Answer:
Step-by-step explanation:
I'll use x instead of theta.
So we have:
sin x / ( 1 + cos x) + (1 +cos x) / sinx
The LCM is sin x(1 + cos x) so we have
sin^2 x + (1 + cos x)^2 / sin x(1 + cos x)
= sin^2 x + cos^2x + 2 cos x + 1 / sin x(1 + cos x)
Now sin^2x + cos^2x = 1 so:
= 2 + 2 cos x / sin x(1 + cos x)
= 2(1+ cos x) / sin x(1 + cos x)
The 1 + cos x is common so we have:
2 / sin x
= 2 cosec x.
Complete the table. At least the first few so I understand how to do it
Answer:
What we need to do is simply multiply the values in both columns e.g 4 * 3/36 = 12/36
Please check explanation for complete answer
Step-by-step explanation:
Here, we are concerned about filling the empty columns of the table.
What we want to do here is simply straightforward. All we need to do is to
multiply the values of x by the values of P(x) in each of the individual rows.
Also recall, we do not need to reduce the fractions.
So we have;
2. 3 * 2/36 = 6/36
3. 4 * 3/36 = 12/36
4. 5 * 4/36 = 20/36
5. 6 * 5/36 = 30/36
6. 7 * 6/36 = 42/36
7. 8 * 5/36 = 40/36
8. 9 * 4/36 = 36/36
9. 10 * 3/36 = 30/36
10. 11 * 2/36 = 22/36
11. 12 * 1/36 = 12/36
simplify 3/7
into a whole number
Answer:
You can't because it's not a "full fraction" like 7/7. The best you can do is turn that into a decimal like 0.43
Step-by-step explanation:
Please help me understand this. Thank you! Gina has borrowed 100 songs from her friend. She plans to download an equal number of songs on her music player each week for 5 weeks. The graph shows the number of songs left to download, y, for a certain number of weeks, x: A graph titled Song Downloading shows the Number of Weeks on x-axis and Number of Songs Left to Download on the y-axis. The x-axis scale is shown from 0 to 5 at increments of 1, and the y-axis scale is shown from 0 to 140 at increments of 20. A straight line joins the ordered pairs 0, 100 and 1, 80 and 2, 60 and 3, 40 and 4, 20 and 5, 0. Part A: What is the rate of change and initial value of the function represented by the graph, and what do they represent in this scenario? Show your work to find the rate of change and initial value. (6 points) Part B: Write an equation in slope-intercept form to model the relationship between x and y. (4 points)
Answer:
Rate of Change/Slope = -20
Equation: y= -20x +100
Step-by-step explanation:
A. We know the rate of change is also known as the slope. If we used the slope formula to find the slope we can find the Rate of Change.
[tex]\frac{y2 - y1}{x2 - x1} = \frac{100-80}{1-2} = \frac{20}{-1} = -20[/tex]
B. Since we know the slope and 1 point on the graph we can substitute them in for 'b'
(0,100)
(100)=-20(0) + b
b = 100
Since we know the slope and the b value we can write the equation:\
y = -20x +100
The rate of change refers to the slope of the line, that is the change in y-axis per unit change in the value on the x-axis. Hence, the rate of change is :
Slope = - 20y = -20x + 100Slope = Rise / Run Rise = (y2 - y1) = (0 - 100) = - 100Run = (x2 - x1) = (5 - 0) = 5Slope = - 100 / 5 = - 20
General form of a slope - intercept relation :
y = bx + cThe intercept, c can be calculated thus:
100 = - 20(0) + c
100 = 0 + c
c = 100
Hence, the slope - intercept equation will be y = - 20x + 100
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What is the y−intercept of the line that passes through the point (4,9)and is parallel to the line y=12x+2?
