Lesson 4.10 - Analytic Geometry
1) Prove that the following is a square. You must show all of your
work and give a written explanation of why the figure is a square. (First picture)
2) Prove that the following is a right - isosceles triangle. You must
show all of your work and give a written explanation of why the
figure is a right-isosceles triangle.
(Isosceles Triangles are triangles with 2 equal sides.) second picture
Answers
Geometric shapes are mathematical shapes that include squares and triangles
How to prove the shape is a squareThe side lengths of a square are congruent, and the adjacent sides are perpendicular.
So, we start by calculating the side lengths using the following distance formula
[tex]d = \sqrt{(x_1 -x_2)^2 + (y_1 -y_2)^2}[/tex]
Using the above formula, we have:
[tex]AB = \sqrt{(3-2)^2 + (4+2)^2} = \sqrt{37[/tex]
[tex]BC = \sqrt{(2+4)^2 + (-2+1)^2} = \sqrt{37[/tex]
[tex]CD = \sqrt{(-4+3)^2 + (-1-5)^2} = \sqrt{37}[/tex]
[tex]DA = \sqrt{(-3-3)^2 + (5-4)^2} = \sqrt{37}[/tex]
The above shows that the side lengths of the square are congruent.
Next, calculate the slope of the sides using:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m_{AB} = \frac{4 +2}{3 -2} = 6[/tex]
[tex]m_{BC} = \frac{-2 + 1}{2+4} = -\frac 16[/tex]
[tex]m_{CD} = \frac{-1 -5}{-4+3} = 6[/tex]
[tex]m_{DA} = \frac{5 -4}{-3-3} = -\frac 16[/tex]
Notice that the opposite slopes are congruent, and the adjacent slopes are opposite reciprocal.
The above highlight, and the equal side lengths show that the figure (1) is a square
How to prove the shape is a right isosceles triangleThe legs of a right isosceles triangle are congruent, and the legs are perpendicular.
So, we start by calculating the lengths of the legs using the following distance formula
[tex]d = \sqrt{(x_1 -x_2)^2 + (y_1 -y_2)^2}[/tex]
Using the above formula, we have:
[tex]XY = \sqrt{(5-4)^2 + (-1-4)^2} = \sqrt{26[/tex]
[tex]XZ = \sqrt{(5-0)^2 + (-1+2)^2} = \sqrt{26[/tex]
The above shows that the legs of the right isosceles triangle are congruent.
Next, calculate the slope of the legs using:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m_{XY} = \frac{5-4}{-1 -4} = -\frac{1}{5}[/tex]
[tex]m_{XZ} = \frac{5-0}{-1+2} = 5[/tex]
Notice that the slopes are opposite reciprocal.
The above highlight, and the equal legs show that the figure (2) is a right isosceles triangle
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Related Questions
RJ has two loans. Loan H has a nominal rate of 5.68%, compounded daily. Loan I has a nominal rate of 6.33%, compounded monthly. Which loan's effective rate had the greater increase, relative to its nominal rate, and how much greater is its increase than that of the other loan?
a.
Loan I’s increase was 0.03 percentage points greater than Loan H’s.
b.
Loan I’s increase was 0.68 percentage points greater than Loan H’s.
c.
Loan H’s increase was 0.16 percentage points greater than Loan I’s.
d.
Loan H’s increase was 0.49 percentage points greater than Loan I’s.
Answers
Answer:
The correct answer for this question is:
The loan's effective rate that had the greater increase, relative to its nominal rate, and how much greater is its increase than that of the other loan is that 'loan H’s increase was 0.16 percentage points greater than Loan I’s.
Step-by-step explanation:
Answer:
A: Loan I’s increase was 0.03 percentage points greater than Loan H’s.
How can you calculate the area of the circle if know the circle’s circumference.
Answers
Answer:
dont cheat
Step-by-step explanation:
HELPP QUICK PLEASE please
Answers
Hi! I hope you're enjoying your day!
