Answer:Triangles BPA and DPC are congruent is used to prove that ABCD is a parallelogram.
Explanation:Here, we have given a quadrilateral ABCD in which diagonals AC and BD bisect each other.
If P is a an intersection point of these diagonals
Then we can say that, AP=PC and BP=PD ( by the property of bisecting)
So, In quadrilateral ABCD,
Let us take two triangles, [tex]\triangle BPA[/tex] and [tex]\triangle DPC[/tex].
Here, AP=PC
BP=PD,
[tex]\angle APB=\angle DPC[/tex] ( vertically opposite angles.)
So, By SAS postulate,[tex]\triangle BPA\cong \triangle DPC[/tex]
Thus AB=CD ( CPCT).
Similarly, we can prove, [tex]\triangle APD\cong \triangle BPC[/tex]
Thus, AD=BC (CPCT).
Similarly, we can get the pair of congruent opposite angle for this quadrilateral ABCD.
Therefore, quadrilateral ABCD is a parallelogram.
Note: With help of other options we can not prove quadrilateral ABCD is a parallelogram.
The congruence of triangles BPA and DPC, proven through the Side-Angle-Side postulate or other congruency postulates, can be used to prove that quadrilateral ABCD is a parallelogram when diagonals AC and BD bisect one another.
The statement used to prove that quadrilateral ABCD is a parallelogram when diagonals AC and BD bisect one another is that triangles BPA and DPC are congruent. The congruence of these triangles can be shown through the Side-Angle-Side (SAS) postulate or other congruency postulates depending on a given figure, and this property that diagonals bisect each other is a defining trait of a parallelogram. Therefore, by showing the congruence of triangles BPA and DPC, we can deduce that ABCD is a parallelogram.
Name four coplanar points
What is the slope ? Thanks
What are the coordinates of the vertices of the triangle under the translation (x, y) mc014-2.jpg (x - 1, y - 3)?
(-4, 5), (0, 0), (4, 5)
(0, -8), (-1, -1), (-5, -4)
(5, -4), (0, 0), (5, 4)
(-8, 0), (-1, -1), (-4, -5)
After applying the translation (x - 1, y - 3), the vertices of the triangle originally at (-4, 5), (0, 0), and (4, 5) will move to new locations (-5, 2), (-1, -3), and (3, 2).
Explanation:The question is about translation in mathematics, specifically in geometry. A translation is a function that moves every point a constant distance in a specific direction. If we have a point at coordinates (x, y), a translation of the form (x - a, y - b) will shift that point a units to the left and b units down:
The point (-4, 5) will shift to (-4 - 1, 5 - 3) = (-5, 2)The point (0, 0) will shift to (0 - 1, 0 -3) = (-1, -3)The point (4, 5) will shift to (4 - 1, 5 - 3) = (3, 2).So, the vertices of the triangle after the translation (x - 1, y - 3) will be (-5, 2), (-1, -3), and (3, 2).
Learn more about Translation here:https://brainly.com/question/38241586
#SPJ12
Alinethatincludesthepoint(6, 3)hasaslopeof 2 . what isitsequationin slope -intercept form?
y=2x-3 is the equation of line that includes the point (6, 3) has a slope of 2
What is slope intercept form of line?The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
We need to find the equation of line that includes the point (6, 3) has a slope of 2.
y minus y one equal to m time of x minus x one.
(y-y₁)=m(x-x₁)
x₁=6,y₁=3 and m is 2
y-3=2(x-3)
Apply distributive property on right hand side.
y-3=2x-6
Shift -3 to the RHS side
y=2x-6+3
y=2x-3
Hence y=2x-3 is the equation of line that includes the point (6, 3) has a slope of 2
To learn more on slope intercept form click:
https://brainly.com/question/9682526
#SPJ5
Penny had $117, which is 9 times as much money as Kari had. How much money did Kari have?
Final answer:
Kari had $13. We found this by dividing Penny's amount, $117, by 9, since Penny's amount is 9 times greater than Kari's.
Explanation:
The question is asking us to determine how much money Kari had if Penny had $117, which is 9 times as much as what Kari had. To do this, we need to perform a division, because if Penny's amount is 9 times Kari's, we can find Kari's amount by dividing Penny's $117 by 9.
To solve for K, divide both sides of the equation by 9: K = $117 / 9.
Therefore, Kari had $13.
What does an exponent in front of a square root mean?
The most efficient first step in the process to factor the trinomial 4x3-20x2+24x
A. factor out –1
B. factor out 4
C. factor out 4x
D. factor out (x – 3)
Factor out 4x from the given trinomial. Therefore, option C is the correct answer.
