James is writing a coordinate proof involving a parallelogram. Knowing that the opposite sides of a parallelogram are congruent, James places his parallelogram on the coordinate plane such that one vertex is at the origin and one side lies along the x-axis. What coordinates should he assign to the fourth vertex of the parallelogram? (2a, a) (2a, a2) (a2, 0) (2a, 2a)
Answers
is ur answer
hope this helps
Answer:-(2a,a) coordinates he should assign to the fourth vertex of the parallelogram.
Explanation:-
Let ABCD be the vertices of the given parallelogram such that A=(0.,0) , B=(a,0) , C(x,y) and D=(a,a)
Construct the diagonals AC and BD of parallelogram ABCD .
We know that diagonals of a parallelogram bisect each other.
⇒ mid point of AC= mid point of BD...(1)
Mid point of BD[tex]=(\frac{a+a}{2},\frac{0+a}{2})=(\frac{2a}{2},\frac{a}{2})=(a,\frac{a}{2})[/tex]........(2)
Mid point of AC[tex]=(\frac{0+x}{2},\frac{0+y}{2})=(\frac{x}{2},\frac{y}{2})[/tex]......(3)
Substitute (2) and (3) in (1), we get
[tex](\frac{x}{2},\frac{y}{2})=(a,\frac{a}{2})\\\Rightarrow\frac{x}{2}=a;\frac{y}{2}=\frac{a}{2}[/tex]
[tex]\Rightarrow\ x=2a\ and\ y=a[/tex]
⇒C=(2a,a)
⇒ (2a,a) coordinates he should assign to the fourth vertex of the parallelogram.
Related Questions
PQ and RS are two lines that intersect at point T, as shown below: Two lines PQ and RS intersect at point T. Angles PTR and STQ are shown congruent. Which statement is used to prove that angle PTR is always equal to angle STQ?
Lines PQ and RS do not have a fixed length.
Angle PTR and angle PTS are supplementary angles.
Lines PQ and RS intersect at an angle less than a right angle.
Angle PTR and angle PTS are complementary angles.
Answers
"Angle PTR and angle PTS are supplementary angles.".
This means that PQ and RS are straight lines, and that their angles follow the properties or supplementary angles, and opposite angles.
This implies the more relevant detail that PTR and STQ are opposite angles, and opposite angles are always equal.
Answer:
B. Angle PTR and angle PTS are supplementary angles.
Step-by-step explanation:
As R, T, S are collinear and PQ intersects RS at T, so ∠RTP and ∠STP are supplementary angles.
[tex]\Rightarrow m\angle RTP+m\angle PTS=180^{\circ}[/tex] -------1
As P, T, Q are collinear and RQ intersects PQ at T, so ∠PTS and ∠QTS are supplementary angles.
[tex]\Rightarrow m\angle PTS+m\angle QTS=180^{\circ}[/tex] ------2
Subtracting equation 1 and 2,
[tex]\Rightarrow m\angle RTP+m\angle PTS-m\angle PTS-m\angle QTS=180^{\circ}-180^{\circ}[/tex]
[tex]\Rightarrow m\angle RTP-m\angle QTS=0[/tex]
[tex]\Rightarrow m\angle RTP=m\angle QTS[/tex]
[tex]\Rightarrow m\angle PTR=m\angle STQ[/tex]
Therefore, to prove that angle PTR is always equal to angle STQ the statement needed is angle PTR and angle PTS are supplementary angles.
What is 27 divided by 735
Answers
Solve for x. 5(x + 1) = 4(x + 8) x = 7 x = 17 x = 27 x = 37
Answers
5x = 4x + 32 - 5
5x = 4x + 27
5x - 4x = 27
x = 27
The value of x in 5(x + 1) = 4(x + 8) is 27.
What is 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. LHS = RHS is a common mathematical formula.
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:
5(x + 1) = 4(x + 8)
Now, applying distributive property
5x+ 5 = 4x+ 32
5x - 4x = 32- 5
x= 27
Hence, the value of x is 27.
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An organization founded by businesses in a specific industry for the purpose of collaboration between companies is called a(n):
Answers
Answer:
The answer is trade association.
