If a ship is 90 miles South and 20 miles east of Port , then for the captain to travel directly to port , the captain should take a bearing of N 12.53° W .
the distance of ship = 90 miles south and 20 miles east of port .
let the bearing that the captain should take to directly travel to the port is = θ ;
So , the bearing angle can be calculated by using the trigonometric ratio ;
⇒ Tanθ = 20/90 ;
⇒ Tanθ = 2/9 ;
⇒ θ = arctan(2/9) = N 12.53° W ;
Therefore , The captain should take a bearing of N 12.53° W .
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The roots of the equation x²-kx+28=0 are alpha (a) and alpha (a) + 3. Find the values of k.
The possible values of k are -11 and 11.
Given that equation is: x²-kx+28
Roots are: [tex]\alpha ,\alpha +3[/tex]
To find: the value of x:
The general quadratic equation is:
ax²+bx+c
Product of roots=c/a
sum of roots=-b/a
From given,
x²-kx+28=0
a = 1
b = -k
c = 28
Therefore,
Product of roots=28/1=28
sum of roots=-k/1=-k
Given roots are:
[tex]\alpha ,\alpha +3[/tex]
Therefore,
The two roots are two numbers whose difference is 3 and whose product is 28
Those two roots are 4 and 7 or -4 and -7
Then, the sum of roots is:
4 + 7 = 11
-4 - 7 = -11
Therefore, the possible values of k are -11 and 11.
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Prompt: We recently completed a unit in math about transformations.
Compare and contrast the three types of transformations: translations, reflections, and rotations.
Include the algebraic rules, whether each transformation preserves congruence and any examples of
real-world application.
The translations, reflections, and rotations are types of transformations that change an original object to form a new image, each with its own specific rule and properties. They are used in a variety of real-world applications to change the position or orientation of objects.
There are 3 types of Transformations :
(i) Translation: A translation involves moving an object from one place to another without changing its size or orientation.
The algebraic rule for a translation is to add the same constant to each coordinate of each point
The Translations preserve congruence, meaning that corresponding parts of congruent figures will still be congruent after a translation.
An example of a real-world application of translation is moving a store to a new location.
(ii) Reflection: A reflection involves flipping an object over a line or point, creating a mirror image.
The algebraic rule for a reflection is to negate the value of one of the coordinates.
Reflections preserve orientation, meaning that the orientation of the reflected image is opposite that of the original object.
An example of a real-world application of reflection is looking at your reflection in a mirror.
(iii) Rotation: A rotation involves turning an object about a fixed point, called the center of rotation, through a certain angle.
The algebraic rule for a rotation is to multiply each coordinate by a rotation matrix.
Rotations preserve distance and angle measures, meaning that the lengths of corresponding parts and the angles between them are equal in the original and rotated images.
An example of a real-world application of rotation is turning a steering wheel to change the direction of a car.
The given question is incomplete , the complete question is
Compare and contrast the three types of transformations: translations, reflections, and rotations.
Include the algebraic rules, whether each transformation preserves congruence and any examples of real-world application.
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Evaluate the expression.
8+(22+15)
=
Step-by-step explanation:
8 + (22 + 15) = 8 + 37 = 45
To evaluate the expression, we must first perform the operations inside the parentheses. In this case, 22 + 15 = 37. Then we can add 8 to that result, which gives us 8 + 37 = 45. So the final value of the expression is 45.
Answer:
Using BODMAS, you are to solve the one in the bracket
22+15 which=37
then you add it to 8
37+8=45
An Olympic-distance triathlon includes a 1. 5 km swim. To determine the swim course of an Olympic-distance triathlon in Shoe Lake, the planners need to first find the distance between points A and B on opposite sides of a lake in order to determine where to place the buoys that will mark the swim course. You have been called in to help with determining the distances. From a point C on the shore, you find that CA = 259 m, CB = 423 m, and angle ACB measures 1320.
