Answer:
(6,-1)
Step-by-step explanation:
let coordinates of K be (x,y) then
[tex]0=\frac{-6+x}{2}\\or~-6+x=0\\x=6\\1=\frac{3+y}{2}\\y+3=2\\y=2-3=-1\\so ~K~is ~(6,-1)[/tex]
The coordinates of endpoint K will be (6,-1).
What is coordinate geometry?A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. The midpoint of a line segment is known as the midpoint in geometry. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.
Given that the midpoint of JK is M(0, 1). One endpoint is (-6, 3). The other end will be calculated as below:-
0 = ( -6 + x ) / 2
-6 + x = 0
x = 6
The value of the y coordinate will be calculated as below:-
y = 2 - 3 = -1
Therefore, the coordinates of endpoint K will be (6,-1).
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If A= -3, B= -7, C= 5, and D= 2, what does AB - CD= Question options: A.11 B.31 C. -11 D. -15
(i)Express 2x² – 4x + 1 in the form a(x+ b)² + c and hence state the coordinates of the minimum point, A, on the curve y= 2x² 4x+ 1.
The line x– y + 4 = 0 intersects the curve y= 2x² – 4x + 1 at points P and Q. It is given that the coordinates of Pare (3,7).
(ii)Find the coordinates of
(iii) Find the equation of the line joining Q to the mid-point of AP.
I already get the (i) but hav no idea with no.(ii) and (iii)
Can anyone help me? Thank you
Answer:
(i). [tex]y = 2\, x^2 - 4\, x + 1 = 2\, (x - 1)^2 - 1[/tex]. Point [tex]A[/tex] is at [tex](1, \, -1)[/tex].
(ii). Point [tex]Q[/tex] is at [tex]\displaystyle \left(-\frac{1}{2},\, \frac{7}{2}\right)[/tex].
(iii). [tex]\displaystyle y= - \frac{1}{5}\, x + \frac{17}{5}[/tex] (slope-intercept form) or equivalently [tex]x + 5\, y - 17 = 0[/tex] (standard form.)
Step-by-step explanation:
Coordinates of the ExtremaNote, that when [tex]a(x + b)^2 + c[/tex] is expanded, the expression would become [tex]a\, x^2 + 2\, a\, b\, x + a\, b^2 + c[/tex].
Compare this expression to the original [tex]2\, x^2 - 4\, x + 1[/tex]. In particular, try to match the coefficients of the [tex]x^2[/tex] terms and the [tex]x[/tex] terms, as well as the constant terms.
For the [tex]x^2[/tex] coefficients: [tex]a = 2[/tex].For the [tex]x[/tex] coefficients: [tex]2\, a\, b = - 4[/tex]. Since [tex]a = 2[/tex], solving for [tex]b[/tex] gives [tex]b = -1[/tex].For the constant terms: [tex]a \, b^2 + c = 1[/tex]. Since [tex]a = 2[/tex] and [tex]b = -1[/tex], solving for [tex]c[/tex] gives [tex]c =-1[/tex].Hence, the original expression for the parabola is equivalent to [tex]y = 2\, (x - 1)^2 - 1[/tex].
For a parabola in the vertex form [tex]y = a\, (x + b)^2 + c[/tex], the vertex (which, depending on [tex]a[/tex], can either be a minimum or a maximum,) would be [tex](-b,\, c)[/tex]. For this parabola, that point would be [tex](1,\, -1)[/tex].
Coordinates of the Two IntersectionsAssume [tex](m,\, n)[/tex] is an intersection of the graphs of the two functions [tex]y = 2\, x^2- 4\, x + 1[/tex] and [tex]x -y + 4 = 0[/tex]. Setting [tex]x[/tex] to [tex]m[/tex], and [tex]y[/tex] to [tex]n[/tex] should make sure that both equations still hold. That is:
[tex]\displaystyle \left\lbrace \begin{aligned}& n = 2\, m^2 - 4\, m + 1 \\ & m - n + 4 = 0\end{aligned}\right.[/tex].
Take the sum of these two equations to eliminate the variable [tex]n[/tex]:
[tex]n + (m - n + 4) = 2\, m^2 - 4\, m + 1[/tex].
