The terminal point of 13π/6 is (-√3/2, 1/2) by using unit circle.
What are the quadrants of a graph?The quadrants of a graph are the four sections that divide the coordinate plane. The quadrants are numbered in a counterclockwise direction starting from the positive x-axis.
1. Quadrant I is located in the upper-right section and contains points with positive x and y-coordinates.
2. Quadrant II is located in the upper-left section and contains points with negative x-coordinates and positive y-coordinates.
3. Quadrant III is located in the lower-left section and contains points with negative x and y-coordinates.
4. Quadrant IV is located in the lower-right section and contains points with positive x-coordinates and negative y-coordinates.
The quadrants are useful for determining the signs of coordinates, angles, and for plotting points on a graph.
To find the terminal point of 13π/6, we can start by recognizing that this angle is greater than 2π, which is one complete revolution around the unit circle.
To bring the angle back within one revolution, we can subtract 2π, which gives us 13π/6 - 2π/1 = 13π/6 - 12π/6 = 1π/6.
The angle 1π/6 is in the standard position between the positive x-axis and the first quadrant. The reference angle is π/6, which is the angle between the terminal side and the x-axis.
Since the angle is in the 2nd quadrant, the x-coordinate will be negative and the y-coordinate will be positive. Using the unit circle, we can find the values of sine and cosine at π/6 and then negate the value of cosine since the angle is in the second quadrant.
cos(π/6) = √3/2
sin(π/6) = 1/2
Therefore, the terminal point of 13π/6 is (-√3/2, 1/2).
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2. Triangle ABC with A(2, 3), B(7, -1), and C(-4, 2) is reflected across the line x = -2. Find the
coordinates of B'
Answer:
B’ = (-11, 1)
Step-by-step explanation:
Because the triangle is reflected across the line x = -2, it is being reflected across a vertical line.
Therefore only the x-coordinate will change.
As B is 9 units right of the line x = 2, the coordinates of B’ will be (-2 - 9, 1)
Which will be (-11, 1)
(40 POINTS)
Data based on past observations can sometimes predict future performance.
a. Give an example where past performance does predict future performance. Explain your reasoning.
b. Give an example where past performance does not predict future performance. Explain your reasoning.
An example of where past performance does predict future performance would be Mt. Kīlauea's eruption in 2018.
An example of where past performance does not predict future performance would be the eruption of Hualālai last happening in 1801.
What does the data show on volcanoes ?Using past data, there was a prediction that Mt. Kīlauea would erupt in the year 2018 and it did happen ( even though it was not very serious ) at the Lower East rift zone of the volcano. Past performance therefore predicted the future.
However, the same prediction said that Hualālai would erupt in 1854 and yet the volcano has not erupted since 1801 which shows that the prediction was wrong.
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Gianah lives in Milton. She bought a bus ticket to travel to her cousin's house in Orlando. She gets on the bus in Milton. The distance between the two cities is 695 kilometers and the bus drives 70 kilometers per hour.
If the bus is kilometers away from Orlando, which of the following equations represents the hours, h, the bus has traveled?
695 divided by 70=9.92 hours
The 20 members of the photography club are trying to raise at least $1,400 for
new photography equipment. They have already raised $540.
Let m represent the amount of money each member must raise, on average, to meet
their goal. Write an expression for the total amount of money going to be raised.
b Write an equation that represents the club raising all the money.
с
Solve the equation. What does the solution mean in context of the scenario?
d Write an inequality representing the amount of money each member must raise,
on average, to meet or exceed their goal.
Write an inequality showing the possible average amount of money each club member
needs to raise.
