What is the measure of angle 1

Answers

Answer 1

The horizontal lines are parallel. Draw the figure on a piece of paper. Now, extend the segment that forms the 36-deg angle with the upper horizontal line until it intersects the lower horizontal line. Now you have a triangle. One angle of the triangle is 31 degrees at the bottom right. At the bottom left, you have an angle that is an alternate interior angle to the 36-deg angle at the top right, so the angle at the bottom left of the triangle also measures 36 deg. Angle 1 is an exterior angle of this triangle. The measure of an exterior angle of a triangle is the sum of the measures of the remote interior angles. The 31-deg angle and the 36-deg angle are the remote interior angles to angle 1, so m<1 = 31 + 36 = 67.

Related Questions

Find an equation of the line l that contains the points left parenthesis 0 comma 0 right parenthesis(0,0) and left parenthesis 3 comma 2 right parenthesis .

Answers

10 out of 10 need ponits please

Can anyone help me to understand how to solve coordinate proofs in Geometry?????

Answers

The coordinate proof is a proof of a geometric theorem which uses "generalized" points on the Cartesian Plane to make an argument.The method usually involves assigning variables to the coordinates of one or more points, and then using these variables in the midpoint or distance formulas .For example, the following is a coordinate proof of the Triangle Midsegment Theorem , which states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and exactly half the length.Without loss of generality, we can assume that one side of the triangle lies on the xx -axis with one vertex at (0,0)(0,0) and the other vertex at(a,0)(a,0).Let the third vertex have the coordinates (b,c)(b,c) . We can assume without loss of generality that this third vertex lies in the first quadrant. (If it doesn't, you can just reflect the triangle over the xx - and/or yy -axis until it does.)

Example:

To Prove: XY¯¯¯¯¯¯XY¯ is parallel to PR¯¯¯¯¯PR¯ and

XY=12PRXY=12PR

Proof:

Using the midpoint formula , the coordinates of the midpoints XX and YY are

X(0+b2,0+c2)=X(b2,c2)Y(a+b2,0+c2)=Y(a+b2,c2)X(0+b2,0+c2)=X(b2,c2)Y(a+b2,0+c2)=Y(a+b2,c2)

First note that the slope is 00 , since

m=riserun =(c2−c2)(b2−(a+b2)) =0(b2−(a+b2)) =0m=riserun =(c2−c2)(b2−(a+b2)) =0(b2−(a+b2)) =0

So, XY¯¯¯¯¯¯XY¯ is parallel to PR¯¯¯¯¯PR¯ .

Now, compare the lengths of the two segments.

XY=a+b2−b2 =a2PR=a−0 =aXY=a+b2−b2 =a2PR=a−0 =a

So,

XY=12PRXY=12PR

Thanks to google for example

hope this helps

The cost of a pair of jeans was changed from $78 to $68.64. What was the percent change?

Answers

Answer:

-12.00%

Step-by-step explanation:

;)

Answer:

12% decrease

Step-by-step explanation:

1. If 1/2 is added to three times the reciprocal of a number, the result is 1. Find the number.

2. The numerator of the given fraction is 4 less than the denominator. If 5 is added to both numerator and denominator, the resulting fraction is equal to 5/7 . What is the original fraction?

TYYYSMMMM

Answers

1. Say the reciprocal of the number is x.

Then:

1/2 + 3x = 1

3x = 1/2
/3 /3

x = 1/6

Since x is the reciprocal of a number, just flip it around to find the real number.

1/6 flipped = 6

So the number is 6.

2. So here we can look at the difference between 5 and 7, because even if you subtract 5 from both numerator and denominator the difference will stay the same.

It's two.

Now you want to find how much you have to multiply two by to get four.

2 * ? = 4

? = 2

So therefore you have to multiply the whole fraction by two to get a fraction with a denominator - numerator equal to 4

5/7 * 2/2 = 10/14

And then just subtract five from the numerator and denominator.

10 - 5 / 14 - 5

5 / 9 was the original fraction

Tia cuts a 4-meter 8-centimeter wire into 10 equal pieces.Marta cut a 540-centimeter wire into 9equal pieces. How much longer is one of Marta's wires than one of Tia's

Answers

Tia's wire is 4 meter and 8 centimeter long which is that is 408 centimeter long and it is divided in 10 pieces.
tia = 408/10 = 40.8 cm
Tia's wire pieces are 40.8 cm long

Marta's wire, it is 540 centimeter long and is divided into 9 pieces
marta = 540/9 = 60 cm
Marta's wires are longer than Tia's
Marta's wire is 19.2 cm longer than tias

60cm - 40.8cm= 19.2 cm

Mentally estimate the total cost of items that have the following prices 1.85 $ .98 $3.49 $9.78 and $6.18 round off your answer to the nearest half dollar

Answers

The total cost is $22.28, rounded to the nearest half dollar is $22.50.

