I'm using goformative to do my work, I have number 13 answer right but the rest show my answers incorrect, I will appreciate if you can help me with my question I will paste the image of the question I have.
Answers
Firstly, we will have to make a representation of the angle
We have this as follows;
As we can see, alpha added to theta is 180 degrees
Firstly, by the use of Pythagoras' theorem, we can get the value of r
r faces the right angle, and that makes it the hypotenuse
According to the theorem, the square of r, the hypotenuse equals the sum of the squares of the two other sides
Thus, we have it that;
[tex]\begin{gathered} r^2=(-2)^2+4^2 \\ r^2\text{ = 4 + 16} \\ r^2\text{ = 20} \\ r\text{ = }\sqrt[]{20} \\ r\text{ = 2}\sqrt[]{5} \end{gathered}[/tex]From here, we can proceed to get the individual trigonometric ratios
a) Sine
This is the ratio of the opposite to the hypotenuse
On the second quadrant, the value of sine is positive
Thus, we have it that;
[tex]\begin{gathered} \sin \text{ }\alpha\text{ = }\frac{4}{2\sqrt[]{5}} \\ \alpha\text{ = }\sin ^{-1}(\frac{4}{2\sqrt[]{5}}) \\ \alpha\text{ = 63.43} \\ \theta\text{ = 180-63.43} \\ \theta\text{ = 116.57} \\ \sin \text{ 116.57 = }\frac{4}{2\sqrt[]{5}\text{ }}=\text{ }\frac{4\sqrt[]{5}}{10}\text{ = }\frac{2\sqrt[]{5}}{5} \\ \\ \sin \text{ }\theta\text{ = }\frac{2\sqrt[]{5}}{5} \end{gathered}[/tex]b) cosine
The cosine of an angle is the ratio of the adjacent to the hypotenuse
Mathematically, we know that;
[tex]\begin{gathered} \cos ^2\theta+sin^2\theta\text{ = 1} \\ \cos ^2\theta=1-sin^2\theta \\ \cos ^2\theta\text{ = 1 - (}\frac{2\sqrt[]{5}}{5})^2 \\ \\ \cos ^2\theta\text{ = 1- }\frac{20}{25} \\ \\ \cos ^2\theta\text{ = }\frac{5}{25} \\ \cos ^2\theta\text{ = }\frac{1}{5} \\ \\ \cos \text{ }\theta\text{ = }\sqrt[]{\frac{1}{5}} \\ \\ \cos \text{ }\theta\text{ = -}\frac{\sqrt[]{5}}{5} \end{gathered}[/tex]We choose the negative value for the cosine since cosine is negative on the second quadrant
c) Tan
The tan of an angle is the ratio of the opposite to the adjacent
Also, by dividing the sine of an angle by the cosine of the same angle, we can get the tan of the angle
Thus, we have it that;
[tex]\begin{gathered} \text{Tan }\theta\text{ = }\frac{\sin \text{ }\theta}{\cos \text{ }\theta} \\ \\ \text{Tan }\theta\text{ = }\frac{\frac{2\sqrt[]{5}}{5}}{\frac{-\sqrt[]{5}}{5}}\text{ = }\frac{2\sqrt[]{5}}{5}\times\frac{5}{-\sqrt[]{5}}\text{ = -2} \end{gathered}[/tex]d) cosec theta
The cosec of an angle is the multiplicative inverse of the sine
Mathematically;
[tex]\begin{gathered} co\sec \theta\text{ = }\frac{1}{\sin \text{ }\theta} \\ \\ co\sec \text{ }\theta\text{ = }\frac{1}{\frac{2\sqrt[]{5}}{5}}\text{ = }\frac{5}{2\sqrt[]{5}}\text{ = }\frac{5\sqrt[]{5}}{10}\text{ = }\frac{\sqrt[]{5}}{2} \end{gathered}[/tex]e) sec theta
The sec of an angle is the multiplicative inverse of the cosine of the angle
Thus, we have it that;
[tex]\text{sec }\theta\text{ = }\frac{1}{\cos \text{ }\theta}\text{ = }\frac{1}{-\frac{\sqrt[]{5}}{5}}\text{ = -}\frac{5}{\sqrt[]{5}}\text{ = -}\frac{5\sqrt[]{5}}{5}\text{ = -}\sqrt[]{5}[/tex]f) cot theta
The cot of an angle is the multiplicative angle of the tan
Thus, we have it that;
[tex]\begin{gathered} \cot \text{ }\theta\text{ = }\frac{1}{\tan \text{ }\theta} \\ \\ \cot \text{ }\theta\text{ = }\frac{1}{-2}\text{ = -}\frac{1}{2} \end{gathered}[/tex]
Related Questions
. Find the value of x when: 4/(x - 8) = 8/2 *
Answers
The value of x is 9
Explanation:Given the equation:
[tex]\frac{4}{x-8}=\frac{8}{2}[/tex]Multiply both sides by 2(x-8)
[tex]\begin{gathered} 4\times2=8(x-8) \\ 8=8(x-8) \end{gathered}[/tex]Divide both sides by 8
[tex]x-8=1[/tex]Finally, add 8 to both sides
[tex]x=1+8=9[/tex]Is there a tutor that can help me?
