In a unit circle, Ф = π radians. What is the terminal point?O A. (-1,0)OB. (1,0)O C. (0, 1)O D. (0, -1)
Answers
Answer:
A. (-1, 0)
Step-by-step explanation:
You want to know the terminal point on the unit circle of an angle of π radians in standard position.
HalfwayThe angle π radians is halfway around the circle. The full measure of a circle is 2π radians. Halfway around puts the terminal point on the -x axis. Since the radius of a unit circle is 1 unit, the coordinates of the terminal point are (x, y) = (-1, 0).
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Additional comment
The point of interest is shown at left-center in the attachment.
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Related Questions
y varies inversely with x. if y=7 when x= -4, find y when x=2
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
y varies inversely with x. if y=7 when x= -4, find y when x=2
Step 2:
Mathematically, we have that:
[tex]\begin{gathered} y\text{ }\propto\text{ }\frac{1}{x} \\ y\text{ =}\frac{k}{x},\text{ where k is a constant} \end{gathered}[/tex][tex]\begin{gathered} \text{when x= -4, then y = 7} \\ 7\text{ = }\frac{k}{-4} \\ \end{gathered}[/tex]cross-multiply, we have that:
[tex]\begin{gathered} k\text{ = 7 x - 4} \\ k\text{ = -28} \end{gathered}[/tex]Hence, the relationship between x and y is:
[tex]y\text{ =}\frac{-28}{x}[/tex]Step 3:
Since,
[tex]\begin{gathered} y\text{ = }\frac{-28}{x} \\ \text{when x = 2, we have that:} \\ y\text{ = }\frac{-28}{2} \\ y\text{ = -14} \end{gathered}[/tex]CONCLUSION:
When x = 2 , then y = -14
What 694+361 i need to know I’m in 2nd grade
Answers
given data:
[tex]694+361[/tex]to add,
[tex]694+361=1055[/tex]Answer: 1055
Step-by-step explanation:
15x + 21 ≥ 120 what's the inequality
Answers
Given the inequality:
[tex]\text{ 15x + 21 }\ge\text{ 120}[/tex]Let's determine the solution to the inequality.
sixteen divided by eight has a quotient of two (written as a expression)
Answers
Solution
For this case we have the following:
[tex]\frac{16}{8}=2[/tex]then the answer for this operation is 2
Dominique paints faces at a carnival. Her goal is to earn $100. She spends $16 on supplies and charges $3 per face. How many faces will she need to paint to meet her $100 goal.
Answers
38 faces
Explanation:
Amount to be earned = $100
Amount spent on supplies = $16
This is an expenses on the business
Amount charged per face = $3
Let x represent the number of faces to be painted
The total calculation:
[tex]\begin{gathered} 100=\text{ 3x -16} \\ 100+16\text{ = 3x} \\ 116\text{ = 3x} \\ \text{Divide through by 3} \\ x\text{ =}\frac{116}{3} \\ x\text{ = 38.67} \\ Since\text{ number of faces can't be decimal or fraction,} \\ we\text{ will approxi}mate\text{ to 39 faces} \end{gathered}[/tex]Note: $16 was subtracted because it was an expense and to make a profit of $100, it snould not include expenses.
Therefore, the number of faces she needs to paint to meet her $100 goal is 38 faces.
what is the value of x in the equation below √x+2=5
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4х – 3 = - 5x - 21 need help
Answers
we have the equation
4х – 3 = - 5x - 21
solve for x
Group terms
4x+5x=-21+3
combine like terms
9x=-18
divide by 9 both sides
9x/9=-18/9
simplify
x=-2
therefore
the answer is x=-2What are the sides of the triangle in order ?
Answers
Solution:
To solve this problem, we need to know a principle:
The higher the angle is, the longer the side opposite the angle.
Since the largest angle is angle C which is 81 degrees, the side opposite it is the longest which is AB.
The second-largest angle is angle A which is 60.4 degrees and its opposite side is side BC.
The smallest angle is angle B which is 38.6 degrees with an opposite side of side AC.
ANSWER: AB, BC, AC (Last Option)
A regular heptagon has an apothem of approximately 5.2 cm and a perimeter of approximately 35.0 cm.Find the area of the heptagon.
Answers
Answer:
[tex]91\operatorname{cm}^2[/tex]Explanation:
Step 1. The information that we have about the regular heptagon is:
The apothem, which we will call ''a'':
[tex]a=5.2cm[/tex]The perimeter, which we will call ''P'':
[tex]P=35cm[/tex]Step 2. The formula to find the area of any regular polygon (in this case a heptagon) is:
[tex]A=\frac{P\times a}{2}[/tex]Where A is the area, P is the perimeter and a is the apothem.
