Given: <2 and <4 are vertical angles.
Prove: <2 ~= <4
Statements Reasons
Assemble the proof by dragging tiles to
the Statements and Reasons columns
Answers
Statement 1: [tex]\angle 2[/tex] and [tex]\angle 4[/tex] are vertical angles
Reason 1: Given
We basically just restate the given information word for word. This is true of any two column proof.
-------------------------------------
Statement 2: [tex]m \angle 2 + m \angle 3 = 180[/tex]
Reason 2: [tex]\angle 2[/tex] and [tex]\angle 3[/tex] are a linear pair
The term "linear pair" means the angles are adjacent and supplementary (they form a straight line), so this is why the two angles add to 180.
--------------------------------------
Statement 3: [tex]m \angle 3 + m \angle 4 = 180[/tex]
Reason 3: [tex]\angle 3[/tex] and [tex]\angle 4[/tex] are a linear pair
--------------------------------------
Statement 4: [tex]m \angle 2 + m \angle 3 = m \angle 3 + m \angle 4[/tex]
Reason 4: Substitution
Each of the equations formed in statements 2 and 3 above have 180 on the right side, so the left hand sides must be the same
--------------------------------------
Statement 5: [tex]m \angle 2 = m \angle 4[/tex]
Reason 5: Subtraction property of equality
We subtracted the quantity [tex]m \angle 3[/tex] from both sides (they go away)
--------------------------------------
Statement 6: [tex]\angle 2 \cong \angle 4[/tex]
Reason 6: Definition of congruence
If two items are congruent, then they have the same measure. In other words, they are the same.
The proof of [tex]\angle 2 \ and \ \angle4[/tex] are vertical angles is explained below.
Given, [tex]\angle 2 \ and \ \angle4[/tex] are vertical angles as shown in fig.
We know that, Vertical angles are formed when two straight lines intersect at a point.Vertical angles are two angles which are vertically opposite and have the same measure. So, the two angles are to be congruent.
We have to prove that angle 2 and angle 4 congruent.
Given [tex]\angle 2 \ and\ \angle 3[/tex] makes linear pair so,
[tex]\angle 2+\angle 3= 180[/tex]
[tex]\angle 3 =180-\angle 2[/tex]..........(1)
Again [tex]\angle 3 \ and \ \angle 4[/tex] makes linear pair so,
[tex]\angle 3+\angle 4= 180[/tex]
[tex]\angle 3 =180-\angle 4[/tex].......(2)
From (1) and (2) we get,
[tex]180-\angle 2=180-\angle 4[/tex]
Subtracting 180 from both the sides we get,
[tex]-\angle 2=-\angle 4[/tex]
Or, [tex]\angle 2=\angle 4[/tex]
Hence angle 2 and angle 4 are congruent.
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Related Questions
Verify the identity. ( 1-sin x)/cosx=cosx/(1+sin x)
Answers
Answer:
See below.
Step-by-step explanation:
I'm going to use what I assume is the correct question.
[tex] \dfrac{1 - \sin x}{\cos x} = \dfrac{\cos x}{1 + \sin x} [/tex]
[tex] \dfrac{\cos x}{\cos x} \times \dfrac{1 - \sin x}{\cos x} = \dfrac{\cos x}{1 + \sin x} [/tex]
[tex] \dfrac{\cos x(1 - \sin x)}{\cos^2 x} = \dfrac{\cos x}{1 + \sin x} [/tex]
Now use the identity
[tex] sin^2 x + cos^2 x = 1 [/tex]
[tex] cos^2 x = 1 - sin^2 x [/tex]
We replace [tex] \cos^2 x [/tex] in the left denominator.
[tex] \dfrac{\cos x(1 - \sin x)}{1 - \sin^2 x} = \dfrac{\cos x}{1 + \sin x} [/tex]
Factor the difference of squares in the left side denominator.
[tex] \dfrac{\cos x(1 - \sin x)}{(1 + \sin x)(1 - \sin x)} = \dfrac{\cos x}{1 + \sin x} [/tex]
[tex] \dfrac{\cos x}{1 + \sin x} = \dfrac{\cos x}{1 + \sin x} [/tex]
Find the area of the region enclosed by the graph of $x^2 + y^2 = 2x - 6y + 6$
Answers
Answer:
16π ≈ 50.27 square units
Step-by-step explanation:
The equation is that of a circle of radius 4. The area of a circle is given by ...
