Given: Lines a and b are parallel and line c is a transversal. Prove: Angle2 is supplementary to Angle8 Horizontal and parallel lines a and b are cut by transversal c. On line a where it intersects line c, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 1, 2, 4, 3. On line b where it intersects line c, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 5, 6, 8, 7. What is the missing reason in the proof? Statement Reason 1. a || b, is a transv 1. given 2. ∠6 ≅ ∠2 2. ? 3. m∠6 = m∠2 3. def. of congruent 4. ∠6 is supp. to ∠8 4. def. of linear pair 5. ∠2 is supp. to ∠8 5. congruent supplements theorem corresponding angles theorem alternate interior angles theorem vertical angles theorem alternate exterior angles theorem
Answers
Answer:
The correct option is;
Corresponding angles theorem
Step-by-step explanation:
Type of lines of lines a and b = Horizontal and parallel lines
The transversal to a and b = Line c
The angles between a and c labelled clockwise from the upper left quarter segment = 1, 2, 4 and 3
The angles between b and c labelled clockwise from the upper left segment = 5, 6, 8 and 7
Therefore, we have;
Statement \({}\) Reason
1. a║b, c is a transversal \({}\) Given
2. ∠6 ≅ ∠2 \({}\) Corresponding angles theorem
3. m∠6 = m∠2 \({}\) Definition of congruent
4. ∠6 is supp. to ∠8 \({}\) Definition of linear pair
5. ∠2 is supp. to ∠8 \({}\) Congruent supplement theorem
Corresponding angles are the angles located in spatially similar or matching corners of two lines that have been crossed by the same transversal. When the two lines having a common transversal are parallel, the corresponding angles will be congruent.
Related Questions
A simple random sample of 31 observations was taken from a large population. the sample mean equals 5. five is a _____.
a. population mean
b. standard error
c. population parameter
d. point estimate
Answers
Based on the fact that in the simple random variable, 5 is the sample mean, then it is a d. point estimate.
What is a point estimate?A point estimate refers to a specific value in a random group of variables that tell us more about the variables.
The mean is therefore a point estimate as it tells us the average value amounts the random sample of 31 observations.
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A toy manufacturer needs a piece of plastic in the shape of a right triangle with one leg 4 cm longer than the other and the hypotenuse 8 cm longer than the shorterleg. What is the perimeter of the triangle?The perimeter is ___(Simplify your answer.)
Answers
It is given that the longer leg is 4 cm longer than the shorter leg.
It is also given that the hypotenuse is 8 cm longer than the shorter leg.
ExplanationLet the shorter leg be x.
The longer leg be y.
Then the relation formed is
\(y=x+4\)It is also given that the hypotenuse is 8 cm longer than the shorter leg.
Let the hypotenuse is z.
\(z=8+x\)Then the perimeter of the right triangle is the sum of all the sides.
\(x+y+z\)But to find the value of x , use the Pythagoras theorem.
\(z^2=y^2+x^2\)Substitute the values.
\(\begin{gathered} (8+x)^2=(4+x)^2+x^2 \\ 64+x^2+16x=16+x^2+8x+x^2 \\ 64+16x=16+8x+x^2 \\ 64-16+16x-8x-x^2=0 \\ -x^2+8x+48=0 \end{gathered}\)Solve the quadratic equation to find the value of x.
\(\begin{gathered} (x-12)(x+4)=0 \\ x=12,-4 \end{gathered}\)As x cannot be negative , then the value of x is 12.
The length of shorter leg is 12.
The length of longer leg is 12+4=16.
The hypotenuse is 12+8=20.
Now , the perimeter of right triangle is
\(\begin{gathered} P=12+16+20 \\ P=48cm \end{gathered}\)AnswerThe perimeter of the triangle is 48 cm.
What is the equation of the line that passes through the point (4, 3) and has a slope
of 1?
Answers
Answer:
y=x-1
Step-by-step explanation:
Answer:
y=x1
Step-by-step explanation:
1 If one leg of a right triangle is 3 meters, and the hypotenuse is 5 meters, what is the length of the
missing leg?
Answers
i'm gonna assume that "leg" refers to length of the triangle, so comment if you think it is wrong.
Now when it comes to a right-angled triangle, the pythagoras theorem formula can be used.
Using algebra,
let the missing length be X.