Answer:
i dont know if this helps, im not sure if you are telling me to do all of these things or B, c, d are answer
Step-by-step explanation:
To find the total amount of money that the photography club will raise to meet their goal, we can multiply the average amount of money each member must raise by the number of members in the club:
Average amount of money each member must raise = m
Number of members in the club = 20
Total amount of money to be raised = Average amount of money each member must raise x Number of members in the club
Total amount of money to be raised = m x 20
We know that the club is trying to raise at least $1,400, and they have already raised $540. Therefore, the amount of money they still need to raise is:
Amount of money still needed to reach goal = $1,400 - $540
Amount of money still needed to reach goal = $860
We can set up an equation to represent the total amount of money the club will raise to meet their goal:
Total amount of money to be raised = Amount of money still needed to reach goal
m x 20 = $860
We can solve for "m" by dividing both sides of the equation by 20:
m = $860 / 20
m = $43
Therefore, the total amount of money the club will raise to meet their goal is:
Total amount of money to be raised = Average amount of money each member must raise x Number of members in the club
Total amount of money to be raised = $43 x 20
Total amount of money to be raised = $860
B))) We can set up an equation to represent the total amount of money the club will raise to meet their goal:
Total amount of money to be raised = Amount of money already raised + Amount of money still needed to reach goal
We know that the club has already raised $540 and they need to raise $860 more to reach their goal of $1,400. Therefore, we can substitute these values in the equation:
Total amount of money to be raised = $540 + $860
Total amount of money to be raised = $1,400
So the equation that represents the club raising all the money is:
$1,400 = $540 + $860
C)))) To solve the equation:
$1,400 = $540 + $860
We can simplify the right-hand side of the equation by adding $540 and $860:
$1,400 = $1,400
This equation is true, which means that it is a consistent equation. The solution to this equation is that the club will be able to raise all the money they need to buy the new photography equipment.
In the context of the scenario, the solution means that the club will be able to meet their goal of raising at least $1,400 for new photography equipment. They have already raised $540, and they need to raise $860 more to reach their goal. The equation shows that the total amount of money they will raise is exactly $1,400, which is the amount they need to meet their goal.
D))))) To represent the amount of money each member must raise, on average, to meet or exceed their goal, we can use the following inequality:
Average amount of money each member must raise ≥ Total amount of money still needed to reach goal / Number of members in the club
We know that the total amount of money still needed to reach the goal is $860, and there are 20 members in the club. Therefore, we can substitute these values in the inequality:
Average amount of money each member must raise ≥ $860 / 20
To simplify the right-hand side of the inequality, we can divide $860 by 20:
Average amount of money each member must raise ≥ $43
This inequality shows that each member must raise at least $43, on average, to meet or exceed their goal of raising $1,400.
To show the possible average amount of money each club member needs to raise, we can use the following inequality:
0 < Average amount of money each member must raise ≤ Total amount of money still needed to reach goal / Number of members in the club
This inequality shows that the average amount of money each member must raise is greater than 0 (since each member must contribute something), but it is less than or equal to $43 (which is the minimum amount each member must raise to meet or exceed their goal).
Solve for x. Round to the nearest tenth, if necessary.
Answer:
Step-by-step explanation:
You are looking for the tangent ratio, which is opposite side over adjacent side. Using the tangent ratio of an angle of 37°.
tan37° = x/89
.75355405 = x/89
.75355405 · 89 = x/89 · 89/1
67.06 = x
rounded to 67.1
Answer:
67.1? that's what I got lol
Point F is at [-10, 12] and point G is at [18, 12]
The midpoint of the line segment FG is the point (4, 12).
What is midpoint?In geometry, the midpoint of a line segment is the point that is exactly halfway between the endpoints of the segment. It is the point that divides the segment into two congruent segments.
The formula for finding the midpoint of a line segment with end points (x₁, y₁) and (x₂, y₂) is:
Midpoint = [(x₁ + x₂)÷2, (y₁ + y₂)÷2]
So, the midpoint of the line segment with endpoints F(-10, 12) and G(18, 12) can be found as:
Midpoint = [(-10 + 18)÷2, (12 + 12)÷2]
= [8÷2, 24÷2]
= [4, 12]
Therefore, the midpoint of the line segment FG is the point (4, 12).
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What expression is or is not equivalent, what is the answer?
Answer:
A and B
Step-by-step explanation:
-10/3= -3.33333333333
(- (-10))/(-3)= -10/3, (negative sign being erased)
=-3.33333333333
hope it helped:)
Question 1b Match each expression on the left with an equivalent expression on the right. Some answer options on the left side will be used more than once. 132 ÷ 11 28 2 288 126 7)98 sixty-four divided by four Jestion ID: 29430 Clear 1b of 12 48 3 36 ÷ 2 36 ÷ 3 Click and hold an item in one column, then drag it to the matching item in the other column. Be sure your cursor is over the target before releasing.
