Answers
Step-by-step explanation:
Let's get an important definition out of the way first. A parallelogram is a quadrilateral with two pairs of parallel sides. We can translate this idea to coordinate geometry by saying that each pair of opposite sides must have the same slope.
Slope, as you might remember, is a measure of change. Specifically, it's the change in a line's y value (Δy) divided by the corresponding change in its x value (Δx). This means that if we can prove that:
The slope of [tex]\overleftrightarrow{KA}[/tex] = the slope of [tex]\overleftrightarrow{IT}[/tex]The slope of [tex]\overleftrightarrow{KT}[/tex] = the slope of [tex]\overleftrightarrow{AI}[/tex]We'll have proved our figure is a quadrilateral. Let's prove those cases, then. For KA and IT:
[tex]slope_{KA}\stackrel{?}{=}slope_{IT}[/tex]
To find the slope of any line segment, we can find the difference between the corresponding coordinates of its endpoints and divide the difference in y-coordinates by the difference in x-coordinates. Since the endpoints of KA are K(0, 0) and A(a, 0), the slope of these points is
[tex]slope_{KA}=\frac{0-0}{a-0} =\frac{0}{a} =0[/tex]
We can do this same for IT using its endpoints I(a + b, c) and T(b, c):
[tex]slope_{IT}=\frac{c-c}{b-(a+b)} =\frac{0}{-a}=0[/tex]
Since 0 = 0, we can say that [tex]slope_{KA}=slope_{IT}[/tex], and we've proven our first condition. Now we just need to prove that [tex]slope_{KT}=slope_{AI}[/tex]:
[tex]slope_{KT}\stackrel{?}{=}slope_{AI}[/tex]
Using K(0, 0) and T(b, c), [tex]slope_{KT}=\frac{c-0}{b-0}=\frac{c}{b}[/tex], and using A(a, 0) and I(a + b, c), [tex]slope_{AI}=\frac{c-0}{(a+b)-a}=\frac{c}{b}[/tex], proving that [tex]slope_{KT}=slope_{AI}[/tex].
Since we've proven that [tex]slope_{KA}=slope_{IT}[/tex] and [tex]slope_{KT}=slope_{AI}[/tex], we've proven that the quadrilateral KAIT is, by definition, a parallelogram.
Related Questions
How much cash did the person who filled out this deposit slip receive? a. $849.25 b. $715.56 c. $7,621.53 d. $721.50
Answers
Answer: its D $721.50
Even would be helpful if you just gave me the equation to solve it and I can do the rest. mart had a sale for labor day on DVD's and video tapes. Katie bought 2 tapes and 3 DVD's and spent 134$. Emily bought 1 tape and 5 DVD's and spent 179$. How much does a tape and DVD cost .
Answers
x - price of a video tape
y - price of a DVD
[tex]\left\{\begin{array}{ccc}2x+3y=134\\x+5y=179&|\text{subtract 5y from both sides}\end{array}\right\\\\\left\{\begin{array}{ccc}2x+3y=134\\x=179-5y&|\text{substitute to the first equation}\end{array}\right\\\\2(179-5y)+3y=134\qquad\text{use distributive property}\\\\(2)(179)+(2)(-5y)+3y=134\\\\358-10y+3y=134\qquad\text{subtract 358 from both sides}\\\\-7y=-224\qquad\text{divide both sides by (-7)}\\\\\boxed{y=32}\\\\\text{Put the value of y to the second equation}\\\\x=179-5(32)\\\\x=179-160\\\\\boxed{x=19}[/tex]
Answer: video tape cost $19 and DVD cost $32.The following function is quadratic.
f(x)=(x+4)(x-6)
What is the value of the positive x-intercept of the graph of the related equation y = (x+4)(x-6)?
Answers
Answer: 6
You replace f(x) or y with 0, and then solve for x
y = (x+4)(x-6)
(x+4)(x-6) = y
(x+4)(x-6) = 0
x+4 = 0 or x-6 = 0 .... zero product property
x = -4 or x = 6
The x intercepts are -4 and 6. In this case, only 6 is the positive x intercept.
side note: The term "root" is another way to say "x-intercept"
Explain how you know that 0.38 is a rational number?
