Answers
Answer:
The angles opposite each other when two lines cross. In the figure, the 1 and 3 are vertically opposite angles and they are always equals. Same goes for angles 2 and 4. The angles in matching corners when two lines are crossed by another line, called the transversal.
Step-by-step explanation:
1. Complementary Angles
Definition
Complementary angles are two positive angles whose sum is 90 degrees.
Examples
For example, complementary angles can be adjacent, as seen in with ∠ABD and ∠CBD in the image below. Or they can be two acute angles, like ∠MNP and ∠EFG, whose sum is equal to 90 degrees. Both of these graphics represent pairs of complementary angles.
complementary angles example
Complementary Angles Example
2. Supplementary Angles
Definition
Supplementary angles are two positive angles whose sum is 180 degrees.
Examples
For example, supplementary angles may be adjacent, as seen in with ∠ABD and ∠CBD in the image below. Or they can be two angles, like ∠MNP and ∠KLR, whose sum is equal to 180 degrees. Both of these graphics represent pairs of supplementary angles.
supplementary angles example
Supplementary Angles Example
What is important to note is that both complementary and supplementary angles don’t always have to be adjacent angles.
3. Adjacent Angles
Definition
Adjacent angles are two angles in a plane that have a common vertex and a common side but no common interior points.
Examples
Angles 1 and 2 are adjacent angles because they share a common side.
adjacent angles examples
Adjacent Angles Examples
And as Math is Fun so nicely points out, a straightforward way to remember Complementary and Supplementary measures is to think:
C is for Corner of a Right Angle (90 degrees)
S is for Straight Angle (180 degrees)
Now it’s time to talk about my two favorite angle-pair relationships: Linear Pair and Vertical Angles.
4. Linear Pair
Definition
A linear pair is precisely what its name indicates. It is a pair of angles sitting on a line! In fact, a linear pair forms supplementary angles.
Why?
Because, we know that the measure of a straight angle is 180 degrees, so a linear pair of angles must also add up to 180 degrees.
Examples
∠ABD and ∠CBD form a linear pair and are also supplementary angles, where ∠1 + ∠2 = 180 degrees.
linear pair example
Linear Pair Example
5. Vertical Angles
Definition
Vertical angles are two nonadjacent angles formed by two intersecting lines or opposite rays.
Huh?
Think of the letter X. These two intersecting lines form two sets of vertical angles (opposite angles). And more importantly, these vertical angles are congruent.
Examples
In the accompanying graphic, we see two intersecting lines, where ∠1 and ∠3 are vertical angles and are congruent. And ∠2 and ∠4 are vertical angles and are also congruent.
vertical angles examples
Vertical Angles Examples
Together we are going to use our knowledge of Angle Addition, Adjacent Angles, Complementary and Supplementary Angles, as well as Linear Pair and Vertical Angles to find the values of unknown measures.
Angle Relationships – Lesson & Examples (Video)
32 min
Introduction to Angle Pair Relationships
00:00:15 – Overview of Complementary, Supplementary, Adjacent, and Vertical Angles and Linear Pair
Exclusive Content for Member’s Only
00:06:29 – Use the diagram to solve for the unknown angle measures (Examples #1-8)
00:19:05 – Find the measure of each variable involving Linear Pair and Vertical Angles (Examples #9-12)
Practice Problems with Step-by-Step Solutions
Chapter Tests with Video Solutions
The required relationship between the angles 1, 2, and 3 is ∠1 +∠2 = ∠3.
Given that,
To determine the relationship between angles 1, 2, and 3.
The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°
Here,
Angles 1 and 2 are remote interior angles while angle 3 is a remote exterior angle. So there is a property of a triangle in that the sum of the remote interior angles is equal to the remote exterior angle.
∠1 +∠2 = ∠3.
Thus, the required relationship between the angles 1, 2, and 3 is ∠1 +∠2 = ∠3.
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Related Questions
PLEASE HELP NOW!!!
How does the graph of the function f(x + 3) compare to the graph of f(x)?
A.f(x + 3) has a vertical shift 3 units up from f(x).
B.f(x + 3) has a vertical shift 3 units down from f(x).
C.f(x + 3) has a horizontal shift 3 units to the right of f(x).
D.f(x + 3) has a horizontal shift 3 units to the left of f(x).
Answers
Carlos spent 1\dfrac141 4 1 1, start fraction, 1, divided by, 4, end fraction hours doing his math homework. He spent 1\dfrac141 4 1 1, start fraction, 1, divided by, 4, end fraction as much time practicing piano. How many hours did Carlos spend practicing piano?
