Answer:
Two angles whose sides are opposite rays are called vertical angles. Two coplanar angles with a common side, a common vertex, and no common interior points are called adjacent angles.
Further explanation
Adjacent Angles are two angles that share a common vertex, a common side, and no common interior points. They share a vertex and side, but do not overlap. The example is shown in the picture below.
Where ∠1 and ∠2 are adjacent angles, ∠ABC and ∠1 are NOT adjacent angles because ∠ABC overlaps ∠1.
Vertical Angles are two angles whose sides form two pairs of opposite rays (straight lines). Vertical angles are located across from one another in the corners of the "X" formed by the two straight lines. The example is shown in the picture below.
Where ∠1 and ∠2 are vertical angles, ∠3 and ∠4 are vertical angles, Vertical angles are not adjacent. ∠1 and ∠3 are not vertical angles (they are a linear pair) and Vertical angles are always equal in measure.
Step-by-step explanation:
You were elected the student council president for the next year at your school. After vacation is over, you have to plan a school carnival for the new school year. You are studying last year’s event and know that 210 people attended last year’s school carnival. The total amount of money collected for tickets was $710. Prices were $5 for regular admission, $3 for students, and $1 for children. The number of regular tickets sold was 10 more than twice the number of children’s tickets sold. Determine how many of each kind of ticket were sold.
The number of regular tickets are 70, the number of student tickets are 110 and the number of children tickets are 30.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Given that, you are studying last year’s event and know that 210 people attended last year’s school carnival.
The number of regular tickets sold was 10 more than twice the number of children’s tickets sold.
Let the number of children tickets be x.
Then, number of regular tickets be 2x+10
Let the number of student tickets be y.
You are studying last year’s event and know that 210 people attended last year’s school carnival.
x+2x+10+y=210
3x+y=200 --------(I)
The total amount of money collected for tickets was $710.
Now, 5(2x+10)+3y+x=710
10x+50+3y+x=710
11x+3y=660 --------(II)
Substitute y=200-3x in equation (II), we get
11x+3(200-3x)=660
11x+600-9x=660
2x=60
x=30
Substitute x=30 in equation (I), we get
3(30)+y=200
y=110
Number of regular tickets =2x+10
= 70
Therefore, the number of regular tickets are 70, the number of student tickets are 110 and the number of children tickets are 30.
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please answer this question
[tex]\bold{\huge{\underline{ Solution }}}[/tex]
Before answering the given question, you should know the difference between polygon and regular polygon.
Polygon :- It is closed figure constitute of straight line having different measurements and also having varies angles. Regular polygon :- It is also a closed figure constitute of straight lines which having equal measuresment and all the angles of the given polygon are equal .There are different types of polygon based on the sides :-
A polygon having 3 sided called triangle ,having 4 sides called quadrilateral ,having 5 sides pentagon and so on. Let's Begin :-I have thought to make a 4 side polygon that is quadrilateral.
Steps of construction :-
Step - 1 :- Draw a 5 cm line AB horizontally Step - 2 :- Then , From a point B, Draw a Vertical line of 5 cm and named it BC Step - 3 :- Then, From a point C, Draw a horizontal line of 5 cm and named it CD Step - 4 :- Now, join the line AD Step - 5 :- Measure all the angles form by the 4 sides of the quadrilateral.Result :- All the angles are equal that is 90° each.
Conclusion :- The above figure is square as it is having equal sides and angles.
Now, we have to find the sum of the angles of the polygon :-Here,
All angles are equal in measure 90°Therefore,
The sum of the angles of the given polygon
[tex]\sf{ = 90{\degree} + 90{\degree} + 90{\degree} + 90{\degree} }[/tex]
[tex]\sf{ = 180{\degree} + 90{\degree} + 90{\degree} }[/tex]
[tex]\sf{ = 270{\degree} + 90{\degree} }[/tex]
[tex]\sf{ = 360{\degree} }[/tex]
Hence, The sum of the angles of the above polygon is 360° .