Please remember that an arithmetic sequence is a sequence where we use either addition or subtraction to get to the next term.
Now, let's find an arithmetic sequence here.
Is it Option A?
Remember: It should have a common difference of 2.
Which means we either add or subtract 2 to get to the next term.
Well, it seems like Option A is right.
Let's check the other options.
Is Option B right? Nope.
Here's why.
Hint: Pay attention to the signs.
We have
1, -3, 5, -7, 9...
So Option B is wrong.
Option C is correct, because we subtract 2 each time.
Option D is wrong, because we multiply by 2 each time.
Hence, the right options are
[tex]\boxed{\boxed{\bold{Options~A~and~C.}}}[/tex]
Hope everything is clear.
If you have any questions, please comment.
#LearningIsFun
[tex]\rule{200}{2}[/tex]
The function H
gives the height, above the ground, of a point on a spinning wheel. The function A gives the height of a point on a different spinning wheel and is defined by
A(t)=1.2H(3t). Here, t is time in seconds since the wheels started moving. How does the spinning wheel modeled by function A compare to the wheel for H
? Explain how you know.
Answers
The expression [tex]A(t) = 1.2\cdot H(3t)[/tex] multiplies the amplitude of [tex]H(3t)[/tex] by 1.2.
Functional analysis for the model of the height of the wheel
The model of the height is represented by the following sinusoidal model:
[tex]H(3t) = D \cdot \sin [B(3t)+E][/tex] (1)
Where:
[tex]D[/tex] - Amplitude[tex]B[/tex] - Angular frequency[tex]E[/tex] - Phase angleThen, the expression [tex]A(t) = 1.2\cdot H(3t)[/tex] multiplies the amplitude of [tex]H(3t)[/tex] by 1.2. [tex]\blacksquare[/tex]
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Question 7 of 10
What is the solution to this equation?
3(4x+3) = 2x - 5(3 - x) + 2
4
O A. x=-
15
10
O B. x=-22
O
5
O x-
O c. x - 22
15
O x
O D. x = -1
5
Answers
Answer:
Option BStep-by-step explanation:
Given Equation :
[tex] \qquad \sf \dashrightarrow \: 3(4x+3) = 2x - 5(3 - x) + 2[/tex]
Using distribute property:
[tex]\qquad \sf \dashrightarrow \: 12x + 9 = 2x - 15 + 5x + 2[/tex]
Adding the like terms we get :
[tex]\qquad \sf \dashrightarrow \: 12x + 9 = 2x + 5x - 15 + 2[/tex]
[tex]\qquad \sf \dashrightarrow \: 12x + 9 = 7x - 13[/tex]
Transposing the variables on the right side and constant terms on the left side :
[tex]\qquad \sf \dashrightarrow \: 12x - 7x = - 13 - 9[/tex]
[tex]\qquad \sf \dashrightarrow \: 5x = - 22[/tex]
Dividing both sides by 5 :
[tex]\qquad \sf \dashrightarrow \: \dfrac{5x}{5} = \dfrac{ - 22}{5} [/tex]
[tex]\qquad \bf \dashrightarrow \: x = \dfrac{ - 22}{5} [/tex]
a box of cookies weighing 4kg was divided into 6 equal shares.
Answers
Answer:
0.67
Step-by-step explanation:
that is 4 divided by 6
your answer is 0.6666666
it's a recurring decimal
or 0.67
If Jose earned 145.60 for 7 hours, how many hours would he have to work to earn $83.20?
Answers
Answer:
4 hours
Step-by-step explanation:
Each hour: 145.60/7 = 20.80
83.20/20.80 = 4
Can you help with this question I will give you 10 points
Answers
Answer:
The elevation of University Peak could be 14,464, which in between the two mountains.
Answer:
It's shorter than Mt. Massive but it's shorter than Mt. Alverstone.
