If x = 45, y = 63, and the measure of AC = 4 units, what is the difference in length between segments AB and AD? Round your answer to the nearest hundredth. (1 point)
A
Answers
Hence , the difference in length between segments AB and AD is 1.17 units .
Trigonometric functions are referred to as Circular Functions will be merely outlined because the functions of associate angle of a triangle. It means the connection between the angles and sides of a triangle area unit given by these trig functions. the essential pure mathematics functions area unit circular function, cosine, tangent, cotangent, secant and trigonometric functionThe angles of circular function, cosine, and tangent area unit the first classification of functions of trig. and also the 3 functions that area unit cotan, secant and trigonometric function will be derived from the first functions. Basically, the opposite 3 functions area unit usually used as compared to the first pure mathematics functions.
The diagram of the given question is given below .
Applying sin rule in triangle ABC , we get
sin(x°) = AC/AB
sin(45°) = 4 / AB
1 /√2 = 4 / AB
AB = 4√2
AB ≈ 5.657
Similarly, apply sin rule in triangle ACD, we get
sin(y°) = AC /CD
sin(63°) = 4 / CD
AD = 4.489
Now distinction in lengths of AB and AD = 5.657 - 4.489
= 1.168
≈ 1.17
Therefore, distinction within the lengths of AB and AD are going to be 1.17 units.
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Related Questions
X^2 +7x +12 divided by x + 2
Answers
The required simplified value of x² +7x +12 divided by x + 2 is x + 5 + [2 / (x + 2)].
To determine the simplified value of x² +7x +12 divided by x + 2.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
As per the given data,
Division of function,
= x² +7x +12/ x + 2
= x² + 7x + 10 + 2 / x +2
= (x + 5)(x + 2) + 2 / x + 2
= (x + 5) (x + 2) / x + 2 + 2 / x + 2
= x + 5 + 2 / (x + 2)
Thus, the required simplified value of x² +7x +12 divided by x + 2 is x + 5 + [2 / (x + 2)].
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What is the most common statistical method of expressing the precision of a series of repetitive measurements?.
Answers
The common statistical method of expressing the precision of a series of repetitive measurements is the standard deviation.
What is a standard deviation?It should be noted that the standard deviation is the measure of how dispersed the data is in relation to the mean.
It should be noted low standard deviation implies that data are clustered around the mean, and high standard deviation means data are more spread out.
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100 points HELP!
A group of friends want to go to the amusement park. They have $416.75 to spend on parking and admission. Parking is $15.25, and tickets cost $36.50 per person including tax. Which equation could be used to determine x, the number of people who can go to the amusement park
A. 36.5 (15.25 + x) = 416.75
B. 416.75 = 36.5x + 15.25
C. 15.25x = 416.75 - 36.5
C. 15.25x + 36.5 = 416.75
Answers
Answer:
tyyyy is my final answer
The height of 4 cups
is 11.0cm.
8 cups has a height of
16.4cm
What would be
the height of
10 cups ?
Answers
Let the height of the cup be h and the extra length be d.
So, when the one cup is placed over another the total height will be h+d.
So, when the one cup is placed over another the total height will be h + d.
When the four cup is placed over each another h + 3d = 11 cm.
So the generalised equation will h +(n-1)d where n is the total number of cups.
When the eight cup is placed over each another = h + 7d = 16.4 cm
h + 3d = 11 cm
h + 7d = 16.4 cm
On solving the above two equation we will get d = 1.35 cm and h = 6.95 cm
So when we put 10 cups on each other = h +9d
6.95 + (9*1.35) = 19.1
Hence, the height of 10 cup will be 19.1cm.
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note: enter your answer and show all the steps that you use to solve this problem in the space provided. simplify the expression 8 2 9 ( 12 ÷ 3 ⋅ 2 ) − 7 . 82 912÷3·2-7. explain each of your steps.
Answers
129 is the value of expression .
What is PEMDAS?
The abbreviation PEMDAS is used to indicate the sequence of steps to be taken when resolving expressions with multiple operations. P is for "parentheses," E is for "exponents," M is for "multiplication," D is for division, A is for addition, and S is for subtraction.We use , P/E/M/D/A/S (Parenthesis, Exponents, Multiply, Divide, Add, and Subtract)
8^2 + 9(12/3*2) - 7
= 64 + 9(8) -7
= 64 + 72 - 7
= 129
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The parking garage charges $3 per hour to park for two hours or less.
The garage charges $3 for each additional hour of parking, up to and
including 5 hours. If a car uses the parking garage for more than 5
hours, there is a flat fee of $20.
Fill in the missing domain values for the following situation.
