Match the reasons to the statements in the proof.
1. m∠1 + m∠5 = 180° and m∠1 + m∠4=180°
Subtraction property of equality
2. m∠1 + m∠5 = m∠1 + m∠4
Substitution
3. m∠5 = m∠4
If alternate interior angles equal, then lines are ||.
4. Ray YZ is parallel to Ray UV
Given
Answers
Given
2. m∠1 + m∠5 = m∠1 + m∠4
Substitution
3. m∠5 = m∠4
Subtraction property of equality
4. Ray YZ is parallel to Ray UV
If alternate interior angles equal, then lines are ||.
Answer:
1. [tex]m\angle 1+m\angle 5=180^{\circ}[/tex] and [tex]m\angle 1+m\angle 4=180^{\circ}[/tex]; given
2. [tex]m\angle 1+m\angle5=m\angle 1+m\angle4[/tex]; substitution
3.[tex]m\angle5=m\angle4[/tex]; subtraction property of equality
4. Ray YZ is parallel to ray UV; if alternate interior angles equal , then lines are parallel.
Step-by-step explanation:
Given
[tex]m\angle1+m\angle5=180^{\circ}[/tex]
[tex]m\angle 1+m\angle4=180^{\circ}[/tex]
To prove that YZ is parallel to UV.
Proof:
1.Statement: [tex]m\angle 1+m\angle5=180^{\circ}[/tex] and [tex]m\angle1+m\angle4=180^{\circ}[/tex]
Reason; Given
2. Statement: [tex]m\angle1+m\angle5=m\angle 1+m\angle4[/tex]
Reason: By using substitution property
3.Statement: [tex]m\angle5=m\angle4[/tex]
Reason: Subtraction property of equality.
4.Statement: Ray YZ is parallel to Ray UV
Reason: If alternate interior angles equal, then lines are parallel.
Related Questions
Amy has 12 pairs of white socks, 2 pairs of gray socks, and 6 pairs of black socks in her drawer. if she takes two pairs without replacement, what is the probability that she will take a white pair and gray pair?
Answers
First of all, there are total 12 + 2 + 6 = 20 pairs of socks.
Probability of getting a pair of white socks the first time is 12/20.
Probability of getting a pair of gray socks without replacement, if first one was white, is 2/19
Therefore the probability that she will take a white pair and gray pair without replacement is 6/95 (I multiplied the two probabilities)
Let me know if there are any other questions!
Write three functions. In the first function, y should vary directly with x. In the second function, y should vary inversely with x. In the third function, the relationship between x and y should be neither inverse variation nor direct variation.
Answers
https://brainly.com/question/8880788
1) y = kx . . . . . for some constant k
.. Here y is directly proportional to x , where k is the constant of proportionality
2) y = k/x . . . . for some constant k
.. Here y is inversely proportional to x , again k is the constant of proportionality.
3) y = 2x +52
..
Here y is linearly related to the x , it is neither directly proportional nor inversely proportional.
Please help thank you. :P
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2. rotation
.. Try it. The amount of rotation depends on the angle between the lines. It's like looking in two mirrors.
Crystal has 81/100 of a dollar. What could be the coins crystal has?
Answers
8 dimes and a penny
16 nickels and a penny
81 pennies
What does (r−c)(3) mean about George's new store?
Answers
subtract r from c to get 8x+10
replace x with 3
8(3) +10 = 34 which in hundreds is 3400 dollars
the answer is C
Based on the abbreviations, translate the following ads into fully spelled-out sentences. The final sentence should state how many rooms each house probably has, not counting bathrooms. LOW CTM - 2 bdrm 1 ba. Qualifying Low monthly payments 555-834-3674 Norris Realty
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555-834-3674 Norris Realty
Find the area of a circle with a circumference of \color{blue}{6\pi}6πstart color blue, 6, pi, end color blue.
Answers
C = 2πR.
Where,
R: radius of the circle.
Substituting we have:
6π = 2πR
We cleared R:
R = (6π) / (2π)
R = 3
Then, look for the area of the circle which will be given by:
A = πR ^ 2
Substituting the values:
A = π (3) ^ 2
A = 9π units ^ 2
Answer:
The area of the circle is:
A = 9π units ^ 2
Simplify the expression. (p^9)^−2
Answers
Changes made to your input should not affect the solution:
(1): "p3" was replaced by "p^3". 1 more similar replacement(s).
