➲ ( 1 + sec x )( cosec x - cot x ) = tan x
Solving for L.H.S[tex] \implies\quad \sf{(1+sec\:x)(cosec\:x-cot\:x) }[/tex]
[tex] \implies\quad \sf{ \left(1+\dfrac{1}{cos\:x}\right)\left(\dfrac{1}{sin\:x}-\dfrac{cos\:x}{sin\:x}\right)}[/tex]
[tex] \implies\quad \sf{ \left(\dfrac{1+cos\:x}{cos\:x}\right)\left(\dfrac{1-cos\:x}{sin\:x}\right)}[/tex]
[tex] \implies\quad \sf{ \left(\dfrac{1-cos^2 x}{cos\:x.sin\:x}\right)}[/tex]
[tex] \implies\quad \sf{ \left( \dfrac{sin^2 x}{cos\:x.sin\:x}\right)}[/tex]
[tex] \implies\quad \sf{ \left( \dfrac{sin\:x.\cancel{sin\:x}}{cos\:x.\cancel{sin\:x}}\right)}[/tex]
[tex] \implies\quad \sf{\left( \dfrac{sin\:x}{cos\:x}\right) }[/tex]
[tex] \implies\quad\underline{\underline{\pmb{ \sf{tan\:x}}} }[/tex]
➲ ( 1+ sec x )( 1- cos x ) = sin x. tan x
Solving for L.H.S[tex] \implies\quad \sf{ ( 1+ sec\:x)(1-cos\:x)}[/tex]
[tex] \implies\quad \sf{\left(1+\dfrac{1}{cos\:x} \right) \left( 1-cos\:x\right)}[/tex]
[tex] \implies\quad \sf{ \left(\dfrac{cos\:x+1}{cos\:x} \right)(1-cos \:x)}[/tex]
[tex] \implies\quad \sf{\dfrac{1-cos^2 x}{cos\:x} }[/tex]
[tex] \implies\quad \sf{\dfrac{sin^2x}{cos\:x} }[/tex]
[tex] \implies\quad \sf{sin\:x.\left( \dfrac{sin\:}{cos\:x}\right) }[/tex]
[tex] \implies\quad\underline{\underline{\pmb{ \sf{sin\:x.tan\:x}}} }[/tex]
I WILL GIVE 100COINS
#1
10,7.5,9,12,7.5,8[tex]\\ \rm\Rrightarrow Mean=\dfrac{10+7.5+7.5+9+12+8}{6}=\dfrac{54}{6}=9[/tex]
#2
12,12,11.5,11.5,12.5,13[tex]\\ \rm\Rrightarrow Mean=\dfrac{12+12+11.5+11.5+12.5+13}{6}=72.5/6\approx 12[/tex]
How many solutions does the system of equations in the graph have? Help ASAP!
Answer:
There is one solution.
Step-by-step explanation:
There is one intersection.
What is the value of 1/2 (4)
Answer:
2
Step-by-step explanation:
We are being asked to multiply the fraction 1/2 * 4
1/2 *4
4/2
Simplify by dividing the top and bottom by 2
2/1
2
Mrs. Adesso wants to take her class on a trip to either the science center or the natural history museum. The science center charges $7 per student, plus $75 for a guided tour. The natural history museum charges $8 per student, plus $50 for a guided tour. For what number of students is the cost of the trip the same at each museum?
Answer:
25
Step-by-step explanation:
see picture for work!
There are 36 squares on each red and white checkered tablecloth. How many squares are there on 7,011 tablecloths
Answer:
36 squares per table cloth, so;
36 x 7,011 = 252,396, there are 252,396 squares.
5(b + 3)
I think that this question is really hard for some reason
Answer: 5(b+3) is b = 3
Step-by-step explanation:
1) 5(b+3) - distribute
2) 5b = 15
3) [tex]\frac{5b}{5} =\frac{15}{5}[/tex] - divide
4) b = 3 - solution
Seven less than the product of a number n and 1/7 is no more than 98.