The equivalent expression for the given expression 132/11 is 12.
1) Given that, 132/11
Here, the equivalent expression is 132/11 =12
2) 126/7 = 18
3) 7)98(14
7
_______
28
28
________
0
4) Sixty-four divided by four
That is, 64/4 = 16
5) 28÷2
= 28/2
= 14
6) 28/2 = 14
7) 48/3 = 16
8) 36÷2
= 36/2
= 18
9) 36÷3
= 36/3
= 12
Therefore, the equivalent expression for the given expression 132/11 is 12.
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Taylor has a gift box that is 6 inches long,5 inches high,and 3 inches wide.What is the surface area of the gift box in square inches?
Level E: The repair department of the bicycle shop repairs three things: flat tires, bent handle bars and ripped seats. Today in the repair department, 25% of the bikes had flat tires only, 5% had bent handlebars only, and 10% had ripped seats only. Just 1/12th of the bikes had all three repairs to do: flat tires, bent handlebars and ripped seats. No bikes were completely fixed and there are a total of 101 repairs to be made. How many bikes are in the repair department? How many bikes need two repairs? If less than half of all the bikes have a ripped seat, what is the range of bikes that need both the tires and handlebars repaired without needing to fix the seat?
There are 960 bikes in the repair department and 1.98% of the bikes need two repairs.
The number of bikes with flat tires only is 0.25x, where x is the total number of bikes
The number of bikes with bent handlebars only is 0.05x
The number of bikes with ripped seats only is 0.1x
The number of bikes that need two repairs is 0.01Tx, where T is the percentage of bikes that need two repairs (expressed as a decimal)
The number of bikes that need all three repairs is 0.0833...x
So we have the equation:
0.25x + 0.05x + 0.1x + 0.01Tx + 0.0833...x = 101
Simplifying and solving for x, we get:
x = 960
So there are 960 bikes in the repair department.
To find the number of bikes that need two repairs, we can use the equation:
0.25x + 0.05x + 0.1x + 0.01Tx = 101 - 0.0833...x
Substituting x = 960, we get:
0.25(960) + 0.05(960) + 0.1(960) + 0.01T(960) = 101 - 0.0833...(960)
240 + 48 + 96 + 9.6T = 101 - 80
9.6T = 19
T = 1.98
About 1.98% of the bikes need two repairs.
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Choose the correct Set-builder form for
the following set written in Roster form:
{4, 5, 6, 7, 8}
The value of correct Set-builder form is,
⇒ { x | x ∈ IR ; 4 ≤ x ≤ 8 }
We have to given that;
The set is,
⇒ {4, 5, 6, 7, 8}
Thus, We can write correct Set-builder form as,
⇒ {4, 5, 6, 7, 8}
⇒ { x | x ∈ IR ; 4 ≤ x ≤ 8 }
So, The value of correct Set-builder form is,
⇒ { x | x ∈ IR ; 4 ≤ x ≤ 8 }
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Correct answer gets brainliest!!!!
Answer:
a) 5
Step-by-step explanation:
the question say how many zero-dimensional objects are labeled on the object. so, you would count how many blue dots you see on the object, as you can see their are four dots on the the bottom, and one dot at the top.
so, 4 dots + 1 dot = ?
5 blue dots
so your answer is 5.
hopefully this helps, let me know if it doesn't.
CAN SOMEONE HELP WITH THIS QUESTION?
Shane has 2 white shirts, 2 blue ones and 1 red one, He has gray pants and black pants. He hung them all up on hangers in his closet, but one shirt and a pair of pants fell on the floor. The probability that a red shirt and black slacks are on the floor is
The probability that a red shirt and black slacks are on the floor is 1/10.
What is the probability?Probability is the odds that a random event would happen. The odds that the event would happen has a probability value that lies between 0 and 1.
Probability that a red shirt and black slacks are on the floor = (number of red shirts / total number of shirts) x (number of black slacks / total number of slacks)
Total number of shirts = 2 + 2 + 1 = 5
Total number of slacks = 1 + 1 = 2
(1/5) x (1/2) = 1 /1 0
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Harvey’s pizzeria has three pizza sizes he wants to work out the outside measurement (circumference) of each size to work out how much cheese he will need for a stuff crust.
