Answers
After solving the equation we know ABCD is a parallelogram.
What is parallelogram?
A parallelogram is a two-dimensional shape with four straight sides. All of the sides are equal in length and the opposite sides are parallel. Additionally, opposite angles are also equal. The shape is called a parallelogram because parallel lines are present on either side. Parallelograms can come in many different forms, such as rectangles and rhombuses. The properties of a parallelogram include the fact that the diagonal line that divides the parallelogram into two halves bisects the angles. Additionally, the cross product of the two diagonals is equal to the area of the parallelogram. Parallelograms are used in a variety of areas, including architecture, engineering, and mathematics. Depending on the application, parallelograms can be used to construct a variety of shapes, such as circles and ellipses.
Given: A (2,5), B (7,6), C (6,2), D (1,1)
AB ⇒ A (2,5), B (7,6) = [tex]\sqrt{(x_{2}-x_{1} ) ^{2} +(y_{2}-y_{1} )^{2} }[/tex]
⇒ [tex]\sqrt{(-5+1)^{2}+(-6-2)^{2} }[/tex]
⇒ [tex]\sqrt{(-4)^2+(-8)^{2} }[/tex]
⇒ [tex]\sqrt{16+64} =\sqrt{80}[/tex]
CD ⇒ C (6,2), D (1,1) = [tex]\sqrt{(x_{2}-x_{1} ) ^{2} +(y_{2}-y_{1} )^{2} }[/tex]
⇒ [tex]\sqrt{(7-3)^{2}+(6+2)^{2} }[/tex]
⇒ [tex]\sqrt{(4)^2+(8)^{2} }[/tex]
⇒ [tex]\sqrt{16+64} =\sqrt{80}[/tex]
BC = B (7,6), C (6,2) ⇒ [tex]\sqrt{(x_{2}-x_{1} ) ^{2} +(y_{2}-y_{1} )^{2} }[/tex]
⇒ [tex]\sqrt{(3+5)^{2}+(-2+6)^{2} }[/tex]
⇒ [tex]\sqrt{(8)^{2} +(4)^{2} }[/tex]
⇒ [tex]\sqrt{16+64} =\sqrt{80}[/tex]
AD ⇒ A (2,5), D (1,1) = [tex]\sqrt{(x_{2}-x_{1} ) ^{2} +(y_{2}-y_{1} )^{2} }[/tex]
⇒ [tex]\sqrt{(7+1)^{2}+(6-2)^{2} }[/tex]
⇒ [tex]\sqrt{(8)^{2} +(4)^{2} }[/tex]
⇒ [tex]\sqrt{16+64} =\sqrt{80}[/tex]
As, AB = CD = BC = AD all sides are equal.
Hence proved, ABCD is a parallelogram.
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Related Questions
please help it about calculus
Answers
The question is based on the calculus and the derivative for given equation [tex]t^{4} - 24t^{2} \\ \\[/tex] is t = 0.
What is calculus?Calculus is a discipline of mathematics that focuses on rates of change, to put it simply. For instance, you could wish to determine how quickly an automobile will slow down when it approaches a stop sign. Calculus can assist you in calculating that change. Calculus introduces movement into math, that's correct!
Calculus is a tool used by engineers to calculate things like rates of change and areas; in fact, calculus is the mathematical "backbone" for dealing with problems where variables change with time or some other reference variable. Calculus is concerned with two basic operations: differentiation and integration.
We are given
x(t) = [tex]t^{4} - 24t^{2} \\ \\[/tex]
we need to find its derivative only then we can comment on its increasing decreasing nature
x'(t) = [tex]4t^3 -48t\\\\[/tex]
we will check where derivative is zero
[tex]4t^3 - 48t = 0\\\\4t^2(t-4) = 0\\\\\\t = 0 \\\\t = 4\\[/tex]
hence increasing for all x E R except interval (0,4)
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Find the slope of the line that passes through (1, 1) and (7, 8).
Answers
Answer:
[tex] slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex]
[tex] slope=\frac{8-1}{7-1} [/tex]
[tex] slope=\frac{7}{6} [/tex]
slope = 7/6
Does anyone know the answer?
