Answers
In order to find the vertex of this quadratic equation, first let's find the coefficients a, b and c from the standard form of the quadratic equation:
[tex]y=ax^2+bx+c[/tex]Comparing with the given equation, we have a = -5, b = -270 and c = -520.
Now, let's calculate the x-coordinate of the vertex using the formula below:
[tex]\begin{gathered} x_v=\frac{-b}{2a} \\ x_v=\frac{-(-270)}{2\cdot(-5)} \\ x_v=\frac{270}{-10} \\ x_v=-27 \end{gathered}[/tex]Using this value of x in the equation, we can find the y-coordinate of the vertex:
[tex]\begin{gathered} y_v=-5x^2_v-270x_v-520 \\ y_v=-5\cdot(-27)^2-270\cdot(-27)-520 \\ y_v=-5\cdot729+7290-520 \\ y_v=-3645+7290-520 \\ y_v=3125 \end{gathered}[/tex]Therefore the vertex is located at (-27, 3125).
Related Questions
The Adventure Club has scheduled a trip to hike a nearby mountain. Since the group started hiking, they gained 456 feet in altitude from their start position. The current altitude is 437 feet, but there is no record of their starting altitude.write a equation to represent this situation Explain what your variable representssolve your equation please someone help me ill give you a star anything please ♡
Answers
Let h be the altitude of the starting position.
Since the group has gained 456 feet from the start position, then the current altitude is:
The total fixed costs of producing a product is $36,000 and the variable cost is $124 per item. If the company believes they can sell 1,800 items at $170 each, what is thebreak-even point?667 items695 items705 items783 itemsNone of these choices are correct.
Answers
Prove the Question according to the theorem of a Circle
Answers
Given -
P,Q,R and S are 4 points on the circle and PQRS is a cyclic quadrilateral
Prove -
[tex]\angle PQR\text{ + }\angle PSR\text{ = 180}[/tex]Explanation -
[tex]\angle1\text{ = }\angle6\text{ ------\lparen1\rparen \lparen Angles in same segment\rparen}[/tex][tex]\angle5\text{ = }\angle8\text{ ------\lparen2\rparen \lparen Angles in the same segment\rparen}[/tex][tex]\angle2\text{ = }\angle8\text{ ------\lparen3\rparen \lparen Angles in the same segment\rparen}[/tex][tex]\angle7\text{ = }\angle3\text{ -------\lparen4\rparen\lparen Angles in the same segment\rparen}[/tex]By using angle sum property of quadrilateral
[tex]\angle P\text{ + }\angle Q\text{ + }\angle R\text{ + }\angle S\text{ = 360}[/tex][tex]\angle1\text{ + }\angle2\text{ + }\angle3\text{ + }\angle4\text{ + }\angle5\text{ + }\angle6\text{ + }\angle7\text{ + }\angle8\text{ = 360}[/tex][tex](\angle1+\angle2+\angle7+\angle8)+(\angle3+\angle4+\angle5+\angle6)=360[/tex]By using equation 1,2,3 and 4
[tex]2(\angle3+\angle4+\angle5+\angle6)\text{ = 360}[/tex][tex]\angle3+\angle4+\angle5+\angle6\text{ = 180}[/tex][tex](\angle3+\angle4)+(\angle5+\angle6)\text{ = 180}[/tex][tex]\angle PQR\text{ + }\angle PSR\text{ = 180}[/tex]Hence Proved
10. If you invest $2000 at 6% compounded monthly, how long will it take the account to double in
value?
Answers
If I invest $2000 at 6% interest compounded monthly, it will take 11.58 years by the account to double in value.
What is compound interest?
The practice of adding interest to the principal amount of a loan or deposit is known as compound interest, sometimes known as interest on principal and interest. It happens when interest is reinvested, added to the lent capital rather than paid out, or required to be paid by the borrower, resulting in interest being created the next period on the principal amount plus any accrued interest. Compound interest is a prominent concept in finance and economics.
The initial investment of $2000 at 6% compounded monthly.
