Plot the points A(7,1), B(-2, 3), C(1, -7) on the coordinate axes below. State the
coordinates of point D such that A, B, C, and D would form a parallelogram.
(Plotting point D is optional.)
Answers
A B
D C
vectors
AB = DC
AB (-2-7 ; 3-1) => AB (-9 ; 2)
DC (1-x : -7-y)
1 - x = -9 => x = 10
-7-y = 2 => y = -9
D(10 ; -9)
Answer:
D = (10, -9)
Step-by-step explanation:
If ABCD is a parallelogram, then AB = DC and BC = AD
Therefore,
[tex]\sf x_A-x_B=x_D-x_C[/tex]
[tex]\sf \implies 7-(-2)=x_D-1[/tex]
[tex]\sf \implies x_D=10[/tex]
[tex]\sf y_A-y_B=y_D-y_C[/tex]
[tex]\sf \implies 1-3=y_D-(-7)[/tex]
[tex]\sf \implies y_D=-9[/tex]
Therefore, D = (10, -9)
Related Questions
Ann deposited $4000into an account with 3.6% interest, compounded annually. Assuming that no withdrawals are made, how much will she have in the account after 9 years?
Answers
In 9 years, you will have $5,499.18
Steps:
Note
A = Final Amount
P = Principal Amount
R = Interest Rate
N = # of times interest is compounded
T = Time in years
A = P(1 + r/n)^nt
A = ?
P = 4000
R = 0.036
N = 1
T = 9
A = 4000(1 + 0.036/1)^1*9
A = 5499.18
The sum of two numbers is 24. Two times the first number minus the second number is 21
Answers
Step-by-step explanation:
x + y = 24
2x - y=21
I'm guessing the question was find both numbers.
3x = 35
x=15
3y = 27
y=9
Billy invested $18 of savings in two major business enterprises which paid interest at the rate of 3% and 6%, respectively. If his annual income for these two enterprises was equivalent to a return of 5% on the entire investment, find how much he invested at 3%.
Answers
Answer:
$6
Step-by-step explanation:
System of equations
x+y = 18
0.03x+0.06y = 5% of 18 = 0.9
(0.03x+0.06y=0.9)*100 = 3x+6y=90
(3x+6y=90)÷3 = x+2y=30
Substract (1)-(2)
x+2y=30 ... (1)
x+y=18 ... (2)
y=12
x+12=18
x=6
Thanks.
What is the area of this quadrilateral(Please show a step by step process)
Answers
Answer:
40ft
Step-by-step explanation:
What you need to know is the formula for the air of a rectangle:
the long side * the short side.
First calculate the area of the rectangle in the middle: 3*8=24ft
Then we are left with two right-angled triangles, one on the left and one on the right. If we juxtapose them, we realize that it forms a rectangle whose large side measures 8 and the small 2 so 2*8=16ft.
Finally, just add the area of the middle rectangle with the area of our rectangle formed by the two triangles on the right and on the left. So 16+24=40ft
Need assistance please
And please put in the full explanation on how you solved it please.
Answers
Answer:
The triangles are not similar
Step-by-step explanation:
We can say whether the triangle UVW is similar to triangle LMN or not by looking at the side lengths' ratio:
If they are similar then the side's must be proportional
VU/LM = VW/NM
35/25 = 22/16 cross multiply expressions
560 = 550 this is not an equation so we cannot say the triangles are similar.
can y’all please helpppp , i’ll give brainliest
Answers
[tex]\qquad\qquad\huge\underline{\boxed{\sf Answer☂}}[/tex]
The y - coordinate of a point lying on that function is represented by f(x) for each value of x, so let's find the corresponding value of x, when f(x) = 0
In the given case, y - coordinate of two points is equal to zero. hence we will get two distinct values of x
that is :
[tex]\qquad \sf \dashrightarrow \: x = - 2 \: \: and \: \: x = 4[/tex]
For his car, Sam spent $138.96 on speakers and $142.89 on new tires. In total, how
much did Sam spend on car parts?
Answers
Answer:
Same spent $281.85 or approximately $282
What is 192 rounded to the nearest ten
Answers
Answer:
190
Step-by-step explanation:
192 is closer to 190 than it is to 200, so the answer is 190.
Hope that helps!
