Because the cosine and sine must be negative when evaluated in theta, the angle lies on the third quadrant.
In which quadrant is the endpoint of the segment that defines the angle?We know that if:
cos(θ) > 0, then we are on the first or fourth quadrantsin(θ) > 0, then we are on first or second quadrant.Here we know that:
sec(θ) < 0
And we know that:
sec(θ) = 1/cos(θ)
Then we have cos(θ) < 0
We also have that:
sec(θ)*csc(θ) > 0
Because sec(θ) < 0, we must have that csc(θ) < 0.
Remember: csc(θ) = 1/sen(θ)
Then sen(θ) < 0.
Then we have the two conditions:
sen(θ) < 0
cos(θ) < 0
The cosine is negative on the third and second quadrants.The sine is negative on the third and fourth quadrants.The only quadrant where both are negative is the third quadrant, so that is the correct option.
If you want to learn more about trigonometric functions:
https://brainly.com/question/8120556
#SPJ1
There are 8 apples in a small fruit basket and 14 apples in a large fruit basket. If Sally buys a total of 5 fruit baskets that have a combined total of 58 apples, write an equation that represents the total number of apples that Sally has.
The equation that represents the total number of apples that Sally has will be the equations x + y = 8 and 8x + 14y = 58
System of equationSystem of equations are equations that consists of two or more equations.
Let the number of small fruits basket be y
Large fruit basket be y
If Sally buys a total of 5 fruit baskets, then;
x + y = 8
If there are 8 apples in a small fruit basket and 14 apples in a large fruit basket with a combined total of 58 apples, then;
8x + 14y = 58
The equation that represents the total number of apples that Sally has will be the equations x + y = 8 and 8x + 14y = 58
Learn more on system of equations here: https://brainly.com/question/25976025
#SPJ1
The sum of four consecutive evan numbers is 660. Find these numbers.
Answer:The numbers are 162,164,166,168,
Step-by-step explanation:
The solution is in the attached
Answer: The numbers are 162,164,166,168,
Step-by-step explanation:
The Investment Research Institute reported in its Mutual Fund Fact Book that the number of mutual funds increased from 5,700 in 1999 to 8,064 in 2009. What is the geometric mean annual percent increase in the number of funds
The geometric mean is 6833.049
The value of fund in 1999 is 5,700
value of fund in 2009 is 8,064
We need to find the geometric mean annual percent increase in the number of funds.
The geometric mean is the average of a set of products, it is defined as the compounding effect of the numbers in the series in which the numbers are multiplied by taking nth root of the multiplication.
The calculation of which is commonly used to determine the performance results of an investment or portfolio.
We know, The Geometric mean is = [tex]\sqrt[n]{x_1*x_2*...*x_n}[/tex]
substituting values:
[tex]\\ GM = (5790*8064)^{0.5} = 6833.049[/tex]
Formula used:Geometric mean is = [tex]\sqrt[n]{x_1*x_2*...*x_n}[/tex]
To know more about Geometric mean visit:
https://brainly.com/question/47038
#SPJ4
2x² - 1 > 6x
Which values are included in the solution set of this inequality?
x = 4
Step-by-step explanation:
2x² - 1 > 6x
2(4)²-1 > 6(4)
2(16)-1 > 24
32-1 > 24
31 > 24
Find the are of the trapezoid
Answer:
355.83 yd²
Step-by-step explanation:
A = (B + b)h/2
A = (21.6 yd + 19.3 yd)(17.4 yd)/2
A = 355.83 yd²
Surface area=
Please help me asap thanks
Answer:
100π
Step-by-step explanation:
The formula for the surface area of a sphere is SA = 4πr^2, where r is the radius of the sphere and SA stands for surface area. We are given that the radius is 5, so if we plug this into the formula, we get that SA = 4π*(5)^2, or SA = 4 * 25 * π. If we solve it out, we get 100π. If the software wants you to let π be 3.14 and evaluate, you will get approximately 314. I hope this helps
You are saving money to buy a pair of pants that costs $53. You have saved $32. How much more money do you need to save?
Answer:
you need to save $21
SOMEONE PLS HELP ASAP, ITS GEOMETRY. ITS URGENT PLSSSS
6) ∠FOC is vertical to ∠EOD
7) m∠POF is complementary to M∠FOB.
8) m∠AOC = 30°
How to determine congruent angles?
6) Vertical angles are angles that are opposite of each other when two lines cross. Thus;
∠FOC is vertical to ∠EOD
7) Given that m∠POF + M∠FOB = 90
Two angles are called complementary when their measures add to 90 degrees. Thus;
m∠POF is complementary to M∠FOB.
