Use the distance formula to show that the two triangles on the coordinate plane are congruent
Answers
Answer:
Step-by-step explanation:
d = [tex]\sqrt{(x_{2} -x_{1} )^2 + (y_{2} - y_{1} )^2}[/tex]
A(- 5, - 2) , B( - 1, - 6) , C ( - 9, - 6)
AB = √[(- 5 + 1)² + (- 2 + 6)²] = 4√2
BC = √[(- 1 + 9)² + (- 6 + 6)²] = 8
AC = √[(- 5 + 9)² + (- 2 + 6)²] = 4√2
D(2, 2) , E(6, - 2) , F( 10, 2)
DE = √[(2 - 6)² + (2 + 2)²] = 4√2
EF = √[(6 - 10)² + (- 2 - 2)²] = 4√2
DF = √[(2 - 10)² + (2 - 2)²] = 8
ΔABC ≅ ΔEDF
The two triangles ABC and DEF are not congruent by SSS.
What is the distance formula between two points?The distance formula between two points is,
[tex]D = \sqrt{(x_2 - x_1_)^2 + (y_2 - y_1)^2[/tex].
Two triangles will be congruent by SSS is the distance of their corresponding sides are equal.
In ΔABC coordinates of A and B are (-5, - 2) and (-1, - 6).
[tex]D_{AB} = \sqrt{(- 1 + 5)^2 + (- 6 + 2)^2}[/tex].
[tex]D_{AB} = \sqrt{(4)^2 + (-4)^2[/tex].
[tex]D_{AB} = \sqrt{(16) + (16)[/tex].
[tex]D_{AB} = \sqrt{32}[/tex].
Similarly, the distance of DF in ΔDEF is [tex]\sqrt{64}[/tex].
hence AB ≠ DF so the triangles are not congruent.
learn more about the distance formula here :
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Related Questions
A plane flies with a speed of 600 mph. What distance will it fly
in 3 /5 hours,11/12 hours, 4/15 hours?
Answers
Answer:
3/5=360 mph 11/12=550 4/15=160
Step-by-step explanation:
The Miller's are comparing babysitting services for their two children.
The Babysitter's Block charges a rate of $15 an hour per child plus an initial fee of $25 per household.
Super Sitters charges a flat rate of $20 an hour per child.
For ________hours of service, both babysitting services would cost the same.
Answers
Answer:
After 5 hours of service, both babysitting services would cost the same.
Step-by-step explanation:
Babysitter's Block: y = 15x + 25
Super Sitters: y = 20x
15x + 25 = 20x
Subtract 15x from both sides;
25 = 5x
Divide both sides by 5;
x = 5
For 5 hours of service, both babysitting services would cost the same.
Solve two fifths minus one seventh equals blank.
solve this and you will get 25 points
Answers
Answer:
9/35
Step-by-step explanation:
A rectangle has a perimeter of 32 in. Find the length and width of the rectangle under which the area is the largest.
a. Let the width to be x and the length to be y , then the quantity to be maximized is (expressed as a function of both x and y) A=_____
b. The condition that x and y must satisfy is y=______
Answers
Answer:
Length of the rectangle is 8 in and the breadth is 8 in.
a. [tex]A=xy[/tex]
b. [tex]y=16-x[/tex]
Step-by-step explanation:
Length = x
Breadth = y
Area is given by [tex]A=xy[/tex]
Perimeter of rectangle is given by
[tex]2(x+y)=32\\\Rightarrow x+y=16\\\Rightarrow y=16-x[/tex]
The condition that x and must satisfy is [tex]y=16-x[/tex]
So, area is
[tex]A(x)=x(16-x)\\\Rightarrow A(x)=16x-x^2[/tex]
Differentiating with respect to x we get
[tex]A'(x)=16-2x[/tex]
Equating with zero
[tex]0=16-2x\\\Rightarrow x=\dfrac{16}{2}\\\Rightarrow x=8[/tex]
Double derivative of A(x)
[tex]A''(x)=-2[/tex]
So [tex]A''(x)<0[/tex] which means [tex]A(x)[/tex] is maximum at [tex]x = 8[/tex]
[tex]y=16-x=16-8\\\Rightarrow y=8[/tex]
So length of the rectangle is 8 in and the breadth is 8 in.
(4x^2-2x-4)(2x+4) what is
the product of the polynomials below?
Answers
Answer:
8x³ + 12x² - 16x - 16
General Formulas and Concepts:
Order of Operations: BPEMDASDistributive PropertyStep-by-step explanation:
Step 1: Define expression
(4x² - 2x - 4)(2x + 4)
Step 2: Simplify
Expand: 8x³ - 4x² - 8x + 16x² - 8x - 16Combine like terms (x²): 8x³ + 12x² - 8x - 8x - 16Combine like terms (x): 8x³ + 12x² - 16x - 16HELP ASAP WILL GIVE BRAINLIEST! Thanks
Answers
Answer:
I believe it's D
Step-by-step explanation:
It takes 3 minutes to download 123 gigabytes of data on a phone, At that rate how many gigabits could you download in 5 minutes
Answers
Answer:
x=205
Step-by-step explanation:
123/3=x/5 ( this is our proportion.) Solve it: 5*123/3. x=205.
