Answers
First, let's calculate the value of cos 2pi/3:
[tex]\cos\frac{2\pi}{3}=-0.5[/tex]Now, let's calculate the value of each option:
[tex]\begin{gathered} \cos\frac{\pi}{6}=0.866\\ \\ \\ \\ \cos\frac{4\pi}{3}=-0.5\\ \\ \\ \\ \sin\frac{5\pi}{3}=-0.866\\ \\ \\ \\ \sin\frac{7\pi}{6}=-0.5\\ \\ \\ \\ \cos\frac{11\pi}{6}=0.866 \end{gathered}[/tex]Therefore the correct options are B and D.
Related Questions
Indenting the zeros and state their multiplicities describe the effect on the graph
Answers
Answer:
6) The given equation is,
[tex]f(x)=(x+7)^2(2x+1)(x-4)^3[/tex]we know that,
The number of times a given factor appears in the factored form of the equation of a polynomial is called the multiplicity.
we get,
Zero Multiplicity Effect
-7 2 Touches the x axis at x=-7
-1/2 1 Passese through the x axis at x=-1/2
4 3 Passes through the point and the curve bend at x=4
write the following comparison as a ratio in simplest form using a fraction, a colon and the word to. _ 198 cents to 234 cents is?
Answers
Given data:
The expression for the kratio of 198 cents to 234 cents is,
[tex]\begin{gathered} \frac{198}{234}=\frac{18\times11}{18\times13} \\ =\frac{11}{13} \\ =11\colon13 \end{gathered}[/tex]Thus, the correct option is (d).
Find the area of the sector of a circle that has a central angle of \Pi radians and a radius of 0.7 in.Round your answer to the nearest hundredth.The area is ___ in^2
Answers
In order to find the area of the sector, let's consider the formula for the area of a circle:
[tex]A=\pi r^2[/tex]The complete circle is equivalent to a sector with central angle 2pi. Knowing this, we can write the following rule of three:
[tex]\begin{gathered} central\text{ }angle\rightarrow area \\ 2\pi\rightarrow\pi r^2 \\ \pi\rightarrow x \end{gathered}[/tex]Now, we can write the following proportion and solve it for x:
[tex]\begin{gathered} \frac{2\pi}{\pi}=\frac{\pi r^2}{x}\\ \\ 2x=\pi r^2\\ \\ x=\frac{\pi r^2}{2}=\frac{\pi\cdot0.7^2}{2}=0.77\text{ in^^b2} \end{gathered}[/tex]Therefore the area is 0.77 in².
Hi can anybody help me with this?(there is a part two)
Answers
ANSWER:
Part A.
D. 6(p - 0.5) = 5.10
Please only solve for angle 1 and ignore the question above.
Answers
Answer:
[tex]m\angle1\text{ = 115}\degree[/tex]Explanation:
Here, we want to get the value of the angle marked 1
From what we have, the bigger arc measures 236°
Now, we need to get the value of the arc ML
We have that as:
[tex]236-70-60\text{ = 106}\degree[/tex]Finally, we use one of the angle theorems to get the value
In using it, we have to consider the value of the smaller arc JK which is 124°
Now, we have its value as:
[tex]\frac{106\text{ + 124}}{2}\text{ = 115}\degree[/tex]We add the value of the arc ML and the value of the smaller arc JK and divide by 2
the sales tax for the city of Los Angeles is 9.75% how much will you pay for an item that costs $200?
Answers
Answer:
$219.5
Explanation
Given
Original cost of an item = $200
Sales tax = 9.75%
Tax = 9.75/100 * 200\
Tax = 9.75 * 2
Tax = $19.5
Amount you will pay = $200 + $19.5
Amount you will pay = $219.5
how many terms the expression x^3+4x^2+2x^-9
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How many terms the expression
x^3+4x^2+2x^-9? 3 TERMS
Let log, 4= 3; log, C = 2; log, D= 5 Ac? Do log What is the value of O A. -11 O B.-15,378 O c. 49 D. 2
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Given:
[tex](x+2)^2+(y-3)^2=9[/tex]Circle equation is
[tex](x-h)^2+(y-k)^2=r^2[/tex](h,k) be the center of the circle and r be the radius.
[tex]\text{Center(-}2,3)\text{ and radius 3}[/tex]Option C is the correct answer.
