Answers
The simplified expression is the one in option B.
How to simplify the expression?Remember that:
[tex]sec(x) = 1/cos(x)\\\\cos(x) = cos(-x)[/tex]
With these two, we can rewrite the numerator as:
[tex]sec(x)*sin(-x) + tan(-x)\\\\\frac{1}{cos(x)}*sin(-x) + tan(x)\\\\\frac{1}{cos(-x)}*sin(-x) + tan(-x)\\\\2*tan(-x)[/tex]
Replacing that in the given expression, we have:
[tex]\frac{2*tan(-x)}{1 + sec(-x)} = \frac{2*tan(-x)}{1 + 1/cos(-x)}[/tex]
Now, if we multiply and divide by cos(-x), we get:
[tex]\frac{2*tan(-x)}{1 + 1/cos(-x)} = \frac{2*tan(-x)}{1 + 1/cos(-x)}*\frac{cos(-x)}{cos(-x)} \\\\= \frac{2*sin(-x)}{1 + cos(-x)}[/tex]
Now remember that:
[tex]cos(x) = cos(-x)\\sin(-x) = -sin(x)[/tex]
With these two properties:
[tex]\frac{2*sin(-x)}{1 + cos(-x)} = \frac{-2*sin(x)}{1 + cos(x)}[/tex]
Then the correct option is B.
If you want to learn more about trigonometric identities:
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Related Questions
Chose whether the fraction and percent are equivalent
Yes. No.
A.
40/1,000 and 40%
B.
6/5 and 120%
C.
50/33 and 117%
D.
1/8 and 12.5%
Answers
Step-by-step explanation:
A No because it's 4%
B Yes
C No
D Yes
1. Use the distributive property to factor out the greatest common factor (GCF) and rewrite the
expression 36 minus 96.
a. 2(18-48)
B.6(6-16)
c 12 (3-8)
D. 12(6-2)
Answers
HELP.................................................................
Answers
Answer:
A. [tex]\frac{1}{6^{2} }[/tex]
Step-by-step explanation:
A. [tex]\frac{1}{6^{2} } = \frac{1}{36} = 0.02777[/tex]
B. [tex]6^{-3} = 0.004629[/tex]
C. [tex]\frac{1}{216} = 0.004629[/tex]
D. [tex]\frac{1}{6^{3} } = \frac{1}{216} = 0.004629[/tex]
Answer:
I think it is A because B or D is not it so I was left with A and C. So I am pretty sure that is A.
Need help ASAP please!!
Don’t know how to give brainliest sorry-
Answers
Answer:
32°
Step-by-step explanation:
All triangles must have a sum of 180°. Given the angle 58° and since this is a right triangle, we have 2 out of the 3 angles to work with.
90 + 58 + x = 180
x = 32
Jimmy's school is selling tickets to the annual dance
competition. On the first day of ticket sales
the school sold 6 adult tickets and 4 child tickets for a
total of $88. The school took in $186 on
the second day by selling 12 adult tickets and 9 child
tickets. Find the price of an adult ticket and
the price of a child ticket.
Answers
1. 6a+4c=88
12a+9c=186
2. so you need to multiply the top number by -2 so you can cancel out the 12a
-2(6a+4c=88)=. -12a-8c=-176
3. then you add them all together
12a+9c=186
-12a-8c=-176
——————————-
c=10
4. now you have to find ‘a’
6a+4(10)=88
6a+40=88
-40. -40
6a=48
divide both sides by 6
a=8
And your final answer should be (8,10)
hoped this helped:)
This is a 2 part question! Use this information for the open-ended question that follows.
Valery and Manuel ride their bikes 40 miles every Saturday. Valery rides at an average speed of 9.6 miles per hour (mph).
Valery increases her speed by 4% the next time she rides her bike. Her goal is to ride faster than Manuel.
Is the 4% increase enough to ride faster than Manuel? yes or no.
As part of your explanation, identify Valery's new speed. Then explain why or why not she met her goal.
Answers
Answer:
ok for the first part of the question This is a 2 part question! Use this information for the open-ended question that follows.
Valery and Manuel ride their bikes 40 miles every Saturday. Valery rides at an average speed of 9.6 miles per hour (mph).
a) EXACTLY how many hours does it take Valery to ride her bike 40 miles?
ANSWER (A) 4.17
b) Use this graph below to identify what Manuels average speed is:
ANSWER (B) 10 mph
I don't know the open ended question
What is the length of one side of this regular pentagon if the area is 50 and apothem is 4?
Answers
Answer:
5
Step-by-step explanation:
i took the test
The required length of one side of the given regular pentagon is 5 units.