8) m∠BOC = 150. Thus;
m∠AOC = 180 - 150
m∠AOC = 30° because they are supplementary angles.
9) m∠EOA = 37. Thus;
m∠FOA = 180 - 37
m∠FOA = 143° because they are supplementary angles.
10) ∠EGH is adjacent to ∠OGH
This is from definition of adjacent angles
11) ∠EGH ≅ ∠DOB
m∠HGO = 128°, m∠DOB = 180° - 128° = 52° because they are supplementary angles.
12) m∠EOA = 67°, m∠DOB = 29°. Thus;
m∠EOD = 180 - (67 + 29)
m∠EOD = 84° because sum of angles on a line is 180°
13) m∠AOD + m∠DOB = 180 means that ∠AOD is supplementary to ∠DOB.
14) ∠COF ≅ ∠DOF and so we can say that;
FO is perpendicular to CD.
15) m∠COP = 72° and m∠POF = 31°. Thus;
m∠EOD = 72 + 31
m∠EOD = 103°
Read more about Congruent Angles at; https://brainly.com/question/1675117
#SPJ1
10 to the 2nd power divided by 0.00541 to the nearist tenth
Answer:
18484.3
Step-by-step explanation:
[tex]\frac{10^2}{0.00541}[/tex]
[tex]\frac{100}{0.00541}[/tex]
18484.3
Which are other possible names for ∠RPE ? Choose each correct answer. ∠2 ∠EPR ∠RPF ∠P ∠DPF ∠PRE
The other possible names of ∠RPE are ∠P and ∠EPR
How to determine the other possible names?The angle is given as:
∠RPE
The angle is named after the middle alphabet.
The middle alphabet in ∠RPE is P
This means that ∠P is a possible name for ∠RPE
Also, the positions of R and P can be interchanged.
So, we have:
∠EPR
Hence, the other possible names of ∠RPE are ∠P and ∠EPR
Read more about angles at:
https://brainly.com/question/13954458
#SPJ1
Match the features of the graph of the rational function.
After applying algebraic analysis we find the right choices for each case, all of which cannot be presented herein due to length restrictions. Please read explanation below.
How to analyze rational functions
In this problem we have a rational function, whose features can be inferred by algebraic handling:
Holes - x-values that do not belong to the domain of the rational function:
x³ + 8 · x² - 9 · x = 0
x · (x² + 8 · x - 9) = 0
x · (x + 9) · (x - 1) = 0
x = 0 ∨ x = - 9 ∨ x = 1
But one root is an evitable discontinuity as:
y = (9 · x² + 81 · x)/(x³ + 8 · x² - 9 · x)
y = (9 · x + 81)/(x² + 8 · x - 9)
Thus, there are only two holes. (x = - 9 ∨ x = 1) Besides, there is no hole where the y-intercept should be.
Vertical asymptotes - There is a vertical asymptote where a hole exists. Hence, the function has two vertical asymptotes.
Horizontal asymptotes - Horizontal asymptote exists and represents the end behavior of the function if and only if the grade of the numerator is not greater than the grade of the denominator. If possible, this assymptote is found by this limit:
[tex]y = \lim_{x \to \pm \infty} \frac {9\cdot x + 81}{x^{2}+8\cdot x - 9}[/tex]
y = 0
The function has a horizontal asymptote.
x-Intercept - There is an x-intercept for all x-value such that numerator is equal to zero:
9 · x + 81 = 0
x = - 9
There is a x-intercept.
Lastly, we have the following conclusions:
How many holes? 2One horizontal asymptote along the line where y always equals what number: 0This function has x-intercepts? TrueOne vertical asymptote along the line where x always equals what number: 1There is a hole where the y-intercept should be? FalseTo learn more on rational functions: https://brainly.com/question/27914791
#SPJ1
Mr. Suksod drives from his house to the office at a rate of speed of 82 km/h in 15 minutes. Mr.
Taylor, whose house is as far from the office as Mr. Suksod's, drives for 10 minutes to reach the
same office. What is the difference in the rate of speed that they drive?
The difference in speed is 41 km /hr.
What is the difference in speed?Average speed is the total distance travelled per time.
Average speed = total distance / total time
The first step is to determine the distance that Mr. Suksod drives.
Distance = average speed x time
82 x (15/60) = 20.50 km
The second step is to determine the average speed of Mr Taylor = 20.50 ÷ (10/60) = 123 km /hr
Difference in speed = 123 - 82 = 41 km /hr
To learn more about average speed, please check: https://brainly.com/question/21734785
#SPJ1
I don’t know the answer
Answer:
[tex]x^{16}[/tex]
Step-by-step explanation:
In this situation, you would add the two exponents (the little numbers at the top) together for the answer.