Answer:
190
Step-by-step explanation:
192 looking a the ones number (2) if the last number is 5 or higher round up if not go down. therefore 190
Determine if the following system of equations has no solutions 4x+3y= -8 -8x-6y= 16
Answers
[tex]\begin{cases} 4x+3y=-8\\\\ -8x-6y=16 \end{cases}~\hspace{10em} \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]4x+3y=-8\implies 3y=-4x-8\implies y=\cfrac{-4x-8}{3}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{4}{3}} x-\cfrac{8}{3} \\\\[-0.35em] ~\dotfill\\\\ -8x-6y=16\implies -6y=8x+16\implies y=\cfrac{8x+16}{-6} \\\\\\ y=\cfrac{8}{-6}x+\cfrac{16}{-6}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{4}{3}} x-\cfrac{8}{3}[/tex]
one simple way to tell if both equations do ever meet or have a solution is by checking their slope, notice in this case the slopes are the same for both, meaning the lines are parallel lines, however, notice both equations are really the same, namely the 2nd equation is really the 1st one in disguise.
since both equations are equal, their graph will be of one line pancaked on top of the other, and the solutions is where they meet, hell, they meet everywhere since one is on top of the other, so infinitely many solutions.
Maths- please help me with this Q
Answers
Step-by-step explanation:
please mark me as brainlest
Answer:
See below ↓
Step-by-step explanation:
Missing values (a)
[tex]\left[\begin{array}{ccc}-1&1\\?&?\end{array}\right][/tex]Substituting x = 1 and x = -1 respectively in the equation y = x² - 4x[tex]\left[\begin{array}{ccc}-1&1\\5&-3\end{array}\right][/tex]Curve which matches the equation
On solving y = x² - 4x = x(x - 4) ⇒ x = 0, 4It intersects the x axis at 0 and 4The blue curve is the right oneWhat is the value of x?
Answers
Answer:
I would say 30
Reasoning:
Because that thing your looking at is 180% degree angle and the other side is 90%. x is small it seems to be acute and I think 2x is about 60%.
If im incorrect im terribly sorry but at least my answer wasnt bad like the 1st guys
The quotient of forty-three and a number m
Answers
Answer:
43/m
Step-by-step explanation:
Quotient refers to the resulting answer when a number is divided by a divisorIn this case, our number is 43 and divisor is mTherefore, the quotient is :43/mAnswer:
43/m
Step-by-step explanation:
We can consider the word phrase 'the quotient of' to be a division property.
We can also contemplate that the phrase 'a number m' represents a variable, m, of an unknown value.
Together, we link these two to create the expression;
43 ÷ m which can also be known as 43/m.
The area of a rectangular garden is 3927cm . If the width of the garden is 51 m , what is its length?
Answers
Answer:
77
Step-by-step explanation:
The area of a rectangle is A = lw. 'A', the area, is 3927, and 'w', the width, is 51. By substituting the values in, we get that 3927 = 51L. Dividing both sides by 51, we get that L, the length, is 77.
Without solving, identify whether this equation has a solution that is positive, negative, or zero: It is positive Solve the equation.
Answers
Please provide one.
Answer:
Step-by-step explanation:
Harold got home from school at 3:50 P.M. and played video games for 1 hour and 5 minutes. Then, it took him 1 hour and 40 minutes to finish his homework. What time was it when Harold finished his homework?
Answers
Answer:
6:35.
Step-by-step explanation:
I start by adding the hours spent to the time leaving me with 5:50, I then add the 40 which brings it to 6:30 and the additional 5 minutes bringing the final answer to 6:35.
Answer:
6:35 PM
Step-by-step explanation:
When Harold got home, it was already 3:50 PM. Then he played games for an hour and five minutes. Adding on an hour, it made the time 4:50 PM, and then adding on the five minutes, made the time 4:55 PM. When he finished playing games, he took an hour and forty minutes to do his homework. 4:55 PM, adding on the hour makes it 5:55 PM, then adding the 40 minutes, makes it 6:45 PM.
- Educationist
Which statement describes the behavior of the function f (x) = startfraction 2 x over 1 minus x squared endfraction?
Answers
The statement that describes the behavior of the function f(x) = 2x/(1-x²) is given by: Option B: The graph approaches 0 as x approaches infinity
How to find the value of the function as x approaches infinity (+ve or -ve)?If limits exist, we can take limits of the function, where x tends to -∞ or ∞, and that limiting value will be the value the function will approach.