if tan=5/12
Find sinx/cosx+tanx
Answer:
[tex] \frac{10}{12} [/tex]
Step-by-step explanation:
given,
tanX = 5/12
sinX/cosX + tanX
= tanX + tanX ( sinX/cosX = tanX)
= 5/12 + 5/12
=
[tex] \frac{10}{12} [/tex]
Step-by-step explanation:
[tex] \tan(x) = \frac{5}{12} \\ \hookrightarrow \: \frac{p}{b} = \frac{5}{12} [/tex]
As,
[tex] \hookrightarrow \: \frac{ \sin(x) }{ \cos(x) } = \tan(x) [/tex]
Now,
[tex] \hookrightarrow \: \frac{ \sin(x) }{ \cos(x) } + \tan(x) \\ \hookrightarrow \: \tan(x) + \tan(x) \\ \hookrightarrow \: \frac{5}{12} + \frac{5}{12} \\ \hookrightarrow \frac{5 + 5}{12} \\ \hookrightarrow \frac{10}{12} [/tex]
A circular "No Parking" road sign has a diameter of 26 inches. Which measurement is closest to the area of the sign in square inches? 81.64 in.² 163.28 in.² 530.66 in.² 2,122.64 in.²
Answer:
530.66 in²
area of circle: πr²
diameter: 26 inradius : diameter/2 = 26/2 = 13 inarea: πr² ⇒ π(13)² ⇒ 530.66 in²
Answer:
pretty sure its 530.66 in.²
Step-by-step explanation:
pls answer the blanks
Answer:
mention the blanks please...if u mention iam ready to answer
find x and y. use proper postulates or theorems to justify your answer
Answer:
x = 110 & y = 28
Step-by-step explanation:
The top and bottom lines are both intersected by a transversal. Because of this, we can say the 100-degree angle is equivalent to the (x-10) angle due to the Corresponding Angles Theorem.
If 100 = x -10 then you add 10 to both sides to get x = 110 degrees.
Then, using the Same Side Exterior Angles Postulate, you can conclude that the 100-angle and the (2y + 24) angle are supplementary, meaning they add up to 180 degrees.
So, 100 + (2y + 24) = 180.
Subtract 100 from both sides to get 2y + 24 = 80
Then subtract 24 from both sides to get 2y = 56
And divide both sides by 2 to get y = 28 degrees.
Which function should be used when evaluating the function at x = -1?
S -x2 + 8x if x < -1
p(x) =
*x? - 4 if x 2-1
O p (x) = {x? - 4
O p(x) = -x2 + 8x
Find the length of a diameter.
22 mm
A diameter of the circle is_____mm
Answer:
44 mm
Step-by-step explanation:
radius = 22 mm
diameter = 2 * radius = 44 mm
Observations of the center of the Milky Way show the presence of a super massive black hole with a mass of 4.6 x 106 solar masses. Compute the Schwarzschild radius of this supermassive black hole. Give your answer in units of astronomical units (AU). At what distance does Mercury orbit from the Sun in AU? If we swapped out the Sun for this super massive black hole, would the event horizon extend beyond the orbit of Mercury? Be sure to show your calculations. 1 AU = 1.5 x 108 km.
The Schwarzschild radius of the black hole depends on its mass
The Schwarzschild radius of this supermassive black holeis 0.091 AU
How to determine the Schwarzschild radius?The Schwarzschild radius (r) is calculated using:
[tex]r_s = \frac{2GM}{c^2}[/tex]
Where:
G = Gravitational constant = 6.67408 × 10-11 m3 kg-1 s-2
M = Mass of the object = 4.6 x 10^6 solar masses
c = Speed of light = 299792458 m / s
Express the mass in Kg
M = 4.6 x 10^6 * 9.2 * 10^18 = 9.15 * 10^36 kg
Substitute the above values in the equation
[tex]r_s = \frac{2 * 6.67408 * 10^{-11} * 9.15 * 10^36}{299792458 ^2}[/tex]
Evaluate the expression
[tex]r_s = 13589425339.6[/tex] m
Express as km
[tex]r_s = 13589425.3396[/tex] km
Expressas AU
[tex]r_s = \frac{13589425.3396}{1.5 * 10^8}[/tex]
Evaluate the quotient
[tex]r_s = 0.09059616893[/tex]
Approximate
[tex]r_s = 0.091\ AU[/tex]
Hence, the Schwarzschild radius of this supermassive black holeis 0.091 AU
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7. The area of the parallelogram is 450 m2. What is
the height?