1.1 p9 divided by p3 = p(9 - 3) = p6
Final result : p6Answer:
[tex](p^9)^{-2}=p^{-18}[/tex]
Step-by-step explanation:
[tex](p^9)^{-2}[/tex]
To simplify the given expression we apply exponential property.
Multiply the outside exponent with inside exponent
[tex](a^m)^n= a^{mn}[/tex]
when we multiply the outside exponent -2 inside 9 , it becomes -18
So the given expression becomes
[tex](p^9)^{-2}=p^{-18}[/tex]
I have a Brainliest reward
Answers
I need help ASAP! will give Brainliest!
It's geomtery
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BD, AB, BC for triangle ABC (angle B is a right-angle)
BD, AD are altitudes for triangle ABD
BD, DC are altitudes for triangle BDC
So in all, altitudes are
BD,AB, BC,AD,DC.
Using metric relations,
BD^2=AD*DC=5*7=35
=>
BD=sqrt(35)=5.916 (to 3 decimal places)
Hence the area of triangle ABC
Area=Base*Height/2 = (5+7)*sqrt(35)/2= 35.496 (to 3 decimal places)
An inheritance of $30,000 will be divided between sisters hannah and taylor. if hannah is to receive $4000 less than taylor, how much does each sister receive?
Answers
Taylor receives $17,000.
Find the product. (2 p + 7)(3 p - 9)
6 p^2 - 3 p - 63
6 p^2 + 3 p - 63
6 p^2 + 39 p - 63
6 p^2 + 3 p - 2
Answers
= 6p^2 +3p -63
The 2nd selection is appropriate.
And airplanes at altitude change -370 ft over 7 minutes what was the mean change of altitude in feet per minute?
Answers
[the mean change of altitude]=[change in altitude]/[time]
[the mean change of altitude]=[-370]/[7]---------------> -52.86 ft/minute
the answer is -52.86 ft/minute (the negative sign means that the plane is descending)
Look at the picture below // 99 points // PLEASEE HELPP
Answers
We can divide the large polygon into 3 smaller known polygons
1 square and 2 rectangles
The dimensions of the square will be:
width: 3 units
length: 3 units
The dimensions of the 1st rectangle will be:
width: 4 units
length: 7 + 13 = 20 units
The dimensions of the 2nd rectangle will be:
width: 5 units
length: 13 units
The area formula of square is (side)²
A = (6)² = 36 units²
The area formula of a rectangle is (length x width)
A (1st) = 4 x 20
= 80 units²
A(2nd) = 5 x 13
= 65 units²
Now, we add all the areas to get the final area
Area total = 36 + 80 + 65
= 181 unit²
Your final answer will be option D
WILL GIVE BRAINLIEST TO PERSON WHO ANSWERS CORRECTLY!!!!!!
Which pair of variables is the most likely to have both correlation and causation?
* the height of a person and the amount of work he does
* the number of hours spent exercising and the number of calories burned
* the length of a person's commute and the amount of money he earns
* the number of customers at a restaurant and the variety of soups ordered
Answers
for the love of God help me
Answers
8b +6r = 44.50 . . . . Paul's first purchase
1b +8r = 25.50 . . . . .Paul's second purchase
b) There are many ways to solve a set of linear equations like this. I like a graphical calculator because it gives me the solution without having to think too much or do any arithmetic.
(b, r) = (3.50, 2.75)
Pine bark mulch costs $3.50 per bag.
Red mulch costs $2.75 per bag.
c) The project cost would have been
.. 14*$3.50 +10*$2.75 = $76.50
Paul would NOT have been able to make that purchase with funds available.
A right triangle has a leg of 13 cm and a hypotenuse of 21 cm. What is the length of the other leg? Round to the nearest tenth
A. 8.0 cm
B.16.5 cm
C. 24.7 cm
D. 272.0 cm
Answers
The other leg of the right triangle will be 16.5cm.
Legs of a right triangle:The side which shares the common/neighboring border to the right angle in a triangle is called legs.
Pythagoras theorem:It states that the sum of the areas of the two squares on the legs equals the area of the of the square on the hypotenuse.
According to the given question, we have
length of one leg of the right triangle is 13cm.
hypotenuse of the right triangle is 21 cm .
Let x be the length of the other leg.