Answer:
1/7(n)-7 < 98
Step-by-step explanation:
9168 divided by 24 long division
Answer:
382
Step-by-step explanation:
what quadrilateral is this
" First of all, this is a hexagon which has 6 sides and 6 angles "
It is usually referred as regular Hexagon.Answer:
Step-by-step explanation:
This is NOT a quadrilateral as the shape has 6 sides with 2 pairs of them parallel to each other. All quadrilaterals have 4 sides instead.
Jasmine bought a 4 kg block for modeling clay she wants to divide it into eight equal blocks what will the mass of each block in grams
Answer:
The mass of each block is 500 grams.
Step-by-step explanation:
4 kg = 4000 grams
Now we divide,
4000 / 8 = 500
Our final answer should be 500.
Hey!!! Can anyone help me please!
Answer:
it will not change
Step-by-step explanation:
the outlier is 3
the mode is the most occuring value in the list which is 16 before and after the 3 is removed
HELP PLEASEEEE 24 points!! 7th grade math
Answer:
I think that A 60 and B is acute it must de a bigger 90.
Step-by-step explanation:
Can anyone solve this?
Answer:
x = 8cm
Step-by-step explanation:
x = 3cm + 5cmx = 8cm#IhopeThisHelp
Which expression represents the value, in dollars, of a certain number of quarters, q, and dimes, d?
0.35qd
0.35q + d
0.10q + 0.25d
0.25q + 0.10d
I am in middle school.
Describe a system of equations that has infinitely many solutions.
Linear equations
Answer:
when the lines are coincident, and they have the same y-intercept
Step-by-step explanation:
Twelve disks with the given measurements are stacked on top of each other. Which expression does NOT give the volume of the cylinder that is formed?
Answer:
The answer is the top right corner. (pi* 3* 12^2)
I did this in TTM
Answer:
π⋅3⋅12^2
Step-by-step explanation:
PLEASE HELP!!!
What is the formula of g in terms of f?
Choose 1 answer:
A. - 1/3 f(x)
B. f(-3x)
C. -3f(x)
D. f (- 1/3x)
Answer:
A
Step-by-step explanation:
y = a f(x)
If |a| > 1 then a f(x) is f(x) stretched vertically by scale factor of a
If 0 < |a| < 1 then f(x) is squashed vertically
If a < 0 then f(x) is also reflected in the x-axis
y = f(ax)
If |a| > 1 then f(ax) is f(x) squashed horizontally by a scale factor of a
If 0 < |a| < 1 then f(x) is stretched horizontally
If a < 0 then f(x) is also reflected in the y-axis
g(x) has been squashed vertically by a scale factor of 1/3 (green on the attached diagram) and then reflected in the x-axis (red on the attached diagram)
Therefore, the solution is [tex]g(x) = -\dfrac13f(x)[/tex]
Select the correct answer. Consider the function f(x) = 10x and the function g(x) shown below. How will the graph of g(x) differ from the graph of f(x)? A. The graph of g(x) is the graph of f(x) shifted up by a factor of . B. The graph of g(x) is the graph of f(x) compressed vertically by a factor of . C. The graph of g(x) is the graph of f(x) stretched vertically by a factor of . D. The graph of g(x) is the graph of f(x) shifted to the right by a factor of .
Answer:
most likely 43
Step-by-step explanation:
fr.
Gas mileage is the number of miles you can drive on a gallon of gasoline. A test of a new car results in 510 miles on 20 gallons of gas. How far could you drive on 65 gallons of gas?
Answer:
The answer is 1,657.5 miles
Step-by-step explanation:
First divide 510 by 20 510 ÷ 20 = 25.5 into 65 = 1657.5
Given that test of a new car results in 510 miles on 20 gallons of gas. By unitary method, you can drive miles on 65 gallons of gas.
Unitary method is a method of solving a problem wherein to find the value of k units, you first calculate the value of one item, then multiply the value of the one item to k.
Given in the question,
distance covered in 20 gallons of gas = 510 miles
distance covered in 1 gallons of gas = [tex]\frac{510}{20} = 25.5[/tex] miles
distance covered in 65 gallons of gas = 25.5 * 65 miles = 1657.5 miles
Learn more about unitary method here
https://brainly.com/question/28276953
#SPJ2
HELPP FOR BRUANLEST!!!
