θ is in quadrant I, so cos(θ) and sin(θ) and hence tan(θ) are all positive.
Recall that
sec²(θ) = 1 + tan²(θ)
We have
cos(θ) = 2/√14 ⇒ sec(θ) = √14/2 = √(7/2)
Then
tan(θ) = +√(sec²(θ) - 1) = √(5/2)
Also recall the identities
sin(x + y) = sin(x) cos(y) + cos(x) sin(y)
cos(x + y) = cos(x) cos(y) - sin(x) sin(y)
from which we get
tan(x + y) = (sin(x) cos(y) + cos(x) sin(y)) / (cos(x) cos(y) - sin(x) sin(y))
tan(x + y) = (tan(x) + tan(y)) / (1 - tan(x) tan(y))
so that
tan(2θ) = 2 tan(θ) / (1 - tan²(θ)) = -(2√10)/3
Solve 2(x+1)=2x+5
-------------------------------------------
All real numbers
No solution
0
3
The answer is "no solution"
The cost for a teacher to offer an art class is represented by the function f(s)=15s+75, where s is the number of students enrolled. What does each parameter represent in this situation? Drag and drop the explanation to the parameter it represents. HELP. Will reward 20 points.
Answer:
look below
Step-by-step explanation:
Slope = materials cost per student
Y—intercept = cost of renting the classroom
Pls help!
A spinner is divided into 6 equal sectors labeled with the letters A through F The spinner is spun 30 times. How many times is it expected that a vowel will be spun? O approximately 5 times O approximately 6 times approximately 10 times o approximately 15 times
The spinner illustrates probability, and it is expected that a vowel will be spun approximately 10 times
How to determine the expected number of vowels?In the spinner, we have:
Sections = 6
Vowels = 2 i.e. A and E
The expected number of vowels in 30 spins is:
Expected = Vowels/Sections * 30
This gives
Expected = 2/6* 30
Evaluate the product
Expected = 10
Hence, it is expected that a vowel will be spun approximately 10 times
Read more about expected values at:
https://brainly.com/question/15858152
Answer:
the answer is 10
Step-by-step explanation:
At a local high school, enrollment in the drama club increases by 5% each year. what is the common ratio in this situation? 0.05 0.95 1.05 1.95
At a local high school, enrollment in the drama club increases by 5%. the common ratio will be 1.05.
What is the percentage?A percentage is a minimum number or ratio that is measured by a fraction of 100.
At a local high school, enrollment in the drama club increases by 5%.
Let an initial number of students in high school be 'a'.
so next year increase in students will be = 5% of a
= 5/100 × a
= 0.05a
and total number of the students will be = ( a + 0.05a )
= ( 1.05a )
So common ratio of the geometric square formed
( 1.05a )/ a = 1.05
Therefore, the common ratio will be 1.05.
Learn more about percentages;
https://brainly.com/question/14816043
You pick a card at random, put it back, and then pick another card at random.
1 2 3 4
What is the probability of picking a number greater than 1 and then picking a number greater
than 2?
Answer:75% percent chance of picking a card greater than 1 and a 50% chance of picking a card greater than 2
Step-by-step explanation:
please pick me as brainliest
what is the answer to 3 x b?
Answer:
3b
Step-by-step explanation:
unless b stands for something it should be just that
help me i forgot how to do this HElp
Answer:
28.27 inches
Step-by-step explanation:
hope this helps :)
thank you n gimme answer
Answer:
I believe its D
If correct please give brainliest
Step-by-step explanation:
Answer:
C)
Step-by-step explanation:
The first inequality, y ≥ 2x + 1 has no solution below the function since it is greater than OR EQUAL to it. Similarly, the second inequality, y > 1/2x - 1 has no solution at or below the function since it is only GREATER THAN this value.
If we look at the graph of these inequalities, we see that they don't overlap at all in quadrant IV. For that reason, this area of the graph there will have no solution, or empty set.
Hope this helps and God bless!
Which of the following statements must be true of a function?
A. Every output value corresponds to only one input value.
B. Every input value corresponds to only one output value.
C. No inout values are repeated.
D. No output values are repeated
Answer:
B: Every input value corresponds to only one output value.
Amin has 16 pots of equal size. He used 9 bags of potting soil to fill 12 of the pots. At that rate, how many bags of potting soil does Amin need to fill the remaining 4 pots?
Answer:
5 1/3 bags
Step-by-step explanation:
12/9 = 1 1/3 bags per pot
4 * 1 1/3 = 5 1/3 bags to fill the pots
Answer:
3 bags
Step-by-step explanation:
Given
Amin has 16 potsHe fills 12 of them with 9 bags of soilSolving
No. of bags per pot = 9/12No. of bags per pot = 0.75Remaining pots = 3Bags needed = 0.75 x 3 = 2.25 bags3 bags (nearest whole number)two gymnasts are running toward each other in a floor routine, and they plan to precisely time a flip to stay synchronized for the audience. The path of the gymnasts is parabolic and modeled by the following equations, where y is the height of the flip and x is the time in seconds:
y = – (x – 5)2 + 3
y = –3(x –3)2 + x + 1
30 POINTS !! To make sure the flip is in unison, after how many seconds should the flip occur?
2 seconds
3 seconds
4 seconds
5 seconds
To make sure the flip is in unison, after 4 seconds should the flip occur, as given by the option C: 4 seconds.
