[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-5}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{6}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 7 -5}{2}~~~ ,~~~ \cfrac{ 6 -4}{2} \right) \implies \left(\cfrac{ 2 }{2}~~~ ,~~~ \cfrac{ 2 }{2} \right)\implies (1~~,~~1)[/tex]
The midpoint of AB is M(-2, -6). If the coordinates of A are (1,−4), what are the coordinates of B?
Applying the midpoint formula, the coordinates of B are: (-5, -8).
How to Apply the Midpoint Formula?The midpoint formula is:
M(x, y) = [(x1 + x2)/2, (y1 + y2)/2].
Given the following:
M(x, y) = (-2, -6)
A(x1, y1) = (1,−4)
B(x2, y2) = (?, ?)
Plug in the values
M(-2, -6) = [(1 + x2)/2, (-4 + y2)/2]
Isolate each coordinate
-2 = (1 + x2)/2
(-2)(2) = 1 + x2
-4 = 1 + x2
-4 - 1 = x2
-5 = x2
x2 = -5
-6 = (-4 + y2)/2
(-6)(2) = -4 + y2
-12 = -4 + y2
-12 + 4 = y2
-8 = y2
y2 = -8
Therefore, applying the midpoint formula, the coordinates of B are: (-5, -8).
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The junior varsity football
team scored 23 points in last Saturday’s
game. They scored a combination of 7-
point touchdowns and 3-point field goals.
How many touchdowns and how many
field goals did they score?
Answer:
2 touchdowns, 3 field goals
Step-by-step explanation:
The number of touchdowns cannot be more than 3, so it is relatively easy to find the solution by trial and error.
23 is not divisible by 3, so 0 touchdowns is not a solution
23 -7 = 16 is not divisible by 3, so 1 touchdown is not a solution
23 -14 = 9 is divisible by 3, so 2 touchdowns and 3 field goals is a solution
21 -21 = 2 is not divisible by 3, so there is only one solution.
Answer:
1 touchdown and 3 field goals
rewrite each expression without using absolute value notation lx-1| if x>1
we can rewrite:
|x - 1| if x >1
as
(x - 1) with x > 1.
How to rewrite the expression?
Remember how the absolute value function works:
|x| = x if x ≥ 0.|x| = x if x < 0.In this case, we have the function:
|x - 1| if x >1
Then the minimum value (not included) that this can take is:
|1 - 1| = 0
So it is only 0 or positive, then we can use the first bullet point only, then we can rewrite:
|x - 1| if x >1
as
(x - 1) with x > 1.
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You are shopping for a new car. The dealer is offering a special deal whereby you can finance the car for 5 years at 0% interest. You can afford monthly payments of $225 with an absolute deviation of no more than $35. Write an absolute value inequality that represents the range of monthly car payments that you can afford. Use the absolute value button and use the variable x.
The absolute value inequality that represents the range of monthly car payments that you can afford is 52 < | x | ≤ 60.
What is absolute value inequality?An absolute value inequality is an inequality that has an absolute value sign with a variable inside.
Example: | x + 2 | > 4
We have,
Financing a car for 5 years.
Monthly payment = $225
Since 5 years = 5 x 12 months = 60 months.
The cost of the car:
= 60 x $225
= $13500
Absolute deviation = $35
This means monthly payments can be increased maximum up to $35.
So if the monthly payment is increased maximum we have the monthly payment as:
= $225 + $35
= $260
If $260 is the monthly payment then,
The number of months the car finance can be done is:
= $13500 / $260
= 51.9 months
The absolute value inequality for the range of months is:
52 < | x | ≤ 60
Where x is the number of months to finance the car.
Thus the absolute value inequality that represents the range of monthly car payments that you can afford is 52 < | x | ≤ 60.
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3
25% of the fish in a pond are trout, of the fish are goldfish and
10
the rest of the fish are perch.
Write the ratio of trout to goldfish to perch in this pond in its
simplest form.
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The ratio of Trout to Goldfish to Perch in the pond by using ratio and proportion theorem in its simplest form is 5:2:13
As per the question statement, we are supposed to find out the ratio of Trout to Goldfish to Perch in the given pond in its simplest form.
It is given that 25% of the fish in a pond are Trout, 10% are Goldfish and the rest 65% are Perch in the given pond.