3x
(Value 1) ≤ x ≤2
f(x) = 6 4(x - 2) (Value 2) < r ≤ 5
20
x> (Value 3)
Value 1 =
Value 2 =
Value 3
Answers
The function will become:
f ( x ) = 3 x ; 0 ≤ x ≤ 2
f ( x ) = 6 + 4 ( x - 2) for 2 < x ≤ 5
f ( x ) = 20 for x > 5
We are given that:
The parking garage charges $ 3 per hour if the car is parked there for less than 2 hours.
So, we get that:
Parking fees = 3 x for 0 ≤ x ≤ 2
Now, we get that, if the car is parked for more than 2 hours and less than 5 hours, then the parking fee is
6 + 4 ( x - 2) for 2 < x ≤ 5
Now, we are given that it charges a fixed fee of $ 20 if car is parked for more than 5 hours. So, the parking fee will be
20 for x > 5
So, the function becomes:
f ( x ) = 3 x ; 0 ≤ x ≤ 2
f ( x ) = 6 + 4 ( x - 2) for 2 < x ≤ 5
f ( x ) = 20 for x > 5
Therefore, we get that, the function will become:
f ( x ) = 3 x ; 0 ≤ x ≤ 2
f ( x ) = 6 + 4 ( x - 2) for 2 < x ≤ 5
f ( x ) = 20 for x > 5
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4. Identify the following according to the information above. Justify your answer.
Answers
The following figures are Line, Ray, Line Segment, Parallelogram and Cuboid in the sequential order.
a) Line - A line is a two-dimensional figure. It is a group of points joining together to form a single entity which extends in both directions infinitely. It has no end points.
b) Ray - A ray is a two-dimensional figure. It is a group of points joining together to form a single entity, but it extends infinitely in only one direction. It has one end point.
c) Line segment - A line segment is a two-dimensional figure. It is a group of points joining together to form a single entity, but it does not extend infinitely in any direction. It has two end points and a finite length.
d) Parallelogram - A parallelogram is a two-dimensional figure having 4 sides whose opposite sides are equal in length and also parallel to each other. The diagonals of the parallelogram intersect each other at equal distance.
e) Cuboid - A cuboid is a three-dimensional figure made up of rectangular faces of varying length, breadth and height. The opposite faces of a cuboid are similar in dimensions. It has 12 edges, 12 vertices and 6 faces.
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Expressed as a product of its prime factors in index form, a number n is n = 3 times 5 squared times x cubed. express 5n squared as a product of prime factors in index form. give your answer in terms of x.
Answers
5n² can be expressed as, 5n² = 3² x 5⁵ x x⁶
Given that n can be written as the product of the primes as
n = 3 x 5² x x³
This expression for n is called the prime factorization of n.
We need to express 5n² as such a product of primes.
For that taking square of n, add the power 2 with the existing powers of 3,5 and x,
So, n² = ( 3 x 5² x x³)² = 3² x 5⁴ x x⁶
So 5n² = 5(3² x 5⁴ x x⁶)
Multiplying 5 with the existing power of 5, 5⁴,
⇒ 5n² = 3² x 5⁵ x x⁶
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Dwayne is selling hamburgers and cheeseburgers. He has 100 burger buns. Each hamburger sells for $3, and each cheeseburger sells for $3.50. Which system of inequalities represents the number of hamburgers, h, and the number of cheeseburgers, c, he must sell to have sales of at least $80?
h + c ≤ 80
3h + 3.5c ≤ 100
h + c ≤ 80
3h + 3.5c ≥ 100
h + c ≤ 100
3h + 3.5c ≤ 80
h + c ≤ 100
3h + 3.5c ≥ 80
Answers
The system of inequalities are:
h + c ≤ 100
3h + 3.5c ≥ 80
What are the system of inequalities?Here are inequality signs and what they mean:
> means greater than< means less than≥ means greater than or equal to ≤ less than or equal toHere are the system of inequalities :
number of hamburgers sold + number of cheeseburger sold ≤ total number of buns
(cost of one hamburger x number of hamburger sold) + (number of cheeseburger sold x number of cheeseburger sold) ≥ $80
h + c ≤ 100
3h + 3.5c ≥ 80
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determine if the collection is not well defined and therefore is not a set. the collection of current nfl players
Answers
The collection of current NFL players is well defined and is a set
Step-by-step explanation:
For a collection to be termed as a set, it is necessary that it has distinct objects that are defined.
For example, a set of first 10 natural numbers is
A= [1,2,3,4,5,6,7,8,9,10]
It is well defined and therefore called as set which has first 10 natural numbers as its elements.