Answers
You have the following equation:
9x - 5y = 6
In order to find the equation of the line, you first calculate the slope of the previous line equation:
9x - 5y = 6 subtract 9x both sides
9x - 9x - 5y = 6 - 9x simplify
-5y = -9x + 6 divide by -5 both sides
-5y/(-5) = -(9/5)x + 6/5 simplify
y = -(9/5)x + 6/5
y = -1.8x + 1.2
Then, the slope of the line is m=-1.8
Now, to find the equation of the line with the point (6,-2) you use the following formula for the slope of a line:
m=(y-yo)/(x-xo)
due to the required line is parallel to the line with slope -1.8, the slope of the required line is the same, m = -1.8. xo and yo are the given coordiantes of the given point (6,-2), that is, xo = 6 and y = -2. You replace these values into the formula for the slope and solve for y:
m = (y - (-2))/(x - 6) = (y + 2)/(x - 6) multiply both sides by (x-6)
(x-6) m= y + 2
y = mx - 6m - 2 = (-1.8)x - 6(-1.2) - 2
y = -1.8x - 5.2
This last equation is the required equation
Is (1, 2). (5,2), (5,4), (7,6). (11, 6) (11,8) a function, yes or no?!!!!
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The group of points (1, 2). (5,2), (5,4), (7,6). (11, 6) (11,8) is not a function as it doesn't satisfy the condition that there is one and only one value in the image space for every element in the domain.
We have the points (5, 2) and (5, 4), which shows two values (y=2 and y=4) for the same point in the domain (x=5).
It also happens for (11, 6) and (11,8).
How do I match these polynomial and what are the correct matches?!
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Add the polynomials:
[tex](-4x^2-3x+6)+(6x^2-2x+1)[/tex]Removing the parentheses:
[tex]-4x^2-3x+6+6x^2-2x+1[/tex]Collecting like terms:
[tex]2x^2-5x+7[/tex]Find the opposite of:
[tex]2x^2+x-7[/tex]We change the signs of all terms:
[tex]-2x^2-x+7[/tex]Subtract:
[tex](-4x^2+2x-1)-(-2x^2+3x+6)[/tex]Remove the parentheses, but the last one requires changing the signs of the second polynomial (find the opposite):
[tex]-4x^2+2x-1+2x^2-3x-6[/tex]Collecting like terms:
[tex]-2x^2-x-7[/tex]Ella finished a bike race in 37.6 minutes. Miranda finished the race 9 1/10 minutes sooner than Ella finished it. How many minutes did it take Miranda to finish the race?A. 32.5 minutes B. 46.7 minutes C. 28.59 minutes D. not here
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The time that it took Ella to finish the race is: 37.6 minutes.
Since Miranda finished the race 9 1/10 minutes sooner, to find Miranda's time we need to subtract 9 1/10 from Ella's time of 37.6 minutes.
Miranda's time:
[tex]37.6-9\frac{1}{10}[/tex]To solve the problem it is easier if we convert 9 1/10 to a decimal number. Since 1/10 is equal to .1, the equivalent value of 9 1/10 is:
[tex]9\frac{1}{10}=9.1[/tex]Updating the expression to find Miranda's time:
[tex]37.6-9.1[/tex]And the result of the subtraction is:
[tex]28.5[/tex]It took Miranda 28.5 minutes to finish the race. Since this value is not one of our options, the answer is D. not here
F(x) =2x^2+12x-6 Does this function have a minimum or maximum value? What is this minimum or maximum value?