Since, the interest rate of 6% is compounding monthly, then the effective annual interest rate will be
= (1+)−1i = (1+rm)m−1
Here, r = interest rate in decimals
= (1+0.0612)12−1i = (1+0.0612)12−1
= 0.061678i = 0.061678
= ×100 = 6.1678%
Now, we are using Rule 72 to calculate the doubling time
Time to double the initial amount = 72 /effective annual interest rate
Time to double the initial amount = 11.58 years
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the points E,F,G and H all lie on the same line segment, in that order, such that ratio of EG:FG:GH is equal to 4:1:5. If EH=10, find EG
Answers
You have that the ratio of EG:FG:GH = 4:1:5.
Moreover, segment EH = 10.
In order to find EG you consider the following ratios:
EG/FG = 4/1
FG/GH = 1/5
Furthermore, EH = EG + FG + GH
Is P(A and B) ≠ 0? Explain.
A.) No. P(A and B) = 0.
B.) Yes. Even if P(A) = 0 or P(B) = 0, P(A and B) will always be non-zero.
C.) No. Because both P(A) and P(B) are not equal to 0, P(A and B) = 0.
D.) Yes. Because both P(A) and P(B) are not equal to 0, P(A and B) ≠ 0. (b)
Answers
The right option is D as P(A and B) ≠ 0 only for the independent probability events for A and B.
What is an independent event in probability?Two events say A and B are said to be independent if the probability of the intersection of A and B is equal to the product of their respective probability, But same events are said to be mutually exclusive if the probability of the intersection of A and B is equal to zero(0).
In the given question, P(A and B) ≠ 0 can only be true if A and B are independent event and P(A) and P(B) are not equal to zero such that
P(A and B)=P(A)× P(B)≠ 0.
Hence, we can deduce from the axiom of independent events of probability that because both P(A) and P(B) are not equal to 0, P(A and B) ≠ 0.
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A basketball player scored 24 times during one game. she scored a total of 38 points, two for each two-point shot and one for each free throw. How many two-point shots did she make? How many free throws?
Answers
The number of two-points shots made is 14
The number of free throws made is 10
What is the number of two-points shots and free throws made?The first step is to formulate a set of linear equations that represent the information in the question:
x + y = 24 equation 1
2x + y = 38 equation 2
Where:
x = number of two-point shots made y = number of free throws madeThe linear equations would be solved using the elimination method.
In order to determine the value of x, take the following steps:
Subtract equation 1 from equation 2
x = 14
Substitute for x in equation 1
14 + y = 24
Combine similar terms:
y = 24 - 14
Add similar terms together
y = 10
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Answer:
Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables are studied under the supposition or demand that they depend, by some law or rule, on the values of other variables.
Step-by-step explanation:
Megan's text messaging plan cost $15 for the first 600 messages and 5¢ for each additional text message. If she owes $24.60 for text messaging in the month of October, how many text messages did she send that month
Answers
Megan sent 792 text messages in the month of October .
In the question ,
it is given that
Cost for first 600 messages = $15
additional text message charge = $0.05
Amount owed by Megan for the month of October = $24.60
Let the number of Additional messages be x.
So, according to the question
15 + 0.05x = 24.60
0.05x = 24.60-15
0.05x = 9.6
x = 9.6/0.05
x = 192
number of extra messages = 192
total messages = first 600 messages + extra messages
= 600+192
= 792
Therefore , Megan sent 792 text messages in the month of October .
The given question is incomplete , the complete question is
Megan's text messaging plan cost $15 for the first 600 messages and 5¢ for each additional text message. If she owes $24.60 for text messaging in the month of October, how many text messages did she send that month ?
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X+87°2x⁰ i have to solve for x it’s a 180 angle
Answers
Answer:
31
Step-by-step explanation:
x + 87 and 2x are linear pair angles.
Sum of linear pair angles is 180,
x + 87 + 2x = 180
x + 2x + 87 = 180
3x + 87 = 180
3x = 180 - 87
3x = 93
x = 93 / 3
x = 31
Eddie brought his DVD set to the secondhand store to sell he was paid for all three DVDs in the set before he left Eddie used $15.70 of his earnings to purchase a pair of headphones had $2.30 remaining which equation can you use to find the amount of money Eddie received for each DVD
15.70(d-3)=2.30
3d-15.70=2.30
15.70d-3=2.30
3(d-15.70)=2.30
Answers
Eddie brought his DVD set to the secondhand store to sell he was paid for all three DVDs in the set before he left Eddie used $15.70 of his earnings to purchase a pair of headphones had $2.30 remaining which equation can you use to find the amount of money Eddie received for each DVD
15.70(d-3)=2.30
3d-15.70=2.30
15.70d-3=2.30
3(d-15.70)=2.30
answer reflects:
3 dvds sold for d price - cost of headphones and a remaining $2.30
what is the volume of a cube with sides 3 cm.be sure to include correct units with your answer
Answers
Answer:
27 cubic feet
Explanation:
The volume of a cube with side length L is given by
[tex]V=L^3[/tex]Now in our case, L = 3 ft; therefore, the volume is
[tex]V=3^3[/tex]which simplifies to give
[tex]\boxed{V=27\text{ ft}^3.}[/tex]which is our answer!