Now, according to the Pythagoras theorem
We can write as
[tex](21)^{2} = x^{2} +(13)^{2}[/tex]
⇒ 441 = [tex]x^{2} +169[/tex]
⇒[tex]441-169 =x^{2}[/tex]
⇒ [tex]272 =x^{2}[/tex]
⇒ [tex]x = \sqrt{272}[/tex]
⇒[tex]x = 16.49[/tex] ≈ 16.5cm
Hence, the other leg of the right triangle will be 16.5cm.
Learn more about Pythagoras theorem here:
https://brainly.com/question/343682
#SPJ2
Daniel Potter bought a new car for $20,000.00. Two years later, he wanted to sell it. He was offered $14,650.00 for it. If he sold it for that amount, what was his depreciation rate?
Answers
$20,000.00-$14,650.00=5350$
Then divide like this:
[tex] \frac{5350.00}{20,000}=75 [/tex]
Now compute the percentage like this:
[tex]0,26\times100=26.75\%[/tex]
In order to compute the rate, divide by the number of years we get:
[tex]\dfrac{26.75}{2}=13.37\%[/tex]
The rate of depreciation is [tex]13.37\%[/tex].
Explanation:
1) Depreciation is the loss of value: $ 20,000.00 - $ 14,650.00 = $ 5,350
2) The percent of depreciation is amount of the depreciation divided by the value of the car when purchased, times 100.
That is (5,350 / $ 20,000) * 100 = 26.75 %
2) The rate is percent of depreciation per year:
depreciation rate = % of depreciation / number of years = 26.75% / 2 = 13.375% per year.
Suppose that in a certain triangle, the degree measures of the exterior angles are in the ratio 2:3:4. If the largest interior angle measures y degrees, what is the value of y?
Answers
2+3+4=9
then divide 360 by 9 (because the total degrees of the exterior angles in polygon is 360)
[tex]360 \div 9 = 40[/tex]
at the end find the amount of the exterior angles:
[tex]2 \times 40 = 80 \\ 3 \times 40 = 120 \\ 4 \times 40 = 160[/tex]
the shortest exterior angle is 80 degrees
so it has the largest interior angle:
180-80=100
the answer is 100
Final answer:
To find the largest interior angle y in a triangle with exterior angles in the ratio 2:3:4, we use the fact that the sum of a triangle's exterior angles is 360° to find the value of each exterior angle, then deduce y as the supplement of the largest exterior angle, resulting in y being 20°.
Explanation:
To find the value of the largest interior angle y in a triangle where the exterior angles are in the ratio 2:3:4, we start by understanding that the sum of the exterior angles of any triangle is 360°.
This means that the exterior angles in this triangle are 2x, 3x, and 4x degrees, respectively, where x is a common multiple.
Given that the sum of these angles must be 360°, we can write the equation 2x + 3x + 4x = 360°, simplifying to 9x = 360° and solving for x gives us x = 40°.
The largest exterior angle is 4x, which equals 160°. Since the exterior angle is supplementary to the interior angle it shares a vertex with, the largest interior angle y is therefore 180° - 160° = 20°.
Thus, the value of y is 20°.
WXYZ is an isosceles trapezoid with legs WX and YZ and a base XY. If the length of WX is 6x+5, the length of XY is 10x+4 and the length of YZ is 8x-3, find the value of x.
Answers
Explanation:
An isosceles trapezoid has two opposite sides (the bases) parallel, and the two other sides (the legs) are of equal length.
So, since the two legs are of equal length, you only need to use the information of the two legs:
Leg WX: 6x + 5
Leg: YZ: 8x - 3
Leg WX = Leg YZ => 6x + 5 = 8x - 3
6x + 5 = 8x - 3
=> 8x - 6x = 5 + 3
=> 2x = 8
=> x = 8 / 2
=> x = 4
helppppppppppppppppppppp
Answers
Ten times the sum of a number and
15
is at least
26
.
Use the variable
b
for the unknown number.
Answers
10 × (15+b) ≥ 26
150+10b ≥ 26
10b ≥ -124
b ≥ -12.4
A boat in calm seas travels in a straight line and ends the trip 16 km west and 50 km north of its original position. Find the direction of the trip to the nearest tenth of a degree.