A. Determine the distance across the lake
B. Is the lake long enough to simply have an "out-and-back" swim course for this triathlon (that is: swimming from point A to point B and then back to point A)? If not, what additional distance will need to be set off of the straight-line distance between A and B in order to meet the distance requirements for this triathlon?
Answer: A. The distance across the lake is 626.6 m.
B. The lake is not long enough Additional 123.4m distance will need to be set off.
Step-by-step explanation:
what is the remainder when 5x-3 is divided by x-4
Answer:
The answer is 4
answer mine
Here is a rectangle with length 5 units and width 2 units.
1. What is the area of the rectangle?
2. Dilate rectangle ABCD from point A by a scale factor of 2. Calculate the area of the image.
3. Dilate rectangle ABCD from point A by a scale factor of 3. Calculate the area of the image.
This refers to the ratio between the scale of a given original object and a new object. It is its representation but of a different size (bigger or smaller). For example, if we have a rectangle of sides 2 cm and 4 cm, we can enlarge it by multiplying each side by a number, say 2.
Solving for the area and scale factor we have:
L= 5 units
W = 2 units
The area of the rectangle =L * WA = (5 x 2)
A = 10 square units.
If the rectangle is dilated from point A by a scale factor of 2, the area of the image:A= (Scale factor of L * W)* L * W
= (2 x 2 x 5 x 2)
A = 40 square units.
If the rectangle is dilated from point A by a scale factor of 3, the area of the image is:A= (Scale factor of L * W)* L * W
= (3 x 3 x 5 x 2)
A= 90 square units
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Two car leave from the ame location but travel in the oppoite direction. The firt car travel an average of 50 mi/hr and leave 15 min before the econd car, which travel an average of 55 mi/hr. How long will each car travel before they are 200 mi apart?
The first car will travel for 38.2 hours and the second car will travel for 38 hours before they are 200 miles apart.
Let x = time in hours for the first car and y = time in hours for the second car. Since the two cars are traveling in opposite directions, we know that the rate of the cars' combined travel is the difference between their two rates. So, we can create the expression:
50x - 55y = 200
We can also create a second expression using the amount of time that passed between the two cars:
x - y = 0.25
We can solve this system of equations with substitution. Let's substitute the second equation into the first:
50x - 55(x - 0.25) = 200
Simplifying, we have:
5.25x = 200.25
Now, we can isolate x:
x = 200.25/5.25 ≈ 38.2 hours
We can use this value to find y. We know that x - y = 0.25, so we have:
y = x - 0.25 = 38.2 - 0.25 = 38 hours
Therefore, the first car will travel for 38.2 hours and the second car will travel for 38 hours before they are 200 miles apart.
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4^{x} = 2^{x-3}[/tex]
Answer:
X 3y 2
Step-by-step explanation:
8x+4y=49
3x+2y=21
solve using elimination
The solution of the equations using elimination method is x = 2.5, y = 5.25
How to solve equations using elimination method?The elimination method is a method used to solve systems of linear equations. It involves manipulating the equations in such a way that one of the variables is eliminated, resulting in an equation in one variable that can be easily solved.
8x+4y = 49 --- (1)
3x+2y = 21 ----(2)
To eliminate x, multiply (1) by 3 and multiply (2) by 8. Then subtract the result. That is:
3 × (8x+4y = 49) = 24x + 12y = 147
8 ×(3x+2y = 21) = 24x + 16y = 168
.......................................................................
4y = 21
.........................................................................
4y = 21
y = 21/4
y = 5.25
Put y = 5.25 into (1):
8x+4y = 49
8x + 4(5.25) = 49
8x + 21 = 49
8x = 49 -21
8x = 28
x = 28/8
x = 3.5
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5
4 Harriet and Kevin are playing a game. There are a total of 11 rounds in the game and at the end
of each round only one of the players will score some points. In each round the number of points
scored is equal to the number of the round, so 1 point is scored in round 1, 2 points in round 2 and
so on.