What is a polygon?Polygon is defined as a geometric shape that is composed of 3 or more sides these sides are equal in length, and an equal measure of angle at the vertex,
Examples of polygons, equilateral triangles, squares, pentagons, etc
Here,
We can use the formula for the area of a regular pentagon to solve for the length of one side,
Area = (1/2) * Perimeter * Apothem
Since the pentagon is regular, all sides are equal, so we can write:
Perimeter = 5 * Length of one side
Substitute in the first expression
50 = (1/2) * 5 * Length of one side * 4
50 = 10 * Length of one side
Length of one side = 5
Learn more about polygon here:
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HELP!!!
A triangle has sides of 6m and 9m . Which is
a possible length, in meters, of the third side?
A-2m
B-3m
C-5m
D-17m
Answers
Answer:
C-5m
Step-by-step explanation:
Answer:
answer is ( b )
What is the approximate area of the shaded region?
Answers
Answer:
196-49 pi
Step-by-step explanation:
diameter of circle is 14
radius-7
7^2=49
49 pi
14^2=area of square
196-49pi= area of shaded area.
Answer:
im pretty sure the area is 196
Step-by-step explanation:
because when finding the area of a rectangle/ square you use the formula Length * Width and as we can see the sides of the shaded are are equivalent and as we know the length of the shaded area is 14.
we would just plug in our information.
L*W
14*14= 196
Can anyone help me with this question...please i really need your help....
(Express the variable in the brackets as the subject of formula)
Answers
9514 1404 393
Answer:
p = q/(2 -3q)
Step-by-step explanation:
[tex]\dfrac{2p}{3p+1}=q \qquad\text{given}\\\\2p=q(3p+1) \qquad\text{multiply by the denominator}\\\\ 2p=3pq+q \qquad\text{eliminate parentheses}\\\\ 2p -3pq = q \qquad\text{subtract $3pq$}\\\\ p(2-3q)=q \qquad\text{factor out $p$}\\\\ \boxed{p=\dfrac{q}{2-3q}} \qquad\text{divide by the coefficient of p}[/tex]
The square root of y^3 simplified
Answers
Answer:
(√y)3
Step-by-step explanation:
2. Carrie listened to the latest country album 3 times in a row in 2.75 hours. Write an equation to find the length of the album.
a. 3t=2.75
b. 2.75(3)=t
c. 2.75t=3
d. 2.75(3)(t)
HELP ME PLEASE
Answers
3 is the number of times she listens and “t” is the length of the album.
i'm really confused on this, anything will help
Answers
Answer:
I think its 1200 not sure though
Answer:
1,200
Step-by-step explanation:
first you would divide 480 copies by 4 minutes to see how many copies per minute (120) Then you would take 120 copies per minute and multiply it by the 10 and you would get 1200 copies per 10 minutes! lmk if that helps:)
Alana completed a problem where she had to find the sum of the polynomials (3x^2+8x-4) and (-8x^3-3x+4) Her answer is 0. Describe and correct her mistake. When graphed, how many times does the sum change directions?
Answers
Answer:
la pregunta está en blanco, ¿podría repetirla?
Step-by-step explanation:
8 + 3n ≥ 38
can yall solve plzzz
Answers
The ratio of the length to the width the official german flag is 5:3.Sanda is making 12 german flags for a cuiture show.Each flag she makes has a length of 20 centimeters . It takes her 4 hours to make all the flag. What is the width of each flag and the average amount of time it takes sandra to make each flag?
Answers
Answer: The width of each flag = 12 cm
The average amount of time it takes Sandra to make each flag = 20 minutes.
Step-by-step explanation:
Given: The ratio of the length to the width the official german flag is 5:3.
Let length = 5x, width = 3x
Length of each flag = 20 cm
i.e. [tex]5x=20\Rightarrow\ x=\dfrac{20}{5}=4\text{ cm}[/tex]
Then width of each flag = 3 x 4 = 12 cm
i.e. width of each flag = 12 cm
Total time to make 12 flags = 4 hours
Time taken to make 1 flag = [tex]\dfrac{4}{12}[/tex] hour
Time taken to make 1 flag = [tex]\dfrac{1}{3}[/tex] hour
1 hour = 60 minutes
Time taken to make 1 flag = [tex]\dfrac{1}{3}\times60[/tex] minutes = 20 minutes.
Hence, the average amount of time it takes Sandra to make each flag = 20 minutes.
I need help asap please
Answers
Step-by-step explanation:
5³×1/5⁵
5×5×5×1/5×1/5×1/5×1/5×1/5
=1/25
or
1/5²
5³-⁵
= 5-²
= 1
-------
5²
B
Please help
A school fundraiser sells holiday cards and wrapping paper. The school is trying to raise at least $400. It makes a profit of $2.50 on each box of holiday cards and 80% of the profit on each holiday box on each pack of wrapping paper. Write an inequality that represents the situation where x is the number of holiday boxes sold and y is the number of packs of wrapping paper sold.
x=
y=
Holiday Cards Profit:
Key word(s):
Linear Inequality:
Answers
Answer:
2.50x+80>4.00
Step-by-step explanation:
PLEASE HELP ASAP
Jonathan has a rectangular rug with whose length is 5 inches less than its width. The area of the rug is 36 square inches
Answers
A lamp post with a height of 12 ft casts a shadow of 6 ft. A fire hydrant near it casts a shadow that is 1.5 ft long. How tall is the fire hydrant?
