To find the coordinates of the other endpoint B given the midpoint M and one endpoint A. Apply the midpoint formula and solve the equations to find the coordinates of B(-1, 5).
Explanation:The midpoint coordinates are given as M(3, -2) and one endpoint is given as A(7, -9). To find the coordinates of the other endpoint, we can use the midpoint formula which states that the coordinates of the midpoint are the average of the coordinates of the two endpoints.
Let the coordinates of the other endpoint be B(x, y). Using the midpoint formula, we have:
[(x + 7) / 2, (y + -9) / 2] = (3, -2)
Simplifying the equation, we get:
(x + 7) / 2 = 3
(y - 9) / 2 = -2
Multiplying both sides by 2, we have:
x + 7 = 6
y - 9 = -4
Subtracting 7 from both sides, we get:
x = -1
Subtracting -9 from both sides, we get:
y = 5
Therefore, the coordinates of the other endpoint are B(-1, 5).
find s15 for the following sequence40,34, 28,22
Answer:
- 30
Step-by-step explanation:
Note the common difference d between consecutive terms in the sequence
d = 34 - 40 = 28 - 34 = 22 - 22 = - 6
This indicates the sequence is arithmetic with sum to n terms calculated as
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
Here a₁ = 40 and d = - 6, thus
[tex]S_{15}[/tex] = [tex]\frac{15}{2}[/tex] [ (2 × 40) + (14 × - 6) ], that is
[tex]S_{15}[/tex] = 7.5(80 - 84) = 7.5 × - 4 = - 30
Answer:
[tex]\displaystyle -44 = s_{15}[/tex]
Step-by-step explanation:
[tex]\displaystyle -6n + 46 = a_n \\ -6[15] + 46 = a_n \\ -90 + 46 = a_n \\ -44 = a_n[/tex]
Use the Arithmetic Sequence to figure this out.
I am joyous to assist you anytime.
At 5:00 p.m., Antonio turned on the oven. While the oven preheated, the temperature in the oven increased from 72°F to 400°F over a 10-minute period. The oven remained at 400°F for 45 minutes until Antonio turned it off. It took 60 minutes for the temperature in the oven to cool, returning to 72°F at 6:55 p.m. Which statement best explains whether or not the temperature in the oven is a function of the time?
A) It is a function because at any given time the oven was exactly one temperature.
B) It is a function because the oven temperature was the same at different times.
C) It is not a function because at any given time the oven was exactly one temperature.
D) It is not a function because the oven temperature was the same at different times.
Option A
It is a function because at any given time the oven was exactly one temperature.
Solution:
Given that,
At 5:00 p.m., Antonio turned on the oven
While the oven preheated, the temperature in the oven increased from 72°F to 400°F over a 10-minute period
The oven remained at 400°F for 45 minutes until Antonio turned it off
It took 60 minutes for the temperature in the oven to cool, returning to 72°F at 6:55 p.m
From above information,
5:00 ------------ 72°F
5:10 ------------------ 400°F
5:45 ------------------ 400ºF
6:55 -------------------- 72°F
Thus at any given time (input) the oven was exactly one temperature (a single output )
Therefore the statement that best explains is:
Option A) It is a function because at any given time the oven was exactly one temperature.
Since the definition of function states that there is a unique image corresponding to a element hence here the temperature at a given time is unique
Answer:
option a
Step-by-step explanation:
which property is illistarted by the statement (4+6.1)+7=4+(6.1+7)
Answer:
Commutative Property of Addition.
Step-by-step explanation:
The Commutative Property of Addition states that no matter what order you add the numbers, the outcome (answer) will all be the same.
~
Solve for 2:
8x - 41°
4x + 35°
Answer: x=19°
Step-by-step explanation:
First, add 41° to 35
Next, subtract 4x from 8x, then you should have your answer from there!
There is a carnival. Children are $1.50 and adults are $4. On this particular day there 2200 in attendance and the total amount of money raised was $5050. how many children and adults attended on that day.
Answer:
On that day 1500 children and 700 adults attended.
