Given ab 12 ac 6 prove c is the midpoint

Answer:

Below

Step-by-step explanation:

You COULD calculate the lengths of the three sides and then use Heron's Formula to calculate the area.....

 Here is perhaps an easier way (see image)

  calculate the entire area of the rectangle then subtract the 3 smaller RIGHT triangles from the total

Area of rectangle =   6 x 7 = 42 units^2

  triangles    1/2 ( 3 x 7    +    3 x 3    +    4 x 6 ) = 27 units^2

42 - 27 = 15 units^2   = area of given triangle

Answer:

15 square units

Step-by-step explanation:

i am using Heron's formula for this question

Firstly, lets calculate the lengths of the triangle. We can do this by using the formula:

[tex]length=\sqrt{(y_{2}\\-y_{1}\\)^{2}+(x_{2}\\-x_{1}\\)^{2} }[/tex]

Calculating the length between D (3,-9) and E (9,-5):

[tex]length(A)=\sqrt{(-9-(-5))^{2}+(3-9)^{2} } \\length(A)=2\sqrt{13}[/tex]

Calculating the length between F (6,-2) and E (9,-5):

[tex]length(B)=\sqrt{(-2-(-5))^{2}+(6-9)^{2} }\\length(B)=3\sqrt{2}[/tex]

Calculating the length between D (3,-9) and F (6,-2):

[tex]length(C)=\sqrt{(-9-(-2))^{2}+(3-6)^{2} }\\length(C)=\sqrt{58}[/tex]

Now, we can find the semi-perimeter with the formula:

[tex]s=\frac{A+B+C}{2}[/tex]

where A, B and C are the lengths

The semi-perimeter is:

[tex]s=\frac{2\sqrt{13}+3\sqrt{2}+\sqrt{58} }{2}\\s=9.534758... (store \, the \, full \, value \, in \, your \, calculator)[/tex]

The formula for the area of the triangle:

[tex]A=\sqrt{s(s-A)(s-B)(s-C)}\\A=\sqrt{9.534758...(9.534758...-2\sqrt{3})(9.534758...-3\sqrt{2})(9.534758...-\sqrt{58} ) }\\A=15[/tex]

The total number of juice bottles is given by the equation J = 3400 bottles

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the proportion be represented as a : b : c

Now , the ratio of mango juices to tomato juice to passion fruit be 4 : 4 : 3

The total number of mango juice = 4x

The total number of tomato juice = 4x

The total number of passion fruit juice = 3x

The total number of passion fruit juice = 1020

Substituting the values in the equation , we get

3x = 1020

Divide by 3 on both sides of the equation , we get

x = 340 bottles

Now , the total number of bottles = 4x + 3x + 3x = 10x bottles

So , substituting the value of x in the equation , we get

The total number of juice bottles = 340 ( 10 ) = 3400 bottles

Hence , the proportion is 40 : 40 : 30

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The area of the given polygon will be 10 square units.

The quantity of space enclosing a three-dimensional shape's exterior is its surface area.

here, we have,

In other meaning, if we say side square then it is an area of the square but for a cuboid, there are 6 faces so the surface area will be external to all 6 surfaces area.

Given the polygon with vertices

N(-2,1), P(3, 1),\ Q(3,-1), R(-2,-1)

If we draw the points in coordinate then it will become a rectangle with side lengths 5 and 2.

Area of rectangle = length × width

Area of rectangle = 5 × 2 = 10 square units.

Hence "The area of the given polygon will be 10 square units".

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The expressions are factorized to;

1.(x + 1)(x + 2)

2.(x + 2) (x + 8)

3. (x -4) (x -6)

Using the factorization method of solving quadratic equations, we have;

1.  x² + 3x + 2

Find the pair factors of 2 that adds up to 3 and  substitute the values, we get

x² + 2x + x + 2

Factorize in pairs

x(x + 2) + 1( x+ 2)

(x + 1)(x + 2)

2. x² +10x+16

Find the pair factors

x² + 8x + 2x + 16

Factorize in pairs

x(x + 8) + 2( x+ 8)

(x + 2) (x + 8)

3. X²-10x+24

Find the pair factors

x² - 6x - 4x + 24

Factor in pairs

x(x -6) - 4(x -6)

(x -4) (x -6)

Hence, use the factorization  method in the expressions

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Answer:

.534

Step-by-step explanation:

add, then convert meters to kilometers

The formula for a curve grade is based on a normal distribution with the average score being 0.