The systolic blood pressure of women is normally distributed with a mean of 150 mmHg. and a standard deviation of 10 mmHg. What percentage of a 50-year-old women have a systolic blood pressure between 130 mmHg. and 170 mmHg.?
Answers
The required percentage of a 50-year-old woman have a systolic blood pressure between 130 mmHg. and 170 mmHg is 95.44%.
Given that,
The systolic blood pressure of women is normally distributed with a mean of 150 mmHg. and a standard deviation of 10 mmHg.
What is probability?
Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
z = [ x - μ]/σ
Accoding to the question,
= p[z < (170-150)/10] - p[z < 130-150/10]
= p [z <2] - p [z < -2]
= 0.9772 - 0.0228
= 95.44%
Thus, the required percentage of a 50-year-old woman have a systolic blood pressure between 130 mmHg. and 170 mmHg is 95.44%.
Learn more about probability here:
brainly.com/question/14290572
#SPJ1
Match each measurement on the left with an equal measurement on the right. Some answer options on the right will not be used.31/2 yards66 inches2 miles21/2 miles51/2 feet10,560 feet101/2 feet91/2 feet12,300 feet13,200 feet
Answers
Solution
Recall
1 yard is 3feet
1 foot is 12inches
1 mile is 5,280 feet
[tex]3\frac{1}{2}\text{yards =10}\frac{1}{2}\text{ ft}[/tex][tex]66\text{inches =5}\frac{1}{2}ft[/tex][tex]\begin{gathered} 1\text{ miles = 5280 ft} \\ 2\text{miles = 10,560ft} \end{gathered}[/tex][tex]\begin{gathered} 1\text{mile = 5280 ft} \\ 2\frac{1}{2}\text{miles =}13,200ft \end{gathered}[/tex]The function f(t) = -5t to the 2nd power+20t +60 models the approximate height of an object t seconds after it is launched. how many seconds does it take the object to hit the ground?
Answers
We know that if we replace t by some number in the equation:
f(t) = -5t² + 20t + 60
the result will be the height of a launched object.
When the object hits the ground its height is 0.
Then
-5t² + 20t + 60 = 0
We want to solve the highlighted equation fot t, the values of t that make it result in 0 will be the seconds when the object is in the ground.
Solving the equation for tIn order to solve the equation
-5t² + 20t + 60 = 0
we want to factor the left side:
Step 1- Common factor
The common factor of -5t², 20t and 60 is -5:
(-5) · 1 = -5
(-5) · (-4) = 20
(-5) · (-12) = 60
Then
-5t² + 20t + 60 = -5(t² -4t - 12)
Then, replacing the equation
-5t² + 20t + 60 = 0
↓
-5(t² -4t - 12) = 0
↓ taking -5 to the right side
(t² -4t - 12) = 0/(-5) = 0
t² - 4t - 12 = 0
Step 2- Factoring a trinomial
We continue the factoring.
We want to factor t² - 4t - 12.
It should look something like:
t² - 4t - 12 = (t + _ )(t + _ )
To complete it we will use two numbers whose:
- product is -12 (third term t² - 4t - 12)
- sum is -4 (second term t² - 4t - 12)
The pair of numbers whose product is -12 are:
(-1) · 12 = -12
1 · (-12) = -12
(-2) · 6 = -12
2 · (-6) = -12
(-3) · 4 = -12
3 · (-4) = -12
We add them, the pairs whose result is -4 is the pair we will use:
-1 + 12 = 11
1 - 12= -11
-2 + 6 = 4
2 - 6 = -4
-3 + 4 = 1
3 - 4 = -1
Then, we will use 2 and -6 (their product is the third term and their sum is the second term):
t² - 4t - 12 = (t + _ )(t + _ )
↓
t² - 4t - 12 = (t + 2)(t - 6)
Then, using the equation we had:
t² - 4t - 12 = 0
↓
(t + 2)(t - 6) = 0
Step 3- finding the possible t values
When a product of two numbers is 0, it means that one of them is 0:
In this case
We have that
(t + 2)(t - 6) = 0
then
t + 2 = 0 or t - 6 = 0
This means that t could have two possible values:
t + 2 = 0 → t = -2
or
t - 6 = 0 → t = 6
Since t means the seconds the object takes to hit the ground, it cannot have a negative value, because it would mean that it happened in the past. so t cannot be -2
Answer: It takes to the object 6 seconds to hit the ground t = 64.The value of x isis order these expressions from least to greatest:χ1- xx-1-1 = x
Answers
To answer this question we have to evaluate each expression at the given value of x.
