9514 1404 393
Answer:
a. 1.88495559215 radians
b. 5.23598775598 radians
c. 1.57079632679 radians
d. 4.93678845564 radians
Step-by-step explanation:
You want the coefficient of pi to be between 0 and 2. That is, you want its value modulo 2--the remainder from division by 2.
a. 13/5 = 2.6; 2.6 mod 2 = 0.6. 0.6π ≈ 1.88495559215 (as you know)
b. -13/3 = -4 1/3; -4 1/3 mod 2 = 1 2/3*. 5/3π ≈ 5.23598775598
c. 57/2 = 28.5; 28.5 mod 2 = 0.5. 0.5π ≈ 1.57079632679
d. 11/7 = 1 4/7. 11/7π ≈ 4.93678845564
All angles are in radians.
__
* My calculator gives the value of -4 1/3 mod 2 as -1/3. We want the positive value, so must add 2 to this. The attachment shows Desmos is smarter than my calculator.
The tickets for the field trip were purchased yesterday for both students and instructors. Children tickets cost $9, adult tickets cost $11. The number of children tickets purchased was three more than ten times the number of adults tickets purchased. How many of each were purchased if all of the tickets cost a total of $936 dollars?
The 9 adult tickets and 93 children tickets were purchased.Let's assume the number of adult tickets purchased is "a" and the number of children tickets purchased is "c."
According to the given information, children tickets cost $9 and adult tickets cost $11. So, the total cost of children tickets is 9c, and the total cost of adult tickets is 11a.
The problem also states that the total cost of all the tickets is $936. Therefore, we can write the following equation:
9c + 11a = 936
Additionally, it is mentioned that the number of children tickets purchased was three more than ten times the number of adult tickets purchased:
c = 10a + 3
We can now solve this system of equations to find the values of "a" and "c." By substituting the value of "c" from the second equation into the first equation, we have:
9(10a + 3) + 11a = 936
90a + 27 + 11a = 936
101a = 936 - 27
101a = 909
a = 909 / 101
a = 9
Substituting this value back into the second equation, we find:
c = 10(9) + 3
c = 90 + 3
c = 93.
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divide 7 by 12 to change 7/12 to a repeating decimal. 7/12 = 7 divided by 12 = ?
Answer:
0.58333333....
can i have brainliest plz
Please help me! I will give you Brainlist if you get it right!
Answer:
B
Step-by-step explanation:
Have a nice day
Answer:
B as well
Step-by-step explanation:
As you can work out the area of rectangle by l ×w
which is 18×36 =648
and you can also work out the area of a segment which is
\(\pi \times {r}^{2} \div 2\)
so pi ×18^2÷2 and then add 648 you get 1156.9.
I just need the right answer with steps
Finde the value of x in the proportion ( 5x+ 1 ):3 =(2x +2): 7(6 x) = (4x) :7
In the proportion (5x + 1):3 = (2x + 2):7, the value of x is -1/29.
In the proportion (6x):(4x) = 7, there is no value of x that satisfies the proportion.
To find the value of x in the given proportions, let's solve them one by one:
(5x + 1) : 3 = (2x + 2) : 7
To solve this proportion, we can cross-multiply:
7(5x + 1) = 3(2x + 2)
35x + 7 = 6x + 6
Subtracting 6x from both sides and subtracting 7 from both sides:
35x - 6x = 6 - 7
29x = -1
Dividing both sides by 29:
x = -1/29
Therefore, the value of x in the first proportion is -1/29.
(6x) : (4x) = 7
To solve this proportion, we can simplify the left side:
6x / 4x = 7
Dividing both sides by 2x:
3/2 = 7
This equation is not true, as 3/2 is not equal to 7.
Therefore, there is no value of x that satisfies the second proportion.
In summary, the value of x in the proportion (5x + 1) : 3 = (2x + 2) : 7 is -1/29, and there is no value of x that satisfies the proportion (6x) : (4x) = 7.
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see attachment please
The solution to the given quadratic graph will be -2 and 0 respectively
Solution to quadratic equationsQuadratic equations are equations that has a leading degree of 2. The graph of a quadratic equation is always parabola in nature,
From the given graph, the solution to the given curve is the point where the curve intersects the x-axis. Since the parabola intersects the x-axis at two points, hence the quadratic equation will have 2 solutions.
The solution to the given quadratic graph will be -2 and 0 respectively
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What value of x makes this equation true?
x/2 − 6 = 10
Drag and drop the number that correctly completes the equation.
x = blank
30 31 32 33 34
A tv has an original price of $549.Enter the new price after the given percent of change. 40%
Step-by-step explanation:
\(0.6 \times 549 = 329.40\)
1
2
b= 2 in.; c= 6 in.