Answer:
y- intercept = - 39
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 )
y = 12x + 2 ← is in slope- intercept form
with slope m = 12
Parallel lines have equal slopes, thus
y = mx + c ← is the partial equation
To find c substitute (4, 9) into the partial equation
9 = 48 + c ⇒ c = 9 - 48 = - 39 ← y- intercept
Answer:
y-intercept = -39
Step-by-step explanation:
if two lines are parallel it means they have the same gradient so we compare the equation given to the default equation of a line
y=mx+c
y=12x+2
comparing we have the gradient m=12 now finding the equation of the line parallel to the given line we use
y-y1=m(x-x1)
y1=9 and x1=4
y-9=12(x-4)
y-9=12x-48
y=2x-48+9
y=2x-39
comparing to the default equation of a line y=mx+c where c is the y-intercept
therefore the y-intercept is -39
Which of the following are natural numbers? There may be more than one correct answer. Select all that apply. If only one answer is correct, select "only" and the answer that applies. A.) only B.) −1,−2,−3,… C.) 7,8,9,… D.) fractions E.) 22
Answer:
Option C and option E
Step-by-step explanation:
C.) 7,8,9,…
E.) 22
Natural numbers are also called counting numbers.
They begin from 1, 2, 3 to infinity.
Natural numbers are greater than zero (0)
They do not have decimal point in them.
They are positive integers, as such they do not have minus
Natural numbers can include commas when they are large like 3,000
Find f(x) and g(x) so the function can be expressed as y = f(g(x)). (1 point) [tex]y=\frac{7}{x^{2} } +10[/tex]
Answer:
The functions are [tex]f(x) = 7\cdot x+10[/tex] and [tex]g(x) = \frac{1}{x^{2}}[/tex], respectively.
Step-by-step explanation:
Let suppose that [tex]g(x) = \frac{1}{x^{2}}[/tex], then [tex]f(g(x))[/tex] is:
[tex]f(g(x)) = 7\cdot \left(\frac{1}{x^{2}} \right) + 10[/tex]
[tex]f(g(x)) = 7\cdot g(x) + 10[/tex]
Thus,
[tex]f(x) = 7\cdot x + 10[/tex]
The functions are [tex]f(x) = 7\cdot x+10[/tex] and [tex]g(x) = \frac{1}{x^{2}}[/tex], respectively.
Which of the following symbols could correctly finish the statement. Select all that apply. 0___-8 = ≠ > < ≥ ≤
Answer:
>
Step-by-step explanation:
Even though its 0 its still greater than any negative number.
Answer:
Step-by-step explanation:
If the geometric mean of a and 120 is 60, find the value of a.
Answer:
The answer is option 4.
Step-by-step explanation:
Given that the mean formula is total score/number of score. So we can assume that total score is (a+120), number of score is 2 and the mean value is 60. Then you have to find the value of a :
[tex] \frac{a + 120}{2} = 60[/tex]
[tex]a + 120 = 60 \times 2[/tex]
[tex]a + 120 = 120[/tex]
[tex]a = 120 - 120[/tex]
[tex]a = 0[/tex]
[tex] \text{ Geometric mean of two numbers } a \text{ and } b , \text{ where } a,b>0 \text{ is given by } G= \sqrt{ab}[/tex]
[tex] \sqrt{a\cdot120}=60 [/tex]
[tex] \implies 60 \cdot 2 \cdot a=60\cdot 60 \qquad \text{Squaring both sides} [/tex]
[tex] \implies a =30 [/tex]
Gene is playing a game with a bag of marbles. 3 of the marbles are blue, 4 are green, and 7 are yellow. See below for awarded prizes. $2 green $0.5 yellow $4 blue What is the expected cost (or payout for Gene's game?
Answer:
$23.5Step-by-step explanation:
Gene is playing a game with a bag of marbles. If 3 of the marbles are blue, 4 are green, and 7 are yellow and awarded prices for the marbles are $2 green $0.5 yellow $4 blue, the expected payout for Gens game is expressed as shown;
If a blue marble costs $4, 3 blue marbles will cost 3*$4 = $12
If a green marble costs $2, 4 green marbles will cost 4*$2 = $8.0
If a yellow marble costs $0.5, 7 yellow marbles will cost 7*$0.5 = $3.5
Total payout for Gene's game will be the equivalent to $12+ $8 + $3.5 = $23.5.