Answers
Answer:
0.38 is a rational number because it can be expressed as fraction, and it isn't a repeating decimal.
Step-by-step explanation:
Repeating decimals aren't rational, and all rational numbers can be expressed as a fraction, or they aren't rational.
It's a rational number because it stops, the decimal is irrational if it continues forever without a pattern
A triangle with side lengths of 11, 13, and 15 is a scalene triangle. True False
Answers
Answer:
True
Hope it helps!!
Hopes this helps
Can someone help me?
Answers
Answer:
y=1/3x+8
Step-by-step explanation:
you can use the formula y=mx+b
y=1/3x-1
10=1/3*6+b
10=2+b
b=8
y=1/3x+8
Solve by elimination. 4x-y=6 3x+2y=21
Answers
Answer:
x=3, y=6
Step-by-step explanation:
4x-y =6
3x+2y = 21
To use elimination we will multiply the first equation by 2
2(4x-y) =6*2
8x -2y =12
We will add this equation to the second equation to eliminate y
8x -2y =12
3x+2y = 21
-----------------
11x = 33
Divide each side by 11
11x/11 = 33/11
x =3
We still need to solve for y
3x+2y = 21
Substituting x=3
3*3+2y = 21
9+2y =21
Subtract 9 from each side
9-9+2y = 21-9
2y = 12
2y/2 = 12/2
y =6
percent of change of $49 to $149
Answers
To find the percentage change, here is what we can do:
difference/original value x 100%
The difference: 149-49 = 100
The original value:149
The percentage change:
100/149 x 100%
=67.11409...%
Therefore the answer is 67.1%(corr. to three significant figures)
Hope it helps!
The percent of change from $49 to $149 is approximately 204.08%.
To calculate the percent of change from $49 to $149, we first find the difference in the two amounts.
The difference between $149 and $49 is $149 - $49 = $100.
Then, we divide the difference by the original amount (in this case, $49) to find the change in terms of the original amount.
This gives us $100 / $49 = 2.0408.
To convert this to a percentage, we multiply by 100. 2.0408 x 100
= 204.08%.
So the percent of change from $49 to $149 is approximately 204.08%.
A wood stove burns 4 logs in 2 hours how many logs burn in 9 hours ?
Answers
Answer:
18 logs.
Step-by-step explanation:
Since a stove burns 4 logs per 2 hours, then the stove will burn 2 logs in one hour. There fore in 9 hours the stove will burn 2*9 which is 18 logs.
4:2= 2 logs per hour
2*9=18 logs per 9 hours.
Answer:
16
Step-by-step explanation:
16 Because 2 divided by 8 equals 4 then 4x4 equal 16
50-u>48
u>?
please help too lazy
Answers
[tex]50-u>48\qquad\text{subtract 50 from both sides}\\\\-u>-2\qquad\text{change the signs}\\\\u<2[/tex]
A 52% video game is advertised for 20% off. If sales tax is 6%,how much will the video game cost
Answers
Answer:
Equation: 52+(52•.20) that is the first part for your answer you should get 10.4 or $10.40. Then you would take 52-10.4=41.60 then keeping that number in mind you do 41.60• .06 and get, rounded, 2.50. Then you would add 41.60+2.50 and get $44.10 as your answer . I hope I could help
Step-by-step explanation:
Hello I need someone to help me with basic science Pls help will do anything!
Answers
Answer:
What you need???
