Simplify the expression using trigonometric identities:
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:
https://brainly.com/question/7331447
#SPJ1
Which is the graph of the equation ?
A coordinate plane with a line passing through (0, negative 3), (2, 0), and (4, 3).
Which equation represents the graphed function?
–3x + 2 = y
–x + 2 = y
x – 3 = y
2x – 3 = y
The equation of the line is y = 3/2x - 3
How to determine the line equation?The points are given as:
(0, -3), (2, 0), and (4, 3).
Start by calculating the slope (m) using:
m = (y2-y1)/(x2 -x1)
This gives
m = (3 + 3)(4 - 0)
Evaluate
m = 3/2
The equation is the calculated as:
y = m(x - x1) + y1
This gives
y = 3/2(x - 0) - 3
y = 3/2x - 3
Hence, the equation of the line is y = 3/2x - 3
Read more about linear equation at:
https://brainly.com/question/14323743
#SPJ1
The four consecutive digits $a$, $b$, $c$ and $d$ are used to form the four-digit numbers $abcd$ and $dcba$. What is the greatest common divisor of all numbers of the form $abcd dcba$
1111 is the greatest common divisor of all numbers.
Lets simplify the problem,
1234 + 4321 = 5555
2345 + 5432 = 7777
3456 + 6543 = 9999
4567 + 7654 = 12221
5678 + 8765 = 14443
6789 + 9876 = 16665
After it , we get:
5555 _=_ 101 * 11 * 5
7777 = 101 * 11 * 7
9999 = 101 * 11 * 3 * 3
12221 = 101 * 11 * 11
14443 = 101 * 11 * 13
16665 = 101 * 11 * 3 * 5
abcd(5555, 7777, 9999, 12221, 14443, 16665) = 101 * 11 = 1111
Hence we get 1111 is the greatest common divisor.
Learn more about Divisor on:
https://brainly.com/question/25524020
#SPJ4
i’ll give brainliest
Answer:
5
Step-by-step explanation:
-2x - y = -3
y = -3x + 2
-2x - (-3x + 2) = -3
-2x + 3x - 2 = -3
x = -1
y = -3*-1 + 2 = 5
Right triangle J K L is shown. Line L J has a positive slope. A dotted and horizontal line is drawn to point J to form an angle of 53 degrees.
What is the measure of the angle of elevation from point L to point J?
37°
45°
53°
137°
The angle formed at J and the angle of elevation at L are alternate angles, such that the angle of elevation is 53°
Which method can be used to find the angle of elevation?The given parameters are;
Triangle ∆JKL is a right triangle
The slope of the line LJ = Positive
The angle formed by the horizontal line at J = 53°
Required;
The angle of elevation from point L to point J
Solution;
The angle of elevation at L is formed by an horizontal line drawn at L.
The two horizontal lines are parallel, and the angle of elevation at L is the alternate angle to the angle formed by the horizontal line at J.
Given that alternate angles formed between parallel lines having a common transversal are equal, we have;
The measure of the angle of elevation at L is the same as the angle formed at J which is 53°Learn more about angles formed by parallel lines that have a common transversal here:
https://brainly.com/question/24607467
#SPJ1
Answer:
C. 53 degrees
Step-by-step explanation:
hype'shfiofaudhskjkwdah
5. Factor
x²-x-72
(x-8)(x+9)
(x-6)(x+12)
(x+6)(x-12)
(x+8)(x-9)
Answer:
(x + 8)(x - 9)
Step-by-step explanation:
(x+8)(x-9)
= x² - 9x + 8x - 72
= x² - x - 72
Then
The factorization of x² - x - 72 is (x+8)(x-9)
Solve the following for x, x∈W
a) 76 x 75 x 74 x ... x 6 = P(76, x)
The required value is 70. Using the permutations formula the required value is calculated. I.e., P(76, x) = P(76, 70).
How to calculate permutations?The formula for permutations is
nPr = P(n, r) = n!/(n - r)!
Where P -number of permutations,
n - number of objects in the given set
r - number of choosing objects
Calculation:The given series is
76 × 75 × 74 × ... × 6 = P(76, x)
We know that,
76! = 76 × 75 × 74 × ... × 1 ...(i)
But to get the required series,
Divide the equation (i) by 6! = (76 - 70)!
