Answers
The measures of the angles are:
m<7 = 47°
m<8 = 62°
m<1 = 62°
m<2 = 71° [vertical angles theorem]
m<5 = 109°
m<3 = 109°
m<4 = 35°
m<6 = 29°
What is the Alternate Interior Angles Theorem?The alternate interior angles theorem states that two interior angles that are formed along a transversal and lie alternate to each other on two parallel lines are congruent to each other.
Measure of angle 7 = 47° [based on the alternate interior angles theorem]
Measure of angle 8 = 180 - 47 - 71 [triangle sum theorem]
Measure of angle 8 = 62°
Measure of angle 1 = measure of angle 8 = 62° [based on the alternate interior angles theorem]
Measure of angle 1 = 62°
Measure of angle 2 = 71° [vertical angles theorem]
Measure of angle 5 = 180 - 71 [linear angle theorem]
Measure of angle 5 = 109°
Measure of angle 3 = measure of angle 5 = 109° [vertical angles theorem]
Measure of angle 4 = 180 - measure of angle 3 - 36 [linear angle theorem]
Measure of angle 4 = 180 - 109 - 36
Measure of angle 4 = 35°
Measure of angle 6 = 180 - measure of angle 5 - 42 [linear angle theorem]
Measure of angle 6 = 180 - 109 - 42
Measure of angle 6 = 29°
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Related Questions
The displacement (in meters) of a particle moving in a straight line is given by s=6t^3+1t+4 where t is measured in seconds.
Find the velocity of the particle at the times given.
Velocity at time t=1, t=2, t=3, and t=a
Answers
Answer:
Velocities
t = 1 : 11 m/s
t = 2 : 27m/s
t = 3: 56.33 m/s
t = a: 6a + 1 + 4/a m/s
Step-by-step explanation:
s(t) = 6t³ + 1t + 4 where s = displacement in meters and t is time in seconds
s(t) = v(t). t where v is the velocity in m/s and t is time in seconds
So v = s/t
At time t = 1
s(1) = 6 x 1³ + 1 x 1 + 4 = 6 + 1 + 4 = 11 meters
v(1) = 11/1 = 11 m/s
At time t = 2
s(2) = 6 x 2³ + 1 x 2 + 4 = 6 x 8 + 2 + 4 = 48+ 2 + 4 = 54 m
v(2) = 54 /2 = 27m/s
At time t = 3
s(3) = 6 x 3³ + 1 x 3 + 5 = 6 x 27 + 3 + 4 = 169 m
v(3) = 169/3 = 56.33 m/s
At time t = a
s(a) = 6a³ + 1a + 4 = 6a³ + a + 4
v(a) = s(a)/a = (6a³ + a + 4)/a = 6a + 1 + 4/a m/s
if p/q=r/s then (p+q)/(r+s) is
Answers
if p/q=r/s then (p+q)/(r+s) is Ratio and proportion
(p+q)/(r+s)=q
Given,
p/q=r/s
ps=rq
p=rq/s
Putting these value of (p+q)/(r+s) is q
The ratio is used to compare two amounts of the same type. For two numbers, a and b, the ratio formula is written as a: b or a/b. The ratio and proportion concepts are based on fractions. Ratio and proportion are the fundamental building blocks for many other notions in mathematics. Ratio and proportion are useful in addressing many everyday difficulties, such as comparing heights, weights, distance, or time, or when combining ingredients in cookery, and so on.
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1. How much of the original cake has not been shared
after the first division of the cake? How much of the
original cake has not been distributed after the fourth
division?
2.write a series that represents the amount of the original cake each person has after the fourth division.
3.how much of the original cake will each person have after the fourth division
4. Suppose you continue this process indefinitely. How much of the original cake will each of you receive?
Answers
The cake sharing process of the process using geometric progression gives the following values;
1. The amount of the cake left after the first division is one quarter of the cake
The amount of cake remaining after the fourth division is 1/256 of the original cake
2. The series is; (1/4 + 1/16 + 1/64+ 1/256 + 1/1024) of the original cake
3. 341/1024 of the original cake
4. If the process continues indefinitely each person gets (1/3) of the original cake
What is a geometric progression?A geometric progression is a sequence of numbers such that a term is found from the previous term by multiplying the previous term by a constant number.