For the considered case, the function is:
[tex]f(x) = \dfrac{2x}{1-x^2}[/tex]
The missing options are:
The graph approaches –2 as x approaches infinity.The graph approaches 0 as x approaches infinity.The graph approaches 1 as x approaches infinity.The graph approaches 2 as x approaches infinity.So we need to find the limit of the function as x approaches infinity.
[tex]lim_{x\rightarrow \infty}f(x) = lim_{x\rightarrow \infty}\dfrac{2x}{1-x^2} = lim_{x\rightarrow \infty}\dfrac{2x/x^2}{1/x^2 - 1} = lim_{x\rightarrow \infty}\dfrac{2/x}{1/x^2 - 1}\\\\lim_{x\rightarrow \infty}f(x) = \dfrac{lim_{x\rightarrow \infty}(2/x^2)}{lim_{x\rightarrow \infty}(1/x^2 - 1)} = \dfrac{0}{0-1} = \dfrac{0}{-1} = 0[/tex]
Since the value of the function approaches 0 as x approaches infinity, so as its graph will do.
Thus, the statement that describes the behavior of the function f(x) = 2x/(1-x²) is given by: Option B: The graph approaches 0 as x approaches infinity
Learn more about limits of a function here:
https://brainly.com/question/13146225
A town has a population of 141,300 and grows at a rate of 5% every year. Which equation represents the town’s population after 6 years?
Answers
Answer:
P=141,300(1+0.05)^6
Step-by-step explanation:
r = rate = 5/100 = 0.05
a = starting amount = 141,300
t = time = 6 years
% growth formula:
a(1+r)^t
141,300(1.05)^6
Answer:
P=141,300(1+0.05)^6
Step-by-step explanation:
r = rate = 5/100 = 0.05
a = starting amount = 141,300
t = time = 6 years
% growth formula:
a(1+r)^t
141,300(1.05)^6
Please help ASAP
Dave is 8 years younger than 4 times Julia's age. If Dave is 16, how old is Julia?
6 years
24 years
32 years
O
56 years
Answers
Step-by-step explanation:
Age of dave = y
Age of Julia = x
y = 4x - 8
if y = 16
then
4x - 8 = 16
4x = 16 + 8
4x = 24
x = 24/4
x = 6
Julia is 6 years old
Answer:
Julia is 6 years old.
Step-by-step explanation:
Dave + 8 = 4 Julia
16 + 8 = 4 Julia
24 = 4 Julia
6 = Julia
Julia is 6 years old
Of the last 16 contestants on a game show, 12 qualified for the bonus round. Considering this data, how many of the next 12 contestants would you expect to qualify for the bonus round?
Answers
Answer:
9 contestants
Step-by-step explanation:
Out of the 16 contestants, 12 of them qualified for the bonus round.
This means, that 12/16, or 75% of the contestants qualified for the bonus round.
Out of the remaining 12 contestants, I would expect (75%)(12), or 9 contestants to qualify for the next bonus round.
Let me know if this helps!
Answer:The answer is 9
Step-by-step explanation:
12 of the 16 contestants on the game show qualified. That is 75% of the contestants. Applying this to the next 12, 12 contestants x 75% is 9 qualifying contestants.
Select the correct answer.
Which number is an irrational number?
A.
B.
C.
D.
Answers
Answer:
its c i just got done doing the same one
Step-by-step explanation:
got it right on my real numbers test and got 100% if you need more help comment under my answer
i need help on this question
Answers
Answer:
1st question
Sry if its wrong xx
A rectangular red sticker has a perimeter of 40 millimeters and an area of 64 square
millimeters. What are the dimensions of the sticker?
millimeters by millimeters
Submit
Answers
Answer:
16 x 4.
Step-by-step explanation:
What multiplies into 64?
could be 16 and 4?
16 x 2 = 32
4 x 2 = 8
32 + 8 = 40, therefore, this is correct.