Then,
76!/(76 - 70)! = 76 × 75 × 74 × 73 ... × 6
So, x = 70.
That is,
n!/(n - r)! = P(n, r)
⇒ 76!/(76 - 70)! = P(76, 70) = 2.618743E+108
Hence the required x value is 70.
Learn more about the permutations here:
https://brainly.com/question/1216161
#SPJ1
Exactly 32% of the students in a school play a sport. Fifty students are randomly selected to determine the probability that, at most, 15 students play a sport. Should a binomial probability density function or cumulative distribution function be used? Explain. (4 points)
A binomial probability density function should be used to represent the probability
How to determine the type of probability density?
The given parameters are:
Proportion that plays sport, p = 32%Number of students selected, p = 50The probability, P = (x ≤ 15)The proportion that plays sport indicates that
68% of the students do not play sport
So, we have two events, which are
Play sport Do not play sportWhen there are two possible events, then the binomial probability density function should be used
Read more about binomial probability density at:
https://brainly.com/question/15246027
#SPJ1
Find the unknown angle
x
4
z
y
[tex]4(x+y)^{2} -20(x+y)^{2} +25z^{2}[/tex]
Answer:
I am pretty sure that it is 625.
Answer:
Step-by-step explanation:
please make sure you indicate whether to factorize , simplify, fatorize by grouping , evaluate, or finding the derivative
70 men constructed 150 meter long wall in 12 days so as hoy many person construct 600 meters long wall in 30 days
112 men construct 600 meters long wall in 30 days.
What is Time and Work formula?
[tex]\frac{M_1\times D_1}{W_1}=\frac{M_2\times D_2}{W_2}[/tex]
We can find the number of persons who can construct 600 meters wall as shown below:
Here, [tex]M_1=70[/tex]
[tex]D_1=12[/tex]
[tex]W_1=150[/tex]
[tex]W_2=600[/tex]
[tex]D_2=30[/tex]
We have to find [tex]M_2[/tex]
Putting in formula
[tex]\frac{70 \times 12}{150}=\frac{M_2\times 30}{600}[/tex]
[tex]M_2=\frac{70\times 12\times 600}{150\times 30}[/tex]
[tex]M_2=112[/tex]
Hence, 112 men can construct 600 meters wall in 30 days.
Learn more about Time and Work here:
https://brainly.com/question/16933248
#SPJ4
A math class's mean test score is 88.4. The standard deviation is 4.0. If Kimmie scored 85.9, what is her z-score
The z-score of Kimmie is -0.625
Calculating z-scoreThe formula for calculating the z-score is expressed as;
z = x-η/s
where
η is the mean
s is the standard deviation
x is the Kimmie score
Substitute the given parameter
z = 85.9-88.4/4.0
z = -2.5/4.0
z = -0.625
Hence the z-score of Kimmie is -0.625
Learn more on z-score here: https://brainly.com/question/25638875
#SPJ1
find x please (look at the image)
Answer:
55
Step-by-step explanation:
Draw a line through the center (horizontally).
Then draw a vertical line through the vertex of the right angle.
You'll get 2 triangles
I'll let you figure this out, it pretty easy
Remember a straight angle add up to 180 degrees, a triangle adds up to 180 degrees.
What's the answer to this question?
Answer:
C
Step-by-step explanation:
The solution to a system equations is the point(s) of intersection of the 2 graphs.
Assuming that each square grid represents 1 unit, the coordinates of the point intersection is (-2, 2). This is because drawing a vertical line straight down from the point of intersection, we notice that the x-coordinate of the solution is 2 square units on the left of the origin. Drawing a horizontal line from the point of intersection to the y-axis gives us the y-coordinate of y= 2. Thus, the solution is (-2, 2) and the answer is C.
This method of finding the solution is also known as graphical method, where the graphs of the 2 equations are drawn, and the solution is where the lines cuts through each other.
Alternative methods of solving equations include substitution and elimination methods.
*Origin is the point (0, 0) on the graph, and it is the point in which the two axes intersect.
