Nathan wants to use coordinate geometry to prove that the opposite sides of a rectangle are congruent. He places parallelogram ABCD in the coordinate plane so that A is (0, 0), B is (a, 0), C is (a, b), and D is (0, b).
What formula can he use to determine the distance from point C to point D?
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We take CD as the hypotenuse of the right-angled triangle and the distance between the x-coordinates and y-coordinates as the length of two short sides.
We can write the formula as
CD = [tex] \sqrt{( x_{1}- x_{0}) ^{2}+ ( y_{1}- y_{0}) ^{2} } [/tex]
CD = [tex] \sqrt{(a-0)^{2}+ (b-b)^{2} } [/tex]
Wrong on apex is is a-0+(b-b)2=a2=a
Related Questions
Periodic tune-ups are important because they
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Tim Duncan is shooting free throws. Making or missing free throws doesn't change the probability that he will make his next one, and he makes his free throws 72% of the time. What is the probability of Tim Duncan making all of his next 8 free throw attempts?
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Answer:
Hence, the probability of Tim Duncan making all of his next 8 free throw attempts is:
[tex](\dfrac{18}{25})^8=0.0722204136[/tex]
Step-by-step explanation:
As the probability of one free throw does not depend on the any other i.e. the probability of each throw is independent.
Hence, the probability of making all of his next 8 free throw is calculated as:
Probability of next 8 free throw=Probability of first free throw×probability o f second free throw×··················× Probability of 8th free throw.
i.e. it is given by:
[tex]Probability=\dfrac{72}{100}\times \dfrac{72}{100}\times \dfrac{72}{100}\times \dfrac{72}{100}\times \dfrac{72}{100}\times \dfrac{72}{100}\times \dfrac{72}{100}\times \dfrac{72}{100}\\\\\\Probability=(\dfrac{72}{100})^8\\\\Probability=(\dfrac{18}{25})^8[/tex]
Hence, the probability is:
[tex](\dfrac{18}{25})^8=0.0722204136[/tex]
We have that the he probability of Tim Duncan making all of his next 8 free throw attempts is mathematically given as
[tex]P=0.72^8[/tex]
From the question we are told
Tim Duncan is shooting free throws. Making or missing free throws doesn't change the probability that he will make his next one, and he makes his free throws 72% of the time. What is the probability of Tim Duncan making all of his next 8 free throw attempts?ArithmeticGenerally the equation for the binomial probability is mathematically given as
[tex]P=\frac{n!}{X!(n-X)!}*p^X*(1-p)^{n-X}\\\\Therefore\\\\ P=\frac{8!}{8!(8-8)!}*0.72^8*(1-0.72)^{0}[/tex]
[tex]P=0.72^8[/tex]
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f(x) = 3x + 10x and g(x) = 4x – 2, find (f – g)(x)
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The question seeks the derivatives of a function, but cannot be answered accurately due to the lack of specific information about the function provided.
The question asks to find the first, second, and third derivatives of a given function f(x). However, further details needed to answer the question, such as the specific form of the function f(x), are not provided in the question itself. Therefore, without the explicit function f(x), we cannot proceed to accurately calculate the requested derivatives.
Complete the equation and tell what property you used 16+31=31+16
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Identify the initial value and rate of change for the graph shown below.
Initial value: 5.5, rate of change: negative 3 over 4.
Initial value: 4, rate of change: negative 3 over 4.
Initial value: negative 3 over 4., rate of change: 4
Initial value: negative 3 over 4., rate of change: 5.5
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Answer:
The initial value is 4 and the rate of change is tex]\frac{-3}{4}[/tex]
Step-by-step explanation:
The initial value is the y intercept of the given line.
Y intercept is the point where the graph crosses y axis
y intercept is (0,4) so initial value is 4
Rate of change is the slope
To find rate of change we use formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Pick two points from the graph
(0,4) and (4,1)
Rate of change = [tex]\frac{1-4}{4-0}=\frac{-3}{4}[/tex]
Find the Solution to the system of equations.
A. (1, 4)
B. (4, 1)
C. (0, 3)
D. (4, -1)
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The solution to the system of equations represented by the graph is (b) (4,1)
How to determine the solution?The solution to the system of equations is the point of intesection of the equations.
