Final answer:
The corresponding angles theorem states angles in matching corners are equal when two parallel lines are intersected by a transversal. To prove this, use properties of parallel lines and transversals, and various established theorems. Euclidean postulates are employed, rather than the Pythagorean theorem or trigonometry.
Explanation:
To prove the corresponding angles theorem, one must understand that when two parallel lines are intersected by a transversal, the angles in matching corners are equal. These are called corresponding angles. For instance, suppose you have two parallel lines L1 and L2, and a transversal T that intersects them at points A and B respectively. The angle ∠PAB on line L1 would correspond to angle ∠QBA on line L2, and they would be equal.
To provide a mathematical proof, one would typically use properties of parallel lines and transversals, or other established theorems such as the alternate interior angles theorem or the exterior angle theorem. By proving all these other angles are equal due to their relationships with each other (alternate interior, consecutive interior, alternate exterior angles, etc.), one can by default establish that corresponding angles must also be equal.
Proof of this theorem often involves constructing supplementary and congruent angles and using the postulates of Euclidean geometry. The Pythagorean theorem and trigonometry need not be involved in this proof unless one is working with right triangles formed by the transversal and the parallel lines, or if dealing with more complex geometric problems.
Graph each equation by using the x- and y-intercepts
The sum of 6 consecutive odd numbers is 204. What is the fourth number in this sequence?
204 /6 = 34
29 +31 +33 + 35 +37 +39 = 207
4th number = 35
The fourth number is 35
If y = 2x - 3, then which of the following ordered pairs lies on the graph?
|3x-2|+2y if x=-4,y=7,and z=-9
Un número entero de tres dígitos es igual a 25 veces la suma de sus dígitos. Si los tres dígitos se invierten, el número que resulta excede al número dado por 198.
El dígito de las decenas en uno menos que la suma de los dígitos de las centenas y de las unidades. Encuentra el número.
Zack is purchasing a bag of apples. The cost of apples is proportional to the weight of the apples in pounds as shown on the graph. Which statements are true about the cost of the apples?
Which statements are true about the cost of the apples?
Select each correct answer
1 lb of apples will cost Zack $2.50.
10 lb of apples will cost Zack t $4.
4 lb of apples will cost Zack $10.
2.5 lb of apples will cost Zack $1.
Answer:
1 lb of apples will cost Zack $2.504 lb of apples will cost Zack $10Step-by-step explanation:
The graph axesand common sense tell you that each ordered pair represents ...
(weight, cost)
So the ordered pairs (1, 2.50) and (4, 10) mean ...
1 lb of apples will cost Zack $2.50
4 lb of apples will cost Zack $10
A and C should be the correct answers if I'm not mistaken
The sides of a triangle are in the ratio 5:12:13. Describe the length of the shortest side is the perimeter is not more than 120 inches
If you shift the linear parent function, f(x) = x, down 6 units, what is the equation of the new function?
A. g(x) = x + 6
B. g(x) = x
C. g(x) = 6x
D. g(x) = x – 6
Answer:
Option D is correct
[tex]g(x) = x-6[/tex]
Step-by-step explanation:
Vertically down :
If y =f(x) is a parent function, then the new function g(x) b units vertically down is, g(x) = f(x) -b.
As per the statement:
Given the parent function:
[tex]f(x) = x[/tex]
To shift linear parent function vertically down 6 units.
By definition we have;
g(x) = f(x) -6
⇒[tex]g(x) = x-6[/tex]
Therefore, the equation of new function g(x) is, [tex]g(x) = x-6[/tex]
A triangle has sides of lengths 6, 2, 7. Is it right triangle?
Please help me i really need help
What is f(-4) if f(x)=|7x-3|
Randy is twice as old as his sister jane. together the sum of their ages is 15. how old is randy?
Final answer:
Randy is 10 years old.
Explanation:
The question is about solving a simple algebraic equation involving ages.
We are told Randy is twice as old as his sister Jane, and the sum of their ages is 15 years.
If we let Jane's age be represented by 'j', then Randy's age would be '2j' as he is twice as old as Jane.
The equation to represent the sum of their ages is:
j + 2j = 15
To find Jane's age, we combine the like terms:
3j = 15
Now, we divide both sides of the equation by 3 to isolate 'j':
j = 15 / 3
j = 5
Therefore, Jane is 5 years old. To find Randy's age, we multiply Jane's age by 2:
Randy's age = 2 * Jane's age
Randy's age = 2 * 5
Randy's age = 10
So, Randy is 10 years old.
50 POINTS! + BRAINLIEST! PLEASE HELP
slope = rise over run = y/x
A (-1,3) slope = 3/-1 = -3
B (1,2) slope = 2/1 = 2
C (-3,-1) slope = -1/-3 = 1/3
2 lines need to be negative reciprocals in order to be a right triangle
negative reciprocal of -3 is 1/3
so this is a right triangle
Answer: yes it is
Step-by-step explanation: put into a graph and it will become clear
When multiplying numbers in scientific notation you blank the coefficients and substract the exponents?
What is the equation in point slope form of the line that passes through the point (−1, −3) and has a slope of 4?
y−1=4(x−3)
y+3=4(x+1)
I agree with the second answer. Was this correct?
What number is 30% of 150?.
We start with triangle ABC and see that angle ZAB is an exterior angle created by the extension of side AC. Angles ZAB and CAB are a linear pair by definition. We know that m∠ZAB + m∠CAB = 180° by the . We also know m∠CAB + m∠ACB + m∠CBA = 180° because . Using substitution, we have m∠ZAB + m∠CAB = m∠CAB + m∠ACB + m∠CBA. Therefore, we conclude m∠ZAB = m∠ACB + m∠CBA using the .
To prove that m∠ZAB = m∠ACB + m∠CBA, we start with triangle ABC and use the fact that angles in a triangle add up to 180°. Angle ZAB and CAB are a linear pair, so they add up to 180°. By substitution, we can conclude that m∠ZAB = m∠ACB + m∠CBA.
Explanation:To prove that m∠ZAB = m∠ACB + m∠CBA, we start with triangle ABC. Angle ZAB is an exterior angle created by the extension of side AC. Angle ZAB and CAB are a linear pair, which means they add up to 180°. We also know that angle CAB + angle ACB + angle CBA = 180° because the angles in a triangle add up to 180°. Using substitution, we have m∠ZAB + m∠CAB = m∠CAB + m∠ACB + m∠CBA. Therefore, we can conclude that m∠ZAB = m∠ACB + m∠CBA using the fact that the angles in a triangle add up to 180°.
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Find the y-intercept of the line whose equation is 2x - 3y = -6.
to find y intercept, make x = 0 then solve equation:
2x-3y=-6
2(0) - 3y=-6
-3y =-6
y = -6 / -3
y=2
so y intercept is (0,2)
The number 1.258201... can be classified as which of the following? Select all that apply. Real, rational, irrational, whole, integer ,natural
Its a multiple choice question
The number can be classified as both real and irrational
The given number:
= 1.258201
A real number is any number that can represent a distance along a line
A rational number is a real number that can be expressed in form a ratio, it usually have terminating decimals.
An irrational number is any real number that cannot be expressed in form of ratio, it doesn't have terminating or repeating decimals.
A whole number does not contain fractions, it is usually positive integers.
Integers are whole numbers that includes negative and positive numbers.
The given number is a real number but it doesn't contain terminating or repeating decimals. Hence it is irrational number.
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Calvin cleans 3/5 of his bathroom with 1/3 of a bottle of cleaning solution how much solution would he use if he cleaned the whole bathroom
which of these ordered pairs is a solution to the inequality 4x+y>-6
The ordered pair is (1, -1) a solution to the inequality 4x+y>-6. which is the correct answer would be option (C).
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
We must determine if the inequality holds for a certain set of ordered pairs in order to determine which ordered pairs constitute the answer to the inequality.
We have been given inequality is:
⇒ 4x + y > -6
Option (A) (1, -12)
⇒ 4x + y > -6
Substitute x = 1 and y = -12 in the inequality, we get
⇒ 4(1) + (-12) > -6
⇒ -8 > -6
This is false.
Option (B) (0, -9)
⇒ 4x + y > -6
Substitute x = 0 and y = -9 in the inequality, we get
⇒ 4(0) + (-9) > -6
⇒ -9 > -6
This is false.
Option (C) (1, -1)
⇒ 4x + y > -6
Substitute x = 1 and y = -12 in the inequality, we get
⇒ 4(1) + (-1) > -6
⇒ 3 > -6
This is true.
Hence, the correct answer would be an option (C).
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Let f(x)=8^x.
Which function represents a transformation of f(x) by a vertical stretch with factor 2??
A- g(x)=1/2*8^x
B- g(x)=8^2x
C- g(x)=2*8^x
D- g(x)=8 1/2^x
Please help and give reasoning with your answer. I’m very unsure.
The function that represents a vertical stretch of factor 2 of f(x) = 8^x is g(x) = 2 * 8^x.
Explanation:The function that represents a vertical stretch of factor 2 of the function f(x) = 8^x is g(x) = 2 * 8^x.
To understand why, consider that a vertical stretch by a factor of 2 means that every y-coordinate in the graph is multiplied by 2. So, if we want to stretch the function f(x) = 8^x vertically by a factor of 2, we multiply the function by 2 to get g(x) = 2 * 8^x.
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The function f(x) = x2 – 4x + 4 is shifted 3 units to the right to create g(x).
A. g(x) = (x – 3)2 – 4(x – 3) + 4
B. g(x) = (x2 – 4x + 4) – 3
C. g(x) = (x2 – 4x + 4) + 3
D. g(x) = (x + 3)2 – 4(x + 3) + 4
Answer:
answer is A for APEX..
Step-by-step explanation:
The function f(x) = [tex]x^{2} -4x+4[/tex] is shifted 3 units to the right to create
g(x) = [tex](x-3)^{2}-4(x-3)+4[/tex] .
What is shifting of a function?A shift is a rigid translation in that it does not change the shape or size of the graph of the function. All that a shift will do is change the location of the graph. A vertical shift adds/subtracts a constant to/from every y-coordinate while leaving the x-coordinate unchanged.
Given
f(x) = [tex]x^{2} -4x+4[/tex]
The function f(x) = x2 – 4x + 4 is shifted 3 units to the right to create g(x).
If the function is shifted to the left it is going to plus(+).
If the function is shifted to the right it is going to minus(-).
So, x = x - 3
g(x) = [tex](x-3)^{2}-4(x-3)+4[/tex]
The function f(x) = [tex]x^{2} -4x+4[/tex] is shifted 3 units to the right to create
g(x) = [tex](x-3)^{2}-4(x-3)+4[/tex] .
Option A is correct.
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The following triangle FOX is transformed using a rotation: Triangle FOX is shown. F is at negative 1, 1, O is at negative 2, 3, X is at negative 3, 0. Which could be coordinates of F'O'X' after the rotation? (4 points)
The answer is F=(1,1), O=(3,2), X=(0,3)
Rational Exponent
Explain why the square root of a number is defined to be equal to that number to the 1/2 power.
Answer:
Sample Response:
Squaring and square root are inverses, so one should "undo" the other. That is, squaring the square root of a number results in the number. Using the power of a power rule, you multiply the exponents. Since a number to the first power is itself, the product of the exponents must equal 1. This means that the power of the square root must be the reciprocal of 2, or one half.
Step-by-step explanation:
For the following geometric sequence, find the recursive formula.
{-80, 20, -5, ...}
Answer:
[tex]a_n =-\frac{1}{4} \cdot a_{n-1}[/tex]
Step-by-step explanation:
{-80, 20, -5, ...}
General recusive formula for geometric sequence is
[tex]a_n = r \cdot a_{n-1}[/tex]
Where 'r' is the common ratio
To find common ratio 'r' we divide second term by first term
[tex]r=\frac{20}{-80} =-\frac{1}{4}[/tex]
Replace 'r' with -1/4
First term is -80
Recursive formula becomes
[tex]a_n =-\frac{1}{4} \cdot a_{n-1}[/tex]
What is the function
When applying for a loan, you should _____.
Julie yard is rectangular.One side of the yard is 100 feet wide. The total area of the yard is 3,000 square feet. What is the length of the other side of the yard?
Please help!!!
System of Equations Applications
Bill and Cody are selling cookie dough for a school fundraiser. Customers can buy packages of white chocolate chip cookie dough and packages of double chocolate chip cookie dough. Bill sold 9 packages of white chocolate chip cookie dough and 2 packages of double chocolate cookie dough for a total of $200. Cody sold 2 packages of white chocolate chip cookie dough and 13 packages of double chocolate chip cookie dough for a total of $283. find the cost each of one package of white chocolate chip cookie dough and one package of double chocolate chip cookie dough.