Additional:
For an example of solving by substitution, do check out the following!
https://brainly.com/question/16296725A teacher chooses two students in a class of 15 girls and 10 boys. The students are randomly chosen. What is the probability that the teacher chooses two girls?
I keep hearing 3/5 and 7/20 but I don’t know which is right, please help.
Answer: I would go with 3/5, the person who said 7/20 doesn't have any thank you's or ratings besides themselves while 3/5 has thank you's , and confirmation
Step-by-step explanation:
24 feet in 10 seconds
Answer:Divide your speed in feet per minute by 60
Step-by-step explanation:
Again pls help out!
Answer:
okay so I think its, horizontal shift right 2 and a vertical shift down 1
Step-by-step explanation:
so x says + 2 so right 2 and y says -y so down 1..?
I'm kinda rusty tho so yeah
slope:
y-intercept:
HELPPPPP PLEASE
Answer:
Slope: -1
Y-intercept: 2
Step-by-step explanation:
Line crosses y-axis at 2, the slope is going down so it is negative, and it is going down by 1.
I hope it helps! Have a great day!
bren~
Find the volume of this cone.
To start calculating the volume of the cone, we obtain the following data:
r = 4 cmh = 9 cmπ = 3To calculate the volume of a cone, we apply the following formula:
[tex]\boldsymbol{\sf{V=\dfrac{\pi r^{2}h }{3} }}[/tex], where
V = volumeh = heightr = radiusπ = piWe solve, substituting our data in the formula:
[tex]\boldsymbol{\sf{V=\dfrac{3*(4 \ cm)^{2}*9 \ cm }{3} }}[/tex]taking the square root
[tex]\boldsymbol{\sf{V=\dfrac{3 *16 \ cm^{2}*9 \ cm }{3} }}[/tex]Multiplying
[tex]\boldsymbol{\sf{V=\dfrac{432 \ cm^{3} }{3} }}[/tex]Dividing
[tex]\boxed{\boldsymbol{\sf{V=144 \ cm^{3} }}}[/tex]Therefore the volume of the cone is 144 cm³.
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{What is the formula for finding the}\\\\\huge\textbf{the volume of a cone?}[/tex]
[tex]\large\boxed{\mathsf{\dfrac{\pi \times r^2\times h}{3} = volume}}[/tex]
[tex]\bullet\large\textsf{ Whereas, \boxed{r} is your \underline{radius}, \boxed{h} is your \underline{height}, \& \boxed{\pi} is your pi.}[/tex]
[tex]\bullet\large\textsf{The pi }\boxed{(\pi)}\large\textsf{ is approximately equal to 3.14.}[/tex]
[tex]\huge\textbf{What are the labels in your equation?}[/tex]
[tex]\star\ \large\boxed{{Radius}}\rightarrow \textsf{\underline{4\ centimeters}}}}}[/tex]
[tex]\star\ \large\boxed{{Height}}\rightarrow \textsf{\underline{9\ centimeters}}}}}[/tex]
[tex]\star\ \large\boxed{{\pi}}\rightarrow \textsf{\underline{3}}}}}[/tex]
[tex]\huge\textbf{What does should the equation look}\\\\\huge\textbf{like?}[/tex]
[tex]\large\boxed{\mathsf{\dfrac{3 \times 4^2 \times9}{3}}}[/tex]
[tex]\huge\textbf{What are the steps to solve for the}\\\\\huge\textbf{question to get the result?}[/tex]
[tex]\large\boxed{\mathsf{\dfrac{3 \times 4^2 \times9}{3}}}[/tex]
[tex]\large\boxed{\mathsf{= \dfrac{3\times4\times4\times9}{3}}}[/tex]
[tex]\large\boxed{= \mathsf{\dfrac{3\times16\times9}{3}}}[/tex]
[tex]\large\boxed{\mathsf{= \dfrac{48\times9}{9}}}[/tex]
[tex]\large\boxed{\mathsf{= \dfrac{432}{3}}}[/tex]
[tex]\large\boxed{\mathsf{= \dfrac{432 \div 3}{3\div3}}}[/tex]
[tex]\large\boxed{= \mathsf{\dfrac{144}{1}}}[/tex]
[tex]\large\boxed{\mathsf{= 144\div1}}[/tex]
[tex]\large\boxed{= \textsf{144}}[/tex]
[tex]\huge\textbf{What is the result to this question?}[/tex]
[tex]\huge\boxed{\frak{144\ cm^3}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]Thank you please
