Answer:
Identities used:
1/cosθ = secθ1/sinθ = cosecθsinθ/cosθ = tanθcosθ/sinθ = cotθsin²θ + cos²θ = 1Question 1 (1 - sinθ)/(1 + sinθ) = (1 - sinθ)(1 - sinθ) / (1 - sinθ)(1 + sinθ) = (1 - sinθ)² / (1 - sin²θ) = (1 - sinθ)² / cos²θSquare root of it is:
(1 - sinθ)/ cosθ = 1/cosθ - sinθ / cosθ = secθ - tanθQuestion 2The first part without root:
(1 + cosθ) / (1 - cosθ) = (1 + cosθ)(1 + cosθ) / (1 - cosθ)(1 + cosθ) (1 + cosθ)² / (1 - cos²θ) = (1 + cosθ)² / sin²θIts square root is:
(1 + cosθ) / sinθ =1/sinθ + cosθ/sinθ =cosecθ + cotθThe second part without root:
(1 - cosθ) / (1 + cosθ) = (1 - cosθ)²/ (1 + cosθ)(1 - cosθ) = (1 - cosθ)²/ (1 - cos²θ) =(1 - cosθ)²/sin²θIts square root is:
(1 - cosθ) / sinθ = 1/sinθ - cosθ / sinθ =cosecθ - cotθSum of the results:
cosecθ + cotθ + cosecθ - cotθ = 2cosecθStep-by-step explanation:
Question 1:
Consider the left-hand side
[tex] \sqrt{ \frac{ 1 - \sin\theta }{1 + \sin\theta} } = \sqrt{ \frac{ 1 - \sin\theta }{1 + \sin\theta} \times \frac{1 - \sin\theta }{1 - \sin\theta } }[/tex]
[tex] = \sqrt{ \frac{ {(1 - \sin\theta )}^{2} }{(1 - { \sin}^{2}\theta) } } = \frac{1 - \sin\theta }{ \cos\theta} [/tex]
[tex] = \frac{1}{ \cos\theta} - \frac{ \sin\theta}{\cos\theta } [/tex]
[tex] = \sec\theta \: - \tan\theta[/tex]
Question 2:
The left-hand side can be rewritten as
[tex] \sqrt{\frac{1+ \cos \theta}{1- \cos\theta} \times \frac{1+ \cos \theta}{1+ \cos \theta} } \: +\sqrt{\frac{1- \cos\theta}{1+ \cos \theta} \times \frac{1 - \cos \theta}{1 - \cos \theta} }[/tex]
[tex] = \frac{1 + \cos\theta}{ \sin\theta} + \frac{1 - \cos\theta}{ \sin\theta}[/tex]
[tex] = \frac{2}{ \sin\theta } = 2 \csc\theta[/tex]
3. XY has an equation of x = 8. What is the equation, in point-slope form, of a line that is
perpendicular to XY and passes through (6, 9)?
(i'm looking for an explanation)
Answer: y=9
Step-by-step explanation:
Plug in (6,9) into the slope intercept form equation:
9=0(6) +b
Then get
9=b
When you make the equation you would end up with:
y=0x+9
which simplifies to y=9
How do I complete this equation
Answer:
130°
Step-by-step explanation:
All the interior angles should add up to 540 degrees because it's a pentagon
∠T ≅∠S, so ∠T is also 115°
∠P and ∠R are both 90°
Add everything up and solve for ∠Q:
115 + 115 + 90 + 90 + m∠Q = 540
410 + m∠Q = 540
m∠Q = 130°
There are 198 calories in 4 ounces of vanilla ice cream. How many calories are in 6 ounces of vanilla ice cream?
just put the answer pls fast
Answer: If there are 198 calories in 4 ounces if ice cream it will be 396
Step-by-step explanation:
i need this answered
Answer:
69 pi is your answer.
7.5% of what number is 15?
Help please
Answer:
7.5% of x = 15
75%x=15
15/75%=x
200=x
Therefore
x=200
Which is most appropriate unit to measure the length of a marathon race?
A. Kilometer
B. Meter
C. Millimeter
D. Centimeter
Answer:
b meter
let me know if this is right
Find the length of the segment that joins the points (-5, 4) and (6,-3).
Answer:
[tex]\boxed {\boxed {\sf d=\sqrt{170} \ or \ d\approx 13.04}}}[/tex]
Step-by-step explanation:
We are asked to find the length of a segment or the distance between the 2 points. The formula for distance is:
[tex]d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
where (x₁ y₁) and (x₂, y₂) are the points. We are given the points ( -5, 4) and (6, -3). If we match the number and the corresponding variable, it is:
x₁= -5 y₁= 4 x₂= 6 y₂ = -3Substitute the values into the formula.
[tex]d= \sqrt{(6--5)^2+(-3-4)^2[/tex]
Solve inside the parentheses.
6--5 (Back to back negative signs become a positive)= 6+5 =11 -3-4= -7[tex]d= \sqrt{(11)^2+(-7)^2[/tex]
Solve the exponents.
(11)²= 11*11= 121(-7)²= -7*-7= 49[tex]d= \sqrt {(121)+(49)[/tex]
Add.
[tex]d= \sqrt {170}[/tex]
[tex]d=13.0384048104[/tex]
Even though it's not specified, we could round to the nearest hundredth to make the answer more concise. The 8 in the thousandth place tells us to round the 3 to a 4 in the hundredth place.
13.0384048104[tex]d\approx 13.04[/tex]
The length of the segment is √170 or approximately 13.04.
