Can anyone help solve this step by step?
Answer:
85.2
Step-by-step explanation:
Pictures below show my steps
so then just do 39.6+45.6
Prove the following tan^2 A/(tan A -1 )+ cot A/(1 - tan A)=1 +sec A cosec A
In Image, Question is No.4 (vi)
See below for the proof of the trigonometry identity [tex]\frac{\tan^2(A)}{\tan(A) - 1} + \frac{\cot(A)}{1 - \tan(A)} =1 + \sec(A)\csc(A)[/tex]
How to prove the trigonometry identity?The trigonometry equation is given as:
[tex]\frac{\tan^2(A)}{\tan(A) - 1} + \frac{\cot(A)}{1 - \tan(A)} =1 + \sec(A)\csc(A)[/tex]
Rewrite the equation as:
[tex]\frac{\tan^2(A) }{\tan(A) - 1} - \frac{\cot(A)}{ \tan(A) - 1} =1 + \sec(A)\csc(A)[/tex]
Take LCM
[tex]\frac{\tan^2(A) - \cot(A)}{ \tan(A) - 1} =1 + \sec(A)\csc(A)[/tex]
Express cot(A) as 1/tan(A)
[tex]\frac{\tan^2(A) - \frac{1}{\tan(A)}}{ \tan(A) - 1} =1 + \sec(A)\csc(A)[/tex]
Take LCM
[tex]\frac{\tan^3(A) - 1}{\tan(A)(\tan(A) - 1)} =1 + \sec(A)\csc(A)[/tex]
Apply the difference of two cubes on the numerator
[tex]\frac{(\tan(A) - 1)(\tan^2(A) + \tan(A) + 1)}{\tan(A)(\tan(A) - 1)} =1 + \sec(A)\csc(A)[/tex]
Cancel out the common factors
[tex]\frac{\tan^2(A) + \tan(A) + 1}{\tan(A)} =1 + \sec(A)\csc(A)[/tex]
Rewrite as:
[tex]\frac{\tan(A) + \tan^2(A) + 1}{\tan(A)} =1 + \sec(A)\csc(A)[/tex]
Split the fraction
[tex]1 + \frac{\tan^2(A) + 1}{\tan(A)} =1 + \sec(A)\csc(A)[/tex]
Express [tex]\tan^2(A) + 1[/tex] as [tex]\sec^2(A)[/tex]
[tex]1 + \frac{sec^2(A)}{\tan(A)} =1 + \sec(A)\csc(A)[/tex]
Divide [tex]\sec^2(A)[/tex] by [tex]\tan(A)[/tex]
[tex]1 + \frac{1}{\sin(A)\cos(A)} = 1 + \sec(A)\csc(A)[/tex]
Take the inverse of sin and cosine
[tex]1 + \sec(A)\csc(A) = 1 + \sec(A)\csc(A)[/tex]
Both sides of the equation are the same.
Hence, the trigonometry identity [tex]\frac{\tan^2(A)}{\tan(A) - 1} + \frac{\cot(A)}{1 - \tan(A)} =1 + \sec(A)\csc(A)[/tex] has been proved
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Select from the drop-down menu to explain how to find the quotient of 4.082 and 10,000.
To find the quotient of 4.082 and 10,000, move the decimal point in 4.082
Choose...
places to the
Choose...
.
Answer:
Move decimal points in 726.02, 3 points in the left direction
Step-by-step explanation:
Given
Quotient of 726.02 and 1000
This is represented as:
The denominator 1000 has 3 zeros.
This implies that the decimal points will be moved in the left direction by 3 points.
So:
There are 6 marbles in a bag: 1 blue, 1 red, 1 white, 1 yellow, 1 green, and 1 black. Mary picks one marble at random and then her sister chooses another from those left in the bag.
What is the probability that Mary picks the red marble and her sister picks the blue marble?
Answer:
1 in 30
Step-by-step explanation:
1 in 6 chance Mary picks the red marble in the first place. After this there is a 1 in 5 chance her sister picks the blue one. 5 multiplied by 6 is 30.