Harriet and Kevin have played a total of 8 rounds. Harriet has scored a total of 19 points.
(a) How many points has Kevin scored?
*****
[1]
Answer: 9 points
Step-by-step explanation: 8 rounds=8 points; If Harriet has 19 points and they have played 8 rounds which equal 8 points, 19-8=9 points
In baseball, each time a player attempts to hit the ball, it is recorded. The ratio of hits compared to total attempts is their batting average. Each player on the team wants to have the highest batting average to help their team the most. For the season so far, Jana has hit the ball 12 times out of 15 attempts. Tasha has hit the ball 9 times out of 10 attempts. Which player has a ratio that means they have a better batting average?
A. Tasha, because she has the lowest ratio since 0.9 > 0.8
B. Tasha, because she has the highest ratio since 27 over 30 is greater than 24 over 30
C. Jana, because she has the lowest ratio since 0.9 > 0.8
D. Jana, because she has the highest ratio since 27 over 30 is greater than 24 over 30
Tasha has the highest batting average because 0.9(27/30) is greater than 0.8( 24/30 ) ( optionD)
What is ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.
The batting average for Jana is 12/15 = 0.8
The battling average for Tasha is 9/10 = 0.9
The battling average of Tasha is higher than that of Jana
0.6 can also be in form of 6/10
0.9 can also be in form of 9/10
therefore 8/10 = 24/30 and
9/10 = 27/30
Therefore Tasha has the highest batting average because 27/30 is greater than 24/30
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Answer:
27/30
Step-by-step explanation:
x is a whole number if three quarters of x is subtracted from 62. the result is less than 40. find the three lowest values of x
The three lowest values of x are 30, 31 and 32.
How to find the three lowest values of x?Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.
The statement "x is a whole number if three quarters of x is subtracted from 62. the result is less than 40" can be written as:
62 - (3/4)x < 40
- (3/4)x < 40 - 62
-3x/4 < -22
-3x < -22 × 4
-3x < -88
x > -88/-3
x > 29.33
Since x > 29.33 and x is a whole number, the three lowest values of x are 30, 31 and 32.
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Determine whether the graph represents a function.
Hi There!
Your Answer must be The Realation is a function or A...
Why did i get this answer?
To Find if a Graph is a Function, We must use the concept called vertical line test.
If the vertical line drawn across at anywhere of the graph intersects the graph at most once, we decide the given graph represents the function.
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The town is mapped on a coordinate grid with the NBI at (2, 3) and Philippine Statistics Authority (PSA) at (-4, -5). How far apart are they?
a. 10 units
b. 13 units
c. 11 units
d. 12 units
The town and PSA are (a) 10 units apart
How to determine how far they are apartFrom the question, we have the following parameters that can be used in our computation:
Points = (2, 3) and (-4, -5)
The distance between the two towns can then be calculated using the following distance equation
distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
substitute the known values in the above equation, so, we have the following representation
distance = √[(2 + 4)² + (3 + 5)²]
Evaluate
distance = 10
Hence, the distance apart is 10 units
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what is 1/6 less than 2/6?
Answer: 1/6
Step-by-step explanation:
2/6 - 1/6 = 1/6
while walking in the country, you count 28 heads and 78 feet in a field of pigs and chickens. how many of each animal are there?
Answer:
There are 11 pigs and 17 chickens.
Step-by-step explanation:
Lets let
p = number of pigs
c = number of chickens
Assuming each animal has only one head, then
p + c = 28
And assuming that pigs have four feet and chickens have two feet:
pig feet = 4p
that is, 4 feet for each pig, and
chicken feet = 2c
right? two feet per chicken.
All the feet are:
4p + 2c = 78
Now we have two equations and two unknowns, so we can solve this "system of equations". You can use substitution or elimination method (or even graphing or matrices) I will run through elimination method.
Multiply p+c=28 times -2.
-2p + -2c = -56
then add the whole equation to the other equation. Do this adding vertically, from top to bottom.