Final answer:

To estimate the total cost, each item's price is rounded to the nearest half dollar: $1.85 to $2.00, $0.98 to $1.00, $3.49 to $3.50, $9.78 to $10.00, $6.18 to $6.00. Summing the rounded figures, the estimated total is $22.50.

Explanation:

To mentally estimate the total cost of the items, we round each item's price to the nearest half dollar and then add them up.

Item 1: $1.85 rounds to $2.00Item 2: $0.98 rounds to $1.00Item 3: $3.49 rounds to $3.50Item 4: $9.78 rounds to $10.00Item 5: $6.18 rounds to $6.00

Adding up the rounded figures gives us: $2.00 + $1.00 + $3.50 + $10.00 + $6.00, which equals $22.50. Thus, the estimated total cost of the items is $22.50, rounded to the nearest half dollar.

The base of a cube is parallel to the horizon. If the cube is cut by a plane to form a cross section, under what circumstance would it be possible for the cross section be a non-rectangular parallelogram?

Answers

The cross-section of a cube can be a non-rectangular parallelogram when the cutting plane is not perpendicular to the cube's base.

The scenario where a cube's cross-section can be a non-rectangular parallelogram occurs when the cutting plane is at an angle other than a right angle to the cube's base. This results in a parallelogram that is not a rectangle, as the cutting plane affects the shape of the cross-section.

When the cutting plane deviates from being perpendicular to the base of the cube, it creates a cross-section that is not a rectangle but can be a parallelogram with unequal angles and sides.

Understanding the geometric implications of the cutting plane's orientation is crucial in visualizing how the cube's cross-section can vary from a rectangular shape to a non-rectangular parallelogram.

HOW CAN I SOLVE IT u=2x-2 for x

Answers

u = 2x - 2

We simply need to isolate x :) That just means that we need to get x onto it's own side of the equal sign.

So, add 2 to both sides.

2 + u = 2x

Then, divide both sides by 2.

2 + u ÷ 2 = 2x ÷ 2

Simplify.

1 + u/2 = x

So, x = 1/2u + 1

~Hope I helped!~ :)

First, you have to isolate 2x in the first step to solving for x, so you would add 2 to both sides. This would look like this: u+2=2x.
Then, divide both sides by 2 to fully isolate x. This would give you an answer of u+2/2 = x.

Sandy had 161 dollars to spend on 9 books. After buying them she had 17 dollars. How much did each book cost

Answers

Each book costs $16.00.

An equilateral triangle has a perimeter of 102 in. What is the length of each side of the triangle?

Answers

I think its 34.Since its equilateral, all sides have the same length. So if you divide 102 by 3 you should have your answer.

What values of k makes the equation true?

Answers

The value of k is 4 because you're adding the exponents and multiplying the coefficients. 5*6 is 30, 3+1 is 4, 6-2 is 4. Therefore, the value of k is 4.

a^2 * a^4 = a^6

answer
k = 4

Your Turn: In the diagram, AB = 12, BX = 2.5, and DX = 5. Find CD. Show all work. *

Answers

CD = 24 Triangles ABX and CDX are similar triangles. So the ratio of lengths between corresponding legs of the triangles will have the same value. You know that they're similar triangles because both of them are right triangles (so you know that one angle is the same in both) and that arc draw on both angles AXB and CXD indicate that those angles match as well. That tells you there's a second angle that's matching in both triangles, and because two of the angles match, you also know that the unmarked angle matches as well since all the angles in a triangle have to add up to 180 degrees. So you know that AB/CD = BX/DX. Substitute known values and you get AB/CD = BX/DX 12/CD = 2.5/5 Now solve for CD 12/CD = 2.5/5 12/CD = 1/2 24/CD = 1 24 = 1 * CD 24 = CD So the value of CD is 24.

What is the area of the figure. Show your work.

Answers

This is a 45-45-90 triangle.
The ratio of the sides is
1: 1: sqrt(2)

The legs have length (24 ft)/(sqrt(2)

The legs are the base and height.

A = bh/2 = [(24 ft)/(sqrt(2)) * (24 ft)/(sqrt(2))]/2 = [(576 ft^2)/2]/2

A = 144 ft^2

What is X in this situation? I'm thinking that you could get X, via vertical angles, but I'm not too sure.