By pythagoras theorem,
5² = 3² + X²
5² - 3² = X²
X² = 5² - 3²
X = sq root ( 5² - 3² )
= 4 m
Therefore, the length of the missing leg is 4m .
the ratio of red marbles to yellow marbles placed in a bag is 2:7. More marbles are added to the bag: 3 red and 3 yellow marbles. Maria states that the ratio is still the same since equal amounts of red and yellow marbles were added to the bag
Answers
Answer: False.
Step-by-step explanation:
Initially, the ratio is 2:7
This means that if we have 2 red marbles, we must have 7 yellow ones.
The quotient here is 7/2 = 3.5
Now, if you add 3 marbles of each colour, then we have:
2 + 3 = 5 red marbles
7 + 3 = 10 yellow marbles.
Now the ratio is 5:10
This means that for every 5 red marbles, we have 10 yellow ones.
But now we can divide both numbers by the same positive integer, because they have a common factor equal to 5.
5/5 = 1
10/5 = 2
Then we have:
5:10 = 1:2
So the new ratio is 1:2
Then the ratio changed when we added the new marbles, which means that Maria was wrong.
what is outlier math definition
Answers
Answer:
In statistics, an outlier is a data point that differs significantly from other observations.
Step-by-step explanation:
a pole that is 3.1m tall casts a shadow that is 1.48m long. at the same time, a nearby tower casts a shadow that is 49.5m long. how tall is the tower? round your answer to the nearest meter.
Answers
Rounding to the nearest meter, the height of the tower is approximately 104 meters.
We can use the concept of similar triangles to find the height of the tower.
Let's denote the height of the tower as "x".
According to the given information, the height of the pole (3.1m) is proportional to the length of its shadow (1.48m). Similarly, the height of the tower (x) is proportional to the length of its shadow (49.5m).
We can set up the following proportion:
3.1m / 1.48m = x / 49.5m
To solve for x, we can cross-multiply and then divide:
3.1m * 49.5m = 1.48m * x
153.45m^2 = 1.48m * x
Dividing both sides by 1.48m:
x = 153.45m^2 / 1.48m
x ≈ 103.59m
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after the equal employment opportunity commission (eeoc) completes its investigation in an employment discrimination case, _____.'.
Answers
After the EEOC completes its investigation in an employment discrimination case, the outcomes can include resolution attempts, lawsuits, or issuing a Notice of Right to Sue to the complainant.
After the Equal Employment Opportunity Commission (EEOC) completes its investigation in an employment discrimination case, several outcomes are possible:
The EEOC may find reasonable cause to believe that discrimination has occurred. In this case, they may attempt to resolve the matter through informal methods such as mediation or settlement negotiations. If these efforts fail, the EEOC may file a lawsuit against the employer on behalf of the aggrieved individual(s).
If the EEOC does not find reasonable cause, they will issue a Notice of Right to Sue to the individual who filed the complaint. This allows the individual to pursue a lawsuit against the employer independently.
In some cases, the EEOC may determine that further investigation is needed, and they may request additional information or evidence from both the complainant and the employer.
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plz help with this question
Answers
Answer:
q⁸/16p¹²Step-by-step explanation:
Use of formulas:
(a/b)⁻ⁿ = (b/a)ⁿ(aᵇ)ⁿ = aᵇⁿSimplifying
(2p³/q²)⁻⁴ =(q²/2p³)⁴ =(q²)⁴/(2p³)⁴ =q⁸/2⁴p¹² =q⁸/16p¹²Answer:
\( { (\frac{2 {p}^{3} }{ {q}^{2} }) }^{( - 4)} = \frac{{2}^{(-4)} {p}^{(3 \times ( - 4))} }{ {q}^{(2 \times ( - 4))} } = \frac{ {p}^{ (- 12)} }{16 {q}^{( - 8)} }=\boxed{\frac{ {q}^{8} }{ 16{p}^{12} }} \\ \)
q⁸/16p¹² is the right answer.f (x) = x2 + 4
What is the value of x when f (x) = 42
A. -2
В. 0
C 12
D. 20
Answers
Answer:
f(x)=X^2+4
f(x)=42
42=X^2+4
X^2+4=42
X^2=42-4
X^2=38
X=sqrt(38)=6.16
\( \sqrt{?} \)
how many numbers are there between 256 and 789 that are divisible by 7
Answers
Answer:
76
Step-by-step explanation:
How many numbers are between 256 and 789 are divisible by 7 ?