Step-by-step explanation:
Such organizations are founded to encourage trade and collaboration between companies. These are also known as industry trade group or business association and is funded by businesses that operate in a particular industry.
Which expression is equal to 3√54−4√24 ?
Answers
Final answer:
The expression 3√54−4√24 simplifies to √6 after factoring out the perfect squares under the radicals and combining like terms.
Explanation:
The student's question requires simplifying the expression 3√54−4√24. To simplify a square root, we look for perfect squares that are factors of the number under the root. For √54, we can notice that 54 = 9 * 6, and since √9 is a perfect square, we have 3√54 = 3*√9*√6 = 3*3*√6 = 9√6. Similarly, for √24, it is 24 = 4 * 6, so √24 = √4*√6 = 2*√6, and thus -4√24 = -4*2*√6 = -8√6. Combining these two results, we have 9√6− 8√6, which simplifies to √6. Therefore, the simplified expression is √6.
Lisa and Bart spin this spinner 60 times the result are below/ black=17 blue=15 orange=21 purple=7 a. What is the experimental probability of a spin of orange? B which color had an experimental probability that matched its theoretical probability
Answers
b) blue because each color has the theoretical probability of 25%. 15÷60=0.25
[tex]\text{Answer: a) }P(\text{ getting an orange )}=\frac{7}{20}[/tex]
b) Blue color had an experimental probability that matched its theoretical probability.
Explanation:
Since we have given that
Number of times this spinner is spinned = 60
Number of times black occur = 17
Number of times blue occur = 15
Number of times orange occur = 21
Number of times purple occur = 7
a) So, Experimental probability of a spin of orange is given by
[tex]P(\text{ getting an orange }=\frac{\text{ Number of times orange occur}}{\text{total number of times the spinner spins}}\\\\P(\text{ getting an orange})}=\frac{21}{60}=\frac{7}{20}[/tex]
b) which color had an experimental probability that matched its theoretical probability.
According to theoretical probability ,
Every event must have equal probability, i.e. [tex]\frac{1}{4}[/tex]
And,
[tex]P(\text{ getting blue color)}=\frac{15}{60}=\frac{1}{4}[/tex]
So, Blue color had an experimental probability that matched its theoretical probability.
If BC = 7 and CD = 24, find AC.
Answers
Answer:
2√42 ≈ 12.961
Step-by-step explanation:
All of the right triangles are similar, so ...
short leg/long leg = BC/AC = AC/CD
AC² = BC·CD = 7·24 = 168
AC = √168 = 2√42
pease help
1) where is the y intercept of any direct variation equation?
2) circle the equation that is a direct variation equation.
1) y=7-3x
2)3x-7y=1
3) 3x-7y=0
4) 3y=7x-1
3) what is the direct variation equation if y=8 and x = 4?
4) what is the direct variation equation if y =-5 and x = 7 /
Answers
1. where is the y intercept of any direct variation equation?
A direct variation equation is one in which the general form is:
y = k x
where k is the constant of proportionality
The y-intercept in this case is therefore zero so it is located on the origin (0, 0)
2. The equation which is a direct variation is:
3) 3x-7y=0
Because we can write this as:
y = (3/7) x
3. what is the direct variation equation if y=8 and x = 4?
We solve for the value of k since we know that:
k = y/x
k = 8/4 = 2
So the equation is:
y = 2x
4. what is the direct variation equation if y =-5 and x =
7?
We also solve for the value of k since we know that:
k = y/x
k = -5/7
So the equation is:
y = (-5/7) x
Kathryn draws three pairs of intersecting lines. In each figure, she measures a pair of angles. What is a reasonable conjecture for Kathryn to make by recognizing a pattern and using inductive reasoning? When a pair of lines intersect, the vertical angles are acute. When a pair of lines intersect, all of the angles formed are right angles. When a pair of lines intersect, the vertical angles are congruent. When a pair of lines intersect, all of the angles formed are congruent.
Answers
1) Vertical angles (or opposite angles) are congruent. In this case, vertical angles could be acute or obtuse depending on the position of the lines.