From the graph, the lines intersect at the point
(x,y) = (4,1)
Hence, the solution to the system of equations is (4,1)
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Mildred brought 1 cent stamps,32 cent stamps, and 33 cent stamps for $21.80. The number of 1 cent stamps exceed the number of 33 cent stamps by 50. The number of 32 cents was 10 less than twice the number of 33 cents stamps. How many of each kind did she buy? Mildred brought 1 cent stamps,32 cent stamps, and 33 cent stamps for $21.80. The number of 1 cent stamps exceed the number of 33 cent stamps by 50. The number of 32 cents was 10 less than twice the number of 33 cents stamps. How many of each kind did she buy?
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0.01x + 0.32y + 0.33z = 21.80
x = z + 50
y = 2z - 10
0.01(z + 50) + 0.32(2z - 10) + 0.33z = 21.80
0.01z + 0.5 + 0.64z - 3.20 + 0.33z = 21.80
0.98z - 2.7 = 21.8
0.98z = 21.8 + 2.7
0.98z = 24.5
z = 24.5 / 0.98
z = 25 <=== 33 cent stamps
x = z + 50
x = 25 + 50
x = 75 <=== 1 cent stamps
y = 2z - 10
y = 2(25) - 10
y = 50 - 10
y = 40 <== 32 cent stamps
Mildred bought 480 1 cent stamps, 410 32 cent stamps, and 520 33 cent stamps.
Explanation:Let's solve this problem using a system of equations.
Let's use the variables x, y, and z to represent the number of 1 cent stamps, 32 cent stamps, and 33 cent stamps respectively that Mildred bought. We can write the following equations based on the information given:
x + y + z = 2180 (since the total cost was $21.80)
x = z + 50 (since the number of 1 cent stamps exceed the number of 33 cent stamps by 50)
y = 2z - 10 (since the number of 32 cent stamps was 10 less than twice the number of 33 cents stamps)
Let's solve this system of equations:
Substitute the value of x from equation 2 into equation 1: (z + 50) + y + z = 2180Substitute the value of y from equation 3 into equation 1: z + 50 + (2z - 10) + z = 2180Simplify and solve for zSubstitute the value of z into equation 2 to find xSubstitute the value of z into equation 3 to find yAfter solving the system of equations, we find that Mildred bought 480 1 cent stamps, 410 32 cent stamps, and 520 33 cent stamps.
Polygons EFHG and E′F′H′G′ are shown on the following coordinate grid: A coordinate grid is shown from positive 6 to negative 6 on the x-axis and from positive 6 to negative 6 on the y-axis. A polygon EFHG is shown with vertex E on ordered pair 2, 2, vertex F on ordered pair 2, 4, vertex H on ordered pair 3, 5 and vertex G on ordered pair 3, 1. A polygon E prime F prime H prime G prime is shown with vertex E prime on ordered pair negative 1, 2, vertex F prime on ordered pair negative 3, 2, vertex H prime on ordered pair negative 4, 3, and vertex G prime on ordered pair 0, 3. What set of transformations is performed on EFHG to form E′F′H′G′?
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All choices involve a rotation by 90° or 270° counterclockwise about the origin.
consider a rotation by 90° counterclockwise. Each point P(a, b) can be rotated 90° cwise about the origin to form P"(a",b") :
by drawing the right angle POP", such that |PO|=|OP"|.
or by plotting each P"(a",b") so that (a",b")=(-b, a)
for example if G(3, 1) is mapped to G(-1, 3) by either of the procedures described.
check picture 2.
EFHG is mapped to E′'F'′H'′G′'.
In order to map E′'F'′H'′G′' to E'F′H'G′, we need to translate the figure 1 unit right.
Answer:
"A 90-degree counterclockwise rotation about the origin followed by a translation 1 unit to the right"
Answer:
A 90-degree counterclockwise rotation about the origin followed by a translation 1 unit to the right
Step-by-step explanation:
i took the test
Sarah is a news anchor. She works 55 hours a week, but she is only on-air about 19% of those hours. Approximately how many hours is Sarah on-air each week?
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Hope this helped! :D
What is the 24% of 40?