Let's suppose there are 100 fishes in the pond so
Number of Trout = 25% of 100 = 25
Number of Goldfish = 10% of 100 = 10
Number of Perch = 65% of 100 = 65
Using ratio and proportion theorem,
Trout : Goldfish : Perch = 25:10:65
Trout : Goldfish : Perch = 5 : 2 : 13
Ratio and Proportion: An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is any equation that sets or uses two ratios at the same value.To learn more about ratio and proportion, click on the link given below:
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Are the red paths in the picture below perpendicular?
A. Yes
B. No
Answer:
Yes
Step-by-step explanation:
Perpendicular lines form 90-degree angles
points B (-6, 0) and C(-1, -5) are translated to B' and C', respectively.
What are the coordinates of B' and C'?
Answer: The answer would be for "B" that it's 6 units to the left and 0 units down and for "C" It would 1 to the left and -5 units down!
Step-by-step explanation: I used a graph to help me determine these coordinates :D
Paisley is deciding between two parking garages. Garage A charges an initial fee of $5 to park plus $3 per hour. Garage B charges an initial fee of $11 to park plus $2 per hour. Let A A represent the amount Garage A would charge if Paisley parks for t t hours, and let B B represent the amount Garage B would charge if Paisley parks for t t hours. Write an equation for each situation, in terms of t , t, and determine the interval of hours parked, t , t, for which Garage A is cheaper than Garage B.
Considering the definition of an inequality, the interval of hours parked for which Garage A is cheaper than Garage B is 6 hours.
Definition of inequalityAn inequality is the existing inequality between two algebraic expressions, connected through the signs:
greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.An inequality contains one or more unknown values called unknowns, in addition to certain known data.
Solving an inequality consists of finding all the values of the unknown for which the inequality relation holds.
Interval of hours parked for which Garage A is cheaper than Garage BIn this case, you know that:
Garage A charges an initial fee of $5 to park plus $3 per hour. Garage B charges an initial fee of $11 to park plus $2 per hour.Being "t" the time parked, in hours. If you want to determinate the interval of hours parked for which Garage A is cheaper than Garage B, the inequality that expresses the previous relationship is
5 + 3t < 11 + 2t
Solving:
3t - 2t < 11 -5
t < 6
Finally, the interval of hours parked for which Garage A is cheaper than Garage B is 6 hours.
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5 boxes of books in the room . Each box has 36 books . How many books in all
Which ordered pair is a solution to the inequality 4x - 3y < 16?
The ordered pair (3, -1) that is a solution is the one which makes the inequality TRUE when the value of the ordered pairs are substitute into the inequality 4x - 3y < 16
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.
WE have been given an inequality as 4x - 3y < 16.
Here, we need to get the ordered pair solution to the system of linear equations.
Then Substitute x = 3 and y = -1 into 4x - 3y < 16
4(3) - 3(-1) < 16
12 + 3 < 16
15 < 16
(TRUE)
Therefore, the ordered pair, (3, -1) is the solution because it is the only given ordered pair which makes the inequality true.
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An air traffic controller is tracking two planes.To start Plane A was at an altitude of 990 meters and plane B was at an altitude of 1476 meters.plane A is loosing altitude at 18 meters per second and plane b is loosing altitude at 27 meters per second.write an equation to show when the two planes would be at the same altitude
The equation representing when the two planes would be at the same altitude is 9x=486
In terms of mathematics, what is an equation?Equation: A declaration that two expressions with variables or integers are equal. In essence, equations are questions, and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.
From (a) we get that: Altitude of Plane A = 990-18x
Altitude of Plane B = 1476-27x
make 890 - 18x = 1476-27x
-18x+27 x = 1476-890
9x=486
X= 54
so pass 54 seconds will the two plane at the same altitude.
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The engineering department of a large company has 25 members. The members must select a chair person, a vice chairperson, a secretary, and a 4-person advisory committee. Determine the number of different ways this can be done.
Using permutations and combinations, The number of different ways this can be done is 316250 ways.
What exactly are combinations and permutations?A permutation is an orderly arrangement of the items or numbers. Combinations are a means to choose items or numbers from a collection or set of items without regard for the items' chronological sequence.
