Answers
The tangent is equal to the sine over the cosine, and the secant is equal to the inverse of the cosine.
Since the angle is in Quadrant II, the sine is positive, the cosine is negative and the secant is negative.
In order to calculate the secant, we can first calculate the cosine using the following equations:
\(\begin{gathered} \tan (\theta)=\frac{\sin(\theta)}{\cos(\theta)} \\ -\frac{2\sqrt[]{3}}{3}=\frac{\sin(\theta)}{\cos(\theta)} \\ \sin (\theta)=-\frac{2\sqrt[]{3}}{3}\cos (\theta) \\ \\ \sin ^2(\theta)+\cos ^2(\theta)=1 \\ (-\frac{2\sqrt[]{3}}{3}\cos (\theta))^2+\cos ^2(\theta)=1 \\ \frac{4}{3}\cos ^2(\theta)+\cos ^2(\theta)=1 \\ \frac{7}{3}\cos ^2(\theta)=1 \\ \cos ^2(\theta)=\frac{3}{7} \\ \cos (\theta)=-\frac{\sqrt[]{3}}{\sqrt[]{7}} \\ \\ \sec (\theta)=\frac{1}{\cos(\theta)}=-\frac{\sqrt[]{7}}{\sqrt[]{3}}=-\frac{\sqrt[]{21}}{3} \end{gathered}\)Therefore the value of sec(theta) is equal to -(√21)/3.
Related Questions
The graph of a system of equations will intersect at exactly 1 point?
Answers
Answer:
A system of equations can intersect at no points; this is when the lines are parallel, which means they have the same slope and different y-intercept. A system of equations can intersect at one point; this is when the lines have different slopes.
Step-by-step explanation:
Find the exact lengths of the sides of quadrilateral ABCD with vertice
A(4, 5), B(-3, 3), C(-6, -13) and D(6, - 2).
Answers
Answer:
\(AB=\sqrt{53}\)
\(BC=\sqrt{265}\)
\(CD=\sqrt{265}\)
\(DA=\sqrt{53}\)
ABCD is a kite.
Step-by-step explanation:
Given vertices of quadrilateral ABCD:
A = (4, 5)B = (-3, 3)C = (-6, -13)D = (6, -2)To find the exact lengths of the sides of the quadrilateral, use the distance formula.
\(\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}\)
\(\begin{aligned}AB&=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\&=\sqrt{(-3-4)^2+(3-5)^2}\\&=\sqrt{(-7)^2+(-2)^2}\\&=\sqrt{49+4}\\&=\sqrt{53}\\\end{aligned}\)
\(\begin{aligned}BC&=\sqrt{(x_C-x_B)^2+(y_C-y_B)^2}\\&=\sqrt{(-6-(-3))^2+(-13-3)^2}\\&=\sqrt{(-3)^2+(-16)^2}\\&=\sqrt{9+256}\\&=\sqrt{265}\\\end{aligned}\)
\(\begin{aligned}CD&=\sqrt{(x_D-x_C)^2+(y_D-y_C)^2}\\&=\sqrt{(6-(-6))^2+(-2-(-13))^2}\\&=\sqrt{(12)^2+(11)^2}\\&=\sqrt{144+121}\\&=\sqrt{265}\\\end{aligned}\)
\(\begin{aligned}DA&=\sqrt{(x_A-x_D)^2+(y_A-y_D)^2}\\&=\sqrt{(4-6)^2+(5-(-2))^2}\\&=\sqrt{(-2)^2+(7)^2}\\&=\sqrt{4+49}\\&=\sqrt{53}\\\end{aligned}\)
A kite has two pairs of adjacent equal sides.
Therefore, quadrilateral ABCD is a kite as:
AB is adjacent to DA and AB = DA.BC is adjacent to CD and BC = CD.
Suppose that you have 4 green cards and 5 yellow cards. The cards are well shuffled. You randomly draw two cards without replacement.
Answers
The probability that two cards will be drawn at random, without replacement, is 13/18.
What is Probability?The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.
The probability of an event can be calculated using the following formula.