The formula for each grade is as follows:

A-grade: S + 20

B-grade: S + 10S< + 20

C-grade: S - 10S< + 20

D-grade: S - 20

F-grade: S < 0

The formula  is based on a normal distribution with the average score being 0.

For example, if the average score is 50 and your score is 55, then you would receive an A-grade because your score is 5 points above the average. This can be calculated by adding 20 points to your score of 55 resulting in a grade of[tex]75 (55 + 20 = 75)[/tex]. Similarly, if your score is 40, then you would receive a C-grade because your score is 10 points below the average. This can be calculated by subtracting 10 points from your score of 40 resulting in a grade of 30 (40 - 10 = 30).

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Area of figure in the graph is 5 square unit.

Correct option is C.

Area is defined as the total space taken up by a flat surface or shape of an object. The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in square units like cm² and m².

Given, By the graph

Figure consists of one triangle and one rectangule

height of the triangle = 2 unit

length of base of triangle = 3 unit

Area of triangle

= (1/2) × height × base

= (1/2) × 2 × 3

= 3 unit²

Length of rectangle = 2 unit

Width of rectangle = 1 unit

Area of the rectangle

= length × width

= 2 × 1

= 2 unit²

Total area of the figure

= area of triangle + area of rectangle

= 3 + 2

= 5 unit²

Hence, 5 square unit is area of the figure in the graph.

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The correct statement about the ordered pair (-4,0) and the system of equations is given as follows:

The ordered pair (-4,0) is a solution to the system because it makes both equations true.

The system of equations for this problem is defined as follows:

The ordered pair (-4,0) means that when x = -4, y = 0.

Hence we verify if the first equation is satisfied, as follows:

2(-4) + 0 = -8

-8 = -8 -> Satisfied.

For the second equation, we have that:

-4 - 0 = -4

-4 = -4 -> Satisfied.

As both equations are satisfied, the ordered pair is a solution for the system of equations.

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The required measures of the angles ∠PQS and ∠SQR are given as 51 and 49.

Complementary angles are two angles whose measures add up to 90 degrees. In other words, if angle A and angle B are complementary, then A + B = 90 degrees.

Here,
∠PQR is a right angle,
So ∠PQS and ∠SQR are supplementary angles, from the figure.

∠PQR = ∠PQS + ∠SQR
90 = 8x + 131 + 10x + 139
90 = 18x + 270
18x = -180
x = -10

Now,
∠PQS = 8x + 131 = -80 + 131 = 51°
Similarly,
∠SQR = 49°

Thus, the required measure of the angles ∠PQS and ∠SQR are given as 51 and 49.

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Ratio of false positives to true positives is 1/7 .

In statistics, when performing multiple comparisons, the false positive rate is the probability of incorrectly rejecting the null hypothesis for a particular test.

Given In the table,

Number of patient test positive, but not have diabetes = 5%

Number of false positives = 5%

Number of patient test positive, and have diabetes = 35%

Number of true positive = 35%

Ratio of false positives to true positives

= 5%/35%

= 1/7

Hence, 1/7 is the ratio of false positives to true positives.

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All possible fourth corners if  the following three points are corners of a parallelogram:(1,2,3),(3,4,7),(2,1,2) is (2, 3, 5) and  (3, 5/2, 9/2)

Let the corners be A(1,2,3);B(3,4,7);C(2,1,2)

Let the fourth vertex D =(x,y,z)

We know that the diagonals of a parallelogram bisect each other. So, the midpoint of AC is same as the midpoint of BD.

Mid point of two points (x 1,y 1,z1) and (x 2,y 2,z2)​  is calculated by the formula ( x 1+x 2/2 , y 1+y 2/2, z1+z2/2 ).

So, midpoint of AC= Mid point of BD

⇒( 1+3/2, 2+4/2, 3+7/2) =(2, 3, 5)

Hence, D=(2, 3, 5).

Same if,

Mid point of two points (x 1,y 1,z1) and (x 2,y 2,z2)​  is calculated by the formula ( x 1+x 2/2 , y 1+y 2/2, z1+z2/2 ).