We will solve it using permutations and combinations
a. The number is ²⁵P₄= 25! / (25 - 4)!
25! / 21! = 25 × 24 × 23 × 22 = 303600 ways.
b. The number is ²⁵C₄= 25! / 4! . (25 - 4)!
= 25! / 4! . 21! = 25 × 24 × 23 × 22 / 4 × 3 × 2
= 12650 ways
Total number of ways to select persons are =
303600 + 12650
= 316250
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Wendell mailed four packages. Each weighed 1 and 3/8 pounds. What was the total weight of the four packages?
The total weight of 4 packets will be equal to 5 and 1 / 2 pounds.
We are given that:
The total number of packages = 4
Weight of each of the package is given as 1 and 3 / 8 pounds
Weight of 1 package = 1 and 3 / 8 pounds.
Weight of 1 package = 11 / 3 pounds
Now, we need to calculate the total weight of 4 packets.
We will do this my multiplying 4 with the weight of each packet.
So, we get that:
Total weight of 4 packets = 4 × 11 / 8 pounds.
Total weight of 4 packets = 11 / 2 pounds
Total weight of 4 packets = 5 and 1 / 2 pounds.
Therefore, the total weight of 4 packets will be equal to 5 and 1 / 2 pounds.
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Which is the graph of y ≤ 1 – 3x?
Step-by-step explanation:
To graph an equation using the slope and y-intercept, 1) Write the equation in the form y = mx + b to find the slope m and the y-intercept (0, b). 2) Next, plot the y-intercept. 3) From the y-intercept, move up or down and left or right, depending on whether the slope is positive or negative.
1. f(x)=5x^2-80x+69
2. f(x)=-9x^2+81x+6
The roots of f(x)=5x^2-80x+69, f(x)=-9x^2+81x+6 is mathematically given as
[tex]x=\frac{40+\sqrt{1255}}{5}, \frac{40-\sqrt{1255}}{5}[/tex]x=9.07347, -0.07347This is further explained below.
What are the roots of f(x)=5x^2-80x+69 f(x)=-9x^2+81x+6?Generally, the equation for the function is mathematically given as
f(x)=5x^2-80x+69
Therefore
Set5 x^2-80 x+69 equal to 0 .
5 x^2-80 x+69=0
Solve for x.
Use the quadratic formula to find the solutions.
[tex]\frac{-b+\sqrt{b^2-4(a c)}}{2 a}[/tex]
Substitute the values a=5, b=-80, and c=69 into the quadratic formula and solve for x.
[tex]\frac{80 \pm \sqrt{(-80)^2-4 \cdot(5 \cdot 69)}}{2 \cdot 5}[/tex]
[tex]x=\frac{40 \pm \sqrt{1255}}{5}[/tex]
The final answer is the combination of both solutions.
[tex]x=\frac{40+\sqrt{1255}}{5}, \frac{40-\sqrt{1255}}{5}[/tex]
In conclusion, we implore the same format to solve for
f(x)=-9x^2+81x+6
Roots
x=9.07347, -0.07347
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Evaluate each expression for the given values of the variables
-3[(w-6)^2+x]^2 ; w=5, x=6
The solution to the above question is -147
-3[(w-6) ^2+x] ^2 where the value of w = 5 and x amounts to 6
Using algebraic identity: (a-b) ^2 = (a^2 -2ab+b^2)
= -3 [(w^2 -2w*6 +6^2) + x] ^2
= -3 [(w^2 -12w+36) + x] ^2
now substitute the value of w = 5
= -3 [(5^2 -12*5+36) + x] ^2
= -3 [(25 -60+36) + x] ^2
= -3 [1+ x] ^2
Using algebraic identity: (a+ b) ^2 = a^2 +2ab + b^2
= -3 [1^2+2x*1+ x^2]
= -3 [1+2x+ x^2]
now substitute the value of x = 6
= -3 [1+2*6+ 6^2]
= -3 [1+12+ 36]
= -3 [49]
= -147
The above answer can be derived through direct substitution also. Both the methods will any way give the same answer.
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PLEASE ANSWER ASAP!!!! FULL ANSWER!! NO BEGGING FOR BRAINLIEST!!