Probability(Event) = Positive Results/Total Results = x/n
In order to better grasp probability, let's look at a straightforward application.
Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.
There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.
According to our answer-
P(at least 1 green) = 1 - P(no green)
P(no green) = draw yellow on both draws
= P(draw yellow on 1st draw) * P( draw yellow on 2nd draw, given draw yellow on 1st draw)
= 5/9 * 4/8 = 20/72 = 5/18
P(at least 1 green) = 1 - 5/18
= 13/18
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The system of equations is graphed on the coordinate plane.
y=x−1
y=−2x−4
Enter the coordinates of the solution to the system of equations in the boxes.
Answers
Answer:
(-1,-2)
Step-by-step explanation:
Hello!
The solution to the system is at the intersection between the two graphed lines.
Remember that a coordinate is written in (x,y) format, so we take the x-value of the points and the y-value of the point.
The coordinate is (-1, -2).
Step by step
You have two equations
y= x -1 (we will call equation A)
y= -2x-4 (we will call equation B)
Substitute equation A for the “y” value in equation B
x-1 = -2x -4
We need to isolate x to one side of the = so first we will add 1 to both sides
x-1+1 = -2x -4 +1
Combine like terms
x = -2x -3
Now add 2x to both sides
2x + x = -2x +2x -3
Combine like terms
3x = -3
Now solve for x by dividing both sides by 3
3/3x = -3/3
X= -1
Now we can solve for “y” by substituting our “x” value into equation A
y = -1 -1
y = -2
Now you can check your work by substituting your x and y values into with equation
A (-2) = -1 -1
A -2 = -2
B -2 = -2(-1) -4
B -2 = -2
Problem solved and graph is correct - see attached
The number 2/5 is both an blank and an blank
Answers
The number 2/5 is both a ratio and a fraction.
How to describe the numberThe number 2/5 is both a ratio and a fraction. Fractions are meant to signify the numerator and denominator in an expression. in the above expression, we have the denominator as 5 and the numerator as 2.
The expression is also a ratio because it indicates the quantitative relationship between the figures.
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HELP QUICKLY!!!
A net of a rectangular prism is shown. A net of a rectangular prism with dimensions 5 and three-fourths centimeters by 4 centimeters by 11 and three-fourths centimeters. What is the surface area of the prism? five hundred fifty and one-fourth cm2 four hundred twelve and three-fourths cm2 two hundred seventy-five and one-eighth cm2 one hundred thirty-seven and nine-sixteenths cm2
PLEASE show a explanation
Answers
The surface area of the prism include the following: C. two hundred seventy-five and one-eighth cm².
How to calculate the surface area of a rectangular prism?In Mathematics and Geometry, the surface area of a rectangular prism can be calculated and determined by using this mathematical equation or formula:
Surface area of a rectangular prism = 2(LH + LW + WH)
Where:
L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.By substituting the given side lengths into the formula for the surface area of a rectangular prism, we have the following;
Surface area of rectangular prism = 2[(23/4 × 4) + (23/4 × 47/4) + (4× 47/4)]
Surface area of rectangular prism = 2[23 + 1081/16 + 47]
Surface area of rectangular prism = 275 1/8 cm².
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Consider the function hh(x) = 32 – 3 with a restricted domain of { -2,0, 2, 10}. What is the range of thefunction?O A. {-2,0, 2, 10}B. all real numbersOC. {-4, -3, -2,2}D. the set of integers
Answers
the given function is,
h(x) = 1/2x - 3
for domain {-2, 0 , 2 , 10 }
the range will be
for x = -2
h(-2) = 1/2(-2) - 3
= -1 - 3
= -4
for x = 0
h(0) = 1/2(0) - 3
= 0 - 3
= -3
for x = 2
h(2) = 1/2(2) - 3
= 1 -3
= -2
for x = 10
h(10) = 1/2(10) - 3
= 5 - 3
= 2
so the range of the function is
{-4 , -3 , -2 , 2 }......
thus, the correct answer is option C
100 Points! Algebra question. Photo attached. Find the missing variable. Round your answers to the nearest hundredth. Please show as much work as possible. Thank you!