So, midpoint of AC= Mid point of BD

⇒( 3+2/2, 4+1/2, 7+2/2) = (3, 5/2, 9/2)

Hence, D=  (3, 5/2, 9/2)

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Answer: 2 hrs

Step-by-step explanation:

4/5 + 4/5 = 1 3/5 + 2/5 (half of 4/5) = 2

         ↑

(4/5 of a room)

The solution of the system of equations by adding method is equal to :

option A. Solution is ordered pair (x ,y) = ( 2.00 , 20.3 ) representing decimal rounded to one decimal place.

System of equations are :

0.9x +0.7y  = 16  ___(1)

-0.3x - 3.5y = - 71.6 ___(2)

To get the solution of the system of equations are:

Multiply (2) by 3 and add it to (1)

0.9x  +0.7y  = 16

-0.9x - 10.5y = -214.8

0x - 9.8y = - 198.8

⇒ y = 20.3

⇒ x = 1.9966

⇒ x = 2.00

Therefore, the value of (x, y ) in the system of equations is given by :

option A. Type of solution is written as ordered pair (x ,y) = ( 2.00 , 20.3 ) having decimal rounded to one decimal place.

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Based on the graph, the slope of this line is equal to 2.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided in the graph, we can logically deduce the following data points on the line:

Substituting the given data points into the slope formula, we have the following;

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (6 + 8)/(5 + 2)

Slope, m = 14/7.

Slope, m = 2.

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Despite its age, the 15 puzzle remains a popular game today, and it has been adapted into many different variations, including digital versions and physical puzzles with different grid sizes and configurations.

15 puzzle is a sliding puzzle game with numbered squares arranged in 4x4 grid with one tile missing. the puzzle is solved when the numbers are arranged in order. the actions are defined in terms of direction where empty square can be moved to up (u), down(d), left(l), right(r)

The 15 puzzle is a classic sliding puzzle game that has been popular for over a century. The game was invented in the late 1800s by Noyes Chapman, and it quickly became a favorite pastime of people all over the world. The puzzle is sometimes called the "Gem Puzzle" or the "Boss Puzzle," and it has also been used as a tool for studying permutation groups and artificial intelligence algorithms.

Solving the 15 puzzle requires a combination of strategy, planning, and spatial reasoning. While the game is relatively simple to learn, it can be quite challenging to master, especially if you're trying to solve it in the minimum number of moves. In fact, there are over 1 trillion possible configurations of the 15 puzzle, and only a fraction of those can actually be solved.

Despite its age, the 15 puzzle is still widely played today. It has been transformed into a variety of games, including digital and physical puzzles with various grid sizes and arrangements.

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Answer:

There are 3.28542 months in 100 days.

Step-by-step explanation:

For every 100 days, there are approximately 3.28542 months. To solve for any given number of days, divide the time value by 30.417.

For example, to solve for 200 days:

Therefore, 100 days make approximately 3.28542 months.

Answer:

Step-by-step explanation:

Value in months = value in days × 0.0328542

Value in months = 100 × 0.0328542 = 3.28542 (months)

93 chocolate chip cookies

Yes, the given figure is a parallelogram.

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

Given is a parallelogram as shown in the image.

We have -

S(0, 0), T(3, 0), U(4, 3), V(1, 3)

For the figure to be parallelogram, we will have to prove -

ST = VU   &   SV = TU

We can calculate -

ST = 3

VU = 3

SV = 3.1

TU = 3.1

So -

ST = VU   &   SV = TU

Hence, it is a parallelogram.

Therefore, yes, the given figure is a parallelogram.  

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The function (f+g)(-1) is equal to 3.

We can evaluate (f+g)(-1) by first finding f(-1) and g(-1), and then adding them together.

To find f(-1), we substitute -1 for x in the expression for f(x):

f(-1) = 5(-1)^2 + 7 = 5 + 7 = 12

To find g(-1), we substitute -1 for x in the expression for g(x):

g(-1) = 3(-1) - 6 = -3 - 6 = -9

Now we can add f(-1) and g(-1) together:

(f+g)(-1) = f(-1) + g(-1) = 12 + (-9) = 3

Therefore, (f+g)(-1) is equal to 3.

