Match the reasons with the statements in the proof.
Given: a | | b, m 2 = m 3
Prove: m 1 = m 3
1. a||b, m∠2 = m∠3
Given
2. m∠1 = m∠2
Substitution
3. m∠1 = m∠3
If lines are ||, corresponding angles are equal.
Answers
Prove: m 1 = m 3
1. a || b, m∠2 = m∠3
Given
2. m∠1 = m∠2
If lines are ||, corresponding angles are equal.
3. m∠1 = m∠3
Substitution
The correct matching of the statement and reasons in the proof given goes thus:
a | | b - - - - - - - - - - GIVEN m∠1 = m∠2 - - - - corresponding angles are equalm∠1 = m∠2 - - - - - SubstitutionThe first reason stated when starting a proof is 'GIVEN' as it has been stated in the question a | | b and m 1 = m 3
From the diagram, the traversal cuts the two parallel lines, creating a corresponding angle at m∠1 and m∠2
Since, we've been told that m1 = m3 in the initial statement, we assign the value of the angle m∠1 to m∠3 (substitution)
Hence, the proof.
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Related Questions
Which function is a shrink of the exponential growth function shown on the graph?
A.) f(x) = 2(3)x
B.) f(x) = 1/2(3)x
C.) f(x) = 2(1/3)x
D.) f(x) = 1/2(1/3)x
Answers
Selection B is appropriate.
Explain why 81 3/4 equals 27
Answers
General Idea:
There are few exponent rules that need to be used to simplify the rational exponent to get to the answer.
Exponent rules:
[tex] Rule\; 1: a \cdot a \cdot a \cdot a =a^4\\ \\ Rule\; 2: (a^m)^n=a^{m \times n} [/tex]
Applying the concept:
Rewriting 81 as a number with an exponent using prime factorization.
[tex] 81=3 \times 3 \times 3 \times 3 = 3^4\\ \\ Applying \; Rule \; 1, \; we\; get\; \\\\81^{\frac{3}{4}}=(3^4)^{\frac{3}{4}} \\ \\ Applying \; Rule \; 2,\; we\; get\\ \\ 3^{4 \times\frac{3}{4} } = 3^{\frac{12}{4} }=3^3=3 \times 3 \times 3 = 27 [/tex]
Conclusion:
The above explanation explains why [tex] 81^{\frac{3}{4}} =27 [/tex]
PLEASE HELP ASAP!!!
Answers
telling a child that he won't amount to anything in life is a form of
(A)neglect
(B)emotional abuse
(C)physical abuse
(D)sexual abuse
Answers
Emotional abuse, also called psychological violence, is a form of abuse where the person or sufferer is exposed to act which can result in psychological trauma and can include depression, anxiety, etc. So, this act of telling a child that he would not amount to anything is considered as emotional abuse.
Someone please help, with a cherry on top?
View attached graph and find the approx. slope
THANK YOU SOOO MUCH!!!
Answers
WORTH 20 POINTS!!
The endpoints of one diagonal of a rhombus are (0, -8) and (8, -4). If the coordinates of the 3rd vertex are (1, 0), what are the coordinates of the 4th vertex? (7, -12)
(7, -8)
(-8, -4)
(-4, -12)
Answers
The rhombus consists of two lines which connecting the endpoints which are intersecting each other. If you have the slopes of these, you can create a relation which says that
[tex]k_1 \cdot k_2 = -1[/tex]
where [tex]k_i[/tex] are the slopes of the lines.
Now you have one slope, which is [tex]k_1 = \frac{-8 - (-4)}{0-8} = \frac{1}{2}[/tex] which means that the slope of the other one has to be
[tex]k_2 = -1 \cdot 2 = -2[/tex]
Given that you have the point (1,0) its trivial to see that this is satisfied by the point (7,-12)[tex]k_2 = \frac{-12-0}{7-1}=\frac{-12}{6} = -2[/tex]
Its worth noting that you want to draw the points, that you have the correct order when you calculate the slope.
WILL GIVE A BRAINLEST!!!!!!
Solve and check : c-4/c-2=c-2/c+2 - 1/2-c
The solution is c =
How many extraneous solutions are there?
Answers
[tex]c=14[/tex]
There is no extraneous solution because as we put the value of c in equation (1), it does not make the equation (1) not define.
Step-by-step explanation:
Given :
[tex]\dfrac {c-4}{c-2} = \dfrac {c-2}{c+2} - \dfrac{1}{2-c}[/tex] --------- (1)
Calculation :
[tex]\dfrac {c-4}{c-2} = \dfrac {(c-2)^2+(c+2)}{(c+2)(c-2)}[/tex]
[tex]c-4 = \dfrac {(c^2-4c+4)+(c+2)}{(c+2)}[/tex]
[tex](c-4)(c+2) = (c^2-3c+6)[/tex]
[tex](c^2-2c-8) = (c^2-3c+6)[/tex]
[tex]c=14[/tex]
There is no extraneous solution because as we put the value of c in equation (1), it does not make the equation (1) not define.