2) The second case is the exception when all the angles are equal. It means that the lines are perpendicular.
3) Again back to the first case, vertical angles are equal or congruent in other words.
4) And again back to the second case when the lines are perpendicular, then all the angles that formed are equal to each other.
You can observe all the cases in the picture attached below.
The reasonable conjecture for Kathryn to make by recognizing a pattern and using inductive reasoning is:
When a pair of lines intersect, the vertical angles are congruent.
Step-by-step explanation:The vertical angles are the opposite angles that are formed by the intersection of two lines. They are also known as Vertically opposite angles.
We know that when a pair of lines intersect then the vertical angles are always congruent.
However the measure of the angles may be acute or obtuse or right angle.
The same could be seen with the help of the figure attached to the answer.
Calculate the average rate of change for the given graph from x = –2 to x = 0 and select the correct answer below.
Answers
3
The equation you use to find the average rate of change, or slope, is [tex] \frac{y_{2}-y_{1}}{x_{2}-y_{1}} [/tex]
the average rate of change for the given graph from x = -2 to x = 0 is:
3
Step-by-step explanation:We know that the average rate of the graph of the function f(x) form x=a to x=b is calculated by the formula:
[tex]Average\ Rate\ of\ change=\dfrac{f(b)-f(a)}{b-a}[/tex]
Here we have:
a= -2 and b=0
Also, from the graph of the function we have:
f(a)=0 and f(b)=6
Hence, the average rate of change of the graph from x= -2 to x=0 is:
[tex]Average\ Rate\ of\ change=\dfrac{6-0}{0-(-2)}\\\\i.e.\\\\Average\ Rate\ of\ change=\dfrac{6}{2}\\\\i.e.\\\\Average\ Rate\ of\ change=3[/tex]
Hence, the answer is: 3
What is the coefficient of the fourth term in the expansion of (x + 3)4?
Answers
Final answer:
The coefficient of the fourth term in the expansion of (x + 3)⁴ is calculated using the binomial theorem, which results in a coefficient of 108.
Explanation:
To find the coefficient of the fourth term in the expansion of (x + 3)⁴, we can use the binomial theorem. The binomial theorem states that when a binomial is raised to a power, the expansion consists of terms in the form of [tex]C(n, k) \times a^{n-k} \times b^k[/tex], where C(n, k) is the binomial coefficient. In our case a = x and b = 3, and n = 4.
For the fourth term where k = 3, the term would be [tex]C(4, 3) \times x^{4-3} \times 3^3[/tex]. The binomial coefficient C(4, 3) is equal to 4 because there are four ways to choose three items out of four. Therefore, the coefficient is 4 × 3³ = 4 × 27 = 108. So, the coefficient of the fourth term in the expansion of (x + 3)⁴ is 108.
A flowchart proof presents a logical argument using blank_____.
Answers
Answer: A flowchart proof presents a logical argument using boxes and arrows.
Step-by-step explanation:
We know that a flowchart proof is a way of representation of a mathematical proof that includes a logical series of statements ( or can say arguments) in boxes with connecting arrows.
i.e. we use boxes and arrows in a flow chart proof.
By the definition of flowchart proof, the complete sentence will be : A flowchart proof presents a logical argument using boxes and arrows.
WHAT IS 6.4 DIVIDED BY 43.52
Answers
Final answer:
To divide 6.4 by 43.52, the approximate quotient is 0.09238.
Explanation:
To divide 6.4 by 43.52, you can simply perform the division operation. Here are the steps:
Set up the division problem as follows: 6.4 ÷ 43.52.Divide the decimal part of the dividend (6.4) by the divisor (43.52). The quotient will have the same number of decimal places as the dividend. In this case, divide 4 by 43, which equals approximately 0.09238.Therefore, 6.4 divided by 43.52 is approximately 0.09238.
Cassandra is trying to think of a good way to keep her financial records. She makes a lot of purchases, using cash, debit cards, and credit cards about equally. When she gets home every day, she tends to be very tired and doesn’t like to do a lot of organized thinking. She tends to lose individual pieces of paper if she doesn’t file them immediately. What might be a good method for Cassandra to use? a. Recording all of her daily expenditures in an organizational computer program. b. Keeping and collecting receipts for everything she buys. c. Tracking and collecting her bank and credit statements every month. d. Carrying a notebook and immediately recording all of her transactions in it.