Solve the system of equations
:−5x−10y=−50
10x+8y=16
The solution is
x
=
,
y
=
Answer:
x=-4, y=7
Step-by-step explanation:
-5x-10y=-50...(1)
Multiply both sides by -1:
5x+10y=50
5x=50-10y
x=(50-10y)/5
Substitute x=(50-10y)/5 into second given eqaution:
10(50-10y)/5+8y=16
Cancel out common factor 5:
2(50-10y)+8y=16
100-20y+8y=16
-12y=16-100
-12y=-84
y=84/12
y=7
Substitute y=7 into equation (1)
-5x-10(7)=-50
-5x-70=-50
-5x=-50+70
-5x=20
x=-20/5
x=-4
Suppose the diameter is 35cm. what is its curumference?include the unit measure in your answer
The circumference of the circle of diameter 35cm is 109.9 cm.
Given the diameter of the circle is 35 cm.
We are required to find the circumference of the circle.
The circumference is the arc length of the circle, The perimeter is the curve length around any closed figure. It is equat to the length of the outer ring of a circle.
Formula of circumference=2πr where r is the radius of the circle.
Diameter=35 cm
Radius=35/2 cm (Radius is half of diameter)
Circumference=2π*35/2
=35π
Put the value of π =3.14 (it can be 22/7 as well.)
=35*3.14
=109.9 cm
Hence the circumference of the circle is 109.9 cm.
Learn more about circumference at https://brainly.com/question/20489969
#SPJ4
W
Mark this and return
X
What is the value of a?
O 5 units
05
units
O 6 units
O 7 units
Save and Exit
Submit
Answer:jio
Step-by-step explanation:
Hicro
children in a class are asked about the animals they own.
between them, they only have cats, dogs, rabbits and hamsters.
the pictogram shows information about the numbers of cats, dogs and rabbits
owned by members of the class.
a total of 33 animals are kept as pets. complete the pictogram.
While solving the pictogram, we get that the number of hamsters owned are 4.
Solution:
total number of pets = 33
total number of cats = 12
total number of dogs = 11
total number of rabbits = 6
then total number of hamsters = total pets - total cats, dogs, and rabbits
total number of hamsters = 33 - ( 12 + 11 + 6)
total number of hamsters = 4
also, on the pictogram one block represents 4 animal. then, total number of hamsters will be represented by one block.
view the second attachment for answer.
What is pictogram?
A pictogram, also known as a pictogramme, pictograph, or just a picto[1], is a graphic symbol that communicates its meaning by a visual likeness to an actual thing.In writing and graphic systems where the characters resemble pictures to a large extent, pictographs are frequently utilized.Geographical, recreational, and tourism-related topics can all benefit from the usage of pictograms.Know more about pictogram numerical
https://brainly.com/question/16299415
#SPJ4
I hope you are trying to ask the question below in the image
What information is needed to shoe ABC~EDC
Answer:
I guess the first one is correct........
Help please explanation as detailed as you can make it but easy to understand
Answer:
tan(x) = (√6)/2
Step-by-step explanation:
The tangent identity is ...
tan = sin/cos
SubstitutionSubstituting the given values of sine and cosine, we have ...
[tex]\tan{x}=\dfrac{\sin{x}}{\cos{x}}=\dfrac{\dfrac{42}{55}}{\dfrac{14\sqrt{6}}{55}}[/tex]
SimplificationAt this point, it becomes a problem in simplifying a compound fraction. This can be done by dividing the fractions in the usual way, and cancelling common factors from numerator and denominator.
We note the denominators (55) are the same, and that 42=3·14, so we can simplify this to ...