Same is the case with the collection of current NFL players.
The collection contains defined number of players. Therefore, this collection is called a set.
The members of the collection or team will be known as the elements of the set.
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Find the value of k. The diagram is not to scale.
Answers
Answer:
[tex] \large{ \boxed{ \tt{answer : \boxed{ \tt{ k = 73 \degree}}}}}[/tex]
Please see the attached picture for full solution!
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in the arithmetic sequence 4,11,18 what is the 10th terms
Answers
Answer:
67
Step-by-step explanation:
Each time the number goes up by 7. After 9 moretimes 4 will increase by 63.
4+63=67.
The 10th term should be 67
Please help me with this question I don't understand it. Please it must be easy for yall genius's
Answers
Answer:
Range is 12 and mean is -6
Step-by-step explanation:
To find the mean, add together all the numbers and divide by 7.
(-1,3), (-12), (92)
(37), (5,7), (5-3)
(52 73), (96, 73), (94, 1483)
(5-5), (1,4) (4₂2)
Graph and find the 4th point to create a rectangle
Answers
a tv show had 4,320,000 viewers for its season premiere. express this number using scientific notation.
Answers
Answer:
Step-by-step explanation:
See attachment
Consider a cube with an inscribed sphere. The function can be used to find the radius, r, of a sphere given the volume, v. The function can be used to find the side length of the cube, s, depending on the radius of the sphere. The function can be used to find the surface area, a, of the cube. Which is the composed function for the surface area of the cube for any given volume of an inscribed sphere?
Answers
The composed function for the surface area of the cube for any given volume of an inscribed sphere, A(V) = 24( [tex]\sqrt[3]{\frac{3V}{4\pi} }[/tex])²
The function used to find the radius r of a sphere given volume V,
r(V) = [tex]\sqrt[3]{\frac{3V}{4\pi} }[/tex]
The function used to find the length of the side s of the cube depending on the radius r of the sphere, s(r) = 2r
The function used to find the surface area A of the cube depending on the side of the cube s, A(s) = 6s²
We need to find the composed function for the surface area A of the cube for any given volume V of an inscribed sphere. i.e., A(V)
We have, A(s) = 6s²
Substituting function for s to A(s)
⇒ A(s(r)) = 6(2r)² = 24r²
Substituting function for r into A(s(r)),
⇒ A(s(r(V))) = 24( [tex]\sqrt[3]{\frac{3V}{4\pi} }[/tex])²
So the function for the surface area of the cube depending on the volume of the inscribed sphere, A(V) = 24( [tex]\sqrt[3]{\frac{3V}{4\pi} }[/tex])²
The question is incomplete. Find the complete question below:
Consider a cube with an inscribed sphere. The function r(V) = [tex]\sqrt[3]{\frac{3V}{4\pi} }[/tex] can be used to find the radius, r, of a sphere given the volume, V . The function s(r) = 2r can be used to find the side length of the cube, s , depending on the radius of the sphere. The function A(s) = 6s² can be used to find the surface area, A , of the cube. Which is the composed function for the surface area of the cube for any given volume of an inscribed sphere?
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Answer:
Answer is D
Step-by-step explanation:
which way the the graph of g(x) = |x + 3| move
Answers
HELP!!!!!! In one serving of trail mix, the ratio of the number of ounces of raisins to the number of ounces of peanuts is 2 to 3. 2). Drag the numbers into the table to show how many ounces of raisins and peanuts are needed for different numbers of serving . tell me the answer you don't have to give me step by step explanation for ratios!!!!!
Answers
The ounces of raisins and peanuts needed for different numbers of serving are :
for 4 serving = 8 raisins and 12 peanuts
for 12 serving = 24 raisins and 36 peanuts
According to the question we have been given that in one number of serving the ratio of number of ounces of raisins to the number of ounces of peanuts is given as :
ratio = 2 : 3
We need to find ounces of raisins and peanuts needed for different numbers of serving.
For 4 serving,
Raisins = 4*2 = 8
Peanuts = 4*3 = 12
and we see that their ratio = 8/12 = 2/3
For 12 serving,
Raisins = 12*2 = 24
Peanuts = 12*3 = 36
and we see that their ratio = 24/36 = 2/3
Hence the ounces of raisins and peanuts needed for different numbers of serving are :
for 4 serving = 8 raisins and 12 peanuts
for 12 serving = 24 raisins and 36 peanuts
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Remy walked to a friends house, m miles away, at an average rate of 4mph. The m-mile walk home was at only 3mph. Remy spent 2 hours walking in all. Find the value of m.