Step 3. Substitute the values of P and a into the formula:
[tex]A=\frac{35cm\times5.2cm}{2}[/tex]Solving the operations we find the area:
[tex]\begin{gathered} A=\frac{182cm^2}{2} \\ \\ A=\boxed{91\operatorname{cm}^2} \end{gathered}[/tex]Answer:
[tex]91\operatorname{cm}^2[/tex]
Tools - Question 1 In the right triangle shown, what is the value of PQ? 17 cm 15 cm A 2 cm B 4 cm с 8 cm OLULI Illuminate Education TM Inc.the answer choices is a. 2cm, b, 4cm. c,8cm.d, 16cm
Answers
Answer:
c. 8
Explanation:
The Pythagorean theorem says that if we have a right triangle with sides a, b, and c, where c is the longest side, then, the following equation applies:
[tex]c^2=a^2+b^2[/tex]In this case, we know the value of c and the value of one of the sides, so we can replace the values and solve the equation for the missing side. Therefore, the value of PQ can be calculated as:
[tex]17^2=15^2+\bar{PQ}^2[/tex]So, solving for PQ, we get:
[tex]\begin{gathered} 289=225+\bar{PQ}^2 \\ 289-225=225+\bar{PQ}-225 \\ 64=\bar{PQ} \\ \sqrt[]{64}=\bar{PQ} \\ 8=\bar{PQ} \end{gathered}[/tex]Therefore, the value of PQ is 8 cm.
find the surface area of the tunnel created inside the block.
Answers
The surface area of the tunnel passing through the block is simply the curved surface area of the cylindrical shape.
The Surface Area is given by
[tex]A=2\pi rh[/tex]where the following are given from the question:
[tex]\begin{gathered} r=\frac{4}{2}=2ft \\ h=4ft \end{gathered}[/tex]Substituting these values:
[tex]\begin{gathered} A=2\times\pi\times2\times4 \\ A=50.27 \end{gathered}[/tex]Therefore, the surface area of the tunnel created inside the block is 50.27 ft² (50.27 square feet)
Can u please help me. I'll send the other options to u as well
Answers
Explanation
We are told to fi
Every year, 20 fewer students eat in the school cafeteria. Assuming this trend continues, write amultiplication expression to show the change in the number of students over the next 4 years. Expressthis change as an integers.
Answers
Explanation:
Let the number of students in sthe initia year = x
The number reduced every year by 20
At year 1 = x-20
l
Emma is buying tickets to a movie for Earth self and some friends there are four options to choose from .ifshe needs 6 ticket which movie theater should she go to in order to get the best deal ?explain reason
Answers
The big screen
y = 12.9x
For 6 y = 12.9(6)
y = $77.4
Perfect picture tickets
$65.5 for 5-tickets
then, for one ticket
65.5 / 5 = 13.1
$65.5 + $13.1
$78.6
Graph
For 6 tickets the cost is $81
So the cheapest tickets are from The big screen, so it is the best deal.
4. Your parents put $5000 in an account in 1994 for your collegeeducation. They did not add any money to the account as you grewup, because it cost so much to raise you!! If the account made 1.2%interest compounded monthly, would they have enough money to sendyou to college in 2012 if the college you want to attend is $10,000?
Answers
interest compounded monthly is
[tex]undefined[/tex]a line is represented by the equation y+1=x.what is the y-intercept of the line represented by the equation
Answers
To find the y-intercept of the function, we solve for y, that is:
[tex]y+1=x\Rightarrow y=x-1[/tex]Since the function has the form:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept, we can determine that the y-intercept equals -1.
show the opposite of 10
Answers
To find the opposite of a number we can draw a number line.
If we go to the right of zero, we have positive numbers.
TO the left, we have negative numbers.
The opposite of a number is the number that is the same distance from zero but on the other side.
So, the opposite of 10 is -10.
Find the 5th term ofSn = 4h + 5n
Answers
Given the equation of the sequence:
[tex]S_n=4n+5n[/tex]To find the 5th term, substitute with n = 5
So,
[tex]S_5=4\cdot5+5\cdot5=20+25=45[/tex]So, the answer will be the 5th term = 45
Matilda builds model. The model is a right rectangular prism and a small cube. How much area does she have to paint if she paints all of the exterior? cube: l:4 w:4 h:4rectangular prism: l:17 w: 14 h: 15
Answers
The exterior area for the paint consist of 5 faces of cube and six faces of rectangular prism minus one face of cube, as one face of cube is placed on upper surface of rectangular prism and covers the certain area of rectangular prism.