Hence Gene expected cost will be $21.5
what is the answer for 6x-4=-26+5x
Answer: x=-22
Step-by-step explanation:
6x-4=-26+5x
6x-4-5x=-26+5x-5x ⇔ subtraction property of equality
x-4=-26
x-4+4=-26+4 ⇔ addition property of equality
x=-22
Answer:
x = - 22Step-by-step explanation:
6x - 4 = - 26 + 5x
First of all group like terms
Send the constants to the right side of the equation and those with variables to the left
That's
6x - 5x = 4 - 26
Simplify
We have the final answer as
x = - 22Hope this helps you
ASAP PLZ ANSWER!!! Can you tell me step by step to this question 8,595 ÷ 24?
Answer:
358 and remainder of 3
Step-by-step explanation:
1. Divide it like any other problem
24 goes into 85, 3 times with 13 left overBring down the 9 and 24 goes into 139, 5 times with 19 left overThen bring down the 5 and 24 goes inside 195, 8 times with 3 left overSo your remainder would be 3Hope this helps
Two students use different methods to solve this multiplication problem:
3/4*-4 2/9
Read each of their methods below and then enter numbers to correctly complete their
work.
Answer/Step-by-step Explanation:
Given, [tex]\frac{3}{4}*-4\frac{2}{9}[/tex]
Ivy solves this problem by writing each number as a fraction and then multiplies as shown below:
[tex] \frac{3}{4}*-4\frac{2}{9} = \frac{3}{4}* -\frac{38}{9} [/tex]
[tex] = \frac{3}{4}*-\frac{38}{9} = -\frac{3*38}{4*9} = -\frac{1*19}{2*3}[/tex]
[tex]= -\frac{19}{6}[/tex]
Fabian solves this problem by writing the mixed number as a sum and applies the distributive method of multiplication as shown below:
[tex] \frac{3}{4}*-4\frac{2}{9} = \frac{3}{4}(-4 + -\frac{2}{9}) [/tex]
[tex] = \frac{3}{4}*-4 + \frac{3}{4}*-\frac{2}{9} [/tex]
[tex] = -\frac{3}{1} + \frac{1}{2}*-\frac{1}{3} [/tex]
[tex] = -3 + (-\frac{1}{6}) [/tex]
[tex] = -3 - \frac{1}{6} = -3\frac{1}{6} [/tex]
Show all work to solve the equation for x. If a solution is extraneous, be sure to identify it in your final answer.
square root of the quantity x minus 3 end quantity plus 5 equals x
Answer:
Step-by-step explanation:
[tex]\sqrt{x-3} +5=x\\\sqrt{x-3} =x-5\\squaring ~both~sides\\x-3=x^2-10x+25\\x^2-10x-x+25+3=0\\x^2-11x+28=0\\x^2-7x-4x+28=0\\x(x-7)-4(x-7)=0\\(x-7)(x-4)=0\\x=7,4[/tex]
put x=7 in the given equation
[tex]\sqrt{7-3} +5=7\\\sqrt{4} +5=7\\2+5=7\\7=7[/tex]
which is true .
∴ x=7 is a solution of the given eq.
now put x=4 in the given eq.
[tex]\sqrt{4-3} +5=7\\1+5=7\\6=7\\[/tex]
which is not true.
∴x=4 is an extraneous solution.
WILL GIVE BRAINLIEST
Question 8(Multiple Choice Worth 1 points) (06.04 LC) Choose the correct product of (6x − 2)(6x + 2). A.36x2 + 4 B.36x2 − 24x + 4 C. 36x2 + 24x + 4 D. 36x2 − 4
Answer:
D) 36x²-4
Step-by-step explanation:
36x²+12x-12x-4
36x²-4
[tex](6x - 2)(6x + 2) \\ = {(6x)}^{2} - {(2)}^{2} \\ = {36x}^{2} - 4[/tex]
Answer:
D.
[tex] {36x}^{2} - 4[/tex]
Hope you could understand.
If you have any query, feel free to ask.
What is m
Round the answer to the nearest whole number.
O 30°
O 35°
O 55°
O 60°
Answer:
30
Step-by-step explanation:
fufyfuf7fjcjcufuy7fufucyyxyvkbuvufudydy shut up
What is the difference between sin^-1 and sin?
