Since we see that P is a point on the perpendicular bisector, l, of MN, we have proven the required PM = PN by the definition of reflection, we can conclude that point P is the image of itself , while point N is the image of M .
How to Interpret the Perpendicular Bisector?We are given :
P is a point on the perpendicular bisector, l, of MN.
Now, we want to prove the assertion that PM = PN
A Reflection is defined as a transformation in which a given figure is the mirror image of the other. This means that every point on the new image is a mirror reflection of itself .
From the question, we can say that by the definition of reflection, we can conclude that point P is the image of itself , while point N is the image of M .
The perpendicular bisector, l is acting as a Line of symmetry which is also called axis of reflection.
Now, due to the fact that reflections preserve lengths in transformation, it means that we have; PM = PN.
Therefore, we see that point N is the image of M .
Read more about Perpendicular Bisector at; https://brainly.com/question/11006922
#SPJ1
Answer:
Point M
Step-by-step explanation:
During the month, Fisher Company's Work in Process inventory account was credited for $120,500, which represented the Cost of Goods Manufactured for the month. Only one job remained in process on May 31; this job had been charged with $9,600 of applied overhead cost. The amount of direct materials cost in the unfinished job would be:
The amount of direct materials cost in the unfinished job would be $97600.
What is direct material cost?The price of direct materials is directly related to the unit of production and is immediately identifiable. For instance, the price of glass is a direct material expense in the production of light bulbs. The primary component needed for the production of commodities or products was material. Costs of raw materials or components used directly in the production of goods are referred to as direct material costs. For instance, if Company A manufactures toys, the cost of the plastic used to build the toys would be an example of a direct material cost.
Given Data
Work in Process inventory account was credited for $120,500.
charged with $9,600 of applied overhead cost.
Direct material cost = Work in progress - Overhead cost - Direct labor
Direct labor = 9600 ×[tex]\frac{100}{75}[/tex]
Direct labor = 12800
Direct material cost = 120000 - 9600-12800
Direct material cost = 97600
The amount of direct materials cost in the unfinished job would be $97600.
To learn more about direct material cost, visit:
https://brainly.com/question/15012260
#SPJ9
Solve please please
Popular Problems Algebra Solve for h A=1/2h(b+B)
A = 1/2h (b+B)
h=2Ab+B
Explanation
Popular Problems Algebra Solve for h A=1/2h(b+B)
A= 1/2 h(b+B)
Rewrite the equation as
1/2⋅(h(b+B))=A.
1/2⋅(h(b+B))=A
Multiply both sides of the equation by 2.
2(1/2⋅(h(b+B)))=2A
hb+hB=2A
Factor h out of hb+hB.
h(b+B)=2A
Divide each term in h(b+B)=2A by b+B and simplify.
h=2Ab+B
How is algebra solved?
A General Rule for Equation Solving
Remove parentheses from each side of the equation and combine similar phrases to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.To learn more about A=1/2h(b+B) refer to:
https://brainly.com/question/368195
#SPJ13
(b)A sight-seeing ship is stopped in the water for an hour, miles from the shore. Then the captain heads the ship back to the shore at a constant rate. The ship docks at shore for awhile, then returns to the open sea
Solution:
Given that a sight-seeing ship is stopped in the water for an hour, miles from the shore. Then the captain heads the ship back to the shore at a constant rate. The ship docks at shore for awhile, then returns to the open sea.
This implies that that:
When a number is added to 20 and 5 is subtracted from the number, their product is 150. Find the two possible numbers.
Answer:
24 ajsndkalxndma skwma wjlslaos ndnajala
Mar GE How many pairs of whole numbers have a sum of 40? many pairs of whole numbers
The pairs of whole numbers which have 40 as a sum is 21
What is Whole numbers ?
All natural numbers and 0 are included in the category of whole numbers. They are a subset of real numbers, which exclude negative numbers, decimals, and fractions. Whole numbers include counting numerals as well.