What does synchronized motion mean?Synchronized motion is a motion of two or more system which goes in syncronization with each other.
For this case, the flip will occur such that both gymnasts are synchronized and flip is unison (simultaneous).
For that, we need the time(x) and the height (y) same.
Since the motion paths are:
[tex]y= -(x-5)^2 + 3\\\\y = -3(x-3)^2 + x + 1[/tex]
Therefore, we need to find the values of x for which same y comes as output.
Let x = t be the time for which the height y is same, then:
[tex]-(t-5)^2 + 3 = -3(t-3)^2 + t + 1[/tex] = height achieved by both gymnasts.
Solving it further:
[tex]-(t-5)^2 + 3 = -3(t-3)^2 + t + 1\\3(t^2 + 9 -6t) -(t^2 + 25 -10t) -t + 2 = 0\\\\2t^2 -9t + 4 = 0\\2t^2 -8t - t + 4 = 0\\2t(t-4) -1(t-4) = 0\\(2t -1)(t-4) = 0\\\\t = 4, t = 1/2[/tex]
Assuming they planned to do flip after integral number of time in seconds, the correct option is t = 4 seconds.
Thus, to make sure the flip is in unison, after 4 seconds should the flip occur, as given by the option C: 4 seconds.
Learn more about solving system of equations here:
https://brainly.com/question/2825832
Answer:
5 seconds
Step-by-step explanation:
Put the equations in desmos and you will see they intersect at 5 seconds.
This is definitely correct. Here is proof:
The school auditorium has 120 seats. The school is selling tickets for 3 performances of the school play. How many tickets are available. Show your work.
Answer:
Friday: 18 tickets Saturday:24 tickets Sunday: 2 tickets
Step-by-step explanation:
120-102=18 tickets
120-96=24 tickets
120-118=2 tickets
TYSM I REALLY NEEDED IT TY!!
it helped me
PLEASE HELP!! What could be the answer?
Answer:
c. 18[tex]\pi[/tex] cubic inches
Step-by-step explanation:
half sphere's volume:
[tex]V=\frac{2}{3} \pi r^{3}[/tex] r = 6/2 = 3 inches
[tex]V=\frac{2}{3} \pi (3)^{3} =\frac{2}{3}( 27\pi )=\frac{54}{3} \pi =18\pi[/tex]
Hope this helps
In a class of students, the following data table summarizes how many
students have a cat or a dog. What is the probability that a student
chosen randomly from the class has a dog?
Answer:
22/29
Step-by-step explanation:
First, add up all of the numbers given:
16 + 4 + 6 + 3 = 29
Now since there are 16 students who have a dog and a cat, and 6 who only have a dog, we add those numbers:
16 + 6 = 22
Now since there are 29 total numbers, that will be the number of outcomes out of the 22 people with dogs:
22/29
Amy is designing a door wedge for her office. The door wedge makes an angle of 30° with the ground. The slant height of the door wedge from the base to the top is 12 inches. What will be the approximate length of the base of the door wedge?
A. 16.4 inches
B. 9.85 inches
C. 12.21inches
D. 10.39 inches
Can someone please solve this problem for me. I'm kind of confused-
This is probability too-
Step-by-step explanation:
(1)The probability of landing on the color gray ONCE
= 2/7
Since it is spun 35 times, the expected number of times that it lands on a gray will be
(2/7 × 35) = 10 times
(2)The probability of landing on the color black ONCE
= 1/7
Since it is spun 105 times, the expected number of times that it lands on a black will be
(⅐ × 105) = 15 times
The formula is:
Expected value = (Number of spinning)×(probability of landing on a colour)
In parallelogram ABCD, m∠B = 32 + 35 and m∠D = 52 + 13. Find m∠C.
Answer:
113°
Step-by-step explanation:
1) according to the condition m(∠B)=m(∠D)=67°;
2) m(∠C)=180°-m(∠B)=180°-m(∠D);
m(∠C)=180-67=113°.
Mike draws five cards from a standard 52-card deck. What is the probability that he draws a card from at least three of the four suits
Answer:
not answered this question
Find the volume of the cylinder, round your answer to the nearest hundredth.
Answer:
V = 1207
Step-by-step explanation:
Diego borrowed $915 for nine months with monthly payments of $108.00.
What is the amount of total payments?
O $1,023
$1,002
S972
$915
Step-by-step explanation:
108 x 9 = 972
so it's 972 dollars
A traveler pulls a suitcase, as shown in the figure. (image below)
The force acting on the handle is 35 N at an angle of θ = 30°. How much work is done if the traveler moves 110 meters? Round to the nearest whole number.