Step-by-step explanation:
Answer:
I will be willing to help
Step-by-step explanation:
1. tell me what ur questions are
2. i will answer them
3. U use the answers for ur personal use
4. U thank me
5. Hope I can help
Yogesh has 3 quarters, 1 dime, and 2 pennies
Answers
How:
quarter = 25¢
dime= 10¢
penny= 1¢
25×3=75
10×1=10
1×2=2
Add them all up
75
+10
+ 2 =87
Answer: Yoghes has $0.87
Step-by-step explanation: We want to know the total amount of money that Yogesh has:
each quarter values 25¢, a dime values 10¢, and a penny values 1¢
(or the values can be written as $0.25, $0.10 and $0.01 respectively)
Yogesh has 3 quarters, so this means he has: 3*$0.25 = $0.75
he has 1 dime, so in dimes, he has: $0.10
he has 2 pennies, so in pennies, he has: 2*$0.01 = $0.02
If we sum up the 3 amounts, we have:
Total = $0.75 + $0.10 + $0.02 = $0.87
Maria is playing a video game. She earns 15 points when she completes level one. Each time she completes a level, she earns twice as many points as the previous level. How many points will Maria earn when she completes level eight?
Answers
Answer:
She will earn 1,920 points. PLEASE GIVE BRAINLIEST!!!
Step-by-step explanation:
Level 1 : 15 points x 2 = level 2
Level 2 : 30 points x 2 = level 3
Level 3: 60 points x2 = level 4
Level 4: 120 points x2 = level 5
Level 5: 240 points x2 = level 6
Level 6: 480 points x2 = level 7
Level 7: 960 points x2 = level 8
Level 8: 1,920 points
The ratio of the number of model cars that Jim owns to the number of model cars Terrence owns is 4 : 3. Terrence owns 36 models cars. How many model cars does Jim own?
Answers
Terrence-3
Terrence has 36
12×3=36
so let's multiply 4 by 12 also and that is 48
so, therefore jim has 48 model cars
consider the triangle below
Answers
Answer:
[tex]m\angle M=90[/tex]
[tex]m\angle A=63[/tex]
[tex]m\angle N=27[/tex]
[tex]\Delta MAN[/tex] is a right triangle.
Step-by-step explanation:
Since we know that sum of all angles of triangles equals to 180 degrees.
To find the measure of our given angles we will have to find the value of x. The value of x can be found by equating the measure of all angles of our given triangle with 180.
[tex]4x-5+9x-9+10x+10=180[/tex]
[tex]23x-14+10=180[/tex]
[tex]23x-4=180[/tex]
[tex]23x=180+4[/tex]
[tex]23x=184[/tex]
[tex]x=\frac{184}{23}[/tex]
[tex]x=8[/tex]
Now let us find measure of each angle by substituting value of x in given expressions.
[tex]m\angle M=10*x+10[/tex]
[tex]m\angle M=10*8+10[/tex]
[tex]m\angle M=80+10[/tex]
[tex]m\angle M=90[/tex]
Therefore, measure of angle M is 90 degrees.
[tex]m\angle A=9*x-9[/tex]
[tex]m\angle A=9*8-9[/tex]
[tex]m\angle A=72-9[/tex]
[tex]m\angle A=63[/tex]
Therefore, measure of angle A is 63 degrees.
[tex]m\angle N=4*x-5[/tex]
[tex]m\angle N=4*8-5[/tex]
[tex]m\angle N=32-5[/tex]
[tex]m\angle N=27[/tex]
Therefore, measure of angle N is 27 degrees.
From the measures of angles we can say that triangle MAN is a right triangle.
m% of n is what percent of p?
FIND FOR PERCENT
Answers
[tex]\( m\% \) of \( n \) is \( \frac{{m \times n}}{{p}}\% \) of \( p \).[/tex]
To find what percentage m% of n is of p, you would calculate:
[tex]\[ \text{Percentage} = \frac{{(m\% \text{ of } n)}}{p} \times 100\% \][/tex]
Substituting [tex]\( m\% \) of \( n \) with \( \frac{m}{100} \times n \), t[/tex]he formula becomes:
[tex]\[ \text{Percentage} = \frac{{\frac{m}{100} \times n}}{p} \times 100\% \][/tex]
Simplify the expression:
[tex]\[ \text{Percentage} = \frac{{m \times n}}{{100 \times p}} \times 100\% \][/tex]
[tex]\[ \text{Percentage} = \frac{{m \times n}}{{p}}\% \][/tex]
So,[tex]\( m\% \) of \( n \) is \( \frac{{m \times n}}{{p}}\% \) of \( p \).[/tex]
Using arithmetic operations, rewrite this polynomial in standard, simplest form. (3x2 + 9x + 6) − (8x2 + 3x − 10) + (2x + 4)(3x − 7)
Answers
Answer:
x∧2+4x-16
Step-by-step explanation:
Answer:x^2+4x-12
Step-by-step explanation: I got it right
10.210 ÷ 10 (Long Division Work)
Answers
hoped this helped
Here is how you solve this problem with long-division. Hopefully it helps!