Recall that to evaluate an expression we substitute the variable by the given value.
Evaluating each expression at
[tex]x=-\frac{1}{4}[/tex]we get:
[tex]\begin{gathered} x=-\frac{1}{4}, \\ 1-x=1-(-\frac{1}{4})=1+\frac{1}{4}, \\ x-1=-\frac{1}{4}-1=-(1+\frac{1}{4}), \\ -\frac{1}{-\frac{1}{4}}=\frac{1}{\frac{1}{4}}=4. \end{gathered}[/tex]Therefore, the numbers ordered from least to greatest are:
[tex]x-1,\text{ x, 1-x, -1/x.}[/tex]Answer:
[tex]x-1,\text{ x, 1-x, -1/x.}[/tex]> Next question Get a similar question You can retry this 8 3 Volume = Surface Area = Lateral Surface Area = Enter an interer or decimal number (more..] Submit Question
Answers
From the question, r = 8 cm, h =3 cm
Volume of a cylinder = pi x r^2x h = 22/7 x 8 x8 x 3 = 4224/7 = 603.43 cm^3
surface area of a cylinder= 2 x pi x r x h = 2 x 22/7 x 8 x 3 = 1056/7 =
150.86 cm^2
6. Write a regression equation for the data above. (MD1)Answer of 5. is C.
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Looking at the graph of item C in question 5, we can see that it is a straight line, so it is represented by a linear equation of the form:
[tex]y=mx+b[/tex]We can also see that, when the value of x increases, the value of y also increases, which means the slope of the line is positive (m > 0).
With this information and looking at the options, we can conclude that the correct option is B.
Hello looking for someone to help me out on this question
Answers
Answer
The value of x = 14
m∠T = 65°
m∠S = 30°
m∠R = 85°
Explanation
From the given ΔRST,
m∠T + m∠S + m∠R = 180° (Sum of angles in a triangle)
m∠T = (4x + 9)°, m∠S = (2x + 2)° and m∠R = (7x - 13)°
⇒(4x + 9)° + (2x + 2)° + (7x - 13)° = 180°
Grouping the terms, we have
4x + 2x + 7x + 9 + 2 - 13 = 180°
13x - 2 = 180°
13x = 180 + 2
13x = 182
Divide both sides by 13
13x/13 = 182/13
x = 14
Therefore,
m∠T = (4x + 9)° = (4(14) + 9)° = (56 + 9)° = 65°
m∠S = (2x + 2)° = (2(14) + 2)° = (28 + 2)° = 30°
m∠R = (7x - 13)° = (7(14) - 13)° = (98 - 13)° = 85°
Find sum of the pairs of complex numbers.2,8
Answers
Given:
Complex numbers are 2 and 8.
Required:
We need to find the sum of the complex numbers.
Explanation:
The given complex can bw\e written as follows.
[tex]2+i(0)\text{ and }8+i(0).[/tex][tex]Add\text{ }2+i(0)\text{ and }8+i(0)[/tex][tex](2+i(0))\text{ + \lparen}8+i(0))=(2+8)+i(0+0)[/tex][tex](2+i(0))\text{ + \lparen}8+i(0))=10+i(0)[/tex]Final answer:
[tex]10[/tex]12-foot-long wooden beam is supported on both ends. When a weight load is placed in the center of the beam,it causes the beam to sag. The sag is called deflection. The graph shows the deflection of the beam,in inches, as a function of the weight load, in pounds, placed in the center of the beam. for every 50-pound increase in the weight load, what will be the change in the deflection?