Match the correct circumference of each pizza using the diameter given.
Small –
Medium-
Large-
The circumference of the small pizza is approximately 47.1 cm, the circumference of the medium pizza is approximately 69.1 cm, and the circumference of the large pizza is approximately 94.2 cm.
The diameter is the distance across the widest part of a circle. To find the circumference of a circle, we use the formula C = πd, where C is the circumference, π is a mathematical constant (approximated as 3.14), and d is the diameter of the circle. Therefore, to find the circumference of each pizza size, we can simply plug in the given diameter into this formula.
For the small pizza with a diameter of 15 cm, the circumference can be calculated as follows:
C = πd
C = 3.14 x 15
C ≈ 47.1 cm
For the medium pizza with a diameter of 22 cm, the circumference can be calculated as follows:
C = πd
C = 3.14 x 22
C ≈ 69.1 cm
For the large pizza with a diameter of 30 cm, the circumference can be calculated as follows:
C = πd
C = 3.14 x 30
C ≈ 94.2 cm
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solve all four parts
The rocket will hit the ground after 19.09 seconds.
How to calculate projectilea) The height of the rocket can be describe as:
h(t) = -16t² + 210t + 75
where
t = time in seconds
h(t) = height of the rocket in feet
b) To find the time at which the rocket reaches its maximum height, we need to find the vertex of the parabolic function. The vertex is given by the formula:
t = -b/(2a)
where
a = -16
b = 210
Substituting these values, we get:
t = -210/(2(-16)) = 6.5625 seconds
To find the maximum height, we substitute this value of t back into the equation for h(t):
h(6.5625) = -16(6.5625)² + 210(6.5625) + 75 = 690.625 feet
This means that the rocket reaches its maximum height of 690.625 feet after 6.5625 seconds.
c) We need to find the time interval during which the height of the rocket is greater than 721 feet. We set the height function h(t) greater than 721 and solve for t:
-16t² + 210t + 75 > 721
-16t² + 210t - 646 > 0
Solving for t using the quadratic formula, we get:
t < 2.975 or t > 14.038
Therefore, the rocket will be more than 721 feet above ground level between 0 and 2.975 seconds, and between 14.038 and infinity seconds.
d) To find the time at which the rocket hits the ground, we set h(t) equal to 0 and solve for t:
-16t² + 210t + 75 = 0
Solving for t using the quadratic formula, we get:
t = [tex]\frac{-b \± \sqrt{b^{2} - 4ac } }{2a}[/tex]
a = -16, b = 210, c = 75
t = [tex]\frac{-210 \± \sqrt{210^{2} - 4(16)(75) } }{2(-16)}[/tex]
t = [tex]\frac{-210 \± \sqrt{22225} }{-32}[/tex]
t = [tex]\frac{-210 \± 149}{-32}[/tex]
t = 2.53125 or t = 13.53125
Since the rocket was launched from the top of a 75-foot building, it will hit the ground after an additional time of:
t + 2.53125 = 5.09375 seconds or t + 13.53125 = 19.09375 seconds
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‼️‼️‼️WILL MARK BRAINLIEST IF HELPFUL‼️‼️‼️
Answer:
2π(10^2) + 2π(10)(16)
= 2π(100) + 2π(160)
= 200π + 320π
= 520π ft^2
On Saturday, the temperature was 75.5°F. The temperature rose by 6°F on Sunday, then dropped by 3.5°F on Monday. What was the temperature, in degrees Fahrenheit, on Monday?
Answer:
78°F
Step-by-step explanation:
If the temperature was 75.5°F, and it rose by 6°F on Sunday, then the temperature on Sunday was:
75.5°F + 6°F = 81.5°F
If the temperature on Sunday was 81.5°F, and it dropped by 3.5°F on Monday, then the temperature on Monday was:
81.5°F - 3.5°F = 78°F
Therefore, the temperature on Monday was 78°F.
1. Josh said that the square root of 100 is a perfect square and a perfect cube. Is Josh correct? Explain your reasoning.