What is the equation in the point-slope form of the line that passes through the point (-1,-4) and has a slope of -3?
Answers
Answer:
y=mx+b; y=-3x+-4
Step-by-step explanation:
Substitute the slope, and the y-intercept in place of m and b
Answer: [tex] (y+4)=-3(x+1)[/tex]
Step-by-step explanation:
We know that the equation a line in point-slope form having slope m and passing through point (a,b) is given by :-
[tex](y-b)=m(x-a)[/tex]
Then , the equation a line in point-slope form having slope '-3' and passing through point (-1,-4) is given by :-
[tex](y-(-4))=-3(x-(-1))\\\\\Righarrow\ (y+4)=-3(x+1)[/tex]
Solve x2 − 7x = −13.
A) x equals quantity of negative 7 plus or minus I square root of 6 all over 2
B) x equals quantity of negative 7 plus or minus I square root of 3 all over 2
C) x equals quantity of 7 plus or minus I square root of 6 all over 2
D) x equals quantity of 7 plus or minus I square root of 3 all over 2
Answers
Answer: the actual correct answer is D
Step-by-step explanation: i know the test answers because i am in flvs too
Please help how to answer this
Answers
Answer:
1563.2
Step-by-step explanation:
The value of 3 in 156.32 is 0.3
The value of 3 in 1563.2 is 3
So 0.3 × 10 = 3
Bob raked 5% more leaves than Adam raked. Bob raked 357 liters of leaves. How many liters did Adam rake?
Answers
Answer:
Adam raked 340 liters
Step-by-step explanation:
Bob raked more leaves than Adam
5% more means take 100 % and add 5% = 105%
105% as a decimal is 1.05
Bob = 1.05 * Adam
We know Bob raked 357
357 = 1.05 Adam
Divide by 1.05
357/1.05 =1.05/1.05 Adam
340 = Adam
Genevieve collected pledges of $3.50 for every complete mile she runs in a charity race. Her goal is to raise at least $50.00. Genevieve wrote the inequality 3.5m ≥ 50 to find out how many miles she needs to run.
Genevieve thinks she needs to run at least 14 miles.
But Carla says Genevieve needs to run more miles than that.
Who is correct and why?
A.
Carla is correct because 3.5 × 14 is less than 50.
B.
Genevieve is correct because 3.5 × 14 is about 50.
C.
Carla is correct because 3.5 × 14 is not equal to 50.
D.
Genevieve is correct because 3.5 × 14 is greater than 50.
Answers
Answer:
A.
Carla is correct because 3.5 × 14 is less than 50.
Step-by-step explanation:
3.5m ≥ 50
To determine how many miles she needs to run, divide each side by 3.5
3.5m/3.5 3.5m ≥ 50 50/3.5
m ≥ 14.28571429
She must run more than 14 miles
Carla is correct because 14* 3.5 = 49. That is less than the 50 she wants to raise.
Which algebraic rule describes the transformation?
A) (x, y) → (x + 1, y − 3)
B) (x, y) → (x + 3, y − 1)
C) (x, y) → (x − 1, y + 3)
D) (x, y) → (x − 3, y + 1)
Answers
Answer:
It's B.