Answers
the change in the deflection with every 100 pounds is,
[tex]=\frac{0.5-0}{100-0}[/tex][tex]=\frac{0.5}{100}[/tex]so for every 50 pounds will be,
[tex]\begin{gathered} =(\frac{\frac{0.5}{100}}{2}) \\ =\frac{0.5}{200} \\ =0.0025 \end{gathered}[/tex]so for every 50 pound increase in the weight, the change in the deflection is 0.25
Mariana receives a $20 gift card for downloading music and wants to determine how many songs she can purchase.Each downloaded song costs $1.29. If m represents the number of songs downloaded, which inequality represents thegiven situation?20m 2 1.2920m 1.2901.29ms 2001.29m 2 20Mark this and retumSave and ExitNextSubmit
Answers
Mariana has a $20 gift card for downloading music → this means that she can spend at most $20 on music, you can symbolize this situation as ≤20
If each song costs $1.29 and she buys "m" number of songs, the total cost of the songs can be expressed as 1.29m
Then the inequality that represents the number of songs she can download is
[tex]1.29m\leq20[/tex]The graphs shows the number of hours that Tammy spends typing for work, x, and the amount of pay that she earns, y. What is the slope of the line?
A: 1/4
B: 8/17
C: 4
D: 6
HELP PLS
Answers
Answer: the answer is 6
Step-by-step explanation:
i did it step by step
9. Find the equation(s) of the line(s) through (2,-2) if the sum of the intercer 10. Find the angle that line l, makes with line l. (a) hirty 10, 4:3x - 2y=5 (b) 1,: 2x + 3y = 6,1 -11. Find the coordinates of the point. (a) equidistant from (4.-) and the origin; as well as on the line 2 (b) equidistant from (3, 8) and (-2,5) on the y-axis (c) J x + 3y = 7 5.1 - 6 = -28 12. Find the equation of the line passing through the point (4.-1) and
Answers
Let:
[tex]\begin{gathered} x+3y=7_{\text{ }}(1) \\ 5x-6y=-28_{\text{ }}(2) \end{gathered}[/tex]From (1):
[tex]x=7-3y_{\text{ }}(3)[/tex]Replace (3) into (2):
[tex]\begin{gathered} 5(7-3y)-6y=-28 \\ 35-15y-6y=-28 \\ 35-21y=-28 \\ -21y=-63 \\ y=\frac{-63}{-21} \\ y=3 \end{gathered}[/tex]Replace the value of y into (3):
[tex]x=7-3(3)=7-9=-2[/tex]Therefore:
x = -2
y = 3
or
(x,y) = (-2,3)
6 Ms. Carson drove 96 miles in 15 hoursWhat was her speed in miles per hour!48 miles per hourB.54 miles per hourС64 miles per hourD. 144 miles per hour
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The radius of a circle is 2 meters. What is the circle's circumference?r=2 mUse 3.14 for л.meters
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To solve this problem, we will use the following formula for the circumference of a circle:
[tex]C=2\pi r,[/tex]where r is the radius of the circle.
Substituting
[tex]\begin{gathered} r=\text{ 2 m, } \\ \pi=3.14 \end{gathered}[/tex]in the above formula, we get:
[tex]C=2\times3.14\times2m.[/tex]Simplifying the above result, we get:
[tex]C=12.56m.[/tex]Answer: [tex]\begin{equation*} 12.56m. \end{equation*}[/tex]Can you show me how to do this problem so I can understand it?
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Let's analyze each option to find which transformation generates a hexagon with a greater area:
1)
A translation is a transformation that doesn't change the image shape or size, therefore the area is the same.
2)
A dilation by a scale factor smaller than 1 will reduce the figure, therefore the area will be smaller.
3)
A rotation, just like the translation, doesn't change the image shape or size, therefore the area is the same.
4)
A dilation by a scale factor greater than 1 will make the image bigger, therefore the area will be greater.
So the correct option is the fourth one.
5] Great America has a season pass that costs $45 plus $7 each time you attend thepark, or you can pay $12 each time you go. How many times do you have to go beforeyou pay the exact same amount?
Answers
Let the number of time he attend the park be represented with n.
So that,
C = 45 + 7n ....eqn(1)
C = 12n ..........eqn(2)
Equating both equations, we have,
[tex]\begin{gathered} 12n=45+7n \\ \text{Collecting like terms, we get} \\ 12n-7n=45 \\ 5n=45 \\ \text{Dividing both sides by 5, we get} \\ n=\frac{45}{5}=9 \end{gathered}[/tex]He has to attend the park 9 times before he can pay exactly the same amount.
So, the correct answer is 9.
Suppose you invest $2200 at an annual interest rate of 5.3% compounded continuously. How much will you have after 7 years?