A= sq. in.
Please help mark brainliest and big points
Answer:
I believe the answer is 5.657 square inches.
Step-by-step explanation:
find the area of the following triangles. (answer rounded off to 2 dp)
Answer:
(a.) Area = 6.00 square units
(b.) Area = 15.59 square units
Step-by-step explanation:
(a.) The regular formula for the area of a triangle is A = 1/2bh, where
A is the area in square units,b is the base, and h is the height.In this triangle, the height is 3 units and the base is 4 units. Thus, we plug in 3 for h and 4 for b in the formula to find A, the area in square units:
A = 1/2(4)(3)
A = 2 * 3
A = 6
Thus, the area of the triangle is 6.00 square units.
(b.)
Before we can find the area of the triangle, we'll need to find the height. The altitude (a line extending from the vertice to the base of the triangle) is the height)Because this is an equilateral triangle with three congruent sides, the altitude splits the base into two congruent parts, whose lengths are 3 units since 3 + 3 = 6.The altitude is perpendicular to the base and creates a right triangle embedded in the larger triangle.Thus, we have a right triangle, where the altitude/height is one side, the 3-unit side is another side, and the 6-unit side is the hypotenuse.Now we can find the height of this embedded triangle using the Pythagorean theorem, which isa^2 + b^2 = c^2, where
a and b are the shorter sides called legs,and c is the longest side called the hypotenuse.Thus, we can plug in 3 for a and 6 for c, allowing us to solve for b, the height of the entire triangle:
3^2 + b^2 = 6^2
9 + b^2 = 36
b^2 = 27
√(b^2) = √(27)
b = √(9 * 3)
b = 3√3 (leaving the answer in the simplest radical form will allow us to get a more exact answer when finding the area of the triangle.
Thus, the height of the triangle is 3√3 units.
Area of the triangle in (b.):
Now, we can plug in 6 for b and 3√3 for h in the triangle area formula to find A, the area of the triangle in square units:
A = 1/2(6)(3√3)
A = 3(3√3)
A = 9√3
A= 15.58845727
A = 15.59
Thus, the area of the triangle is about 15.59 square units.
I attached a picture that shows how the triangle in (b.) can be divided into two triangles.
Determine wether the relation is a function (4,0),(2,0),(1,2),(2,4),(4,4),(5,2)
Answer:
This is not a function
Step-by-step explanation:
Hope this helps
araceli renta un local rectangular de 4.2 metros de frente y 7.3 metros de largo para su panaderia, ¿cuantos metros cuadrados tiene el local que rento?
The number of square meters that the space that Araceli rents is, is 30. 66 square meters.
How to find the area ?The space that Araceli rents has a rectangular space so to find the area of the rectangular space that Araceli rents, we need to multiply the length by the width.
The given width is 4. 2 meters and the length is 7. 3 meters.
The area of the space in square meters is therefore :
Area = Length × Width
Area = 7. 3 meters × 4. 2 meters
Area = 30. 66 square meters
In conclusion, the space that Araceli rents has an area of 30. 66 square meters.
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Prove that if x is a non-empty set of real numbers which is bounded above, then there is a sequence of real numbers in x converging to sup(x).
For all sufficiently large n, which shows that (xn) converges to sup(x) as desired. Therefore, if x is a non-empty set of real numbers that is bounded above, then there is a sequence of real numbers in x converging to sup(x).
Let x be a non-empty set of real numbers that is bounded above. Then, by the least upper bound property of the real numbers, sup(x) exists and is a real number.
For each positive integer n,
let xn be an element of x such that sup(x) - 1/n < xn ≤ sup(x).
Such an element xn exists because sup(x) is the least upper bound of x, so there must be elements of x arbitrarily close to sup(x).
We claim that the sequence (xn) converges to sup(x).
To see this, let ε > 0 be arbitrary.
Since xn ≤ sup(x) for all n,
we have sup(x) - xn ≥ 0, and so sup(x) - xn < ε for all n such that 1/ε is an integer. Thus, we have
|sup(x) - xn| < ε
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Write a number patttern that follows the rule subtract 6 and also has all odd numbers. the number patttern should be at least 4 numbers long
I had to edit my answer bc it was wrong ignore this block teehee sorry
Answer:
99, 93, 87, 81
Step-by-step explanation:
Anna is a microbiology student. She was doing research on optimum temperature for the survival of diffrent strains of bacteria. Studies showed that bacteria x needs an optimum temperature of -31°C while bacteria Y needs an optimum temperature of -56°C. What is the temperature diffrence?
The temperature difference between the optimum temperatures of bacteria X and Y is 25°C.