Answer:
x¹⁶
Step-by-step explanation:
x⁷ × x⁹ = x⁷⁺⁹ = x¹⁶
y=x^2+8
Find the Domain, explain your answer
Step-by-step explanation:
look at the attachment above ☝️
A piecewise function g(x) is represented by the graph.
Which functions represent a piece of the function? Select three options.
The piecewise functions that are represented by the graph are; g(x) = −2, x < −2; g(x) = −2x + 6, x ≥ 1; g(x) = x/2 + 1, –2 ≤ x < 1
How to Interpret a Piecewise Function graph?From the attached graph of the piecewise function, we can access each option as follows;
A) g(x) = −2x, −2 < x < 0
This is not represented by the graph because g(x) = −2x has negative slope which means it goes downward. There's also no y-intercept in g(x) = −2x.
B) g(x) = −2, x < −2;
This is represented by the graph because g(x) = −2 is a horizontal line which is only on the left side of x = -2.
C) g(x) = x − 2, −2 < x < 1;
This is not represented by the graph because g(x) = x − 2 has y-intercept at y = -2 and slope of 1 which means that graph of g(x)= x - 2 must be going upward and crossing at y = -2.
D) g(x) = −2x + 6, x ≥ 1
This is represented by the graph because g(x) = −2x+6 satisfies the graph which is going downward.
E) g(x) = x/2 + 1, –2 ≤ x < 1
This is represented by the graph because g(x) = (x/2) + 1 satisfies the graph which is going downward.
The options are;
g(x) = −2x, −2 < x < 0
g(x) = −2, x < −2
g(x) = x − 2, −2 < x < 1
g(x) = −2x + 6, x ≥ 1
g(x) = x/2+ 1, –2 ≤ x < 1
Read more about Piecewise Function at; https://brainly.com/question/3628123
#SPJ1
Students of different ages are kept in a row,All of them have age difference of 3 years who are consecutive to each other. The age of first students row is 8 years. a) Restate the formula of to find the nth term of AP b) find the age of fourth student in rowc) find the sum of total ages if there are 20 students in a row
The formula to find the nth term of the AP is 8 + 3(n - 1).
How to calculate the values?a = first term = 8
d = common difference = 3
The nth term will be:
= a + (n - 1)d
= 8 + (n - 1)3
= 8 + 3(n - 1)
The age of the 4th student will be:
= a + (n - 1)d
= 8 + (4 - 1)3
= 8 + 9
= 17 years
The sum of total ages if there are 20 students in a row will be:
= n/2[2a + (n - 1)d]
= 20/2 [2×8 + (20 - 1)3]
= 10 [16 + (19 × 3)]
= 10(16 + 57)
= 10(73)
= 730
Learn more about AP on:
brainly.com/question/24205483
#SPJ1
Tavon has a gift card for 80$ that loses $3.50 for each 30-day period it is not used. He has another gift card for $70 that loses $3 for each 30-day period it is not used.
Answer:
Im guessing you want it as a equation
80-3.50x+70-3x
x being the ammount of time
Step-by-step explanation:
Kevin built a wooden flower box for his garden. The area of the base of the box is 264 square centimeters. If the rectangular base has the dimensions shown below, what
is the value of x?
I'm not sure
this app is the wrst don't trust it
The value of the variable x will be 44 cm.
What is the area of the rectangle?Let L be the length and W be the width of the rectangle.
Then the area of the rectangle will be
Area of the rectangle = L × W square units
Kevin built a wooden flower box for his garden. The area of the base of the box is 264 square centimeters.
If the rectangular base has the dimensions shown below.
Then the value of the variable x will be
A = L × W
264 = 6x
x = 264 / 6
x = 44 cm
The value of the variable x will be 44 cm.
The top view of the wooden flower box is given below.
More about the area of the rectangle link is given below.
https://brainly.com/question/20693059
#SPJ2
A university is applying classification methods in order to identify alumni who may be interested in donating money. The university has a database of 58,205 alumni profiles containing numerous variables. Of these 58,205 alumni, only 576 have donated in the past. The university has oversampled the data and trained a random forest of 100 classification trees. For a cutoff value of 0.5, the following confusion matrix summarizes the performance of the random forest on a validation set:
Predicted Actual Donation No Donation 268 Donation 268 20 No Donation 5,375 23,439 The following table lists some information on individual observations from the validation set:
Observation ID Actual Class Probability of Predicted Class Donation A Donation 0.8 Donation B No Donation 0.1 No Donation C No Donation 0.6 Donation a) Compute the values of accuracy, sensitivity, specificity, and precision.
b) Explain how the probability of Donation was computed for the three observations. Why were Observations A and C class fled as Donation and Observation Donation?