Answers
Answer:
Carlos spent [tex]\frac{5}{16}[/tex] hours in practicing piano
Step-by-step explanation:
Carlos spent hours in doing his maths homework =[tex]1 \frac{1}{4}[/tex]
Carlos spent hours in doing his maths homework = [tex]\frac{5}{4}[/tex]
We are given that He spent 1/4 of his time practicing piano
So, Time spent by Carlos in practicing piano = [tex]\frac{1}{4} \times \frac{5}{4}[/tex]
Time spent by Carlos in practicing piano = [tex]\frac{5}{16}[/tex]
Carlos spent hours in practicing piano = [tex]\frac{5}{16} hours[/tex]
Hence Carlos spent [tex]\frac{5}{16}[/tex] hours in practicing piano
I need help on this
Answers
Answer: Second company (in the table), aka #1 toys, produces at a slower rate
============================================================
Explanation:
The equation y = 123x is in the form y = mx+b with m = 123 as the slope. The slope is the rate of change telling us how many toys per minute are produced. In this case, 123 toys per minute is the rate for the first company.
----------
We'll need the slope of the other function. So we need to pick two rows from the table and use the slope formula. I'll pick the first two rows.
m = (y2-y1)/(x2-x1)
m = (1320-600)/(11-5)
m = 720/6
m = 120
The second company produces at a rate of 120 toys per minute. This is the smaller rate, so this company produces at a slower speed.
Jocelyn can bake 48 cookies per hour. She needs to bake 120 total cookies and has already baked 24 cookies
Answers
Answer:
Step-by-step explanation:
it will take jocelyn 2 hours to make 120 cookies
what is x+x+y×y simplified
Answers
Answer:
x+x+yxy
= x^2 + y^2
x^2 + y^2 is the answer.
What is a simplification in math?In mathematics, genuinely or simplification is reducing the expression/fraction/hassle in a less complicated form. It makes the problem smooth with calculations and fixing.
Does simplifying suggest fixing?Associated with "simplification" troubles are some "solving" troubles. just as a few expressions include parentheticals or even nested grouping symbols, so additionally do some equations. The simplification manner is identical, whether we're running with expressions (and consequently handiest simplifying) or equations (so we are also solving).
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Endpoint: (2,5) midpoint (3,4)
Missing endpoint:
Answers
Answer:
(4,3)
Step-by-step explanation:
The perimeter of a rectangle is 64 feet. The length of the rectangle is 3 times the width of the rectangle. If w represents the width of the rectangle, the equation that represents the perimeter is 2 (3 w) + 2 w = 64. Which shows the first step that should be taken to verify that the width of the rectangle is 8? A regular hexagon and a rectangle have the same perimeter, P. A side of the hexagon is 4 less than the length, l, of the rectangle. The width of the rectangle, w, is 2 less than the length of the rectangle. What is the perimeter of the hexagon?
Answers
Step-by-step explanation:
given the perimeter is
64ft
the length l= 3w
we know that the perimeter of a rectangle is given as
P=2l+2W
but L=3w
64=2(3w)+2w
64=6w+2w
64=8w
divide both sides by 8 we have
w=64/8
w=8ft
also
let the lenght of the rectangle be l
side of hexagon=l-4
perimeter of hexagon
P=5(l-4)
P=5l-20
width of rectangle w=l-2
perimeter of rectangle= 2l+2w
but w=l-2
5l-20= 2l+2(l-2)
5l-20=2l+2l-4
5l-20=4l-4
5l-4l=-4+20
l=16ft
perimeter of hexagon
P=5(l-4)
put l=16
perimeter of hexagon
P=5(16-4)
p=5(12)
P=60ft
Answer: 2(3(8))+(2+8)=64 or c
Step-by-step explanation:
You have to replace w with 8 meaning 8 is now the width, therefore, c is the correct answer.
Simplify a - {b - [C- (d - e) -f]-g}.
Answers
Answer:
C+a−b−d−f+g+e
Step-by-step explanation:
Does anybody know anything about measuring Angles I need help?