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Answer:
14 and Zero
Step-by-step explanation:
Five is a solution of (Y < -3)
A.True
B.False
Answers
The integer '5' has a higher value than -3 as it leans on the right side of a number scale, while -3 sits on the left side.
I hope this helps!
Which expression can you simplify by combining like terms? Clear Check 6 d 2 +5cd−3dc+8 6d2+5cd-3dc+8 12 c 2 −8 d 2 c+3dc+4 12c2-8d2c+3dc+4 7 d 2 −3 c 2 +6d−c 7d2-3c2+6d-c 16 c 2 +8cd+7c−8d 16c2+8cd+7c-8d
Answers
The expression that can be simplified by combining like terms is 16 c^2 + 8cd + 7c - 8d, where 8cd and -3dc are like terms and can be combined to simplify the expression to 16c^2 + 5cd + 7c - 8d.
Explanation:The expression 16 c2 + 8cd + 7c - 8d can be simplified by combining like terms. Like terms in an algebraic expression are terms that have the same variable raised to the same power. Here, the terms 8cd and -3dc are like terms and can be combined.
Here's the step-by-step simplification:
First, identify like terms in the expression. In 8cd and -3dc, since multiplication is commutative (meaning ab = ba), cd and dc are essentially the same term. So, 8cd and -3dc can be combined.Combine the like terms by adding their coefficients. For 8cd and -3dc, we have 8 - 3 to get 5cd.Now, the simplified expression is 16c2 + 5cd + 7c - 8d.This process of combining like terms helps in simplifying algebraic expressions, making them easier to work with.
After combining like terms, it's important to always check the answer to see if the simplification is reasonable and if there are any other like terms that can be combined.
So, the simplified expressions are:
1. [tex]\(6d^2 + (5c - 3d)d + 8\)[/tex]
2. [tex]\(12c^2 - (c(8d - 3)) + 4\)[/tex]
3. [tex]\(7d^2 - 3c^2 + 6d - c\)[/tex]
4. [tex]\(16c^2 + c(8d + 7) - 8d\)[/tex]
Let's simplify each expression by combining like terms:
1. [tex]\(6d^2 + 5cd - 3dc + 8\)[/tex]
Combine like terms:
[tex]\(6d^2 + (5cd - 3dc) + 8\)[/tex]
[tex]\(6d^2 + (5c - 3d)d + 8\)[/tex]
2. [tex]\(12c^2 - 8d^2c + 3dc + 4\)[/tex]
Combine like terms:
[tex]\(12c^2 - (8d^2c - 3dc) + 4\)[/tex]
[tex]\(12c^2 - (c(8d - 3)) + 4\)[/tex]
3. [tex]\(7d^2 - 3c^2 + 6d - c\)[/tex]
No like terms to combine.
4. [tex]\(16c^2 + 8cd + 7c - 8d\)[/tex]
Combine like terms:
[tex]\(16c^2 + (8cd + 7c) - 8d\)[/tex]
[tex]\(16c^2 + c(8d + 7) - 8d\)[/tex]
A farmer has a collection of chickens and dogs. all together there are 120 legs and 43 heads. how many of each animal does he have? answer
Answers
(26*2)+(17*4)=120 legs
26 chickens and 17 dogs
Number of chicken = 26
And, Number of dogs = 17
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
A farmer has a collection of chickens and dogs.
And, all together there are 120 legs and 43 heads.
Hence, Number of chicken = x
And, Number of dogs = y
Thus, We get;
⇒ x + y = 43
⇒ x = 43 - y .. (i)
⇒ 2x + 4y = 120
⇒ x + 2y = 60 .. (ii)
Substitute value of x from (i) to (ii);
⇒ x + 2y = 60
⇒ 43 - y + 2y = 60
⇒ y = 60 - 43
⇒ y = 17
And, From (i);
⇒ x = 43 - y
⇒ x = 43 - 17
⇒ x = 26
Thus, Number of chicken = 26
And, Number of dogs = 17
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Consider the diagram. What is the length of segment AB?
Answers
we know that
A median of a triangle is a line segment joining a vertex to the midpoint of the opposing side, bisecting it.
In this problem the line DB is a median of triangle ADC
The line DB is also the altitude of a triangle ADC, because is perpendicular to the side AC
so
AB=BC
we have that
[tex]BC=9\ units[/tex]
therefore
[tex]AB=9\ units[/tex]
the answer is the option
[tex]9[/tex]
The area of a triangle is 1440 cm^2. the base of the triangle is 5 times the height. what is the height of the triangle?