Hope this helps plz mark brainliest :D
What is J/-12 > 9??
Answers
Answer:
j > - 108
Step-by-step explanation:
Step 1:
j / - 12 > 9 Equation
Step 2:
j > 9 × - 12 Multiply - 12 on both sides
Answer:
j > - 108
Hope This Helps :)
Answer:
j<−108
Step-by-step explanation:
j
−12
>9
Step 1: Simplify both sides of the inequality.
−1
12
j>9
Step 2: Multiply both sides by 12/(-1).
(
12
−1
)*(
−1
12
j)>(
12
−1
)*(9)
j<−108
Answer:
j<−108
The difference of 9 and three times a number is that number increased by 5. Find the number. just give me the equation
Answers
Answer:
9-3n=n+5
Step-by-step explanation:
n= the number
Graphs which present the values on the horizontal axis and the number of times this occurs on the vertical axis are known as what?
Answers
Answer:
The horizontal axis represents TIME
Step-by-step explanation:
In a time-series plot, the horizontal axis represents time, and the vertical axis represents the value of the variable we are measuring. -The values of the variable are plotted at each of the times, then the points are connected with straight lines.
Which has the greater value? The sum of 89 and 45 or the difference between 89 and 45
Answers
Answer:
The sum of 89 and 45
Step-by-step explanation:
Because the sum of 89 and 45 is 134 and the difference of 89 and 45 is 44. And 134 > 44
EMILY COOKIE RECIPE CALLS FOR 3 CUPS OF FLOUR AND 1 CUP OF SUGAR WHAT IS THE RATIO OF FLOUR TO SUGAR
Answers
For a certain automobile, M(x)=−.015x^2+1.42x−7.8, 30≤x≤60, represents the miles per gallon obtained at a speed of x miles per hour. (a) Find the absolute maximum miles per gallon and the speed at which it occurs. (b) Find the absolute minimum miles per gallon and the speed at which it occurs.
Answers
9514 1404 393
Answer:
maximum: 25 121/150 mpg at 47 1/3 mphminimum: 21.3 mpg at 30 mphStep-by-step explanation:
A graph can be helpful. It can show the locations of the maximum and minimum.
__
The maximum is found at the vertex of the parabola, located where ...
x = -b/(2a)
x = -1.42/(2(-0.015)) = 47 1/3
The value M(47 1/3) is ...
M(47 1/3) = (-0.015(47 1/3) +1.42)(47 1/3) -7.8 = 0.71(47 1/3) -7.8 = 25 121/150
The maximum gas mileage is 25 121/150 ≈ 25.8067 mpg at 47 1/3 mph.
__
The minimum will be at one end or the other of the interval. Here, the maximum is farther from the lower end of the domain, so we expect to find the minimum there:
M(30) = (-0.015(30) +1.42)(30) -7.8 = 0.97(30) -7.8 = 21.3
The absolute minimum gas mileage is 21.3 mpg at 30 mph.
I need help in seventh grade math
Answers
Answer:
Below in bold.
Step-by-step explanation:
5. 1/8 and 0.125 = 12.5%
6. 6/100 = 3/50.
and 6/100 = 0.06.
7. 7/9 = 0.777....
and 77.78%.
8. 44/100 = 11/25.
and 0.44*100 = 44%
9. 625/1000 = 625/125 / 1000 / 125 = 5/8.
and 0.625.
10. 13/25 = 13*4/25/4 = 52/100 = 0.52
and 0.52 * 100 = 52%.
John's salary is $1600. Peter 's salary is $400 less than John's salary. Find the ratio Peter's salary to John's salary in the simplest form.
Answers
$300 to $400
Step-by-step explanation:
A cone has a height of 5 inches and a radius of 4 inches. What is its volume?
Use a ~ 3.14 and round your answer to the nearest hundredth.
Answers
9514 1400 393
Answer:
83.73 in³
Step-by-step explanation:
It is appropriate to use the formula for the volume of a cone:
V = (1/3)πr²h
V = (1/3)(3.14)(4 in)²(5 in) ≈ 83.73 in³
The volume of the cone is about 83.73 in³.
If a baseball player get a hit in 31% of his at-bats, what is the probability that he will
get a hit 5 at-bats in a row?
Answers
Given:
A baseball player get a hit in 31% of his at-bats.
To find:
The probability that he will get a hit 5 at-bats in a row.
Solution:
Since, a baseball player get a hit in 31% of his at-bats, therefore
Probability that he get a hit = [tex]\dfrac{31}{100}[/tex]
= [tex]0.31[/tex]
Now, the probability that he will get a hit 5 at-bats in a row is
[tex]P=0.31\times 0.31\times 0.31\times 0.31\times 0.31[/tex]
[tex]P=(0.31)^5[/tex]
[tex]P=0.0028629151 [/tex]
Therefore, the required probability is [tex](0.31)^5[/tex] and it can be written as 0.0028629151 .