Answers
Answer:
d = 5m
Step-by-step explanation:
Look at point (1, 5).
When the number of months is 1, the amount in dollars is 5.
The amount in dollars is always 5 times the number of months.
d = 5m
Please help!!! And show your work or not I don’t care I need the answers
Answers
Answer:
Step-by-step explanation:
1. Lin, Tyler, and Jada's information is missing.
2. 9 1/8 = 73/8
1 2/8 = 10/8
73/8 - 10/8 = 63/8.
His shoe length was 63/8 inches.
which age group has more variable finish times
Answers
Answer:
l
v
Step-by-step explanation:
80, 5, 30, 7, and 3,
A recently televised broadcast of a popular television show had a 15 share, meaning that among 5000 monitored households with TV sets in use, 15% of them were tuned to the show. A 0.01 significance level is used to test an advertiser’s claim that among the households with TV sets in use, less than 20% were tuned in to the show. Find the P-value.
1.9998
0.9999
0.0001
0.0002
Answers
The p-value of the given hypothesis is; 0.9999
How to find the p-value of the statistics?The formula for the z-score of proportions is;
z = (p^ - p)/√(p(1 - p)/n)
where;
p^ is sample proportion
p is population proportion
n is sample size
We are given;
p^ = 15% = 0.15
p = 20% = 0.2
n = 5000
Thus;
z = (0.15 - 0.2)/√(0.2(1 - 0.2)/5000)
z = -8.8388
From p-value from z-score calculator, we have;
P(Z < -8.8388) = 1 - 0.0001 = 0.9999
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help me please, please write what i put on the sides too and what i put in the bottom right please and thank youuuuu
Answers
The values obtained after solving the given equation is x = 6 and y = 10.
What is an equation?Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.
This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.
As per the information given in the question,
The given equations are,
-5x + 3y = 0 (i)
7x - 4y = 2 (ii)
Multiply equation (i) by -7 and equation (ii) by 5.
35x - 21y = 0 (iii)
35x - 20y = 10 (iv)
Now, solve the equation for y, because 35x in positive and 35x in negative cancel out each other.
-y = -10
y = 10
Substitute y = 10 in equation (i)
-5x + 3(10) = 0
-5x = -30
x = 30/6
x = 5
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50 POINTS IF ANSWERED PLSS!!!!!
Mr. Hansen has three sticks that measure 5 inches, 10 inches, and 17 inches. If he connects the sticks ends, will the three sticks form a triangle?
Answers
Answer:
This would not form a triangle
Step-by-step explanation:
due to the triangle inequality theorem, in order to find out if three numbers can form a triangle, you have to have each pair of numbers add up to more than the remaining number. The first combination added is 5+10 which is 15, and that is not greater than 17, so the answer is no, this is not a triangle.
hope this helps! :3
Which model represents the equation 6x = 18
Answers
Answer:
top right
Step-by-step explanation:
6x3=18
what is the least amount of money you can spend if you want to increase the computer performance by 25%, assuming that you can improve one or all the
Answers
$150 is the least amount of money you can spend if you want to increase the computer performance by 25%, assuming that you can improve one or all the components in the computer.
What is RAM?RAM is a type of volatile memory, which means that data is only stored there while the chip is powered and is completely erased when the computer is turned off. In gigabytes, RAM memory is measured (GB).
Random access memory is referred to as RAM. Because the data may be swiftly read and updated in any sequence, it is termed random access. Compared to previous storage devices like CD-RWs, which access data in a slower, predetermined order, this is faster.
There are much more methods through which we can improve computer performance but by spending the least amount of money we can do it by upgrading your RAM. We can upgrade the RAM of the system to 8 GB and 16 GB. If we want to upgrade the RAM to 8 GB then it can be done for around $75 and If we want to upgrade the RAM to 16 GB then it can be done for around $150.
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The complete question is as follows:
What is the least amount of money you can spend if you want to increase the computer performance by 25%, assuming that you can improve one or all the components in the computer?
