To create a system of constraints that defines a parallelogram, we need to establish conditions that satisfy the properties of a parallelogram: opposite sides are parallel and equal in length, and opposite angles are congruent.
Here's an example of a system of constraints that represents a parallelogram:
Let's consider a parallelogram with vertices (x, y):
1. Constraint 1: Opposite sides are parallel.
This can be represented by the equation: y = ax + b, where a is the slope and b is the y-intercept.
2. Constraint 2: Opposite sides are equal in length.
This can be represented by the equation: [tex](x - x_1)^2 + (y - y_1)^2 = (x - x_2)^2 + (y - y_2)^2[/tex] are the coordinates of two opposite vertices.
3. Constraint 3: Opposite angles are congruent.
This can be represented by the equation: [tex]m_1 = m_2[/tex], where [tex]m_1[/tex] and [tex]m_2[/tex] are the slopes of two adjacent sides.
By combining these three constraints, we can define a system of equations that represents a parallelogram. The specific values of a, b, ([tex]x_1, y_1[/tex]), and ([tex]x_2, y_2[/tex]) will determine the properties and shape of the parallelogram.
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Make an equation to find the area of this figure.
Answer:
20x20=400
Step-by-step explanation:
A young sumo wrestler decided to go on a special diet to gain weight rapidly. WWW represents the wrestler's weight (in kilograms) after ttt months. W=80+5.4tW=80+5.4tW, equals, 80, plus, 5, point, 4, t What was the wrestler's weight before his special diet?
Answer:
80kg
Step-by-step explanation:
Given:
W = 80 + 5.4t
Where,
W = the wrestler's weight (in kilograms
t = number of months
What was the wrestler's weight before his special diet?
W = 80 + 5.4t
When t = 0 (that is before the weight gain)
W = 80 + 5.4t
= 80 + 5.4(0)
= 80kg
When t = 1 ( first month of the weight gain)
W = 80 + 5.4t
= 80 + 5.4(1)
= 80 + 5.4
= 85.4 kg
The wrestler's weight before his special diet is 80kg
ALTERNATIVELY
W = 80 + 5.4t
80 = the fixed weight
5.4 = weight gained per month
t = number of months
Therefore,
The fixed weight which is 80kg is the weight of the wrestler before the special diet.
Answer:
10.8
Step-by-step explanation:
This is correct on khan academy.
Find f(0)
(-3
f(x) = {10+ x
(4-x
-55x<-1
0
Answer:
34o
Step-by-step explanation:
I apologize , but I still don’t get none of these questions , can I have help ?
Answer:
The measures of the angles: m∠1 = 51°, m∠2 = 39°
Step-by-step explanation:
In this type of question, you should substitute the measures of the angle by the given values and solve the equation to find x, then find the measure of each angle.
∵ m∠1 + m∠2 = 90°
∵ m∠1 = 3x°
∵ m∠2 = (x + 22)°
→ Substitute m∠1 by 3x° and m∠2 by (x + 22)° in the equation above
∴ 3x° + (x + 22)° = 90°
→ Add the like terms in the right side
∴ (3x + x) + 22 = 90
∴ 4x + 22 = 90
→ Subtract 22 from both sides
∴ 4x + 22 - 22 = 90 - 22
∴ 4x = 68
→ Divide both sides by 4 to find the value of x
∴ [tex]\frac{4x}{4}=\frac{68}{4}[/tex]
∴ x = 17
→ Now substitute the value of x in each angle to find them
∵ m∠1 = 3x°
∴ m∠1 = 3(17) = 51°
∵ m∠2 = (x + 22)°
∴ m∠2 = (17 + 22) = 39°
The measures of the angles: m∠1 = 51°, m∠2 = 39°
Write an equation to represent the following statement. j is 7times as large as 6 .
Find the equation of the line containing (3,-2) and (6,3).
