Given:
[tex]\dfrac{1+\sin \theta}{\cos \theta}+\dfrac{\cos \theta}{1+\sin \theta}=2\sec \theta [/tex]
To prove:
The given statement.
Proof:
We have,
[tex]\dfrac{1+\sin \theta}{\cos \theta}+\dfrac{\cos \theta}{1+\sin \theta}=2\sec \theta[/tex]
Taking LHS, we get
[tex]\text{LHS}=\dfrac{1+\sin \theta}{\cos \theta}+\dfrac{\cos \theta}{1+\sin \theta}[/tex]
Taking LCM, we get
[tex]\text{LHS}=\dfrac{(1+\sin \theta)^2+cos^2\theta }{\cos \theta(1+\sin \theta)}[/tex]
[tex]\text{LHS}=\dfrac{(1)^2+2\sin \theta +\sin^2 \theta+cos^2\theta }{\cos \theta(1+\sin \theta)}[/tex] [tex][\because (a+b)^2=a^2+2ab+b^2][/tex]
[tex]\text{LHS}=\dfrac{1+2\sin \theta +1}{\cos \theta(1+\sin \theta)}[/tex] [tex][\because \sin^2 \theta+cos^2\theta =1][/tex]
[tex]\text{LHS}=\dfrac{2+2\sin \theta}{\cos \theta(1+\sin \theta)}[/tex]
[tex]\text{LHS}=\dfrac{2(1+\sin \theta)}{\cos \theta(1+\sin \theta)}[/tex]
[tex]\text{LHS}=\dfrac{2}{\cos \theta}[/tex]
[tex]\text{LHS}=2\sec \theta[/tex] [tex][\because \sec\theta=\dfrac{1}{\cos \theta}][/tex]
[tex]\text{LHS}=\text{RHS}[/tex]
Hence proved.
First to answer and get right gets brainleist and there is ma points pls help
Answer:
#11 is D. x = u - k
#12 is D. x = gc
Step-by-step explanation:
I plugged random integers to test this. Anyhow, just do the inverse operation.
#11:
13 = x + 8
x = 13 - 8
x = 5
Here, x = u - k is the new equation.
#12:
23 = x/9
x = 23(9)
x = 207
Here, x = gc is the new equation.
PLZZZ HELP NO ONE WILL HELP ME PLZZZZ IM GIVING 50 POINTS PLZZZZ
A function is graphed below.
Which of the following represents the range of the function?
Answer:
el ranho de algo que esm ansgwne
Patty used 740.88 gallons of water over the course of 7 days. How much water did Patty use, on average, each day?
105.84 water used on average each day.
740.88 divided by 7 will give you 105.84
Or, 7 times 105.84 will get you 740.88
There were many ways you could get this, hope this helped!
Who gets this correct gets the brainliest answer
Answer:
(-1,3) (0,-2) are two points that the line goes directly through. count the rise/run from the point furthest left to the one further right. you go down 5 and right 1. since you had to go down to get there, the slope is negative. slope is rise over run so in this case it's -5/1 or slope is = -5
to find the y-intercept, you find where the line crosses the y-axis. you find what y is when x is 0. in this case it's -2
slope = -5
y-intercept = -2
and if it asks for an equation of the line, you plug those given values above, into the slope intercept form which is : y=mx+b
where m is the slope
b is the y-intercept
the equation of this line is " y = -5x -2 "
Question Help The mean finish time for a yearly amateur auto race was 185.64 minutes with a standard deviation of 0.314 minute. The winning car, driven by Sam, finished in 185.29 minutes. The previous year's race had a mean finishing time of 110.3 with a standard deviation of 0.129 minute. The winning car that year, driven by Rita, finished in 110.02 minutes. Find their respective z-scores. Who had the more convincing victory?
Answer:
Sam has the more convincing victory with a greater Zscore value
Step-by-step explanation:
Given that :
Year 1:
Mean finish time (m) = 185.64
Standard deviation (s) = 0.314
Sam's time (x1) = 185.29
Year 2:
Mean finish time (m) = 110.3
Standard deviation (s) = 0.129
Rita's time (x1) = 110.02
Zscore = (x - mean) / standard deviation
Sam's Zscore :
(185.29 - 185.64) / 0.314
= - 0.35 / 0.314
= −1.114649
= - 1.115
Rita's Zscore :
(110.02 - 110.3) / 0.129
= - 0.28 / 0.129
= −2.170542
= - 2.171
Sam has the more convincing victory with a greater Zscore value
6x2 + 7x - 49
What is the answer
Answer:-
Step-by-step explanation:
Answer:
7x - 37
Step-by-step explanation:
If someone can just answer the first question that would be so helpful plzzz
Answer:
I'm guessing that when you graph it, the graph changes direction when it's not on the x-axis. the "real zeros" of a graph are the ones that go through the x-axis and then imaginary ones are the ones that don't.