Determine the exterior area available for the paint.
[tex]\begin{gathered} A=2(15\cdot14+17\cdot14+17\cdot15)-4\cdot4+5\cdot4\cdot4 \\ =2(210+238+255)-16+80 \\ =1406-16+80 \\ =1470 \end{gathered}[/tex]So area for the paint to the exterior is 1470 square inch.
the cost C in dollars sign of producing X items in the equation C equals x over 7 plus 1 which of the following choices will find the cost C if x is 35
Answers
Writing the equation described, we have:
[tex]C=\frac{x}{7}+1[/tex]Now, calculating the value of the cost C for x equal to 35, we have:
[tex]\begin{gathered} C=\frac{35}{7}+1 \\ C=5+1 \\ C=6 \end{gathered}[/tex]So the cost C for 35 products is $6.
Jorge rolls a six-sided die. What is the probability that he rolls a 1 or a prime number
Answers
0.67
ExplanationThe probability formula provides the ratio of the number of favorable outcomes to the total number of possible outcomes. The probability of an Event = (Number of favorable outcomes) / (Total number of possible outcomes)
[tex]P=\frac{favorable\text{ outcomes}}{\text{total outcomes}}[/tex]then,let
total outcomes= 6 ( a six-sided die)
favorable outcomes= 1 or a prime number
hence, let's check the prime numbers( a prime number is a number that is divisible only by itself and 1 =
[tex]\begin{gathered} s=\lbrace1,2,3,4,5,6\rbrace \\ \text{primer numbers=}\lbrace1,2,3,5\rbrace \end{gathered}[/tex]so, the total of prime numbers and 1 is
Favorable outcomes(1 or a prime number)=4
Now, replace in the formula.
[tex]\begin{gathered} P=\frac{favorable\text{ outcomes}}{\text{total outcomes}} \\ P=\frac{4}{6} \\ P=0.666 \\ P=0.67 \end{gathered}[/tex]so, the probability is 0.67
I hope this helps you
Find the equation of the line with the given slope and containing the given point: Slope -6/5 through (- 9,0)
Answers
From the given: Slope (m) = -6/5 and point (-9, 0), we will use the Slope-Intercept Form in making the equation.
[tex]\text{ y = mx + b}[/tex]The slope-intercept form is given a y=mx+b where m is the slope and b is the y-intercept at point (0,b).
Let's solve for the y-intercept (b) substituting the slope (m) = -6/5 and (x,y) = (-9,0).
Thus, we get,
[tex]\text{ y =mx + b}[/tex][tex]\text{ 0 = (}\frac{-6}{5})(-9)\text{ + b }\rightarrow\text{ b = -(}\frac{-6\text{ x -9}}{5})\text{ = }\frac{-54}{5}[/tex]Let's now make the equation substituting the slope (m) = (-6/5) and y-intercept (b) = (-54/5). We get,
[tex]\text{ y = (}\frac{-6}{5})x\text{ + (}\frac{-54}{5})[/tex][tex]\text{ y = -}\frac{6}{5}x\text{ - }\frac{54}{5}[/tex]if f(x)=5x+2 determine f(-1)
Answers
f(x)= 5x+2
To determine f (-1) replace x by -1 and solve:
f(-1)= 5(-1) +2
f(-1)= -5+2
f(-1)= -3
16 100 4. Find the height if the area is 70 square meters: h 10 mI need help
Answers
Given:
Area of the triangle, A = 70 square meters
Base of the triangle, b = 10 meters
To find the height, h, of the triangle, use the area of the triangle formula below:
[tex]A=\frac{1}{2}\times b\times h[/tex]Rewrite the formula for h:
[tex]\begin{gathered} 2A=b\times h \\ \\ \frac{2A}{b}=\frac{b\times h}{b} \\ \\ \frac{2A}{b}=h \\ \\ h=\frac{2A}{b} \end{gathered}[/tex]To find the height, h, we have the equation:
[tex]h=\frac{2A}{b}[/tex]Input values into the equation:
[tex]h=\frac{2(70)}{10}=\frac{140}{10}=14\text{ }[/tex]Therefore, the height of the triangle is 14 meters
ANSWER:
14 meters
The total cost (in dollars) of producing a coffee machines is C(x) = 2100 + 50x - 0.1x^2.(A) Find the exact cost of producing the 21st machine.Exact cost of 21st machine= __(B) Use marginal cost to approximate the cost of producing the 21st machine.Approx. cost of 21st machine =
Answers
we know that
the function of the cost is equal to
[tex]C(x)=2,100+50x-0.1x^2[/tex]Part A
For x=21 machine
substitute in the function above
[tex]C(21)=2,100+50(21)-0.1(21)^2[/tex]C(21)=$3,105.90
therefore
The exact cost of 21st machine=$3,105.90Part B
Use marginal cost to approximate the cost of producing the 21st machine
Remember that
The marginal cost function is the derivative of the total cost function, C(x)
so
Find out the first derivative of the function C(x)
[tex]C^{\prime}(x)=50-0.2x[/tex]For x=21
substitute
[tex]\begin{gathered} C^{\prime}(21)=50-0.2(21) \\ C^{\prime}(21)=\$45.8 \end{gathered}[/tex]The table shows the results for spinning the spinner 80 times. What is therelative frequency for the event "spin a 4"?21414Experiment TableOutcome 1 2 3 4 Number ofTrials18 30 12 20 80FrequencyThe relative frequency for the event "spin a 4" is
Answers
Relative frequency is the ratio of the number of times or frequency of an outcome to the total number of outcomes.
