Answers
Answer:
The value of [tex]m\angle 3-m\angle 1[/tex] = [tex]50^{\circ}[/tex]
Step-by-step explanation:
Vertical Angle theorem: It is about the angles that are opposite to each other.
Also, vertical angle are congruent that means vertical angles are equal.
In the given figure; [tex]m\angle 3[/tex] and [tex]70^{\circ}[/tex] are vertical angle
then, by vertical angle theorem, [tex]m\angle3 =70^{\circ}[/tex].
Supplementary angle: the sum of the angles whose measure on the straight line is 180 degree.
From the figure, [tex]70^{\circ}[/tex] , [tex]\angle 1[/tex] and [tex]m\angle 2 =90^{\circ}[/tex] forms a straight line.
then, by the definition of Supplementary angle;
[tex]70^{\circ}+m\angle 1 +m\angle 2=180^{\circ}[/tex]
Substituting the value of [tex]m\angle 2 =90^{\circ}[/tex] in above equation:
[tex]70^{\circ}+m\angle 1 + 90^{\circ} =180^{\circ}[/tex] or
[tex]160^{\circ}+m\angle 1=180^{\circ}[/tex]
Simplify:
[tex]m\angle 1=180^{\circ}-160^{\circ} =20^{\circ}[/tex]
therefore, [tex]m\angle 1= 20^{\circ}[/tex] and [tex]m\angle 3=70^{\circ}[/tex],
the value of [tex]m\angle3-m\angle1= 70^{\circ}-20^{\circ} =50^{\circ}[/tex].
Related Questions
Which of these is false?
A) 21,730 < 22,341
B) 21,730 > 22,341
C) 22,341 > 21,730
D) 22,341 < 24,687
Answers
The false statement among the given options is B) 21,730 > 22,341. The greater than, less than symbols should be accurately used to compare two numbers. The other given statements are true.
Explanation:The false statement in the given options is B) 21,730 > 22,341. This statement is saying that 21,730 is greater than 22,341, which is false. In mathematics, '<' symbol represents 'less than' and '>' represents 'greater than'. So, the statement B) is false because 21,730 is not greater than 22,341, but less.
Comparing the following two statements A) 21,730 < 22,341 and C) 22,341 > 21,730, we can see they are actually the same statement, restated in a different manner. Both statements are saying that 21,730 is less than 22,341 which is true.
The statement D) 22,341 < 24,687 is also true because 22,341 is less than 24,687.
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At a toy factory, toy cars are produced on an assembly line. It takes 8.216 seconds to attach the wheels. It takes 3.652 seconds to attach the hood. How long does it take to attach the wheels and hoods on 42 toy cars
Answers
At a toy factory, it takes 498.456 seconds to attach the wheels and hoods on 42 toy cars.
We have been given that toy cars are manufactured on an assembly line in a toy factory. Attaching the wheels takes 8.216 seconds. Attaching the hood takes 3.652 seconds.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.
* Multiplication operation: Multiplies values on either side of the operator
For example 12×2 = 24
To determine the time it takes to attach the wheels and hoods on 42 toy cars
According to the given condition, the arithmetic form would be as
⇒ 42 × (8.216 + 3.652)
Calculate the sum of the difference to get,
⇒ 42 × (11.868)
Apply the multiplication operation, and we get
⇒ 498.456
Therefore, it takes 498.456 seconds to attach the wheels and hoods on 42 toy cars.
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In the triangles below, ma + md = 90°. using the information given about the triangles below, determine how the triangles can be shown to be similar.
Answers
Answer:
The triangles are similar by AA
Step-by-step explanation:
The larger of two numbers is one more than four times the smaller number. if the sum of the numbers is 106, find the numbers.
Answers
x + y = 106
4y + 1 + y = 106
5y = 105
y = 21
We have y, so now we can solve for x using either original equation:
x + y = 106
x + 21 = 106
x = 85
To solve the problem, create two equations based on the information given, then solve these equations step-by-step. After calculation, the two numbers are 21 and 85.
Explanation:Given the problem, we can translate and create two equations which are:
The larger number is one more than four times the smaller number. We can express this as: L = 4S + 1 The sum of the numbers is 106. We can express this as: L + S = 106
Step 1: From the first equation, we know that L = 4S + 1. We can substitute this into the second equation in place of L, giving us 4S + 1 + S = 106.
Step 2: Add up, and we get 5S + 1 = 106. Subtract 1 from both sides and we get 5S = 105.
Step 3: Divide both sides by 5 to solve for S, we get S = 21.
Step 4: Substitute S = 21 into the equation L = 4S + 1, you can calculate and find L = 85.
Therefore, the two numbers are 21 and 85.
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An office uses 478 pounds of paper in one week. The paper comes in packages that hold 18 pounds of paper each. How many packages of paper does the office use each week?
Answers
The office uses 26 and a half package of papers.
What is division?Division is the process of splitting a number or an amount into equal parts.
Given that, An office uses 478 pounds of paper in one week. The paper comes in packages that hold 18 pounds of paper each.
