The coordinates of point B are calculated using the midpoint formula. Substituting given values for points A and M allows us to find B's coordinates, which are (2, 8).
Explanation:The midpoint of a line segment is calculated using the formula M=(x1 +x2)/2, (y1+y2)/2 where x1 and y1 are the coordinates of the first point and x2, y2 are the coordinates of the second point. Given that the coordinates of point A are (6,-4) and the coordinates of the midpoint M are (4, 2), we can set up the following equations to solve for the coordinates of point B (x2, y2): (6+x2)/2 = 4 and (-4+y2)/2 = 2. Solving for x2 and y2 gives us the coordinates of Point B: (2, 8).
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Which graph represents the solution set of the system of inequalities?
−2x+y≤4
{
y>x+2
Answer:
Graph 2
Step-by-step explanation:
Given system of inequalities,
−2x + y ≤ 4,
y > x + 2
∵ Related equation of −2x + y ≤ 4 is,
-2x + y = 4 ⇒ y = 4 + 2x ----(1)
While, the related equation of y > x + 2 is,
y = x + 2
From equation (1),
4 + 2x = x + 2 ⇒ 4 + 2x - x = 2 ⇒ 4 + x = 2 ⇒ x = 2 - 4 ⇒ x = -2
Again by equation (1),
y = 4 + 2(-2) = 4 - 4 = 0
Hence, the intersection point of the related equation is (-2,0),
∴ Graph 1 and graph 3 can not be the graph of the given system.
Now, −2(0) + (0) ≤ 4 ( true )
That is, −2x+y ≤ 4 would contain the origin,
Also, 0 > 0 + 2 ( False )
That is, y > x + 2 does not contain the origin.
Therefore, by the above explanation it is clear that,
Grap 2 represents the solution set of the system of inequalities.
What is 3/8 equivalent to
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Question reads....}[/tex]
[tex]\large\textbf{What is }\rm{\bf \dfrac{3}{8}}\large\textbf{ equivalent to?}[/tex]
[tex]\huge\textbf{Now, let's solve for the given question:}[/tex]
[tex]\mathbf{\dfrac{3}{8}}[/tex]
[tex]\mathbf{= \dfrac{3\times2}{8\times2}}[/tex]
[tex]\mathbf{\approx \dfrac{3 + 3}{8 + 8}}[/tex]
[tex]\mathbf{= \dfrac{6}{16}}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{\dfrac{6}{16}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]The function f(x) is graphed on the coordinate plane.
What is f(−4) ?
Enter your answer in the box.
f(−4) =
For this case, what you should do is observe in the graph the value of the function when x = -4.
The value of the function is observed when looking at the vertical axis.
Remember that in a function of the form y = f (x) we have:
x: independent variable
y: dependent variable.
Therefore, for x = -4 we have:
f (-4) = 4
Answer:
The value of the function evaluated at x = -4 is given by:
f (-4) = 4
An open rectangular tank is made so as to contain 4.5 metres cube of liquid. The length must be twice the breadth and the amount of material used to make the tank must be minimum. Find the dimensions of the tank.
To find the dimensions of an open rectangular tank that holds 4.5 m3 of liquid with minimal material, set the length as twice the breadth and use calculus optimization to derive the breadth, length, and height.
Explanation:The student is asking for the dimensions of an open rectangular tank that can hold 4.5 m3 of liquid, where the length is twice the breadth, and the amount of material used should be minimal. To solve this, we will use optimization techniques often found in calculus.
Let the breadth be b, the length be l = 2b, and the height be h. The volume V of the tank is given by V = l \b \h = 4.5 m3. Therefore, 2b2h = 4.5.
The surface area A of the tank, which we need to minimize, is A = 2lh + 2bh + lb (since the top is open). Substituting l = 2b, we get A = 2(2b)h + 2bh + (2b)b.