For finding the term we use Arithmetic Progression which is :
a(n) = a + (n - 1)d
where,
a(n) = the nᵗʰ term in the sequence
a = the first term in the sequence
d = the common difference between terms
Given,
The first term a₁ = 0
The common difference d = 1 (from 1 - 0, 2 - 1, etc.)
The last term aₙ = 20
Putting the values in the formula we get,
20 = 0 + (n - 1)1
20 = 0 + n- 1
20 + 1 = n
21 = n
Hence, there are 21 pairs of whole numbers that have a sum of 40
To learn more about Whole numbers click on the link
https://brainly.com/question/461046
#SPJ9
The vertices of a triangle are as follows:
(4, 4), (6, 7), and (8, 0)
If you dilate the triangle by a scale factor of 3, what are the vertices of the new triangle?
hurry plsss
The vertices after dilation are (12, 12), (18, 21), and (24, 0)
How to determine the vertices of the new triangle?The vertices of the triangle are given as
(4, 4), (6, 7), and (8, 0)
The scale factor of dilation is given as 3
This means that
k = 3
The vertices of the new triangle are calculated as
Vertices = scale factor * Old vertices
So, we have
[(4, 4), (6, 7), and (8, 0)] * 3
Evaluate
(12, 12), (18, 21), and (24, 0)
Hence, the vertices of the new triangle are (12, 12), (18, 21), and (24, 0)
Read more about dilation at
https://brainly.com/question/3457976
#SPJ1
Suppose that events E and F are independent, P(E) = 0.25, and P(F) = 0.7. What is the P(E and F) ?
the value of P(E and F) is equal to 0.175 when E and F are independent events with P(E) = 0.25 and P(F) = 0.7.
We are given the two events:
E and F
We are also given that these events are independent events and:
P (E) = 0.25
P (F) = 0.7
We need to find:
P (E and F)
We know, that when two events are independent events that is they don't relate to each other, then P(E and F) is given by:
P(E and F) = P (E) × P (F)
P(E and F) = 0.25 × 0.7
P(E and F) = 0.175
Therefore, we get that, the value of P(E and F) is equal to 0.175 when E and F are independent events with P(E) = 0.25 and P(F) = 0.7.
Learn more about independent events here:
https://brainly.com/question/22881926
#SPJ1
Helpppppppppppppppppppp!!!!
Given:
Diagram is given.
Measure of X and Y forms a linear pair of supplementary.
[tex]m\angle X+m\angle Y=180\degree[/tex]if die us rolled once what is the probability of getting a number that is not 3
The rule of probability is
[tex]P(A)=\frac{A}{\text{total}}[/tex]Since the die has 6 numbers, then
The total = 6
Since there are 5 numbers without 3, then
A = 5
Substitute them in the rule above
[tex]P(\text{not}3)=\frac{5}{6}[/tex]The answer is 5/6
Find an equation to represent a line that goes through (1, 10) and (2, 8).
y = -2x + 12 is the linear equation of the line that passes through the coordinates of points (1, 10) and (2, 8).
What is the equation of line with the given coordinates?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
The slope of a line is expressed as change in y over change in x.
Slope m = (y₂-y₁)/(x₂-x₁)
Given the data in the question;
Point 1 ( 1, 10 )
x₁ = 1y₁ = 10Point 2 ( 2, 8 )
x₂ = 2y₂ = 8First, we determine the slope of the line.
Slope m = (y₂-y₁)/(x₂-x₁)
Slope m = ( 8 - 10 )/( 2 - 1 )
Slope m = (-2)/( 1 )
Slope m = -2
Now, determine the y-intercept b, by substituting the slope and the coordinates of one point into the equation of line formula.
y = mx + b
10 = -2(1) + b
Solve for b
10 = -2 + b
b = 10 + 2
b = 12
Now that we have the slope m and y-intercept b, plug these into y = mx + b to determine the equation of the line.
y = mx + b
y = -2(x) + 12
y = -2x + 12
Therefore, the equation of the line that goes through the given points is y = -2x + 12.