To find the number of packages of paper, the office use each week, we will divide the total paper used in one week to paper in 1 package
Therefore, the number of packages of paper, the office use each week = 478 / 18 = 26.5
That means they are using 26 package plus a half package in one week.
Hence, The office uses 26 and a half package of papers.
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If 5 people including mary and bob are arranged randomly in a line, what is the probability that mary and bob are next to one another?
Answers
MBXXX
BMXXX
XMBXX
XBMXX
XXMBX
XXBMX
XXXMB
XXXBM
There are 8 arrangements out of the 120 where Mary and Bob are next to each other, which means that they have an 8/120 = 1/15 chance of ending up in that situation.
The length of a rectangle is 3 meters less than twice the width. if the area of the rectangle is 527 square meters, find the dimensions.
Answers
Answer:
w=17
l=31
Step-by-step explanation:
correct
Suppose you are going to make a sandwich. You have mayonnaise and mustard to spread on the bread. You have white, wheat, and rye bread. You have ham, turkey, and pastrami. How many different sandwiches can you make using one spread, one type of bread, and one type of meat?
Answers
m8 thats alot of samiches
2 spreads
3 breads
3 meats
2 * 3 *3 = 18
18 different sandwiches....now I'm hungry
What is 4,080,499 rounded to the nearest thousand?
Answers
How do you write 100, in an exponential form
How do write 100,000, in an exponential form
And how do you write 10,000 ,in an exponential form
Answers
1. 10^2
2. 10^5
3. 10^4
Hope this helped!
Nate
Numbers can be written in exponential form with a base of 10. For example, 100 is written as 10^2, 100,000 as 10^5, and 10,000 as 10^4.
Explanation:To write numbers in exponential form, you need to understand the concept of exponential notation which is a way to express a number as a base raised to a power. In each of the given cases, the base is 10.
For 100, there are two zeros following the 1. This means that 100 can be written as 10 to the power of 2, or 10^2.
Similarly, for 100,000, there are five zeros following the 1. This would be written as 10 to the power 5, or 10^5.
Lastly, 10,000, has four zeros following the 1. This would be written as 10 to the power of 4, or 10^4.
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Ive been super sick so im a little behind. Help please .
1. A line goes through the points (8,9) and (-2,4)
(a) What is the slope of the line? Show your work
(b) Write the equation of the line in point-slope form. Show your work
(c) Write the equation of the line in slope-intercept form. Show your work.
Answers
(4-9)/(-2-8) = (-5)/(-10) = 0.5
(b) formula: y-y0 = m(x-x0) where x0,y0 is a point on the line and m is the slope
y - 9 = 0.5 ( x - 8 )
(c) formula: y=mx + b
Start with formula from (b)
y -9 = 0.5x - 4
Add 9 to both sides
y = 0.5x +5
The answers are in the top right corner.
Ohhhhh! I have a Brainliest!
Answers
2. 4 1/3
hope this helps please give brainliest and 5 stars and a thank you
Which statement is true about the difference 2√7-√28
Answers
2*sqrt(7) - sqrt(28) = 2*sqrt(7) - sqrt(4*7)
2*sqrt(7) - sqrt(28) = 2*sqrt(7) - sqrt(4)*sqrt(7)
2*sqrt(7) - sqrt(28) = 2*sqrt(7) - 2*sqrt(7)
2*sqrt(7) - sqrt(28) = (2-2)*sqrt(7)
2*sqrt(7) - sqrt(28) = (0)*sqrt(7)
2*sqrt(7) - sqrt(28) = 0
So the whole complicated expression simplifies to 0 (zero)
This is because sqrt(28) = 2*sqrt(7) when you simplify sqrt(28)
Side Note: "sqrt" is shorthand for "square root"
Reflection : Across the line y = 1
Answers
Reflecting across y = 1 means each point's position stays the same horizontally but mirrors vertically across the line.
When reflecting a point or shape across a line, y = 1,
it means that each point is mirrored on the other side of the line while maintaining the same distance from the line.
Here, the line y = 1 acts as a "mirror" or "axis of reflection."
To reflect a point (x, y) across the line y = 1, follow these steps:
Find the vertical distance between the point and the line y = 1. Let's call this distance "d."
If the point is above the line (y > 1), then d = y - 1.
If the point is below the line (y < 1), then d = 1 - y.
Move the point to the same vertical distance on the other side of the line y = 1.
If the point was above the line (y > 1), the new reflected point will be (x, 1 + d).
If the point was below the line (y < 1), the new reflected point will be (x, 1 - d).
Keep in mind that the x-coordinate remains the same in both cases since the line of reflection is vertical (parallel to the y-axis).
By repeating these steps for all points in a shape, obtain the reflection of the entire shape across the line y = 1.
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A train travels 750 miles in 15 hours. which unit rate describes the speed of the train?
a. 50 miles per hour
b. 75 miles per hour
c. 150 miles per hour
d. 350 miles per hour
Answers
Assume that lines that appear to be parallel are parallel. Find the value of x and the measure of angle y
Answers
(9x+1)+(14x-34)=180
There, we have an equation we can fairly easily solve for x. What about y?
If we take a look at the line y° occupies, we can see that it shares a straight angle with our (14x-34)° term and - as implied by the right angle on the bottom line - a 90° angle.