Simplify and solve for [tex]m[/tex]:
[tex]2\, m^2 - 5\, m -3 = 0[/tex].
[tex](2\, m + 1)\, (m - 3) = 0[/tex].
There are two possible solutions: [tex]m = -1/2[/tex] and [tex]m = 3[/tex]. For each possible [tex]m[/tex], substitute back to either of the two equations to find the value of [tex]n[/tex].
[tex]\displaystyle m = -\frac{1}{2}[/tex] corresponds to [tex]n = \displaystyle \frac{7}{2}[/tex]. [tex]m = 3[/tex] corresponds to [tex]n = 7[/tex].Hence, the two intersections are at [tex]\displaystyle \left(-\frac{1}{2},\, \frac{7}{2}\right)[/tex] and [tex](3,\, 7)[/tex], respectively.
Line Joining Point Q and the Midpoint of Segment APThe coordinates of point [tex]A[/tex] and point [tex]P[/tex] each have two components.
For point [tex]A[/tex], the [tex]x[/tex]-component is [tex]1[/tex] while the [tex]y[/tex]-component is [tex](-1)[/tex].For point [tex]P[/tex], the [tex]x[/tex]-component is [tex]3[/tex] while the [tex]y[/tex]-component is [tex]7[/tex].Let [tex]M[/tex] denote the midpoint of segment [tex]AP[/tex]. The [tex]x[/tex]-component of point [tex]M[/tex] would be [tex](1 + 3) / 2 = 2[/tex], the average of the [tex]x[/tex]-components of point [tex]A[/tex] and point [tex]P[/tex].
Similarly, the [tex]y[/tex]-component of point [tex]M[/tex] would be [tex]((-1) + 7) / 2 = 3[/tex], the average of the [tex]y\![/tex]-components of point [tex]A[/tex] and point [tex]P[/tex].
Hence, the midpoint of segment [tex]AP[/tex] would be at [tex](2,\, 3)[/tex].
The slope of the line joining [tex]\displaystyle \left(-\frac{1}{2},\, \frac{7}{2}\right)[/tex] (the coordinates of point [tex]Q[/tex]) and [tex](2,\, 3)[/tex] (the midpoint of segment [tex]AP[/tex]) would be:
[tex]\displaystyle \frac{\text{Change in $y$}}{\text{Change in $x$}} = \frac{3 - (7/2)}{2 - (-1/2)} = \frac{1}{5}[/tex].
Point [tex](2,\, 3)[/tex] (the midpoint of segment [tex]AP[/tex]) is a point on that line. The point-slope form of this line would be:
[tex]\displaystyle \left( y - \frac{7}{2}\right) = \frac{1}{5}\, \left(x - \frac{1}{2} \right)[/tex].
Rearrange to obtain the slope-intercept form, as well as the standard form of this line:
[tex]\displaystyle y= - \frac{1}{5}\, x + \frac{17}{5}[/tex].
[tex]x + 5\, y - 17 = 0[/tex].
Find the sum of 4x^2
-4x + 10 and 2x^2+ 5x – 8.
Answer:
6x2+x+2
Step-by-step explanation:
Mark Brainliest?
Find the midpoint of the line segment joining the points (-1, -2) and (-3, 13).
The midpoint is
(Simplify your answer. Type an ordered pair)
midpoint =(X1+X2)/2 ,(Y1+Y2)/2
therefore=
( -1+-3)/2, (-2+13)/2
=(-4/2,11/2)
=(-2,5.5)
Round 45.396 to the nearest tenth
Answer:
Step-by-step explanation:
45.396
tenth place is 3
on the right of 3 is 9. 9 is higher than 5. Therefore 3 becomes a 4.
the answer is 45.4
Which statement describes a disadvantage of Marnie paying a bill by telephone with a credit card or a debit card? Marnie will not have to find a stamp and a mailbox. Marnie will have to share her card account information. Marnie’s bill is paid immediately. Marnie may be eligible for a discount
Answer:
The Answer is B Marnie will have to share her card account information.
Plus I took this test so
Answer:
B) Marnie will have to share her card account information.
Step-by-step explanation:
I took the test on Edge
Are all fractions integers?
Answer:
No
Step-by-step explanation:
Fractions and decimals are not integers. Any and all whole numbers like 1, 2, 3... Or even negative numbers like -1, -2, -3 etc. are all integers. However any fractions, decimals, etc. are NOT integers.