1,893 Nm
1,925 Nm
2,703 Nm
3,334 Nm
Answer:
3334 N·m
Step-by-step explanation:
Work is the product of force and distance. The force used in the product is the force that is in the direction of motion.
__
The horizontal component of the applied force is ...
F = (35 N)cos(30°) ≈ 30.311 N
Then the work done is ...
W = Fd
W = (30.311 N)(110 m) = 3334 N·m
Using the distributive property to find the product (y−4x)(y2 4y 16) results in a polynomial of the form y3 4y2 ay−4xy2−axy−64x. what is the value of a in the polynomial? 4 8 16 32
The product (y−4x)(y^2 + 4y + 16) results in a polynomial of the form y3 4y2 ay−4xy2−axy−64x then the value of a is 16.
What is distributive property?The distributive property states that an expression of the form A(B + C) can be solved by a multiplication over addition operation that is
A(B + C) = AB + AC
This property is known by distributive law and applies to subtraction also.
First let w = y-4x make distribution a bit easier
(y−4x)(y^2 + 4y + 16)
[tex]w(y^2 + 4y + 16)\\wy^2 + w4y + w16\\[/tex]
now put the values of w in the equation
[tex](y-4x)y^2 + (y-4x)4y + (y-4x)16\\y^3-4xy^2 + 4y^2-16xy+16y-64x\\[/tex]
Here the value of a is 16.
Learn more about the distributive property:
https://brainly.com/question/26207297
Answer:
16
Step-by-step explanation:
You cut the board into two pieces: one of the pieces is 10 centimeters long and the other piece is 20 centimeters long. Which piece has the greatest diameter?
Answer:
The same
Step-by-step explanation:
length does not mean anything in terms of diameter
Please help me with this question!
It's urgent!!!!
Those who explains clearly will be given extra points and voted as brainliest
Algebra Find the value of x.
Answer:
8 :)
Step-by-step explanation:
Side 1: 15
Side 2: 14
Side 3: 7 + x
Side 1 and 3 are the same length so we subtract :D
15 - 7 = 8
Have an amazing day!!
Please rate and mark brainliest!!
Which transformation is this an example of?
A. reflection
B. rotation
C. translation
D. None of these
Answer:
B. rotation
Step-by-step explanation:
A reflection would mean that the shape would be mirrored across the y-axis or the x-axis. A translation means that nothing about the shape changes except for the location. A dilation (not an answer option but still helpful to know) is the change in size of the shape. And finally, the correct answer for this problem, a rotation means that the shape is rotated at a specific point.
I included a picture that uses a shape to help explain this idea. I hope this helps! Have a lovely day!! :)
• A principal is planning for 120 parents
to attend the Eighth Grade Open House.
In the multipurpose room, round tables
seat 6 and square tables seat 8. Let x
equal the number of round tables needed.
Let y equal the number of square tables
needed. Write an equation that represents
this situation. Then use the equation to
determine the number of round tables
needed if no square tables are used.
Answer:
✏If the rod is held straight then the angle alpha equals 90°,therefore the required solution is 45°
Step-by-step explanation:
find the inverse of the function
as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.
[tex]\stackrel{h(x)}{y}~~ = ~~6\sqrt[3]{2x+5}-1\implies \stackrel{\textit{quick switcheroo}}{x~~ = ~~6\sqrt[3]{2y+5}-1} \\\\\\ x+1=6\sqrt[3]{2y+5}\implies \cfrac{x+1}{6}=\sqrt[3]{2y+5}\implies \left( \cfrac{x+1}{6} \right)^3=\left( \sqrt[3]{2y+5} \right)^3[/tex]
[tex]\left( \cfrac{x+1}{6} \right)^3=2y+5\implies \left( \cfrac{x+1}{6} \right)^3-5=2y\implies \cfrac{\left( \frac{x+1}{6} \right)^3-5}{2}=y \\\\\\ \cfrac{\left( \frac{x+1}{6} \right)^3}{2}-\cfrac{5}{2}=y\implies \cfrac{~~ \frac{(x+1)^3}{6^3}~~}{2}-\cfrac{5}{2}=y\implies \cfrac{(x+1)^3}{432}-\cfrac{5}{2}=\stackrel{y}{h^{-1}(x)}[/tex]
Given the function below, find f(-5).
f(x)= (x - 3)² +17
Answer:
81
Step-by-step explanation:
f ( x ) = ( x - 3 )² + 17
To find : f ( - 5 )
f ( - 5 ) = f ( x )
Here,
x = - 5
f ( - 5 ) = ( - 5 - 3 )² + 17
= ( - 8 )² + 17
= 64 + 17
f ( - 5 ) = 81
a line that includes the point (7,-9) has a slope of -2. v
Answer:
y = - 2x + 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - 2 , then
y = - 2x + c ← is the partial equation
to find c substitute (7, - 9 ) into the partial equation
- 9 = - 14 + c ⇒ c = - 9 + 14 = 5
y = - 2x + 5 ← equation of line