A = πr²
A = π(4²) = 16π ≈ 50.27 . . . . square units
_____
The equation can be put into the standard form for a circle to find its radius.
(x^2 -2x) +(y^2 +6y) = 6 . . . . collect variable terms on the left
(x^2 -2x +1) +(y^2 +6y +9) = 6 + 1 + 9 = 16 . . . . . complete the squares
(x -1)^2 +(y +3)^2 = 4^2 . . . . . the radius is 4
Compare to the form ...
(x -h)^2 +(y -k)^2 = r^2 . . . . circle of radius r centered at (h, k)
Witch relations is a function
Answers
So basically everything but choices B and C are functions.
====================================
Explanation:
A. This is a function as there are no repeated input x values. Each input (x) leads to exactly one output (y).B. This is not a function. We have the input 2 lead to more than one output (1 and 4 at the same time)C. This is not a function. Similar to choice B, we have multiple outputs for a given input. In this case, x = 20 has more than one output.D. This is a function. Any x input will produce only one y output. When graphed, it passes the vertical line test.E. This is a function. This graph passes the vertical line test. It is not possible to draw a vertical line through more than one point on the blue curve, so that's what I mean by "passing the vertical line test".F. This is a function. At any given hour (x), there is exactly one temperature (y) possible. The thermometer is not going to produce multiple readings at any one specific moment in time.Order least to greatest: 1.5, 1.1, .9, 1, 1.7, 1.25
Answers
Answer:
1,1.1,1.25,1.5,1.7,9
Gina gets money from her grandfather every day for the entire week of her birthday, starting on Monday. She gets $2 on Monday, $4 on Tuesday, and the previous day's amount gets multiplied by 2 each day. Which of the following would represent how much money Gina would receive on Thursday?
Answers
Answer:
Gina would receive $16 equivalent to 2^4 on Thursday from her grandfather
Step-by-step explanation:
A. 2^5
B. 2^4
C. 2^3
D. 2^2
Gina gets:
Monday =$2 = $2^1
Tuesday =$4 = $2^2
Previous day's amount get multiplied by 2
Wednesday = Tuesday's amount × 2
= $4 × 2
= $8
= $2^3
Thursday = Wednesday's amount × 2
= $8 × 2
= $16
= $2^4
Gina would receive $16 equivalent to 2^4 on Thursday from her grandfather
Answer:
the answer is 2^4
Step-by-step explanation:
What are the coefficients in the expression, 2 + 6 + 10b – 8a?
Answers
Answer: 10 and 8
Step-by-step explanation: A coefficient is the number that comes before the variable. I hope this helps :)
The coefficients are the numbers to the left of the variable terms
10b is one variable term with the coefficient 10
-8a is the other variable term with the coefficient -8
The terms 2 and 6 are constants as they don't have any variables multiplied with them.
In a small town, only 3 of the 10 stores
stay open after 5pm what percentages of stores close at 5pm?
A)30%
B)50%
C)65%
D)70%
Answers
Answer:
70%
Step-by-step explanation:
100%-30% = 70%
How far does a train travel and 3.5 hours if it moves at an average speed of 35 miles /hours?
Answers
Answer:
d =122.5 miles
Step-by-step explanation:
We know the formula is
d= rt
d is distance r = rate and t is time
d = 35 miles per hour * 3.5 hours
d =122.5 miles
Answer:
122.5 miles traveled
Step-by-step explanation:
35 miles x 3.5 hours = 122.5 total miles traveled
What is the solution to y + 7 = -9 A. y = -16 B. y = -2 C. y = 2 D. y = 16
Answers
Answer:
A. y = -16
Step-by-step explanation:
Hello!
What we do to one side of the equation we have to do to the other.
y + 7 = -9
We have to get y by itself so we have to get rid of the seven by doing the opposite of what it says
The opposite of addition is subtraction so we subtract 7 from both sides
y + 7 - 7 = -9 - 7
Solve
y + 0 = -16
Simplify
y = -16
The answer is A. y = -16
Hope this helps!
A two digit number is chosen at random. Find the probality that the number is a perfect square
Answers
Answer:
[tex]\Large \boxed{\frac{1}{15} }[/tex]
Step-by-step explanation:
The two-digit perfect squares are 16, 25, 36, 49, 64, 81.
There are 6 numbers that are two-digit perfect squares.
There are a total of 90 numbers that have two-digits.