The accuracy in the research done by university is 0.81, sensitivity is 0.93, specificity is 0.81 and precision is 0.047.
Given sample size of 58205 and proportion of people donated 576. Cutoff is 0.5.
Probability is the chance of happening an event among all the events possible. It lies between 0 and 1.
TP=total people donated in sample, TN=total number of people,FP=donation,FN=No donation
Accuracy is calculated as under:
=(TP+TN)/(TP+TN+FP+FN)
=(268+23439)/(238+23439+5375+20)
=23707/29102
=0.81
Accuracy=0.81
Sensitivity is calculated as under:
=TP/(TP+FN)
=268/(268+20)
=268/288
=0.93
Precision is calculated as under:
=TP/(TP+FP)
=268/(268+5375)
=268/5643
=0.047
Their values are the probabilities in itself.
Hence accuracy is 0.81, sensitivity is 0.93, specificity is 0.81 and precision is 0.047.
Learn more about probability at https://brainly.com/question/24756209
#SPJ4
If one line passes through the points open parentheses negative 3 comma space minus 5 close parentheses space and open parentheses 1 comma space 3 close parentheses space and another line passes through the points open parentheses 0 comma space 1 close parentheses space and open parentheses 2 comma space 0 close parentheses determine if the two lines are parallel, perpendicular, or neither.
The pair of lines are parallel.
What is line?A line is a one-dimensional figure, which has length but no width.
Given:
lines passes through (-3, -5) and (1, 3)
and, line passes through (0, 1) and (2, 0)
equation of line
y + 5 = -1/2 (x + 3)
-2y - 10 = x + 3
x + 2y + 13 = 0
and, equation of line
y - 1 = -1/2 (x - 0)
-2y + 2 = x
x + 2y -2 = 0
m1= -1/2 and m2 = -1/2
Hence, the lines are parallel.
Learn more about this concept here:
https://brainly.com/question/13778052
#SPJ1
In the diagram, ΔGHJ ≅ ΔSTU.
Triangles G H J and T U S are shown. The lengths of sides G H and G J are 5 centimeters. Angle G H J is 67 degrees. The lengths of sides T S and U S are 5 centimeters. The length of T U is 3.7 centimeters.
What are the missing measures in the diagram?
m∠J =
°
m∠T =
°
m∠G =
°
ST =
cm
HJ =
cm
Step-by-step explanation:
angle J is also 67 deg since the triangle is an isosceles triangle
angle T is 67 deg since the 2 triangles are congruent
angle G = 180 - 2x67 = 46 deg
ST is 5cm
HJ is 3.7cm
Answer:
What are the missing measures in the diagram?
m∠J =
✔ 67
°
m∠T =
✔ 67
°
m∠G =
✔ 46
°
ST =
✔ 5
cm
HJ =
✔ 3.7
cm
Step-by-step explanation:
In the following exercises, multiply the binomials. Use any method.
246. (q − 5)(q + 8)
Answer:
Hence the expression [tex]$$(q-5)(q+8)=q^2+3q-40$$[/tex]
Step-by-step explanation:
Explanation
The given expression is (q-5)(q+8).We have to multiply the given expression.Multiply the (q-5) by 8 , multiply the (q-5) by q then add like terms.[tex]$$\frac{\begin{matrix}{} & {} & q & - & 5 \\ \times & {} & q & + & 8 \\ \end{matrix}}[/tex]
_____________
[tex]{\frac{\begin{matrix}{} & {} & 8q & - & 40 \\ {{q}^2} & - & 5q & {} & {} \\ \end{matrix}}{\begin{matrix}{{q}^2} & + & 3q & - & 40 \\ \end{matrix}}}$$[/tex]
A 2-column table with 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, positive 1, positive 2. The second column is labeled f(x) with entries negative 13, negative 10, negative 7, negative 4, negative 1. What is the rate of change of the linear function represented by the table? StartFraction one Over three EndFraction StartFraction one Over two EndFraction 2 3
The rate of change of the linear function represented by the table is 3
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The standard linear equation is in the form:
y = mx + b
Where m is the rate of change and b is the y intercept.
From the table, using the point (0, -7) and (2, -1):
m = [-1 - (-7)] / (2 - 0) = 3
The rate of change of the linear function represented by the table is 3
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
Angles related to a circle. Solve for x.
