Answer:
(¹/₂, 0)Step-by-step explanation:
2x + 5y = 1 ⇒ 2x = 1 - 5y
y = 2xy + 5
y = (1 - 5y)y + 5
y = y - 5y² + 5
5y² = 5
y² = 1
y₁ = 1 ∨ y₂ = -1
2x₁ = 1 -5(1) 2x₂ = 1 - 5(-1)
2x₁ = 1 - 5 2x₂ = 1 + 5
2x₁ = -4 2x₂ = 6
x₁ = -2 x₂ = 3
Midpoint:
[tex]M=\left(\frac{x_1+x_2}2\ ,\ \frac{y_1+y_2}2\right)=\left(\frac{-2+3}2\ ,\ \frac{1+(-1)}2\right)=\left(\frac12\ ,\ 0\right)[/tex]
The coordinates of the midpoint of the line AB is (0, 1/2).
The equation of the curve is given by y = 2xy + 5.
The equation of the line is given by 2x + 5y = 1.
We have to first find the point of intersection between the curve and the line and then find the coordinates of the midpoint of line AB where A and B is the point of intersection between the curve and the line.
What is the formula for finding the coordinates of a point that divides a given line in the ratio m:n?If C(x, y) divides a line AB in m:n then we have,
[tex]x = \frac{mx_2 +nx_1}{m+n},~~~y =\frac{my_2+ny_1}{m+n}[/tex]
And if C(x,y) is the midpoint then m = n.
we have,
[tex]x = \frac{x_2 +x_1}{2},~~~y =\frac{y_2+y_1}{2}[/tex]
Where x and y are the coordinates of the midpoint o the line AB.
Find the point of intersection between the line and the curve.
y = 2xy + 5............(1)
2x + 5y = 1..............(2)
From (2) we have,
2x = 1 - 5yx = (1-5y) / 2..........(3)
Substituting (3) in (1).
[tex]y =2\frac{(1-5y)}{2}y + 5\\\\y =\frac{2y-10y^2}{2} + 5\\\\2y = 2y - 10y^2 + 10\\\\10y^2 = 10\\\\y^2 = 1[/tex]
So we have,
y = 1 and y = -1
Puttin y = 1 in (3) we get,
x = (1 - 5) / 2 = - 4 / 2 = -2
Puttin y = -1 in (3) we get,
x = {1-5(-1)} / 2 = (1+5) / 2 = 6 / 2 = 3
Now we have two points of intersection A( 1, -2 ) and B( -1, 3 ).
Finding the coordinates of the midpoint of the line AB.
we have,
[tex]A(1, -2) = A (x_1, y_1)~~and~~B(-1, 3) = B(x_2, y_2)[/tex]
Substituting in the given equation.
[tex]x = \frac{x_2 +x_1}{2},~~~y =\frac{y_2+y_1}{2}\\\\x = \frac{-1 +1}{2},~~~y =\frac{3+(-2)}{2}\\\\x = 0,~~~y=\frac{1}{2}[/tex]
So the coordinates of the midpoint is (x,y) = ( 0, 1/2 ).
Learn more about the midpoint of a given line here:
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Diego pours 6.8 ounces of water from a full bottle. He estimates that he poured out 20% of the water in the bottle. About how much water was in the full bottle? Diego pours out 25% of the remaining water. About how many ounces did he pour the second time? Explain your reasoning.
Answer:
34 ounces were in the full bottle , The second time he poured about 7.48 ounces
Step-by-step explanation:
20 times 5 = 100 so,
6.8 times 5 = 34
PART 2
Diego poured out 20% wich is equal to 6.8 and if you subtract both pour's that he did you get 20.4. The you subtract that amount that he had already poured from the total wich gives you 13.6 and 5% of 13.6 is 0.68. Add 0.68 and 6.8 to get 7.48
Pls help solve this question
Interpretation of axes and scales:
The horizontal axis (x-axis): There is time in seconds on the horizontal axis
Scale: 1 unit in the x-axis = 1 second
The vertical axis (y-axis): There is the distance in feet which is the height of the elevator from the ground on the horizontal axis
Scale: 1 unit in the y-axis = 20 feet
Interpretation of the origin:
The coordinate is represented by the point (0,0) in the graph. This means at time = 0 the height of the elevator =0, i.e the elevator is on the ground at the starting time.
2. Mrs. Ellison brought 30 cookies to the school picnic last year. This year she brought 45
cookies. What was the percent of change?
Answer:
15%
Step-by-step explanation:
45 - 30 = 15
Answer - 15%
I need that r d d d d d. D d d d d d d. D
Answer:
D is not a function.
Step-by-step explanation:
The first option is a function because it makes up a straight line. The second option is also a function because it is also known as y = -3/2x + 2 creating a slope function. The third option is also a function because there is no more than one point for each x value. The last option is not a function because the number 2 is going for 2 variables A and B and you can't have them with more than one so D is your answer.