PLS HELP Which function has the same slope as the graph of the function represented by the table.
Answers
The slope of the given function is 0.25. The function that has the same slope is y = 0.25x + 5. Option B is the correct option.
What is a function?
A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Given table is
x 0 1 2 3
y -0.5 -0.25 0 0.25
The slope of a function that passes through the points (x₁, y₁) and (x₂, y₂) is m = (y₂ - y₁)/(x₂ - x₁)
Assume that x₁ = 0, y₁ = -0.5, x₂ = 1, y₂ = -0.25
The slope of the function is [-0.25 - (-0.50)]/(1 - 0) = 0.25
Now compare the equation y = -0.25x - 2 with y = mx + c
m = -0.25
The slope of the function is -0.25.
Now compare the equation y = 0.25x + 5 with y = mx + c
m = 0.25
The slope of the function is 0.25.
Now compare the equation y = 4x - 5 with y = mx + c
m = 4
The slope of the function is 4.
Now compare the equation y = -4x + 34 with y = mx + c
m = -4
The slope of the function is -4.
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Use the reciprocal property to solve for a 36/15 8/a
Answers
Applying reciprocal property the equation 36 / 5 = 8 / a is solved to find the value of a as 10/9
What is reciprocal property?The definition of reciprocal in mathematics is the inverse of a value or a number.
If n is a real number, then 1/n will be n's reciprocal.
Therefore, we must change the number to its upside-down form. For instance, 1 divided by 9 is the reciprocal of 9, or 1/9.
The result of multiplying a number by its reciprocal now equals one. multiplicative Inverse is another name for it.
Similarly, 36 / 5 = 8 / a
the reciprocal is 5 / 36 = a / 8
cross multiplying
5 * 8 = 36 * a
36a = 40
a = 40 / 36
a = 10/9
The value of a is 10/9
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solve each of these equations.
Answers
Answer:
a.) x=6 b.) y=-7 c.) a=0.25
Step-by-step explanation:
a.) 2(3x+2)=2x+28
6x+4=2x+28
subtract 4 on both sides
6x=2x+24
subtract 2x on both sides
4x=24
divide both sides by 4
x=6
b.) 5y+13=-43-3y
add 43 on both sides
5y+56=3y
subtract 5y on both sides
56=-8y
divide both sides by 8
-7=y or y=-7
c.) 4(2a+2)=8(2-3a)
8a+8=16-24a
add 24a on both sides
32a+8=16
subtract 8 on both sides
32a=8
divide both sides by 32
a=0.25
(hope you understood how I solved for each equation..)
In Japan, the ratio of vending machines to people is 1 to 24. In the city of Osaka there are about 2,400,000 people. How many banding machines are there in Osaka?
Answers
From the given ratio, there is a total of 100,000 vending machines in Osaka.
What is the ratio?
By comparing two amounts of the same units, the ratio can be used to calculate how much of one item is included in the other. There are two different categories for ratios. The first is a part-to-part ratio, whereas the second is a part-to-whole ratio.
Given, the ratio of vending machines to people is 1 to 24
That means, for every vending machine, there are 24 people.
In the city of Osaka, there are about 2,400,000 people.
So, the number of vending machines = 2400000/24 = 100000
Hence, there is a total of 100,000 vending machines in Osaka.
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Graph y=1/2x=+1
Use the table or identify m and b if it helps you graph.
Answers
Answer: 1/3
Step-by-step explanation:
50000x6000000000000 what is it?
Answers
Answer: 300000000000000000
Step-by-step explanation:
50000x6000000000000 can be written as 3 times 10^17
So the answer is 300000000000000000
Please answer with the equation
The perimeter of a rectangle is 80 inches. The width of the rectangle is 5 less than triple the width?
Answers
The length is 28.75 inch and width is 11.25 inch.
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:
Perimeter= 80 inches
let the width be x.
length= 3x- 5
Now, perimeter of a rectangle = 2( l+ w)
80= 2( x+ 3x- 5)
40 = 4x -5
45 = 4x
x= 11.25
and, length = 3(11.25)- 5 = 28.75
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A sign made of aluminum is in the shape of a pyramid. The base is a triangle with a base of 3 feet and a height of 5 feet. The height of the sign is 6 feet. The aluminum costs $8 per cubic foot. What is the cost of the sign?