The probability that Mary picks the red marble and her sister picks the blue marble is [tex]\frac{1}{30}[/tex] .
Concept:Firstly, we need to find the probability of Mary picking a red marble from the 6 marbles.Secondly. we need to find the probability of Mary's sister picking a blue marble from the 5 left marbles.As both are mutually exclusive events , the required probability is the multiplication of both above.How to solve the given question?P(A) = Mary picking a red marble out of 6 marbles = [tex]\frac{1}{6}[/tex]P(B) = Mary's sister picking a blue marble out 5 left marbles = [tex]\frac{1}{5}[/tex]P(E) = Required probability = P(A) × P(B) = [tex]\frac{1}{6}[/tex] × [tex]\frac{1}{5}[/tex] =Thus, the probability that Mary picks the red marble and her sister picks the blue marble is [tex]\frac{1}{30}[/tex] .
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Point b has coordinates (1,2). the x-coordinate of point a is negative −11. the distance between point a and point b is 15 units. what are the possible coordinates of point a?
find the area of a triangle with the side lengths 14, 14, and 20
Answer:
Step-by-step explanation:
Elias was given a lock for his school locker. The lock contains numbers between
O and 59 (60 different numbers). If 3 numbers are used to unlock the lock, and
the numbers can't repeat, how many codes can his lock have?
Answer:
34,220
Step-by-step explanation:
Because order doesn't matter, but the numbers can't be repeated, we need to find the number of combinations where 3 individual numbers can be chosen out of 60 possible numbers using the binomial coefficient:
[tex]\binom{n}{k}=\frac{n!}{k!(n-k)!}\\ \\\binom{60}{3}=\frac{60!}{3!(60-3)!}\\\\\binom{60}{3}=\frac{60!}{3!(57)!}\\\\\binom{60}{3}=\frac{60*59*58}{3*2*1}\\ \\\binom{60}{3}=34220[/tex]
Thus, Elias can make 34,220 unique 3-number codes given 60 different numbers.
On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0. it crosses the y-axis at (0, 4). what is the initial value of the exponential function shown on the graph? 0 1 2 4
Answer:
its 4
Step-by-step explanation:
trust me bro im a geinus
The initial value of the exponential function shown on the graph should be 4.
What is an exponential function?The exponential function represents a dependency relationship. In this type of mathematical operation there is a variable in the exponent and the real number in the base.
In this case, the exponential function is:
F(X)=Y
Knowing that the given points correspond to X=0 and Y= 4, when placing in the formula of the function, one finds:
F(0)=4
F(4)=0
So, the initial value of the exponential function shown on the graph should be 4.
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What is the polynomial function of lowest degree with lead coefficient 1 and roots 1 and 1 i? f(x) = x2 – 2x 2 f(x) = x3 – x2 4x – 2 f(x) = x3 – 3x2 4x – 2 f(x) = x2 – x 2
The polynomial with the lowest degrees and a leading coefficent of 1 will be f(x) = x^2 – x
Polynomial functionThese are function with leading degree of 3 and above
Given the standard polynomial function of degree 3
ax³+bx²+cx+d
The leading coefficient is "a"
The polynomial with the lowest degrees and a leading coefficent of 1 will be f(x) = x^2 – x
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Classify the shapes shown below. Write the letter of each shape in the category that describes it. Shapes may fall into more than one category, and not all shapes will be used. At Least 1 Right Angle At Least 2 Sides of Equal Length At Least 1 Pair of Parallel Sides (sorry i can´t show the shapes it wont let me)
The classification of the shapes into the categories described is as follows;
At Least 1 Right Angle; Right triangle, Square and Rectangle.At Least 2 Sides of Equal Length; Rectangle, Square, isosceles triangle, Parallelogram. At Least 1 Pair of Parallel Sides; Square, Rectangle, Parallelogram.What are the characteristics of place shapes?Plane shapes have peculiar characterization in each case. A triangle can either be isosceles (2 sides of equal length) or right (90⁰ angle measure).