Please answer this question fast
Answers
ddddddddddddddAnswer:
Step-by-step explanation:
fffffffffff
State whether the following function is a linear function f(x)=x-4
Answers
what is equivalent to x+x ?
a)xx
b)2x
c)x^2
d)2^x
Answers
Answer:
b
Step-by-step explanation:
I think it is B because x+x is two x's so it would be 2x. I hope this helped have a good day
In how many ways can a class of nineteen students be divided into 3 sets so that 4 students are in the first set, 6 students are in the second set and nine students are in the third set?
Answers
Answer:
216
Step-by-step explanation:
Choose the formula for the volume of a cone V = mrh written in terms of h.
Answers
Answer:
Choose the formula for the volume of a cone V = mrh written in terms of h.
(Isolate h by itself by dividing)
h=V/mr
what is the value of h in the triangle
Answers
Answer:
I think the answer is 7.2
which of these statements is true for 89.033
Answers
A bag of M & M’s has 4 red, 2 green, 3 blue, and 8 yellow M &M’s. What is the probability of randomly picking: a yellow, a blue or green, an orange? Round 4 decimal
Answers
Answer:
probability of picking a yellow =0.4706
a blue or green = 0.2941
an orange = 0 ( there is no orange bag)
Consider the transformations performed on quadrilateral WXYZ.
. Translate 7 units to the right and 4 units up.
• Then, rotate 180° about the origin.
Answers
Do yk the answer ? Now ?
Answer:
(-4, -5)Step-by-step explanation:
Point Z has coordinates: (-3, 1)
Translate 7 units to the right and 4 units up: (x + 7, y + 4)
Z(-3, 1) → Z'(-3 + 7, 1 + 4) = (4, 5)Then, rotate 180° about the origin: (x, y) → (-x, -y)
Z'(4, 5) → Z''(-4, -5)In the equation
2
3
x
=
10
, what is the value of x?
Answers
Answer:
23/10 or 15
Step-by-step explanation:
Tasia’s bank account balance was -$25.64. She deposited a check into her bank account and her new balance is $152.29. How much was the check that Tasia deposited into her account?
Answers
Answer:
$177.93
Step-by-step explanation:
Answer:
The check is 177.93$
Step-by-step explanation:
I did 25.64+152.29= 177.93
U can check it by doing -25.64+177.93
Given that f(x)= [tex]\frac{x^{2}-3 }{2}[/tex]
A) Find [tex]f^{-1}(x)[/tex]
B) Find [tex]f^{-1} (11)[/tex]
Separate your 2 answers for part B with a comma.
I've solved [tex]f^{-1}(x)[/tex], which was [tex]\sqrt{2x+3}[/tex]
However after this I do not see how I can get another value other than 5.
Answers
Answer:
[tex]x=5,-5[/tex]
Step-by-step explanation:
[tex]\\ y=\frac{x^2-3}{2}\\\\ x=\frac{y^2-3}{2}\\\\ 2x=y^2-3\\\\ y^2=2x+3\\\\ f^{-1}(x)=\pm\sqrt{2x+3}\\\\ f^{-1}(x)=\pm\sqrt{2(11)+3}\\=\pm\sqrt{25}=\pm 5[/tex]
According to the U.S. Census Bureau, 11% of children in the United States lived with at least one grandparent in 2009 (USA TODAY, June 30, 2011). Suppose that in a recent sample of 1640 children, 225 were found to be living with at least one grandparent. At a 2% significance level, can you conclude that the proportion of all children in the United States who currently live with at least one grandparent is higher than 11%? Use both the p-value and the critical-value approaches.
Round your answers for the observed value of z and the critival value of z to two decimal places, and the p-value to four decimal places.
Answers
Answer:
The decision rule is
Fail to reject the null hypothesis
The conclusion is
There is no sufficient evidence to show that the proportion of all children in the United States who currently live with at least one grandparent is higher than 11%
Step-by-step explanation:
From the question we are told that
The population proportion is [tex]p = 0.11[/tex]
The sample size is n = 1640
The number found to be living with at least one grandparent is [tex]k = 225[/tex]
The level of significance is [tex]\alpha = 0.02[/tex]
The null hypothesis is [tex]H_o : p = 0.11[/tex]
The alternative hypothesis is [tex]H_a : p > 0.11[/tex]
Generally the sample proportion is mathematically represented as
[tex]\^ p = \frac{ k }{n}[/tex]
=> [tex]\^ p = \frac{ 225 }{1640 }[/tex]
=> [tex]\^ p = 0.1372[/tex]
Generally the test statistics is mathematically represented as
[tex]z= \frac{\^ p - p }{ \sqrt{\frac{p(1- p)}{n} } }[/tex]
=>[tex]z = \frac{ 0.1372 - 0.11 }{ \sqrt{\frac{0.11(1- 0.11)}{1640} } }[/tex]
=>[tex]z = 0.0077[/tex]
From the z table the area under the normal curve to the left corresponding to 0.0077 is
[tex]p-value = P(Z > 0.0077) = 0.4969[/tex]
From the value obtained we see that [tex]p-value > \alpha[/tex] hence
The decision rule is
Reject the null hypothesis
The conclusion is
There is no sufficient evidence to show that the proportion of all children in the United States who currently live with at least one grandparent is higher than 11%