Answers
Let's compare the given function with the model for a quadratic equation:
[tex]\begin{gathered} f(x)=ax^2+bx+b \\ a=2,b=12,c=-6 \end{gathered}[/tex]Since the value of a is positive, the parabola has its concavity upwards, and the function has a minimum value.
The minimum value can be found calculating the y-coordinate of the vertex:
[tex]\begin{gathered} x_v=-\frac{b}{2a}=-\frac{12}{4}=-3 \\ \\ y_v=2\cdot(-3)^2+12\cdot(-3)-6 \\ y_v=2\cdot9-36-6^{} \\ y_v=-24 \end{gathered}[/tex]Therefore the minimum value is -24.
eighty-two million, eighty thousand, eleven to standard notation
Answers
Given: eighty-two million, eighty thousand, eleven
To Determine: The standard notation of the given number
Solution
Let us first write the numbers in figure
[tex]\begin{gathered} 82,000,000+80,000+11 \\ =82,080,011 \end{gathered}[/tex]Please note Standard notation of a number is when a number is written with only number digits
Hence, the standard notation of the given is 82, 080, 011
Complete the two-column proof that the diagonals of a rhombus are perpendicular. Glven: JKLM Is a rhombus Prove:JL I MK J N M K L Part 1 out of 7 Statements Reasons 1.JM JK 1. Definition of rhombus 2. MN AKN 2. (select) Check Next
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Corresponding parts of the congruent triangles are congruent. This implies that the corresponding part of the triangles are equal
Also, all the four angles are congruent and they are equal to 90 degrees.
The diagonals are perpendicular to each other
lan's mom works two part time jobs, one in the morning and one in the afternoon, for a total of 35 hours each 5-daywork week. If her schedule is the same each day, and she works 4 hours each morning, how many hours does she workin the afternoon?
Answers
lan's mom work for total 35 hours in 5-days week, so each day she worked for,
[tex]\frac{35}{5}=7[/tex]So Ian's mom worked 7 hours each, in which she work 4 hours each morning.
Determine the number of hour's Ian's mom work in afternoon in one day.
[tex]7-4=3\text{ }[/tex]So each day Ian's mom work 3 hours in the afternoon.
Let g(x) = - 7x + 4. Find g(2)
Answers
The given expression : g(x) = -7x+4
to find the value of g(2)
Substitute x = 2 in the function of g(x)
g(x) = -7x + 4
g(2) = -7 (2) +4
g(2) = -14+4
g(2) = -10
Answer : -10
What is the growth percentage of h(x) = .5(2)" ?A200%B2%100%D10%
Answers
We can compute the growth percentage, computing first, two consecutive values, as follows:
[tex]\begin{gathered} h(1)=0.5(2)^1=0.5(2)=1 \\ h(2)=0.5(2)^2=0.5(4)=2 \end{gathered}[/tex]Then, the growth percentage is:
[tex]\frac{h(2)-h(1)}{h(1)}\cdot100=\frac{2-1}{1}\cdot100=100\text{ \%}[/tex]Select the correct answer.What is the value of the third quartile of the data set represented by this box plot?HHHH12 14 16 18 20 22 24 26 28 30 32 34 36OA19B.21C26OD.29
Answers
A box plot is a standardized way of displaying the distribution of data based on a five-number summary (“minimum”, first quartile (Q1), median, third quartile (Q3), and “maximum”).
The points at the beginning and end of the graph show the outliers (minimum and maximum values).
The outer lines on the left and right of the box show the first quartile and third quartile respectively, while the line inside the box is the median.
From the question, the third quartile (Q3) is the outer line to the right of the box, and its value is 29.
Therefore, OPTION D (29) is correct.
solve the polynomial in standard form1) y=(x-3)^2-3(x-4)
Answers
we reduce the equal terms and we obtain the answer is
[tex]y=x^2-9x+21[/tex]What is the range of the function?Type the range using interval notation example : (#,#]
Answers
The range of the function is the values of y
Then to find it, look for the smallest and the greatest value of y of the graph of the function
From the given figure
The lowest value of y is -1
The highest value of y is 3
Then the range of the function is [-1, 3]
A house increase value by 32% since it was purchased. If the current value is $495,000, what is the value when it was purchased?