-2p + -2c = -56
4p + 2c = 78
_____________
2p = 22
Divide by 2 to solve
p = 11
There are 11 pigs.
Remember,
p + c = 28
11 + c = 28
subtract 11
c = 17
There are 17 chickens.
Given
B
(
2
,
2
)
,
C
(
−
5
,
−
2
)
,
D
(
−
2
,
6
)
,
B(2,2),C(−5,−2),D(−2,6), and
E
(
5
,
y
)
.
E(5,y). Find
y
y such that
B
C
‾
∥
D
E
‾
BC
∥
DE
.
Points ( 2 , 2 ) , C ( − 5 , − 2 ) , D ( − 2 , 6 ) are equally distant from the point P(x, y) y y such that B C ‾ ∥ D E ‾ BC ∥ DE .
How to solve the poind?Assume that points ( 2 , 2 ) , C ( − 5 , − 2 ) , D ( − 2 , 6 ) are equally distant from the point P(x, y)
( 2 , 2 ) , C ( − 5 , − 2 ) , D ( − 2 , 6 )
∴PA=PB
With the aid of the distance formula
= (x 2 −x 1 )
2 +(y 2 −y 1 )
2
There are
⇒ (x+2) 2 +(y+2) 2
= (x-5) 2 +(y−2)2
(x-2) 2 +(y+6)2
⇒(x+2) 2 +(y+2)
2 =(x+2) 2 +(y+2) 2
⇒ x2−4x+4+y 2
−7y+10= x2 +4x+4+y 2 −7y+14
⇒−4x−4x−10y+7y+14−16=0
⇒−8x−3y+2=0
⇒3x+y−5=0
ΔAD
Eare Similar triangles
∴( CB / DE )=( AB / AD )
B C ‾ ∥ D E ‾ BC ∥ DE .
Points ( 2 , 2 ) , C ( − 5 , − 2 ) , D ( − 2 , 6 ) are equally distant from the point P(x, y) y y such that B C ‾ ∥ D E ‾ BC ∥ DE .
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problem 5 (30 points, each 10 points). in a chemical plant, 24 holding tanks are used for final product storage. four tanks are selected at random and without replacement. suppose that four of the tanks contain material in which the viscosity exceeds the customer requirements. 1. what is the probability that exactly one tank in the sample contains high-viscosity material? 2. what is the probability that at least one tank in the sample contains high-viscosity material? 3. in addition to the four tanks with high-viscosity levels, four different tanks contain material with high impurities. what is the probability that exactly one tank in the sample contains high-viscosity material and exactly one tank in the sample contains material with high impurities?
1. The probability of selecting exactly one tank with high-viscosity material is 0.
2. The probability of selecting at least one tank with high-viscosity material is 1.
3. The probability of selecting exactly one tank with high-viscosity material and exactly one tank with high impurities is 0.25.
1. The probability of selecting exactly one tank with high-viscosity material is calculated by the binomial distribution formula, P(X = n) = (nCx)p^x(1-p)^n-x, where n is the number of trials, x is the number of successes, and p is the probability of success. In this case, n = 4, x = 1, and p = 24/24 = 1. Therefore, P(X = 1) = (4C1)1^1(1-1)^4-1 = 0.
2. The probability of selecting at least one tank with high-viscosity material is calculated by the complement rule, P(X > 0) = 1 - P(X = 0). In this case, P(X > 0) = 1 - (4C0)1^0(1-1)^4-0 = 1.
3. The probability of selecting exactly one tank with high-viscosity material and exactly one tank with high impurities is calculated by the binomial distribution formula, P(X = n) = (nCx)p^x(1-p)^n-x, where n is the number of trials, x is the number of successes, and p is the probability of success. In this case, n = 8, x = 2, and p = 24/24 = 1. Therefore, P(X = 2) = (8C2)1^2(1-1)^8-2 = 0.25.