Step-by-step explanation:
(x, y) ---> (x + 3, y - 1)
Using point X as an example:
(x, y) ---> (x + 3, y - 1)
(0, 0) ---> (0 + 3, 0 -1)
(0, 0) ---> (3, -1)
The algebraic rule that describes the transformations is;
B) (x, y) → (x + 3, y − 1)
What are coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
Given, A graph where we can see a Graph of a triangle XYZ that transforms to become x'y'z'.
Since the given graph is transformed not scaled.
Thus, the dimension will be the same and we can justify the means by just Calculating for one point.
For Point x:
Original coordinates os x = (0, 0)
coordinates of the x after transformation = (3, -1)
Thus,
horizontal displacement in X = +3
vertical displacement in X = -1
therefore, (x, y) → (x + 3, y − 1) is the algebraic rule that describes the transformation.
Learn more about coordinates here:
https://brainly.com/question/20282507
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which expression is equivalent to 0.4 x 8.7
A: (4x87) x (1/100 x 1/10)
B: (4x87) x (100 x 10)
C: (4x87) x (1/100 x 1/100)
D: (4 x 87) x (1/10 x 1/10)
Answers
Each time a solid bicycle wheel turns, the bicycle travels 197cm. What is the area of the wheel?
Answers
Answer:
38809/(4pi) cm^2
Step-by-step explanation:
So the circumference of the wheel is 197. So to find the radius, we divide by 2 pi. So now we have 197/(2pi) as the radius. Now we have to find the area, so it is 38809/(4pi)
The area of the solid wheel is 3090 cm².
What are the circumference and diameter of a circle?The circumference of a circle is the distance around the circle which is 2πr.
The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.
We know circumference is the distance around the circle which is 2πr.
Given, Each time a solid bicycle wheel turns, the bicycle travels 197cm.
Therefore,
2πr = 197.
r = 197/π×2.
r = 31.37 cm.
Therefore, The area of the solid wheel is,
πr².
= 3.14×(31.37)² cm².
= 3090 cm².
learn more about circles here :
https://brainly.com/question/29142813
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Note that
a2 + b2 = c2.
To work under a car, a mechanic drives it up steel ramps like the ones shown below. Find the length of each side of the ramp.
a = ft
b = ft
c = ft
Answers
[tex](x + 1)^{2} + {x}^{2} = (x + 2)^{2} \\ x ^{2} + 2x + {1}^{2} + {x}^{2} = {x}^{2} + 4x + {2}^{2} \\ 2 {x}^{2} + 2x + 1 = {x}^{2} + 4x + 4 \\ {x}^{2} - 2x - 3 = 0[/tex]
Solve quadratic equation:
x= 3 or x=-1 (rejected.because length cannot be negative)
I need help!!!!
Can someone help me
Answers
But to be accurate, this isn't even a function. For it to be a function, that -2 couldn't be without a pair. There should be a 1 on the right side. So, when you do f(x) = -2 + 3 you get 1. This set of numbers (-2, -1, 3 and 5) is called domain, and all elements of the function's domain has to have a pair in the codomain(2, 6, 8, 4). That doesn't happen, as we don't see a 1 there, that could be assigned to the - 2 of the domain.
Vector u has its initial Point at (15,22) and it’s terminal point at (5,-4)
Answers
Final answer:
The position vector of vector u is (-10, -26). The magnitude of vector u is sqrt(776). The direction of vector u is 68.2 degrees.
Explanation:
The position vector of vector u can be found by subtracting the initial point from the terminal point. So, the position vector of u is (5-15, -4-22) = (-10, -26).
The magnitude of vector u can be found using the distance formula, which calculates the length of a vector. The formula is: magnitude = sqrt(x^2 + y^2), where x and y are the components of the vector. So, for vector u, the magnitude is: sqrt((-10)^2 + (-26)^2) = sqrt(100 + 676) = sqrt(776).
The direction of vector u can be found using trigonometry. The direction angle (theta) is given by tan(theta) = y/x. So, for vector u, the direction angle is: tan(theta) = (-26)/(-10) = 2.6. Converting to degrees, theta = arctan(2.6) = 68.2 degrees.