Learn more about equation of line here: brainly.com/question/2564656
#SPJ1
Mr. rivas bought 12 tickets to the high school drama production and spent $40. he purchased a combination of child tickets for $2 each & adult tickets for $6 each, write a system of equations to determine the number of child’s tickets (x) and adult tickets (y) he bought , the solve this system using any method you’d like.
Answer:
x = 8, y = 4
This can also be written as an ordered pair: (8, 4)
Step-by-step explanation:
First, set up a system of equations:
x + y = 12, $2x + $6y = $40
The first equation shows that there are a total of 12 tickets, and the other shows that the total of money for all the tickets adds to $40.
Then, solve by elimination by subtracting twice the first equation from the second to isolate y:
2x + 6y = 40
- (2x + 2y = 24)
0 + 4y = 16
And now we can solve for y:
4y = 16
y = 4
Then, put this back into the original equation to solve for x:
x + y = 12
x + 4 = 12
x = 8
Solve the following equation.
x
5
+
64
x
2
=
0
x
5
+64x
2
=0
The value of x in the equation x⁵ + 64x² = 0 is x = 0 or x = -8 after taking common.
What is a polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
It is given that the polynomial equation is:
x⁵ + 64x² = 0
x²(x³ + 64) = 0
x² = 0 or x³ + 64 = 0
x = 0 or x³ = -64
x = 0 or x = -8
Thus, the value of x in the equation x⁵ + 64x² = 0 is x = 0 or x = -8 after taking common.
Learn more about Polynomial here:
brainly.com/question/17822016
#SPJ1
A store sells two sizes of fresh wreaths. An 18-inch wreath costs $20, and a 22-inch wreath costs $30. In one day, the number of 22-inch wreaths sold was four more than five times the number of 18-inch wreaths, for a total of $1310. How many of each were sold?
Sonya drinks a 32 oz energy drink containing 80 calories per 12 oz how many calories did she drink
Answer:
213
Step-by-step explanation:
First we decide how many ounces 12 has in 32 (2.6)
Then we multiply 2.6 to 80 calories and get 213 calories
I need this asap!!!!!
Answer:
average rate of change = 23
Step-by-step explanation:
the average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
here [ a, b ] = [ 4, 9 ] , then
f(b) = f(9) = 212 ← from ordered pair in table
f(a) = f(4) = 97 ← from ordered pair in table , then
average rate of change = [tex]\frac{212-97}{9-4}[/tex] = [tex]\frac{115}{5}[/tex] = 23
In the figure below, Z is the center of the circle. Suppose that QR=14, ST=14, UZ=3x+5, and VZ=23. Find the following.
S
Z
W
R
X =
0
TV = 0
8 08
X
S
The value of x is given by 6 units and the value of TV is given by 7 units.
A circle may be defined as a closed loop which has a fixed point around which the loop is made called the center and the fixed distance from the center of the circle to its periphery is known as the radius of the circle. We are given a circle with center at Z. In the circle QR and ST are the chords such that QR = ST = 14 that is both are of equal length, and we know that equal chords are at equal distance from the center. Therefore,
VZ = UZ
23 = 3x + 5
18 = 3x
=> x = 18/3
=> x = 6 units.
Now, we also know that perpendicular drawn from center of the circle to the chord bisects the chord. Thus,
TV = (1/2)×ST
TV = (1/2)×14
TV = 7 units.
Learn more about Circle at:
brainly.com/question/10645610
#SPJ1
Find the first derivative.
Answer: y’ = 2/3 x^1/2 - 2/ sqrt of x - 5/2x^2/3
I’m given an answer but don’t know how to get it.