A. 25 m
B. 36 m
C. 50 m
D. 72m
I am not sure how to do for this question! Pls help
Answer:
wheres the question
Step-by-step explanation:
??????
PLEASE HELP!
The scatter plot shows the number of years of experience, x, and the
amount charged per hour, y, for each of 25 dog sitters in Texas.
(a) Write an approximate equation of the line of best fit for the data. It doesn't have to be the exact line of best fit.
(b) Using your equation from part (a), predict the amount charged per hour by a dog sitter with 18 years of experience.
Answer:
(a) [tex]\sf y=\dfrac{11}{20}x+7[/tex]
(b) $16.90
Step-by-step explanation:
Part (a)
Add a line of best fit (see attached).
Find two points on the line: (7, 0) and (20, 18)
Use these points to find the slope of the line:
[tex]\sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{18-7}{20-0}=\dfrac{11}{20}[/tex]
Use the found slope and one of the points in the point-slope form of the linear equation to find an equation for the line of best fit:
[tex]\sf\implies y-y_1=m(x-x_1)[/tex]
[tex]\sf\implies y-7=\dfrac{11}{20}(x-0)[/tex]
[tex]\sf\implies y=\dfrac{11}{20}x+7[/tex]
Part (b)
Substitute x = 18 into the equation and solve for y:
[tex]\sf\implies y=\dfrac{11}{20}(18)+7=\$16.90[/tex]
Write each expression without the absolute value symbol.
PLEASE HELP
Step-by-step explanation:
| x - 19 + 11 | = | x - 8 |
look at the picture.
The expression without the absolute value symbol is:
|x - 8| = x - 8, if x > 8
|x - 8| = 0, if x = 8
|x - 8| = 8 - x, if x < 8
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
|(x - 19) + 11|
This can be written as,
= |x - 19 + 11|
= |x - 8|
Now,
|x - 8| = x - 8, if x > 8
|x - 8| = 0, if x = 8
|x - 8| = 8 - x, if x < 8
Thus,
The expression without the absolute value symbol is:
|x - 8| = x - 8, if x > 8
|x - 8| = 0, if x = 8
|x - 8| = 8 - x, if x < 8
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(7 point)
13. Amir posts on social media frequently, while Naomi posts rarely. Their number of posts over
the last six days are given in the table below. Compare the spreads of the data sets using both
range and IQR
Amir Naomi
15
2
12
4
14
10
16
2
15
3
19
0
The number of social media post of Noami has a greater spread when compared to that of Amir.
What is the range and intequartile range of the social media posts?Range is the difference between the highest and lowest values of a set of observations
Range = highest value - lowest value
The range of Amir's social media posts = 19 - 15 = 4 The range of Noami's social media posts = 10 - 0 = 10The inter quartile range is the difference between the third quartile and the first quartile of a data set.
IQR = Q3 - Q1
The IQR of Amir's social media posts: 7
The IQR of Naomi's social media posts = 10
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Answer:
Naomi"s data set has more spread since her range is 10 and her IQR is 3.
Step-by-step explanation:
Range IQR
12,14,15,15,16,19 16-14=2
0,2,2,4,5,10 5-2=3
19-12=7 10-0=10
Approximate the temperature of the water after 6 intervals
The time it takes me to wash the dishes is uniformly distributed between 7 minutes and 16 minutes. What is the probability that washing dishes tonight will take me between 8 and 15 minutes?
Answer as a fraction = 7/9 which is exact
Answer in decimal form = 0.778 which is approximate
=========================================================
Explanation:
The time gap from 8 to 15 is 15-8 = 7 minutes.
