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.
Please help!
Write an equation of the line in slope-intercept form.
Answer:
y=4/2m-3 OR y=2m-3
Step-by-step explanation:
Lynn paid $94 for 6 meals how much would 9 meals cost
determine whether the decimal is terminating repeating or irrational 0.4286
Answer:
irrational decimal
Step-by-step explanation:
It can't be repeated, can't go on forever, so it is an irrational decimal.
Which is smaller, one-ninth of 54 or one-fourth of 36?
Answer:
one-ninth of 54
Step-by-step explanation
54*1/9=6
36*1/4=9
Answer:
1/9 of 54 is smaller than 1/4 of 36
Step-by-step explanation:
1/9 of 54 is 54/9 and that is 6
1/4 of 36 is 36/4 and that is 9.
Please mark brainliest
HELP PLEASE!!!! WILL GIVE 100 POINTS
Answer:
w to r to a
Step-by-step explanation:
e to c to p
Answer:
w to r to a
Step-by-step explanation:
The graph y=f(x) is graphed below. What is the end behavior of f(x)?
Answer:
as x → -∞, y → ∞ and as x → ∞, y → -∞
Step-by-step explanation:
Just check the first quadrant of the given graph.
In the first quadrant, when x gets smaller, the value of y is increasing to positive infinity.
In other words, as x → -∞, y → ∞
Now, observe the behavior of the graph in the 4th quadrant.
In the 4th quadrant, when x gets larger, the value of y is decreasing to negative infinity.
In other words, as x → ∞, y → -∞
Therefore, the behavior of f(x):
as x → -∞, y → ∞ and as x → ∞, y → -∞
Therefore, option (C) is true.
The end behavior of a graph is defined as what is going on at the ends of each graph when the function approaches positive or negative infinity.
End behaviour of given graph is, x⇒ -∞ then y⇒∞ and x ⇒∞ then y⇒ -∞
Since, here a graph is attached.
From graph it is observed that, when x tends to negative side, graph is going to upward direction. and when x tends to positive side then graph is going to downward direction.
So, when x tends negative infinity then y tends to positive infinity.
when x tends to positive infinity then y tends to negative infinity.
Therefore, end behaviour of given graph are,
x⇒ -∞ then y⇒∞ and x ⇒∞ then y⇒ -∞
Learn more:
https://brainly.com/question/14962400
Solve the equation.
x² + 6x+15=0
Answer:
x = -3 + i√6 and x = -3 - i√6
Step-by-step explanation:
Let's apply the "completing the square" method to find the roots of this equation.
Take half of the coefficient 6 of x, square it and add this result to x^2 + 6x. Then subtract the same quantity:
x^2 + 6x + 15 becomes
x^2 + 6x + 3^2 - 3^2 + 15 = 0
Rewriting the first three terms as the square of a binomial, we ge:
(x + 3)^2 - 9 + 15 = 0, which simplifies to:
(x + 3)^2 + 6 = 0, or (x + 3)^2 = -6
Taking the square root of both sides:
x + 3 = ±i√6
Then the two roots are complex:
x = -3 + i√6 and x = -3 - i√6
(11 + 42 - 5) / (11 - 4) (11+42-5) 48/(11-4) 48/7
Answer:
= -24576/7
or
-3510.857142
both are the correct answer
Which of the following inequalities is correct?
Answer:
B
Step-by-step explanation:
Most living things need oxygen to survive you breathe in oxygen and it is carried to this Organ. here the red blood cells pick up the oxygen and carry the oxygen to all the body cells that need it what is this organ
Answer:
The lungs
Step-by-step explanation:
becuase biology
Ariel bought 3 raffle tickets for $5. How many tickets could Ariel
buy for $15?
Answer:
9 raffle tickets
Step-by-step explanation:
Because 3 raffle tickets are $5
and to find out the number of tickets you can buy with $15 you have to
divide $15 by $5 which is 3
then multiply the 3 times 3 to get 9 raffle tickets
Have a great day, I hope this is helpful to you.
Answer:
9
Step-by-step explanation:
3=5 6=10 9=15
Hy can you figure out
(100 x 50) - (1/8 x 50) ÷ by 2?
Answer:
4996.875 or 39975/8
Step-by-step explanation:
brainly pls
What is the product of(5)(3)
Answer:
15
Step-by-step explanation:
just cause
10 points for correct answer and giving brainliest
Answer: B
Step-by-step explanation:
This graph shows the distance that a robot walks. What is the robot's speed?
Waliking Time and Distance
2 3 4 5
Time (minutes)
OA 10 feet per minute
OB. 5feet per minute
Oc. 30 feet per minute
OD. 20 feet per minute
The speed of the robot from the graph is m = 10 feet per minute
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let y represent the distance of the robot
Let x represent the time taken
Let the first point be P ( 1 , 10 )
Let the second point be Q ( 2 , 20 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
The slope of the line will give the speed of the robot
Substituting the values in the equation , we get
Slope m = ( 20 - 10 ) / ( 2 - 1 )
m = 10 feet per minute
Hence , the speed is 10 feet/min
To learn more about equation of line click :
https://brainly.com/question/14200719
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The complete question is attached below :
This graph shows the distance that a robot walks. What is the robot's speed?