Josh is incorrect because 100 is perfect square not a perfect cube.
We have the number 100.
Now, factorising the number 100 as
100 = 2 x 2 x 5 x 5
100= (2 x 5) x ( 2x 5)
100 = 10 x 10
As, 100 can be factorised as 10 x 10 which shows 100 is prefect square of 10.
But 100 is not a perfect cube because for the cube we need pair of three number.
Thus, Josh is incorrect.
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please help! I don't understand this at all
The equation that represents the consecutive odd numbers whose product is 63 is; (x + 9) (x + 7) = 0
What are odd numbers?Odd numbers have special properties and relationships to other numbers, which make them important in mathematics. For instance, the sum of two odd numbers and the difference between two odd numbers both always equal one.
We can see that we can solve the double brackets by equation them to zero so we have that;
(x + 9) (x + 7) = 0
x = -9
x = -7
Thus;
(-9) (-7) = 63
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An angle measures 158.2° less than the measure of its supplementary angle. What is the measure of each angle?
Answer:
the 2 angles are 169.1° and 10.9°
Step-by-step explanation:
Supplementary angles add to 180
x = first angle
y = second angle = x - 158.2
x + y = 180
x + (x - 158.2) = 180
2x = 180 + 158.2
2x = 338.2
x = 338.2/2 = 169.1
y = 169.1 - 158.2 = 10.9
x + y = 169.1 + 10.9 = 180
Divide and state the quotient in simplest form.
The quotient of the two fractions is (x - 5) / (x - 4).
Option D is the correct answer.
We have,
To divide two fractions, we can multiply the first fraction by the reciprocal of the second fraction.
In this case, that means we need to multiply:
(x² - 2x - 15) / (x + 2) x (x + 2) / (x² - x - 12)
Notice that the (x + 2) terms in the numerator and denominator of the first fraction cancel out with the denominator of the second fraction, so we can simplify before multiplying:
(x² - 2x - 15) / 1 x 1 / (x² - x - 12)
Now we can multiply the numerators and the denominators separately:
(x² - 2x - 15) / (x² - x - 12)
To simplify further, we can factor both the numerator and the denominator:
(x - 5)(x + 3) / (x - 4)(x + 3)
Notice that the (x + 3) terms in the numerator and denominator cancel out, leaving:
(x - 5) / (x - 4)
Therefore,
The quotient of the two fractions is (x - 5) / (x - 4).
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Draw and describe the plane section that results from the following cut: a cylinder cut parallel to the base.
When a cylinder is cut parallel to its base, the plane section that results is a circle. This circle will have the same radius as the cylinder's base. The center of the circle will be located at the center of the cylinder's base. This type of cut will create a circular cross-section that is parallel to the base of the cylinder.
find the inverse given T(y)=6.056y+601.39
Answer:
5 (100y -601.39)
3028
Step-by-step explanation:
Each ice cube measures 1.2in high and 1in in diameter. What is the volume of all 3 ice cubes
[tex]\sf V_{3 Cylinders} =2.8274(in^{3} ).[/tex]
Step-by-step explanation:1. Find a formula for the volume (assuming the shape of the ice cubes is cylindrical).From the provided information about the ice cubes (height and diameter), it's safe to assume that they are cylinder shaped ice cubes. They could be circular cone ice cubes, but the safest assumption is cylinders. Now, to find the volume of a cylinder we use the following formula:
[tex]\sf V_{Cylinder} =\pi r^{2} h[/tex] or [tex]\dfrac{\pi d^{2} h}{4}[/tex].
For the fist equation, "r" stands for radius, and "h" for height.
On the alternate equation, "d" stands for diameter.
2. Calculate.Since we're given the diameter and height, let's use the alternate equation:
[tex]\sf V_{Cylinder} =\dfrac{\pi (1(in))^{2} 1.2(in)}{4}=\dfrac{3}{10} \pi (in^{3} )=0.9425(in^{3} ).[/tex]
3. Calculate the volume of the 3 cubes.This can be done by just multiplying the volume of a single cube ([tex]\dfrac{3}{10} \pi (in^{2} )[/tex]) by 3.