Answers
Answer:
the answer is d
Step-by-step explanation:
everybody else keeps getting it wrong, the answer is d
(HURRY!!!)
What is the slope of a line that is perpendicular to the line shown on the graph?
A)-2
B)-1/2
C)1/2
D)2
Answers
slope = (1+1)/(0+1) = 2
perpendicular lines, slope is opposite and reciprocal
so slope = -1/2
answer
B)-1/2
Answer:
slope of perpendicular line = [tex]-\frac{1}{2}[/tex]
Step-by-step explanation:
Find the slope of a line that is perpendicular to the line shown on the graph
To find slope of the given line , we pick two points from the graph
(0,1) and (1,3)
[tex]slope = \frac{y_2-y_1}{x_2-x_1} =\frac{3-1}{1-0} = 2[/tex]
Slope of given line = 2
slope of perpendicular line = negative reciprocal of slope of given line
slope of perpendicular line = [tex]-\frac{1}{2}[/tex]
Paul has a tack stuck in his four-wheeler tire. If the tire has a diameter of 36 inches, how far does the tack travel in 62° of rotation?
Answers
Wheel diameter = 36 inches
Rotation = 62°
The radius is diameter/2 = 36/2 = 18 inches
Note that 1 revolution = 360° = 2π radians
Therefore
62° rotation = (62/360)*(2π) = 1.0821 radians.
The distance that the tack travels is
(18 in)*(1.0821 rad) = 19.478 in
Answer: 19.48 inches (approximately 19.5 inches)
If two chords are the same distance from the center of a circle then they are
Answers
The value for the angles is not provided.
Therefore, i'd say the answer is congruent.
Hope This Helps You!
Good Luck :)
- Hannah ❤
If two chords are the same distance from the center of a circle then they are congruent.
Given that, two chords are the same distance from the center of a circle.
What is the chord on a circle?The chord of a circle is a line that connects two points that are located on the circumference of the circle. These two points can be located anywhere on the same circumference.
Chords are equidistant from the center if and only if their lengths are equal. Equal chords are subtended by equal angles from the center of the circle.
Hence, if two chords are the same distance from the center of a circle then they are congruent.
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Ed counts 23 black cars, 9 red cars, 17 blue cars, 25 white cars and 21 silver cars during 20 minutes of watching. How many more white and blue cars are there than silver and red cars?*
Answers
9 red cars
17 blue cars
25 white cars
21 silver cars
(white cars + blue cars) - (sliver cars + red cars)
(25 + 17) - (21 + 9)
(42) - (30)
12 more blue and white cars
What is the area of a triangle whose vertices are J(−2, 1) , K(4, 3) , and L(−2, −5) ?
Enter your answer in the box.