Bob can row 9 mph in still water. The total time to travel downstream and return upstream to the starting point is 6 hours. If the total distance downstream and back is 30 miles, determine the speed of the river (current speed).
Current Speed = __________
If the total time to travel downstream and return upstream to the starting point is 6 hours. If the total distance downstream and back is 30 miles, the speed of the river (current speed) is 6.
Current speedTime = Distance/speed
Time taken to row upstream:
(30/2) /(9 - x)
15/(9-x)
Time taken to row downstream:
15/(9 + x)
Total time spent is 6 hours hence,
15/(9- x) + 15/(9 + x) = 6
Cross multiplying
15(9 + x) + 15(9 - x) = 6(9+ x)(9 - x)
= 135 + 15x + 135- 15x =6(81 -9x + 9x - x²)
=270 = 6(81 - x²)
270/6 = 81- x²
45 = 81- x²
x² = 81- 45
x²= 36
x =√36
x = 6
Therefore If the total time to travel downstream and return upstream to the starting point is 6 hours. If the total distance downstream and back is 30 miles, the speed of the river (current speed) is 6.
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You have a canteen that holds 32 fluid ounces and weighs 0.25 pounds when empty. Water weighs 0.065 pound per fluid ounce. You begin a hike with a full canteen of water. Write and simplify an expression for the weight of the canteen and water after you drink x fluid ounces.
The simplification of the expression for the weight of the canteen after drinking is 2.33 lbs
How to write the expressionThe total weight can be gotten as:
weight of empty canteen + ( 32 - x ) of the water x weight of water
This would be represented by
total weight = 0.25 + 0.065 * (32-x)
We have to open up the expression
weight = 0.25 + 2.08 - 0.065x
When the weight is 0 we would have
0.25 + 2.08 - 0.065x0
= 2.33 lbs
Hence the simplification of the expression for the weight of the canteen after drinking is 2.33 lbs
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In item 16, how many bacteria will there
be after 5 splittings?
(1) 2
(2) 4
(3) 8
(4) 16
(5) 32
Answer: 32 i think
Step-by-step explanation:
assuming there was one original bacteria, then multiplying it by two, or splitting it in two five times means 32
Serenity's car used 1/50 of a gallon to travel 5/8 of a mile. At what rate does the car use gas, in miles per gallon? On the double number line below, fill in the given values, then use multiplication to find the missing value.
Using proportions, it is found that the car uses gas at a rate of 31.25 miles per gallon.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
The gas consumption of the car is given by the proportion of number of miles divided by the number of gallons, hence:
(5/8)/(1/50).
To divide two fractions, we multiply the numerator by the inverse of the denominator, hence:
5/8 x 50 = 31.25.
The car uses gas at a rate of 31.25 miles per gallon.
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lee is traveling by train. he has 270 miles left to travel.after 2 hours,he has 180 miles remaining.the train travels at a constant rate for the entire trip.what is the speed of the train and the distance of the trip?
8. The number of steps needed to get from one floor to the next in a hotel staircase is 14. The ground level is floor 0.
a. Complete the table.
n(floor number)
s(total steps to reach floor)
1
14
2 3 4 5
Step-by-step explanation:
0 steps to reach floor 0.
a.
floor 0 to floor 1 = floor 0 + 14 = 0 + 14 = 14
floor 1 to floor 2 = floor 1 + 14 = 14 + 14 = 28
floor 2 to floor 3 = floor 2 + 14 = 28 + 14 = 42
floor 3 to floor 4 = floor 3 + 14 = 42 + 14 = 56
floor 4 to floor 5 = floor 4 + 14 = 56 + 14 = 70
b.
when we look at the calculation for the stairs to floor 1, then we see
floor 1 = floor 0 + 14 = 0 + 14 = 14
and for floor 2
floor 2 = floor 1 + 14 = floor 0 + 14 + 14 = 0 + 14 + 14 = 28
and for floor 3
floor 3 = floor 2 + 14 = floor 0 + 14 + 14 + 14 = 42
and so on.
we see
floor n = s(n) = s(0) + 14×n = 0 + 14×n = 14n
s(n) = 14n
2x - 3y less than or equal to 27?
