A right angled isosceles triangle is a triangle with two sides of equal length and one right angle. To prove that the points (-3, 3), (3, -7) and (7,9) are the vertices of a right angled isosceles triangle, we can use the distance formula and the Pythagorean theorem.
The distance formula is used to calculate the distance between two points in a coordinate plane. It is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Using the distance formula, we can find that the distance between the points (-3, 3) and (3, -7) is:
d = √((3 - (-3))^2 + ((-7) - 3)^2) = √(6^2 + (-10)^2) = √(36 + 100) = √136
Similarly, we can find that the distance between the points (-3, 3) and (7, 9) is also √136 and the distance between the points (3, -7) and (7, 9) is √36.
Now, we can use the Pythagorean theorem, which states that in a right angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
The Pythagorean theorem can be written as:
c^2 = a^2 + b^2
Since d1 and d2 are equal, we can say that the triangle is isosceles.
So, using the distance formula and the Pythagorean theorem, we have proven that the points (-3, 3), (3, -7) and (7,9) are the vertices of a right angled isosceles triangle.
HELP!!! Bill paid $45in tax on a laptop that cost $500. What percent sales tax did Bill pay?
Answer:
He paid 9% in sales tax
Step-by-step explanation:
6 grade math pls help and do step by step
how many solutions does 3-2x=5-x+3
Answer:
x-2x=5+3-3
-x=5
x=-5
Step-by-step explanation:
That's the answer
What is the AREA of the given circle?
62.83 in²
157.08in²
314.16 in²
628.32 in²
Answer:
314.16 in²
Step-by-step explanation:
Answer:
[tex]A[/tex] ≈ [tex]314.16[/tex]
Step-by-step explanation:
[tex]A=\pi r^2[/tex]
[tex]A = \pi (10)^2[/tex]
[tex]A = \pi (100)[/tex]
[tex]A[/tex] ≈ [tex]314.16[/tex]
Find the degree measure of each angle in the triangle.
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Please do not create new Amazon accounts until we verify your billing information. Any new orders that you place may be delayed or cancelled.
Tripp swims 50 laps a day in
hopes of becoming a collegiate
swimmer. Write an equation to
represent y, the total number of
laps Tripp has swam after x
days.
Answer:
y = 50x
Step-by-step explanation:
Please help me !!!!!!!!!
Answer:
f(-2) = 0
f(1) = 12
f(2) = 5
Step-by-step explanation:
f(-2) will lie in the function [tex] f(x) =x^2 - 4[/tex]
[tex]\therefore f( - 2) = {( - 2)}^{2} - 4 = 4 - 4 = 0 [/tex]
f(1) will lie in the function [tex] f(x) =2x^2 +10[/tex]
[tex]\therefore f(1) = 2 {(1)}^{2} + 10 = 2 + 10 = 12 [/tex]
f(2) will lie in the function [tex] f(x) =5[/tex]
[tex]\therefore f(2) = 5[/tex]
BRAINLIEST + 25 POINTS
Part A: a^2 + 6 for a = 5
Part B: Show your work and/or explain how you arrived at your answer
Answer:
31
Step-by-step explanation:
Plug in 5 as a into the expression:
a² + 6
(5)² + 6
25 + 6
= 31
So, the answer is 31 when a = 5
substitute a=5 into the equation.
5²+6
25+6=31
hope that helps^^
Benito runs 1/10 of a mile each day. which shows how to find the number of days it will take for benito to run 3/5 of a mile
I would say divide 3/5 by 1/10
what is the value of y?(PLEASE ANSWER QUICKLY!!
5/16y=5/24
a.1/2
b.1/3
c.3/2
d.2/3
Answer:
The answer is D. 2/3
Step-by-step explanation:
We have to find out what number times 5/16 will equal 5/24. This isolates y.
You can plug in all the answers.
5/16 times 2/3 equals 5/24 which is the answer!
Answer:
D.2/3
Step-by-step explanation:
Which of these triangle pairs can be mapped to each other using a translation and a rotation about point A?
Answer:
Step-by-step explanation:
p
Step-by-step explanation:
23. Since 3 x 1/2 is the same as 1/2+ 1/2 +1/2 , what mixed number is the same
as 3 x 1/2?
Answer:
Step-by-step explanation:
3×1/2 = 1/2 + 1/2 + 1/2 = 3/2 = 1½
If $9450 is invested at a rate of 12.5%,
compounded continuously, how much will it
be worth in 20 years?
Answer:
The final balance is $113,645.52.
The total compound interest is $104,195.52.