Express the equation in slope-intercept form,
Answer:
Y= 5/3x -7
Step-by-step explanation:
To find the slope with the given points you find the distance between the y values and the x values. (Rise/Run = Y/X). Once you find the pattern you can use it until you find the y intercept if you're using graph paper!
Hope this helps! :)
(Side Note: The distance for the y values from -2 and 3 is +5. The distance for the x values is +3 )
Item New Price Price Change Decrease Bike $110 $96 Scooter $45 $56 Tennis Racket $79 Increase Skis $580 25% Decrease
Did it increase or decrease..?
Answer:
increase
Step-by-step explanation:
help pls im bad at math
Answer:
1.5 would be a rational number and the irrational number could be the sqrt(2)
Step-by-step explanation:
1.5 is a rational number because it can be a fraction 3/2, but the square root of 2, written as [tex]\sqrt{2}[/tex], cannot be simplified into a fraction, and it written like this. This number is equal to around 1.414 approximately, so it satisfies the question
Item 17 You have 13 gallons of lemonade to sell. You use cone-shaped cups that are 7 centimeters in diameter and 11 centimeters tall. Each customer uses one paper cup. How many paper cups will you need if you sell all of the lemonade? (1 gal ≈ 3785 cm3)
answer please ? i don’t understand
Answer:
It is letter C
Step-by-step explanation:
f(x) = 3x – 2 if f(x) =7
Answer:
19
Step-by-step explanation:
3(7)-2
21-2=19
this explanation needs to be more than 20 characters so that's why I'm typing this sentence
Answer: 19
Step-by-step explanation:
1. Substitute 7 for x
2. 3x7=21
3.21-2=19
5x + 7 = 42, Is x = 7 the solution for this equation? Justify your answer for
it is or it is not
Answer:
7 is a solution.
Step-by-step explanation:
Step 1: Write equation
5x + 7 = 42
Step 2: Solve for x
Subtract 7 on both sides: 5x = 35Divide both sides by 5: x =7Answer:
x = 7Step-by-step explanation:
5x + 7 = 42
5x = 42 - 7
x = 35 / 5
x = 7
Need help for one question for geometry !
The data set shows the ages of the members of a book club. What is the shape of the distribution of this data set?
19, 21, 18, 19, 16, 21, 20, 17, 16, 17, 20, 18
A.
symmetrical
B.
uniform
C.
skewed to the left
D.
skewed to the right
Answer:e
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
have a great day
In a car race, car 5's speed is 200 kilometers per hour. The
distance it runs can be modeled by the equation s = = 200h
where s is the distance traveled in kilometers and h is the
number of hours the car have traveled. Graph this function and
see how far the car will travel after 0.5 hours.
kilometers.
Enter the answer
Answer:
100 kilometers
Step-by-step explanation:
Eight less than the product of two and a number c.
Answer:
2c-8
Step-by-step explanation:
2c-8
product is multiplication of 2 numbers/terms
that would be 2 and c together
eight less than that would be 2c-8
Pls awnser the question (I will name brainliest)
Answer:
Yes, the last digit i think its 10 is a outlier.
Step-by-step explanation:It is one because it just stick in the chart, like it fit in
Answer:10 foot is the outlier
Step-by-step explanation:it differs
from the rest
Aman decleared that he will give 20% discount on each items
in his shop. Sita bought a rice cooker from the shop at Rs.
3,500. If the shopkeeper made a profit of 5% on selling rice
cooker to Sita, find the cost price, marked price and discount
amount of the rice cooker.
Answer:
Let be cost price =Rs.100
Then mark price =Rs.120
∴ Selling price =90% of 120
=
100
120×90
=Rs.108
Profit = Selling price− Cost price
=Rs.(108−100)=Rs.8
Profit % =
100
8×100
=8%
FINDING ANGLE MEASURES Find the value of x. Then classify the triangle by its angles.
Answer:
i hope my answer is right for you
In the given triangle, the value of x is 60°.