1. Taking the dimensions of the cake as a square, let x represent the side length of the cake, we have;
Amount of cake left after the first division = x/4
The amount of the cake left after the first division is one quarter of the cakeAmount left after the second sharing = x/(4×4) = x/16
Amount left after the third division = x/(4×4) = x/(16×4) = x/64
Amount left after the fourth division = x/(64×4) = x/256
The amount of cake remaining after the fourth division is 1/256 of the original cake2. After the fourth division, each person receives x/(256×4) = x/1024
The series that represents the amount each person receives after the fourth division is therefore;
(1/4 + 1/16 + 1/64+ 1/256 + 1/1024) of the original cake3. The amount of the original cake each person gets after the fourth division is therefore;
1/4 + 1/16 + 1/64+ 1/256 + 1/1024 = 341/1024 of the original cake4. The amount each person receives is given by the sum of a geometric series up to infinity, where;
The first term, a = 1/4
The common ratio, r = 1/4
S = (1/4)/(1 - (1/4)) = (1/4)/(3/4) = (1/4)×(4/3) = 1/3
The amount of the original cake each gets if the process continues indefinitely is (1/3) of the original cake.
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Please help with work shown (Geometry)
Answers
Answer:
RS= 45
Step-by-step explanation:
According to the rules of the triangle...
RS = RQ
226 divided by 896451
Answers
what line is perpendicular to the line passing through the points (-4, 2) and (4, -1)
Answers
The line that is perpendicular to the line passing through the points (-4, 2) and (4, -1) is y = (8/3)x + 1/2
Equation of a lineFrom the question, we are to determine the equation of the line that is perpendicular to the line passing through the given points
First, we will determine the equation of the line passing through the given points
The given points are (-4, 2) and (4, -1)
Using the formula,
(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)
x₁ = -4
y₁ = 2
x₂ = 4
y₂ = -1
Thus,
(y - 2)/(x - -4) = (-1 - 2)/(4 - -4)
(y - 2)/(x + 4) = (-3)/(4 + 4)
(y - 2)/(x + 4) = (-3)/(8)
8(y -2) = -3(x + 4)
8y - 16 = -3x -12
8y = -3x -12 + 16
8y = -3x + 4
y = -(3/8)x + 1/2
Now,
NOTE: A line perpendicular to another has a slope that is the negative reciprocal of the slope of the other line
In the above equation,
The slope of the line is -3/8
∴ The slope of the line that is perpendicular to the line will be 8/3
Thus,
The equation of the line will be y = (8/3)x + 1/2
Hence, the line that is perpendicular to the line passing through the points (-4, 2) and (4, -1) is y = (8/3)x + 1/2
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A car is driving at 45 kilometers per hour. How far, in meters, does it travel in 5 seconds?
Answers
The car travels 62.5 meters in 5 seconds
How to calculate the distance the car travelled ?
The car is driving at 45 kilometres per hour
The first step is to convert kilometres to meters
1 km= 1000 meters
= 45×1000
= 45,000
The next step is to convert hours to seconds
1 hour= 3600 seconds
= 45000/3600
= 12.5
The distance travelled in 5 seconds can be calculated as follows
= 12.5 × 5
= 62.5
Hence the distance travelled in 5 seconds is 62.5 meters
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Which of the following is the point and slope of the equation y - 8 = 4(x + 3)? a. (8, -3), 4 b. (3, -8), 4 c. (-8, 3), 4 d. (-3, 8), 4
Answers
Answer:
d
Step-by-step explanation:
This is point-slope form, and these coordinates make both sides equal to 0.
jijuygtfrdw34w2dddggjhtfexer34dutkeiritnty88
Answers
Answer:
The answer is 7.
-1-(-8)
Subtracting a negative number from a negative number (-) a minus sign followed by a negative sign, turns the two signs into a plus sign.
^ I forgot what I was trying to prove.
Given mn, find the value of x.
(2x-16)°
(4x+4)°
Answers
Answer:
x = 32
Step-by-step explanation:
Since m||n and the angles formed are on the same transversal, the angles are corresponding angles i.e. their sum adds up to 180°
Using given data
2x - 16 + 4x + 4 = 180
==> 6x - 12 = 180
==> 6x = 180 + 12 (by adding 12 on both sides)
==> 6x = 192
x = 192/6
x = 32
Solve the equation for v.
v over 4 minus 2 equals negative 10
v/4 - 2 = -10
v = −32
v = −48
v = 12
v = 38
Answers
Answer:
the answer is v = -32
Step-by-step explanation:
where
v/4 - 2 = -10
v/4 = -10 + 2
v/4 = -8
v = -8 × 4
v = -32
hope this helps
Answer: The answer for this question is v = -32
Step-by-step explanation: just do math.
Use additive inverse and their properties to find equivalent expressions 3+(-5)
Answers
The additive inverse of the given mathematical operation 3+(-5) is 2.