Answers
Answer:
yes ....I can help please
let's take the example 2
x° and 68° forms right angle so it's 90°
so we'll add them to find x
x° = 90°- 68° = 22°
2. X = 22
3. X = 56
4. X = 137, Y = 43, Z = 137
5. X = 108, Y = 72, Z = 47
6. Measure D = 105
7. Measure B = 48
8. Measure P = 116
9. Measure K = 67
Hope this helped :)
I would love if someone helps me w this one
Answers
Answer:
2,7 is where the lines intersect
X=2
Y=7
correct me if i am wrong
Step-by-step explanation:
1. Which is the smallest set of real numbers that contains the value below? -18 /6
A. Irrational Numbers
B. Rational Numbers
C. Natural Numbers
D. Integers
Answers
Answer:
Integers
Step-by-step explanation:
The correct option to choose is the integers option. Integers are simply whole numbers.
Thus-18/6 = -3
The term -3 is a whole number
So the term to choose is the integers option
The smallest set of real numbers that contains the value -18 /6 is an integer.
The smallest set of the real number that contains the value -18/6 can be determined after we have simplified the expression -18/6.
To simply the given expression, we will divide both the numerator and the denominator by 6, by doing so, we have:
= -3
Now, the smallest set of the real number is = -3 which is an integer
This is because an integer is a whole number that is not a fraction and can be negative or positive.
The reason why it is not a natural number is because of the negative sign, since we know that natural numbers are numbers with positive signs only.
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F and g are functions such that
F(x)=3/x2 and g(x)=2x3
A) find f(-4)
B) find fg(1)
Answers
f(-4)= 3/-8
f(g(1))= 3/(2(1)^3)(2)
f(g(1))= 3/(2)(2)
f(g(1))= 3/4
a. The value of f(-4) is [tex]3 \div -8[/tex]
b. The value of fg(1) is [tex]3\div 4[/tex]
Calculation of the value of f(-4) and fg(1):Since [tex]F(x)=3\div x\times 2\ and\ g(x)=2\times x\times 3[/tex]
So,
a. The value of f(-4) is
[tex]= 3\div (-4)(2)\\\\= 3\div -8[/tex]
And,
b. The value of fg(1) is
[tex]= 3\div (2(1)^3)(2)\\\\= 3\div (2)(2)\\\\= 3\div 4[/tex]
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Lisa bought 5 CDS from a store. The price of each CD was the same. After she bought the CDs, her account balance showed a change of -$64.95. What would have been the change to Lisa’s account balance had she only bought 1 CD from the store?
Answers
Answer:
47
Step-by-step explanation:
They are dumpy because they can’t try
Prove that in any triangle the length of a side is less than the half of the perimeter in statement reason format.
Answers
Answer:
Proved
Step-by-step explanation:
I am going to pose c as the largest side in a random triangle
If so then remember that, by the triangle inequality, a + b > c. Let's start from there...
Statement: | Reasoning:
1. a + b > c 1. Triangle Inequality
2. a + b + c > c + c (adding c on both sides), 2. Algebra + Def. Of Perimeter
a + b + c > 2c (simplified)
Perimeter > 2c (definition of perimeter)
c < 1/2 * Perimeter
The prove of statement ''in any triangle the length of a side is less than the half of the perimeter'' is shown.
What is Perimeter?
The sum of all sides of a quadrilateral is called a perimeter.
Given that;
The statement is,
''In any triangle the length of a side is less than the half of the perimeter''.
Now,
Let sides of triangles are a, b and c.
The triangle inequality is;
a + b > c
Add both side by c;
a + b + c > c + c
a + b + c > 2c .... (i)
Since, Perimeter of a triangle with sides a, b and c is;
Perimeter (P) = a + b + c
Substitute value of perimeter in equation (i), we get;
a + b + c > 2c
P > 2c
c < P/2
Thus, In any triangle the length of a side is less than the half of the perimeter.
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Choose an equivalent expression for 106 ÷ 104.
Answers
Answer:
10^2
Step-by-step explanation:
When we divide exponents we subtract the exponenets in the top (in this case 6-4). This will give us 10^2. You can also check this.
The equivalent expression for 10⁶ ÷ 10⁴ will be 10². Then the correct option is A.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
The numbers are given below.
10⁶ and 10⁴
The division of the numbers 10⁶ and 10⁴ will be given below.
⇒ 10⁶ ÷ 10⁴
⇒ 10⁶ / 10⁴
⇒ 10⁶⁻⁴
⇒ 10²
The equivalent expression for 10⁶ ÷ 10⁴ will be 10². Then the correct option is A.
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PLEASE HELP!!!!