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grace tiene 240 en el banco ella quiere compre tantos videojuegos de 15 como sea posible ¿Cuantos videojuego podria comprar si ¿Queria mantener al menos 120 en el banco? Ayudenme porfa
Grace can buy 8 video games of price $15 each if she wants to save $120 from $240.
Grace puede comprar 8 videojuegos si quiere ahorrar $120 de $240
What does pricing mean?Pricing is the procedure of determining the value that a manufacturer will receive in the exchange of goods and services. To make the cost of the producer's products suitable for both the manufacturer and the customer, a pricing method is used. Pricing is determined by the firm's average prices as well as the consumer's estimation of an item's value in relation to that of similar goods from rival companies.
The remainder must be $12, so
(El resto debe ser $12, entonces)
240 - 120
= $120
Number of video games she could buy with $120
(Número de videojuegos que podría comprar con $120)
⇒ 120/15
= 8
Therefore, Grace can buy 8 video games if she wants to save $120 from $240.
Por lo tanto, Grace puede comprar 8 videojuegos si quiere ahorrar $120 de $240
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Translated question:
Grace has $240 in the bank. She wants to buy as many $15 video games as possible. How many video games could she buy if she wanted to keep at least $120 in the bank? help me please
What is the value of 1/2 ÷ 1/3? Pls someoneeeeeeee answerrr
Answer: 1 1/2
Step-by-step explanation:
You have to do the keep change flip method where you keep the first fraction the same change the sign to a multiplication sign and flip the other fraction, it would then look like this: 1/2 x 3. after just multiply across and you get 1.5
Please answer quick! The information is in the picture.
The measure of the side length CL is equal to 9m using trigonometric ratio of cosine 60° for thy right triangle ACL
What are trigonometric ratiosThe trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.
Angle m∠BAC = 180° - (m∠C + m∠ABC)
m∠BAC = 180° - (90° + 30°)
m∠BAC = 60°
line AL is an angle bisector so;
m∠CAL = 30° and m∠BAL = 30°
which implies triangle ∆ALB is an isosceles with line LB = AL = 18m
considering the right triangle ∆ACL;
angle m∠L = 180° - (90° + 30°)
m∠L = 60°
cos 60° = CL/18 {adjacent/hypotenuse}
1/2 = CL/18m {cos 60° = 1/2}
CL = 18m/2 {cross multiplication}
CL = 9m
Therefore, the side length CL is equal to 9m using trigonometric ratio of cosine 60° for the right triangle ACL.
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How much of the circle is shaded? Write your answer as a fraction in simplest form.
Answer:
3/8
Step-by-step explanation:
In these type of problems, I like making all of my denominators the same.
1/8 is good.
1/2 is half. 4/8 is also half. I'll use 4/8 because 1/8 also has the 8
A whole circle is 100%, which is 1/1. It's also 8/8
To find the shaded area, we'll first add 1/8 and 4/8. That equals 5/8. We just have to add nominators/top now because the denominator/bottom is the same
Now we'll subtract 8/8 from 5/8. Again denominator is the same, so we only need to subtract the top
8-5=3
Also known as 3/8
1. A softball player bats six times in a game. Each at-bat results in an out, getting on base or hitting a homerun.
2. A sandwich shop has three types of sandwiches: ham, turkey, and chicken. Each s andwich can be ordered with white bread or multi-grain bread. Customers can add any combination of the six available toppings
1. A softball player can have six (6) possible outcomes
2. Six (6) combinations can be made.
How do we make the values?Since the player bats six times, it means that there is possibility of having six outs, or six on base, or six homerun or even a mixture of the three outcomes in six times. The constant touch is six times
Since the sandwiches are just three types and can be ordered with either white bread or multi-grain bread, it means that there is possibility of having two different pairs each making six possible combinations of the available toppings.
Therefore, there will be six possible outcomes and six possible combinations of the sandwiches.