Answers
Triangle Area = .5 * base * height
1,440 = .5 * 5h * h
1,440 = 2.5 h^2
576 = h ^2
height = 24 centimeters
and the base is therefore 120 centimeters
Double Check
base = 120 cm
height 24 cm
area = .5 * 120 * 24
area = 1,440
Rico travelled from the United States to the United Kingdom. Once Rico arrived, he converted his American dollars into British pounds (the currency in the U.K.). He gave the bank teller $500 and was given back 295 pounds. At the end of his vacation Rico had 75 pounds left over which he converted back into US dollars. How much money (in US dollars ) did Rico have when he got home? Round the answer to the hundredth.
Answers
How to calculate linear distance between two points on circle circumference?
Answers
θ/360 × 2πr.
“How many times did you ride the Ferris wheel today?” Is the question a statistical question? Explain why or why not.
Answers
Use k as the constant of proportionality to write the equation expressing the relationship: y varies inversely as x. if y = 10 when x = 5, determine k.
Answers
[tex]y= \dfrac{k}{x} [/tex]
you can solve for k, the constant of variation (or proportionality), by multiply both sides of the function to get [tex]xy=k[/tex]. Substituting 5 for x and 10 for y, you see that k = 50.
y = k/x
Step-by-step explanation:
helppppppppppppppppppppppppppppp
Answers
x = 4
Explanation:
For the right hand side:
log base 9 of 8 + log base 9 of (x-2) = log base 9 (8*(x-2))
= log base 9 of (8x-16)
For the left hand side:
2*log base 9 of x = log base 9 of x^2
Now, equating the two sides and solving for x:
log base 9 of (8x-16) = log base 9 of x^2
This means that:
x^2 = 8x - 16
x^2 - 8x + 16 = 0
(x-4)^2 = 0
Therefore:
x = 4
Hope this helps :)
An initial investment of $200 is now valued at $350. The annual interest rate is 8% compounded continuously. The equation mc022-1.jpg represents the situation, where t is the number of years the money has been invested. About how long has the money been invested? Use a calculator and round your answer to the nearest whole number.
Answers
Answer:
7 years
Step-by-step explanation:
An initial investment of $200 is now valued at $350.
The annual interest rate is 8% compounded continuously.
Formula:
[tex]A=Pe^{rt}[/tex]
Where,
A is amount, A=350
P is principle, P=200
R is rate of interest, r=0.08
t is time, t=?
Substitute the value into formula
[tex]350=200e^{0.08\cdot t}[/tex]
[tex]e^{0.8t}=1.75[/tex]
Taking ln both sides
[tex]0.08t = ln(1.75)[/tex]
[tex]t=6.99\approx 7[/tex]
Hence, 7 years ago money was invested.
Answer:
Its 7 years
Step-by-step explanation:
The band is selling wrapping paper for a fundraiser. Customers can buy rolls of plain wrapping paper and rolls of shiny wrapping paper. The band sold a total of 55 rolls and made $950. If a roll of plain wrapping paper cost $14 and a roll of shiny cost $20, how many rolls of each did they sell ?
Answers
y= # shiny rolls
QUANTITY EQUATION:
x+y=55
COST EQUATION:
$14x + $20y= $950
SOLVE:
Solve for one variable in quantity equation. Substitute that answer in cost equation.
STEP 1:
x+y=55
subtract y from both sides
x= 55-y
STEP 2:
$14x + $20y= $950
14(55-y) + 20y= 950
multiply 14 by all in parentheses
(14*55)+(14*-y) + 20y= 950
770-14y+20y= 950
combine like terms
770+6y= 950
subtract 770 from both sides
6y= 180
divide both sides by 6
y= 30 shiny rolls
STEP 3:
Substitute y answer in either equation to solve for x.
x+y=55
x+30=55
subtract 30 from both sides
x= 25 plain rolls
Hope this helps! :)
The roll of plain wrapping paper sold is 25.
The roll of shiny wrapping paper sold is 30.
What are the linear equations that represent the question?a + b = 55 equation 1
14a + 20b = 950 equation 2
Where:
a = roll of plain wrapping paper sold
b = roll of shiny wrapping paper sold
What is the roll of shiny wrapping paper sold?Multiply equation 1 by 14
14a + 14b = 770 equation 3
Subtreact equation 3 from equation 2
6b = 180
Divide both sides by 6
b = 30
What is the roll of plain wrapping paper sold?
Subtract 30 from 55
55 - 33 = 25
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Write an equation in point-slope form for the line through the given point with the given slope. (–3, –7); m = -6/5
Answers
Goes through (-3, -7) and the slope = -6/5
Since we are given the slope and the x₁ as well as y₁, we can simply plug everything into the point slope formula.
y - (-7) = -6/5(x - (-3))
Simplify.
y + 7 = -6/5(x + 3)
~Hope I helped!~
Which of the following values is closest to the mean for the set of data shown below?