What are factors of polynomial?The factors are the polynomials which are multiplied to produce the original polynomial.
The given trinomial is 4x³-20x²+24x.
Here, 4x(x²-5x+6)
= 4x(x²-3x-2x+6)
= 4x[(x(x-3)-2(x-3)]
= 4x(x-3)(x-2)
Therefore, option C is the correct answer.
To learn more about the factorisation of polynomial visit:
https://brainly.com/question/16789195.
#SPJ3
Jan has 3 1/3 feet of rope to use on a camping trip. Assume 1 foot = 30.48 centimeters. What is the best estimate of the centimeters of rope Jan has?
Which equations represent the line that is parallel to 3x − 4y = 7 and passes through the point (−4, −2)? Check all that apply.
y = -3/4x + 1
3x − 4y = −4
4x − 3y = −3
y – 2 = –3/4(x – 4)
y + 2 = 3/4 (x + 4)
Answer:
Option B and E
Step-by-step explanation:
A line is given as 3x - 4y = 7
We have to find the equation of a line parralel to the given line which passes through point (-4, -2).
Let the equation is y = mx + c
Line parallel to 3x - 4y = 7 will have same slope
3x - 4y = 7
-4y = 7 - 3x
4y = 3x - 7
y = [tex]\frac{1}{4}[/tex] (3x - 7 ) ≈ [tex]\frac{3}{4}[/tex]x - [tex]\frac{7}{4}[/tex]
So slope of the line will be m = [tex]\frac{3}{4}[/tex]
Since the given line passes through (-4, -2)
So we put the values in y = mx + c to get the value of c.
-2 = [tex]\frac{3}{4}[/tex] (-4 ) + c
-2 = -30 +c
c = 3 - 2 = 1
Therefore, equation will be
y = [tex]\frac{3}{4}[/tex]x + 1 ----------(1)
We further solve equation (1)
4y = 3x + 4
3x - 4y = -4 ---Option B
By solving the equation (1) in other way
y + 2 = [tex]\frac{3}{4}[/tex]x + 1 + 2
[tex]\frac{3}{4}[/tex]x + 3
y + 2 = [tex]\frac{3}{4}[/tex] (x+4) --Option E
Option B and E are the answers.
Vincent has cut three pieces of rope to complete a science project. two pieces are of equal length. the third piece is one-quarter the length of each of the others. he cut the three pieces from a rope 54 meters long without any rope left over. find the number of meters in each piece.
Bret saw a coat on sale for $28.55 it was originally priced at $33.59 what was the percent decrease in the price of the coat
There is a line whose slope is 5 and whose y intercept is 7 what is its equation in slope intercept form ?
Write your answer using integers proper fractions and improper fractions in simplest form
The equation of the line with a slope of 5 and a y-intercept of 7 is y = 5x + 7.
Explanation:The equation of a line in slope-intercept form is given as y = mx + b, where m is the slope of the line and b is the y-intercept. Given that the slope (m) is 5 and the y-intercept (b) is 7, the equation of the line can be written as y = 5x + 7. This equation tells us that for every increase of 1 on the x-axis, the value of y rises by 5 units, and the line crosses the y-axis at the point (0, 7).
The weekly revenue for a company is r equals negative 3 p squared plus 70 p plus 988r=−3p2+70p+988, where p is the price of the company's product. use the discriminant to find whether there is a price for which the weekly revenue would be $18001800.
EXPERTS/ACE ONLY!! explain! Ill mark as brainlist!!
Graph the function by the table. Is the function linear or nonlinear?
A. Nonlinear
B. Linear
Answer:
Option A - Non-linear
Step-by-step explanation:
Given : Graph the function by the table.
x y
1 12.3
2 19.6
3 26.6
4 34.2
5 41.5
To find : Is the function linear or nonlinear?
Solution :
The function is linear when there slopes are equal.
So, we find the slope of the points.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Taking point, [tex](x_1,y_1)=(1,12.3)[/tex] and [tex](x_2,y_2)=(2,19.6)[/tex]
[tex]m=\frac{19.6-12.3}{2-1}[/tex]
[tex]m=\frac{7.3}{1}[/tex]
[tex]m=7.3[/tex]
Taking point, [tex](x_1,y_1)=(2,19.6)[/tex] and [tex](x_2,y_2)=(3,26.6)[/tex]
[tex]m=\frac{26.6-19.6}{3-2}[/tex]
[tex]m=\frac{7}{1}[/tex]
[tex]m=7[/tex]
We have seen that slope between points are not equal.
Therefore, The given points are non-linear.
So, Option A is correct.
Factor completely 5c5 + 60c4 + 180c3.