Answers
Using the z-score, mean and sample mean, the standard deviation of the sample is 7.57
What is z-score?A z-score describes the position of a raw score in terms of its distance from the mean when measured in standard deviation units. The z-score is positive if the value lies above the mean and negative if it lies below the mean.
The formula is given as;
z = x - μ / σ
z = z -scoreμ = mean x = sample meanσ = standard deviationSubstituting the values into the formula;
-2.13 = 19.3 - 29 / σ
Cross multiply both sides;
-2.13σ = 19.3 - 29
-2.13σ = -9.7
Divide both sides by the coefficient;
-2.13σ / -2.13 = -9.7 / -2.13
σ = 7.57
The standard deviation is 7.57
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If the manager sold 15 corn dogs, how would this quantity be represented in her table?
Answers
Answer:
Not enough information.
Step-by-step explanation:
What kind of table do you want.
Answer:
I had the same question, it would be -15 because in the video on the assignment it says the answers are the opposite.
Step-by-step explanation:
-0.9 -1.2 which one is greatest
Answers
Answer:
-0.9
Step-by-step explanation:
it is closer to 0
Please help. I don’t really understand this topic and I’m having trouble with this question
Answers
Answer: 2nd one trust me
Step-by-step explanation:
If you order 3 hamburgers, 2 orders of fries, and 3 milkshakes for your friends, how much do they owe you?
Answers
Answer:
31.55
Step-by-step explanation:
6.Imagine that you are driving your car in Canada. As you're driving along, you notice that the speed
limit signs have numbers like 120 (on the highway) and 50 (in the city). As you start to speed up, you
realize that the signs are in km/hour. Unfortunately, your speedometer only reads in mi/hour. Figure out
how fast you're allowed to go if the sign says:
Answers
Answer:
31 miles
Step-by-step explanation:
for an approximate result divide speed value
what the answer please help marking brainliest if it's correct and explain¡
Answers
Answer:
median
Step-by-step explanation:
because you have the smallest to the largest number and its one to five so once it counts from one to five its median
Answer:
Its Either B or C.
Step-by-step explanation:
So, the median and the interquartile range are the most appropriate measures to describe the center and the variation.The range is a measure of variability because it indicates the size of the interval over which the data points are distributed. A smaller range indicates less variability (less dispersion) among the data, whereas a larger range indicates the opposite.
Hope this helped!!!!
Set up equation and solve.
1. Water/Wastewater Treatment Two tanks must have a total capacity of
400 gallons. If one tank needs to be twice the size of the other, how many
gallons should each tank hold?
Answers
Answer:
Below.
Step-by-step explanation:
3x=400
x=400/3 or 133.33
2x= 266.66
Therefore, the tanks must have sizes, 133.33 and 266.66 gallons!
Solve similar triangles (advanced)
Solve for x
x=?
Answers
Answer:
x = 1.2
Step-by-step explanation:
AD/AB = DE/BC (Similarity Theorem)
AD = 6 + 4 = 10
AB = 6
DE = 2
BC = x
Plug in the values
10/6 = 2/x
Cross multiply
10*x = 2*6
10x = 12
Divide both sides by 10
x = 12/10
x = 1.2
Use the figure to find the measures of the numbered angles.
Answers
Answer:
Every numbered angle is 90 degrees
Step-by-step explanation:
Using the right angle we are given, linear pairs and a vertical angle give us that angles 1, 2, and 3 are also right angles.
Then using corresponding angles we can find that one of the 4-7 angles. From there we can use linear pairs the same as the first step.
Use the bar graph to find the probability of the event
Not spinning a 1
Answers
10+8 you add all the data to get your answer
How many 11-card hands are possible with a 20-card deck?
Answers
There is only 1 possible 11-card hand that can be formed from a 20-card deck.
To determine the number of 11-card hands possible with a 20-card deck, we can use the concept of combinations.
The number of combinations, denoted as "nCk," represents the number of ways to choose k items from a set of n items without regard to the order. In this case, we want to find the number of 11-card hands from a 20-card deck.