Hence, the volume of the cube with the side length of 3 cm is 27 cubic cm.
Select the correct answer from each drop-down menu.Glven: W(-1, 1), X(3, 4), Y(6, 0), and Z(2, -3) are the vertices of quadrilateral WXYZ.Prove: WXYZis a square.
Answers
ANSWER
all four sides have a length of 5
EXPLANATION
The distance between two points (x₁, y₁) and (x₂, y₂) is,
[tex]d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]Let's find the distance between each pair of points, WX, XY, YX, and WZ,
[tex]WX=\sqrt{(3-(-1))^2+(4-1)^2}=\sqrt{(3+1)^2+(4-1)^2}=\sqrt{4^2+3^2}=\sqrt{16+9}=\sqrt{25}=5[/tex][tex]XY=\sqrt{(6-3)^2+(0-4)^2}=\sqrt{(3)^2+(-4)^2}=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5[/tex][tex]YZ=\sqrt{(2-6)^2+(-3-0)^2}=\sqrt{(-4)^2+(-3)^2}=\sqrt{4^2+3^2}=\sqrt{16+9}=\sqrt{25}=5[/tex][tex]WZ=\sqrt{(2-(-1))^2+(-3-1)^2}=\sqrt{(2+1)^2+(-4)^2}=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5[/tex]Hence, using the distance formula we found that all four sides have a length of 5.
Which of the following could be the areas of the three squares below? A. 12ft^2, 16ft^2, 20ft^2B. 10ft^2, 18ft^2, 30ft^2C. 4ft^2, 5ft^2, 12ft^2D. 8ft^2, 16ft^2, 24ft^2i have to show work too :(
Answers
The correct option is D
8ft^2, 16ft^2, 24ft^2 could be the three areas of the given squares
Explanation:To know the area of the three squares, we need to know the side length of each square. This can be done by applying Pythagorean rule on the right-angle triangle formed in the middle.
The square of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides (legs).
The area of a square is the square of its side length.
Taking the square roots of each of the given options, which ever option has Pythagorean triple is the correct option.
A.
[tex]2\sqrt[]{3},4,2\sqrt[]{5}[/tex]This is NOT a Pythagorean triple.
B.
[tex]\sqrt[]{10},3\sqrt[]{2},\sqrt[]{30}[/tex]This is NOT a Pythagorean triple.
C.
[tex]2,\sqrt[]{5},2\sqrt[]{3}[/tex]This is NOT a Pythagorean triple
D.
[tex]2\sqrt[]{2},4,2\sqrt[]{6}[/tex]This is a Pythagorean triple.
CHECK[tex]\begin{gathered} (2\sqrt[]{2})^2+4^2=(2\sqrt[]{6})^2 \\ 8+16=24 \\ 24=24 \end{gathered}[/tex]The table shows a linear relationship between x and y. Drag and drop the options provided into the correct boxes to complete the equation. х 1 0 6 -4 41 у 9 -39 The equation that represents the relationship Is y = -8 -41 ON 9 4 O?
Answers
To calculate the equation first we need to choose two points of the table
P1 (1,1)=(x1,y1)
P2(0,9)=(x2,y2)
then we calculated the slope m
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]substituting the points we have
[tex]m=\frac{9-1}{0-1}=\frac{8}{-1}=-8[/tex]then we can calculate the equation
[tex](y-y1)=m(x-x1)[/tex][tex](y-1)=-8(x-1)[/tex][tex]y-1=-8x+8[/tex][tex]y=-8x+8+1[/tex]the equation is
[tex]y=-8x+9[/tex]How come my answer is wrong? It says it’s equal to the correct answer but it’s not the right answer.