Classify the variable according to the set of numbers that best describes its values, the amount of money m spent is a vending machine. The answers I can chose are. A rational numbers, B Irrational numbers, C integers, D natural numbers
The variable will be a natural number according to the set of numbers that best describes its values, the amount of money m spent is a vending machine option (D) is correct.
What is the number?A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.
It is given that:
The amount of money m spent is a vending machine.
As we know, in the vending machine we cannot insert money in negative quantity.
And integers range from (-∞, ∞)
The real number starts from 1 and continues 2, 3, 4,5 ,6 and so on
Thus, the variable will be a natural number according to the set of numbers that best describes its values, the amount of money m spent is a vending machine option (D) is correct.
Learn more about the number here:
brainly.com/question/17429689
#SPJ2
URGENT: Find two functions f(x) and g(x) such that f[g(x)] =x but g[f(x)] does not equal x.
How do I find 680% as a fraction mixed number or whole number in simplest form
To convert 680% to a fraction, write it as 680/100 and simplify to 34/5. This improper fraction can also be written as the mixed number 6 [tex]\frac{4}{5}[/tex].
To convert 680% to a fraction or mixed number, follow these steps:
First, write the percent as a fraction with a denominator of 100. So, 680% becomes 680/100.
Next, simplify the fraction by finding the greatest common divisor (GCD) of 680 and 100. The GCD of 680 and 100 is 20.
Divide both the numerator and the denominator by their GCD:
680 ÷ 20 = 34
100 ÷ 20 = 5
So, 680/100 simplifies to 34/5.
Finally, convert the improper fraction to a mixed number. To do this, divide the numerator by the denominator:
34 ÷ 5 = 6 (with a remainder of 4).
This gives us the mixed number 6 [tex]\frac{4}{5}[/tex].
Therefore, 680% as a fraction is 34/5 and as a mixed number is 6 [tex]\frac{4}{5}[/tex].
An arithmetic series contains 20 numbers. The first number is 102. The last number is 159. Which expression represents the sum of the series?
Answer:
It's B
Step-by-step explanation:
20(102+159/2)
In a paper airplane contest Amanda plane flew 19 ft farther than Darren plane Darren plane flew twice as far ad Rachel plane Rachel plane 20 ft .How far did Amanda plane fly
Answer:
59 ft
Step-by-step explanation:
Given;
Amanda plane flew 19 ft farther than Darren plane Darren plane flew twice as far ad Rachel planeRachel plane 20 ftThen Darren's plane must have flown (2 × 20ft) = 40 ft
Amanda's plane would have flown (40ft + 19ft) = 59 ft
Amanda's plane flew 59 ft far.
The distance of the paper plane thrown by Amanda is given by the equation A = 59 feet
What is an 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.
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 data ,
Let the distance of the paper plane thrown by Amanda be A
Now , the equation will be
The distance of the paper plane thrown by Rachel R = 20 feet
The distance of the paper plane thrown by Darren D = 2 x distance of the paper plane thrown by Rachel R
Substituting the values in the equation , we get
The distance of the paper plane thrown by Darren D = 40 feet
And , Amanda plane flew 19 ft farther than Darren plane Darren plane
Substituting the values in the equation , we get
The distance of the paper plane thrown by Amanda A = 19 + distance of the paper plane thrown by Darren D
On simplifying the equation , we get
The distance of the paper plane thrown by Amanda A = 19 + 40
The distance of the paper plane thrown by Amanda A = 59 feet
Hence , the distance is 59 feet
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ2
Heterogeneous mixtures can be physically separated into their individual components.
True
False
True because their different
PLEASE HELP
Mrs. Williams is deciding between two field trips for her class. The Science Center charges $80 plus $5 per student. The Dino Discovery Museum simply charges $7 per student. For how many students will the Science Center charge less than the Dino Discovery Museum charges?
fewer than 40 students
78 or fewer students
78 or more students
more than 40 students
Two mathematically similar frustums have heights of 20cm and 30cm.
The surface area of the smaller frustum is 450cm².
Calculate the surface area of the larger frustum.
The larger frustum has a surface area of 1516.875cm². This is calculated by first finding the ratio of the heights, then cubing this ratio and finally multiplying the result by the surface area of the smaller frustum.
Explanation:In Mathematics, similar frustums follow a rule in which the ratio of their dimensions is the cube root of their surface area ratio. Since the height of the larger frustum is 30cm, and the height of the smaller one is 20cm, their ratio is 30:20 or 1.5:1.
To find the ratio of the surface areas, you'll want to cube this ratio (1.5 ^ 3 = 3.375).