Answer:
D is not a function.
Step-by-step explanation:
The first option is a function because it makes up a straight line. The second option is also a function because it is also known as y = -3/2x + 2 creating a slope function. The third option is also a function because there is no more than one point for each x value. The last option is not a function because the number 2 is going for 2 variables A and B and you can't have them with more than one so D is your answer.
Please help ASAP!! WILL GIVE BRAINLIEST!!!!! This will get my grade up to passing, please. Who ever helps tysm. :)
Answer:
J=18.5
K= 16
L= 17
M= 18
W= 625
X=645
Y= 729
Z= 1000
I don't understand this?
Answer:
THE ANSWER IS B. If someone owes something the number is negative, and if someone has money the number is positive, MARK ME BRAINLIEST!!!!!!
Step-by-step explanation:
On a test with 25 problems, Grace got 88% correct. How many problems did Grace get correct?
Answer:
3 I think forgive me if im wrong.
Step-by-step explanation:
Pls help will give brainiest
Answer:
0.75
Step-by-step explanation:
two right triangles that are not similar can still have a pair of congruent acute angles.
A. True
B. False
Answer:False.
Step-by-step explanation:Any two right triangles, similar or not, must have one pair of congruent angles, the right angles. If one pair of acute angles angles is congruent, then by AA Similarity, the triangles are similar.
Triangle GHI with vertices G(4, 1), H(5, -4), and I(2, -8) REFLECTED over the line y = x.
Answer:
[tex]G' = (1,4)[/tex]
[tex]H' = (-4,5)[/tex]
[tex]I = (-8,2)[/tex]
Step-by-step explanation:
Given
[tex]G = (4,1)[/tex]
[tex]H = (5,-4)[/tex]
[tex]I = (2,-8)[/tex]
Reflection: [tex]y = x[/tex]
Required
Determine the coordinates of G'H'I'
The following applies when a line A is reflected over [tex]y = x[/tex]
[tex]A = (x,y)[/tex]
[tex]A' = (y,x)[/tex]
i.e, we simply swap the positions of x and y
So, for:
[tex]G = (4,1)[/tex]
[tex]H = (5,-4)[/tex]
[tex]I = (2,-8)[/tex]
The reflections are:
[tex]G' = (1,4)[/tex]
[tex]H' = (-4,5)[/tex]
[tex]I = (-8,2)[/tex]
See attachment
5+(−3)(6x−5) using distributive property
Answer:
x= -1.8
Step-by-step explanation:
5+(-3)(6x-5)
the -3 goes into the 6x and -5
5+(-18x)+15
switch so like terms are together
5+(-5) these cancel out leaving you with
-18x+15-5
combine like terms
-18x+10
divide both sides by -18
x=-1.8
what is the value of (-5)^4?
Answer:
625
Step-by-step explanation:
(-5)×(-5)×(-5)×(-5) = 625
Answer:
625
Step-by-step explanation:
-5x-5x-5x-5=625
Graph the function f(x)=−14x−2.
Use the line tool and select two points to graph.
Answer:
You should do this on your own but if you consider the way I graph it, the slope should be going downwards and in the middle of the graph, the y-intercept should be two units down. Each unit for the x line should be 14 units apart as stated in the function.
Step-by-step explanation:
Hopefully this helps ^^
Answer:
F
(
x
)
=
−
7
x
2
−
2
x
+
C
Step-by-step explanation:
simplify
plzzzzzzzzzzzzzzzzzzzzzzzzz
Answer:
I think it's 12 a⁹ b⁷ correct me if I'm wrong
Answer:
4a3b2×3a6b5
=12a9b7
Help me I need this quick
Answer:
I think 3,9, and 15
Step-by-step explanation:
its all in the picture
Answer:
6
Step-by-step explanation:
..............................
Answer:
f(- 3) = 6
Step-by-step explanation:
f(- 3) means what is the value of f(x) when x = - 3
Locate x = - 3 on the x- axis
Then go vertically up to meet the graph at (- 3, 6 )
The value of f(- 3) is therefore 6, that is
f(- 3) = 6
help please? don't put anything If you don't know the answer or else ill report
Answer:
d. (-3,-1)
Step-by-step explanation:
what is 1x+3y=18 in slope intercept form
Answer:
y = -x/3 + 6
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra I
Standard Form: Ax + By = C
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define
Standard Form: x + 3y = 18
Step 2: Rewrite
Find slope-intercept form
Subtract x on both sides: 3y = -x + 18Divide 3 on both sides: y = -x/3 + 6Answer:
y=-3x+6
Step-by-step explanation:
slope int. form is y=mx+b
want to get y by itself, so subtract 1x
so you are left with 3y=-1x+18
then divide 3
left with y=-1/3x+6
simplified is y=-3x+6
Solve the equation. 15 = 2w – 5
Answer:
hope my answer is helpful to you
plz mark me as brainlist and also follow me
Answer:
w=10
Step-by-step explanation:
you would first add 5 on both sides. Then you would get 20=2w then you would divide 2 by both sides. w=10
What percent is represented by the shaded area?