Hope this helps and have a nice day!
Answer:
no
Step-by-step explanation: no fractions are integers bc the are not orginally positive or negative but u can put them on a number line
A computer programmer works 40 hours per week. what is the equation that relates to the number of hours "h" that the programmer works and the number of weeks "w" that the programmer spends working?
Answer:
h = 40w
Step-by-step explanation:
40 per week
hours = 40 x amount of weeks
h = 40w
How do I find the domain and range of a graph?
The domain is the x-axis and the range is the y-axis.
To find the domain, you measure or count the widest part of this oval horizontally. So that is 3 units to the right of 0 and 3 units to the left of 0. I counted it exactly on the axis because that is the widest part of the oval.
To find the range, you again count or measure the widest part of the oval vertically. So that is 4 units above 0 and 4 units below 0.
Final Answer
D: -3 ≤ x ≤ 3
R: -4 ≤ x ≤4
The temperature of a freezer started at 18°C after cooling for a few hours the freezer had a temperature of -12°C what is the difference between the new colder temperature in the original temperature
Answer:
-273.15
Step-by-step explanation:
trust me and ull see
Find the remainder when x4+x3-2x2+x+1 is divided by x-1
(a)1
(b)5
(c)2
(d)3
Answer:
For example, if you want to find printable activities for third grade, click the "3" ... For each clock eliminated, the bedtime increases by one minute. ... Description: This activity requires students to tell time to the half-hour (e.g. 4:00, 5:30, 11:30).
Step-by-step explanation:
Simplify 9x + 4(x + 2) - 5:
Answer:
Step-by-step explanation:
9x+4x+8-5
=13x+3
Help me please 20 is 1/10 of
Answer:
20 is 1/10 of 200
Step-by-step explanation:
20* 10 = 200
Answer:
the answer is 200/1
A gym charges $45 per month and a $75 one-time starting fee. Which of these
will show how much it costs to join the gym for one year?
)
(45 x 12) + 75 = c
(45 + 75) x 12 =c
(75 - 45) x 12 = c
(75 x 12) + 45 = c
Answer:
(45 × 12) + 75 = c
Step-by-step explanation:
45 × 12 months + 75 starting fee
A horizontal line has points D, B, C. A line extends vertically from point B to point A.
Given that Ray B A bisects ∠DBC, which statement must be true?
a) m∠ABD = m∠ABC
b) AB ≅ BC
c) B is the midpoint of DC.
d) m∠DBC = 90°
Answer:
a) m∠ABD = m∠ABC
Step-by-step explanation:
The meaning of angle bisector is that each of the created angles is congruent to the other:
m∠ABD = m∠ABC
Answer:
A: m∠ABD = m∠ABC
A model of a plane is made using a scale of 1:5. If the wings of the model are 1.2m long, what is the actual length of the wings on the plane?
Answer:
6 m
Step-by-step explanation:
Multiply your scale by 1.2 m:
1 : 5 = 1.2 m : 6.0 m
The wings on the plane are 6.0 m long.
Is Happyville linear or exponential
Answer:
expoential
Step-by-step explanation:
Is the ration of 3/4 the same as the fraction of 3/4
Answer:
yes but there might be slightly change in it
Answer:
Yes 3/4 is the same as 3/4.
(I might be wrong)
Step-by-step explanation:
Step One: Rewrite the ratio as a fraction
[tex]3 : 4 = \frac{3}{4}[/tex]
Step Two: Reduce and simplify the fraction
This fraction is already reduced so no further work is needed
Hope this helped you!
Miguel did the following math problem: 65 ∙ 64 = 369. Which of the following is a true statement? 1.He is correct. 2.He is incorrect because he should have subtracted the exponents. 3.He is incorrect because he should have multiplied the exponents. 4.He is incorrect because he multiplied the bases.
Answer:
He is incorrect.
Step-by-step explanation:
The correct answer is 4,160.
Answer:
3. He is incorrect because he should have multiplied the exponents.
Step-by-step explanation:
6∧5 × 6∧4 = 369 Incorrect
Correct: 6∧5 = 7776
6∧4 = 1296
7776 × 1296 = 10,077,696
1. He is not correct, therefore the first answer is wrong.
2. You do not subtract the exponents unless one of the exponents is negative and you have the same bases. You have the same bases in this equation, however, neither one of them are negative. Therefore, the second answer is wrong.