A) $722
B) $240
C) $120
D) $168
Answers
The cost of the pyramid shape sign is $240.
What is a pyramid?A pyramid is a 3D figure that has a base made of a polygon and faces that are all triangular and connected. The conventional shape of a pyramid is created by joining each vertex of the base to a single common tip or apex. In this section, let's study more about pyramids.
We know the volume of a pyramid is (1/3)×length of the bese×width of the base×height.
∴ The volume of the pyramid with base length of 6feet, base width of 3feet and height 5 feet is,
= (1/3)×6×3×5 cubic feet.
= 30 cubic feet.
Given, The aluminum costs $8 per cubic foot.
∴ The total cost of the pyramid is = (30×8) = $240.
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If co(x)= 2/3 and x i in quadrant I, then find exact value for (without olving for x) in(2x)
Answers
If cos x= 2/3 and x is in quadrant I, then the exact value of sin(2x) is (4/3)sin x.
What is trigonometry?A branch of mathematics called trigonometry examines the connections between triangles' angles and sides. It is predicated on the idea of right triangles, where one angle is 90 degrees and two sides are perpendicular to one another. The six fundamental functions of trigonometry—sine, cosine, tangent, cotangent, secant, cosecant. These values of functions can be used to address real-world angle and length issues, such as determining the height of a structure or the distance between two locations. Calculus, geometry, and other areas of mathematics are all strongly connected to trigonometry.Modeling actual phenomena like item motion, wave behaviour, and light dispersion is possible with these functions. Physics, engineering, and astronomy are just a few of the disciplines that use trigonometry extensively.
How to solve?
In quadrant I, cos x = 2/3 and sin x > 0.
sin(2x) = 2sin x cos x
sin(2x) = 2 * 2/3 * (sin x)
sin(2x) = (4/3)sin x
If sin x > 0, then sin(2x) = (4/3)sin x > 0.
The exact value of sin(2x) is (4/3)sin x
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(3+2)to the power of 2 + 4x8*
Pls help asap
Answers
5 to the second power + 4x8
25+4x8
25+32
57
6/22, 3:45 PM
Kris said, "The Rawlings Rockets basketball team does not have any really tall players." These are the players'
heights in inches:
70, 77, 75, 68, 88, 70, and 72.
a. Which number does not seem to fit this set of data? 1
b. Do you agree or disagree with Kris?
2
Answers
Answer:
a. 88
b. I disagree with Kris
Step-by-step explanation:
88 is by far the biggest outlier here being 11 numbers away from the second highest being 77. This means there is one kid that is much higher than the rest of the group.
........ i need help past due
Answers
Part a: y = -6x + 5 is : Not proportional.
Part b: y = 7/8x proportional: proportionality constant = 7/8.
Explain the term proportional relation?Relationships among two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, each variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant.For the stated question;
Part a: y = -6x + 5
To check the proportional relation, put value of 'x' and find the corresponding value of 'y'.
The ratio = y/x must be same.
For x = 1, y = -1
y/x = -1
And, for x = 2, y = 7
y/x = 7/2
Thus, ratio is not equal, Not proportional.
Part b: y = 7/8x
For x = 1, y = 7/8
y/x = 7/8
Now, For x = 2, y = 14/8
y/x = 7/8, both ratios are equal.
Thus, y = 7/8x proportional: proportionality constant = 7/8.
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A shop increased the price of a shirt by 10% , then decided to decrease the price of the shirt by 10%. What was the percent change in price of the shirt. Explain your answer using words
Answers
Answer:
Step-by-step explanation:
1. Increase of 10% in price of shirt.
2. Decrease of 10% in price of shirt.
Hence- both amounts cancel out, therefore there is 0% change in price of shirt as both percentages cancelled out, or we can say nullified each other. Because they added the same amount to the item and then subtracted the same percent leading to no change.