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{ \sqrt{x} (2x - 4) -( \frac{{x}^{2} - 4x + 5) }{2 \sqrt{x} } )}{x } [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{ {x}^{2} - 4x + 5 }{ \sqrt{x} } [/tex]
We know, division rule of differentiation :
[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{u}{v} [/tex]
then,
[tex]\qquad\displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{v\frac{du}{dx} - u \frac{dv}{dx} }{(v) {}^{2} } [/tex]
So, let's do the same in given equation :
[tex]\qquad\displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{ \sqrt{x} \frac{d}{dx}(x {}^{2} - 4x + 5) - ( {x}^{2} - 4x + 5) \frac{d}{dx}( \sqrt{x} ) }{( \sqrt{x} ) {}^{2} } [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{ \sqrt{x} (2x - 4) -( {x}^{2} - 4x + 5) \frac{1}{2 \sqrt{x} } }{x } [/tex]
[ This is the required Answer, but you can simplify it however you want according to the choices given ]
[tex]\qquad\displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{x \bigg( \frac{\sqrt{x} (2x - 4)}{x} -( {x}^{2} - 4x + 5) \frac{1}{2x \sqrt{x} } \bigg)}{x } [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{\sqrt{x} (2x - 4)}{x} -( {x}^{2} - 4x + 5) \frac{1}{2x \sqrt{x} } [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{(2x - 4)}{ \sqrt{ x}} - \frac{( {x}^{2} - 4x + 5) }{2 \sqrt{x {}^{3} } }[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
For whom would a car loan be a better option than a car lease?
A.
Kate frequently changes her cars, constantly switches professions, and detests selling and trading cars.
B.
Brian likes the feeling of owning his own car. He takes good care of it and doesn't like changing cars often.
C.
Joe hates the idea of maintaining his car. He prefers to have a car that is always under warranty.
Brian likes the feeling of owning his own car. He takes good care of it and doesn't like changing cars often is whom a car loan would be a better option than a car lease and is denoted as option B.
What is a Car loan?This is referred to as the total money borrowed which is used in the purchase of a car while on the other hand car lease involves the vehicle being made available to be driven for certain period of time or limit.
Since Brian likes the feeling of owning his own car and doesn't change cars often, then the car loan is best for him as it becomes his after the money or amount to be repaid is completed.
Read more about Car loan here https://brainly.com/question/26011426
#SPJ1
A ratio is a….of … numbers. It can be written …different ways.
Let's analyze the example of the ratio of 9 to 15.
This ratio helps us to compare those two numbers. We can express it in different ways:
[tex]\begin{gathered} \frac{9}{15} \\ 9\colon15 \\ 9\text{ to 15} \end{gathered}[/tex]Answer: A ratio is a omparisonof … numbers. It can be written …different ways.1. El rectángulo A mide 12 cm por 3 cm. El Rectángulo B es una copia a escala del Rectángulo A. Seleccione todos los pares de medidas que podrían tener las dimensiones del Rectángulo B.
A. 6 cm por 1,5 cm
B. 10 cm por 2 cm
C. 13 cm por 4 cm
D. 18 cm por 4,5 cm
E. 80 cm por 20 cm
2. El rectángulo A tiene 12 de largo y 8 de ancho. El rectángulo B tiene 15 de largo y 10 de ancho. El rectángulo C tiene 30 de largo y 15 de ancho.
una. ¿Es el Rectángulo A una copia a escala del Rectángulo B? Si es así, ¿cuál es el factor de escala?
b. ¿Es el Rectángulo B una copia a escala del Rectángulo A? Si es así, ¿cuál es el factor de escala?
C. Explica cómo sabes que el Rectángulo C no es una copia a escala del Rectángulo B.
d. ¿Es el Rectángulo A una copia a escala del Rectángulo C? Si es así, ¿cuál es el factor de escala?
1. The pairs of measurements that could have the dimensions of Rectangle B include:
A. 6cm by 1.5cm
D. 18cm by 4.5cm
E. 80cm by 20cm
2. Rectangle A is a scaled copy of rectangle B as the scale factor is 3:2.
Rectangle C isn't a scales factor of rectangle B since they have different ratio.
How to illustrate the information?1. It should be noted that from the information, Rectangle A measures 12 cm by 3 cm. Rectangle B is a scaled copy of Rectangle A.
Therefore, it should be noted that the ratio will be:
= 12 / 3
= 4 / 1
= 4:1
Therefore, the values that will give same ratio will be:
6cm by 1.5cm = 6/1.5 = 4:1
18cm by 4.5cm = 18/4.5 = 4:1
80cm by 20cm = 80/20 = 4:1
In conclusion, the correct options are A, D, and E.