Step-by-step explanation:
The branch manager of an outlet (Store 1) of a nationwide
chain of pet supply stores wants to study characteristics of her
customers. In particular, she decides to focus on two variables: the
amount of money spent by customers and whether the customers
own only one dog, only one cat, or more than one dog and/or cat.
The results from a sample of 70 customers are as follows:
Amount of money spent: X = +21.34, S = +9.22.
Thirty-seven customers own only a dog.
Twenty-six customers own only a cat.
Seven customers own more than one dog and/or cat.
Construct a 95% confidence interval estimate for the
population mean amount spent in the pet supply store.
Construct a 90% confidence interval estimate for the population proportion of customers who own only a cat.
The branch manager of another outlet (Store 2) wishes to conduct
a similar survey in his store. The manager does not have access to
the information generated by the manager of Store 1. Answer the
following questions:
c. What sample size is needed to have 95% confidence of
estimating the population mean amount spent in this store
to within { +1.50 if the standard deviation is estimated to
be $10?
d. How many customers need to be selected to have 90% confidence of estimating the population proportion of customers who own only a cat to within {0.045?
e. Based on your answers to (c) and (d), how large a sample should the manager take?
Answer:
1. ( 19.1416, 23.5384,)
2. (0.276348, 0.46651)
3. the sample size = 170.73 approximately 171
4. sample size = 334.07 approximately 334
5. sample of 334 should be taken by manager
Step-by-step explanation:
mean = bar x = 21.34 dollars
size of sample n = 70
standard deviation of sample = 9.22
we use t distribution as the population standard deviation is not known.
95% Confidence interval
1-α = 0.95
α = 0.05
degree of freedom = 70-1 = 69
α/2 = 0.025
using the t distribution tsble,
= 1.9949
confidence interval = [tex]21.34+-1.9949*[\frac{9.22}{sqrt(70)}] \\[/tex]
= 21.34 +- (1.9949*1.10200)
= 21.34 + 2.1984, 21.34 - 2.1984
= (23.5384, 19.1416)
the confidence interval of the mean amount spent at the supply store can be written as 19.1416<u<23.5384
2. sixe of those who only have a cat
p = 26/70 = 0.371429
at 90 % confidence interval,
1-α = 0.90
α = 0.10
we use the z table here
z(0.10/2) = Z(0.05)
= 1.645
[tex]0.371429+-1.645\sqrt} \frac{0.371429(1-0.371429)}{70}[/tex]
= 0.371429 +-( 1.645 x 0.0578)
= 0.371429 + 0.095081, 0.371429 - 0.095081
= (0.276348, 0.46651)
3. sd = 10$
margin of erro,r e = 1.50$
α = 0.05
using z table
α/2 = Z0.025
= 1.96
sample size = 1.96² * 10² / 1.50²
= 3.8416 * 100/ 2.25
= 170.73
the sample size is approximately 171
d. we have 0.5 as sample proportion now
margin of error = 0.045
α = 0.10
Zα/2 = 0.05
= 1.645
sample size = 1.645²x0.5(1-0.5) / 0.045²
= 0.676506/0.002025
= 334. 07
sample size = 334
5. sample of 334 should be taken by manager
What is the solution to a system with parallel lines?
Step-by-step explanation:
no solution because they never intercept
120
'N
A) 350
C) 135
D) 120
Answer:
it is d 120
Step-by-step explanation:
Si un vendedor gana $ 450 por cada venta de $ 50 000, ¿cuál es su tasa de comisión?
Answer:
..?.?..............???............
Help!!!!
Given that slope = -4 and a point (-2,5), write an equation in standard form
of the line.
Help plzzz!! Marking most Brainly;)
Answer:
D it
Step-by-step explanation:
We have two equations, A quadratic and a linear equation.
The domain of a linear equation and quadratic equation is all real numbers but since it dealing with time we must make sure the roots or x-intercepts is positive.
Looking at the quadratic equation, we can use the discramnt formula to see if all roots are positve.
[tex]b {}^{2} - 4ac [/tex]
[tex] { - 6}^{2} - 4(1)(8.75)[/tex]
[tex]36 - 35 = 1[/tex]
The discramnt is greater than zero so there is two distinct real roots. So let check if they are positve
If you graph the equation, it intercepts at two positve roots so it is D
Find the circumference of the circle.
10 cm
The circumference is cm.
(Type an exact answer in terms of t.)
Answer:
the answer is either one or two answers
62.83 or 31.42
Step-by-step explanation:
This is the formula i used.