3. The third answer is correct because if you were adding the two terms together then you would add the exponents together then multiply the base as many times as needed. However, since you are multiplying the two terms together, you also need to multiply the exponents together. From there, you then multiply the terms and get your answer.
4. The fourth answer is also incorrect because you need to multiply the bases together in order to get a correct answer.
I hope this helps!
An experienced computer technician can set up a network in 12 hours. It would take an intern 20 hours to set up the same network. If they work together, how long will it take to set up the network?
Answer:
X
Step-by-step explanation:
Answer:
ANSWER IS TIME
Step-by-step explanation:
time
list out the problem of solution of communication in Nepal
Answer:
the problem of solution of communication in Nepal are
Step-by-step explanation:
Usage of modern wireless and satellite based networking system keeping a backup networking system for the cases of nature disasterPlease help me ASAP
Answer:
Step-by-step explanation:
Base 5 uses 0, 1 , 2, 3, 4
When we add 2+ 1 = 3
When we add 4 +3 = 7 = 5 +2 . 5 will be carried as 1
4 + 3= 12
In subtraction, 32 - 4
From 2 we cannot subtract 4. So, borrow 5 from 3. So, 2+5 = 7.
7-4=3
32 -4 = 23
I have attached the sums
10+x=19 need your help
Answer:
9
Step-by-step explanation:
10+x=19
move 10 over the =
x =19-10
x=9
Hey there!
ANSWER: [tex]x=9[/tex]EXPLANATION:[tex]10+x=19[/tex]
To solve, you can just do 19 - 10.
[tex]19-10=9[/tex]
Now let's complete x.
[tex]10+x(9)=19\\10+9=19\\x=9(ANSWER)[/tex]
Hope this helps!
[tex]\text {-TestedHyperr}[/tex]
Find the midpoint of (-4,6) and (10,-10)
Answer:
(3,-2)
Step-by-step explanation:
10+4=14; 14/2=7
-4+7=3
x=3
6+10=16; 16/2=8
6-8=-2
y=-2
Answer:
(3,-8)
Step-by-step explanation:
m=x1+x2/2,y1+y2/2
m--4+10/2,-10-6/2
m=6/2,-16/2
m=3,-8
Jill sold half her comics and then bought sixteen more. She now has 36. How many did she begin.
Answer: 10 I think
Step-by-step explanation: Jill sold half and you dont know how much it is you know that now she has 36, but before she bought 16 so 36 - 16 = 20 but she sold half
Answer:10 magazines
Step-by-step explanation:
36-16/2=m
20/2=m
10=m. m=magazine
what is 1/4 to the power of 34???????
Answer:
I believe it is 3.3881318e-21 but you could round that
Step-by-step explanation:
Si en una proporción geométrica continua, la media geométrica es 24 y la razón es 2/3 ¿Cuánto es la diferencia de los extremos?. a)18 b)20 c)24 d)16 e)12
Write an equation of the parabola in intercept form that passes through (-2,0.05) with x-intercepts of -7 and -3.
Answer:
y = 0.01(x +7)(x +3)
Step-by-step explanation:
For intercepts p and q, the equation will be ...
y = a(x -p)(x -q)
For the given intercepts, the equation is ...
y = a(x +7)(x +3)
We can find the value of 'a' by using the given point:
0.05 = a(-2+7)(-2+3) = 5a
0.01 = a . . . . divide by 5
The complete equation is ...
y = 0.01(x +7)(x +3)
what is the gradient of the line 3x+y=4
Answer:
The slope is - 3Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
The equation is 3x+y = 4
To find the slope of the line we must first write the equation in the general form above
Make y the subject
That's
y = - 3x + 4
Comparing with the general equation above
Slope of the line = - 3
Hope this helps you
WHO WANTS A BRAINLIEST?
A (-3.5,1.25) B (-5,-3) C (-4,2) (-4,0) (-4.5,-2.25)
Answer:
A
Step-by-step explanation:
Find the midpoint by using A and B.
Then use the midpoint and B to find the 3/4 point.