The tape diagram below represents 100%, percent.
Hyan has saved $300 more than two-thirds of the cost of the down
payment on a car. If he has $1240 saved, how much is the down payment?
algebra problem
Answer:
$1410
Step-by-step explanation:
Hyan has $1240 saved, which is equal to 2/3 of the down-payment, plus an additional $300
$1240-$300= $940
$940 is equal to 2/3 of the payment, in other words, it's two 1/3 payments, so we can split $940 into two to see how much is equal to 1/3 of the payment.
$940/2= $470 = 1/3
Three 1/3 equal 1 whole so we multiply $470 by 3 to find the amount of the whole payment
$470x3= $1410
rs=5y+2 , st=2y+3 , rt=12y-15 what is the value y
Answer:
6
Step-by-step explanation:
5y + 2 +2y + 3 = 12 - 15
7y + 5 = 12y - 15
7y + 20 = 12y
20 = 5
6
Lana is deciding whether to buy a pool pass for the summer. A pass costs $36.00 and
$1.00 for admission each day. Without a pass, the cost is $5.00 per day. Use the
system of equations below to find the number of days, d, Lana will need to go to the
pool for the cost, c, to be the same with and without a pass.
Answer:
9 days
Step-by-step explanation:
Help pls! will give brainliest!
what is a 11 percent markup of $18
Answer:
$16.02
Step-by-step explanation:
Answer:
$20.22
Step-by-step explanation:
If Roger ran 5 miles in 150 minutes, Ryan ran 10 miles in 300 miles, and Rick ran 5 miles in 2 and ½ hours, who had the best rate of running(fastest time)?
Answer:
All three have same rate of running.
Step-by-step explanation:
Given that:
Distance covered by Roger = 150 minutes
Time taken by Roger = 5 miles
Distance covered by Ryan = 300 minutes
Time taken by Ryan = 10 miles
Distance covered by Rick = 2[tex]\frac{1}{2}[/tex] hours
Time taken by Rick = 2 miles
To find:
Who has the fastest rate of running?
Solution:
First of all, we need to convert the time in hours and then we need to apply the formula for relation between Speed, time and distance.
Then we can compare the Speed.
60 minutes = 1 hour
150 minutes = [tex]\frac{1}{60} \times 150 = 2.5\ hours[/tex]
300 minutes = 5 hours
Formula for Speed:
[tex]Speed = \dfrac{Distance}{Time}[/tex]
Rate of running (speed) of Roger = [tex]\frac{5}{2.5}[/tex] = 2 miles/hr
Rate of running (speed) of Ryan = [tex]\frac{10}{5}[/tex] = 2 miles/hr
Rate of running (speed) of Rick = [tex]\frac{5}{2.5}[/tex] = 2 miles/hr
Therefore, All three have same rate of running.
Suppose that point R is the center of a circle that is circumscribed about an equilateral Triangle ABC,and points M,P,and Q are midpoints of the sides of ABC. Part A: Prove that RM=RP=RQ
Answer:
Solution in image
Step-by-step explanation:
The diameter of a football is 12 cm. Calculate its volume.
Answer:
(4/3)*(22/7)*6*6*6
answer is 905.14
An angle is 58º less than its supplement. What is the measure of the angle?
Answer:
i think it is 122 degrees, as the solution would be to subtract 58 from 180
Step-by-step explanation:
180-58=122
angle1 = x
angle2 = x - 58
given,
these are supplementary angles
Therefore,
(x) + (x - 58) = 180
x + x - 58 = 180
2x - 58 = 180
2x = 180 + 58
2x = 238
x = 238/2
x = 119
angle1 = 119
angle1 = 119angle2 = 61
please help!! I'm confused
Can someone please help me I have been stuck what one
Answer:
The inequality matches the graph is 2n + 5 ≤ 7 ⇒ A
Step-by-step explanation:
Let us solve the question
From the given graph
∵ The arrow starts from 1 and pointed to the left (negative part)
∵ The starting point of the arrow is bold
∴ The sign of the inequality is ≤ (smaller than or equal)
→ That means the solution of the inequality is all the numbers ≤ 1
∴ The solution of the inequality is n ≤ 1
→ Look at the choices and find which one has the sign ≤ and check if
it will give the same solution or not
∵ The inequality is 2n + 5 ≤ 7
→ Subtract 5 from both sides
∴ 2n + 5 - 5 ≤ 7 - 5
∴ 2n ≤ 2
→ Divide both sides by 2
∴ n ≤ 1
∵ The inequality gives the same solution of the given graph
∴ The inequality matches the graph is 2n + 5 ≤ 7