Answers
Answer:
$3188.20
Explanation:
From the information given:
• Principal, P = $2200
,• Interest Rate, r=5.3% = 0.053
,• Time, t=7 years
For a principal compounded continuously, we use the formula to determine the amount in the account:
[tex]A(t)=Pe^{rt}[/tex]Substituting the given values, we have:
[tex]\begin{gathered} A(t)=2200\times e^{0.053\times7} \\ =\$3188.20 \end{gathered}[/tex]You will have $3188.20 after 7 years.
Which of the following is the median of the data set? 15 20 20 25 30 35 40 40 45 50 55(1) 28(2) 30(3) 32(4) 34
Answers
Median: The media is the middle number in a list of values. If there is an even number of values (so there is no middle number) then average the middle two values together.
so:
[tex]set\colon\mleft\lbrace15,20,20,25,30,35,40,40,45,50,55\mright\rbrace[/tex]From the data set, we can conclude that the middle number (median) is:
[tex]35[/tex]A quadratic function and an exponential function are graphed below. How do the decay rates of the functions compareover the interval -2
Answers
To check the decay rate, we need to check the variation in y-axis.
Since our interval is
[tex]-2We need to evaluate both function at those limits.At x = -2, we have a value of 4 for both of them, at x = 0 we have 1 for the exponential function and 0 to the quadratic function. Let's call the exponential f(x), and the quadratic g(x).
[tex]\begin{gathered} f(-2)=g(-2)=4 \\ f(0)=1 \\ g(0)=0 \end{gathered}[/tex]To compare the decay rates we need to check the variation on the y-axis of both functions.
[tex]\begin{gathered} \Delta y_1=f(-2)-f(0)=4-1=3 \\ \Delta y_2=g(-2)-g(0)=4-0=4 \end{gathered}[/tex]Now, we calculate their ratio to find how they compare:
[tex]\frac{\Delta y_1}{\Delta y_2}=\frac{3}{4}[/tex]This tell us that the exponential function decays at three-fourths the rate of the quadratic function.
And this is the fourth option.
If using the method of completing the square to solve the quadratic equationX2 + 15x + 7 = 0, which number would have to be added to "complete thesquare"?
Answers
ANSWER
225/4
EXPLANATION
To complete the square we want to write a part of the equation in the form:
[tex](a+b)^2=a^2+2ab+b^2[/tex]The second term squared is the one we have to add to the equation in order to complete the square.
In this case, the coefficient of x is 15, so b is:
[tex]b=\frac{15}{2}[/tex]And b²:
[tex]b^2=\frac{225}{4}[/tex]If we add 225/4 to both sides of the equation:
[tex]x^2+15x+\frac{225}{4}+7=\frac{225}{4}[/tex]We complete the square:
[tex](x+\frac{15}{2})^2+7=\frac{225}{4}[/tex]Find the solutions to 2x² - 10x+12= 0.Check all that apply, as there can be more than one awnserA. 2B. 3C. 12D. 4
Answers
The given equation is expressed as
2x^2 - 10x + 12 = 0
Dividing each term by 2, it becomes
x^2 - 5x + 6 = 0
This is a quadratic equation. We would solve by applying the method of factorization. The first step is to multiply x^2 with 6. It becomes 6x^2. We would find two terms such that their sum or difference is - 5x and their product is 6x^2. The terms are - 3x and - 2x. By replacing - 5x with - 2x - 3x, we have
x^2 - 2x - 3x + 6 = 0
Factorize by grouping. It becomes
x(x - 2) - 3(x - 2) = 0
(x - 2)(x - 3) = 0
x - 2 = 0 or x - 3 = 0
x = 2 or x = 3
The solutions are
A. 2
B. 3
Pat is 20 years older than his son Patrick. In 2 years, the sum of their ages will be 90. How old are they now?Patrick is years old, and Pat is ?years old.
Answers
Let "x" be the age of Patrick.
Pat is 20 years older than his son Patrick so we can represent this as "x+20".
In two years, the age of patrick will be x+2 and the age of Pat will be x+22.
Since in 2 years, the sum of their ages will be 90, we can write:
[tex]\begin{gathered} x+2+x+22=90 \\ 2x+24=90 \\ 2x=66 \\ x=33 \end{gathered}[/tex]And, the age of Pat is x+20 which is 53.
Therefore, Patrick is 33 years old, and Pat is 53 years old.