[tex]\sf V_{3 Cylinders} =(3)\dfrac{3}{10} \pi (in^{3} )=\dfrac{9}{10} \pi (in^{3} )=\boxed{\sf 2.8274(in^{3} )}.[/tex]
4. Alternative answer (assuminng the ice cubes have a circular cone shape).Assuming the ice cubes have the shape of a circular cone, this is the process for calculating the volume of all 3 cubes:
[tex]\sf V_{Cone} =\dfrac{1}{3} \pi r^{2} h\\ \\\\ \\ V_{3Cones} =3*\dfrac{1}{3} \pi r^{2} h\\ \\ \\= \pi r^{2} h\\ \\ \\=\pi (\dfrac{1(in)}{2} )^{2} (1.2(in))\\ \\\\ =\dfrac{3}{10} \pi (in^{3} )=\boxed{\sf 0.9425(in^{3} )}[/tex]
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The teacher gave a true and false quiz where P(true) = 0.5 for each question. Interpret the likelihood that the first question will be true.
Likely.
Unlikely.
Equally likely and unlikely.
This value is not possible to represent probability of a chance event.
The likelihood that the first question will be true is equally likely and unlikely.
Interpreting the likelihood that the first question will be true.From the question, we have the following parameters that can be used in our computation:
The teacher gave a true and false quiz where P(true) = 0.5 for each question.
This means that
P(true) = 0.5
As a percentage,, we have
P(true) = 50%
When the probability of an event is 50%, then the event is equally likely and unlikely.
Hence, the liikelihood is (c) qually likely and unlikely.
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a triangle has vertices P(-4,8), I (0,2) and N (4,-2). What are. the coordinates of the centroid of the triangle
The coordinates for the centroid of the triangle is (0, 2.67)
How do we calculate the centroid of the triangle?The centroid of a triangle is the place where the three medians of the triangle meet or intersect.
To find the centroid of the triangle, we use the formula
(x₁ + x₂ + x₃)/3 , (y₁ + y₂ + y₃)/3
We add all the x coordinates together and divide by 3, we also do the same for the y coordinates.
It becomes x = (-4 + 0 + 4)/3
y = (8 + 2 + (-2))/3
Therefore, the centroid is (0, 2.67)
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please help with these questions it's due tommore
7:
To find 6% of 45.50=
0.06x45.50= 2.73
and than 17% of 45.50
0.17x45.50= 7.735
so add 2.73 and 7.735= 10.465
than add 10.465 to $45.50 = $55.965 So the answer is $55.965.
8:
again the same thing but with the different numbers.
0.06x105.75= 6.345
0.20x105.75= 21.15
21.15+6.345= 27.495
so than 105.75-27.495= $78.255
9:
same thing again
146.75x0.25= 36.6875
0.09x146.75= 13.2075
But this time add the tax (13.2075)= 146.75+13.2075= 159.9575
but than you subtract the discount which is 25% so 159.9575-36.6875=123.7
So that is the price! $123.7
I hope that helps!
7.003x10^-5 in standard form
Answer:
0.00007003 is the standard form of 7.003x10^-5. In scientific notation, the number is expressed as 7.003 multiplied by 10 raised to the power of negative five. To convert it to standard form, the decimal point has to move to the left by five places since the exponent is negative. The resulting number is a decimal with four zeros before the first nonzero digit. Standard form is a way of representing numbers that does not use exponents and is useful in comparing and performing operations on numbers.
The average score of 22 students on a math online quiz is 86.3 with a standard deviation of 7.2. The average population score is 83.5. What is the
t-value?
Based the provided information, the t-value is approximately 1.824.
How do we determine the t-value?We shall work out the t-value by calculating the difference between the sample mean and the population mean, divided by the standard error of the mean.
We shall use the t-test formula to calculate the t-value:
t = (sample mean - population mean) / (sample standard deviation / [tex]\sqrt(sample size)[/tex])
where:
sample mean = 86.3
population mean = 83.5
sample standard deviation = 7.2
sample size = 22
Plugging in these values, we have:
t = (86.3 - 83.5) / (7.2 / √22)
t = 2.8 / (7.2 / 4.69)
t = 2.8 / 1.535
t ≈ 1.824
Therefore, the t-value is approximately 1.824.
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