Will give you brainliest
and 5 stars
Answers
Answer:
f(x)=3/2 x
Step-by-step explanation:
it starts at 0 and rise 3 and goes over 2
The answer is [tex]f(x)=\frac{3}{2}x[/tex]
First, you must find 2 points.
(0,0) (2,3)
Then, you must use the slope equation
[tex]\frac{3-0}{2-0}=\frac{3}{2}[/tex]
The line crosses the y axis at 0, so there is no y intercept
[tex]f(x)=\frac{3}{2}x[/tex]
Seven subtracted from twice a number gives 41, find this number.
Answers
2x = 48
x = 24
Answer:
2x -7 = 41
2x = 41 +7
2x = 48
x = 24
A company is trying to decide which container of coffee to buy for a staff meeting. Which of the following would be the best deal? Hint: find the best unit cost
Group of answer choices
32 ounces for $4.00
60 ounces for $6.75
48 ounces for $5.00
45 ounces for $4.50
Answers
If 9 bottles of soy sauce cost $32.85 and the price of each bottle is the same, how much does each bottle cost?
Answers
Answer:
$3.65
Step-by-step explanation:
32.85/ 9 = $3.65
Answer:
$3.65
Step-by-step explanation:
this is easy lol
Please help I'm trying too keep my grades up I was crying I dont wanna fail
Answers
Answer:
No.
Step-by-step explanation:
[tex]10^{4} =(10)(10)(10)(10)\\10^{4} =10000\\[/tex]
[tex](10)(4)=40[/tex]
[tex]10000\neq 40[/tex]. Therefore, [tex]10^{4} \neq[/tex]10x4.
**Exponents expresses how many times the number it multiplied by it's own value. Such as [tex]x^{2}[/tex] is the same as (x)(x) since it is times by itself 2 times. Or, [tex]6^{8}[/tex] is the same as (6)(6)(6)(6)(6)(6)(6)(6) since it is times by itself 8 times.
In the adjoining figure , AB = 6 , BC = 8 , [tex] \angle[/tex] ABC = 90° , BD ⊥ AC and [tex] \angle[/tex] ABD = [tex] \theta[/tex] , find the value of sin [tex] \theta[/tex].
Answers
Here we are given with a triangle with smaller triangles formed due to the altitude on AC. Given:
AB = 6BC = 8<ABC = 90°BD ⊥ AC<ABD = [tex] \theta[/tex]We have to find the value for sin [tex] \theta[/tex]
So, Let's start solving....
In ∆ADB and ∆ABC,
<A = <A (common)<ABC = <ADB (90°)So, ∆ADB ~ ∆ABC (By AA similarity)
The corresponding sides will be:
[tex] \sf{ \dfrac{AD}{AB} = \dfrac{AB}{AC} }[/tex]
We know the value of AB and to find AC, we can use Pythagoras theoram that is:
AC = √6² + 8²
AC = 10
Coming back to the relation,
[tex] \sf{ \dfrac{AD}{6} = \dfrac{6}{10} }[/tex]
[tex] \sf{AD = \dfrac{6 \times 6}{10} = 3.6}[/tex]
In ∆ADB, we have to find sin [tex] \theta[/tex] which is given by perpendicular/base:
[tex] \sf{\sin( \theta) = \dfrac{AD}{AB} }[/tex]
Plugging the values of AD and AB,
[tex] \sf{\sin( \theta) = \dfrac{3.6}{6} }[/tex]
Simplifying,
[tex] \sf{ \sin( \theta) = \dfrac{3}{5} = \boxed{ \red{0.6}}}[/tex]
And this is our final answer.....
Carry On Learning !
Zhang is designing protective packaging. He tests his design by dropping a raw egg protected by his packaging from various heights. He finds that the egg is protected up to a height of 11 meters. Zhang needs to convert the height from meters to yards for his report.
Unit of Length
Customary System Units
Metric System Units
1 inch
2.54 centimeters
1 foot
0.3048 meters
1 mile
1.61 kilometers
How many yards can the packaged egg drop without breaking? Use the table to find the answer. Round to the nearest hundredth.
10.06 yards
12.03 yards
18.04 yards
36.09 yards
Answers
Answer:
12.
03
Step-by-step explanation:
eight increased by a number *
O 8n
n - 8
8/n
O
n + 8
Answers
Answer:
n+8
Step-by-step explanation:
"A number" signifies the need for a variable, in this case, n. The keyword increased shows that the operation is addition. So put it together and you get n+8.