P(two-digit perfect square) = [tex]\frac{6}{90} =\frac{1}{15}[/tex]
The Probability that the number is a perfect square out of two-digit number is chosen at random is [tex]\frac{1}{15}[/tex] .
What is the probability?Probability is a branch of mathematics that deals with the occurrence of a random event.
For example, when a coin is tossed in the air, the possible outcomes are Head and Tail.
Probability formula :
Probability(Event) = Favorable Outcomes/Total Outcomes
According to the question
A two digit number is chosen at random.
Total number of two digit number are from 10 to 99
i.e
=99-10+1 = 90
or Total Outcomes = 90
Total of perfect square of two-digits are: 16,25,36,49,64,81
Total number of perfect square of two-digits = 6
or Favorable Outcomes = 6
Now , The Probability that the number is a perfect square
Probability(Event) = Favorable Outcomes/Total Outcomes
Probability(Event) = [tex]\frac{6}{90}[/tex]
Probability(Event) = [tex]\frac{1}{15}[/tex]
Hence, the Probability that the number is a perfect square out of two-digit number is [tex]\frac{1}{15}[/tex] .
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After Luca took his dogs for a walk, he gave them 6 dog treats. When Luca's dad got home from work, he gave the dogs t more treats. All together that day, Luca's dogs got 10 dog treats. Write an equation to describe this situation. How many dog treats did Luca's dad give the dogs?
Answers
Answer:
6 + t= 10
4 dog treats
Step-by-step explanation:
Luca took his dogs out for a walk.
He gave his dogs 6 dog treats.
Luca's dad came back home that same day and gave the dogs "t" more treats
This means "t" more treats added to the initial 6 treats.
6 + t
All together that same day, Luca's dogs got a total of 10 treats
6 + t = 10
Hence the equation to describe this situation can be written as 6 + t= 10
The number of treats that Luca's dad gave to the dogs can be calculated as follows
6 + t= 10
t = 10-6
t= 4
Hence the number of treats that Luca's dad gave to the dogs is 4 treats
0.5x-7= 0.3 solve the equation
Answers
Answer:
[tex] \boxed{ \bold{ \boxed{ \sf{x = 14.6}}}}[/tex]Step-by-step explanation:
[tex] \sf{0.5x - 7 = 0.3}[/tex]
Move 7 to right hand side and change it's sign
⇒[tex] \sf{0.5x = 0.3 + 7}[/tex]
Add the numbers
⇒[tex] \sf{0.5x = 7.3}[/tex]
Divide both sides of the equation by 0.5
⇒[tex] \sf{ \frac{0.5x}{0.5} = \frac{7.3}{0.5} }[/tex]
Calculate
⇒[tex] \sf{x = 14.6}[/tex]
Hope I helped!
Best regards!!
1
9. By what rational number must
26
be divided to get
?
39
Answers
Answer:
let the unknown rational number be X.
26/X=39
X=39/26
X=3/2
c+d is the of c and d
Answers
Answer:
sum
Step-by-step explanation:
The sum of c and d is c+d.
Darryl bought nine candy bars for a total of $54. How much did each candy bar cost?
Answers
Answer:
$6
Step-by-step explanation:
Divide $54 with 9 canday bars
So, 54/9
=$6
Each candy bar cost $6
Determine which package
of laundry soap is the better
buy: 65 oz. for $6.99 or
120 oz. for $12.99.
Answers
Answer:
The answer is $3.00
Step-by-step explanation:
None
Answer:
120 oz. for $12.99
Step-by-step explanation:
yegeheyeueu3hehueueu3h3he
produce your answer Frombase four to base 10
Answers
Answer:
A. 54₁₀
B. 81₁₀
Step-by-step explanation:
To convert from base 4 to base 10, we simply do the following:
A. 312₄ to base 10
312₄ = (3×4²) + (1×4¹) + (2×4⁰)
312₄ = (3×16) + (1×4) + (2×1)
312₄ = 48 + 4 + 2
312₄ = 54₁₀
Therefore, 312₄ is equivalent to 54₁₀.
B. 1101₄ to base 10
1101₄ = (1×4³) + (1×4²) + (0×4¹) + (1×4⁰)
1101₄ = (1×64) + (1×16) + (0×4) + (1×1)
1101₄ = 64 + 16 + 0 + 1
1101₄ = 81₁₀
Therefore, 1101₄ is equivalent to 81₁₀.
FInd BD, Given FE=23.5 will mark Brainliest please answer ASAP
Answers
=================================================
Explanation:
Points B, C, and D are midpoints of triangle AFE. This is due to the similar tickmarks showing how the segments are congruent (eg: AB = BE).
