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Prove the identity
secx-1/ tan x= tanx/ secx+1
To verify the identity, start with the left side and transform it to obtain the right side. Choose the correct step and transform the expression according to the step chosen.
secx-1/ tan x= sec-1 / tanx
Answer:
Proved
Step-by-step explanation:
The options are not given. So, I will solve from scratch
Given
[tex]\frac{secx-1}{tan x}= \frac{tanx}{secx+1}[/tex]
Required
Prove
Multiply the right-hand side by [tex]\frac{secx + 1}{secx + 1}[/tex]
[tex]\frac{secx-1}{tan x} * \frac{secx + 1}{secx + 1}= \frac{tanx}{secx+1}[/tex]
Apply difference of two squares on the numerator
[tex]\frac{sec^2 x - 1}{(tanx)(secx + 1)} =\frac{tanx}{secx+1}[/tex]
In trigonometry:
[tex]tan^2x = sec^2x - 1[/tex]
So, we have:
[tex]\frac{tan^2 x}{(tanx)(secx + 1)} =\frac{tanx}{secx+1}[/tex]
[tex]\frac{tan x * tan x}{(tanx)(secx + 1)} =\frac{tanx}{secx+1}[/tex]
tan x cancels out
[tex]\frac{tan x}{secx + 1} =\frac{tanx}{secx+1}[/tex]
Proved
PLS ANSWER!!!
A car purchased for $18,000 depreciates annually at a rate of 5%.
What will be the approximate value of the car in the 10th year?
Answer:
I answered already but, here:
Step-by-step explanation:
$18,000 x 5% = 900 x 10 years = $9000
please answer this it is 25 points
Answer:
18 stamps
Step-by-step explanation:
3/5(30) = 90/5 = 18
Answer:
18 stampsStep-by-step explanation:
The chart tells you Zack has 30 stamps in total.
3/5 are animal stamps.
So you do
30 x 3/5 = 90 / 5 = 18
OR
30 / 5 x 3 = 6 x 3 = 18
Hope that helps!
charlie uses the expression 2x + 2x to represent the perimeter of a square. What does the variable x represent in this expression?
The area
The perimeter
The side lengths
The sum of 2 side lengths
Answer:
D The Sum of 2 Numbers
Step-by-step explanation:
2+2=4 > 24 > 24 + 24
Answer:
The side length
Step-by-step explanation:
Which one shows a positive linear association?
Answer:
D
Step-by-step explanation:
I think that is the answer
What is the greatest common factor of 138 and 345?
Answer:
Step-by-step explanation:
Step by Step Solution. Calculate Greatest Common Factor for : 138, 345. Factorize of the above numbers : 138 = 2 • 3 • 23. 345 = 3 • 5 • 23. Build a prime factors table. ...
Why learn this.
Terms and topics. GCF calculator.
Related links. Greatest common factor (GCF) explained | Arithmetic (video) | Khan Academy. LCM on Purplemath.
Answer:
69 I believe.
Step-by-step explanation:
What is the area of the figure below?
15 in 2
20 in 2
30 in 2
25 in 2
Answer:
25 [tex]in^{2}[/tex]
Step-by-step explanation: we can move the little triangle on the side to the missing part of the square and it says the length of the little triangle is 2 so we can do 2+3 since the height of the square with the missing side is 3. then we end up with the height being 5 and the base being 5. we know that A=bh so we can do A=5x5 and get 25 in squared
pls mark me branliest!!
Answer:
25ft2
Step-by-step explanation:
Q4. Three students A, B and C had 3 soil samples. Each student poured 180 mL of water
into the soil samples they had. Time taken for the percolation of water through the three
soil samples was 25 min, 10 min and 40 min respectively. Which student had the soil with
the highest percolation rate?
Answer:
Student B
Step-by-step explanation:
Soil percolation is the porosity of soil to the downward flow of water through it. A soil with high percolation allows water to drain through it downwards in a less period of time.
From the given experiment by students, it takes 25 min for water to percolate through the soil sample of student A, 10 min for the soil sample of student B and 40 min for the soil sample of student C. Thus, the student that had the soil sample with highest percolation rate is B.