Step-by-step explanation:
Jenny has a new box of 8 colored pencils. Each one is perfectly sharpened. Together the colored pencils have a mass of 56 grams
Answer:
If you are trying to find how much grams are in one color pencil it is 7 grams.
please help me asap
Answer:
d > -8
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define
25 > 1 - 3d
Step 2: Solve for d
Subtract 1 on both sides: 24 > -3dDivide -3 on both sides: -8 < dRewrite: d > -8Here we see that any value d greater than -8 would work as a solution to the inequality.
State the domain and range of the function:
domain:
range:
Answer:
Domain: [-5, 1)
Range: (5, 1]
General Formulas and Concepts:
Algebra I
Domain is the set of x-values that can be inputted into function f(x) Range is the set of y-values that are outputted by function f(x)Step-by-step explanation:
According to the graph, our x-values span from -5 to 1. Since -5 is a closed dot, it is inclusive in the domain. Since -1 is an open dot, it is exclusive in the domain:
[-5, 1)
According to the graph, our x-values span from -5 to 1. Since -5 is an open dot, it is exclusive in the range. Since 1 is a closed dot dot, it is exclusive in the range:
(5, 1]
State the transformation(s) from the parent function f(x).
will mark as branliest
Answer:
Try C and see if it works, but read info below
Step-by-step explanation:
Refer to the equation y=a(x-h)^2+k
If a>0 then the parabola opens up and horizontally compresses (shrinks)
If 0<a<1 then the parabola opens up and horizontally stretches
If a<0 then the parabola opens down and horizontally compresses (shrinks)
h is the horizontal shift (along the x-axis)
k is the vertical shift (along the y-axis)
Given the function f(x)=3(x+1)^2-2, we can identify the values:
a=3, so the parabola opens down and horizontally compresses (shrinks) by a factor of 3
h=-1, so the horizontal shift is one unit to the left
k=-2, so the vertical shift is 2 units down
Given the above information, none of the answer choices are correct unfortunately. Your best option to pick is C.
Kevin went fishing and is using a scatterplot to analyze the relationship between the weight of each of the fish he caught in pounds and in kilograms. He uses the weight in pounds as the independent variable and the weight in kilograms as the dependent variable. Which statement is correct?
The points on the scatterplot will go up from left to right because as the weight in pounds increases, the weight in kilograms increases.
The points on the scatterplot will go up from left to right because as the weight in pounds increases, the weight in kilograms decreases.
The points on the scatterplot will go down from left to right because as the weight in pounds increases, the weight in kilograms increases.
The points on the scatterplot will go down from left to right because as the weight in pounds increases, the weight in kilograms decreases.
Answer:
The answer is A.The points on the scatter plot will go up from left to right because as the weight in pounds increases, the weight in kilograms increases, because when the pounds (lbs.) increases, the kilograms (kg.) increase.
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
just did the quiz and got it right
what is the LCD of 8/9 and 7/8
Answer:
72 I think
Step-by-step explanation:
I'm not 100% sure but I think its 72
Answer:
The Least Common Multiple (LCM) of 8 and 9 is 72,
and the Least Common Multiple (LCM) of 7 and 8 is 56.
Find the value for x.
5x - 12
3x + 30
48
The value of x will be;
⇒ x = 3.75
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 5x - 12 + 3x + 30 = 48
Now,
Solve the expression for x as;
The expression is,
⇒ 5x - 12 + 3x + 30 = 48
⇒ 8x - 12 + 30 = 48
⇒ 8x + 18 = 48
Subtract 18 both side as,
⇒ 8x - 18 = 48 - 18
⇒ 8x = 30
Divide by 8 as;
⇒ x = 30/8
⇒ x = 3.75
Thus, The value of x will be;
⇒ x = 3.75
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ2
Mr.Harrison is reading a map to plan his vacation route. The map has a scale of 1 cm Equal 18 miles. He measure the length on the map for his vacation route to be 14 centimeters. What is the length of vacation route in miles?