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Answer: (0,0)

Step-by-step explanation: 3+5=8-4=4-4=0

The capacitance is [tex]1.58*10^{-12} F[/tex], the charge is 12000 e, the charge density is [tex]4.80*10^{7} C/m^{2}[/tex], and the electric field is [tex]3.92*10^{6} N/C[/tex].

Here's how you can solve the above problems:

(a) To find the capacitance of a parallel-plate capacitor, we use the formula:

C = ε0A/d

where ε0 is the vacuum permittivity constant [tex](8.85*10^{-12}F/m )[/tex], A is the area of the plates, and d is the distance between the plates. Substituting the given values, we get:

C =[tex](8.85 * 10^{-12} F/m) (2.50* 10^{-4}m^{2} )/(1.40*10^{-7}m )[/tex]

= [tex]1.58*10^{-12} F[/tex]

(b) To find the amount of charge on the positive plate of the capacitor, we use the formula:

Q = CV

where Q is the charge, C is the capacitance, and V is the voltage across the capacitor. Substituting the values from (a) and the given voltage, we get:

Q = [tex](1.58*10^{-12}F )(3.00 V)[/tex]

= [tex]4.74*10^{-11} C[/tex]

= 12000 e

(c) To find the charge density on the positive plate, assuming the density is uniform, we divide the charge on the plate by the area of the plate:

ρ = Q/A = [tex](12000e)/(2.50*10^{-4}m^{2} )[/tex]

= [tex]4.80*10^{7} C/m^{2}[/tex]

(d) To find the magnitude of the electric field between the plates, we use the formula:

E = V/d

where E is the electric field, V is the voltage across the capacitor, and d is the distance between the plates. Substituting the given values, we get:

E = [tex](3.00 V)/(1.40*10^{-7}m )[/tex]

= [tex]2.14*10^{-7} V/m[/tex]

= [tex]3.92*10^{6} N/C[/tex]

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Referring to the given statements,

a) p → q: "If it is Friday, then I don't go to class."

b)  -q → -p:  "If I don't go to class, then it is not Friday."

c)  p ∧ q :  "It is both Friday and I don't go to class."

d)  p V -q: "Either it is Friday, or I don't go to class (or both)."

In this problem, the propositions are:

p : It is Friday

q :  I don't go to class

Hence,

a)  p → q is an implication and read as: "If it is Friday, then I don't go to class."

b). -q → -p

-q is negation of q and read as: I go to class

-p is negation of p and read as: It is not Friday

Therefore, -q → -p means "If I don't go to class, then it is not Friday."

c)  p ∧ q is a conjunction. p ∧ q can be read as: "It is both Friday and I don't go to class."

d)  p V -q  is a disjunction. p V -q can be read as: "Either it is Friday, or I don't go to class (or both)."

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The probability of having i children, i = 1,2,3,4,5 is 0.2, 0.4, 0.25, 0.1, 0.05 respectively. The probability that a randomly chosen child comes from a family with i children are 0.0741, 0,2963, 0.2773, 0.1481, 0.0926.

The probability that a randomly chosen family has i children is given by the ratio of the number of families with i children to the total number of families. Therefore:

P(1 child) = 4/20 = 0.2

P(2 children) = 8/20 = 0.4

P(3 children) = 5/20 = 0.25

P(4 children) = 2/20 = 0.1

P(5 children) = 1/20 = 0.05

(b) To calculate the probability that a randomly chosen child comes from a family with i children, we need to take into account the different numbers of children in each family. There are a total of 4+8x2+5x3+2x4+1x5=54 children in the community organization. Therefore, the probabilities are:

P(child from 1-child family) = 4/54 ≈ 0.0741

P(child from 2-child family) = 2x8/54 ≈ 0.2963

P(child from 3-child family) = 3x5/54 ≈ 0.2778

P(child from 4-child family) = 4x2/54 ≈ 0.1481

P(child from 5-child family) = 5/54 ≈ 0.0926

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____The given question is incomplete, the complete question is given below:

A small community organization consists of 20 families, of which 4 have one child, 8 have two children, 5 have three children,2 have four children, and 1 has five children.

(a) If one of these families is chosen at random, what is the probability it has i children, i = 1,2,3,4,5?

(b) If one of the children is randomly chosen, what is the probability this child comes from a family having i children, i =1,2,3,4,5?

Answer: please look at the image for the answer

Step-by-step explanation:

The equation of the straight line would be -

y = 2x.