Charity is four times as old as her daughter. She is also six years younger than her husband. The sum of their ages ten years to come will be 117 years. How old is Charity today?
Answer: Charity is 36 years old today.
Step-by-step explanation:
Let x = Present age of daughter.
Age of Charity = 4x
Age of her husband = 4x+6
After 10 years,
Age of daughter = x+10
Age of Charity = 4x+10
Age of her husband = 4x+6+10=4x+16
As per given,
[tex]x+10+4x+10+4x+16=117[/tex]
[tex]9x+36=117\\\\ 9x=117-36\\\\ 9x=81\\\\ x=9[/tex]
Present age of Charity = 4(9)=36 years
Hence, Charity is 36 years old today.
Find the area of the shaded figure below
Answer:
I think 40 units
Step-by-step explanation:
hope you have a wonderful day
Hence, determine the connection between the discriminant and the nature of the
roots of each equation in the table below:
A facilities manager at a university reads in a research report that the mean amount of time spent in the shower by an adult is 5 minutes. He decides to collect data to see if the mean amount of time that college students spend in the shower is significantly different from 5 minutes. In a sample of 8 students, he found the average time was 5.55 minutes and the standard deviation was 0.75 minutes. Using this sample information, conduct the appropriate hypothesis test at the 0.05 level of significance. Assume normality.
Answer:
0.0384 < 0.05, which means that we can conclude that the mean amount of time that college students spend in the shower is significantly different from 5 minutes.
Step-by-step explanation:
A facilities manager at a university reads in a research report that the mean amount of time spent in the shower by an adult is 5 minutes.
This means that the null hypothesis is [tex]H_{0} = 5[/tex]
He decides to collect data to see if the mean amount of time that college students spend in the shower is significantly different from 5 minutes.
This means that the alternate hypothesis is [tex]H_{a} \neq 5[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
Null hypothesis:
Tests [tex]H_{0} = 5[/tex], which means that [tex]\mu = 5[/tex]
In a sample of 8 students, he found the average time was 5.55 minutes and the standard deviation was 0.75 minutes.
This means, respectively, that [tex]n = 8, \mu = 5.55, \sigma = 0.75[/tex]
Test statistic:
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{5.55 - 5}{\frac{0.75}{\sqrt{8}}}[/tex]
[tex]z = 2.07[/tex]
Pvalue:
Since we are testing if the mean is different from a value, and z is positive. The pvalue is two multiplied by 1 subtracted by the pvalue of z = 2.07.
z = 2.07 has a pvalue of 0.9808
2*(1 - 0.9808) = 2*(0.0192) = 0.0384
Decision:
0.0384 < 0.05, which means that we can conclude that the mean amount of time that college students spend in the shower is significantly different from 5 minutes.
Find the value of X.
Answer:
ummmmm if im not wrong 34
Step-by-step explanation:
Which type of sequence is shown?
-2,0, 2, 4, 6, ...
Answer:
+2 or adding 2 each step
So it is a linear function
Step-by-step explanation:
-2 + 2 = 0
0 + 2 = 4
4 + 2 = 6
So forth..
Answer:
Arithmetic sequence.
Step-by-step explanation:
HELP ASAP PLEASE
Which best describes parallel lines?
Otwo lines that are always equidistant
O two lines that curve to form a circle
O two lines that intersect at multiple points
O two lines that originate from the same point
Can you please help me..
Answer:
7
Step-by-step explanation:
The answer is 7
Trust me :)
Mary's puppy weighs 12.4 pounds. This 27.9 pounds less than the weight of her dog. Write a SUBTRACTION equation to help you figure out many pounds Mary's dog weigh. Let d represent the weight of Mary's dog.
Answer:
x-27.9=12.4
Step-by-step explanation:
MUST HELP!!!! (50 POINTS) +BRAINLEST +5 STARS +THANKS ON PROLFILE!!!!
Figure A’B’C’ is an __________________________of figure ABC.
*fill in the blank*
Answer:
similar shape!!!!