C=2πr
Circumference = 2·π·5 ≈ 31.41593 / 2·π·10 ≈ 62.83185
therefore,
t = 31.41593
or
t = 62.83185
Driving 65 mph, it takes Alicia 3 hours to reach the airport to go on a vacation. It then takes her 4 hours to get to her destination with the jet traveling at a speed of 400 mph. How many miles does Alicia travel to get to her destination?
Answer:
1,795 mi. traveled in total
Step-by-step explanation:
3 × 65 = 195 mi. driven by car
4 × 400 = 1,600 mi. flown by jet
1,600 + 195 = 1,795 mi. traveled in total.
What is the equation of this line? ILL MARK BRAINLIST
A ~ y = -x + 2
b~ y = 2x -2
C ~ cannot be determined
D~ y = 2x + 2
Solve 5x -2.5 = 17.5
Answer:
x=4
Step-by-step explanation:
5x-2.5=17.5
5x=17.5+2.5
5x=20
x=20/5
x=4
The solution of the given equation is x=4
What does it mean to solve an equation?An equation represents equality of two or more mathematical expression.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
Solutions to an equation are those values of the variables involved in that equation for which the equation is true.
We are given the equation as;
5x-2.5=17.5
Solving for x;
5x=17.5+2.5
5x=20
x=20/5
x=4
Learn more about solving equations here:
https://brainly.com/question/18015090
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The spinner is divided into 4 equal parts: yellow (Y), green, (G), blue (B) and red (R). Dorian says that if you spin the spinner twice, then there are exactly 12 possible outcomes. he lists the outcomes in a table. Which statement explains Dorian’s mistake?
Answer:
The spinner can land on the same color twice in a row, so there should be 16 possible outcomes
Step-by-step explanation:
4 possible outcomes with the same color
RR, OO, GG and BB.
Total Ways = 12+4=16
-3/4 × = 1/4 need Help to answer this question
Answer:
x = -1/3
Step-by-step explanation:
step one - Simply both sides of the equation
step two - Multiply both side by 4/(-3)
Complete each statement then state the property or properties illustrated by each statement on
Answer:
(8n)(-77)=-77(n*8)
We move all terms to the left:
(8n)(-77)-(-77(n*8))=0
We add all the numbers together, and all the variables
8n(-77)-(-77(+n*8))=0
We multiply parentheses
-616n-(-77(+n*8))=0
We calculate terms in parentheses: -(-77(+n*8)), so:
-77(+n*8)
We multiply parentheses
-616n
Back to the equation:
-(-616n)
We get rid of parentheses
-616n+616n=0
We add all the numbers together, and all the variables
=0
n=0/1
n=0
the property is Associative Property
Step-by-step explanation:
this one was kinda hard pls let me know it its right or not
Michael is organizing a game of chance for his class. He asks each student to pick a ribbon from a bag and then put it back into the bag. The bag
has 12 yellow ribbons, 7 red ribbons, and 3 blue ribbons. If Jane picks a ribbon, what is the probability that the ribbon will be yellow and what is
the likelihood of this event?
OA. The probability is 1, and the event is certain.
OB. The probability is î and the event is likely.
OC. The probability is it and the event is unlikely.
OD The probability is it, and the event is neither likely nor unlikely.
Answer:
b
Step-by-step explanation:
Using the probability concept, it is found that the correct statement regarding the probability of picking a yellow ribbon is given by:
D The probability is of 0.5454 = 54.54%, and the event is neither likely nor unlikely.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, 12 out of 22 ribbons are yellow, hence:
p = 12/22 = 6/11 = 0.5454 = 54.54.
The probability is greater than 0.05 but less than 0.95, hence it is neither likely nor unlikely, which means that option D is correct.
More can be learned about probabilities at https://brainly.com/question/14398287
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Given the perimeter is 180cm what is the length and breadth of the rectangle?
234235342421323254123+323546534311234
Answer:
I gotchu.
Step-by-step explanation:
234235342421323254123+323546534311234 = 2.34235666E20
Have a good day! :)
Please help will give brainliest.
Answer:
D
Step-by-step explanation:
a is false since x could be 0.
b is easy to check, just plug numbers in, and we can see that it's false(you would get 0+0=1 and -0-0=-1 once plugged in)
c is also easy to check, just plot the line or simplify the first equation. since (2x+2y)/2=4/2 is also x+y=2, the second equation is also x+y=2, so it must have infinitely many solutions.
d must be true due to process of elimination but let's check to make sure.
7y=14x, divide both sides by 7 to get y=2x and since they're the same equation it must mean that they have infinitly many solutions and we can see that it is correct