Answers
Answer:
$375,000.
Explanation:
Let the value of the house when it was purchased = x
If its value increases by 32%, then its current value will be:
[tex]x+(32\%\text{ of x)}[/tex]Since we are told that the current value is $495,000, then:
[tex]x+(32\%\text{ of x)=495,000}[/tex]We solve for x.
[tex]\begin{gathered} x+0.32x=495,000 \\ 1.32x=495,000 \\ x=\frac{495,000}{1.32} \\ x=\$375,000 \end{gathered}[/tex]The value of the house when it was purchased was $375,000.
Zeros 4 and -3iI already asked for the last question, but I’m confused for the i
Answers
Given:
The zeros of the polynomial are 4 and 3i.
Required:
To find the polynomial of the function.
Explanation:
Here
[tex]\begin{gathered} x=4 \\ x=-3i \end{gathered}[/tex][tex]\begin{gathered} x-4=0\text{ and} \\ x+3i=0 \end{gathered}[/tex]Therefore
[tex]\begin{gathered} (x-4)(x+3i)=0 \\ \\ x^2-4x-3ix-12i=0 \\ \\ x^2-(4+3i)x-12i=0 \end{gathered}[/tex]Final Answer:
[tex]x^2-(4+3i)x-12i=0[/tex]A grocery store is giving a reusable bag to every person who donates more than $5 to charity. Daniel donates $5. Will he get a bag? Explain how you know?The problem deals with the same thing if they get a reusable bag if they donate $5 dollars to charity but it says Courtney donates $1.25 dollars will she get a bag? Explain why?
Answers
Daniel will not going to get a bag
why?
lets read the statement, a part of it
person who donates more than $5 to charity
the key word here is more,
daniel donates exact 5 dollars,
so he will not get a bag
Courtney cant get a bag, because she donates even less,
to get a bag you need to donate, according to the statement , 5 dollars or more,
so for example, you need to donate 5.01 dollars to get a bag
Find an equation of the line parallel to the graph of y = -3x - 11 that passes through the point of (2,4). Write your equation in slope-intercept form.
Answers
Find an equation of the line parallel to the graph of y = -3x - 11 that passes through the point of (2,4). Write your equation in slope-intercept form.
__________________________________________________________
Line parallel to the graph of y = -3x - 11
1. The slope-intercept form.
y = mx + b
m= slope
y-intercept is (0, b)
The lines parallel has the same slope (m) = -3
_______________________________________
Using the point-slope form
(y-y1)= m (x-x1)
2. Replacing the point and the slope
(2,4) x1= 2; y1 = 4
(y- 4)= -3 (x- 2)
3. Write your equation in slope-intercept form.
y = -3x +6 +4
y = -3x + 10
___________________
Answer
y = -3x + 10
IncorrectYour answer is incorrectA vehicle factory manufactures cars. The unit cost C (the cost in dollars to make each car) depends on the number of cars made. If x cars are made, then theunit cost is given by the function C()0.3x-66x + 13,267. What is the minimum unit cost?Do not round your answer.Unit cost: S1dxCheckSave For LaterSubmit AssignmentPrencyAceeshhy1125 PMWednesday1620212021 MMcGraw-H Education, All Riathts Resered.Torms of Use9Type here to search
Answers
Please check that the expression for the cost you typed reflects what you read in the problem.
Isn't there a "square" in one of the "x" values of the cost equation?
Great. I see now the actual equation for cost to be:
Cost = 0.3 x^2 - 66 x + 13267.
The minimum unit cost will be given by the minimum of this quadratic function (a parabola) which has a minimum at the parabola's vertex. Notice this is a parabola with branches pointing UP because the coefficient of the term in x^2 is POSITIVE.
Recall then the equation for the x position of the vertex of a pparabola with equation of the form:
y = a x^2 + b x + c
the x-position of the vertex is: x = - b / (2a)
which in our case gives:
x of the vertex = - (- 66) / (2 * 0.3) = 110
Then, since the x values represent the number of cars that are made , we now that that minimum occurs when the number of cars produced is 110.