The formula for combinations is:
nCk = n! / (k!(n-k)!)
Where "!" denotes the factorial of a number.
Substituting the values into the formula:
20C11 = 20! / (11!(20-11)!)
Simplifying further:
20C11 = 20! / (11! * 9!)
Now, let's calculate the factorial values:
20! = 20 * 19 * 18 * ... * 2 * 1
11! = 11 * 10 * 9 * ... * 2 * 1
9! = 9 * 8 * 7 * ... * 2 * 1
By canceling out common terms in the numerator and denominator, we get:
20C11 = (20 * 19 * 18 * ... * 12) / (11 * 10 * 9 * ... * 2 * 1)
Performing the multiplication:
20C11 = 39,916,800 / 39,916,800
Finally, the result simplifies to:
20C11 = 1
Consequently, with a 20-card deck, there is only one potential 11-card hand.
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A right triangle ABC is shown below:
The are of the triangle above will equal one-half of a rectangle that is 5 units long and __ units wide. (Input only whole numbers, such as 8) (1 point)
Answers
5
1
a)
20
77. Modulus of 'i' is
a) i
Answers
Answer:
¿que? no tiene sentido
which of these is not a linear graph.
Answers
Answer:
D
Step-by-step explanation:
It isn't linear
Answer:
D)
Step-by-step explanation:
Linear graphs are straight they can be positive or negative but they do not have bending points in them.
I added a picture to help you
Can somebody help me as soon as possible
Answers
The length of segment F'G' is 7 units
LengthThe length of a line segment is the number of units on the line.
CoordinatesThe coordinates are given as:
\(F = (-2,-4)\)
\(G = (5,-4)\)
DistanceStart by calculating the length of segment FG using the following distance formula
\(FG = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\)
So, we have:
\(FG = \sqrt{(-2- 5)^2 + (-4+ 4)^2}\)
\(FG = \sqrt{49}\)
\(FG = 7\)
The transformation of segment FG to F'G' is a rigid transformation.
This means that:
The lengths of segments FG and F'G' are the same
So, we have:
\(F'G' = 7\)
Hence, the length of segment F'G' is 7 units
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Given the following sets:
A = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}
B = {3, 6, 9, 12, 15, 18}
C = {4, 8, 12, 16, 20}
Find:
n (A)
Answers
Answer:
n (A) = { 2,4,6,8,10,12,14,16,18,20}
n(A) = 10
I hope it helps
Carole worked her 40 regular hours plus 5 O.T. hours at time-in-a-half rate. Her gross pay was $1,163.75. What is her regular hourly rate?
Answers
Let her standard pay rate = x
She worked 40 hours for x per hour she also worked 5 hours at 1.5x ( time and a half)
Write an equation:
40x + 5(1.5x) = 1163.75
Simplify:
40x + 7.5x = 1163.75
Combine like terms:
47.5x = 1163.75
Divide both sides by 47.5
X = 24.50
Her regular hourly rate is $24.50
Answer:
let rate be x
by question
40x+7.5x=1163.75
x=1163.75/47.5=24.5
her regular income is $24.5 per hour.
what's the area of the quadillateral
Answers
Answer:
The area of the quadillateral is 360 degree.
Step-by-step explanation:
Hope this helped!
Have an amazing day!
In 1999, 68% of households with TV’s subscribed to cable TV. If 8,000 more subscribers are added to the number of households with cable, the total number of households with cable TV would be 67,600,000. How many households were there with TV in 1999?
Answers
Answer:
45962560
Step-by-step explanation:
Tell whether the ratios are equivalent: 3 miles to 4 minutes and 9 miles to 12 miles. Show your work.
Answers
Answer:
they are
Step-by-step explanation:
divide 12*4=3
9*3=3
same ratio
What is the lowest common multiple of 10 and 12
Answers
Answer:
Your answer would be 60.
Step-by-step explanation:
12 doesn't equal anything that ten can equal until it reachest 60, therefore 60 is the least common multiple.
12 x 5 = 60
10 x 6 = 60
the sum of three consecutive even number is 27