Answer:
252 miles
Step-by-step explanation:
Help please need this soon
Answer:
I'm too dum to help but thanks for the points dude
Step-by-step explanation:
Answer:
4 and 5:yes and no
Step-by-step explanation:
4.one to many is not a function
5.It is a function because it is a many to one relation
The graph shows the relationship between the gallons of water a sprinkler system uses and the number of minutes the system is used.
Answer:
??? what graph
Step-by-step explanation:
bro I'm really stuck with this, and my brain cells are too small to figure this. out, can someone help me? thank you :)
Answer:
B
Step-by-step explanation:
First isolate the variable, x. To do this, use inverse operations. The inverse operation of -4 is +4. So, add 4 on both sides of the equals sign. The positive 4 cancels out the negative 4 on the left side. Add 4 to the other side, -18, for -14. You are left with 7x = -14. Now to get rid of the coefficient, 7. The inverse of x7 is ÷7. So divide 7x by 7 to completely isolate x. On the right side, -14 is divided by 7 to get -2. You are left with x = -2. Wow that was a ted talk :P Anyway, hope this was helpful ^^ lmk if I need to clarify about anything :D Good day man
9. Find (f.g)(a) if f(a) = . and g(a) = 2². Fully simplify your answer.
A. (F•g) = 1/a
B. (F•g) (a) = a
C. (F•g) (a) = 1/a^2
D. (F•g) = 1
D is your answer ....
Order this set of numbers from greatest to least. Then explain the order, referring to the number line in your explanation.
-1.79, 2, 2.54, -4
Answer:
-4,-1.79,2,2.54
Step-by-step explanation:
You'll have to do the explanation yourself, but here are a few pro tips!
-Explain which numbers are farthest from 0.
-Explain where each number will go on the plot.
-Use words like farthest, less than, greater than, negative, and integer.
-Make your explanation at least 2 sentences long!
You got this, I know you can do it-! Have a meme to help! <3
Will give brainliest foe correct answer
Answer:
true
Step-by-step explanation:
Please help me if u know
Answer: x = [tex]\frac{3+\sqrt{21} }{4}[/tex]
x = [tex]\frac{3-\sqrt{21} }{4}[/tex]
Step-by-step explanation:
Ben earns an annual income of $12,800 a year. The income tax he has to pay is 15%. What is the amount of income tax in dollars and cents that Ben has to pay? thanks!
A $1,664
B $10,880
C 12,000
D $1,920
Find 15% of 12,800,
[tex]\frac{15}{100}[/tex] ×[tex]\frac{12,800}{1}[/tex]
= 1,920
The function f(x) varies inversely with x and f(x)=2 when x = 16.
What is f(x) when x = 4?
Answer: The correct answer is: [D]: "8" .
Step-by-step explanation:f y varies inversely with x; then y = k/x ; with "k" being the "constant" in this equation.
You can find the constant by substituting the values given: x = 16, f(x) = y = 2 ;
So, f(x) = y = 2 = k/16 ;
→ 2 = k / 16 ;
Solve for the constant; "k" ;
Multiply EACH SIDE of the equation by "16"
→ 16* (2) = (k / 16) * 16 ;
→ 32 = k ;
↔ k = 32 ;
As such, we can write the equation:
y = k/ x ; as:
→ y = 32/ x ;
Since we are given: "x = 4" ; Plug in that value; and solve for "y" ;
y = 32/4 = 8 .
y = 8 .
y = f(x) ;
So; f(x) = 8 ; which is: Answer choice: [D]: "8" .
2.31 (1 repeating) as a fraction
Answer:
[tex]\frac{231}{100}[/tex]
This is assuming that you can simplify the 2.31 to the nearest hundredth.
If f(x) =2x²-x, find f(-4)-f(9)
What is the value of |5| - | -5| - (-5)? The solution is
Answer:
5
Step-by-step explanation:
when we simplify it we get 5-5+5 which equals 5
A Six packs of undershirt cost $13.98. This is $3.96 less the cost of buying six individual shirts if each undershirt cost the same amount how much does each undershirt cost when purchased individually?
What is the standard form of y-7=-2(x+1)