Answer:
17/18
Step-by-step explanation:
okay this one is a bit different
you have to take the total number that are batwing-shaped (12) and the total number that are made of cotton (12) and then subtract the ones that are both batwing-shaped and made of cotton.
so 12+12-7 which is 17
then you put that over the total (18)
17/18 doesn't simplify
HELP 100 POINTS The population of a city is modeled with the function P=250,000e^0.013t, where t is the number of years since 2000. In what year will the population reach 450,000?
please help me out !
Answer:
NO
Step-by-step explanation:
Try the offered solution to see if it works
y = 1/2x -7 . . . . for (x, y) = (-4, -5)
-5 = 1/2(-4) -7 = -2 -7
-5 = -9 . . . . . . false
The point does not satisfy the function. (NO)
PLEASE HELP AS SOON AS POSSIBLE!
Step-by-step explanation:
(i) 240 ÷ 4000 = 0.06
(ii) 760 ÷ 4000 = 0.19
(iii) (20 + 10) ÷ 4000 = 0.0075
I guess this is the answer
i am not sure!!!!
Can someone help me with this question? I’ll mark you brainliest if you answer!!!
Circle E has a radius of 5.3 meters.
F
G
¯
is a chord and
H
E
↔
is a perpendicular bisector of
F
G
¯
. If FG = 7.3 meters, calculate the distance of IH .
Answer:
1.46m
Step-by-step explanation:
construction ; join EF
we know that EF is a radius, so EF = 5.3m
In triangle EFH,
∡EHF = 90° (EH is the perpendicular bisector of GF)
FH = FG/2 = 7.3m / 2 = 3.65m (EH is the perpendicular bisector of GF)
According to pythagoras theorem,
FH² + EH² = EF²
3.65² + EH² = 5.3²
EH² = 5.3² - 3.65²
EH² = 28.09 - 13.32 = 14.77m
EH = √14.77m
EH = 3.84m
EI is a radius, so EI = 5.3m
IH = EI - EH
= 5.3m - 3.84m
= 1.46m
Please read directions do number 1
a ramp 19 ft long rises to a platform that is 17 ft off the ground. Find x, the angle of elevation of the ramp
If jake runs 3 miles in 36 minutes how many miles could he run in 60 minutes
Answer:
5 miles
Step-by-step explanation:
We will use the method of cross multiplying and dividing.
You will multiply 60 x 3
Then, take the answer (180) and divide it by 36.
That will give you 5 and your answer.
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. The business literature involving human capital shows that education influences an individual’s annual income. Combined, these may influence family size. With this in mind, what should the real estate builder be particularly concerned with when analyzing the multiple regression model?
When analyzing the multiple regression model, the real estate builder should be concerned with Multicollinearity.
What is Multicollinearity?This is a phenomenon in regression analysis where some of the independent variables are correlated. This can present an issue because the correlation leads to less reliable results.
The income in this research is influenced by the education and they both influence family size. There is therefore an issue of multicollinearity here because some variables are correlated.
Find out more on Multicollinearity at https://brainly.com/question/16021902.
Hello people ~
The sides of a triangle are 5, 12 & 13 units. Check if it has a right angle or not.
Step-by-step explanation:
The sides of triangle are 5,12 and 13
Here, the greatest side is 13
Therefore,
13²=5²+12²169=25+144169=169 (True)Hence, these sides will form a right angled triangle.
[tex]\qquad \qquad\huge \underline{\boxed{\sf Answer}}[/tex]
To check if the triangle is congruent or not, we have to see if they form Pythagorean triplet, that is :
sum of squares of smaller sides should be equal to square of the longest side.
let's check it out ~
[tex]\qquad \sf \dashrightarrow \: {5}^{2} + 12 {}^{2} = {13}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: {25}^{} + 144 = 169[/tex]
[tex]\qquad \sf \dashrightarrow \: 169= 169[/tex]
Therefore, the sides 5, 12 and 13 forms a right angle.