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40 times 0.24 = 9.6
Therefore 24% of 40 = 9.6
Anyhow, lets start working out this problem, shall we? 24(40) = ? 24 ÷ 100 = 0.24 0.24 (40) = 9.6 Your answer would be: 9.6
Please answer correct for brainliest
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So area = (12 + (2*2 + 12) ) *13 / 2 = 182
Find the quotient of the quantity [tex]
\frac{4x^3y+12x^2y^3-20xy}{4xy} [/tex].
A.[tex]
x^2+3xy^2+5[/tex]
B. [tex]
x^2+3xy-5[/tex]
C. [tex]
4x^3y+12x^2y^3-5[/tex]
D. [tex]
x^2+3xy^2-5[/tex]
Please tell me how to get the correct answer! Thank you!
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remember ab+ac=a(b+c)
so
[tex]\frac{4x^3y+12x^2y^3-20xy}{4xy}=[/tex]
[tex]\frac{(4xy)(x^2)+(4xy)(3xy)+(4xy)(-5)}{4xy}=[/tex]
[tex]\frac{(4xy)(x^2+3xy-5)}{4xy}=[/tex]
[tex]x^2+3xy-5[/tex]
answer is B
Answer:
answer:b
Step-by-step explanation:
we need to factor out the things like in distributive
remember ab+ac=a(b+c)
so
The basement of a large department store features discounted merchandise. Their policy is to reduce the previous month's price of the item by 5 % each month for 6 months, and then give the unsold items to charity. Let Upper S Subscript 6 be the sale price for the sixth month and Upper P the original price. Express Upper S Subscript 6 as a function of Upper P Baseline Number .
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S = P(1-0.05t)
Simplifying,
S = 0.95Pt
So, after 6 months, the sales price would be:
S₆ = 0.95P(6)
S₆ = 5.7P
A theater company charges $4.50 per ticket for people of all age groups. If c represents the total number of children who bought tickets and a represents the total number of adults who bought tickets, which expression best represents the total money earned by the company from the sale of tickets? 4.5(c + a) 4.5c + a c + 4.5a 9(c + a)
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Answer:
4.5 c+a)
Step-by-step explanation:
How many quarts in a gallon
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Simplify 8(x + 6) - 10. 8x - 4 8x + 28 8x + 38
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8x + 48 - 10
8x + 38 <------------- answer
8x + 38 should be the answer...not sure.
Hunter bought a package of 24 pencils for $3.12. Write and solve an equation to determine the cost of each pencil in the package
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p = 3.12 / 24
p = 0.13
answer
the cost of each pencil in the package = $0.13
The cost of each pencil in the package is $0.13.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that a Hunter bought a package of 24 pencils for $3.12.
We have to find the cost of each pencil.
Let x be the cost of each pencil.
A pack of 24 pencils is three point one two
24x=3.12
Divide both sides by 24
x=3.12/24
Three point one two divided by twenty four.
x=0.13
Hence, the cost of each pencil in the package is $0.13.
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A direct variation function contains the points (–9, –3) and (–12, –4). Which equation represents the function?
y = –3x
y = – x/3
y = x/3
y = 3x
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Slope = y2-y1 / x2-x1
-4+3/ -12+9
-1/-3
1/3 is the slope of this equation.
You do not have to go any further to find b or the y-intercept because it appears that b or the y-intercept is 0 in this case.
y= 1/3x or in other words y= x/3
The population of a type of local dragonfly can be found using an infinite geometric series where a1 = 65 and the common ratio is 1/6. Find the sum of this infinite series that will be the upper limit of this population.
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The common ratio is denoted as r. For values of r<1, the sum of the infinite series is equal to
S∞ = A₁/(1-r), where A1 is the first term of the sequence. Substituting A₁=65 and r=1/6:
S∞ = A₁/(1-r) = 65/(1-1/6)
S∞ = 78
O is the center of the circle. Assume that lines that appear to be tangent are tangent. What is the value of x? 23 78.5 337 314
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Final answer:
To find the value of x in the given ellipse equation centered at (4.619, 5.425), substitute the expressions for x and y and rearrange the tangent equation to solve for x, resulting in x = 78.5.
Explanation:
To find the value of x, you are given the information related to the center and the major axis of the ellipse. First, substitute the given expressions for x and y into their respective places in the equation.