What is additive inverse?An additive inverse of a number is defined as the value that results in zero when added to the original number. It is the value we add to a number in order to get zero. If an is the original number, then its additive inverse is minus a, i.e., -a, such that a+(-a) = a - a = 0. 2 2 is the additive inverse of -2.So, 3+(-5):
3+(-5)-2Then, add 2 as follows:
-2 + 2 = 0Therefore, the additive inverse of the given mathematical operation is 2.
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Point G is the midpoint of segment FH. GH= 16x-19 and FG=12x+9. Find GH
Answers
The value of GH is 93.
Given,
Point G is the midpoint of segment FH.
GH= 16x-19 and FG=12x+9.
We need to find GH.
What is a midpoint?If there is a midpoint between two points the midpoint divided the line between two points into two equal lengths.
Example:
A ________B__________C
AB = BC
We have,
F_______G_______H
G is the midpoint.
GH= 16x-19
FG=12x+9.
FG = GH
16x-19 = 12x+9
16x - 12x = 9 + 19
4x = 28
x = 7
Now,
GH = 16x - 19
= 16 x 7 - 19
= 112 - 19
= 93
Thus the value of GH is 93.
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I will mark brainliest
Answers
Answer:
The 3rd one
Step-by-step explanation:
My mom is a teacher lol
the product of 2.5 and t. to a algebraic expressions
Answers
To an algebraic expression, the product of 2.5 and t is 2.5*t=2.5t.
An algebraic equation is what?In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.).
Terms comprise expressions.
As said, "The word product" refers to the result of a multiplication.
To find out which two integers are multiplied together, look for the term "AND." The result of adding 2 and 3 is 6
The two numbers being multiplied in this example are 2.5 and an unidentified number, only called t.
The formula is 2.5*t
= 2.5t.
We are at our limit at this point. Since the solution has not been provided, we are unable to write an equation.
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12. A private corporation owned by 35 shareholders is worth $1.7 million.
The corporation loses a lawsuit worth $3 million. What is the value
of any personal property of the shareholders that can be taken to pay
the settlement? Explain.
vo sv.
wested... the
od oqually by 13 partners is worth $1.3 million.
Answers
Final answer : Shareholders' personal property cannot be taken to settle the company
Definition : A company is treated as a person with the legal capacity to enter into a contractual obligation, own properties, sue or be sued. A company uses a common seal as its signature and any documents bearing company seal are legally enforceable.
Given Data:
A private corporation owned by 35 shareholders is worth $1.7 million.
The corporation loses a lawsuit worth $3 million.
To find :
What is the value of any personal property of the shareholders that can be taken to pay the settlement?
Solution:
shareholders' liability is limited.
A shareholder cannot lose more than the value of stock owned in a company.
Shareholders' personal property cannot be taken to settle the company obligation because a company is a different entity from its shareholders.
Main Answer : Shareholders' personal property cannot be taken to settle the company
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evavluate the limit, lim x→−8 (4x − 6)
Answers
Answer: -38
Step-by-step explanation:
lim x→−8 (4x − 6)=
4(-8) − 6=
-32-6=
-(32+6)=-38
Help.........................................
Answers
Answer:
the bottom left graph is a function
Step-by-step explanation:
for questions like this pertaining a graph, you can use the vertical line test. essentially for a function, an x value cannot have multiple y values. so, the function cannot have any two or more points that lie on the same vertical line.
the top left graph is literally a vertical line, so that doesn't work
the top right is a circle. draw a vertical line and you see it always intersects two points
the bottom right graph draw a vertical line. two points again, right?
only the bottom left works with the vertical line test.
Can someone help with this problem?✨
Answers
this function is increasing from (2, 4)
this function is decreasing from (negative infinity, 2) and (4, infinity)
the domain is all real numbers or (negative infinity, infinity)
the range is all real numbers or (negative infinity, infinity)
Aunt rose baked 2 1/2 dozen cookies. Her grandson, ricky ate _ of them. How many cookies did rocky eat?
Answers
Dji manufactured the Mavic air 2 quadcopter and offered a 10/8/7 chain discount to primary customers. Drone nerds is a primary customer and ordered 15 mavic Air2's for a total $23,500 list price
Answers
The price of the DJI Mavic Air2 drones after the chain discount is applied will be $18,095.94.
What is the chain discount?An assortment of trade discount rates or their sum is referred to as a chain discount.
DJI produced the Mavic Air 2 quadcopter and gave its top clients a 10/8/7 chain discount. The company's main client, Drone Nerds, bought 15 Mavic Air2 drones for a total of $23,500 list price.