Answers
For one of the meals eaten duringthe field trip to Williamsburg, VA,WHMS will be charged $115.50 foradults to eat and $712.50 forstudents to eat WHMS will leave a10% tip. How much money willWHMS leave for the tip
Answers
The total amount the WHMS would be charged for adults and students to eat is
115.5 + 712.5 = $828
We were told that WHMS will leave a 10% tip. Recall that percentage is expressed in terms of 100. This means that the amount of money that WHMS will leave for the tip is
10/100 * 828 = $82.8
WHMS would leave $82.8 for the tip
3. (02.04 MC)
Choose the equation that represents a line that passes through points (-6, 4) and (2, 0).
Answers
The answer to the question is here
20g of radioactive substance decays by 1/2 of it's original
amount every 30 days. How much is left after 10 days.
Answers
The amount of radioactive after 10 days with the same rate of change of decay will be 16.67 g.
What is the rate of change?The rate of change is the change of a quantity over 1 unit of another quantity.
Most of the time the rate of change is the change with respect to time.
For example the speed 3meter/second.
As per the given,
Radioactive decays by 1/2 of its original in 30 days.
1/2 of original → 30 days.
Divide both sides by 3
1/6 of original → 10 days
Therefore, in 10 days amount of decays will be,
1/6 of 20 ⇒ 20/6 = 3.33
The amount left = 20 - 3.33 = 16.67.
Hence "The amount of radioactive after 10 days with the same rate of change of decay will be 16.67 g".
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How many megagrams(Mg) are there in 3.6 tons?[ ? ] MgMass in MgEnter
Answers
Step 1
Given;
[tex]3.6\text{tons}[/tex]Required; To find how many megagrams(Mg) are in 3.6 tonnes
Step 2
Find how many megagrams(Mg) are in 3.6 tonnes
[tex]\begin{gathered} 1\text{ tonne=1000000}g \\ 1\text{ megagram=1}000000g \end{gathered}[/tex]Therefore,
[tex]1\text{ tonne = 1 megagram}[/tex][tex]\frac{1\text{ tonne}}{3.6\text{ tonnes}}=\frac{1\text{ megagram}}{x\text{ megagram}}[/tex][tex]\begin{gathered} x\text{ megagram(1 tonne)=1 megagram(3.6 tonnes)} \\ \frac{x\text{ megagram}(1\text{ tonne)}}{1\text{ tonne}}\text{=}\frac{\text{1 megagram(3.6 tonnes)}}{1\text{ tonne}} \\ x=\text{ 3.6 megagrams} \\ x=3.6Mg \end{gathered}[/tex]
Question 5The table below shows the coordinates of a figure that was transformed.Pre-ImageImageA(5,2)B(6, 1)A'(0,0)B'(1, -1)C'(-1,3)C(4,5)Which is a correct description of the transformation?
Answers
You have the following A, B and C points, which are transformed to the points A', B' and C', jus
Determine the angle of rotation of the conic section given by: 32x2 +50xy + 7y2 = 100 (round your answer to the nearest tenth of adegree).
Answers
The formula to obtain the angle of rotation is as follows:
[tex]\cot 2\theta=\frac{A-C}{B}[/tex]Compare the given equation to the general equation of a conic.
[tex]Ax^2+Bxy+Cy^2+Dx+Ey+F=0[/tex]Thus, the values of A, B, and C are as follows.
[tex]\begin{gathered} A=32 \\ B=50 \\ C=7 \end{gathered}[/tex]Substitute the values into the equation.
[tex]\begin{gathered} \cot 2\theta=\frac{32-7}{50} \\ \cot 2\theta=\frac{25}{50} \\ \cot 2\theta=\frac{1}{2} \end{gathered}[/tex]Find the value of the θ.