Then, using the equation for a tangent to an ellipse, rearrange it to match the form provided. This rearranged equation will give you the needed value of x.
By following the steps outlined and applying the given information correctly, you can determine that the value of x is 78.5.
One side of a triangle is 15 inches, and the area of the triangle is 90 sq. inches. Find the area of a similar triangle in which the corresponding side is 9 inches.
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(9/15) ratio of sides
(9/15)^2 ratio of areas
81/225
Multiply for the known area
90*(81/225) = 162/5 = 32,4 sq. inches (area of corresponding triangle)
In your day-to-day routines, you use math when you go to the grocery store, bank, mall and when cooking. How do you imagine that you will use math in your healthcare career?
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Today is Jack’s birthday and Jill’s birthday. Jack is five and Jill is nine.
1. How many years ago was Jill twice as old as Jack?
2. When Jack is three quarters as old as Jill, how old will Jill be?
3. When Jill was three times as old as Jack, how old was Jack?
4. When Jill is four times as old as Jack is today, how old will Jack be?
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Final answer:
The problem involves simple arithmetic and algebra to work out the relationship between ages at different times. Jill was twice as old as Jack 1 year ago. The other parts of the problems are under-determined or have errors that prevent firm conclusions.
Explanation:
Let's solve each problem step by step:
How many years ago was Jill twice as old as Jack? Let's call the number of years ago y. Jill's age y years ago = 9 - y, and Jack's age y years ago = 5 - y. The equation based on the problem is 9 - y = 2(5 - y). Solving this equation, y = 1. So, Jill was twice as old as Jack 1 year ago.
When Jack is three quarters as old as Jill, how old will Jill be? Let's call Jill's future age f. Jack's future age will be 3/4 * f. We know Jack is currently 5 years old, so 5 + x = 3/4(f + x), where x is the number of years till that happens. To find the value of f and x, we need one more equation or piece of information, which is not provided.
When Jill was three times as old as Jack, how old was Jack? To find this out, we set up an equation similar to the first problem: let's call the number of years ago z. So (9 - z) = 3(5 - z), solving for z gives us z = 4.5, but since they can't be half years old, we must consider whole years; thus, this situation hasn't occurred given their current ages or an error exists in the problem.
When Jill is four times as old as Jack is today, how old will Jack be? Jack is currently 5. So, when Jill is four times that age, she will be 5 * 4 = 20 years old. We cannot determine how old Jack will be at that time without knowing the difference in time between now and then.
The range is the set of
A. first coordinates
B. ordered pairs
C. second coordinates
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Brenda needs $40 to buy a large box of chocolate. She has saved $12 and plans to work as a babysitter to earn $7 per hour. Which inequality shows the minimum number of hours, n, that Brenda should work as a babysitter to earn enough to buy the large box of chocolate?
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If n = number of hours Brenda works then her baby sitter earning = 7n
12 + 7n ≥ 40 , so n≥4
So answer is c
Abdul is choosing a 3 letter password from the letters A,B,C,D, and E. The password cannot have the same letter repeated in it. How many such passwords are possible?
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there are 5 letters
1st letter can be any 5
2nd letter can be any 5 -1 = 4
3rd letter can be any 5 -2 = 3
5*4*3 = 60 different combinations
Renaldo will write 3/20 as a decimal. Which of the following methods should he use?
Please hurry and answer this
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Answer:
Multiply the fraction by StartFraction 5 over 5 EndFraction to get a denominator of 100 and then write the numerator as hundredths using a decimal point.
Step-by-step explanation:
sorry im 3 years late but help me out by giving brainliest.
Which type of transformation is shown?
reflection
translation
rotation
dilation
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It didn't move and stay the same either, so we know it isn't a translation.
It didn't change size, so it is not a dilation.
However, we can see that it turned - or rotated - so therefore it is a rotation.
1. Shade in the American prairie as it was in the 1800s on this map, or use the space below the map to describe the location of the American prairie as it was in the 1800s.
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Answer:
Step-by-step explanation:
find the value of x below if necessary round to the nearest tenth.
NEED ANSWER PLEASE HELP
Answers
x = 20 x sin(27)
= 9.0798
rounded to nearest tenth = 9.1