Then the price of the DJI Mavic Air2 drones after the chain discount is applied will be
⇒ $23,500 x 0.90 x 0.92 x 0.93
⇒ $18,095.94
The price of the DJI Mavic Air2 drones after the chain discount is applied will be $18,095.94.
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A prize is divided into the ratio 5:3 if the difference between the shares is £42 what is the total price?
Ty for helping :)
Answers
Answer:
£168
Step-by-step explanation:
Let the total prize be 8x, then the two prizes will be 5x and 3x.
Then, difference between the prizes = 2x
=> 5x - 3x = £42
=> 2x = £42
=> x = £42/2
=> x = £21
As mentioned above, the total prize is 8x.
So, total prize = 8 × x = 8 × £21 = £168
Factor the expression by factoring out the greatest common factor
32z18+8z11+12z7=
Answers
I am assuming this is 32z^18 + 8z^11 + 12z^7.
The highest exponent you can factor from each of the terms is z^7 and the highest constant is 4 (as it is a factor of 32, 8, and 12).
Write this like:
4z^7 (8z^11 + 2z^4 + 3) = 0
help please i need it
Answers
Answer:
You need 7 strawberries to make 1 cup of smoothy
so that means 21 strawberries for 3
and 10 smoothies need 70 strawberries
Find the GCF of the two numbers, and rewrite the sum of the two numbers using the distributive property.
12 + 18
Answers
Answer:
GCF = 6
The original sum rewrites to 6(2+3)
=================================================
Explanation:
Notice we have these factorizations
12 = 6*2
18 = 6*3
Which shows that 6 is the greatest common factor (GCF)
So,
12+18 = 6*2+6*3 = 6*(2+3)
We use the distributive property which is a(b+c) = ab + ac
I'll leave the 2+3 part un-simplified so that you can see the two original pieces, and how the 6 can multiply with them both to get back to 12+18 again.
A pattern defines the relationship between the first two terms. Determine the relationship and identify the missing term of the second pair, such that both pairs are analogous. AGD : EKH :: IOL :
Answers
The missing term of the second pair, such that both pairs are analogous is WKPA.
How to explain the information?For the first two terms, S is 1 letter before Q,
For the first two terms, S is 1 letter before Q,F is 1 letter before D,
For the first two terms, S is 1 letter before Q,F is 1 letter before D,Y is next to X,
For the first two terms, S is 1 letter before Q,F is 1 letter before D,Y is next to X,N is next to FM.
For the first two terms S is 1 letter before Q,F is 1 letter before D,Y is next to X ,N is next M.Similarly, UIOZ : WKPA. Where W is 1 letter before U,K is 1 letter before I, O is next to P,Z is next A.
Therefore, the correct option is D.
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Refer to the terms given below. There is a pattern that defines the relationship between the first two terms. Determine this relationship and then identify the missing term of the second pair, such that both the pairs are analogous. QDXM : SFYN :: UIOZ : 1) PAQM 2) LPWA 3) QNLA 4) WKPA
The test scores for 9 students on the Unit 1 Test were 35, 25, 50, 95, 80, 60, 45, 100, and 90. What is the
value of the first quartile for this data set?
OA. 40
OB. 60
OC. 80
OD. 100
Answers
Answer:
40
Step-by-step explanation:
how many data? : 9
(9+1) x 1/4 = 2.5 (no 2.5: between 35 and 45)
(35+45)/2 = 40
help pleaseeeeeeeeeeeeeeeeeeee !!
Answers
Step-by-step explanation: Just plug in -6 into the x
Answer:
g(x) = x² + 8x
x + 4
if x = -6 (replace x with -6 )
Using the formula above
g(-6) = -6² + 8(-6)
-6 + 4
= 36 - 48
-2
= -12
-2
(minus cancels each other)
Answer = 6
Remember you can always use a calculator to check (I'm using also)
Hope this helps xoxo :-)
X and y are integers.
Answers
The points that fulfill all inequalities are shaded on the graph given at the end of the answer.
What are the points that respect the inequality?The points that respect the inequality must respect these three conditions:
They must be above the horizontal line y = 2.They must be to the left of the line y = 4 - x.They must be to the right of the line 2x + 2.These three lines are plotted on the graph given at the end of the answer, and the shaded region in blue is the solution to the inequality, that is, it contains the set of points that respects all three conditions.
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An interior decorator needs border trim for a home she is wallpapering. She needs 51 feet of border trim for the living room, 39 feet of border trim for the bedroom, and 48 feet of border trim for the dining room. How many yards of border trim does she need? She needs yards of border trim.
Answers
Answer:
138
Step-by-step explanation:
51+39+48 because its total