Step-by-step explanation:
Given:
There is a carnival. Children are $1.50 and adults are $4.
The total amount of money raised was $5050.
On this particular day there 2200 in attendance.
Now, to find the children and adults attended on that day.
Let the children attended be [tex]x[/tex].
And the adults attended be [tex]y[/tex].
The total number in attendance:
[tex]x+y=2200[/tex]
⇒ [tex]x=2200-y[/tex]........( 1 ).
Now, the total amount of money raised:
[tex]1.50x+4y=5050[/tex]
Putting the equation ( 1 ) in the place of [tex]x[/tex] we get:
⇒ [tex]1.50(2200-y)+4y=5050[/tex]
⇒ [tex]3300-1.50y+4y=5050[/tex]
⇒ [tex]3300+2.50y=5050[/tex]
Subtracting both sides by 3300 we get:
⇒ [tex]2.50y=1750[/tex]
Dividing both sides by 2.50 we get:
⇒ [tex]y=700.[/tex]
The adults attended = 700.
Now, putting the value of [tex]y[/tex] in equation ( 1 ) we get:
[tex]x=2200-700[/tex]
⇒ [tex]x=1500.[/tex]
The children attended = 1500.
Therefore, on that day 1500 children and 700 adults attended.
The fuel for a chain saw is a mix of oil and gasoline.
Answer:
it should be a 50:1 gas oil ratio.
Step-by-step explanation:
The school board administered a reading test to all eighth-grade students at High Achievers Charter School and determined that 10%, percent of them were reading below grade level.
Based on this data, which of the following conclusions are valid?
Choose 1 answer:
A 10% percent of students in this sample are reading below grade level, but we cannot conclude anything about the eighth-grade students at HACS.
B 10% percent of all students at HACS are reading below grade level.
C 10% percent of all eighth-grade students at HACS are reading below grade level.
The correct conclusion based on the data is that 10% of all eighth-grade students at the High Achievers Charter School are reading below grade level.
Explanation:Based on the information provided in the question, the most accurate conclusion we can make is that 10% of all eighth-grade students at High Achievers Charter School (HACS), specifically, are reading below grade level. This is because the sample data was only collected from eighth-grade students at HACS. Therefore,
answer C
is correct. That being said, these results only apply to this specific school and grade level and cannot be generalized for all students at HACS or all other schools.
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todd takes 3 tennis lessons and 4 swimming lessons a week whcih eqaution can be used to to find out how many lessons todd takes in 8 weeks
Answer:
8(3+4)
Step-by-step explanation:
simple use pemdas
parenthesis 3+4= 7
multiply 8x7=56 :)
Solve for x: 5/x = 4/x+3
Answer:
Step-by-step explanation:
5/x = 4/x+3
5 * ( x+3) = 4 * x
5x + 15 = 4x
5x - 4x = -15
x = ( -15)
What is the value of x in -4(5x-5)=120
Answer: x = -5
Step-by-step explanation: To solve this equation, we start by distributing the -4 through the parentheses on the left side.
So we have -4 times x which is -20x and -4 times -5 which is positive 20. So our equation now reads -20x + 20 = 120.
Solving from here, we subtract 20 from both sides of the equation and we have -20x = 100 and dividing both sides by -20, we find that x = -5.
Although I will not provide work to check our answer, the great thing about solving equations is that your can always check your answer by substituting what you got as a final answer into the original equation.
Answer:
The answer is X = -5.
At the start of the month, Jodie had sold 885 copies of her new book. At the end of the month, she had sold 1,364 copies of her book. If each book profits $13.97, approximately how much did the book profit in the entire month? A. $6,706 B. $31,486 C. $19,096 D. $12,390
Answer:
Option A. $6,706
Step-by-step explanation:
we know that
To find out how much was the book profit in the entire month, subtract the number of copies at the start of the month from the number of copies at the end of the month, and the result multiply by $13.97 (each book profits)
so
[tex](1,364-885)(13.97)\\479(13.97)=\$6,691.63[/tex]
so
approximately $6,706
what must be the value of y below so that the line passing through the points(4,4) and (-3,y) has a slope of -2?