The number between 14,500 and 14,428 is 14464, that would be a great guess
An electric utility worker wants to anchor a guy wire from the top of a 13.2-foot utility pole to a spot that is 5.5 feet from the base of the pole on level ground. How long does the guy wire need to be?
Answers
Answer:
a^2+b^2=c^2
Step-by-step explanation:
13.2^2+5.5^2=c^2
204.49=c^2
sqrt(204.49)=14.3
If we divide the polynomial P by the factor x - c and we
obtain the equation P(x) = (x – c)Q(x) + R(x), then we say
that x - c is the divisor, Q(x) is the
and R(x) is
the
Answers
Hello
Step-by-step explanation:
hello I'm Filipino people
here a subtraction problem that has been solved incorrectly 21-9=11 choose the addition sentence that check this subtraction problem here the choices are 21+9=30 11+9=20 11+21=32 which one is correct
Answers
Answer:
Answer:
11+ 9 = 20
Step-by-step explanation:
=> 21-9=11
21 - 9 equals to 11 is actually a wrong answer
So in order to find the subtraction problem that will help us truly know whether the equation is wrong
=> 11+ 9 = 20
OR THE SECOND EQUATION IS
=> 21 - 11 = 10
Please look at the picture and answer it. Thank you.
Answers
Answer:
not clear.
please send another..
What is the equation of the line that passes through the point (2,3) and has a slope that is undefined?
Answers
Answer:
x=2
Step-by-step explanation:
An undefined slope is the slope of a vertical line.
line through (2,3) is y=mx+b
Answer: x=2
Each equation below is followed by several stories.
Select all of the stories that can be represented by the equation.
If none of the stories can be represented, select "None of the above".
(a)x+11=44
Answers
Typically, there are keywords in the story that tell us what operations we need to use.
For instance, in terms of age:
"Younger" or "older" connotes to subtraction from the age of the older person. It can also connote to the addition to the age of the younger person."Years ago" typically connotes to the subtraction of x years from the person's current age."More years" typically connotes to the addition of x years to the person's current age.Solving the QuestionLet's take a look at our first option.
Yousif is x years old. Rana is 44 years older than Yousif. Rana is 11 years old.Firstly, this option doesn't even make sense. How can Rana be 11 years old but also 44 years older than Yousif?
Let's look at our second option.
Rana is x years old. in 11 more years, she will be 44 years old.Immediately, we see "11 more years". This means that we will be adding 11 to Rana's current age, which is x:
[tex]x+11[/tex]
This expression above is equal to 44, since the question tells us that Rana will be 44 years old in 11 years:
[tex]x+11=44[/tex]
This is our final expression. It is the same as the given expression in the question.
AnswerRana is x years old. in 11 more years, she will be 44 years old.
Use trigonometric rates to find the missing angle.
Answers
Because the two sides are the hypotenuse and adjacent of the angle, use cosine to figure out x! cosine is CAH (cosine= adjacent/hypotenuse) so you would do cosx-1=8/17 on the calculator which is around 62 degrees.
Answer:
Step-by-step explanation:
21% of U.S. adults say they are more likely to make purchases during a sales tax holiday. You randomly select 10 adults. Find the probability that the number of adults who say they are more likely to make purchases during a sales tax holiday is (a) exactly two, (b) more than two, and (c) between two and five, inclusive.