Answers

Use alternate interior angles.
The angle to the left of x is 32
The angle to the right of x is 68
Since the three angles(32, x, and 68) form a straight line, they are supplementary.
32+x+68=180
100+x=180 x=80

The homegrown Turkey farm is preparing their Thanksgiving shipment. In one container they can put 8 big turkey boxes or 10 small turkey boxes. They send 96 turkey boxes using more big boxes than small boxes. How many containers did they use?

Answers

They used 11 containers. 7 containers contained 56 big turkey boxes while 4 containers contained 40 small turkey boxes. 56 is the largest number which is divisible by 8 when deducting 96 by 10. This method ensured that all the containers are shipped at full capacity.

The correct answer is:

11 containers.

Explanation:

We want 96 boxes total. Each container can hold either 10 small boxes or 8 large boxes. To solve this, we want to subtract multiples of 10 from 96 until we have a number that is divisible by 8. This is because we cannot have a fraction of a container full of either big or small boxes.

96-10(1) = 96 - 10 = 86; this is not divisible by 8.

96-10(2) = 96 - 20 = 76; not divisible by 8.

96-10(3) = 96 - 30 = 66; not divisible by 8.

96-10(4) = 96 - 40 = 56; this is divisible by 8.

This means there are 4 containers of small boxes, for 4(10) = 40 boxes, and 56/8 = 7 containers of large boxes, for 56 boxes. This is a total of 4+7 = 11 boxes for our 40+56 = 96 boxes.

30 POINTS! ANSWER ASAP PLEASE!!! WILL THANK ACCOUNT AND ALL ANSWERS!!

The coordinates of the vertices of a polygon are (−2,−2), (3,−3), (4,−6), (1,−6), and (−2,−4).

What is the perimeter of the polygon to the nearest tenth of a unit?

15.3 units
16.9 units
17.5 units
17.9 units

Answers

Answer:

16.9 units

Step-by-step explanation:

Sometimes the easiest way to work these problems is to get a little help from technology. The GeoGebra program/app can tell you the length of a "polyline", but it takes an extra segment to complete the perimeter. It shows the perimeter to be ...

14.87 + 2 = 16.87 ≈ 16.9 . . . units

_____

The distance formula can be used to find the lengths of individual segments. It tells you ...

d = √((Δx)² +(Δy)²)

where Δx and Δy are the differences between x- and y-coordinates of the segment end points.

If the segments are labeled A, B, C, D, E in order, the distances are ...

AB = √(5²+1²) = √26 ≈ 5.099

BC = √(1²+3²) = √10 ≈ 3.162

CD = Δx = 3

DE = √(3²+2²) = √13 ≈ 3.606

EA = Δy = 2

Then the perimeter is ...

P = AB +BC +CD +DE +EA = 5.099 +3.162 +3 +3.606 +2 = 16.867

P ≈ 16.9

Which is correct regarding the statement: “If x is an odd integer, then the median of x, x + 2, x + 6, and x + 10 is an odd number”

Answers

any odd number can be represened as 2n+1 where n is a whole number

the median is the number in the middle when the numbers are arranged in increasing order
if there are an even number of numbers in the set, take the average of the middle 2

we have x,x+2,x+6,x+10
there are 4 numbers, so the median will be the avergage between x+2 and x+6 which is [tex]\frac{x+2+x+6}{2}=\frac{2x+8}{2}=x+4[/tex]
now, if x is odd, then replace x with 2n+1

(2n+1)+4=
2n+1+4=
2n+5=
2n+2(1)+1
even+even+odd=odd
the statement is true

x is odd
x+2 is also odd (eg: x = 3, so x+2 = 3+2 = 5)
x+6 is also odd for similar reasons above
x+10 is also odd

We have four values. The median is found in the middle, so exactly halfway between x+2 and x+6

Add up x+2 and x+6 to get
(x+2)+(x+6) = 2x+8

Then divide that result by 2. In other words, divide everything by 2
2x/2+8/2 = x+4

The result x+4 is odd since adding any even number to an odd number is going to result in an odd value

So the claim is true

--------------------------------------------------------------------------------

Alternative method:
x is odd so x = 2k+1 where k is any integer
x+2 = 2k+1+2 = 2k+3
x+6 = 2k+1+6 = 2k+7
x+10 = 2k+1+10 = 2k+11

Add up the two middle terms
(x+2)+(x+6) = (2k+3)+(2k+7) = 4k+10

Divide that result in half
4k+10 ---> 4k/2 + 10/2 = 2k+5 = 2k+4+1 = 2(k+2)+1

The expression 2(k+2)+1 fits the form 2m+1 where m = k+2 is an integer

So 2(k+2)+1 is odd making the median to be odd.