Answer:
the answer to it is n + 8. :3
Matt is going to sign up for the "Fruit of the Month Club." He must pay a $25 enrollment fee, as well as $17 each month to continue his membership. He is going to stop receiving fruit once he has spent $280. Write the equation of this problem in Slope-Intercept form (hint: y=mx+b): How much as he spent on fruit after 5 months? In how many months until he has spent $280?
Answers
Answer:
He spent on fruit after 5 months is $110.
In 15 months he spent $280.
Step-by-step explanation:
Fixed pay for membership is $25
And enrollment fee is $17 for each month.
The equation represents this situation is
y= 17 x + 25
He is going to stop receiving fruits once he spent $280.
Now, to find how much he spent on fruit after 5 months is plugin x as 5 into
y=17x+25 for x
y=17(5)+25
y=85+25
y=110 dollars
Now, to find how many months until $280 is to plug in y as 280 then solve the equation for x.
280 = 17 x+25
Subtract both sides 25
255 =17 x
Divide both sides by 17
x= 15 months
Write the relation as a set of ordered pairs.
a ordered pairs: {(-1,-2), (0, 0), (1, 2)}
b. ordered pairs: {(2,-1), (0, 0), (2, 1)}
c. ordered pairs: {(1, 2). (0, 0), (2, 1)}
d. ordered pairs: {(2,-1), (0, 0), (1, 2)}
Answers
Answer:
A
Step-by-step explanation:
Answer:
Option A
Step-by-step explanation:
it's Y over X
I also took this test on edge :)
SOMEONE PLEASE HELP ME IM STRUGGLING ON THIS PROBLEM 7 I NEED HELPPP
Answers
Answer:
B——A for top two
C——D for bottom two
Which of the following shows a translation of f(x) two units down?
Answers
Answer:
f(x) - 2
Step-by-step explanation:
I just took the quiz
. A bakery sells 1,230 cakes during a holiday season. One-third of them are caramel cakes, one-half are chocolate cakes, and the remaining are banana cakes. What is the total amount earned by the bakery by selling the cakes during the holiday season?
Answers
Answer:
See Explanation
Step-by-step explanation:
Given
[tex]Cakes = 1230[/tex]
[tex]Caramel = \frac{1}{3}[/tex]
[tex]Chocolate = \frac{1}{2}[/tex]
[tex]Banana = ??[/tex]
Required
Determine the total amount earned
The given parameters can't be used to determine the total amount earned.
However, we'll make some assumptions
First, we need to solve for the amount of each cake sold
[tex]Caramel = \frac{1}{3}[/tex]
[tex]Caramel = \frac{1}{3} * 1230[/tex]
[tex]Caramel = 410[/tex]
[tex]Chocolate = \frac{1}{2}[/tex]
[tex]Chocolate = \frac{1}{2} * 1230[/tex]
[tex]Chocolate = 615[/tex]
[tex]Banana = 1230 - 410 - 615[/tex]
[tex]Banana = 205[/tex]
Assume that:
Each caramel were sold at x
Each chocolate were sold at y
Each banana were sold at z
[tex]Total\ Amount = 410 * x + 615 * y + 205 * z[/tex]
[tex]Total\ Amount = 410x + 615y + 205z[/tex]
- A quadratic model for a certain stock on Wall Street is P=-3d2 + 50d, where d
represents the days of trading and P is the price per share.
a. What is the maximum price per share of the stock?
Help please I’m stuck
Answers
Answer:
208.333
Step-by-step explanation:
A quadratic model for a certain stock on Wall Street is given by :
[tex]P=-3d^2+50d[/tex] ...(1)
(a) We need to find the maximum price per share of the stock. For maximum value, put :
[tex]\dfrac{dP}{dd}=0[/tex]
[tex]\dfrac{d(-3d^2+50d)}{dd}=0\\\\-6d+50=0\\\\d=\dfrac{50}{6}\\\\d=8.34[/tex]
price per share of the stock is maximum when the value of d = 8.34. Put the value of d in equation (1).
[tex]P=-3(8.34)^2+50(8.34)\\\\P=208.333[/tex]
So, the maximum price per share of the stock is 208.333.
what is the slope of a line perpendicular to the line whose equation is x+y=-1
Answers
Answer:
perpendicular is opposite and reciprocal
Step-by-step explanation:
The slope is -1 and the reciprocal/ perpendicular is 1x
Answer:
the answer is 1
Step-by-step explanation: