GEOMETRY
1.) find the value of z and show work
a) Explain the difference in how an inscribed angle and central angle are draw
b) Explain the difference in how their measures compare to the subtended arc.
Answers
Answer:
z = 8.5
Step-by-step explanation:
Let O be the center of the circle, and A, B, C are three points on the circle.
Draw OA and OC are shown in the figure. To make the central angle.
In the figure the measure of arc AC is 118 degrees. measure of central angle and subtrahend arc is same. So, central angle is
[tex]\angle AOC=118^{\circ}[/tex]
Subtended angle on arc AC is
[tex]\angle ABC=(6z+8)^{\circ}[/tex]
According to central angle theorem of circle, central angle is twice of angle subtended by the arc.
[tex]\angle AOC=2\times \angle ABC[/tex]
[tex]118^{\circ}=2\times (6z+8)^{\circ}[/tex]
[tex]118=12z+16[/tex]
[tex]118-16=12z[/tex]
[tex]102=12z[/tex]
[tex]\dfrac{102}{12}=z[/tex]
[tex]8.5=z[/tex]
Therefore, the value of z is 8.5.
Related Questions
Find the legs of a 30° -60°-90° triangle whose hypotenuse is:
10 in.
PLEASE ANSWER ASAP IM really STRUGGLING!!
Answers
You use Pythagoras' Theorem and the theorem of 30-60-90 triangle
Jose unlocks his cellphone by placing his right thumb on a square of 1 centimeter by 1 centimeter at the center of the screen. Upon recognizing his thumbprint, the square expands outward. The cellphone unlocks when the perimeter reaches 32 centimeters, taking a total of 2.5 seconds. What is the perimeter of the square after 1.5 seconds?
Answers
Answer: 20.8 cm
Step-by-step explanation:
Notice that the corners of the squares form a line.
Set the x-axis to time and the y-axis to length of a side (not perimeter) to create coordinates.
At 0 seconds the side length is 1 --> (0, 1)
At 2.5 seconds the perimeter is 32 (side length is 32/4 = 8) --> (2.5, 8)
First, find the slope between the coordinates using [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Let (x₁, y₁) = (0, 1) and (x₂, y₂) = (2.5, 8)
[tex]m=\dfrac{8-1}{2.5-0}\quad =\dfrac{7}{2.5}\quad =\dfrac{7}{\frac{5}{2}}\quad =\dfrac{14}{5}\quad =2.8[/tex]
Next, use the Point-Slope formula to find the equation of the line:
[tex]y-y_1=m(x-x_1)\\\\y-1=2.8(x-0)\\\\y=2.8x+1[/tex]
Lastly, find the side length (y) when x = 1.5
y = 2.8(1.5)x + 1
= 4.2 + 1
= 5.2
Perimeter of a square = 4 times the side length
P = 4(5.2)
= 20.8
Kabir wants to know the volume of a solid right pyramid with a square base.
Answers
The side length of each square is 6 units. Find the areas of the inscribed shapes.
Answers
Answer:
a) 18
b) 20
c) 12
d) 12
Step-by-step explanation:
a) The triangle is half of the square, so you can find the area of the square(36) and divide by 2: so 18
b) There are 4 same sized blank triangles with area of 4 ( (2*4)/2 ) so 4 * 4 is 16. 16 is the blank area so the area of the shaded is 36 - 16: 20
c) There are 2 blank triangles which areas are 6, and 18, so you subtract those numbers from 36: 36 - (6+18) = 12
d) Another 2 same blank triangles with areas of 12 ( (6 *4)/2 )so you subtract them from 36 too: 36 - (12*2) = 36 - 24 = 12
Help help help help help
Answers
for example with 4-6a
you would put 4 = 2•2 so 2 is it’s GCF
and 6= 3•2 so 3 is it’s GCF
however the question is asking for the combined GCF (meaning the whole problem)
so 4-6a’s GCF would be 2 considering it is the only greatest common factor between BOTH numbers
for 12a^2 - 8a you would use the same method:
12a^2= 3a•2a•2 and 3a is it’s GCF
8a = 2•2•2a and 2a is it’s GCF
but combined, the greatest factor BOTH numbers have in common is 2a, so 2a is the answer!
i hope i helped you :)!❤️
The monthly membership fee for a social club is $10.00. A member is charged an additional fee whenever he or she participates in a social event organized by the club. The additional fee for participation is $35.00 per event. For one month, Amanda was charged $115.00. In how many social events did Amanda participate during the month?
Answers
The number of social events will be 3.
What is an expression?Numeral variables and operations marked by the signs for addition, subtraction, multiplication, and division are combined in the mathematical equation.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented using mathematical symbols. They can also signify other characteristics of logical grammar, such as the operation order.
Given that a social club's monthly membership cost is $10. Every time a member takes part in a social event that the club hosts, a separate cost is applied. A $35.00 participation fee is charged for each event. Amanda was charged $115.00 for a month.
The number of events will be calculated as follows:-
TC = 10 + 35N
115 = 10 + ( 35 x N)
N = ( 115 - 10 ) / 35
N = 105 / 35 = 3
Therefore, the number of social events will be 3.
To know more about an expression follow
https://brainly.com/question/9390127
#SPJ2
HELP MEEEEEEE please
Answers
Answer:
scale factor = [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Consider the ratio of corresponding sides, image to original, that is
scale factor = [tex]\frac{T'V'}{TV}[/tex] = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]
Factor this polynomial expression, and wrote it in its fully factored form 3x^3 + 3x^2 - 18x
Answers
Answer:
fourth option
Step-by-step explanation:
Given
3x³ + 3x² - 18x ← factor out 3x from each term
= 3x(x² + x - 6) ← factor the quadratic
Consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term (+ 1)
The factors are + 3 and - 2, since
3 × - 2 = - 6 and 3 - 2 = + 1, thus
x² + x - 6 = (x + 3)(x - 2) and
3x³ + 3x² - 18x = 3x(x + 3)(x - 2) ← in factored form
I need the answer now
Answers
Answer:
i) TRUE
ii) TRUE
iii) TRUE
Step-by-step explanation:
[tex](ab+bc)(ab-bc)+(bc+ca)(bc-ca)+(ca+ab)(ca-ab)=\\\\=\underline{(ab)^2}-(bc)^2\ \,+\ \,(bc)^2-(ca)^2\ \,+\ \,(ca)^2-\,\underline{(ab)^2}=\\\\=0+0+0=0[/tex]
[tex](a+b+c)(a^2+b^2+c^2-ab-bc-ca)=\\\\=a^3\,\underline{\,+ab^2}\ \underline{\underline{+\,ac^2}}\,-a^2b\ -\,abc\ \underline{\underline{\underline{-\,a^2c}}}+a^2b+b^3+bc^2\,\underline{-\,ab^2}\ \underline{\underline{\underline{ \underline{-\,b^2c}}}}\,-\,abc+\\{}\qquad\qquad\qquad\qquad\qquad\qquad \qquad\qquad \underline{\underline{ \underline{+\,a^2c}}}\ \underline{\underline{\underline{\underline{+\,b^2c}}}}+c^3\,-\,abc-bc^2\ \underline{\underline{-c^2a}}=[/tex]
[tex]=a^3\ \underline{-\,a^2b}\ \underline{\underline{-\,abc}}\ \underline{+\,a^2b}+b^3\ \underline{\underline{\underline{+\,bc^2}}}\ \underline{\underline{-\,abc}}+c^3\ \underline{\underline{-\,abc}}\ \underline{\underline{\underline{-\,bc^2}}}=\\\\=a^3+b^3+c^3-3abc[/tex]
[tex](p-q)(p^2+pq+q^2)=\\\\=p^3\ \underline{+\,p^2q}\ \underline{\underline{+\,pq^2}}\ \underline{-\,p^2q}\ \underline{\underline{-\,pq^2}}-q^3=\\\\=p^3-q^3[/tex]
Answer: see proofs below
Step-by-step explanation:
7i) (ab + bc)(ab - bc) = a²b² - ab²c + ab²c - b²c² → a²b² - b²c²
+ (bc + ca)(bc - ca) = b²c² - abc² +abc² - a²c² → b²c² - a²c²
+ (ca + ab)(ca - ab) = a²c² - a²bc + a²bc - a²b² → a²c² - a²b²
= a²b² + 0 + 0 - a²b²
= 0
7ii) a(a² + b² + c² - ab - bc - ca) = a³ + ab² + ac² - a²b - abc - a²c
+ b(a² + b² + c² - ab - bc - ca) = b³ - ab² + bc² + a²b - abc - b²c
+ c(a² + b² + c² - ab - bc - ca) = c³ - ac² - bc² - abc + a²c + b²c
= a³ + b³ + c³ + 0 + 0 + 0 + 0 - 3abc + 0 + 0
= a³ + b³ + c³ - 3abc
7iii) p(p² + pq + q²) = p³ + p²q + pq²
-q(p² + pq + q²) = - p²q - pq² - q³
= p³ + 0 + 0 - q³
= p³ - q³
Jules adds a border around his mirror. The mirror is shaped like a triangle. Each side is 35\,\text{cm}35cm35, start text, c, m, end text long. How long is the border?
Answers
Answer:
105 m
Step-by-step explanation:
Given that Jules has a mirror that has a shape of a triangle, the length of the border Jules would add = the perimeter of the triangular mirror.
The perimeter of the triangular mirror is simply the sum of all the 3 sides of the triangle.
Since, each side is of equal length (35 cm), therefore, perimeter of the mirror = 35 + 35 + 35 = 105 m
Perimeter of mirror = length of border to add = 105 m
The border is 105 m long.
The speed at which a bike travels can be determined by the formula s=d/t, where S represents speed, D represents distance, and T represents time. Select yes or no to indicate if the measurement unit given is an appropriate measurement unit for the speed at which a bike travels
Answers
Answer:
Yes, No, Yes
Step-by-step explanation:
Yes for m/s which is meters per second.
No for min/ft which is reversed and should be feet per minute.
Yes for km/h which is kilometers per hour.
The correct unit for speed is distance per time.
Answer:
MPH
Step-by-step explanation:
A small airplane can fly 12 miles in 3 minutes. At this rate, how far can the airplane fly in 1 hour?
Answers
Answer:
The airplane can fly up to 240 miles in a hour
Step-by-step explanation:
Cross multiply
(12)(60)=3x
720=3x
Divide 3 on both sides
x=240
There are 60 minutes in 1 hour.
60 ÷ 3 = 20
12 × 20 = 240
In one hour, the airplane could fly at 240 miles.
If the m1 = 40, what is the m 3
Answers
Explanation:
m1 = 40
m3 = 40 x 3
m3 = 120
Answer:
Your Answer is 120Step-by-step explanation:
m1=40
Taking m3
m3=40 ×3
m3= 120
Hope It helps UA man is 26 years older than his son. He is also 8 years older than three times his son’s age. Find the son’s age. A. 9 years B.10 years C. 12 years D. 14 years
Answers
Answer:
9 years
Step-by-step explanation:
hope it helps the
the explanation is kinda long
Select the correct answer.
Which table shows a proportional relationship between x and y?
x y
1
5
2
6
3
7
x y
2
3
4
6
6
9
x y
4
16
8
64
12
144
x y
1
3
2
9
3
27
Answers
Answer:
I think
x y
2
3
4
6
6
9
Step-by-step explanation:
but i don't see any table
What is the vertex of the quadratic equation below? y=x^2-8x+1 Explanation?
Answers
To find the vertex, you need to find the axis of symmetry first.
In order to find the axis of symmetry we have to do -b/2a.
In our case, the b is -8 and the a is 1.
Plug it in.
-(-8)/2(1)
8/2 = 4
Our axis of symmetry is 4.
Now, we plug it into the equation to find the rest of the vertex.
y = 4^2 - 8(4) + 1
y = 16 - 32 + 1
y = -16 + 1
y = -15
Put it together.
Our vertex is (4,-15).
2.) Calculate x, to the nearest tenth of a meter
Answers
Answer:
63.4°
Step-by-step explanation:
The following data were obtained from the question:
Opposite = 6 cm
Adjacent = 3 cm
Angle x =?