Consider Y= F(x) =2- 3x. using the space determine the equation that represents the inverse of f(x) 
Answers
Answer: [tex]f^{-1}(\text{x}) = \frac{2-\text{x}}{3}\\\\[/tex]
===============================================
Work Shown:
[tex]f(\text{x}) = 2-3\text{x}\\\\\text{y} = 2 - 3\text{x}\\\\\text{x} = 2 - 3\text{y}\\\\\text{x} + 3\text{y} = 2\\\\3\text{y} = 2-\text{x}\\\\\text{y} = \frac{2-\text{x}}{3}\\\\f^{-1}(\text{x}) = \frac{2-\text{x}}{3}\\\\[/tex]
-----------------
Explanation:
The process to find the inverse involves this outline.
Replace f(x) with y.Swap x and y.Solve for y.This process is followed in the "work shown" portion above.
To confirm the answer, let g(x) be the inverse of f(x).
If they were inverses of each other, then these two properties would hold true:
f( g(x) ) = xg( f(x) ) = xHere's the verification for the first part.
[tex]f(\text{x}) = 2-3\text{x}\\\\f(g(\text{x})) = 2-3*g(\text{x})\\\\f(g(\text{x})) = 2-3*\frac{2-\text{x}}{3}\\\\f(g(\text{x})) = 2-(2-\text{x})\\\\f(g(\text{x})) = 2-2+\text{x}\\\\f(g(\text{x})) = \text{x}\\\\[/tex]
I'll let you do the other confirmation.
Triangle ABC is translated 4 units to the right and 3 units down.
What are the coordinates of the new triangle?
Responses
(−2,3),(3,1),(−2,1)
( − 2 , 3 ) , ( 3 , 1 ) , ( − 2 , 1 )
(−2,0),(3,−2),(−2,−2)
( − 2 , 0 ) , ( 3 , − 2 ) , ( − 2 , − 2 )
(0,−2),(−2,3),(2,−2)
( 0 , − 2 ) , ( − 2 , 3 ) , ( 2 , − 2 )
(−6,0),(−6,−2),(−1,−2)
Answers
Hence, the coordinates of the new triangle are [tex]A(2,0),B(7,-2),C(2,-2)[/tex].
What is the coordinates?
A pair of numbers that describe the position of a point on a coordinate plane by using the horizontal and vertical distances from the two reference axes. Usually represented by [tex](x,y)[/tex] the x-value and y-value.
Here given coordinates are
[tex](-2,3),(3,1),(-2,1)\\\\(-2,0),(3,-2),(-2,-2)\\\\( - 2 , 0 ) , ( 3 , - 2 ) , ( - 2 , -2 )[/tex]
Suppose [tex]a[/tex] units on the horizontal and [tex]b[/tex] units on the vertical. Then, the new coordinate become
[tex]A(x,y)=A(x+a,y+b)[/tex]
As per the question triangle [tex]ABC[/tex] is translated [tex]4[/tex] units to the right and [tex]-3[/tex]units down.
So, [tex]a=4,b=-3[/tex] and the coordinates are
[tex]A(-2,3),B(3,1),C(-2,1)\\\\[/tex]
Then,
[tex]A(-2+a,3+b)=A(-2+4,3-3)=A(2,0)\\\\B(3+a,1+b)=B(3+4,1-3)=B(7,-2)\\\\C(-2+a,1+b)=C(-2+4,1-3)=C(2,-2)[/tex]
Hence, the coordinates of the new triangle are [tex]A(2,0),B(7,-2),C(2,-2)[/tex].
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You have two exponential functions. One has the formula h(x) = 3x – 2. The other function, g(x), has the graph shown below.
Which inequality below is true for all points on the indicated interval?
A g( x) ≥ h( x) on the interval –3 ≤ x ≤ 3
B g( x) ≥ h( x) on the interval –2 ≤ x ≤ 2
C g( x) ≤ h( x) on the interval –3 ≤ x ≤ 3
D g( x) ≤ h( x) on the interval –2 ≤ x ≤ 2
Answers
The correct statement regarding the exponential functions g(x) and h(x) is given as follows:
B g( x) ≥ h( x) on the interval –2 ≤ x ≤ 2.