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The complete question goes thus:
1. A softball player bats six times in a game. Each at-bat results in an out, getting on base or hitting a homerun. How many possible outcomes can the player have?
2. A sandwich shop has three types of sandwiches: ham, turkey, and chicken. Each s andwich can be ordered with white bread or multi-grain bread. Customers can add any combination of the six available toppings. How many combinations can be made?
A recipe for hot chocolate requires 4 cups of milk , 1/4 cup of chocolate powder , 1/3 cup of honey. Write the ratio of milk to chocolate powder to honey as a whole ratio in its simplest form PLS ANSWER. ILL HIVE WHOEVER AMSWERS BRAINLIEST
A recipe for hot chocolate requires 4 cups of milk , 1/4 cup of chocolate powder , 1/3 cup of honey and for which Simplified Ratio is 16 : 1 : 3.
This can be calculated by following steps:
Find the ratio of milk to chocolate powder.
Ratio of Milk to Chocolate Powder = 4 : 1/4
Find the ratio of chocolate powder to honey.
Ratio of Chocolate Powder to Honey = 1/4 : 1/3
Find the ratio of milk to chocolate powder to honey.
Ratio of Milk to Chocolate Powder to Honey = 4 : 1/4 : 1/3
Simplify the ratio in its simplest form.
Simplified Ratio = 16 : 1 : 3
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A walker notes that a monument is due North and 7.5 Km from him. He then walks on a bearing of 041. Calculate how far he is from the monument at this point to 2 decimal places.
In a case whereby walker notes that a monument is due North and 7.5 Km from him. He then walks on a bearing of 0.41 the distance from the monument at this point is 5.63km
How can the the distance be calculated?The concept that will be use is bearing. A bearing is the angle, measured in degrees clockwise from north, in mathematics. In most cases, bearings are specified as three-figure bearings. For instance, the standard notation for 30° clockwise from north is 030°.
From the diagram we can see that the interpretation gave us a triangle and from trigonometry,
Cos θ= adjacent / hypothenus
Then Cos 41 = XY/XM
Cos 41 = XY/7.5
0.75 = XY/7.5
0.75 *7.5 =5.63km
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true or false: residuals measure the vertical distance between two observations of the response variable.
Residuals measure the vertical distance between two observations of the response variable - False.
An individual data point's residual is a measurement of how well a line fits it. Take a look at this straightforward data set with a line of fit through it.
The discrepancy between expected values of y (the dependent variable) and actual values of y is the residual for each observation. Relative to projected and actual y values, residual is equal to yi. Actual y value minus expected y value equals residual; therefore, r I = y I y i.
A symbol (often a letter) used in mathematics to represent an unknowable numerical value in an equation or algebraic statement.
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Which of the following is a solution set for the following graph?
The solution set for the given graph is (4, 1)
How to determine the solution set of the graphFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have two straight lines of inequalites
The point that represent the solution set is any point in the shaded region
This is so because the lines are inequality lines
An instance of these points is (4, 1)
Hence, the point is (4, 1)
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How do you write the sum of b and 5 times 2?
Answer: So 2(b+5) would be the answer to your question.
Step-by-step explanation:
Find the coordinates of the midpoint of with endpoints K(–20, 3) and L(12, –2).
The midpoint between the two given points is given by M(-4,-11)
what is the Cartesian coordinate system?A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates
Given here: The coordinates of the two points as K(–20, 3) and L(12, –2).
We know that the midpoint of the line between the two points is given by
x=a+b /2
and y= c+d/ 2
Where the end points of the line is given by (a,b) and (c,d)
Thus x=-20+12 /2
=-4
y= -20-2 /2
=-11
Thus the midpoint has the co-ordinates M(-4,-11)
Hence, The midpoint between the two given points is given by M(-4,-11)
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Answer: A - (-4,1/2)
Step-by-step explanation: trust me bro...
Which is equivalent to 49^3/2?
a. 21
b. 98
c. 294
d. 343
Answer: D
Sorry if it is not.