From the volume equation, we can express h in terms of b, which is h = 4.5 / (2b2). Substituting this into the area equation and differentiating it with respect to b will give us a minimum. Finally, solving the equations will determine the breadth, from which we can find the length and height. By this process, we can find the dimensions with the least surface area.
A robot can complete 8 tasks in 5/6 or an hour.each tasks takes the same amount .how long does it take the robot to complete one task
Marika and her three friends attended a school play. Tickets cost 5.75 each and marina paid for everyone find the total cost of the tickets justify answer by using distributive property
The total cost of tickets for Marika and her three friends to attend a school play, with each ticket costing $5.75, is calculated using the distributive property to be $23.
Explanation:The question asks to find the total cost of tickets for Marika and her three friends attending a school play, with each ticket costing $5.75, and to justify the answer using the distributive property.
To calculate the total cost, we can use the formula for the total cost which is the number of tickets times the cost of one ticket. In this case, Marika is buying tickets for herself and three friends, making it a total of 4 tickets.
Therefore, using the distributive property, the total cost can be calculated as 4 tickets × $5.75 per ticket.
Using the distributive property, we can represent this as:
(4 × $5) + (4 × $0.75) = $20 + $3 = $23
Thus, the total cost of the tickets is $23.
help please ..................... and look below for full question instead of reporting me
You put $500 in your bank account. With an interest rate of 5%, how long will it take the account to reach $600?
What is:
1.8 divided by ——— = 60
Fill in the blank
Plz help I need this really quick
What is the maximum height of a projectile, such as a rocket, called?
what is three fourths of 500
out of 40 students in billy's class, 18 are girls. what percent of the students are boys?
There are 22 boys in Billy's class of 40 students, which means that 55% of the students are boys.
Explanation:To find the percent of students that are boys in Billy's class, we can start by calculating the number of boys. There are 40 students in total and 18 are girls. Therefore, the number of boys is 40 students minus 18 girls, which is 22 boys. Now, to calculate the percentage of boys, we use the formula:
Percentage = (Number of boys / Total number of students) × 100%
By inserting the numbers we have:
Percentage = (22 / 40) × 100%
Percentage = 0.55 × 100%
Percentage = 55%
So, 55% of the students in Billy's class are boys.
Please solve problem # 23
a theater has 4650 seats. if the theater sells all the tickets for each of its 5 shows, about how many tickets will the theater sell in all?
how many hours is it from 12am-5am
Plot the line for the equation on the graph. y−2=−2(x+4)
The plot of the given line is required.
The graph is shown below with two points [tex](0,-6)[/tex] and [tex](-3,0)[/tex].
The line is
[tex]y-2=-2(x+4)\\\Rightarrow y=-2x-8+2\\\Rightarrow y=-2x-6[/tex]
Let us find two points on the line
[tex]x=0[/tex]
[tex]y=-2\times0-6=-6[/tex]
[tex](0,-6)[/tex]
[tex]y=0[/tex]
[tex]0=-2x-6\\\Rightarrow x=\dfrac{6}{-2}=-3[/tex]
[tex](-3,0)[/tex]
Join the two points on the graph and the line will be constructed.
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The greatest common factor of 56 f^3g^2 and 70 fg^3 is 7 fg^3 .
true or false
Answer: False
Step-by-step explanation:
You can see 7*3*2*f*g is not the same as 7fg3, so the statement is false.
What percent of 100 is 40
an electrician can wire on average 4.5 houses per week. how many months will it take her to wire 55 houses if she wires the same number each week and figures on 4.5 week per month?
Final answer:
The electrician would take approximately 3 months to wire 55 houses at a rate of 4.5 houses per week.
Explanation:
An electrician can wire 4.5 houses per week.
To wire 55 houses at a rate of 4.5 houses per week, the electrician would take 55 / 4.5 = 12.22 weeks. As there are 4.5 weeks per month, dividing the total weeks by the weeks per month gives 12.22 / 4.5 = 2.72 months, which rounds up to 3 months.