Rectangles, squares and Parallelograms all have parallel sides.
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Which factor do 64x2 + 48x + 9 and 64x2 – 9 have in common?
Answer:
They have the factor (8x +3) in common.
Explanation:
Factorize 1
64x² + 48x + 9
64x² + 24x +24x + 9
8x(8x +3) +3(8x +3)
(8x +3)(8x+3)
Factorize 2
64x² – 9
(8x)² – 3²
[tex]\sf {Apply\:Difference\:of\:Two\:Squares\:Formula:\:}x^2-y^2=\left(x+y\right)\left(x-y\right)[/tex]
(8x-3)(8x+3)
Evaluate
6x+4y-z. X:4,y:-2,z:3
Step-by-step explanation:
x = 4
y = -2
z = 3
= 6x + 4y - z
= 6.4 + 4.-2 - 3
= 24 - 8 - 3
= 13
Segment side a e is 7 inches and side a h is 7 startroot 3 endroot inches. what is the length of side e h? round to the nearest tenth. a cube. the top face has points a, b, d, c. the bottom face has points e, f, h, g. 7.0 inches 9.9 inches 12.1 inches 14.0 inches
The length of the side eh can be found using Pythagoras theorem. Therefore, EH = 9.9 inches
How to use Pythagoras theorem?Pythagoras theorem can be used to find eh.
Therefore,
c²= a² + b²
where
c = hypotenuse sidea and b are the other two legs.Therefore,
AE = 7 inches
AH = 7√3 inches
Therefore,
EH² = ( 7√3 )² - 7²
EH² = 147 - 49
EH = √98
EH = 9.89949493661
EH = 9.9 inches
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Answer: ITS BBBBBBBBBBBBBBBBBBBBB
Step-by-step explanation:
Solve the following literal equation for y 16=2y-4x
Answer:
y=2x+8
Step-by-step explanation:
Move 4x to other side and divide everything by 2
Janet and Bill leave their home at the same time, Janet has 60 miles to travel and drives at 40 mph. Bill has 80 miles to travel and also drives at 40 mph.
a) How long does Janet's journey take?
b) How much longer does Bill spend driving than Janet?
Answer:
Question 1 = 1 hour 30 minutes
Question 2 = he spent 30 more minutes driving
Step-by-step explanation:
time = distance ÷ speed
Answer:
Below in bold.
Step-by-step explanation:
Speed = distance / time.
a) Janet's journey:
40 = 60 / t
4ot = 60
t = 60/40 = 1 1/2 hours.
Janet's journey takes 1 1/2 hours.
b) Bills journey:
40 = 80/t
t = 80/40 = 2 hours.
Bill travels for 1/2 hour more than Janet.
a shoe company needs to create a shoe box...
Answer:
Step-by-step explanation:
21/7=3
5*3=15 width
3*3=9 height
This graph represents gasoline price trends in New Mexico.
First, the price of gasoline in New Mexico _______ (increases quickly, increases slowly, decreases slowly, decreases quickly) , and then it _____ (increases quickly, increases slowly, decreases slowly, decreases quickly)
Answer:
Increases slowly, increases quickly
Step-by-step explanation:
The first part of the graph is a slope that's not very steep, but in a positive direction. That means it's increasing slowly. The second segment has a much steeper slope, and it's going upwards, meaning it is increasing quickly.
I hope this helped!
I really need help pls
Answer:
126
Step-by-step explanation:
Answer:
the answer us 140
Step-by-step explanation:
the answer is 140 because if you add them all the answer will come 140 but if we divide it or multiply it the answer will not come so the answer is 140
◄) There were 60 dogs at the dog park last Saturday, and 30 of them were purebreds.
Considering this data, how many of the next 18 dogs to arrive at the park next Saturday
should you expect to be purebreds?
purebreds
Submit
30!outcof 60 were purebreds 30/60 = 1/2
1/2 of the dogs were purebreds.