Given is that a straight line passes through the points (2, 4) and (3, 6).

Refer to the graph of the function attached. We can see that the function that represents the graph is -

[tex]$y=\sqrt[3]{x+6} \;+1[/tex]

Therefore, the function representing the graph is -

[tex]$y=\sqrt[3]{x+6} \;+1[/tex]

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First we multiply 9 and 15, which is 135cm. 100cm = 1m so the plant will grow 1.35m, so the plant is now 9.35m

The function which represents the value of the car is [tex]y = 11000(0.85)^x[/tex].

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

From the table, we can conclude the function of the car as:-

[tex]y = 11000(0.85)^x[/tex]

At x = 0, the value of y is,

[tex]y = 11000(0.85)^0[/tex].

y = 11000

At x = 1 the value of y is,

[tex]y = 11000(0.85)^1[/tex]

y = 11000 x 0.85

y = 9350

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The volume of a paraboloid with height h and base radius r can be found by treating it as a solid of revolution, rotating the parabolic cross-section about the y-axis.

The equation for the parabola is y = x^2 / (4h), so the equation for the cross-section is x = 2sqrt(hy). The volume can be found by integrating the area of the cross-section from y = 0 to y = h, and then multiplying by 2pi:

V_parab = 2pi * ∫[0,h] (2sqrt(hy))^2 dy, = 2pi * ∫[0,h] 4hy dy= 2pi * 2hy^2]_[0,h] = 4/3 * pi * h^3

The volume of a cylinder with the same height and base radius r is V_cyl = pi * r^2 * h. The ratio of the volume of the paraboloid to the volume of the cylinder is: V_parab / V_cyl = (4/3 * pi * h^3) / (pi * r^2 * h)

= (4/3 * h^2 * r)

For the second part, the volume of a sphere with radius r can be found by treating it as a solid of revolution, rotating a semicircle about its diameter.

The equation for a semicircle with radius r is y = sqrt(r^2 - x^2), so the equation for the cross-section is x = sqrt(r^2 - y^2). The volume can be found by integrating the area of the cross-section from y = -r to y = r, and then multiplying by 2pi: V_sphere = 2pi * ∫[-r,r] (sqrt(r^2 - y^2))^2 dy

= 2pi * ∫[-r,r] (r^2 - y^2) dy = 4/3 * pi * r^3

The volume of a cylinder with the same radius and height (which is equal to the diameter of the sphere) is V_cyl = pi * r^2 * 2r = 2pi * r^3. The ratio of the volume of the sphere to the volume of the cylinder is: V_sphere / V_cyl = (4/3 * pi * r^3) / (2pi * r^3) = 2/3

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In a 3×4 matrix with reduced row echelon form given by U=[1,0,5,1;0,1,1,1;0,0,0,0], where a1=[−1,3,−2], and a2=[2,-3,-1]  is given and the value of a3 = [-5, -1, 1, 0], a4 = [-1, -1, 0, 1] .

Since the reduced row echelon form of A has only two pivot columns, the matrix A can have at most two linearly independent columns. We already know that a1 and a2 are linearly independent (neither is a scalar multiple of the other), so we can use them as a basis for the column space of A.

To find a3 and a4, we need to find two vectors that are linearly independent of a1 and a2 and that span the null space of A (i.e., are solutions to the homogeneous equation Ax=0).

To find a basis for the null space of A, we can set the non-pivot columns of A equal to free variables, and then solve for the corresponding pivot variables in terms of the free variables. In this case, the non-pivot columns are columns 3 and 4, so we set x3=t and x4=s for some scalars t and s, and solve for x1 and x2:

x1 = -5t - s

x2 = -t - s

Thus, the general solution to Ax=0 can be written as a linear combination of the vectors [-5, -1, 1, 0] and [-1, -1, 0, 1]. We can check that these two vectors are linearly independent, so they form a basis for the null space of A. We can use them as a3 and a4:

a3 = [-5, -1, 1, 0]

a4 = [-1, -1, 0, 1]

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____The given question is incorrect, the correct question is given below:

Let A be a 3×4 matrix with reduced row echelon form given by U=[1,0,5,1;0,1,1,1;0,0,0,0]. If a1=[−1,3,−2], and a2=[2,-3,-1] Find a3 and a4