From the information given,
Total number of times of spinning a 4 = 20
Total number of spins = 80
Thus,
The relative frequency of the event 'spin a 4' = 20/80 = 1/4
1) The depth of a lake in Lowell changes over time due to rainfall and evaporation. A few months ago, the depth was 70 feet. Currently, the depth is 63 feet. By what percent has the depth of the lake decreased?
Answers
To find the percentage decrease, we will simply use the the formula;
new depth - original depth /original depth x100%
new depth =63 feet
original depth = 70 feet
63 - 70 / 70 x100%
-7/70 x100%
= -10% or 10% decrease.
paddy spent $63.00 on three tickets to a concert. javier spent $80 on four tickets. which person paid less per ticket
Answers
Let's find the unit price
Paddy =$63.00/3 = $21 per ticket
Javier = $80 /4 = $20 per ticket
This implies Javier paid less per ticket
Find the solution to the following system with algebra. Check by graphing both equations to verify that the lines intersect at the solution you found algebraically, y + 2x = -3 3y - x = 12
Answers
Given the set of equations:
y + 2x = -3.......................equation 1
3y - x = 12........................equation 2
Let's find the solution to the system of equations by graphing.
The solution of the system of equations will be the point where the lines of both equations meet (point of intersection).
To graph, rewrite both equations to slope-intercept form: y = mx + b
Where m is the slope and b is the y-intercept.
Equation 1:
y + 2x = -3
Subtract 2x from both sides:
y + 2x - 2x = -2x - 3
y = -2x - 3
Equation 2:
3y - x = 12
Add x to both sides:
3y - x + x = x + 12
3y = x + 12
Divide all terms by 3:
[tex]\begin{gathered} \frac{3y}{3}=\frac{x}{3}+\frac{12}{3} \\ \\ y=\frac{1}{3}x+4 \end{gathered}[/tex]Thus, we have both equations in slope intercept form:
y = -2x - 3
y = ⅓x + 4
We have the graph below:
From the graph of both equations above, we can see the point both lines intersect is at the point: (x, y) ==> (-3, 3)
Where:
x = -3, y = 3
Therefore, the solution to the system of equations is (-3, 3)
ANSWER:
(-3, 3)
4) If an object is dropped from a tower of unknown height, the velocity of the object after t secondscan be obtained by multiplying t by 32 and adding 10 to the result. Therefore, you can express V asa linear function of t. Find the domain of this function.A) (-.,)B) [1,4]C)[0,-)D) (-1, .)
Answers
4) If an object is dropped from a tower of unknown height, the velocity of the object after t seconds
can be obtained by multiplying t by 32 and adding 10 to the result. Therefore, you can express V as
a linear function of t. Find the domain of this function.
Step 1
Let's find that equation!!
define
v as the velocity
Also
"the velocity of the object after t seconds can be obtained by multiplying t by 32 and adding 10 to the result" in math words ,it is
[tex]\begin{gathered} v=(32\cdot t)+10 \\ \end{gathered}[/tex]where v is the velocity, t the time in seconds
now, we have our function, now we need to find its domain
remember:
The domain of a function f (x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes
so, for us
t can take any value, in other words , there are not values for x to make a indetermination
so, t can take any value, the domain is all the real numbers
[tex]\text{Domain=(-}\infty,\infty)[/tex]I hope this helps you