The value of x from the given circle is 12
Circle theoremAngle at the vertex of the circle is half the angle at its intercepted arc.
From the given circle;
The measure of <DEF = 80/2 = 4x -8
Equate both angles
4x - 8 = 80/2
Add 8 to both sides
4x - 8 + 8 = 40 + 8
4x = 48
x =12
Hence the value of x from the given circle is 12
Learn more on circle theorem here: https://brainly.com/question/26594685
#SPJ1
Dana is buying Grandparents' Day gifts at the mall. She spends $13.75 on a teacup for her grandmother. She spends 4/5 of that on a coffee mug for her grandfather. How much money does Dana spend in all?
The total money Dana spent in all is $24.75
Ratio and proportionsRatio are written as fractions of two integers. For instance a/b.
Amount spent for grandmother = $13.75
Amount spent on grand father = 4/5 * 13.75
Amount spent on grand father = $11
Take the sum
Total money spent = $13.75 + $11
Total money spent = $24.75
Hence the total money Dana spent in all is $24.75
Learn more on proportion here: https://brainly.com/question/19994681
#SPJ1
Graph the function f(x)=(−x−4)(x+2).
The points of the graph of function be (0,-8) , (1,-15) ,(2,-24).
Given f(x)=(-x-4)(x+2)
We have to first multiply both the expressions to get f(x)
Expression refers to combination of numbers, symbols, variables, etc. It is usually not in equal to form. It expresses the relationship between variables. To find out the graph we need to first points of function.
f(x)=[tex]-x^{2} -2x-4x-8[/tex]
Now we have to add 2x and 4x
f(x)=[tex]-x^{2} -6x-8[/tex]
Put the value of x=0
f(0)=0-0-8
=-8
Put the value of x=1
f(1)=-1-6-8
=-15
Put the value of x=2
f(2)=-4-12-8
=-24
Now plot these points on the graph to get the graph of function f(x)=(-x-4)(x+2).
Learn more about function at https://brainly.com/question/10439235
#SPJ10
can somebody , help me find the answer , pls and ty for ur help and pls dont give me a wrong answer just for the points pls and ty .
Please Help!!
1. Research the history of the Great Pyramids of Giza. In your research, be sure to include the pyramids' actual dimensions such as height and base measurements.
2. Choose one of the Great Pyramids of Giza and create a scale drawing using an exact proportion between the pyramid and scale drawing.
The actual dimensions of the Great Pyramid include a height of 146.6m and a base of 230.33m.
How to illustrate the information?The Great Pyramid is the largest Egyptian pyramid and also the tomb of rge Fourth dynasty Pharaoh.
It should be noted that the actual dimensions of the Great Pyramid include a height of 146.6m and a base of 230.33m.
It is also the oldest of the seven wonders of the world.
A scale scale drawing using an exact proportion between the pyramid will be 147 to 230.
Learn more about the Pyramid on:
brainly.com/question/10662534
#SPJ1
Answer:
The actual dimensions of the Great Pyramid include a height of 146.6m and a base of 230.33m.
How to illustrate the information?
The Great Pyramid is the largest Egyptian pyramid and also the tomb of the Fourth dynasty Pharaoh.
It should be noted that the actual dimensions of the Great Pyramid include a height of 146.6m and a base of 230.33m.
It is also the oldest of the seven wonders of the world.
A scale drawing using an exact proportion between the pyramid will be 147 to 230.
write y=1/6x+7 in standard form using integers
The standard form using integers of the equation is 6y - x = 42
How to determine the standard formNote that solving in standard form means writing it as a simple equation
Given y = 1/6x + 7
Find the LCM of the right side, we have
y = [tex]\frac{x + 42}{6}[/tex]
Cross multiply
6 × y = x + 42
6y = x + 42
Make the variables move to the left side
6y - x = 42
Thus, the standard form using integers of the equation is 6y - x = 42
Learn more about algebraic expressions here:
https://brainly.com/question/723406
#SPJ1
Find the area of the region defined by the region defined by the inequality 2|x| + 3|y-1| ≤ 6.
The area of the region defined by the inequality 2|x| + 3|y-1| ≤ 6 is 12 square units
How to determine the area?The inequality is given as:
2|x| + 3|y-1| ≤ 6
Next, we plot the inequality
From the graph of the inequality (see attachment), we have the following highlights:
The shape is a rhombusThe diagonals are 6 and 4 unitsThe area of a rhombus is:
A = 0.5 * d1 * d1
This gives
A = 0.5 * 6 * 4
Evaluate
A = 12
Hence, the area of the region is 12 square units
Read more about area at:
https://brainly.com/question/9485980
#SPJ1