We replace this value in the cost equation and get:
Cost = 0.3 (110)^2 - 66 (110) + 13267 = 9637
Then, the unit cost for making the 110 cars is $9637, which is in fact the minimum value we were looking for.
PLEASE HELP!!!
Match the number with the most specific number set to which it belongs.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
-45
100−−−√
89−−√
4.91919191.....
-2/5
0.12112111211112....
Answers
The translation rule that matches the transformation for congruent angles is given as follows:
(x,y) -> (x + 4, y - 5).
What are the translations?The translations are movements to the triangle in each of these directions:
Up.Down.Left.Right.There were two translations in this problem, listed as follows:
From triangle GHI to triangle G'H'I'.From triangle G'H'I' to triangle G''H''I''.For the first translation, the triangle was moved down five units, hence the rule is given as follows:
y -> y - 5.
For the second translation, the triangle was moved right four units, hence the rule is given as follows:
The complete translation, obtained by the combination of each translation, is given as follows:
(x,y) -> (x + 4, y - 5).
Meaning that the first option is the correct option.
More can be learned about translations at brainly.com/question/28174785
#SPJ1
Harry owns a car dealership during a sale one week he sold 8 small cars out of 11 cars he sold Harry sold a total of 33 cars doing the sale. How many cars did he sell during the sale?a. 8b. 9c. 24d. 33
Answers
Harry sold 8 smalls cars out of 11 cars.
At the end of the sale He sold 33 cars.
In order to determine how many small cars did Harry sell in the week, you take into account that the proportion of small cars for each sale is 8/11.
To find the total small cars sold in the week you multiply the proportion of small cars by the total cars sold in the week, just as follow:
(8/11)33 = 8(33/11) = 8(3) = 24
Hence, the small cars sold during the week were 24.
c. 24
Simplify the expression by combining like terms [tex]16 + 8a - 3a + 6b - 9[/tex]
Answers
There are two kinds of like terms:
• Variable like terms: These are the terms that have the same variable. For example, 10x and -3x are like terms.
,• Independent like terms: are the terms that don't have any variables. For example, 7 and -30 are like terms.
The important thing about like terms is that we can combine them.
The expression we have is:
[tex]16+8a-3a+6b-9[/tex]The terms 8a and -3a are variable like terms because they have the same variable "a", so we combine them by subtracting 8a-3a which results in 5a:
[tex]16+5a+6b-9[/tex]The term 6b does not have any like term because there are no other terms that contain the variable "b", so we leave that term as is.
Now, the terms 16 and -9 are independent like terms, so we can also combine them.
To combine 16 and -9, we subtract 16-9, and the result is7, so we put 7 in the expression in the place of 16-9:
[tex]5a+6b+7[/tex]Answer:
5a+6b+7
The function g(x) is a transformation of the quadratic parent function, f(x) =2. What function is g(x)?5f(x)5g(x)O A. g() = {x?O B. g(x) = -122C. g(x) = 4x2O D. g(x) = -4x2
Answers
we have that
the aprent function
f(x)=x^2
g(x) is a reflection over x -axis of the parent function with a vertical dilation
so
g(x)=-ax^2
Find the value of the leading coefficient a
looking at the graph
For x=1
the value of g(x) is -4
therefore
the answer is the option g(x)=-4x^26.) find a formula for the area of a rhombus ( see figure 12.52) in terms of the good distances between opposite vertices. Explain why your formula is valid.