[tex]\tan{x}=\dfrac{3}{\sqrt{6}}=\dfrac{3\cdot\sqrt{6}}{\sqrt{6}\cdot\sqrt{6}}=\dfrac{3\sqrt{6}}{6}\\\\\boxed{\tan{x}=\dfrac{\sqrt{6}}{2}}[/tex]
The step of multiplying by (√6)/(√6) is for the purpose of "rationalizing the denominator," making the denominator a rational number: (√6)² = 6.
__
Additional comment
If sin(x) = 42/55, then cos(x) = (√1261)/55. There is no angle x that will have these values of its trig functions. (Another example of poor curriculum editing.)
You are playing the new Simpsons board game and it comes with a six sided dice with one of the following colors on each side, red, blue, green, purple, indigo and orange. If you roll orange you win a donut, if you roll green you get eaten by Maggie. What is the probability that you will roll anything but orange
The probability that person will be eaten by Maggie is 16.67%.
Given there are 6 sided coloured dice. Colours are red, blue,green,purple, indigo and orange.
We have to find the probability that the person will be eaten by Maggie.
Probability is the likeliness of happening an event among all the possible events. It lies between 0 and 1. The probability is the numberof items divided by the total number of items.
Number of green coloured sides=1
Total number of sides=6
Probability of getting green when the dice is rolled 1 time=1/6=0.1667
We have been told that if green comes then person will be eaten by Maggie so the probability that the person will be eaten by Maggie is 0.1667 which is 16.67%.
Hence the probability that the person will be eaten by Maggie is 16.67%.
Learn more about probability at https://brainly.com/question/24756209
#SPJ4
Question is incomplete as the complete question is :
What is the probability that the person will eaten by Maggie?
Jack's cow is tied to a
beanstalk with a piece
of rope that is 15 ft long.
What is the area of the
circle in which the cow can graze
Answer:
706.86ft² or 225π ft²
Step-by-Step Explanation:
r = 15ft
Now solve the area of the circle! :)
A=πr²
A=π15²
A=225π ft²
or to simplify further!
A=706.86ft²
HELP HELP HELP
HELP HELP
HELP
(STEP BY STEP)
With some simple rearrangement, we can rewrite the numerator as
[tex]2x^3 - 3x^2 - x + 4 = 2(x^3 - x) - 3x^2 + x + 4 \\\\ ~~~~~~~~ = 2x(x^2-1) - 3(x^2 - 1) + x + 1 \\\\ ~~~~~~~~ = (2x-3)(x^2-1) + x+1[/tex]
Then factorizing the difference of squares, [tex]x^2-1=(x-1)(x+1)[/tex], we end up with
[tex]\dfrac{2x^3 - 3x^2 - x + 4}{x^2 - 1} = \dfrac{(2x-3)(x-1)(x+1) + x+1}{(x-1)(x+1)} \\\\ ~~~~~~~~ = \boxed{2x-3 + \dfrac1{x-1}}[/tex]
Select the correct answer from each drop-down menu.
Graph of 2 polygons. Polygon 1 at A (minus 6, 6), B (minus 4, 6), C (minus 4, 4), D (minus 6, 2) in quadrant 2. Polygon 2, A prime (minus 6, minus 6), B prime (minus 6, minus 4), C prime (minus 4, minus 4), D prime (minus 2, minus 6) in quadrant 4.
Polygon ABCD goes through a sequence of rigid transformations to form polygon A′B′C′D′. The sequence of transformations involved is a reflection across the
, followed by a reflection across the line
.
The Polygon ABCD was reflected across the x axis, followed by a reflection across the line y = x to form polygon A'B'CD'.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
The Polygon ABCD was reflected across the x axis, followed by a reflection across the line y = x to form polygon A'B'CD'.
Find out more on transformation at: https://brainly.com/question/4289712
#SPJ1
Someone help me please
Answer:
[tex]\sqrt{60}[/tex]
Step-by-step explanation:
Use the Pythagorean theorem a^2 + b^2 = c^2
In this case you are given a and c, so set the equation up like
2^2 + b^2 = 8^2
b^2 = 8^2 - 2^2
b =[tex]\sqrt{8^{2} -2^{2} }[/tex]
b =[tex]\sqrt{60}[/tex]