Because we have D and B as midpoints, this means segment DB is a midsegment of triangle AFE.
FE = 23.5, so half that is (1/2)*FE = 0.5*23.5 = 11.75 which is the length of DB.
The midsegment DB is half as long as FE, and DB is parallel to FE.
If FE=23.5 in triangle AFE then BD=11.75.
What is triangle?A triangle is a two dimensional figure having three sides, three angles. Two triangles are said to be congruent if all the corresponding sides and corresponding angles are equal.
How to find length of a side?We have been given the length of FE=23.5 and we have to find the length of BD. From the figure we have found that B,C and D are mid points of triangle AFE. This is due to the similar signs shown in the figure showing how the segments are congruent. Because we have D and B are mid points, this means segment BD is a mid segment of triangle AFE.
Therefore BD=1/2* 23.5= 11.75.
Hence if the length of FE=23.5 then the length of BD=11.75.
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What is the value of -32+(-4+7)(2)?
0-28
0 -3
O 3
O 15
Answers
nunber a that is -27
hope it helps
Answer:
it should be -26
Step-by-step explanation:
-32+(-4+7)(2)
=-32+3×2
=-32+6
=-26
Estimate the slope m of the line. (If an answer is undefined, enter UNDEFINED.)
Answers
Answer:
slope = - 3
Step-by-step explanation:
The slope m of the line is calculated as
m = [tex]\frac{rise}{run}[/tex] = [tex]\frac{-6}{2}[/tex] = - 3
b.
Write this expression 20 x 20 x 20 x 20 x 20 using exponent
Answers
Answer:
Step-by-step explanation:
I don’t think I can type exponents here so I’ll write it and take a picture
Answer:
20 x 20 x 20 x 20 x 20= 3200000
20^6
PLEASE HELP!!!
Find the value of x.
A. 13 B. 9 C. 12 D. 10
Answers
Answer:
C. 12
Step-by-step explanation:
[tex] x \times 3 = 9\times 4[/tex]
[tex] x \times 3 = 36[/tex]
[tex] x = \frac{36}{3}[/tex]
[tex] x = 12[/tex]
If f(x) x^2 — 5 + 3 and g(x) = 1 — 2x, find f(g(x).
Answers
Answer:
f(g(x))= 1-2(x^2-5+3)
Step-by-step explanation:
To do this you would plug in x^2-5+3 into the x for the g(x) so you would get f(g(x))= 1-2(x^2-5+3)
Answer:
4x^2+6x-1
Step-by-step explanation:
the question asks for f(g(x)). this means you have to plug in the value of g(x) into the "x" of f(x). (you should always work inside out.)
if you do that, you get this equation : (-2x+1)^2-5(-2x+1)+3 (i changed the 1-2x into -2x+1) because you plug in the g(x) (in this case, -2x+1) into the x's in the f(x) equation.
first you foil the (-2x+1)^2 and get 4x^2-4x+1.
then you distribute -5(-2x+1) and get +10x-5
and you bring down the 3.
so you have 4x^2-4x+1+10x-5+3 and you combine your like terms and get
4x^2+6x-1
which is your answer!
Im not sure if this is correct. I need help!
Answers
Answer:
Option 3
Step-by-step explanation:
If (x, y) is on h(x), then (y, x) is on the inverse.
Thus, if (4, 2) is on the inverse, then (2, 4) must be on the original. (Which it is not, so this option is incorrect)
If (0, 1/2) is on the inverse, then (1/2, 0) must be on the original. (It is not, so this option is also incorrect)
If (0, 1) is on the inverse, then (1, 0) must be on the original. (It is not, so this option is also incorrect)
If (-5, 1) is on the inverse, then (1, -5) must be on the original. (It is not, so this option is incorrect)
The correct answer would be the third option.
Choose the percent that is equivalent to the number. 0.75 A. 0.75% B. 7.5% C. 0.0075% D. 75%
Answers
Answer:75
Step-by-step explanation:
Answer:
D. 75%
Step-by-step explanation:
Hello!
To convert a decimal to a percent we move the decimal point two times to the right
0.75 ⇒ 75%
The answer is D.75%
Hope this helps!