Answers
For the Rhombus you know that:
The opposite sides are parallel
All sides have equal length
Its diagonals bisect each other in right angles
You can calculate the area of the Rhombus by either mutiplying its whide by its length, and sice its 4 sides are of equal lenght, the area will be equal to the square of one of it's sides (s):
[tex]A=s^2[/tex]Or using its diagonals (d1 and d2) you can calculate its area as:
[tex]A=\frac{(d_1\cdot d_2)}{2}[/tex]angle1=73°angle2=34°angle3=73°Classify the triangle(by the side and by the angles)
Answers
isosceles triangle
Explanation
we have a triangle with two equal angles
[tex]\text{angle}1=\text{angle}3=73\text{ degr}ees[/tex]An isosceles triangle, therefore, has both two equal sides and two equal angles
19. Charlotte has a success rate of about 20%for making baskets in attempts duringbasketball games. She wants to determinethe probability that she will have to make atleast 5 attempts during a game in order tomake a basket. She designed a simulationwhere she spun a spinner that was dividedinto 5 equal sections, one of which wascolored red. She counted how many timesshe had to spin the spinner in each trialbefore it landed on red. The results of her20 trials are shown below.5, 2, 7, 2, 3, 4, 10, 6,4,6,3, 6, 6, 4, 8,5,7,7,1,5According to this simulation, what is theprobability that Charlotte will have tomake at least 5 attempts in order to makea basket?
Answers
We have the results of a simulation that consists of 20 trials, they are the following:
5, 2, 7, 2, 3, 4, 10, 6, 4, 6, 3, 6, 6, 4, 8, 5, 7, 7, 1, 5
Each number of the results represent the number of attempts needed to make a basket.
Q) We want to know the probability to have to make at least 5 attempts to make a basket.
A) According to the question, we must compute P(# attemps ≥ 5). We can comput
how would you solve d=9rt for t
Answers
d = 9rt
9 and r are multiplying on the right, then they will divide on the left
[tex]\frac{d}{9r}=t[/tex]Consider the function [tex]y = x ^{3} - 3x[/tex]Find the intervals the function is increasing. Express your answer in interval notation (a,b)
Answers
The given expression is
[tex]y=x^3-3x[/tex]To know the intervals where this function is increasing, we graph it
As you can see from the graph, the increasing intervals are
[tex]I=(-\infty,-1)\cup(1,\infty)[/tex]Find the simple interest and the total amount after three years.Principal = 7800 rupeesAnnual rate of interest = 9.5%Total interest=rupeesTotal amount =rupees
Answers
Answer:
The value of the simple interest and the total value after three years is;
[tex]\begin{gathered} \text{Total interest = 2223 rupees} \\ \text{Total amount = 10023 rupees} \end{gathered}[/tex]Explanation:
Given the following;
[tex]\begin{gathered} \text{ Principal P= 7800 rupees} \\ \text{Annual rate of interest = 9.5\%} \end{gathered}[/tex]We want to find the simple interest and the total amount after three years.
[tex]t=3\text{ years}[/tex]The simple interest formula;
[tex]\begin{gathered} I=\frac{Prt}{100} \\ F=P+I \end{gathered}[/tex]substituting the given values;
[tex]\begin{gathered} I=\frac{7800\times9.5\times3}{100} \\ I=2223\text{ rupees} \end{gathered}[/tex][tex]\begin{gathered} F=P+I=7800+2223 \\ F=10,023\text{ rupees} \end{gathered}[/tex]Therefore, the value of the simple interest and the total value after three years is;
[tex]\begin{gathered} \text{Total interest = 2223 rupees} \\ \text{Total amount = 10023 rupees} \end{gathered}[/tex]Hello there I need help with this.Ben and his friend go to buy some water.Still water and sparkling water both cost $p per bottle. Ben and his friend bought 2 bottles of sparkling water and 3 bottles of still water.They spent $6.50 altogether.What is the algebraic equation of the total price T?
Answers
ANSWER
The algebraic equation of the total price T is T = 3p + 2p or (6.50 = 3p + 2p)
STEP-BY-STEP EXPLANATION:
Given parameters
• Cost of still water per bottle = $p
,• Cost of sparkling water per bottle = $p
,• The number of sparkling water bottles purchased = 2
,• The number of still water bottles purchased = 3
,• The total amount of money spent altogether = $6.50
As you can see from the question, Ben and his friend spent $6.50 altogether to purchase 2 bottles of sparkling water and 3 bottles of still water. This implies that the total cost is $6.50
Total cost = (number of still water bottles x cost per bottle) + (number pf sparkling water bottles x cost per bottle)
Let the total cost be T
Mathematically, this can be written as
T = (3 * p) + (2 * p)
T = 3p + 2p
Recall that, T = $6.50
6.50 = 3p + 2p
Hence, the algebraic equation of the total price T is T = 3p + 2p or (6.50 = 3p + 2p)