A handyman charges fixed or r to visit a customer house in addition the handyman charges an hourly rate of H for each hour worked write a formula to represent T the total amount this handyman would charge for a job that requires N hours of work
Answer:
T = HN + r
Step-by-step explanation:
A handyman charges $H for each hour worked.
If the handyman works for N hours then the expression for the charges will be = $HN
Handyman charges a fixed amount = $r
Then the total amount charged T will be represented by
T = HN + r
Therefore, formula to calculate the total charges by handyman will be
T = HN + r
The perpendicular bisectors of ΔPQR intersect at point A as shown in the diagram. What is the radius of the circumscribed circle of ΔPQR?
A chef has 15 3/4 lb of beans. She packs them in freezer bags that weigh 2 1/4 lb each. How many freezer bags of beans does the chef pack?
A game involves rolling two dice, one after the other. jenny wins the game if both dice are even. Henry wins the game if either die is a 4.
-How may different outcomes are there ?
-list the outcomes for Jenny
-list the outcomes for Henry
-What is the probability that Jenny wins?
-What is probability that Henry wins?
-Is the game fair? why
-Are there any outcomes where the game will result in a tie ?
A. The total outcomes would simply be the product of the number of sides of the two dice, that is:
Total different outcomes = 6 * 6
Total different outcomes = 36
B. The combinations that both dice are even are:
2 – 2, 4 – 4, 6 – 6, 2 – 4, 2 – 6, 4 – 2, 4 – 6, 6 – 2, 6 – 4
So 9 combinations for Jenny
C. The combinations that at least one die is a 4 are:
4 – 4, 4 – 1, 4 – 2, 4 – 3, 4 – 5, 4 – 6, 1 – 4, 2 – 4, 3 – 4, 5 – 4, 6 - 4
So 11 combinations for Henry
D. The probability that jenny wins would simply be the ratio of the number of combinations for Jenny over the total number of combinations, that is:
P (Jenny) = 9 / 36 = 0.25 = 25%
So there is a 25% chance that Jenny will win.
E. The probability that Henry wins would simply be the ratio of the number of combinations for Henry over the total number of combinations, that is:
P (Henry) = 11 / 36 = 0.3056 = 30.56%
So there is a 30.56% chance that Jenny will win.
F. No the game is not fair because Henry has a higher chance of winning than Jenny. For it to be fair, they should have the same probability of winning.
G. We can see that there are actually combinations in which both Jenny and Henry would win. These are:
4 – 4, 4 – 2, 4 – 6, 2 – 4, 6 – 4
So there are 5 combinations in which both of them would win.
So the chance of being tie is:
P(tie) = 5 / 36 = 0.1389 = 13.89%
Hence a 13.89% chance of getting a tie
the estimated product of 20.7 and 9.18 after rounding both factors to the nearest whole number is
Determine the least common multiple of 12, 48, and 96.
12
36
48
96
Please help me!
x + 6 ≤ 8
helppppp pleaseeeeeeee
What is 121,580 Rounded to the nearest thousand?
ben 56 years, Kevin will be 9 times as old as he is right now.
Which graph represents y=⌈x⌉ over the domain 3≤x≤6 ?
Answer:The third graph (left of the bottom) represents [tex]y=\left \lceil x \right \rceil[/tex]over the domain 3≤x≤6.
Step-by-step explanation:
The Least Interger Function is represented by [tex]y=\left \lceil x \right \rceil[/tex].
The least integer function is a discontinuous function whose value at any number x is the smallest integer greater than of equal to x .It is denoted by [tex]\left \lceil x \right \rceil[/tex].and It is also known as ceiling of x. For example
[tex]\left \lceil3.4\right \rceil=4,\left \lceil5.6\right \rceil=6. \left \lceil4.4\right \rceil=5[/tex]
So the third graph (left of the bottom) represents [tex]y=\left \lceil x \right \rceil[/tex]over the domain 3≤x≤6.
[we can see all the value of x starting from 3 pointed at y=3 and for x≤ 4 are converging to y=4 which is represented by solid dot and so on ... ]