Answer:
18
Step-by-step explanation:
Find the equation for the line in slope-intercept form: y = mx + b.
x and y are points on the line. Points are written in the form (x, y).
m is the slope.
b is the y-intercept, when it hits the y-axis.
Substitute the point (4, 4) and slope. x = 4; y = 4; m = -2. Find b
y = mx + b
4 = (-2)(4) + b
4 = -8 + b
b = 4 + 8
b = 12
Get the equation of the line using slope and the y-intercept.
y = -2x + 12
Substitute -3 as x and find the missing y.
y = -2(-3) + 12
y = 6 + 12
y = 18
The point was (-3, 18)
Therefore the missing value for y is 18.
To find the y-value, you substitute the given points into the formula for slope and solve for 'y'. In this case, the required value of 'y' is 18.
Explanation:The subject of your question is mathematics, specifically the concept of calculating the slope of a line. The slope (m) of the line through two points (x1,y1) and (x2,y2) is defined as m = (y2 - y1) / (x2 - x1). You are given that the points are (4,4) and (-3,y) and the slope is -2. Substituting the given points into the formula gives -2 = (y - 4) / (-3 - 4 ). Solving this equation will give you the value of 'y'.
First, simplify the denominator to get -2 = (y - 4) / -7. Afterward, multiply both sides by -7 to eliminate the fraction: -2 * -7 = (y - 4). This yields 14 = y - 4. Solve for 'y' by adding 4 to both sides of the equation, which gives that y = 18.
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A circle has a mass of 3 grams and a square has a mass of 2 grams. Which is the mass of a triangle?
Answer:
C
Step-by-step explanation:
The diagram shows the system in equilibrium. Left part consists of 3 circles, 2 triangles and 6 squares. Right part consists of 2 circles, 5 triangles and 3 squares.
If this system is in equilibrium, then the mass of the left part is the same as the mass of the right part.
The mass of the left part:
[tex]3\cdot 3+2\cdot \triangle +6\cdot 2=2\triangle+9+12=2\triangle+21\ grams[/tex]
The mass of the right part:
[tex]2\cdot 3+5\cdot \triangle+3\cdot 2=5\triangle +6+6=5\triangle +12\ grams[/tex]
Hence,
[tex]5\triangle +12=2\triangle +21\\ \\5\triangle -2\triangle =21-12\\ \\3\triangle =9\\ \\\triangle =3\ grams[/tex]
The mass of the triangle is 3 grams.
Given information:
A circle has a mass of 3 grams and a square has a mass of 2 grams.
From the given diagram of a mass balance, it can be concluded that:
The left side of the balance contains 6 squares, 2 triangles, and 3 circles.The right side of the balance contains 3 squares, 5 triangles, and 2 circles.Now, the left and right sides are balanced. So, the mass of left side will be equal to the mass of right side.
Let x be the mass of a triangle shape.
So, the value of x can be calculated as,
[tex]\texttt{mass of left side = mass of right side} \\6\times 2+2x+3\times 3=3\times 2+5x+2\times 3\\12+9+2x=6+6+5x\\3x=9\\x=3[/tex]
Therefore, the mass of the triangle is 3 grams.
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For the class of 2013's prom Norman's dress shop sold cheaper dresses for $90 each and more expensive dresses for $140 each. They took in $5250 and sold 20 more of the cheaper dresses than the expensive dresses. How many of each kind did they sell? Simply need help setting up the equations. I can solve them on my own.
Answer:
Number of cheaper dresses sold is 35
Number of expensive dresses sold is 15
Step-by-step explanation:
Given:
Cost of cheaper dresses = $90
Cost of expensive dresses = $140
Total cost of the dresses = $5250
To Find:
Number of cheaper dress = ?
Number of expensive dress = ?