Answers
Answer:
[tex]\left(a\right)\ 21.066\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \left(b\right)\ 66.872\\ \left(c\right)\ 81.567[/tex]
Step-by-step explanation:
[tex]\left(a\right)\ P\left(2\right)=C^{\begin{matrix}2\\10\\\end{matrix}}\bullet(32)^2\bullet(1-32)^{10-2}\\ =C^{\begin{matrix}2\\10\\\end{matrix}}\bullet(32)^2\bullet(68)^8=0.21066=21.066[/tex] [tex]percent[/tex]
[tex]cb)\ P(x > 2)=P(x\le2)=1-(P(x=0)+P(x=1)+P(x=2))\\ =1-C^{\begin{matrix}0\\10\\\end{matrix}}(0.32)degrees(0.68)^{10}-C^{\begin{matrix}1\\10\\\end{matrix}}(0.32)\prime(0.68)^9-C^{\begin{matrix}1\\0\\\end{matrix}}(008)(66)^9\\ =1-0.02114-0.09948-0.21066\\ =0.66872=66.872\\[/tex]
[tex](C)\ \ \ \ \ P(2\preccurlyeq[/tex] [tex]5)=P(2)+P(3)+P(4)+P(5)5)=P(2)+P(3)+P(4)+P(5)[/tex]
[tex]=C^{\begin{matrix}2\\10\\\end{matrix}}(0.32)^{)^2}\bullet(0.68)^3+C^{\begin{matrix}3\\10\\\end{matrix}}(0.32)^3\bullet(0.68)^7+C^{\begin{matrix}4\\10\\\end{matrix}}(0.32)^4\bullet(0.68)^6+C^{\begin{matrix}5\\10\\\end{matrix}}\bullet(0.32)^5\bullet(0.65)^5)[/tex]
[tex]=0.2186+0.26436+0.21771+0.12294\\ =0.81567=81.567 percent[/tex]
[tex](binomial\ distribution)[/tex]
I hope this helps you
:)
What is 49 times 69 equal to?
Answers
Answer:
3381 is the answer
Answer:
3,381
Step-by-step explanation:
hope this helps
When x=5, the value of the expression 20/-25+x-2(x-10)is
Answers
Shoes sold at the Shoe Express are discounted 25% off the original price. If a pair of shoes originally cost $46, calculate the sale price of the shoes
Answers
Answer:
$34.50
Step-by-step explanation:
$46*.25 = $11.50
$46 - 11.50 = $34.50
Solution:
We know that:
Discounted price: Original price - (Original price × Discount)Original cost of a pair of shoes: $46Discount: 25%This means that:
Sale price of a pair of shoes: 46 - (46 × 25%)Step-1: Convert "25%" into a fraction.
25% = 25/100 = 1/4Step-2: Find the discounted price.
Sale price of a pair of shoes: 46 - (46 × 1/4)Sale price of a pair of shoes: 46 - (23/2)Sale price of a pair of shoes: 46 - 11.5Sale price of a pair of shoes: $34.544% of the doctors in a hospital are females and the number of male doctors is 62. Find the total number doctors in the hospital.
don't scam,
Answers
is this correct?
hope you liked it!
For which equations is x = 9 a possible solution? Check all that apply.
|x| = 9
–|x| = 9
–|–x| = 9
–|–x| = –9
|x| = –9
|–x| = 9
|–x| = –9
Answers
Answer:
|x|=9
Step-by-step explanation:
Absolute value is |x|=9
What is the value of 0.6–0.3? Write your answer as a fraction in lowest terms.
Answers
Answer: 3/10
Step-by-step explanation:
Give me feedback if I am wrong.
Answer:
0.6-0.3=0.3. convert to fraction=1/3
In a quadrilateral OABC, D is the midpoint of BC and E is the point on AD such that AE : ED=2: 1. Given that OA = a, OB = b and OC = c, express OD and OE in terms of a, b and c.
Answers
Answer:
Step-by-step explanation:
CB=OB-OC;
CD=CB/2=(OB-OC)/2=(b-c)/2;
OD=OC+CD=c+(b-c)/2=c/2+b/2;
AD=OD-OA=c/2+b/2-a;
AE=2/3*AD=2/3*(c/2+b/2-a)=c/3+b/3-2*a/3;
OE=OA+AE=a+c/3+b/3-2*a/3=a/3+b/3+c/3;
-------------------------------------------------------------------------------------------------
OD=c/2+b/2;
OE=a/3+b/3+c/3;
The value of OE = (a+ b+ c)/3 and OD = (b + c)/2.