Answers
we know that
The Heron's Formula is a method for calculating the area of a triangle when you know the lengths of all three sides. The formula is equal to
[tex]Area=\sqrt{p(p-a)(p-b)(p-c)}[/tex]
where
a,b,c -----> are the lengths of the sides of a triangle
p ----> is half the perimeter
we have
[tex]J(-2,1)\ K(4,3)\ L(-2,-5)[/tex]
The formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Step 1
Find the distance JK
[tex]J(-2,1)\ K(4,3)[/tex]
Substitute the values in the formula of distance
[tex]d=\sqrt{(3-1)^{2}+(4+2)^{2}}[/tex]
[tex]d=\sqrt{(2)^{2}+(6)^{2}}[/tex]
[tex]dJK=\sqrt{40}\ units[/tex]
Step 2
Find the distance KL
[tex]K(4,3)\ L(-2,-5)[/tex]
Substitute the values in the formula of distance
[tex]d=\sqrt{(-5-3)^{2}+(-2-4)^{2}}[/tex]
[tex]d=\sqrt{(-8)^{2}+(-6)^{2}}[/tex]
[tex]dKL=10\ units[/tex]
Step 3
Find the distance JL
[tex]J(-2,1)\ L(-2,-5)[/tex]
Substitute the values in the formula of distance
[tex]d=\sqrt{(-5-1)^{2}+(-2+2)^{2}}[/tex]
[tex]d=\sqrt{(-6)^{2}+(0)^{2}}[/tex]
[tex]dJL=6\ units[/tex]
Step 4
Find the perimeter of the triangle
we know that
the perimeter of a triangle is the sum of the length sides of the triangle
so
[tex]P=dJK+dKL+dJL[/tex]
substitute the values
[tex]P=\sqrt{40}\ units+10\ units+6\ units=22.32\ units[/tex]
Find half the perimeter
[tex]p=22.32/2=11.16\ units[/tex]
Step 5
Find the area of the triangle
Applying the Heron's Formula
[tex]Area=\sqrt{p(p-a)(p-b)(p-c)}[/tex]
we have
[tex]p=11.16\ units[/tex]
[tex]a=dJK=\sqrt{40}\ units=6.32\ units[/tex]
[tex]b=dKL=10\ units[/tex]
[tex]c=dJL=6\ units[/tex]
substitute the values
[tex]Area=\sqrt{11.16(11.16-6.32)(11.16-10)(11.16-6)}[/tex]
[tex]Area=\sqrt{11.16(4.84)(1.16)(5.16)}[/tex]
[tex]Area=17.98\ units^{2}[/tex]
[tex]Area=18\ units^{2}[/tex]
therefore
the answer is
The area of the triangle is [tex]18\ units^{2}[/tex]
The area of the triangle with given vertices is 18 units squared.
Explanation:To find the area of a triangle with given vertices, we can use the formula:
Area = 1/2 * |(x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2))|
Plugging in the coordinates of the vertices:
A = 1/2 * |(-2 * (3 - (-5)) + 4 * (-5 - 1) + (-2) * (1 - 3))|
Simplifying the expression:
A = 1/2 * |(-2 * 8 + 4 * (-6) + (-2) * (-2))|
A = 1/2 * |(-16 - 24 + 4)|
A = 1/2 * |-36|
A = 1/2 * 36
A = 18
Therefore, the area of the triangle is 18 units squared.
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Paulo scored "x" on his first math test, then scored 10 points higher on his second, scored 5 points lower on the third than the second, and scored half as well on the fourth test as the second. if his average for the four tests is 75 points, what did he score on the second test?
Answers
[tex] \frac{x+(x+10)+(x+10-5)+ \frac{x+10}{2} }{4} = 75 [/tex]
Then we simplify to get this:
[tex] \frac{(3x+15)+ \frac{x+10}{2} }{4} = 75[/tex]
Then we get common denominators and add:
[tex] \frac{ (\frac{6x+30}{2})+ (\frac{x+10}{2}) }{4} = 75[/tex]
[tex] \frac{ \frac{7x+40}{2} }{4} = 75[/tex]
Then reciprocalize the main denominator and simplify:
[tex]\frac{7x+40}{2} * \frac{1}{4} = 75[/tex]
[tex] \frac{7x+40}{8} = 75[/tex]
And then solve for x:
[tex]7x + 40 = 600[/tex]
[tex]7x = 560[/tex]
[tex]x = 80[/tex]
Since he scored ten points higher than x (x is what he earned in the first test), we can add:
[tex]80 +10 = 90[/tex]
So, he got 90 points on his second test.
In what time will $400 amount to $512 if the simple interest is calculated at 14% p.a.
Answers
The time is 2 years:
Important variables to know:
A= Amount
P = Principal
I = simple Interest
T = time in years
R = rate in years
Formulas:
A = P + I
I = PRT
What we have? Amount ($512), Principal ($400), Rate (14%)
What we need? Time and Interest (simple interest)
So, first let's find the interest.
512 = 400 + I
Subtract 400 from both sides.
I = 112
Then plug that into the second formula:
112 = 400*.14(T)
Multiply 400*.14= 56
112 = 56T
Divide both sides by 56
T = 2 years
30 POINTS!!
Which construction correctly shows how to bisect ∠X?