The value of angle x can be obtained as follow:
Tan x = Opposite/Adjacent
Tan x = 6/3
Tan x = 2
Take the inverse of Tan.
x = Tan¯¹ 2
x = 63.4°
Therefore, the value of angle x is 63.4°
Answer:
63.4°
Step-by-step explanation:
plzzz helpp ASAP 1. Why is it important to know what the limitations of a particular model are? A. so you can create a prototype based on your model B. so you don't make the mistake of confusing an object and a system C. so you can revise your model to represent every property of the real thing D. so you don't confuse properties of the model with properties of the real thing
2. Mathematical and computer models are similar because both involve _____. A. using calculations to represent an object or system B. comparisons between an object or system and something familiar C. building a complex object or system isolated from the natural world D. creating real-life objects that show features of the modeled object or system
3. Some models can illustrate a system. What does the term system refer to? A. a collection of interacting things B. a set of rules or laws about things C. something with advantages and limitations D. something illustrating parts of a real-life thing
4. J.J. Thomson's Plum Pudding Model is an example of _____. A. a picture B. an analogy C. a prototype D. a mathematical model
5. An advantage of describing a cell as being like a factory is that it _____. A. makes cells easier to understand B. shows the limitations of cells clearly C. prevents having to study the complexities of cells D. is cheaper to do experiments in a factory than on a cell
6. Scientists like using models because they are often _____ than the real thing. A. more accurate B. more enjoyable to study C. cheaper and more complex D. cheaper and easier to work with
7. An advantage of J.J. Thomson's Plum Pudding Model was that it _____. A. was a much less expensive way to study atoms B. simplified the calculations necessary to describe an atom C. clearly explained where electrons were located in an atom D. is much less expensive to bake a plum pudding than to look at an atom
8. A small clay model of a volcano is an example of _____. A. an analogy B. a prototype C. a physical model D. a computer model
9. An advantage of using a model instead of the real thing is that models _____. A. include better detail B. can be easier to change C. are much more interesting to study D. don't include any features of the real thing
Answers
Answer:
D. so you don't confuse properties of the model with properties of the real thing.
2-Mathematical and computer models are similar because both involve using calculation to represent an object or system
3- Some models can illustrate a system. What does the term system refer to
A. a collection of interacting things
4-J.J. Thomson's Plum Pudding Model is an example of _____B. an analogy
5. An advantage of describing a cell as being like a factory is that it _____
A. makes cells easier to understand
6- C. cheaper and more complex
7-C. clearly explained where electrons were located in an atom
8-C. a physical model
9-B. can be easier to change
GOOD LUCK
52.85 rounded to the nearest tenth
Answers
Answer: 52.9
Step-by-step explanation:
The value 5 is rounded up.
Hope it helps <3
Answer:
52.9
Step-by-step explanation:
round up using the last number. since its 5, you round up
. Factorize a² +3ab - 5ab - 15b²
Answers
Answer:
a² +3ab - 5ab - 15b² = (a+3b) (a-5b)
Step-by-step explanation:
We need to factorize a² +3ab - 5ab - 15b². Firstly we need to rearrange the expression such that,
[tex]a^2-5ab+3ab-15b^2=(a^2-5ab)+(3ab-15b^2)[/tex]
Now taking a common from the first two terms and 3b from last two terms, then :
[tex](a^2-5ab)+(3ab-15b^2)=a(a-5b)+3b(a-5b)[/tex]
In the above expression, a factor (a-5b) is in both the terms. It would mean that,
[tex]a(a-5b)+3b(a-5b)=(a+3b)(a-5b)[/tex]
So, the factors of a² +3ab - 5ab - 15b² are (a+3b) (a-5b).
what is a measure ∠x
Answers
Answer:
x = 138
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the opposite interior angles
x = B+ C
x = 68+ 70
x =138
Answer:
138 degrees
Step-by-step explanation:
A triangle is made up of 180 degrees, it lists 2 values already, 68&70. when added that equals 138.
So 180-138 is 42 degrees, which would be the last angle within the triangle.