2. Rectangle A is 12 long and 8 wide. The ratio will be:
= 12/8 = 3/2 = 3:2.
Rectangle B is 15 long and 10 wide. The ratio will be:
= 15/10 = 3/2 = 3:2
Rectangle C is 30 long and 15 wide. The ratio will be:
= 30/15 = 2:1
Therefore, rectangle A and B have same scale.
Learn more about rectangles on:
https://brainly.com/question/25292087
Rectangle A measures 12 cm by 3 cm. Rectangle B is a scaled copy of Rectangle A. Select all pairs of measurements that could have the dimensions of Rectangle B.
A. 6cm by 1.5cm
B. 10cm by 2cm
C. 13cm by 4cm
D. 18cm by 4.5cm
E. 80cm by 20cm
The graph illustrates a normal distribution for the prices paid for a particular model of HD television. The mean price paid is $2000 and the standard deviation is $75.
The approximate percentage of buyers who paid between $1925 and $2075 is; 68%
The approximate percentage of buyers who paid between $1925 and $2000 is; 34%
How to Interpret Normal Distribution Graph?We are given;
Mean = $2000
Standard Deviation = $75
1) We want to find the approximate percentage of buyers who paid between $1925 and $2075
The formula that is used to calculate the z-score of a a normal distribution is;
z = (x' - μ)/σ
where;
z is z-score
x' is sample mean
μ is population mean
σ is standard deviation
For a payment of 1925;
z = (1925 - 2000)/75 = -1
For a payment of2075;
z = (1925 - 2000)/75 = 1
Thus, this is 1 standard deviation from the mean.
Thus, this is a percentage of 68%
2) We want to find the approximate percentage of buyers who paid between $1925 and $2000?
For a payment of 1925;
z = (1925 - 2000)/75 = -1
For a payment of 2000;
z = (2000 - 2000)/75 = 0
This translates to a percentage of (1/2) * 68% = 34%
Read more about Normal Distribution at; https://brainly.com/question/4079902
#SPJ1
Missing options are;
1) What is the approximate percentage of buyers who paid between $1925 and $2075?
2) What is the approximate percentage of buyers who paid between $1925 and $2000?
solve for x 7x^2+49=0
Answer:
[tex]7 {x}^{2} + 49 = 0 \\ 7( {x}^{2} + 7) = 0 \\ \frac{7( ({x}^{2} + 7) }{7} = \frac{0}{7} \\ {x}^{2} + 7 = 0 \\ {x}^{2} = - 7[/tex]
NOTE THERE IS NO SOLUTION FOR THE GIVEN EQUATION SINCE THE SQUARE OF ANY NUMBER CANNOT GIVE A NEGATIVE NUMBER.
THE SQUARE OF ANY NUMBER WHETHER IT'S POSITIVE OR NEGATIVE ALWAYS GIVES A POSITIVE NUMBER.
GOODLUCK!!
HELP ASAP
Do you think that people are too free in the United States to do and say whatever they want or that there is not enough freedom? Do you feel that Americans have just the right amount of freedom? Explain your answer.
I believe that Americans have just the right amount of freedom.
How to illustrate the information?The First Amendment protects our freedom of speech and association, so the government cannot stop us from writing or speaking what we choose. We also have the right to create clubs and groups and participate in protests and rallies.
As long as you don't "materially and substantially" interrupt classrooms or other school activities, you have the right to voice your ideas. School administrators can disperse you if you stage a demonstration on the steps of the building and block the entrance. Additionally, they may be able to prevent you from using words that they deem to be "vulgar or indecent."
The above shows that despite the right of freedom, it's important to checkmate what people do.
Learn more about freedom on:
https://brainly.com/question/13273450
#SPJ1
What are the next two terms after -13, 8, -5, 3,-2
The next two terms in the sequence, -13, 8, -5, 3,-2 is 1 and -1.
What are the next two terms?The mathematical operations that would be used to determine the next two terms are addition and subtraction. Addition is used to determine the sum of two or more numbers. Subtraction is used to determine the difference between two or more numbers.