[tex]\begin{gathered} \frac{1}{\tan 2\theta}=\frac{1}{2} \\ \tan 2\theta=2 \\ 2\theta=\tan ^{-1}(2) \\ 2\theta\approx63.4349 \\ \theta\approx31.7 \end{gathered}[/tex]given A(2, 3), B(8, 7), C(6 1), which will make line AB perpendicular to line CD?D(9, 3)D(4, 4)D(3, 3)D(8, 4)
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
A(2, 3), B(8, 7), C(6 1)
Step 02:
Line AB
Slope formula
m = (y2 - y1) / (x2 - x1)
A (2 , 3) x1 = 2 y1 = 3
B (8 , 7) x2 = 8 y2 = 7
[tex]m\text{ = }\frac{7-3}{8-2}=\frac{4}{6}=\frac{2}{3}[/tex]Step 03:
Slope of the perpendicular line, m’
m' = -1 / m
[tex]m\text{'}=\text{ }\frac{-1}{m\text{ }}=\text{ }\frac{-1\text{ }}{\frac{2}{3}}\text{ = -}\frac{3}{2}[/tex]Step 04:
Line CD
m' = (y2 - y1) / (x2 - x1)
C (6 , 1) x1 = 6 y1 = 1
D ( x2, y2) x2 = x2 y2 = y2
[tex]-\frac{3}{2}=\text{ }\frac{y2-1}{x2-6}[/tex][tex]\frac{3}{2}=\frac{1-y2}{6-x2}[/tex]We must test the numerical values to verify equality,
x2 = 9
y2 = 3
[tex]\frac{3}{2}=\frac{1-9}{6-3}\text{ = }\frac{-8}{3}\text{ }[/tex]x2 = 4
y2 = 4
[tex]undefined[/tex]2 x— =-------7 x+ 10x = ???
Answers
Answer:
x = 4
Explanation:
Given the expression;
2/7 = x/x+10
Cross multiply
2(x+10) = 7x
Expand the bracket
2x + 20 = 7x
Subtract 7x from btoh sides
2x+20-7x = 7x - 7x
2x-7x+20 = 0
-5x + 20 = 0
-5x = -20
Divide both sides by -5;
-5x/-5 = -20/-5
x = 4
hence the value of x is 4
laws exponents multiplication band power to a power simplifymake it small steps please the smallest you canbare minimum of steps
Answers
Answer:
[tex](4r^4s^{-2})(-3rs^{-3})(rs)=-12r^6s^{-4}[/tex]Explanation:
Given the expression:
[tex](4r^4s^{-2})(-3rs^{-3})(rs)[/tex]This can be rearranged using law of multiplication (That multiplication is cummutative) to become:
[tex](4)(-3)(r^4rr)(s^{-2}s^{-3}s)[/tex]This becomes, using the law of exponents:
[tex]-12r^{4+1+1}s^{-2-3+1}[/tex]and finally, we have:
[tex]-12r^6s^{-4}[/tex]Model Real Life You have 3 toy bears. Yohave more yo-yos than toy bears. How mamore yo-yos do you have?
Answers
Solution
Step 1
Let the number of yo-yos than toy bears = x
Enter an equation that passes through the point (12, 7) and forms a system of linear equations with no solution when combined with the equation y=−3/4x+8.
Answers
To answer this question, we need to know that two linear equation that does not have solutions must not cross to each other, that is, they do not have a common point. For this case, both lines must be parallel lines. So in the question, we need to find a parallel line to the given line. Two parallel lines have the same slope.
Then, we have that the line must pass through (12, 7), and, because it is parallel to y = -3/4x + 8, and the slope for this line is m = -3/4, then, the line equation is, applying the point-slope form of the line:
[tex]y-y_1=m(x-x_1)[/tex]And
x1 = 12
y1 = 7
m = -3/4
Then
[tex]y-7=-\frac{3}{4}(x-12)\Rightarrow y-7=-\frac{3}{4}x+\frac{3}{4}\cdot12\Rightarrow y-7=-\frac{3}{4}x+\frac{36}{4}[/tex][tex]y-7=-\frac{3}{4}x+9\Rightarrow y=-\frac{3}{4}x+9+7\Rightarrow y=-\frac{3}{4}x+16[/tex]Then, the line equation is y = -3/4 x + 16.
We can check this if we use the elimination method as follows:
This is a FALSE result, and we do not have solutions for this system. Therefore, the line equation is y = -3/4 x + 16.
Swine Flu is attacking Springfield. The function below determines how many people have swine where t=time in days and S=the number of people in thousands.
