is 28 inches. What is the circle's circumference
Answers
Answer: 87.92.
Step-by-step explanation: To find the circumference of a circle, you need the following equation:
2 x π x r, where π is ≈ 3.14 and r is the circle's radius. If you are ever given the diameter instead of the radius, just cut the diameter in half. In this case, the diameter was given, so we need to cut 28 in half, which makes 14. Your equation should look like this:
2 x 3.14 x 14 ≈ 87.92.
Hope this helps! :)
27/54 simplified to its simplest form need answer ASAP
Answers
Answer:
1/2
Step-by-step explanation:
Divide both the numerator and denominator
27/54 ÷ 27/27
Reduced fraction:
1/2
Therefore, 27/54 simplified to lowest terms is 1/2.
Answer:
27/54 =1/2
Step-by-step explanation:
27 and 54 are both multiples of 9, so 9 is a common divisordivisor.
Divide numerator and denominator by 91:
(27/9) / (54/9) = 3/6
Now 3 and 6 are both multiples of 3, so 3 is a common divisor
Divide numerator and denominator by 3:
(3/3) / (6/3) = 1/2
1 and 2 has no common divisors so 1/2 is the final answer
The basketball team has 20 more players than the baseball team does. There are 100 players total. How many players play basketball? How many players play baseball?
Answers
Answer:
Basketball team has 60 players
Baseball team has 40 players
Step-by-step explanation:
60 + 40 = 100