Walking Time and Distance
2 3 4 5
Time (minutes)
A) 10 feet per minute
B) 5feet per minute
C) 30 feet per minute
D) 20 feet per minute
PLEASE I NEED HELP WITH MATH
Answer:
117
Step-by-step explanation:
Hi, If you were to add 75 to 42, you would get 117. Since a triangle's angles all have to add up to 180, the last angle would be 63. However, you are looking for the outside angle, which would then just be 117. Hope this is right!
Which of the following is equivalent to 12950+750-750
Answer:
12950
Step-by-step explanation:
Would appreciate some help first to answer gets brainliest
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:
(2^2*3)+(6*3) Plzz tell me fast
Answer:
30
Step-by-step explanation:
(4×3) + (6×3)
(12) + (18)
= 30
Joseline has 347 marbles. Ever has 4 times as many as Joseline. Pablo has 799 fewer than Ever. How many marbles does Pablo have? Joseline tiene 347 canicas. Ever tiene 4 veces más que Joseline. Pablo tiene 799 menos que nunca. ¿Cuántas canicas tiene Pablo?
Answer:
its D
Step-by-step explanation:
The new owners of Bluegrass Natural Foods, Inc., have hired you to help them diagnose and cure problems that the company has had in maintaining adequate liquidity. As a first step, you perform a liquidity analysis. You then do an analysis of the company’s short-term activity ratios. 3
Your calculations and appropriate industry norms are listed.
Current ratio bluegrass 4.5 industry norms 4.0
Quick ratio bluegrass 2 industry norms 3.1
Inventory turnover bluegrass 6 industry norms 10.4
Average collection period bluegrass 73 days industry norms 52 days
Average payment period bluegrass 31 days industry norms 40 days
a. What recommendations relative to the amount and the handling of inventory could you make
to the new owners?
b. What recommendations relative to the amount and the handling of accounts receivable could
you make to the new owners?
c. What recommendations relative to the amount and the handling of accounts payable could you
make to the new owners?
Answer:
I don't understand make is more simplify
Nineteen less than four times a number is greater than forty-seven.
Please i will give away all my points to the person that answers this in number form thanks
Answer: pretty sure it's the number you multiply by 4 is 17
Step-by-step explanation:
when you multiply 4 and 16 you'll get 64 then you subtract 19 and get 45 which is less than 47 so by reasoning if you were to multiply 4 and 17 you'll get 68 then you subtract 19 from 68 and you should get 49 ( you didn't include how much greater than 47 the number should be but the safest bet would be to use 17)
If $2000 is deposited into an account paying simple interest of 6% per year on a monthly basis, in how many months will this account increase by $90?
A. 22
B. 15
C. 9
D. 4
What is the slope of line that passes through the points (-3, 5) and (0, -1).
Answer:
[tex]m=-2[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (-3, 5)
Point (0, -1)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m.
Substitute [SF]: [tex]m=\frac{-1-5}{0+3}[/tex]Subtract/Add: [tex]m=\frac{-6}{3}[/tex]Divide: [tex]m=-2[/tex]Solve the equation.
8 (2-6v) +19=-61
Answer:
v = 2
Explanation:
8(2 − 6v) + 19 = −61
[ Simplify both sides of the equation ]
8(2 − 6v) + 19 = −61
(8)(2) + (8)(−6v) + 19 = −61 (Distribute)
16 + −48v + 19 = −61
(−48v) + (16 + 19) = −61 (Combine Like Terms)
−48v + 35 = −61
−48v + 35 = −61
[ Subtract 35 from both sides ]
−48v + 35 − 35 = −61 − 35
−48v = −96
[ Divide both sides by -48 ]
−48v / -48 = −96 / -48
v = 2
- PNW
0.123
0.795
0.1
0.654
0.21
0.001
0.78
0.007
0.012
0.56
0.61
0.45
0.47
0.85
0.79
0.12.
0.124
0.5
Answer:
um what?
Step-by-step explanation:
What the heck are all these numbers
A package states that there are 60 calories in 12 crackers and 75 calories in 15 crackers. Since the relationship is
proportional, how many calories are there in 180 crackers?
x х
12
15
y
60
75
36 calories
108 calories
720 calories
900 calories
PLEASE HELP QUICK!!
A flagpole casts a shadow that is 24 ft long at the same time you cast a shadow that is
4.5 ft long. If you are 6 ft tall, how tall is the flagpole?
Answer:
32 ft tall
Step-by-step explanation:
24 divided by 4.5 is 5.3 repeating. 6 times 5.3 is around 32
What is the domain of the relation (8, -2), (4, -2), (-3, 2), (-5, -3)?
A. {8, 4, 3, -5}
B. {-8, -4, 3,5}
C. {-5, -3, 4, 8}
D. {-3, -2, 2}
Answer:
C
Step-by-step explanation:
Domain (and range) don't necessarily have to be in smallest to largest order unless your teacher requires it, so don't worry about the order.
Let's remind ourselves that the domain is the input value, or the x value, and y is the output value, or the y value. We know that in an ordered pair, the first # is x and the second # is y (because x comes before y in the alphabet). Lets look at our ordered pairs and see what the x values are.
{(8, -2), (4, -2), (-3, 2), (-5, -3)}
The x values are 8, 4, -3, and -5, therefore:
Domain: {8,4,-3,-5}
Range would equal all the y values. Remind yourself that if an x value is repeated to only write it down ONCE.
Remember, the order does not matter, so the answer would be C.
Hope this helped!