Solution:
Let
The number of cheaper dresses be x
The number of expensive dresses be y
(Number of cheaper dresses X cost of cheap dress) + (Number of Expensive dresses X cost of expensive dress) = $5250
[tex]x \times90 +y \times 140 = 5250[/tex]= $5250
It is given that the 20 more of the cheaper dresses than the expensive dresses is sold
So,
number of cheaper dress = 20 + number of expensive dress
x = 20 + y---------------------------------------(1)
[tex](20+y) \times90 +y \times 140 = 5250 = 5250[/tex]
[tex](20 \times 90 +y\times 90) +y \times 140= 5250 [/tex]
[tex]1800 + 90y+ 140y = 5250 [/tex]
[tex]1800 + 230y = 5250 [/tex]
[tex] 230y =5250 -1800[/tex]
[tex] 230y = 3450 [/tex]
[tex]y = \frac{3450}{230}[/tex]
y = 15
Substituting y in (1)
x = 20 +15
x= 35
Helppppppp! Please
Comment the right answer
Answer:
The fourth option
Step-by-step explanation:
48 is the minimum height, 42 is his current height, and h is the height he must grow. 42 +h is at least 48 so that rules out the first and third options. The second option would be around twice the required height, so it must be the fourth option.
Determine if the ordered pair (−1, −5) is a solution to the inequality y is less than or equal to negative three fourths times x minus 1. No, because (−1, −5) is above the line Yes, because (−1, −5) is below the line No, because (−1, −5) is on the line Yes, because (−1, −5) is on the line
Answer:
Yes, because (−1, −5) is below the line.
Step-by-step explanation:
The given inequality is [tex]y \leq -\frac{3}{4} x - 1[/tex] .......... (1)
Now, rearranging this equality relation we get,
4y = - 3x - 4
⇒ 3x + 4y = - 4
⇒ [tex]\frac{x}{- \frac{4}{3} } + \frac{y}{- 1} = 1[/tex] .......... (2)
This equation is in intercept form and the line represented by this equation passes through the x-intercept [tex](- \frac{4}{3}, 0)[/tex] and y-intercept (0,-1).
Now, it is clear that (0,0) point is above the equation.
But (0,0) point does not satisfy the inequality equation (1).
Hence, the solution of the inequality equation (1) is below and including line (2).
Now, point (-1,-5) is below the line (2) and hence, it is a solution of the inequality (1) as it is below the line. (Answer)
Answer:
the answer is [yes, because (-1, -5) is below the solid line].
Step-by-step explanation:
I took the test and got it right
mridul jogs around a rectangular park of 100m by 80m at the rate of 9km per hour. how much time will he take in jogging 6 rounds
Final answer:
Mridul will take 14.4 minutes to jog around a rectangular park for a total of 6 rounds, considering the total jogging distance of 2.16 kilometers at a pace of 9 kilometers per hour.
Explanation:
To calculate the time Mridul will take to jog around a rectangular park for 6 rounds, we need to compute the total distance he will cover and then use his speed to find the time. The perimeter of the rectangle is the sum of all its sides. Since the park is 100m by 80m, the perimeter will be (2 × 100m) + (2 × 80m), which equals 360 meters. For 6 rounds, the total distance will be 6 × 360 meters = 2160 meters or 2.16 kilometers.
Next, we use the formula for time:
Time = Distance / Speed
Given Mridul's jogging rate is 9 kilometers per hour, we can convert this speed into meters per second to match the distance units by multiplying by 1000 and dividing by 3600 (the number of seconds in an hour), which gives us 2.5 meters per second. Finally, to find the time taken:
Time = 2160 meters / (2.5 meters/second)
This calculation results in 864 seconds, which when converted to minutes is 14.4 minutes. Therefore, Mridul will take 14.4 minutes to jog 6 rounds around the park.
How do u solve X- 98=104
Answer: x=202
Step-by-step explanation:
1st: Add 98 to 104, this should give you your answer of x=202
Answer:
202
Step-by-step explanation:
x-98=104
+98 +98 (you add because 98 is a negative)
x= 202you earn 360 dollars every 4 weeks how much money do you make in one week
Answer:$90
Step-by-step explanation:
360/4=90
Answer: $90 in one week
Step-by-step explanation:
Since you earn $360 every 4 weeks, you would have to divide $360 by 4 to find the amount of money you earn in one week.