The time gap from 7 to 16 is 16-7 = 9 minutes.
Divide those differences: 7/9 = 0.778 approximately
The 7's go on forever, but rounding at some point will bump the last 7 to an 8.
If HI = IJ = 14 and GH = 12, what is HJ?
Answer:
24 unitsStep-by-step explanation:
Missing drawing but assumed that:
HI and IJ are equal sides of the isosceles triangle HIJIG is the perpendicular bisector of same triangleSince G is the midpoint of HJ, we have:
GH = GJ = 12So
HJ = 2*GH = 2*12 = 24Answer:
24 units
Step-by-step explanation:
IJ = 14 and GH = 12
Gh=gj=12
Hj=2gh
2*12=24
This recipe makes 4 pancakes.
Sanjay follows the recipe but wants to make 12 pancakes.
How much of each ingredient does he need?
Recipe: Makes 4
135 g flour
1 teaspoon (tsp) baking powder
2 tablespoons (tbsps) sugar
130 ml milk
1 egg
2 tablespoons (tbsps) oil
Answer:
405g of flour, 3 teaspoons baking powder, 6 tablespoons sugar, 390ml of milk and 3 eggs and 6 tablespoons of oil
Step-by-step explanation:
She wants to triple the recipe, so she must multiply each amount of each ingredient by three:
135 × 3 = 405
1 × 3 = 3
2 × 3 = 6
130 × 3 = 390
1 × 3 = 3
2 × 3 = 6
Find measure of <1. (The figure may not be drawn to scale)
Answer:
t = 55
Step-by-step explanation:
The figure is a straight line and the sum of angles that make a straight line is 180 degrees
90 + t+ 35 = 180
125+t = 180
Subtract 125 from each side
125 +t-125 = 180-125
t = 180-125
t = 55
Solve completely (all missing sides and all missing angles) using trig ratios or laws. Round to the nearest tenth.
Answer:
Step-by-step explanation:
3. Use Cosine law to find the length of the unknown side (PR)
q² = p² + r² - 2prCos Q
q is the opposite side of ∠Q;
p is the opposite side of ∠P; p = 33
r is the opposite sides of ∠R ; r = 67
q² = 33² + 67² - 2* 33*67 Cos 19°
= 1089 + 4489 - 4422 * 0.95
= 1089 + 4489 - 4200.9
= 1377.1
q = √1377.1
q = 37.1
PR = 37.1
To find the angle use law of sin
[tex]\sf \dfrac{q}{Sin \ Q} =\dfrac{p}{Sin \ P}\\\\\\\dfrac{37.1}{Sin \ 19}=\dfrac{33}{Sin \ P} \\\\\\\dfrac{37.1}{0.33}=\dfrac{33}{Sin \ P}\\\\\\37.1* Sin \ P = 33 *0.33\\\\Sin \ P =\dfrac{33*0.33}{37.1}[/tex]
Sin P = 0.3
[tex]P = Sin^{-1} 0.3\\[/tex]
P = 17.5°
∠R = 180 - (19 + 17.5)
= 143.5°
Help picture below problem 3
angle ksp+61=108(being straight angle)
or,angle ksp=180-61
angle ksp=119
B.A ECO
(b) Prices of three commodities A, B and Crised by 4096, 60% and 90% respectively.
Commodity A is six times more important than Qy and B is three times more important than
C. what is the mean fise of these three commodities?
multiply the two plynomials
(x + 3)( + 9)
(x + 2)(x + 9)
(x - 8)(x - 6)
im really looking for ways to solve it rather than the solution because it would make my hw alot easier. thanks!
Answer:
1. x² + 12x + 27
2. x² + 11x + 18
3. x² + -14x + 48
Step-by-step explanation:
When you multiply polynomials, you use FOIL.