Generalizing, we could look for a procedure that, given two integers A and B, with B>A , and a module M, tells us how many integers x, with A<=x<=B , are divisible by M.
a) let n1 be the lowest integer >=A such that n1 is divisible by M.
If n1>B , than not even n1 has the required properties and the output of the procedure is 0; otherwise, go to the next step.
n1 will be the first number of the sequence of numbers divisible by M.
b) let n2 be the highest integer <=B such that n2 is divisible by M.
Notice that it’s not possibile that n2<A , as you alway have the possibility n2=n1 .
n2 w
A simple way to think about this is by calculating the largest multiple of 7 less than 256 (let’s call it y) and the smallest multiple of 7 greater than 789 (let’s call it x). The answer is then all the multiples of 7 in between these two numbers, which can be represented by:
x−y7−1
Let’s do it:
252 is the largest number less than 256 divisible by 7. y = 252
791 is the smallest number greater than 789 that’s divisible by 7.
Thus, our answer is 113-36–1 = 76.
Note: we subtract 1 or else we would include the number on the top end of the range (in this case, 791).
Hope it helped you!!
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Mary borrows $5,000 dollars from her mother at a 3% simple interest rate and pays her $600 in interest after t years. What is the value of t?
Answers
I = P * r * t
where I is the interest, P is the principal amount borrowed, r is the interest rate, and t is the time period in years.
In this case, Mary borrowed $5,000 at a 3% simple interest rate, so we can substitute these values into the formula:
$600 = $5,000 * 0.03 * t
Dividing both sides by $5,000 * 0.03, we get:
t = $600 / ($5,000 * 0.03)
t = 4 years
Therefore, the value of t is 4 years.
Please show the answer along with how you got that answer!
Answers
Answer:
\( 4 \times \frac{4 - 3y}{4} = 4 \times (- 17)\)
4-3y=-68
-3y=-72
-3y/(-3)=-72/(-3)
y=24
Answer:
\(4 - 3y = 4 \times - 17 \\ \\ 4 - 3y = - 68 \\ 3y = 68 + 4 \\ y = \frac{72}{3} \\ y = 24\)
26. Which function is increasing and decreasing over the same intervals as the function in the graph?
Answers
Answer:
B.y=(x+2)
Step-by-step explanation
What is the volume of the cube shown???
Answers
Answer:
Hello! answer: 11 25/64
Step-by-step explanation:
Volume is just length × width × height since its a cube all of those will be the same so...
2 1/4 × 2 1/4 × 2 1/4 = 11 25/64 Hope that helps!
Answer:
11 25/64
Step-by-step explanation:
To find the volume of a cube, you have to cube the side length.
2 1/4^3=2 1/4•2 1/4•2 1/4=9/4•9/4•9/4=729/64=11 25/64.
Each day, 1035 new apps are uploaded to a web server. After 28 days, how many apps would have been uploaded?
Answers
Answer:
count 1035 28 times i guess.
Step-by-step explanation:
What is the equation for the line on the graph
Answers
Answer:
x = -1
Step-by-step explanation:
11) What is the value of x? *
X
Your answer
X
5 points
Answers
Answer:
Step-by-step explanation:
The value of X is 45 because all the angles of a triangle add up to 180 degrees. The triangle is a right triangle as shown in the picture, the square in the corner of the triangle indicates this, any right angle is 90 degrees and when you minus 90 from 180 you get 90. Now, there are two more angles in the triangle so the value of X is 45, (90/2=45).
How to write a vertex equation, y=a(x-h)+k ,when given directrix and focus NOT USING (x-h)^2=4p • (y-k). Thank you
Answers
The equation of the parabola in vertex form is y = 2x² + 4.
How do you identify a parabola?
When the coordinates of a given figure satisfies the equation of a parabola then we say that the given figure is a parabola.
To write the vertex equation of a parabola given its directrix and focus, you can follow these steps:
Determine the axis of symmetry: The axis of symmetry is a line perpendicular to the directrix and passing through the focus.
Find the vertex: The vertex is the point where the axis of symmetry intersects the directrix.
Determine the distance between the vertex and the focus: This distance is equal to the distance between the vertex and the directrix.
Determine the value of a: The value of a is the distance from the vertex to the focus.
Write the equation: Once you have determined the values of a, h, and k, you can write the equation of the parabola in vertex form as y = a(x - h) + k.
Here is an example:
Suppose the directrix is the line y = 4 and the focus is the point (0, 2).
The axis of symmetry is the vertical line x = 0.
The vertex is the point where the axis of symmetry intersects the directrix, which is (0, 4).
The distance between the vertex and the focus is 2 units.
The value of a is also 2.
Hence, The equation of the parabola in vertex form is y = 2x² + 4.
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i have four identical oranges. how many ways are there for me to divide these oranges into at most three groups? (by definition, a group must have at least one orange.)
Answers
Answer:
put 1 orange in each group and then cut the last in thirds and each group will have 1 and 1/3 oranges
Step-by-step explanation:
a life table provides data on the number of living individuals in a particular age class. age classes are often represented by a time period of
Answers
A life table provides data on the number of living individuals in a particular age class. Age classes are often represented by a time period of 12 month(s).
A life table delivers data on the number of living individuals in a particular age class. Age classes are often represented by a time period of 1 year.
This means that the data in the life table will reflect the number of individuals who are alive in a specific age group, such as 0-1 year, 1-2 years, 2-3 years, and so on. The data in a life table is used to study mortality patterns, life expectancy, and other demographic measures.
By grouping the data into age classes of 1 year, the life table provides a snapshot of the population at different stages of life, making it easier to analyze trends and patterns in the data.
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--The given question is incomplete; the complete question is
"A life table provides data on the number of living individuals in a particular age class. Age classes are often represented by a time period of ______ month(s)."--
Astrid says the function being graphed is y=-4x + 1/3
. She says that her equation is correct because the slope of the line is -4.
Matt says the function that is being graphed is y= 1/3x
. He says that the slope of the line is actually 1/3
.
Is Astrid correct? Is Matt correct? Explain your reasoning
Answers
Using the slope-intercept form we know that Astrid is correct as the slope of the line is -4.
What is the slope-intercept form?You can use the slope-intercept formula, y = mx + b, when you know the slope of the line to be studied and the provided point is also the y-intercept (0, b).
The formula's symbol b stands for the y value of the y-intercept point.
y=mx+b is a formula that expresses a line's slope and y-intercept.
The point where the line crosses the y-axis is known as the y-intercept and is typically represented in coordinate form as (0,b).
So, according to the given description of the slope-intercept form, we know that:
m = -4 and b = 1/3
Hence, we know that Astrid is correct.
Therefore, using the slope-intercept form we know that Astrid is correct as the slope of the line is -4.
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Reasoning There are 65 vehicles in a parking lot. The frequency table shows data about the types and colors of the vehicles. Complete a relative frequency
table to show the distribution of the data with respect to color. Use pencil and paper. Explain why the first two numbers in each row must add up to 100%
Answers
The first two numbers in each row of the relative frequency table represent the percentage of cars and trucks of a particular color out of the total number of vehicles in the parking lot.
To create a relative frequency table, we need to divide the frequency of each color by the total number of vehicles (65) and then multiply by 100 to get a percentage.
Relative Frequency Table by Color:
The first two numbers in each row must add up to 100% because we are calculating the relative frequency of each color with respect to the total number of vehicles (65). Therefore, the percentage of cars and trucks of each color must add up to 100% of that color's total frequency. The total row must also add up to 100% because it represents the entire population of vehicles.
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The given question is incomplete, the complete question is:
There are 65 vehicles in a parking lot. The frequency table shows data about the types and colors of the vehicles. Complete a relative frequency table to show the distribution of the data with respect to color. Use pencil and paper. Explain why the first two numbers in each row must add up to 100%. Frequency Table Type of Vehicle Color Car Truck Total Blue 22 14 36 Red 12 17 29 Total 34 31 65
The volume of a cube is 270cm cubed. Work out the length of its side rounded to 1 DP
Answers
Answer:
a ≈ 6.5 cm
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityGeometry
Volume of a Cube Formula: V = a³
a is a side lengthStep-by-step explanation:
Step 1: Define
Identify
V = 270 cm³
Step 2: Solve for a
Substitute in variables [Volume of a Cube Formula]: 270 cm³ = a³[Equality Property] Cube root both sides: 6.4633 cm = aRewrite: a = 6.4633 cmRound: a ≈ 6.5 cmAnswer:
The length of it's side is 6.5 cm.
Step-by-step explanation:
Here's er have given that the Volume of cube is 270 cm³. And we have to find the length of its side rounded to 1DP.
To find the length of its side we apply the formula ; Volume of cube and then simplify .
Volume of cube = ( a )³
Where , a is the length of side and Volume of cube have given in the question which is 270cm³ .plug the values
270 cm ³ = a³
Taking cube root of both side
\( \small \sf \sqrt[3]{270 \: cm {}^{3} } = \sqrt[3]{a {}^{3} } \)
6.4633 cm = a
Rewrite
a = 6.4633 cm
Round nearest to 1DP
a ≈ 6.5 cm
Hence , Length of it's side is 6.5 cm.
f(x) = x2. What is g(x)?
pls help it’s due soon!!
Answers
Answer:
A. g(x) = (2x)²
Step-by-step explanation:
From the diagram of the two functions graph f(x) is the parent function and g(x) is the transformed function. you can see that the graph of g(x) is stretched vertically compared to the graph of g(x). The Parent function has y =1 corresponding to x =1 while for the transformed function when x = 1, y = 4 the graph is vertically stretched by a factor of 4, and horizontally The Parent function has y =1 corresponding to x =1. while for the transformed function when x = 0.5, y = 1, it is stretched horizontally by 2 (√4), i.e
This means that g(x) = 4x² = (2x)²
8q=3(10+q) what is the value of Q
Answers
Answer:
Step-by-step explanation:
8q=30+3q
5q=30
q=6
write a story to go with 3/4 times 1/2.
Answers
Answer:
2/3 = 0.666666667
hopefully i helped :)
Answer:
I hope this is what you were looking for.
Step-by-step explanation:
There was a party 30 people were supposed to show up, but only 1/2 of those people did. There was a pie with 4 pieces, until someone ate a quarter of the pie they were left with 3/4. Only 3 more people will get a piece of pie.
The gold trophy has 27 racers, she will 12 racers on the racetrack that runs.
How many racers did she have runs?
Answers
She will have run a total of 2.25 racers in 27 racers
How to determine the number of racers?From the question, we have the following parameters that can be used in our solution:
Total number of racers = 27 racers
Number of racers in a run = 12 racers
From the above parameter, we can calculate the total number of racers using the following equation
The total number of racers is calculated as
Total number of racers in the run = Total number of racers/Number of racers in a run
Substitute the known values in the above equation
So, we have the following equation
Total number of racers in the run = 27/12
Evaluate the quotient
Total number of racers in the run = 2.25
Hence, the total number of racers in the run is 2.25 racers
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Which expression is equivalent to (10 7r − r2) (−6r2 − 18 5r)?
Answers
Answer
6r^4-330r^3-6300r^2
Step-by-step explanation:
suppose that f ( x , y ) = x y . the directional derivative of f ( x , y ) in the directional ⟨ − 5 , − 2 ⟩ and at the point ( x , y ) = ( − 4 , 3 ) is
Answers
The directional derivative can also be interpreted as the slope of the tangent line to the function f(x, y) in the specified direction at the given point. In this case, the slope of the tangent line is -7, which means that as we move along the direction ⟨-5, -2⟩ from the point (-4, 3), the function decreases by 7 units for every unit of movement in that direction.
D_⟨u,v⟩(f(x, y)) = ∇f(x, y) ⋅ ⟨u, v⟩
where ∇f(x, y) is the gradient of f(x, y) and ⟨u, v⟩ is the direction vector.
First, we calculate the gradient of f(x, y):
∇f(x, y) = (∂f/∂x, ∂f/∂y)
= (y, x)
Substituting the values from the given point (-4, 3), we have:
∇f(-4, 3) = (3, -4)
Next, we substitute the direction vector ⟨-5, -2⟩ into the formula:
D_⟨-5,-2⟩(f(x, y)) = (3, -4) ⋅ ⟨-5, -2⟩
Using the dot product, we get:
D_⟨-5,-2⟩(f(x, y)) = (3)(-5) + (-4)(-2)
= -15 + 8
= -7
Therefore, the directional derivative of f(x, y) in the direction ⟨-5, -2⟩ at the point (x, y) = (-4, 3) is -7.
The directional derivative measures the rate of change of the function in a specific direction. In this case, we are interested in the rate of change of the function f(x, y) = xy in the direction ⟨-5, -2⟩ at the point (-4, 3). The negative sign of the directional derivative (-7) indicates that the function is decreasing in that direction at the given point.
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