23, 32, 20, 43, 41, 66, 63, 59, 54, 36, 45, 61, 55, 44, 47
A.45.9 B.50 C.58 D.54.3
Answers
hoped it helped!!!
then divide by how much numbers there are (49.9)
so your answer is b
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If you wanted to predict the value of the y variable when the x variable is 15, you would be _____ the data.
A.) Correlating
B.) Extrapolating
C.) Interpolating
Answers
Answer:
If you wanted to predict the value of the y variable when the x variable is 15, you would be extrapolating the data.
Step-by-step explanation:
If you wanted to predict the value of the y variable when the x variable is 15, you would be Extrapolating the data.
Extrapolation means, estimating the value of a variable beyond its given range.
The perimeter of an equilateral triangle with a side of 6 inches is
12 in.
18 in.
36 in.
Answers
the factors of m^2 + 12m + 35 are?
Answers
Factored:
(m+5)(m+7)
Check:
(m+5)(m+7)
(m*m) + (m*7) + (5*m) + (5*7)
m^2 + 12m + 35
Hope this helps! :)
Using radicals , write an equivalent expression for the expression 2 1/3
Answers
If so, then [tex]2^{1/3} = \sqrt[3]{2}[/tex]
Which is the cube root of 2. Raising any value to the 1/3 power is the same as taking the cube root.
I'm assuming that the 1/3 is an exponent.
If so, then
Which is the cube root of 2. Raising any value to the 1/3 power is the same as taking the cube root.
Lisa made $286 for 13 hours of work. at the same rate, how many hours would she have to work to make $242 ?
Answers
what is the approximate distance between the points (1 -2) and (-9 3) on a coordinate grid?
Answers
Answer:
11.18
Step-by-step explanation:
Is the transformation a rotation about point j?
Answers
Find the volume of this square pyramid, given that its height is 8 m.
A) 24 m3.
B) 72 m3.
C) 216 m3.
D) 648 m3.
Answers
Answer:
A) [tex]24\text{ m}^3[/tex].
Step-by-step explanation:
We have been given an image of a square pyramid and we are asked to find the volume of our given pyramid.
[tex]\text{Volume of square pyramid}=\frac{a^2*h}{3}[/tex], where,
a = Base length of square,
h = height of pyramid.
Upon substituting our given values in above formula we will get,
[tex]\text{Volume of square pyramid}=\frac{\text{(3 m)}^2*\text{ 8 m}}{3}[/tex]
[tex]\text{Volume of square pyramid}=\frac{9\text{ m}^2*\text{ 8 m}}{3}[/tex]
[tex]\text{Volume of square pyramid}=\frac{72\text{ m}^3}{3}[/tex]
[tex]\text{Volume of square pyramid}=24\text{ m}^3[/tex]
Therefore, the volume of our given square pyramid is 24 cubic meters and option A is the correct choice.
Answer:
A. 24 m3.
Step-by-step explanation:
Determine the volume of the pencil
Answers
[Volume of the pencil]=[Volume of cylinder]+[volume of cone]
[Volume of cylinder]=pi*(0.5²)*15=11.78 cm³
[volume of cone]=pi*(0.5²)*2/3=0.52 cm³
[Volume of the pencil]=[11.78]+[0.52]=12.30 cm³
the answer is 12.30 cm³
The volume of the pencil is approximately 4.05 cm³.
To determine the volume of the pencil, we need to calculate the volumes of the cylindrical body and the conical tip separately and then add them together.
Volume of the cylindrical body:
The formula for the volume of a cylinder is [tex]V = \pi r^2h[/tex], where r is the radius and h is the height.
[tex]V_{cylinder} = \pi (0.5 cm)^2 * 15 cm[/tex]
Volume of the conical tip:
The formula for the volume of a cone is [tex]V = (1/3)\pi r^2h[/tex], where r is the radius and h is the height.
[tex]V_{cone} = (1/3) * \pi (0.5 cm)^2 * 2 cm[/tex]
Now, we can calculate the volumes:
[tex]V_{cylinder} = \pi * (0.5 cm)^2 * 15 cm = 3.53 cm^3\\\\V_{cone} = (1/3) * \pi * (0.5 cm)^2 * 2 cm = 0.52 cm^3[/tex]
Finally, we can add the volumes of the cylindrical body and the conical tip to get the total volume of the pencil:
[tex]Total\ volume = V_{cylinder} + V_{cone} = 3.53 cm^3 + 0.52 cm^3 = 4.05 cm^3[/tex]
Therefore, the volume of the pencil is approximately 4.05 cubic centimeters ([tex]cm^3[/tex]).
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