This further helps support why the claim is true

How many sides of a polygon have if the sum of the measures of its angle is 2880?

Answers

Using the sum of interior angles formula;

(n-2)×180=sum
(n-2)×180=2880
n-2=2880/180
n-2=16
n=16+2
n=18

Therefore, this polygon would have 18 sides.

Hope I helped :)

The region bounded by the given curve is rotated about the specified axis. Find the volume V of the resulting solid by any method. x2 + (y − 4)2 = 16; about the y-axis

Answers

[tex]\bf x^2+(y-4)^2=16\implies x^2=16-(y-4)^2 \\\\\\ x=\sqrt{16-(y-4)^2}\implies x=\sqrt{16-(y^2-8y+16)} \\\\\\ x=\sqrt{8y-y^2}\\\\ -------------------------------\\\\ 0=\sqrt{8y-y^2}\implies 0=8y-y^2\implies 0=y(8-y) \implies y= \begin{cases} 0\\ 8 \end{cases}\\\\ -------------------------------\\\\ \displaystyle \stackrel{\textit{disk method}}{\int\limits_{0}^8~\pi (\sqrt{8y-y^2})^2\cdot dy}\implies \pi \int\limits_{0}^8~ 8y-y^2\cdot dy[/tex]

[tex]\bf \displaystyle \pi \int\limits_{0}^8~8y\cdot dy - \pi \int\limits_{0}^8~y^2\cdot dy\implies \pi \left[ 4y^2~-~\cfrac{y^3}{3} \right]_{0}^8 \\\\\\ \pi \left[ \left[ 256-\cfrac{51}{3} \right]~-~[0] \right]\implies \pi \cdot \cfrac{256}{3}\implies \cfrac{256\pi }{3}\implies 85\frac{\pi }{3}[/tex]

If their food and beverages cost $25.30 and there is an 8% meals tax

Answers

Hey there,
Tax = 8% x $23.50
= $18.80
End cost = $25.30 + $18.30
= $44.10

Hope this helps :))

~Top

Answer:

Then they'll pay $27.32

Step-by-step explanation:

In order to determine this, start by multiplying the cost of the meal by the tax amount.

25.30 * 8% = 2.02

Now add the tax to the meal cost

25.30 + 2.02 = 27.32

The ages of the members of a family are 46, 48, 21, 12, 15, and 8. what is the mean age?

Answers

mean means to average. in order to average, add all the numbers then divide by how many numbers you have.

All these ages add up to 150. because there are 7 ages, divide by 7. this is 21.4 which can be rounded to about 21

46 + 48 + 21 + 12 + 15 + 8 = 150
150 ÷ 7= 21.4285 = 21

The mean age of the family members (46, 48, 21, 12, 15, and 8) is calculated by adding all the ages to get a sum of 150, and then dividing by the number of family members, which is 6, resulting in a mean age of 25 years old.

To calculate the mean age of the family members, you add up all of the ages and then divide by the number of family members. The ages given are 46, 48, 21, 12, 15, and 8. Let's find their sum:

Add the ages together: 46 + 48 + 21 + 12 + 15 + 8 = 150.

Count the number of family members, which is 6.

Divide the total sum of ages by the number of family members: 150 \/ 6 = 25.

Therefore, the mean age of the family members is 25 years old.

A person standing on top of a 11 11-foot high sand pile wishes to estimate the width of the pile. he visually locates two rocks on the ground below at the base of the sand pile. the rocks are on opposite sides of the sand pile, and he and the two rocks are in the same vertical plane. if the angles of depression from the top of the sand pile to each of the rocks are 28 ∘ 28∘ and 19 ∘ 19∘, how far apart are the rocks rounded to the nearest foot?

Answers

Refer to the diagram shown below.

The distance between the two rocks is (a + b).
By definition,
tan(28°) = 11/a
a = 11/tan(28°) = 20.688 ft
Similarly,
b = 11/tan(19°) = 31.9463 ft

The distance between the rocks is
20.688 + 31.9463 = 52.6343 ft

Answer: 53 ft (nearest foot)

Final answer:

The problem involves trigonometry to determine the width of the sandpile. The angles of depression equate to angles of elevation from ground up. Using the tangent function and the provided angles of depression, the distances to the rocks are calculated and added together to get approximately 52 feet as the pile's width.

Explanation:

This problem involves the application of trigonometry, specifically the tangent function (tan) in relation to angle of depression. To start with, we need to note that the angle of depression is equivalent to the angle of elevation as observed from the ground upwards. Hence, if the angles of depression are 28° and 19° respectively, it would mean that the angles of elevation at the rocks would be 28° and 19° respectively.