All three of these should add up to 180°, so we have:
(14x-34) + y + 90 = 180
Another think to note is that, upon inspection, (14x-34)° and y° are complementary - they add up to 90° - and subtracting the 90 from both sides of our equation confirms that fact:
(14x-34) + y = 90
If you've solved for x prior to this, solving for y should be pretty straightforward.
Answer:
The answer would be (14x-34) + y = 90.
Step-by-step explanation:
2+1/6y=3x+4 solve for y
Answers
Answer y=18x+12
× 6y throughout
12y + 1 = 18xy + 24y
Send 12y to the other side
12y + 18xy = 1
Y is common
y (12 + 18x) = 1
y = 1/ (12 + 18x)
Hope it helped!
Suppose you go shopping for a new futon bed for your apartment/home. The model you really like happens to be on sale for $1100. It's original price is $1200. What percent of the original price will you save if you purchase it? Write your answer to the nearest tenth of a percent, but in decimal form.
Answers
Lisa purchased a prepaid phone card for $25 . Long distance calls cost 12 cents a minute using this card. Lisa used her card only once to make a long distance call. If the remaining credit on her card is $19.96 , how many minutes did her call last?
Answers
Find the difference between 25 and 19.96 and divide the difference by 12.
How do I graph this equation?
Answers
for example when x = 0 y = 0-9 = -9
do the same with values of x from -3 to + 3 in steps of 1.
Find four consecutive integers with the sum of 54
Answers
54/4 = 13.5
take the 2 whole numbers below 13.5 and the 2 whole numbers above 13.5
12 + 13 + 14 + 15 = 54
Hanks pickup can travel 60miles on 4gallons of gas. How many gallons will hanks pickup need to travel 30miles?
Answers
ALGEBRA 2- Which equation has the solutions x = 1 ± √5 ?
A. x2 + 2x + 4 = 0
B. x2 – 2x + 4 = 0
C. x2 + 2x – 4 = 0
D. x2 – 2x – 4 = 0
Answers
You can solve this problem 2 different ways.
1. Plug in a value of x = 1 ± √5 into each of the possible equations and see if the result is 0.
or
2. Use the Quadratic formula to solve each of the equations and see which comes up with the correct answer.
For this case, I'll use the 2nd option.
A. x^2 + 2x + 4 = 0
a = 1, b = 2, c = 4
Upon attempting this, you'll quickly discover that you're going to try to get the square root of -12. Since there's no imaginary terms in the desired root, this equation can't be it.
B. x^2 – 2x + 4 = 0
Same issue here, trying to get the square root of a negative number. So this one doesn't work either.
C. x^2 + 2x – 4 = 0
Getting closer. Have (-2 ± sqrt(20)) / 2 = -1 ± √5
Still not it, but closer. At least not trying to get the square root of a negative number.
D. x^2 – 2x – 4 = 0
Since the other 3 are wrong, this must be right. But let's do the math anyway.
a = 1, b = -2, c = -4
The quadratic formula gets (2 ± sqrt(20)) / 2 = (2 ± 2√5)/2 = 1 ± √5
And it works out. So this is the answer.
Cynthia besch wants to buy a rug for a room that is 18 ft wide and 30 ft long. she wants to leave a uniform strip of floor around the rug. she can afford to buy 220 square feet of carpeting. what dimensions should the rugâ have?
Answers
What is the square root of 83 to the nearest tenth?
Answers
9 to the closest tenth is 10.
Hope I helped :)
Based on the information given the square root of 83 to the nearest tenth is 9.1.
Square root:To determine the square root to the nearest tenth we will have to find the square root of the given number which is 83.
Hence,
Square root=√83
Square root= 9.1104335791443
Square root=9.1 nearest tenth
Inconclusion the square root of 83 to the nearest tenth is 9.1.
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a boat salesperson earns a 2.5% commission on the sale of each boat Find the commision earned on a boat that sells for 18,500
Answers
2.5% = 0.025
So now we know the decimal that corresponds to 2.5%, so all we have to do is multiply the price of the boat by this value in order to find the commission earned:
18 500 x 0.025 = $462.50
For example, find the 20% commission of a $10,000 car sale
Calculation:
0.20x$10000 = $2000
Answer:
the commission would be $2000
That’s how you do it. I hope that helps. You should be able to solve it on your own now.
Evaluate a + b2 for a = 2 and b = 3. 8 11 25
Answers
= 2 + 3^2
= 2 + 9
= 11
answer
11
a+b2
replace the letter with it's number
2+3(2)
multiply 3 and 2
2+6
add
8
Brainliest reward math question
Answers
hard questions im trying. too hard
To do find the deduction, you do 978 x.05.
2. I don't understand the question at all, I'm very sorry.
3(b-4)=5b-2 plz help I'm confused
Answers
3b - 12 = 5b - 2
3b - 5b = 12 - 2
-2b = 10
b = -5
hope this helps
-12=2b-2
-10=2b
b=-5
When the factors ofa trinomial are (x+ p) and (x + q) then the coefficient ofthe x- term in the trinomial is:?