An angle measuring (870n)° is in standard position. for which value of n will the terminal side fall on the y-axis? n = 3 n = 4 n = 5 n = 6
Answers
The value of n will the terminal side fall on the y-axis at n=3
The terminal side of an angle fall along the positive portion of the y-axis,
If it can written in the form of [tex](90^0)a[/tex]
Where a = positive odd integer,
We hyave given the given angle is,
[tex](870n)^0,[/tex]
What is terminal side?The terminal side of an angle theta drawn in angle standard position is the side which isn't the initial side
Now for n=3
[tex](870(3))^0=2610^0[/tex]
The angle will be 2610°
Its terminal side fall along the positive portion of the y-axis,
[tex]2610^0 = (90^0)a \implies a = 29[/tex]......( Positive odd integer )
Therefore for n = 3, the terminal side of the angle (870n)° falls along the positive portion of the y-axis,
For n = 4,
Our angle will be 3480°
Its terminal side fall along the positive portion of the y-axis,
[tex]3480^0 = (90^0)a \implies a = 38.6667 ( Not possible )[/tex]
Therefore for n = 4, the terminal side of the angle (870n)° does not fall along the positive portion of the y-axis
Next is for n = 5,
Our angle will be 4350°
Its terminal side fall along the positive portion of the y-axis,
[tex]4350^0 = (90^0)a \implies a = 48.333.. ( Not possible )[/tex]
Thus, for n = 5, the terminal side of the angle (870n)° does not fall along the positive portion of the y-axis,
For n = 6,
Our angle will be 5220°
Its terminal side fall along the positive portion of the y-axis,
[tex]5220^0 = (90^0)a \implies a = 58..... ( Not possible )[/tex]
Thus, for n = 6, the terminal side of the angle (870n)° does not fall along the positive portion of the y-axis.
Therefore,the value of n will the terminal side fall on the y-axis at n=3.
To learn more about the terminal side visit:
https://brainly.com/question/24680641
Answer:
a
Step-by-step explanation:
x=3 on edge
HELP ASAP I GIVE BIG BRAIN
Give one example of a relationship that IS a function and explain how you know (explain it as if you are talking to someone who has never heard of a function before). In ur own words please...
Answers
A function is a relation where there is only one output for every input. In other words for every x value, there is only one y value.
Example : Multiply by 3 is a very simple function.
Input : 0 Output : 0
Input : 1 Output : 3
Input : 2 Output : 6
Input : 3 Output :9
And so on!
Hope this helps!
1 yards equals 3 feet in one mile equals 5280 feet how many yards are in 5 MI
Answers
Answer:
A conversion calculator gave me 8800
because it's a drag and drop, I added a screenshot below.
Answers
Answer:
The one on top is y^8 - 1/y^8 (option 1)
The one on the bottom is 1/y^8 + 1/y^2 (option 5)
Which is the algebraic representative for a rotation 180 degrees clockwise?
Answers
Answer:
algebraic expression for 180 degree clockwise rotation about the origin (x,y) → (-y, x) algebraic expression for 270 degree clockwise rotation about the origin equals a 270 degree counterclockwise rotation 90 degree clockwise rotation equals a 90 degree counterclockwise rotation
Step-by-step explanation:
hope this helps
have an awesome day -TJ
A surveyor determines that the angle of elevation between herself and the top of an observation tower is 60^o. She determines that the distance between her position and the base of the tower is 20 meters. Approximately how tall is the tower?
Answers
There is a bag a filled with 3 blue and 4 red marbles.
A marble is taken at random from the bag, the colour is noted and
then it iS not replaced.
Another marble is taken at random.
What is the probability of getting 2 of the same colour?
Answers
Answer:
3/7Step-by-step explanation:
Given
Red = 4, Blue = 3Total number of marbles is
3 + 4 = 7Probability of getting 2 of the same color is
P(2 same) = P(red, red) + P(blue, blue)Probability of 2 reds is:
P(red, red) = 4/7*3/6 = 2/7Probability of 2 blues is:
P(blue, blue) = 3/7*2/6 = 1/7Required probability is
P(2 same) = 2/7 + 1/7 = 3/7Today only, a table is being sold for 134.40 . This is 32% of its regular price. What was the price yesterday?
Answers
Answer:
$177.41
Step-by-step explanation:
when it says 32% OF , of always means multiply in word problems so we multiple 132% (1.32) times 134.40
$177.41
Answer:
420
Step-by-step explanation:
32% of its original price
32%=134.40
100%=?
cross multiply
100/100 x 134.40 × 100/32
1×134.40×3.125
=420