Answers
Step-by-step explanation:
speed = mph or miles/hour
so, when we are dealing with a distance and compare the time spent on the distance, we have to divide distance by speed
miles / miles/hour = hour
so, we have
m/4 + m/3 = 2
as the sum of the time it took to walk the distance at 4mph and the time it took to walk the distance at 3 mph is 2 hours.
now we multiply by the denominators one after the other to eliminate the fractions.
m + 4m/3 = 8
3m + 4m = 24
7m = 24
m = 24/7 = 3.428571429... miles
the numbers to order them from greatest to least sqrt(29); (sqrt(6))/4; 19/7 1.538392 ...
Answers
The order of numbers from Greatest to Least is 5.385, 2.714, 1.538, 0.612.
Descending Order :Arranged in a series that begins with the greatest or largest and ends with the least or smallest.
We can also call it Greatest to Least.
To order the number from greatest to least first we have to find the value of given square root,
√29 = 5.385
√6/4 = 0.612
19/7 = 2.714
Now, we have the numbers :
5.385, 0.612, 2.714, 1.538
So, we will arrange the above numbers greatest to least
1) 5.385
2) 2.714
3) 1.538
4) 0.612
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Jenny polled her 35 co-workers to find out which type of candy they liked best. She found that 10 like chocolate, 8 like gumdrops, 2 like hard candy, and 3 like taffy. There were 5 people who said they like BOTH hard candy and taffy and the remaining co-workers said they like BOTH chocolate and gum drops. How many of Jenny’s co-workers enjoy gumdrops or chocolate?
a.
10
d.
7
b.
8
e.
25
c.
18
Answers
The number of co-workers that like gumdrops and chocolate is 7 (option b).
How many like chocolate and gumdrops?The mathematical operations that would be used to determine the answer are addition and subtraction.
Addition is determining the total value or summing two or more numbers. The sign used to represent addition is +. Subtraction is the process of determining the difference between two or more numbers. The sign used to denote subtraction is -.
The first step is to add the total number of people who like a particular type of candy : 10 + 8 + 2 + 3 + 5 = 28
The second step is to subtract that number gotten in the previous step from the total number of co-workers.
Co-workers that like both chocolate and gum drops = 35 - 28 = 7
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A fisherman can row upstream at 2 mph and downstream at 8 mph. He started rowing upstream until he got tired and then started downstream to his start point. How far did the fisherman row if the entire trip took 2 hours?
Answers
If a fisherman can row upstream at 2 mph and downstream at 8 mph. He started rowing upstream until he got tired and then started downstream to his start point. How far did the fisherman row if the entire trip took 2 hours is: 6.4 miles.
DistanceLet d = the distance to the turn around point
Time = Distance/ Speed
Up time + Down time = 2hrs
d/2 +d/8 =2
Multiply by 8
8×d/2 +8×d/8 =8 (2)
4d + d = 16
5d = 16
Divide both side by 5d
d=16/5
d = 3.2 miles to turn around
Hence,
Round trip = (3.2 miles ×2)
Round trip= 6.4 miles
Therefore If a fisherman can row upstream at 2 mph and downstream at 8 mph. He started rowing upstream until he got tired and then started downstream to his start point. How far did the fisherman row if the entire trip took 2 hours is: 6.4 miles.
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a manager of a fast food restaurant wants the drive-thru employee to ask every fifth customer if he or she is satisfied with the service. who makes up the sample?
Answers
The population of this fast food business is made up of all customers who use the drive-thru window, whereas the sample, or representative group of the population, is made up of every fifth customer as per the concept of statistics.
What are statistics?
A branch of mathematics, statistics is a body of knowledge that deals with the gathering, examination, interpretation, and presentation of data. Instead of being a subfield of mathematics, some people view statistics as a separate mathematical discipline.A population is a total group from which a statistical sample is taken in statistics. Here, the manager only inquires about the fifth customer's pleasure after becoming interested in his drive-through staff. Therefore, those customers who do not use the drive-thru window at this restaurant are not part of the sample population about whom it is possible to inquire.
As a result, the population of this fast food business is made up of all customers who use the drive-thru window, whereas the sample, or representative group of the population, is made up of every fifth customer.
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In the figure below, m Z1 = (x+84)° and m2 = 2xº.
Find the angle measures.