360 divided by 4 = 90
So you earn $90 in one week.
How do I do 2/13×2/16
Answer:
1/52
Step-by-step explanation:
4/208=1/52
if x+ay =b and
ax-by=c
Then find out x , y . (with process)
Answer:
The solution of the given system of equations is,
[tex]x=\frac{b^2+ac}{a^2+b};\; y=\frac{ab-c}{a^2+b}[/tex]
Step-by-step explanation:
The given equations are :
x + ay = b .......(1)
ax - by = c .......(2)
We will use 'Substitution Method' to solve the given system of equations.
In this method, we will find out the value of either of the two variables that is 'x' and 'y' from one of the two equations in terms of the another variable and then substitute that value in the other equation to find the value of the another variable.
Now, we will be finding out the value of 'x' in terms of 'y' from equation (1) and then substitute it in the equation (2).
Consider the equation (1), that is,
x + ay = b ⇒ x = b - ay ........(3)
Substitute the value of 'x' from (3) in (2), we get
a(b - ay) - by = c
⇒ab - a²y - by = c
⇒-a²y - by = c - ab
⇒-y(a²+b) = c - ab
⇒y(a²+b) = ab - c
[tex]\implies y=\frac{ab-c}{a^{2}+b}[/tex]
Now, substituting the above value of 'y' in equation (3), we get
[tex]x=b-a(\frac{ab-c}{a^2+b})[/tex]
[tex]\implies x=\frac{b(a^2+b)-a(ab-c)}{a^2+b}[/tex]
[tex]\implies x=\frac{a^2b+b^2-a^2b+ac}{a^2+b}[/tex]
[tex]\implies x = \frac{b^2+ac}{a^2+b}[/tex]
Hence, the solution of the given system of equations is,
[tex]x = \frac{b^2+ac}{a^2+b} ;\; y = \frac{ab-c}{a^2+b}[/tex]
Jenny has $25 and earns $10 for each lawn that she mows.
Jenny wants to buy a concert ticket that costs $115.
Enter the minimum number of lawns Jenny needs to mow
to be able to buy the concert ticket.
Answer:
9 lawns
Step-by-step explanation:
If she already has $25 of the $115 dollars needed for the ticket, she only needs to make $90 more. If she makes $10 each lawn, she would need to mow 9 lawns in order to get the $90 dollars.
The range of y-sinx is the set of real numbers.
True
False
Answer:
False
Step-by-step explanation:
Image (graph) of y = Sinx is attached.
First, lets understand domain and range.
Domain is the set of all x-values for which a function is defined (x axis).
Range is the set of all y-values for which a function is defined (y axis).
We are said that range of y = Sin x is the set of all real numbers.
If we look at the graph and look at the y-values for which the function is defined, we see that the Sin Curve oscillates between y = -1 and y = 1.
So the range would be:
[tex]-1 \leq y \leq 1[/tex]
It is not defined for other values, certainly not for ALL REAL NUMBERS!
So, this statement is false.
tammy typed 40 pages of a report on Monday and 3/8 of the report on Tuesday. She completed the remaining 1/3 of the report on Wednesday . How manypages are there in the report?
Answer:
Step-by-step explanation:
R = report length
R = 40 + (3/8)R + (1/3)R
3/8 = 3*3/8*3 = 9/24
1/3 = 8*1 / 3*8 = 8/34
R = 40 + (9/24)R + (8/24)R
R = 40 + (17/24)R Subtract 17/24 from the left
R-17/24 R = 40
7/24 R = 40 Multiply both sides by 24
7R = 40 * 24
7R = 960 Divide by 7
R = 960/7
R = 137.1 which breaks the rounding rule and becomes 138 because something has to be typed on page 138
|60| ___ |-60| is it greater than > equal to = or less than
Answer:
[tex] |60| = | - 60| [/tex]
Step-by-step explanation:
They are equal. When the negative sign is inside the box the absolute value is positive, when the negative sign is outside the box THEN it is negative.