18 x 1/2 = 9
Answer: 9 dogs
Answer:9 points
Step-by-step explanation:in the hyperproberbillity of things it’s this answer.
a water barrel that had 4 gallons of water is being filled with water at a rate of 4 gallons per minute . write a function
Answer:
y=4x+4
Step-by-step explanation:
using y=mx+b, y is y since we are writing a function. 4 would be the slope, as that is added per minute, so that takes the place of m, and x stays the same, which leaves b, the y intercept, to be 4. this is because the barrel already had 4 gallons inside before.
what is the surface area of a rectangular prism that has a length of 5 cm, a height of 14 cm, and a width of 12 cm? a. 298 cm2 b. 378 cm2 c. 616 cm2 d. 596 cm2
Answer:
sorry for being late but the answer is c 616 cm
Step-by-step explanation:
Nabhitha has a collection of vintage action figures that is worth $420. If the collection appreciates at a rate of 13% per year, what equation would represent the value of the collection after 6 years?
Answer:
498
Step-by-step explanation:
dI'd the math
The equation that represents the value of collection after 6 years is $420 + 54.6(6).
What is an expression?Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.
As per the given data provided by the question,
The worth of the vintage collection = is $420
The price of the collection appreciates per year = by 13%
The price appreciates per year = 420 × 13/100 = $54.6.
So, the equation for n years is,
$420 + $54.6(n)
Where n is the number of years.
$420 + $54.6(6) = $747.6
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Find the slope of the line passing through the points (-2, 7) and (-7, 3)
Answer:
m = 4/5 or m = 0.8
Step-by-step explanation:
hope it helps
question 7. HELP ME WITH THIS
Reduce the expression, if possible, by cancelling the common factors.
−3 is your answer!
have a nice day! please mark brainliest :)
.
Angad and Alex have played 40 tennis matches.
Angad has won 16 times.
Alex won the rest.
a) Estimate the probability that Angad wins.
b) Estimate the probability that Alex wins.
Answer:
estimate the probability that angad wins
Solve for y y/8 = 4
Answer:
32
Step-by-step explanation:
Multiply both sides by 8.
y/8 = 4
y/8 × 8 = 4 × 8
y = 32
Find the area of the triangle repost because no one answered last time
Check the picture below.
bear in mind that for a triangle, the height or "altitude" is the perpendicular distance from the top of the triangle to the base.
Simplify the expression.
-81 ÷ (-9)
Please help
Answer:
-81/-9
both minus will be cut so
81/9
9
Step-by-step explanation:
the answer is 9
Please Help I will mark brainpower. Please:
a) show how pip can complete the circuit by adding less than 120cm of track
b) show how pip can complete the circuit by adding more than 270cm of track
c) explain why, no matter how the circuit is completed, pip must place an even number of additional curved plates
d) explain why, no matter how the circuit is completed, pip must place an odd number of additional straight plates
In order to complete the circuit, the curved plate on the topmost right side of the circuit must be moved downwards to the end. The length of the total plates to be added is 100cm. Refer to the use of polygons.
How did we arrive at 100cm above?Step 1
In order to complete the circuit, the curved plate on the topmost right side of the circuit must be moved downwards to the end. This is already existing on the circuit so it is not part of the plate to be added.
Step 2
Using the plate with the straight line, the other spaces which are 5 in number will be completed. The total length of plates used will amount to 100cm.
Because the plate is equal in length and height, the total number of plates used is:
20 * 4 = 100cm.
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Find the equation of a line parallel to -x + y = -5 that passes through the point
(-6,-8).
Oy=x-5
O-x+y=-2
Submit Answer
Oy=-x-2
O-z-y=14
Answer:
O -x+y=-2
Step-by-step explanation:
-x + y = -5
⇔ y = x - 5
a line parallel to y = x - 5 must have the same slope as the line y = x - 5
Then
The equation of the parallel line is of the form : y = x + p
Finding p :
the point (-6,-8) lies on the parallel line means :
-8 = -6 + p
Then
p = -8 + 6 = -2
Finally :
y = x - 2 ⇔ -x + y = -2