Step-by-step explanation:
Answer:
Dialation
Step-by-step explanation:
Dilation is an increase in size, but does not change the shape
Sasha ordered a kite online. When it arrived, the kite was missing the crossbar. What length crossbar does Sasha need to complete the kite? Round to the nearest tenths if necessary.
Answer:
Approximately [tex]5.7[/tex] inches
Step-by-step explanation:
The crossbar and two given lengths form a right triangle. We know this because we see a right angle marked on the diagram in between the two given sides.
In this case, we have a right triangle with legs of [tex]4[/tex] and [tex]4[/tex], and we need to find the hypotenuse. By the Pythagorean Theorem ([tex]a^{2} +b^{2} =c^{2}[/tex], where [tex]a[/tex] and [tex]b[/tex] are the legs and [tex]c[/tex] is the hypotenuse), we get:
[tex]4^{2} +4^{2} =c^{2}[/tex]
[tex]16+16=c^{2}[/tex] (Evaluate exponents)
[tex]32=c^{2}[/tex] (Combine like terms)
[tex]\sqrt{32}=\sqrt{c^{2}}[/tex] (Take the square root of both sides of the equation to get rid of [tex]c[/tex]'s exponent)
[tex]c=4\sqrt{2} ,c=-4\sqrt{2}[/tex]
The latter solution is an extraneous solution because the side lengths of a triangle cannot be negative. Therefore, the answer is [tex]4\sqrt{2} \approx 5.7[/tex] inches. Hope this helps!
A small college has 800 students
Answer:
ok
Step-by-step explanation:
Manny buys 16 apples at the market and 8 oranges. what are the ratios of apples to oranges ?
Answer:
2:1 or 16:8
Step-by-step explanation:
Answer:
2:1
Apple: orange
Step-by-step explanation:
Divide the number of apples by the number of oranges
A scale model of a buliding is 18 inches tall. The actual building is 240 feet tall. What is the scale factor of the model? Write your answer as a fraction in simplest form.
Answer:
The scale factor of the model is 160.
Step-by-step explanation:
18 inches : 240 feet tall is also equal to
18 inches : 2880 inches
2880/18 = 160
5-(x-3)+4x simplify equation
Answer: 3x+8
Step-by-step explanation:
Answer:
3x+8
Step-by-step explanation:
5-(x-3)=4x
5-x+3+4x
3x+8
If you were to rotate ABCD 180° about the origin,
what would the coordinates of B' be?
(-1,3)
(0,0)
(-6, -5)
(-6, 2)
Answer:
both elements will be negative in rot.180°
7x + 2x^2 + 3x^2 - 2x
Answer:
Step-by-step explanation:
Explanations are below
Step 1
7x + 2x^2 + 3x^2 - 2x Observe the equation
Step 2
7x + 2x^2 + 3x^2 - 2x Combine the like terms
(2x^2+3x^2)+(7x+-2x)
Step 3
(2x^2+3x^2)+(7x+-2x) Simplify by adding and subtracting
Answer: 5x^2+5x
Is (4, 2) a solution to the system y-x=2 and -3x-2y=-8?
Answer:
It is only a solution to y = x - 2, not -3x - 2y = -8
Step-by-step explanation:
I) Check y = x - 2:
y = x - 2
2 = 4 - 2
As you can see, (4, 2) is a solution to this system.
II) Check -3x - 2y = -8:
-3x - 2y = -8
(-3)(4) - (2)(2) = -8
-12 - 4 =/= 8
-12 - 4 = -16, not 8. So (4, 2) is not a solution to this system.
When a normal six sided die is rolled what is the probability of getting a 7
Answer:
0% chance
Step-by-step explanation:
Answer:
0/6
You can't roll a 7 on a 6 sided die.
What is the domain of the function above? I HATE GRAPHS pls help
tyyyy
Answer:
-1<x<4
BLUE
Step-by-step explanation:
Cuantos megametros hay en ocho millones de metros ?
Answer:
1 megámetro = 1000000 metros
Step-by-step explanation:
Which polynomial is in standard from
I'm sorry Wrong Send!!!
Iba sana sasagutin ko Na pindut ko lang naman BTW Sorry