What is an exponential function?The standard definition of an exponential function is given as follows:
y = ab^x.
In which the coefficients of the function are described as follows:
a is the y-intercept, the value of y at which the function crosses the y-axis.b is the rate of change of the exponential function.Function h(x) is defined as follows:
h(x) = 3^x - 2.
For the graphed function g(x), when x = 0, y = 4, hence the intercept of the function is given as follows:
a = 4.
When x = 1, y = 5, hence the rate of change of the function is obtained as follows:
b = 5/4.
b = 1.25.
Then function g(x) is given as follows:
g(x) = 4(1.25)^x.
Due to the higher intercept, g(x) ≥ h( x) at x = 0. This will change when they intersect, which from the image given at the end of the answer is at x = 1.906, which is approximately 2, hence statement B is correct.
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The population of a heard of buffalo after t
years is represented by the function
() = 2186(0.954)^t
What does the value 0.954 represent in this
situation?
a. The initial population of the town is 0.954
b. The population of the town increases by 0.954
each year.
c. The population of the town decreases by 0.954
each year.
d. The population of the town is 0.976 times the
population of the town in the previous year.
Answers
0.954 represents population of the town increases by 0.954 each year.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
The population of a heard of buffalo after t
years is represented by the function
[tex]f(x)=2186(0.954)^{t}[/tex]
We need to find the what does the value 0.954 represent in this
situation.
In the given function 2186 represent the initial population.
t represents the time in years
and 0.954 represents population of the town increases by 0.954 each year.
Hence, 0.954 represents population of the town increases by 0.954 each year.
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Consider the line -7x-3y = 1.
Find the equation of the line that is perpendicular to this line and passes through the point (-7, 4).
Find the equation of the line that is parallel to this line and passes through the point (-7, 4).
Note that the ALEKS graphing calculator may be helpful in checking your answer.
Equation of perpendicular line:
Equation of parallel line:
0
X
0=0
S
Answers
Answer:
Parallel: Y= -7/3x - 37/3
Perpendicular: Y=3/7x + 7
Step-by-step explanation:
Use the formula: Y - Y1 = M(X - X1) Plug in -7 as X1 and 4 as Y1 and your M value is your slope. (-7, 4) where it passes from.
Remember when the slope is parallel it's always the same slope in this case -7/3
When perpendicular flip it and change the sign 3/7
How does a number change in total when it is decreased by 60% and increased by 80%? PLEASE HELP ASAP!
Answers
The number will be decreased by a percentage of 32%.
How does the number change?
If a number N is increased by a percentage X, then the new value is:
N' = N*(1 + X/100%)
If instead the number is decreased, then the new value is:
N' = N*(1 - X/100%)
So if we apply a decrease by 60% followed by an increase of 80%, we will have:
N' = N*(1 - 60%/100%)*(1 + 80%/100%)
N' = N*(1 - 0.6)*(1 + 0.8)
N' = N*(0.4)*(1.8)
N' = N*0.72
We can rewrite that as:
N' = N*(1 - 0.32)
0.32 = 32%/100%
So that is equivalent to a decrease by 32%
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Andrei has a glass tank. First, he wants to put in some marbles, each of which has a volume of 0. 40. 040, point, 04 liters. Then, he wants to fill the tank with water until it's completely full. If he uses 505050 marbles, he will have to add 333333 liters of water. What is the volume of the tank?.
Answers
The total Volume of tank = 35 liters
What is Volume ?In three dimensions, everything takes up some space. What is being measured here is the area's volume. The volume of an object is the area occupied inside its three-dimensional boundaries. Sometimes it is referred to as the
According to the Given information
Volume of each marble = 0.04 liters
Number of marbles to be put in the water tank = 50 marbles
Volume of 50 marbles = 0.04 × 50 = 2 liters
Volume of water added to the tank = 33 liters
Total Volume of tank = 2 liters + 33 liters
= 35 liters
SO,
The total Volume of tank = 35 liters
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