Please save for x the. The perimeter
Answers
Answer:
x = 1
Step-by-step explanation:
The perimeter of the square is 4(2x + 3) = 8x + 12 and the perimeter of the triangle is 3x + 2(x + 3) + 5x + 4 = 10x + 10. Since they are equal, we can write:
8x + 12 = 10x + 10
-2x = -2
x = 1
Answer:
x =1Step-by-step explanation:
Perimeter of a square = 4(a)
Where a = side=2x+3
[tex]P = 4(a)\\P= 4(2x+3)\\Perimeter \: = 8x +12[/tex]
Perimeter of a triangle =
[tex]a +b +c[/tex]
[tex]3x + 2(x+3) +5x+4\\3x +2x +6 +5x+4\\Simplify\\: \\3x+2x+5x = 10x\\6+4 =10\\\\= 10x+10[/tex]
[tex]8x +12 = 10x+10\\Collect like terms\\8x -10x = 10-12\\-2x =-2\\Divide\:both\:sides\:of\:the\:equation\:by \:-2\\\frac{-2x}{-2} = \frac{-2}{-2} \\\\x = 1[/tex]
Line a is a perpendicular bisector of line segment K M. It intersects line segment K M at point L. Line a also contains point N. Line segment K L is 9 x +5. Line segment K N is 14 x minus 3. What is the length of segment LM? units
Answers
Answer:
The value of segment LM is 9x + 5.
Step-by-step explanation:
Consider the image below.
A perpendicular bisector is a line segment that bisects another line segment into two equal parts and is perpendicular to this line segment.
So from the diagram below we know:
KL = LM
line a is ⊥ to KM
∠NLK = 90°
Since the angle measure of ∠NKL is not provided we cannot determine the value of x.
So, the value of segment LM is 9x + 5.
The answer is 23 units. I got this answer right on this question, if this do help please tap the heart or comment that this helped you. : ) have a lovely day
The linear scale factor of two similar shapes is in ratio 3:4. If the area of the smaller shape is 72cm square, find the area of the bigger shape.
Answers
Answer:
128 cm²
Step-by-step explanation:
Given the scale factor of 2 similar figures is a : b , then
ratio of areas = a² : b²
Here the scale factor = 3 : 4 , thus
ratio of areas = 3² : 4² = 9 : 16
let x be the area of the larger figure then by proportion
[tex]\frac{9}{72}[/tex] = [tex]\frac{16}{x}[/tex] ( cross- multiply )
9x = 1152 ( divide both sides by 9 (
x = 128
Thus area of larger figure is 128 cm²
The required area of the bigger shape is 128 cm².
The linear scale factor of two similar shapes is in ratio 3:4. the area of the smaller shape is 72cm square. To determine the area of the bigger shape.
What is the Ratio?
The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.
Linear scale factor ratio of two similar shapes = 3:4
Let the area of the bigger shape = x²
Area of the smaller shape = 72
Now since the ratio is linear = 3 : 4
squaring the ratio = 3²:4²
= 9:16
Now the ratio of the are = 72: x²
Equating the ratios
72/x² = 9/16
x² = 16/9 * 72
x² = 1.77 * 72
x² = 128
Thus, the required area of the bigger shape is 128 cm².
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What is the value of [tex](8/3)+(-3)^2-(1/2)[/tex]? (Write your answer as a fraction in reduced form).
Answers
Answer:
Exact Form 67/6
Mixed Number Form 11 1/6
Step-by-step explanation:
Removed Parenthesis 8/3+(-3)^2-1/2
Group like terms 8/3 - 1/2 + (-3)^2
Apply the exponent rule 8/3 - 1/2 + 3^2
Find the LCM (least common multiple) of 3 & 2; 6
Adjust Fraction based on LCM 8/3 = 8*2/3*2 = 16/6 1/2 = 1*3/2*3 = 3/6
16/6 - 3/6
since denominators are equal combine the fraction [tex]\frac{16-3}{6}[/tex]
Subtract the numbers 3^2 + 13/6
3^2 = 9 = 9 +13/6
9*6/6 + 13/6
[tex]\frac{9*6 + 13}{6}[/tex] = 67/6
Help me !!! Please
And explain me
Answers
Answer:
D
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 3, 5) and (x₂, y₂ ) = (-3, - 2)
m = [tex]\frac{-2-5}{-3+3}[/tex] = [tex]\frac{-7}{0}[/tex] ← undefined
Note that division by zero is undefined thas the slope is undefined.
This indicates that the line going through the 2 points is vertical and parallel to the y- axis.
Answer:
Undefined
Step-by-step explanation:
When you calculate he slope it ends up being a vertical line