First
Outer
Inner
Last
For example, to solve the first polynomial (x + 3)(x + 9), you would multiply the first term in each parenthesis to each other. In this case, it would be x · x, which would be equal to x². The next step would be to multiply the first term in the first parenthesis to the last term in the second parenthesis, which are the outer terms. You get 9x when you multiply x by 9. Then, you multiply the inner terms of the polynomial, which is the last term of the first parenthesis and the first term of the second parenthesis. You get 3x. The last part of FOIL is to multiply the last term in each parenthesis to each other. You would multiply 9 and 3 and get 27. Your answer would be x² + 9x + 3x + 27. Simplify the equation to get x² + 12x + 27. That is your final answer. Do the same thing to the other equations to find the answer. (MAKE SURE TO CHECK THE SIGN OF THE TERMS YOU ARE MULTIPLYING FIRST. )
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Point G is on line segment FH. Given FG = 7 and GH = 2, determine the length
FH.
Point G is on line segment FH. Given FG = 7 and GH = 2, the length of line segment FH is 9 units.
The length of line segment FH can be determined by adding the lengths of its two parts, FG and GH.
This is based on the property that the whole length of a line segment is equal to the sum of its parts.
Given that FG = 7 and GH = 2,
we can find the length of FH as follows:
FH = FG + GH
FH = 7 + 2
FH = 9
So, the length of line segment FH is 9 units.
This is a basic principle in geometry where the total length of a segment can be calculated by adding the lengths of its individual parts.
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There is exactly 1 pair of parallel sides. 6 3 9
Answer:
Step-by-step explanation:
The given properties of one pair of parallel sides in the four sided
quadrilateral, indicates that the shape is a trapezium.
Response:
The area of the shape is 35 square unit
Area of trapezoid
1/2(Sum of parallel sides)(Height)1/2(6+9)(3)1/2(15(3))12(45)22.5units^2help is super appreciated this should probably be fast
2. Determine the y – intercept, zeros, the equation of the axis of symmetry and vertex of each quadratic
relation.
y = (x − 3)(x+3)
[tex]\\ \rm\rightarrowtail y=(x-3)(x+3)=x^2-9[/tex]
Zeros are x intercepts
(3,0) U(-3,0)#2
Y intercept=-9#3
Axis of symmetry=x=0
#4
Vertex=(0,-9)Answer:
Given quadratic equation: y = (x - 3)(x + 3)
Zeros (x-intercepts)
The zeros of a quadratic equation are the points where the graph of the quadratic equation crosses the x-axis. So the x-intercepts (zeros) are when y = 0
⇒ (x - 3)(x + 3) = 0
⇒ (x - 3) = 0 so x = 3
⇒ (x + 3) = 0 so x = -3
Therefore, the x-intercepts are at (3, 0) and (-3, 0).
y-intercept
The y-intercept is the point where the graph crosses the y-axis. So the y-intercept is when x = 0
⇒ (0 - 3)(0 + 3) = -9
Therefore, the y-intercept is at (0, -9)
Vertex
Expand the equation so that it is in standard form y = ax² + bx + c:
⇒ y = x² - 9
x-value of vertex is -b / 2a ⇒ -0 / 2 = 0
substitute the found value of x into the equation to find y:
⇒ y = (0)² - 9 = -9
Therefore, the vertex is (0, -9)
Axis of symmetry
Axis symmetry of a quadratic equation is x = a where a is the x-value of the vertex.
Therefore, the axis of symmetry is x = 0
How many times does 8 go into the 12 1/2?
Answer:
1.5625
Step-by-step explanation:
rround to 2
Solve for X and Y
1. y = 2x
6x + 3y = 12
2. y = -4x + 2
y = 6x - 8
3. y = x - 4
-4x - 6y = -16
4. x = 3y + 1
2x + 4y = 12
Answer:
What do you mean?
Step-by-step explanation:
100.2and 19.400 which is greater
Answer:
19.400
Step-by-step explanation:
19.400 equals out to 42769.67886386625
Which of the following is true for the function y = log3(x)?
It is the inverse of the function y = x3.
It is the inverse of the function y = 3x.
It is the reciprocal of the function y = x3.
It is the reciprocal of the function y = 3x.
Answer:
B
Step-by-step explanation:
ED