Since a line is also 180 degrees, its 180-42, which makes x 138 degrees
Hope is the coach of the Wilson High School girls' soccer team. There are 3 minutes left in the game they are currently playing, and they are losing by 1 goal. In the past, when losing by 1 goal, Hope has pulled a defender out of the game and replaced her with a forward a total of 9 times. When in the same position, she has left the defender in the game 10 times. In the situations when Hope has pulled her defender, the team has lost 4 times, tied 2 times, and won 3 times. In situations when she has left her defender in the game, the team has lost 1 time, tied 3 times, and won 6 times. Based on the information above, if the goal is to either tie or win the game, should Hope pull the defender or leave her in the game?
Answers
Answer:
Hope should not pull her defender.
Step-by-step explanation:
When Hope has pulled her defender:
The team had lost 4 times, tied 2 times, and won 3 times.
Hence, the total number of times she meets her goal is:
6 times (Since the goal is to either tie or win the game )
Hence, the probability that she meets her goal is = 6/9=2/3=0.66
When she left her defender in the game:
The team has lost 1 time, tied 3 times, and won 6 times.
Hence, the total number of times she meets her goal is: 9
Hence, the probability that she meets her goal is: 9/10=0.9
As the probability of meeting her goal is more when she left her defender in the game is more.
Hence, Hope should not pull her defender.
6 root 5 plus 6 root 5
Answers
Answer:
12√5
Step-by-step explanation:
6√5 + 6√5 = (6 + 6) * √5 = 12 * √5 = 12√5.
Answer:
12 [tex]\sqrt{5}[/tex]
Step-by-step explanation:
When you add the surds which are the same type, (both are root 5), just add the integers before them together.
Which property justifies this statement?
If x=3, then x−3=0.
Answers
Answer:
Step-by-step explanation:
identitiy property
How much material would you need to fill the following cylinder? Radius 13 in. and Height 9 in.
39π in3
117π in3
1053π in3
1521π in3
Answers
Answer:
1521 pi in^3
radius x radius x height x pi = volume
13 x 13 x 9 = 1521
We do not multiply by pi because it is already included
Hope this helps
Step-by-step explanation:
Factor .
X2-x-56=0
PLEASE HELP!!!
Answers
Answer:
use factoring x (see attachment)
-8 x 7 = -56
-8 + 7 = -1
(x - 8)(x + 7) = 0
x = 8, -7
hope this helps :)
Please answer this in two minutes
Answers
Answer:
20/29
Step-by-step explanation:
SOH CAH TOA
so its opposite/hyp...
20/29
is the answer
Pam works as an office administrator. She spends $7500 of her income on personal expenses each year. If this represents 18% of her salary, how much money does Pam earn in one year? Round your answer to the nearest whole dollar.
Answers
Answer: Pam earns $41,667 in one year.
Step-by-step explanation:
Hi, to answer this question we have to write an equation:
Pam's salary (x) multiplied by the percentage represented by expenses (18%) in decimal form (divided by 100) must be equal to $7500.
Mathematically speaking:
x (18/100) = 7500
Solving for x:
x (0.18) = 7500
x = 7500/0.18
x = 41,667
Pam earns $41,667 in one year.
Feel free to ask for more if needed or if you did not understand something.
Here are two sets of cards.
X has the same value on both cards.
Each set of cards has a range of 4.
Work out the value of X
Answers
Answer:
3
Step-by-step explanation:
In Set A, the minimum is 4 and the maximum is 7 without X which would make the range 7 - 4 = 3 but we want the range to be 4, therefore X has to be 4 + 4 = 8. Unfortunately, this would then make the range of Set B 8 - 1 = 7 so X has to be the smallest number in Set A which would be 7 - 4 = 3.
THE LANDSCAPER IS PLANTING A TREE THAT IS NOW 55 CM TALL. THE TREE WILL GROW 4 CM PER MONTH FOR X MONTHS. THE TREE WILL GROW TO BE AT MOST Y CM TALL. WRITE AN INEQUALITY SHOWING THIS RELATIONSHIP.
Answers
Answer: 55cm + X*4cm < Y.
Step-by-step explanation:
The initial height of the tree is 55cm
The tree will grow 4cm per month, for X months.
then the height of the tree is the initial height, plus X times 4cm
H = 55cm + X*4cm
If Y is the maximum height that this tree can grow, then we can write the inequality as:
H < Y.
55cm + X*4cm < Y.