Answer: equal to
Step-by-step explanation: Absolute value means distance from zero on a number line. To represent the absolute value of a number, we use a vertical bar on either side of the number like we see in this problem.
So for the absolute value of 60, we know that 60 is 60 units from zero on a number line which means that the absolute value of 60 is just 60.
For the absolute value of -60, we know that -60 is also 60 units from zero on the number line so the absolute value of -60 is also 60.
Now we know that the absolute value of -60 is 60 and the absolute value of 60 is also 60. Since 60 is the same as 60, it means that 60 is equal to 60.
Another way of thinking about absolute value is that no matter what number you have inside the absolute value, your result will always be positive except for 0 which has an absolute value of 0.
In other words, the absolute value of any number is the positive version of that number. Again, not including zero.
Karen has $1.70 in coins. Karen has 8 coins, all of which are quarters or dimes.
1. Write an equation to represent the amount of coins Karen has.
2.Write an equation to represent the value of the coins Karen has.
☆ The equations has to be in the systems of linear equations and Inequalities.
So can someone help me with these 3 parts?
x+y=8 and 25x+10y=170 are the linear equations.
x+y≤8 and 25x+10y≤170 are the inequalities.
Step-by-step explanation:
Given,
Worth of coins = $1.70 = 1.70*100 = 170 cents
Number of coins = 8
1 quarter = 25 cents
1 dime = 10 cents
Let,
x represent the number of quarters
y represent the number of dimes
1. Write an equation to represent the amount of coins Karen has.
x+y = 8
2.Write an equation to represent the value of the coins Karen has.
25x+10y=170
x+y=8 and 25x+10y=170 are the linear equations.
For inequalities, the amount cannot increase number of coins and worth but it can be less, therefore,
x+y≤8
25x+10y≤170
x+y≤8 and 25x+10y≤170 are the inequalities.
Keywords: linear equations, addition
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If the area of a living room wall is 70 square feet, how many feet long is the living room wall
Answer: 4.25 feet
Step-by-step explanation:
a-living room wall in feet
area=a²
70sqf²=a²
a=√70
a=4.248 feet
Find ( f o g) (x) when f (x) = x^2+6x+5 and g(x)=1/x+1
The composite function (f o g)(x) is found by substituting g(x) into the f(x) expression. Upon simplification, (f o g)(x) when f (x) = x²+6x+5 and g(x) = 1/(x+1) is: 1/(x² + 2x + 1) + 6/(x+1) + 5.
Explanation:To find the composite function (f o g)(x) when f (x) = x²+6x+5 and g(x) = 1/(x+1), we substitute g(x) into f(x). That is, wherever you see 'x' in f(x), replace it with what g(x) is equal to.
Start with f(g(x)) = f(1/(x+1)). In f(x), replace x with 1/(x+1), which gives us: (1/(x+1))² + 6*(1/(x+1)) + 5. This is the composite function (f o g)(x).
To simplify further: the first term '(1/(x+1))²' becomes '1/(x² + 2x + 1)', the second term '6*(1/(x+1))' becomes '6/(x+1)', and the third term is just '+5'. So the composite function (f o g)(x) simplifies to: 1/(x² + 2x + 1) + 6/(x+1) + 5.
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What is 18 divided by 6 and add 4? lk it sounds easy but yep
18 divided by 6 is 3
when you add 3 with 4 it gives you 7
7 is your total answer
18/6 + 4
18/6 = 3
3 + 4 = 7
The answer is 7.
2.) The graph of a proportional relationship is shown.
Money
Total Savings (5)
Number of Weeks
What is the amount of savings per week?
Answer:
[tex]\$47\ per\ week[/tex]
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
In his problem
The amount of savings per week is equal to the constant of proportionality k or slope of the linear equation
so
Looking at the graph
take the point (2,94)
x=2 weeks, y=$94
Find the value of k
[tex]k=\frac{y}{x}[/tex]
substitute the values of x and y
[tex]k=\frac{94}{2}[/tex]
[tex]k=\$47\ per\ week[/tex]