The first step is to determine the relationship between the numbers in the sequence. Looking at the numbers, it can be seen that the the difference between the first number and the second number gives the third number.
-13 + 8 = -5
-5 + 3 = -2
3 - 2 = 1
-2 + 1 = -1
To learn more about mathematical sequence, please check: https://brainly.com/question/26578277
#SPJ1
I need help on this :)
Explanation
We are given the following equation:
[tex]x^2=-12[/tex]We are required to determine the solution of the given equation.
This is achieved thus:
[tex]\begin{gathered} x^2=-12 \\ \text{ Square root both sides} \\ x=\pm\sqrt{-12} \\ \text{ We know that }\sqrt{-1}=i \\ x=\pm\sqrt{3\times4\times-1} \\ x=\pm\sqrt{3}\times2\times i \\ x=\pm2\sqrt{3}i \\ x=-2\sqrt{3}i\text{ }or\text{ }2\sqrt{3}i \end{gathered}[/tex]The only solution to this equation involves complex numbers. So, there is no real solution.
Hence, the answer is:
[tex]No\text{ }solution[/tex]Find where line a & tne line that has an undefined slope intersect.
Write the
coordinates of the point.
The coordinates of the point of intersection are (-6, -7)
How to find the point of intersection between the lines?The graph represents the given parameter
On the graph, we can see that there are two lines with the following properties:
Line 1: A slant line that extends indefinitelyLine 2: A vertical line that extends indefinitelyLine 3: A horizontal line that extends indefinitelyThe above properties means that:
Line 1: Has a defined slope i.e. the line ALine 2: Has an undefined slopeLine 3: Has a slope of 0From the graph, we can see that the lines A and the other line meet at a point
The point where these lines meet is referred to as the point of intersection
The coordinates of this point are (-6, -7)
Hence, the coordinates of the point where line a & tne line that has an undefined slope intersect are (-6, -7)
Read more about slopes at
https://brainly.com/question/3493733
#SPJ1
A landlord charged $865 per month to rent an apartment in 2010. The rent increased
at a constant rate and reached $1065 per month in 2018.
a. Write a linear model that represents the monthly rent as a function of the number
of years since 2010.
b. Use the model to estimate the monthly rent in 2021.
Answer:
y = 25x + 865
so the monthly rent in 2021 is 1,140
do you need an explanation or is this fine?
I need help with the 16
NSWER
EXPLANATION
In a isometry the distances between points are conserved, so the image of segment PQ has to have the same length as segment PQ.
When we have a translation defined by a vector the x-coordinate of the vector tells the horizontal translation and the y-coordinate the vertical translation.
For this problem, if the vector is <3, 5>, we have to translate each point 3 units to the right and 5 units up.
[tex]Q(-2,-2)\to Q^{\prime}(-2+3,-2+5)=(1,3)[/tex][tex]P(-4,-4)\to P^{\prime}(-4+3,-4+5)=(-1,1)[/tex]The endpoints of the image segment are Q'(1, 3) and P'(-1, 1)
number of odd number outcomes when a die is rolled
Answer:
Explanation:
A die has 6 faces numbered 1 to 6.
The sample space when a die is rolled is:
[tex]\lbrace1,2,3,4,5,6\rbrace[/tex]Thus, the number of odd number outcomes when a die is rolled is:
Can someone help me with exterior angle theorem?
According to the exterior angle theorem, an external angle's measure is equal to the sum of its remote interior angle's two measurements. The opposite interior angles are another name for the remote interior angles. Where can I determine a triangle's outer angle? In a triangle, how can I determine the interior and outside angles?
Take the total of two interior angles of a triangle that are known and deduct it from 180 to find the internal angle of the triangle.
Simple addition of the triangle's two opposite internal angles will yield the triangle's external angle. 180° minus the inside angle equals each exterior angle. Using this formula requires the knowledge of the corresponding internal angle. Exterior angle = Total.
To learn more about Exterior angle theorem refer to:
https://brainly.com/question/12230244
#SPJ13