Answers
sin(∠boat)= 50/52.5
(take the invers sin of (50/52.5)
∠boat= 80.3° North West
ANSWER:
The boat's traveled 80.3° North West
You are driving at an average speed of 50 miles per hour. You drive 22 hours, and you still need to drive another 175 miles. Which graph models how far you are from your destination at any point in time?
Answers
pls xd
KAN SOMEBODY HEPLME #ONSANGRE #ON9INE3REY
Derek wrote the following paragraph proof for the Vertical Angles Theorem:
The sum of angle 1 and angle 4 and the sum of angle 3 and angle 4 are each equal to 180 degrees by the definition of supplementary angles. The sum of angle 1 and angle 4 is equal to the sum of angle 3 and angle 4 by the transitive property of equality. Angle 1 is equal to angle 3 _____________________.
Which phrase completes the proof?
by construction using a straightedge
by the definition of a perpendicular bisector
by the subtraction property of equality
by the vertical angles theorem
Answers
It's important to remember that vertical angles are congruent. They are angles that you could draw a line through the vertex, and it would create 2 more equal angles.
Also, the question even states that "Derek wrote the following paragraph proof for the vertical angles theorem."
So, the answer is 'the vertical angles theorem".
I hope this helps!
~kaikers
subtraction property of equality (i just took that test and got it right)
help:/
Determine if the number is written in scientific notation. If not explain.
1. 4.8x100^7
No; it is not written as a number times a power of 10
yes; the number is written in scienfic notation
no; the first factor is not a number between 1 and 10
2. 5.1x10^-8
yes; the number is written in scienfic notation
no; the first factor is not a number between 1 and 10
no; it is not written as a number times a power of 10
Answers
1. 4.8x100^7 is not in scientific notation.
No; it is not written as a number times a power of 10. It should not be "times 100" because in scientific notation, the highest number to be expanded by the degree is 10.
2. 5.1x10^-8 is in scientific notation.
yes; the number is written in scienfic notation. This is because it has a base number and multiply to x10^-8 which is the exponent indicating that the expanded value is 0.000000051
help !! Which represents the solution(s) of the graphed system of equations, y = x2 – 2x and y = –2x – 1?
a (1, –1)
b (0, 0) and (0, –1)
c (0, 0) and (2, 0)
d no solutions
Answers
y = 0^2 - 2(0) = 0 (0, 0)
y = -2(0) - 1 = -1 (0, -1)
What is the x-intercepts of the graph of y = 12x-5x-2
Answers
first simplify the equation by subtracting like terms (in this case):
12x - 5x = 7x
y = 7x - 2
Since you are finding the x, you must isolate the x. Do the opposite of PEMDAS.(Note: because there is a equal sign, what you do to one side, you do to the other)
y = 7x - 2
y (+2) = 7x - 2 (+2)
y + 2 = 7x
(y + 2)/7 = 7x/7
x = (y + 2)/7
x = (y + 2)/7 is your answer
hope this helps
y = 12x^2 -5x -2
when y = 0
12x^2 -5x -2 = 0
(3x - 2) (4x + 1) = 0
x = 2/3 or x = 1/4
So the x-intercept are (2/3, 0) and (1/4, 0)
Sue’s Corner Market has a markup of 60% on bottled water. If the market sells a bottle of water for $2, find the original amount that Sue pays.
Answers
Markup is the amount added to the cost price of goods to cover overhead and profit.
Sue’s Corner Market has a markup of 60% on bottled water.
Let us say original price was $x.
Now price after markup is $2.
So we can make an equation like:
original price + markup price = price after markup
x + 60% of x =2
[tex] x + 0.6x =2 [/tex]
[tex] 1.6x =2 [/tex]
dividing both sides by 1.6
x= 1.25
So original price was 1.25 dollars.
Answer:
1.25 dollars.
Step-by-step explanation:
frank purchased a boat for $7,525. he made a down payment of $475. he applied for a six year installment loan with an interest rate of 8.4% in the amount of $7,050. what is the total cost of the boat after six years?
Answers
Answer:
$9474.40
Step-by-step explanation:
A spreadsheet can be used to calculate the amortization of the loan. The one attached uses rounding to the penny for all dollar amounts. The result is that the payment amount is rounded down, and the final payment is about 12¢ short. The total repaid on the loan will be slightly more than the product of payment amount ($124.99) and number of payments (72).
The total cost of the boat is the sum of down payment, loan amount, and interest amount. That sum is $9474.40.