Answers
Answer:
1. m ∠ 1 = 86°
m ∠ 2 = 4°
- Problem in the picture
2. m ∠ 1 = 6°
m ∠ 2 = 84°
Step-by-step explanation:
I'm confused, so I'll just solve both problems (assuming that they are the same type of angle)
1.
m Z1 = (x+84)° and m2 = 2xº.
m ∠ 1 = (x + 84)°
m ∠ 2 = 2x°
Complementary angles are equal to 90°
(x + 84) + 2x = 90
x + 84 + 2x = 90
3x + 84 = 90
-84 -84
----------------------
3x = 6
÷3 ÷3
-----------
x = 2°
m ∠ 1 = (x + 84)°
m ∠ 1 = (2 + 84)°
m ∠ 1 = 86°
m ∠ 2 = 2x°
m ∠ 2 = 2(2)°
m ∠ 2 = 4°
2. (Problem in the picture)
m ∠ 1 = (x - 6)°
m ∠ 2 = 7x°
Complementary angles are equal to 90°
(x - 6) + 7x = 90
x - 6 + 7x = 90
8x - 6 = 90
+6 +6
---------------------
8x = 96
÷8 ÷8
----------------
x = 12
m ∠ 1 = (x - 6)°
m ∠ 1 = (12 - 6)°
m ∠ 1 = 6°
m ∠ 2 = 7x°
m ∠ 2 = 7(12)°
m ∠ 2 = 84°
I hope this helps!
find the angle between a diagonal of a cube and an adjacent edge. (enter your answer in degrees. round your answer to two decimal places.)
Answers
The angle between a diagonal of a cube and an adjacent edge is 54.75°;
Assuming the length of a side of the cube as 1 unit, the three sides are given by the vectors;
a = (1, 0, 0)
b = (0, 1, 0)
c = (0, 0, 1)
The diagonal is given by the vector, v = (1, 1, 1)
The angle between the diagonal and one edge of the cube is given by
cos θ = v. a / |v|.|a|
v. a = (1, 1, 1).(1, 0, 0)
= 1(1) + 1(0) + 1(0
= 1 + 0 + 0
v. a = 1
Magnitude of vector V = √[(1)² + (1)² + (1)²]
|v| = √3
Similarly, |a| = √1;
So, |v|.|a| = √3.√1 = √3
Now, cos θ = 1/√3
So, θ = cos¹(1/√3)
θ = 54.75°
Therefore, the required angle is 54.75°.
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Limits and Piecewise functions help please
Answers
Answer: -2, 2
Step-by-step explanation:
The derivative of a function, f(x), at a point where f(x) has a sharp turn (or cusp) does not exist.
The derivative of a function, f(x), at a point where f(x) has a vertical tangent line does not exist.
Using this information, we can see that f(x) is not differentiable when x=3 since there is a vertical tangent line. We can also see that f(x) is not differentiable when x=-1 since there is a cusp.
In a cycle 1 school in Abu Dhabi , the ratio of boys to girls in the 3rd grade is 5 to 8. If there are 72 girls, how many boys will there be?
Answers
72/8 = 9,
9x5 = 45 boys
Therefore answer is 45 boys
How many solutions are in the problem two thirds(6j+9)=3j+7
Answers
The problem two thirds(6j+9)=3j+7 has one solution.
How many solutions does the problem have?The given problem is 2/3(6j + 9) = 3j + 7
In order to determine the number of solutions, take the following steps:
Expand the bracket on the left:
(2/3 x 6j) + (2/3 x 9)
4j + 6
4j + 6 = 3j + 7
Combine similar terms :
4j - 3j = 7 - 6
Add similar terms
j = 1
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The polynomial function f(x) has degree 4, a y-intercept of 40, roots of -5 and 4, and a multiplicity 2 root of 1. Enter f(x).
the graph of the equation is shown
Answers
The polynomial is:
f(x) = -2*(x + 5)*(x - 4)*(x - 1)*(x - 1)
How to get the polynomial function?Let's assume the leading coefficient is A, we know that the degree is 4, the y-intercept is 40, and we have the roots (-5, 4, 1, 1)
Then the polynomial is:
f(x) = A*(x + 5)*(x - 4)*(x - 1)*(x - 1)
Now we use the fact that the y-intercept is 40, so we have:
f(0) = 40 = A*(0 + 5)*(0 - 4)*(0 - 1)*(0 - 1)
40 = A*-20
40/-20 = A = -2
Then the polynomial is:
f(x) = -2*(x + 5)*(x - 4)*(x - 1)*(x - 1)
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will give u brainliest
Need 2 submit by tonight need help asap please <3
Three angles add up to 180 degrees, angle one has a measure of 7x+6, angle two has a measure of 2x+3 and angle three has a measure of 10x+9.
Given that the sum of the angles is 180 degrees, what is the measure of angle one? Round your answer to the hundredths place IE 79.50.
Answers
Step-by-step explanation:
please find attached file for the problem. hope it will help you , let me know if you have any further query