To find the temperature difference between the optimum temperatures of bacteria X and Y, we subtract the temperature of bacteria Y from the temperature of bacteria X.
Temperature difference = Optimum temperature of bacteria X - Optimum temperature of bacteria Y
Temperature difference = -31°C - (-56°C)
When we subtract a negative number, it is equivalent to adding its positive value. Therefore, -(-56°C) is the same as +56°C.
Temperature difference = -31°C + 56°C
To add these temperatures, we need to consider the sign of the result. In this case, we have a negative temperature (-31°C) and a positive temperature (+56°C). When adding numbers with different signs, we subtract the smaller absolute value from the larger absolute value and use the sign of the number with the larger absolute value.
Absolute value of -31°C = 31°C
Absolute value of +56°C = 56°C
Since 56°C > 31°C, the result will have a positive sign.
Temperature difference = 56°C - 31°C = 25°C
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Solve the inequality 9y+5(y+3)<4y−35 and write the solution in interval notation.
Answer:
( −∞,−5) interval notation, and inequality solution y < -5 ,
Step-by-step explanation:
Answer:
y<-5
Your Interval Notation would be an open circle and the arrow would be pointing to the left. (<-- (-6) --- (-5) --- (-4) -->) This will be your # line.
Step-by-step explanation:
9y+5(y+3) < 4y-35
1) Distribute the 5 in 5(y+3).
9y+5y+15 < 4y-35
2) Combine like terms. 9y and 5y.
9y+5y= 14y
14y+15 < 4y-35
3) MY TIP is to keep the variables on the left side, bc if you don't at the end you will have to flip the sign. so.. Subtract 4y from both sides
14y+15 < 4y-35
-4 -4
10y+15 < -35
3) Then you will subtract 15 from both sides
10y+15 < -35
-15 -15
10y < -50
4) Last is to divide to get your variable by itself.
10y < -50
÷10 ÷10
Answer : y < -5
Interval Solution: Open circle, -5 in the middle of the line and you will shade in the numbers to the left. .
If m∠EBA = x + 7 and m∠EBF = 3x - 1, find x.
Answer:
x = 21
Step-by-step explanation:
ABF is a right angle and m∠EBA + m∠EBF = m∠ABF
3x - 1 + x + 7 = 90 add like terms
4x + 6 = 90 subtract 6 from both sides
4x = 84 divide both sides by 4
x = 21
A ship is anchored off a long straight shoreline that runs north and south. From two observation points
miles apart on shore, the bearings of the ship are
and
. What is the distance from the ship to each of the observation points? Round each answer to the nearest tenth of a mile.
The distance from the north most ship to the observation is
miles.
The distance from the south most ship to the observation is
miles.
The distance from the north most ship to the observation is 2.9 miles and the distance from the south most ship to the observation is 9.9 miles.
The bearing is defined as the angle measured clockwise from the north direction. A ship is anchored off a long straight shoreline that runs north and south.
From two observation points miles apart on shore, the bearings of the ship are 52 degrees and 134 degrees respectively. To find the distance from the ship to each of the observation points, we can use trigonometry.
Let's call the distance from the north observation point to the ship x, and the distance from the south observation point to the ship y. The bearings from the north and south observation points can be drawn as follows:
[asy]
unitsize(1cm);
pair O = (0,0), N = (-2,0), S = (2,0), A = (-2,1), B = (2,-1);
draw(O--N--A,Arrow);
draw(O--S--B,Arrow);
\(label("$52^\circ$", N + 0.3*dir(52), NE);\)
\(label("$134^\circ$", S + 0.3*dir(134), SE);\)
draw(O--A--B--cycle,dashed);
\(label("$x$", (N+A)/2, W);\)
\(label("$y$", (S+B)/2, E);\)
[/asy]
We can use the tangent function to find x and y, since we have the angle and opposite side.
From the north observation point, we have:
\($$\tan(52^\circ) = \frac{x}{2}$$$$x = 2\tan(52^\circ) \approx 2.95$$\)
From the south observation point, we have:
\($$\tan(134^\circ) = \frac{y}{2}$$$$y = 2\tan(134^\circ) \approx 9.88$$\)
Therefore, the distance from the north most ship to the observation is 2.9 miles and the distance from the south most ship to the observation is 9.9 miles.
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Find the remainder when f(x)=2x^3-x^2+x+1 is divided by 2x+1
Answer:
0
Step-by-step explanation:
By the remainder theorem, this is the same as finding f(-1/2), which is equal to 0.
A coffee place is selling coffees for $2.50 each and cappuccinos for $3.75 each.
Today the coffee place sold a total of 70 drinks (coffees and cappuccinos) for a total of $222.50.
a) Write an equation that represents the information.
b) Solve the equation in (a) to find how many coffees and how many cappuccinos the coffee place sold today.