Answers
A.find s(4)
[tex]\begin{gathered} s(4)=9(4)-4 \\ s(4)=36-4 \\ s(4)=32 \end{gathered}[/tex]B. means that in 4 days there will be 32000 infected people
C. find t to S(t)=23
[tex]\begin{gathered} 23=9t-4 \\ 9t=23+4 \\ t=\frac{27}{9} \\ t=3 \end{gathered}[/tex]D. means there will be 23,000 infected people after 3 days
E. Graph
to draw the line we need two points which we already have but we will add another to make a table of 3 values the new value is t=1
[tex]\begin{gathered} s(1)=9(1)-4 \\ s(1)=5 \end{gathered}[/tex]table
graph
Explaining the Converse of the Pythagorean TheoremThe converse of the Pythagorean Theorem states that if the three sides of a triangle work for the equation a^2 + b^2 = c^2, then the triangle is a right triangle. To prove this, you can use what’s called a proof by contradiction. That is, you can prove something is true because it cannot be false.Start by assuming a triangle is not a right triangle and the sides work for the equation a^2 + b^2 = c^2. Here is a diagram of the triangle. Keep this diagram window open as you work on the tasks in this section.Now, create a right triangle with legs a and b. Call the hypotenuse n. Here is a diagram of the triangle. Keep this diagram window open as you work on the tasks in this section.questionsPart ASince triangle 2 is a right triangle, write an equation applying the Pythagorean Theorem to the triangle.Part BSince the equations for both triangles have a^2 + b^2, you can think of the two equations for c^2 and n^2 as a system of equations. Substitute what a^2 + b^2 equals in the first equation for a^2 + b^2 in the second equation. After you substitute, what equation do you get?Part CNow, take the square root of both sides of the equation from part B and write the resulting equation.Part DIs there any way for this equation to be true? How?Part EWhat does this show about the relationship between the two triangles?Part FDoes this mean that triangle 1 is a right triangle? Why or why not?
Answers
Part A: Since triangle 2 is a right triangle, write an equation applying the Pythagorean Theorem to the triangle.
Triangle 2 has the following sides: a, b and n
Writing it into an equation will be:
[tex]\text{ a}^2\text{ + b}^2\text{ = n}^2[/tex]The answer is a² + b² = n²
Part B: Since the equations for both triangles have a^2 + b^2, you can think of the two equations for c^2 and n^2 as a system of equations. Substitute what a^2 + b^2 equals in the first equation for a^2 + b^2 in the second equation. After you substitute, what equation do you get?
Equation 1 (Triangle 1): a² + b² = c²
Equation 2 (Triangle 2): a² + b² = n²
Substitute what a^2 + b^2 equals in the first equation for a^2 + b^2 in the second equation, it will be:
[tex]\text{ a}^2\text{ + b}^2\text{ = n}^2[/tex][tex]\text{ c}^2\text{ = n}^2[/tex]The answer is c² = n²
Part C : Now, take the square root of both sides of the equation from part B and write the resulting equation.
[tex]\text{ c}^2\text{ = n}^2[/tex][tex]\text{ }\sqrt{c^2}\text{ = }\sqrt{n^2}[/tex][tex]\text{ c = n}[/tex]The answer is c = n
The points (-6, -10) and (23, 6) form a line segment.
Write down the midpoint of the line segment.
Answers
Answer:
(8.5, - 2 )
Step-by-step explanation:
given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
here (x₁, y₁ ) = (- 6, - 10 ) and (x₂, y₂ ) = (23, 6 ) , then
midpoint = ( [tex]\frac{-6+23}{2}[/tex] , [tex]\frac{-10+6}{2}[/tex] ) = ( [tex]\frac{17}{2}[/tex] , [tex]\frac{-4}{2}[/tex] ) = (8.5, - 2 )
Refer to the diagram below to prove that the exterior angle equals the
Answers
To prove that the sum of the remote interior angles and the exterior angle have the same value, we recall 2 things:
1.- the inner angles of a triangle add up 180 degrees
2.- angle 3 and angle 4 are supplementary which means that they add up 180 degrees.
[tex]\begin{gathered} \measuredangle1+\measuredangle2+\measuredangle3=180^{\circ} \\ \measuredangle3+\measuredangle4=180^{\circ} \\ \Rightarrow \\ \measuredangle1+\measuredangle2+\measuredangle3=\measuredangle3+\measuredangle4 \\ \Rightarrow \\ \measuredangle1+\measuredangle2=\measuredangle4 \end{gathered}[/tex]Answer:
They are linear pair and therefore supplementary.
Triangle sum theorem.
Substitution.
Subtraction property of equality.