Answers
An angle bisector is a ray, segment, or line that divides a given angle into two angles of equal measure. Therefore, the correct answer is option C.
What is an angle?An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.
An angle bisector is defined as a ray, segment, or line that divides a given angle into two angles of equal measures.
Steps to Construct an Angle Bisector:
Step 1: Draw any angle, say ∠ABC.
Step 2: Taking B as the center and any appropriate radius, draw an arc to intersect the rays BA and BC at, say, E and D respectively. (Refer to the figure below)
Step 3: Now, taking D and E as centers and with the same radius as taken in the previous step, draw two arcs to intersect each other at F.
Step 4: Join B to F and extend it as a ray. This ray BF is the required angle bisector of angle ABC.
Step 2: Taking B as the center and any appropriate radius, draw an arc to intersect the rays BA and BC at, say, E and D respectively. (Refer to the figure below)
Therefore, option C is the correct answer.
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Kaitlin is on her way home in her car. She has driven 30 miles so far, which is two-thirds of the way home. What is the total length of her drive?
Answers
30/x to 2/3
30 x 3 = 90
90/2
45 miles
Which line is parallel to line r?
line p
line q
line s
line t
Answers
Hope this helps
Use the unit circle to find tan sin 90
a.1
b.0
c.-1
d.undefined
Answers
The answers are [tex]a[/tex] and [tex]d[/tex] respectively.
To evaluate tan(sin(90°)), first determine sin(90°) which equals 1. However, tan(1) is not a standard unit circle value, and if the question intended to find tan(90°), this would be undefined.
The correct option is (d).
The question is asking to use the unit circle to find the value of tan(sin(90°)).
Firstly, the sin(90°) on the unit circle is 1, as the sine function corresponds to the y-coordinate of the unit circle at that angle. Therefore, sin(90°) = 1.
Now, we need to find the tangent of this value, which is tan(1). However, tan(1) is not solvable by standard unit circle values, so it seems we may have a misunderstanding in the question. If the intention was to find tan(90°) instead, then the answer would be undefined as the tangent function at 90 degrees is undefined due to division by zero.
Find the first six terms of the sequence.
a1 = 4, an = 2 • an-1
Answers
You are asked to draw an equiangular rhombus, an equilateral rectangle, and a parallelogram with four right angles. will all three figures be squares?
Answers
All the three figures given in the problem cannot be squares.
What is a parallelogram?A parallelogram is a type of quadrilateral of which the opposite sides are equal and parallel. A diagonal of a parallelogram divides it into two congruent triangles.
Given that,
There are an equiangular rhombus, an equilateral rectangle, and a parallelogram with four right angles.
They can be explained one by one as follows,
(a) A rhombus has all the four sides as equal and its opposite sides are parallel.
When all the angles of a rhombus becomes equal, its each angle is a right angle.
It implies that it will have all angles equal to right angle and all sides are equal as well.
Thus, an equiangular rhombus is a square.
(b) A rectangle has all its angle equal to right angle.
Opposite sides are equal and parallel.
When all the sides become equal, it will be a square.
(c) A parallelogram has its opposite sides as equal and parallel.
When all the angles become right angles, it can be a rectangle.
Hence, an equiangular rhombus and an equilateral rectangle can be a square but a parallelogram with four right angles cnnot be so.
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What are the x and y intercepts of the line described by this equation? 4x-3y=12.3
Answers
4x-3(0)=12.3
4x=12.3
x=12.3/4
x=3.075 (x-intercept)
y-intercept is when x=0
4(0)-3y=12.3
-3y=12.3
y=12.3/-3
y=-4.1 (y-intercept)
Hope I helped :)
so; 4x - 3y = 12.3 will be
-3y = 12.3 - 4x
rearrange so it will be easy to isolate your y.
-3y = -4x + 12.3
divide both sides by -3
-3y/-3 = -4x/-3 + 12.3/-3
y = 4x/3 - 4.1
so: slope 'm' = 4x/3
y-intercept = -4.1
x-intercept = 0
drag each label to the correct location on the table each label can be used more than once but not all labels will be used
Answers
this is the question...
Write an expression that represents "the difference of eight and two, added to x"