Answers
Answer:
3ft
Step-by-step explanation:
We are given that
Height of lamp, h=12ft
Height of shadow, l=6ft
Height of shadow of hydrant, l'=1.5ft
Let height of hydrant=h'
We have to find the height of fire hydrant.
All right triangles are similar
When two triangles are similar then, the ratio of their corresponding sides are equal.
Using the property
[tex]\frac{h}{h'}=\frac{l}{l'}[/tex]
[tex]\frac{12}{h'}=\frac{6}{1.5}[/tex]
[tex]h'=\frac{12\times 1.5}{6}[/tex]
[tex]h'=3[/tex]ft
Hence, the height of fire hydrant=3 ft
Write an exponential function for a graph that passes through the points (2,16) and (3,32).
Answers
Answer:
[tex]y = 4(2^{x} )[/tex]
Step-by-step explanation:
The general form for an exponential function is [tex]y = kb^{x}[/tex]
When x = 2, y = 16 So, [tex]16 = kb^{2}[/tex]
and when x = 3, y = 32 So, [tex]32 = kb^{3}[/tex]
Divide [tex]\frac{32}{16} = \frac{kb^{3} }{kb^{2} }[/tex]
2 = b
Now, [tex]16 = k2^{2}[/tex]
16 = 4k
k = 4
Therefore, the exponential function is [tex]y = 4(2^{x} )[/tex]
Find the length of the hypotenuse of the triangle. 4.5 m 6 m The length of the hypotenuse is meters.
Answers
Answer:
c = 7.5 meters.
Step-by-step explanation:
hello :
use phtagore - rule :
c² = 6²+4.5²
c² = 36 + 20.25
c² =56.25
c = √56.25
c = 7.5 meters.
What are all t possible names for these?? Help plz
Answers
Answer:
13.....square
14....parallelogram
15....rhombus
16....trapezium
17...kite
18....rectangle
Answer:
#13 is a square, #14 is a rectangle, #15 is a rhombus, #16 is a trapezoid, #17 is a qaudrilateral, and #18 is a rectangle also.
Hope this helps :)
What is the variable for For the equation 2n - 3 = 7
Answers
Answer: n= 5
Step-by-step explanation:
Which have the following has a slope of 3 and y - intercept of 4
Answers
Answer:
The first table, and the graph.
Step-by-step explanation:
Suppose f(x) = x^3 + 1. Find the graph of
f(2x).
Answers
Step-by-step explanation:
I am sorry. I just typed the equation into my calculator app. Refer to the attached image above to make a deduction.
Answer:
Mga madlang pipol. The answer is graph 2
Sandra saves 7% of her salary for retirement. This year her salary was $2,000 more than her salary than in the previous year, and she saved $3,290. What was her salary in the previous year?
complete the equation 0.07( x+____) = 3,290
Sandras salary in the previous year was _____
Answers
9514 1404 393
Answer:
2,000$45,000Step-by-step explanation:
Where x represents the previous year's salary, its amount this year is said to be ...
x + 2000
The equation is trying to reflect the fact that 7% of that is $3,290. The missing number is 2000:
0.07(x +2000) = 3290
__
Solving for x, we find ...
x = (3290/0.07) -2000 = 45000
Sandra's salary the previous year was $45,000.
cuánto mide el ángulo ABF
Answers
Answer:
no tengo suficiente information para responder
Step-by-step explanation:
Solve this system of linear equations. Separate
the x- and y-values with a comma.
9x = 1 - 4y
-7x = -7 + 4y
Answers
Answer:
y = 7 and x =3
Step-by-step explanation:
use elimination method
so we gonna eliminate y first
9x = 1 - 4y
-7x = -7 + 4y
7| 9x = 1 - 4y
9| -7x = -7 + 4y
63x = 7 - 28y
-63x = -63 + 36y
add eqtn 1 to eqtn2
you will get
0 = -56 + 8y
56 = -56 + 56 + 8y
56 = 8y
56÷8 = 8y÷ 8
7 = y
also eliminate x as we have done wth y
4| 9x = 1 - 4y
4| -7x = -7 + 4y
36x = 4 - 16y
-28x = -28 + 16y
add the two equations
u will get
8x = -24 + 0
8x = -24
8x÷8 = 24÷ 8
x = 3
What is the cross product of 1/4 = 5/20?
Answers
THhe cross product is found by multiplying the numerator (top number) of one fraction by the denominator (bottom number) of the other fraction.
1/4 = 5/20
1 x 20 = 20
4 x 5 = 20
The cross product is 20
Answer:
20
Step-by-step explanation:
1 x 20 = 20
4 x 5 = 20
Hope that helps!