Answer:
Step-by-step explanation:
sin of angle x is the trig ratio sine of x.
sin-1 x is the angle whose sine is x.
sin-1 x can also be written as arcsin x.
help help help me plZZZZZ ill give you brainly ;DDD
Answer:
the answer is 60.7
Step-by-step explanation:
60 to has a between numbers like given in the picture
so as number line it's
60.1 . 60.2 60.3 60.4 60.5 60.6 60.7 60.8 and continue
if u get any 3 digit number like 600 to 650 in number line
u do it like it the same 600.1 600.2.... and go on
Answer:
63½ or 63.5
Step-by-step explanation:
65-60=5
10points=5
1point=?
1×5/10= ½
that means the sequence continues after adding ½ i.e
60..60½...61...61½...62...62½...63...63½...64..64½...65
you have been asked the 8th number which is 63½
in a 10 team league, each teams play every other team exactly twice. find the total number of games played in the league
Addition can be defined as the process of adding two numbers. The total number of games played in the league is 90.
What is Addition?Addition can be defined as the process of adding two numbers such that the result is the combined value of the two numbers.
Given that in a 10-team league, each team play every other team exactly twice. Therefore, the total number of games that will be played by the first team is 18, similarly, the number of games that will be played by the second team is 16.
Therefore, as mentioned above the series will continue with a common difference of -2 and will continue till 0. Thus, the total number of games played in the league is,
Total number of games = 18 + 16 + 14 + 12 + 10 + 8 + 6 + 4 + 2 = 90
Learn more about Addition:
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**Yoxelt buys 4 1/2 gallons of soda. One-fourth of the soda he bought was Pepsi and the rest was Sprite. How many gallons of Pepsi did Yoxelt buy? Show all work below.
Answer:
1 1/8
Step-by-step explanation:
1/4 of the 4 1/2 gallons were Pepsi, so the amount is ...
(1/4)(9/2) = (1·9)/(4·2) = 9/8 = 1 1/8
Yoxelt bought 1 1/8 gallons of Pepsi.
-7p+2(5p-8)=6(p+6)-7
Answer:
-15
Step-by-step explanation:
-7p+10p-16=6p+36-7
3p-16=6p+29
3p-6p=29+16
-3p=45
p=45/-3
p=-15
help8b2 • 2b3 a) 16b-2 ,b) 16b6 ,c) 16b-4 ,d) 16b5
Answer:
16b^5
Step-by-step explanation:
8b^2×2b^3
= 16b^2+3
= 16b^5
Answer:
D)16b5
Step-by-step explanation:
8b2×2b3
= 16b2+3
= 16b5
Wait times at a dentist's office are typically 21 minutes, with a standard deviation of 2 minutes. What percentage of people should be seen by the doctor between 17 and 25 minutes for this to be considered a normal distribution?
Answer:
95%
Step by step explanation:
z = 17-21 / 2 and z = 25-21/2
z=-2 (2.28%) z=2 (97.72%)
97.72 - 2.28 = 5.44
100% - 5.44% is about equal to 95%
Please answer this question now
Answer:
30.9 cm²
Step-by-step explanation:
To find the surface area of this figure, we find the area of the base and the 3 identical sides.
The base is split into two identical right triangles. Let's find the area of one and multiply by two.
Half of 3: 1.5
[tex]1.5\cdot2.6=3.9\\3.9\div2=1.95[/tex]
There are two right triangles:
[tex]1.95\cdot2=3.9[/tex]
The area of one of the sides will be the same thing, except the height is 6.
[tex]1.5\cdot6=9\\9\div2=4.5\\4.5\cdot2=9[/tex]
There are 3 sides identical to this one:
[tex]9\cdot3=27[/tex].
Add 27 and 3.9:
[tex]27+3.9=30.9[/tex]
Hope this helped!
Answer:
30.9 square centimeters
Step-by-step explanation:
3 * 1/2(3)(6) + 1/2(3)(2.6) = 30.9
Which data set matches the box-and-whisker plot?