Answer:
Step-by-step explanation:
a) Let's denote the number of coffees sold as 'x' and the number of cappuccinos sold as 'y'.
The equation that represents the given information is:
2.50x + 3.75y = 222.50
b) To solve the equation, we need to find the values of 'x' and 'y' that satisfy the equation.
Since we have two variables and only one equation, we cannot determine the exact values of 'x' and 'y' independently. However, we can find possible combinations that satisfy the equation.
Let's proceed by assuming values for one of the variables and solving for the other. For example, let's assume 'x' is 40 (number of coffees):
2.50(40) + 3.75y = 222.50
100 + 3.75y = 222.50
3.75y = 222.50 - 100
3.75y = 122.50
y = 122.50 / 3.75
y ≈ 32.67
In this case, assuming 40 coffees were sold, we get approximately 32.67 cappuccinos.
We can also assume different values for 'x' and solve for 'y' to find other possible combinations. However, keep in mind that the number of drinks sold should be a whole number since it cannot be fractional.
Therefore, one possible combination could be around 40 coffees and 33 cappuccinos sold.
please help, if you do thank you so muchhh ur a life saver
Based on the information, we can infer that the theoretical probability of these colors would be 33.33%. However, the table reflects different data.
How to calculate the theoretical probability of drawing the colors?To calculate the theoretical probability of each color we must perform the following mathematical operation.
Bearing in mind that 300 is 100% of the people, we must divide 300 by 3 to know how many people should choose a specific color. In this case, every 100 people should choose a different color.
Additionally, these 100% would represent 33.33% of the total population.
100 * 100 / 300 = 33.33%
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The sixth-graders at Scott's school got to choose between a field trip to a museum and a field trip to a factory. 57 sixth-graders picked the museum. If there are 100 sixth-graders in all at Scott's school, what percentage of the sixth-graders picked the museum?
Answer:
57%
Step-by-step explanation:
because percentages go up to a hundred so 57 would be 57%.
Answer:
57%
Step-by-step explanation:
The answer is 57%. The reason is because when we are talking about percentage, it always out of 100. 57 out of 100, you would make that into a fraction so it would be 57/100. You would then divide 57/100 to get 0.57. Move the decimal two places to the right to get 57%.
A major league soccer field is 350 feet long. A model of the
soccer field is 5 feet long. What is the scale of the model?
Answer:
1/70
Step-by-step explanation:
divide 350 by 5
Rewrite the following phrase as a mathematical expression: twice a number increased by eighteen. 18 n + 2 2n + 18 2 + 18 O2/18 1) NEXT QUESTION 2 ASK FOR HELP
Answer:
2(n+18)
18(2+n)
2•(18•n)
I hope this helps
PLEASE HELP!!!!!!!!!
f(x)=(-3x^2-1)/3x^3 does f have an inverse function?
Answer: Yes, Probably
A takeaway sells 10-inch pizzas and 12-inch pizzas.
The profit made in week 1 is 0.69 and week 2 is 0.71.
What is Proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
A takeaway sells 10-inch pizzas and 12-inch pizzas.
From the table
For week 1:
Proportion= 509/ 736 = 0.69
and, week 2:
Proportion= 765/ 1076 = 0.71
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2x² + 5x, what will it a Perfect Square? make
Answer:
2x² + 5x + c = 0
For this quadratic equation to have one double root, the discriminant must equal 0.
5² - 4(2)(c) = 0
25 - 8c = 0
c = 25/8
2x² + 5x is not a perfect square because the coefficient of x², 2, is not a perfect square.
Explanation:2x² + 5x is not a perfect square.
A perfect square is an expression that can be factored into the square of a binomial. To determine if an expression is a perfect square, we can look at the coefficient of x². In this case, the coefficient is 2, which is not a perfect square.Learn more about Perfect Square here:https://brainly.com/question/34063927
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A, B, C and D are four towns.
B is 30 kilometres due East of A.
C is 30 kilometres due North of A.
D is 45 kilometres due South of A.
a) Work out the bearing of B from C.
A.
B
b) Calculate the bearing of D from B.
The bearing of B from C is 90 degrees, and the bearing of D from B is 90 degrees
From the given parameters, we can deduce that the positions of locations B, C and D are directly on the vertical and horizontal axes with respect to point A.
See attachment for the diagram that illustrates the positioning of these points.
From these diagram, we can conclude that the bearing and the bearing of D from B is 90 degrees
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1. Find the area. 15 cm summ · 12 cm 20 cm
It seems there are two numbers missing between "15 cm summ" and "12 cm". Please provide the complete values so I can help you solve the problem.