We can use the formula for tangent, which is tan(θ)=Opposite/Adjacent. In this context, 'Opposite' is the height of the pile (11 feet), and 'Adjacent' is the distance from the base of the pile to the rock. We get two equations:

tan(28°)= 11/D1, with D1 being the distance from the rock to the pile on one side;and tan(19°)= 11/D2, with D2 being the distance from the rock to the pile on the other side.

We rearrange to find D1 and D2. Finally, the total distance (width of the pile) is simply D1 + D2. Using a calculator, D1 is approximately 21 feet and D2 is approximately 31 feet. Hence, the width of the sandpile is approximately 52 feet when rounded to the nearest foot.

Learn more about Trigonometry here:

https://brainly.com/question/11016599

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Point M and N are midpoints of AB and DA respectively.
Complete the following table to prove triangle CDN ≅ triangle CBM
For the last reason choose from: SSS, SAS, or ASA.
*image attached below*

|
Statement | Reason
line DC ≅ _____ | The sides of a square are congruent.
line BM ≅ _____ | They are both half the length of a side of the square.
angle _____ ≅ angle B | All the angles of a square are congruent.
triangle CDN ≅ CBM | ____________________________________
|

Answers

triangle CDN ≅ triangle CBM

Statement | Reason
line DC ≅ __BC___ | The sides of a square are congruent.
line BM ≅ __DN___ | They are both half the length of a side of the square.
angle __D___ ≅ angle B | All the angles of a square are congruent.
triangle CDN ≅ CBM |
by
SAS

Answer:

triangle CDN ≅ triangle CBM

Statement | Reason

line DC ≅ __BC___ | The sides of a square are congruent.

line BM ≅ __DN___ | They are both half the length of a side of the square.

angle __D___ ≅ angle B | All the angles of a square are congruent.

triangle CDN ≅ CBM |

SAS

Step-by-step explanation:

A study of several cities shows a positive correlation between the percent of people late to work and the amount of pollution on the roadways. Which statement is most likely true?
A. Pollution makes people late to work.
B. People who tend to be late make more pollution than those who tend to be on time
C.The correlation is due to a third variable: traffic.
D. The correlation is due to a third variable: cost of windshield wiper fluid.

Answers

In this instance, option C is the most likely cause of the correlation. Pollution rises as the number of vehicles in an area increases. In periods of high traffic, vehicles run longer. High traffic also causes time delays that increase tardiness of employees.

Answer:Its C

Step-by-step explanation:

does a line that bisects an angle of a triangle also bisects the side that is opposite the angle?

Answers

yes, the bisecting line will also bisect the side

yes it does bisect an angle

What are the key variables that must be weighed against each other when considering an HMO, PPO, fee-for-service, or other plan?

Answers

You should consider cost and whether the plan covers the things you want it to. Deductible would also be an important factor. You want to make sure to get the right kind of plan for your needs so you can stay healthy and can get medical care.

A newspaper carrier can deliver 49 papers in one hour at this rate how many newspaper can the carrier deliver in 3 hours

Answers

The newspaper carrier can deliver 147 newspapers in 3 hours

You would multiply the time by how many newspapers he can deliver. He can deliver 147 in 3 hours. Hope this helps

Have a nice day.

The fourth term of an arithmetic sequence is 8. if the common difference is 2, what is the first term

Answers

Question:The fourth term of an arithmetic sequence is 8. if the common difference is 2, what is the first term
Answer: the answer to the problem is 6

The first term of the given arithmetic sequence is 2.

What is an arithmetic sequence?

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is aₙ=a+(n-1)d.

Given that, the fourth term of an arithmetic sequence is 8 and the common difference is 2.

Here, a₄=a+(4-1)×2

8=a+6

a=2

Therefore, the first term of the sequence is 2.

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What is slope and how is it determine from a graph?

Answers

Pick two points on the line and determine their coordinates.Determine the difference in y-coordinates of these two points (rise).Determine the difference in x-coordinates for these two points (run).Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).

Slope is Y= mx + b
rise over runexample y= 3x+2
the three

What is the simplified form of the following expression square root 1/121
A 2/121
B 1/242
C 11
D 1/11

Answers

When you multiply a fraction, you do the top and the bottom separately, right?

Since a square root is like the opposite of multiplying, you can think of the top and the bottom separately for this too!

First, let's start with the top. The square root of 1 is 1, so the numerator is 1.

Now, let's do the bottom. The square root of 121 is 11, so the denominator is 11.

So, the answer is D, 1/11. You can check your answer by squaring it, and getting 1/121.

Hope this helps!

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