A) 12 13 15 19 23 23 25 26.5 28 30
B) 15 13 19 21 23 24 27 29 32
C) 11 31 13 15 19 21 21 25 27 29 31
D) 11 13 15 19 23 23 24 26.5 28 33
Answer:
D) 11 13 15 19 23 23 24 26.5 28 33
Step-by-step explanation:
The box-and-whisker plot displayed above has the following key values that we can use to identify which of the given data set it matches. It has:
Minimum value = 11
Q1 = 15
Median = 23
Q3 = 26
Maximum value = 33
From the options given, using just the max and min value, we can conclude that the data set in option D matches the box plot.
The data set in option D has a minimum value of 11, and a maximum value of 33.
help plz I think the first one is correct but I'm not sure
The left side 10x+25 is the cost expression for Black Diamond, while the right hand side 5x+50 is for Bunny Hill. The x is the number of hours.
Carey earns $9.75 working part time on weekends. The table below shows the amount, a, Carey earns for working h hours. Carey’s Earnings h 0 1 3 a $0 $9.75 ? Which value completes the table to show the amount Carey earns for working 3 hours?
Answer:
$29.25
Step-by-step explanation:
For every 1 hour, Carey earns $9.75. Multiply $9.75 by 3 to find out how much she earns for 3 hours of work.
$9.75 × 3 = $29.25
Carey earns $29.25 for working 3 hours.
Answer:
29.25
Step-by-step explanation:
I got it right on edge!! trust me
what equation accurately represent this statement three less than 4 times a number is less than 12
Answer: 4t - 3 < 12
Step-by-step explanation:
a second degree equation in one variable example how many solutions does it have ?a second degree equation in one variable example how many solutions does it have ? is it possible to have many solutions or no solutions tions give an example for each
Answer:
0, 1, or 2 real solutions
Step-by-step explanation:
Including complex and repeated solutions, a polynomial with real coefficients, and of degree n, always has n solutions.
If you're only concerned about real solutions, a 2nd degree equation in one variable may have 0, 1, or 2 real solutions. Here are some examples.
0 solutions: x^2 +1 = 01 solution: x^2 = 02 solutions: x^2 -1 = 0please helppp ill give brainliest the question is attached below
Answer: It is false, the diameter is not 16 m.
Step-by-step explanation:
P 4m are 8 m are 32 m away. The diameter= 32 m.
(I hope its rights!!!)
HELP ASAP ITS SO HARD! Kelsey did the following division problem. Her teacher says that the quotient she found is wrong. −2 5/6 ÷ 1 1/3 −17/6 ÷ 4/3 −6/17• 3/4 −6×3 divided by 17×4 −18/68 −9/34 A. Identify what Kelsey did wrong in her calculations. B. Find the correct quotient, showing all of your calculations.
Part A
Her steps were
[tex]-2 \frac{5}{6} \div 1 \frac{1}{3}\\\\-\frac{17}{6} \div \frac{4}{3}\\\\-\frac{6}{17} \times \frac{3}{4}\\\\-\frac{6\times 3}{17\times4}\\\\-\frac{18}{68}\\\\-\frac{9}{34}\\\\[/tex]
Kelsey made a mistake on line 3. Note how the 17/6 flips to 6/17. This is not correct. You keep the first fraction the same, but you do flip the second fraction. This only applies when you divide two fractions.
The third step should look like [tex]-\frac{17}{6}\times \frac{3}{4}[/tex]
=======================================================
Part B
Here's what she should have written
[tex]-2 \frac{5}{6} \div 1 \frac{1}{3}\\\\-\frac{17}{6} \div \frac{4}{3}\\\\-\frac{17}{6} \times \frac{3}{4}\\\\-\frac{17\times 3}{6\times 4}\\\\-\frac{51}{24}\\\\-\frac{17}{8}\\\\[/tex]
If you want to convert that improper fraction to a mixed number, then you could do something like this
[tex]-\frac{17}{8} = -\frac{16+1}{8}\\\\-\frac{17}{8} = -\frac{16}{8}-\frac{1}{8}\\\\-\frac{17}{8} = -2 \frac{1}{8}\\\\[/tex]
Or you could divide 17 over 8 using long division to get 2 remainder 1. The 2 is the quotient that goes to the left of the 1/8. The remainder of 1 is the numerator of 1/8.