What are triangles?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.So, the value of 'x':
We easily know that te given triangle is an equilateral triangle.Where all 3 angles are equal.The Sum of triangles is 180°.Now,
60 + 60 + x = 180120 + x = 180x = 180 - 120x = 60°
Therefore, in the given triangle, the value of x is 60°.
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between which two whole number is v12
Answer:
3 and 4
Step-by-step explanation:
Consider perfect squares either side of 12, that is
9 < 12 < 16 , then
[tex]\sqrt{9}[/tex] < [tex]\sqrt{12}[/tex] < [tex]\sqrt{16}[/tex] , that is
3 < [tex]\sqrt{12}[/tex] < 4
The picture is above no one answers my questions can someone please answer this I will be so thankful!
Answer:
Step-by-step explanation:
81 is the anwer
Answer:
105
Step-by-step explanation:
2(6^2)+2*6-3
2*36+2*6-3
72+2*6-3
72+36-3
105
On a coordinate plane, a curved line with a minimum value of (1.5, negative 1) and a maximum value of (negative 1.5, 13), crosses the x-axis at (negative 3, 0), (1, 0), and (2, 0), and crosses the y-axis at (0, 6).
Which lists all of the x-intercepts of the graphed function?
0, 6)
(1, 0) and (2, 0)
(1, 0), (2, 0), and (–3, 0)
(1, 0), (2, 0), (–3, 0), and (0, 6)
Someone pls help me answer this is worth a lot of points on my test.
Answer:
(-3,0) and (1,0)
Answer
The answer is C, because those are the points that cross the x-axis.
Step-by-step explanation:
i worked it out on paper
16 + 8 to the power of 2 divided by 4 - 4, Add on set of parenthesis to make it undefined
Answer:
(16+8)²÷(4-4)
POWERS OF 10 PRACTICE 7TH GRADE
Answer:
0.001 and 1/1000
Step-by-step explanation:
find the value of the x for the following 5x - 7 = 18
Answer:
x = 5
Step-by-step explanation:
Step 1: Write equation
5x - 7 = 18
Step 2: Solve for x
Add 7 to both sides: 5x = 25Divide both sides by 5: x = 5Step 3: Check
Plug in x to verify it's a solution.
5(5) - 7 = 18
25 - 7 = 18
18 = 18
Answer:
.x =5Step-by-step explanation:
5x - 7 = 185x = (18+7)5x = 25divide 5 both sides.
x = 5
Evaluate the expression for x=5, y=-3 and z=7
(x2 – z) (22+5)
Answer:
81
Step-by-step explanation:
(Refer to image)
Plug in x and z and follow order of operations to simplify the expression
fast plssss help me out !
Answer:
combine like terms
Step-by-step explanation:
7x and 4x were added together to get 11x. 35 and 20 were added together to get 55
There is 1/8
of a pizza left to split between 2 of your friends. If you split the pizza equally, what fraction of the pizza will each of your friends get?
Answer:
youll get 1/16 each
Step-by-step explanation:
1/16 + 1/16 = 2/16 = 1/8
each person will get 1/16
Can someone please help me asap I’ll mark brainlist!!?!?
Answer:
32/13
Step-by-step explanation:
2 6/13
2(13)=26
26+6=32
32/13
Answer:
32/13
Step-by-step explanation:
13x2=26
26+6=32
Denominator stays the same
The function C(x) = 25x + 50 represents the labor cost (in dollars) for Certified Remodeling to build a deck, where x is
the number of hours of labor. The table shows sample labor costs from its main competitor, Master Remodeling.
Answer:
Master RemodelingStep-by-step explanation:
Original question is attached
Option 1C(x) = 25x + 50C(8) = 25*8 + 50 = $250Option 2As per table, the rate of change is $30 per 2 hours.So 8 hours will cost $190 + $30 = $220As we see the second option is cheaper so we should hire the Master Remodeling