So, the surface area of the larger frustum is the surface area of the smaller frustum (which is 450cm² ) multiplied by this ratio. In mathematical terms, 3.375 * 450 = 1516.875cm².
Learn more about frustums here:https://brainly.com/question/32863103
#SPJ12
The Ukita family from Japan probably has a greater ecological footprint than the Wu family from China.
True
False
Answer:
True
Step-by-step explanation:
If you look at the different countries ranked based off of the size of their ecological footprint, you will see that Japan is ranked around 5 and china around 10.
This means The average ecological foot print of a person living in Japan is larger than a person living in China.
What is the correct way to name these congruent triangles?
Help!!!
What equation is graphed in this figure?
y − 4 = −1/3 (x + 2)
y − 3 = 1/3 (x + 1)
y + 2 = −3 (x − 1)
y − 5 = 3 (x − 1)
The equation of the line is y + 2 = −3 (x − 1). The correct option is C.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
The points from which the line passes are ( 0,1) and (1,-2). The slope of the line will be calculated as,
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( -2 - 1 ) / ( 1 )
Slope = -3
The equation of the line will be written as,
y - y₁ = m ( x - x₁ )
y +2 = -3 ( x - 1 )
To know more about an equation of the line follow
https://brainly.com/question/18831322
#SPJ3
Please explain
Use a matrix to find solution to the system of equations
{-8x - 8y = -16
6x - 9y = -108
(-6,8)
(6,8)
(8,-6)
(6,-8)
Answer:
Step-by-step explanation:
the right answer is a (-6,8) where x=-6 and y=8
We're going to use Cramer's rule to resolve this question.
First of all, we're going to give a number to the equations:
(1) -8x-8y=-16
(2) 6x-9y=-108
where constant 1=c1=-16 and the constant 2=c2=-108
now we need to find the next determinants:
D: system determinant,Dx and Dy.
now we're going to find "D."
for that, we're going to take the coefficients of x and y in (1) and (2)
x y
D= [tex]\f\left[\begin{array}{ccc}-8&-8\\6&-9\end{array}\right][/tex]
this is how we need to put the matrix, using the numbers next to x and y in the (1) and (2) equation.
to solve this matrix, we need to multiplicate in X, and subtract the results; so for D we have:
(-8*-9)-(6*-8)
72-(-48)=
72+48=120
now we're doing the same process to find Dx and Dy, but in each case, we're going to replace x or y with the constants (the constants are the numbers right to the "=")
to find Dx we're going to use the values of c1 and c2 instead of x
C1&2 y
Dx= [tex]\f\left[\begin{array}{ccc}-16&-8\\-108&-9\end{array}\right][/tex]
Now we do the same as with D
(-16*-9)-(-108*-8)=
144-(864)
144-864=-720
and now for Dy=
x C1&2
Dy= [tex]\f\left[\begin{array}{ccc}-8&-16\\6&-108\end{array}\right][/tex]
= (-8*-108)-(6*-16)=
864-(-96)=
864+96=960
now the last step is to find x and y .
x= [tex]\frac{Dx}{D}[/tex] Y= [tex]\frac{Dy}{D}[/tex]
x= -720/120=-6
y=960/120=8
x=-6 y= 8
answer = (-6,8)
David is taking an economics course in which there will be 4 tests, each worth 100 points. he has scores of 89, 92, and 95 on the first three tests. he must make a total of at least 360 in order to get an
a. what scores on the last test will give david an a?
To get an A, David must score at least 85 on the last test.
David has taken three tests so far, with scores of 89, 92, and 95. To find out what score he needs on the last test to achieve a total of at least 360 points, we first calculate the total points he has accumulated from the first three tests:
[tex]\[ 89 + 92 + 95 = 276 \][/tex]
Now, we subtract this total from the minimum total points required for an A:
Therefore, David needs to score at least 84 points on the last test to reach a total of 360 points. However, since test scores are whole numbers, we round up to the nearest whole number that David can actually achieve on the test. Thus, David needs to score at least 85 on the last test to ensure he gets an A.
A triangle has one angle that measures 15 degrees, one angle that measures 44 degrees, and one angle that measures 121 degrees. what kind of triangle is it
The given triangle can be known as a scalene triangle.
What is a triangle?A triangle is a two dimensional shape bound by three sides. The sum of the interior angles of a triangle is 180°. The longest side of a triangle is always less than the sum of other two sides.
The measures of the different angles are given as 15°, 44° and 121° respectively.
Since, all the angles have different measures.
The given triangle is neither equilateral or isosceles.
Thus, the given triangle is scalene triangle.
Hence, the given triangle can be called as a scalene triangle.
To know more about triangle click on,
https://brainly.com/question/2773823
#SPJ5