Answer:less
Step-by-step explanation:
Answer:
Less Than
Step-by-step explanation:
Solve for yy. y=2x3y=2x3 Rewrite in slope-intercept form.y=23xy=23xUse the slope-intercept form to find the slope and y-intercept.Slope: 2323y-intercept: (0,0)(0,0)Any line can be graphed using two points. Select two xx values, and plug them into the equation to find the corresponding yyvalues.xy0032xy0032Graph the line using the slope and the y-intercept, or the points.
Find the formula for the nth term of the following sequence:
648, 108, 18, 3...
Include "n=" in your answer, and do not use any spaces.
The nth term of the sequence is Tn = 3888^n - 1
What is a geometric sequence?A geometric sequence can be defined as a sequence in which each term is determined by multiplying the preceding term in the sequence by the same value.
The formula for the nth term of a geometric sequence is expressed as;
Tn = ar^n - 1
Where;
Tn is the nth terma is the first termr is the common ratioFrom the given sequence, we have that;
a = 648
r = 6
Substitute into the formula
Tn = 648 × 6^n - 1
Tn = 3888^n - 1
Thus, the nth term of the sequence is Tn = 3888^n - 1
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Two of the dozen eggs in a carton are cracked. About what percent of the carton is cracked?
The most appropriate choice of percentage will be given by-
16.67 % of carton is cracked
What is Percentage?
Percentage is a ratio expressed as a percentage of 100.
Here,
Number of eggs cracked = 2
Total number of eggs = 12
Percentage of carton cracked = [tex]\frac{2}{12} * 100[/tex]
= 16.67 %
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What was the vertical distance, d, of his jump, rounded to the nearest tenth?
The vertical distance of the jump is 4.8 feet.
What was the vertical distance, d, of his jump, rounded to the nearest tenth?We know that the equation that relates the vertical distance of the jump and the time is:
t = √d/2
In this case, we know that the time is t = 1.09 seconds, replacing that in the equation we get:
1.09 = √d/2
Now we can solve that equation for d.
1.09*2 = √d
Now we apply an exponent of 2 in both sides to remove the square root:
2.18^2 = d = 4.8 ft
The vertical distance of the jump is 4.8 feet.
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What are the coordinates of the point on the directed line segment from (2, -1) to (9, 6) that partitions the segment into a ratio of 5 to 2?
Answer:
Fill in the blanks to declare sum equal to a + b (int _ = a __b)Which of the following is not a valid variable name in python?What shape represents the start and end of a flowchart?Which of the following is not a valid variable name in python?An integer data type can hold decimal values.Which of the following is not a valid variable name in python?An integer data type can hold decimal values.Which of the following is not a valid variable name in python?Fill in the blanks to declare sum equal to a + b (int _ = a __b)Variables must be defined with a name and a data type before they
can be usedAn integer data type can hold decimal values.Which of the following is not a valid variable name in python?Fill in the blanks to declare sum equal to a + b (int _ = a __b)Variables must be defined with a name and a data type before th
I NEED HELP. I NEED TO SOLVE THIS BUT I DONT KNOW HOW TO! I NEED TO TURN IT IN BEFORE THE 29TH!
Answer: 1: $27.92
Step-by-step explanation: Multiply the amount of goodie bags (8) by how much they cost individually ($3.49) and you should come out with the answer $27.92.
Answer: 2 : $37.5
Step-by-step explanation: This would be considered not using long division but this should be the only practical answer. Using long division you would come up with 37 with a remainder of 2, which doesn't seem to be correct.
Answer: 3 : $177.92
Step-by-step explanation: Adding the cost of both the goodie bags and the 4 hours worth of the bounce house the total should have came out to be, $177.92
Look at this triangle.
B
8 cm
A
22 cm
Work out length AB.
The length of AB of the given triangle ABC is 23.41cm.
What are triangles?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. The symbol for a triangle with the vertices A, B, and C is △ABC. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.So, Pythagoras's Theorem is used: a²+b² = c²
Where the hypotenuse is c and the sides of the triangle are a and b.If we swap the values,
B= 8 cmA= 22 cmThen,
22²+8² = c²484 + 64= c²√548 = cC= 23.41Therefore, the length of AB of the given triangle ABC is 23.41cm.
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PLEASE HELP MEEE.....
im not sure sry man....... delete this answer bc im not sure how to