In quadrilateral OABC, we are given that D is the midpoint of BC,
and E is a point on AD such that AE : ED = 2 : 1.
Also, OA = a, OB = b and OC = c
Now, By the Midpoint Theorem, we also have
OD = (1/2)OB + (1/2)OC.
OD = (1/2)(OB + OC)
OD = (1/2)(b + c)
OD = (b + c)/2.
and, CD= (OB- OC)/2 = (b-c)/2
Now, AD=OD-OA= (c+b)/2 - a
and, AE=2/3 x AD
= 2/3 x (c+ b)/2 - a
= (c + b - 2a)/3
Then, OE = OA + AE
= a + (c + b - 2a)/3
= (a+ b+ c)/3
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Translate the triangle.
Anyways but I’ve been on this question for about 20 minutes because I can’t find the answer anywhere.
Answers
Answer:
A: (2,2) B: (3,-1) C: (-1,0)
Step-by-step explanation:
Change the coordinates of each point using the given translation. So 2 left 3 up.
a rectangular swimming pool has an area of x²-6x-16, what expression could represent the length and width of the pool
Answers
Answer:
the answer is A im not sure so check with another person.
Step-by-step explanation:
if you divide 10 divided by 2 it gives you 5 and then subtract it by 2.2 = 2.8
there goes your answer.
Find the value of x, y and z.
Answers
Answer:
Step-by-step explanation:
The table shows Avery’s net worth statement.
Net Worth Statement. Item; Value. Bank accounts; $3,900; Car (current value); question mark; Credit card debt; negative $2,950; Real estate; $37,425; Student loans; negative $1,700; Investments; $4,600.
Avery’s net worth is $53,755. Based on the information in the table, what is the current value of Avery’s car?
Answers
The current value of Avery’s car is $12,480.
Current valueFirst step is to calculate the Net Worth
Bank accounts $3,900
Credit card debt ($2,950)
Real estate $37,425
Student loans ($1,700)
Investments $4,600
Net worth $41,275
Second step is to calculate the current value of Avery’s car
Current value=$53,755-$41,275
Current value=$12,480
Inconclusion the current value of Avery’s car is $12,480.
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Riley set up a snack table for her dog's birthday party. She invited all the neighborhood dogs
-and their owners! For the dogs, she filled small toy balls with peanut butter. The balls have
a radius of 1.75 inches. What is the volume of each ball?
Use a = 3.14 and round your answer to the nearest whole number.
cubic inches
For her neighbors, Riley filled mini cone-shaped bags with popcorn. Riley notices that the
bags have the same radius as the balls, but a volume of 44 cubic inches. What is the height
of each bag?
Use na 3.14 and round your answer to the nearest whole number.
inches
Answers
The volume of each ball is: 22.45 in.³.
The height of the cone-shaped bag = 14 inches.
What is the Volume of a Sphere and a Cone?Volume of a sphere = 4/3πr³Volume of a cone = 1/3πr²hVolume of each ball = 4/3πr³ = 4/3π(1.75³) = 22.45 in.³.
Radius (r) of the cone-shaped bag = 1.75
Height (h) = ?
Volume of the cone-shaped bag = 44 cubic inches
44 = 1/3(3.14)(1.75²)h
44 = 3.2h
44/3.2 = h
h ≈ 14 inches.
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Wendy works at a kite shop. Yesterday she made 2 large kites and one small kite, using 16 square yards of nylon fabric. The day before, she used 9 square yards of nylon fabric to make 1 large kite and 1 small kite. How much nylon does Wendy need to make each size kite?
Write a system of equations to describe the situation and solve using elimination. (use x for a large kit and y for a small kite)
Answers
Answer:
x=7 and y =2.
2x+y = 16
x+y = 9
Help will be much appreciated...
Answers
Answer:
conclusion statement four sentences about you and exothermic heat was realised or absorbed it was changed beacsue positive 9r negative.