A frosting is made of cream cheese and powdered sugar in
the ratio 3:2. If you use 120g of cream cheese, how much
powdered sugar should you use?
Plz help
Answer:
80g
Step-by-step explanation:
Answer:
80g
Step-by-step explanation:
80g
find three fifth of Ghana cedis 200
Answer:
Hi.
three fifth of 200 is 120.
HELP PLZ!!!
C=5/9(F−32)
The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?
A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 59 degree Celsius.
A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
A temperature increase of 59 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.
A) I only
B) II only
C) III only
D) I and II only
Answer:
C=5/9F−5/9(32)
you can see the slope of the graph is 5/9, which means that for an increase of 1 degree Fahrenheit, the increase is 5/9 of 1 degree Celsius. Therefore, statement I is true.
This is the equivalent to saying that an increase of 1 degree Celsius is equal to an increase of 9/5 degrees Fahrenheit. Since 95 = 1.8, statement II is true.
On the other hand, statement III is not true, since a temperature increase of 9/5 degrees Fahrenheit, not 5/9 degree Fahrenheit, is equal to a temperature increase of 1 degree Celsius.
The final answer is D.
please help quick. In triangle ABC,
Answer:
What is triangle ABC and what are the measures and what are the angles. Please provide enough information
Step-by-step explanation:
Estimate 91 +94 by first rounding each number to the nearest ten.
Answer:
about 180
Step-by-step explanation:
(when rounding, numbers 0-4 "stay" meaning you'd round down. If the numbers are 5-9, you round up)
91 rounded to the nearest ten would be 90
94 rounded to the nearest ten would be 90 as well
So, 90 + 90 = 180
Technically though, 91+94 = 185. So rounding this to the nearest ten would be 190.
Do what you will :)
Which of the following terms correctly describe the object below?
Check all that apply.
A. Square
B. Solid
C. Cube
D. Polygon
E. Prism
F. Pyramid
Its a solid and a cube
You were wrong with square because a square only has one face while a cube has 6.
You were also wrong with polygon because while polygons are 1-dimensional a cube is 3-dimensional
The following terms correctly describe the given object Square, Solid, Cube, Polygon.
Options A, B, C, D are correct.
What is a cube?A cube is a 3-D solid shape, which has 6 faces. A cube is one of the simplest shapes in three-dimensional space. All the six faces of a cube are squares, a two-dimensional shape.
Square is a figure in which all four sides are equal.
Solid is a three dimensional figure.
A Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges.
Polygon is two dimensional figure with straight lines.
The following terms correctly describe the given object Square, Solid, Cube, Polygon.
Options A, B, C, D are correct.
Find out more information about cube here
https://brainly.com/question/14075440
#SPJ2
The value of y varies directly with x. If x = 3, then y = 4. What is the value of x when y = 120 ?
Answer:
x = 90
Step-by-step explanation:
If x = 3 and y = 4 then when y = 120 just find out what times 4 = 120
which is 30.
so just multiply 30 for x = 3, then the answer will be 90
x = 90
Answer:
x=90
Step-by-step explanation:
x is directly proportional to y
Therefore, if the initial y value was 4 and the final y value is 120. This means that y initial had been multiplied 120/4 times, which is 30.
Same goes for x. If x initial is 3, then the final x value would be x/3=30. This means that x=3×30, which is equal to 90.
can someone answer this
h: 79 = 23 + 8h
Answer:
79=23+8h
or,79-23=8h
or,56/8=h
or,7=h
therefore the value of h is 7.
Step-by-step explanation:
Hope it helps you!!
first you have to do the 23+ you have to make 23 into a subtraction problem in these expressions. 79-23= 56
Now you have to cancel out the 8in 8h and do the opposite of multiplication and do division on both sides 8h/8 cancels out and 56 divided by 8 = 7
your answer is 7 hope this helps
can someone anyone help me with my hegaty maths work
I'll post the answers on here you just answers them
Answer:
sure
Step-by-step explanation:
Answer:
okey I'm not sure but
I can try to help u...
Find the circumstances
Answer:
15π = 47.12
Step-by-step explanation:
C = pi(diameter)
C= 15π
Answer:
Solution given:
diameter [d]=15m
circumference =?
we have
circumference of circle =πd=π×15=15π or 47.12m
Jen can bike 12 miles in 40 minutes how much time will she need to bike 30 miles if her speed remains the same
Please help I will mark brainliest
Answer:
100 minutes / [tex]1 \frac{2}{3}[/tex] hours
First, we need to do 40 ÷ 12 = 3 1/3
Next, multiply 3 1/3 by 30 = 100
So, it is 100 minutes. But wait! We can simply it...
100 minutes = 1 2/3 hours
You can always convert it into different time labels. I think this is the most popular.
The diameter of a sphere is 16 cm. What is the sphere's volume? Round to the nearest tenth. A) 971.7 cm3 B) 1072.3 cm3 C) 1137.4 cm3 D) 2143.6 cm3
Answer:
A
Step-by-step explanation:
Estimate the product. 313×418=
which number is the greatest
-5/3
-5/2
-7/3
Answer:
-5/3 would be the greatest.
because 5/3= -1.66666666667
Use the picture to name one tangent
im gonna go to summer shcool if I don't pass
. A student bought a book for $7.50 and a pen. The total cost was $9.50. Which of the following equations can be used to find the cost of the pen?
A p = 7.5b B p = 9.5b C 9.50 +p = 7.50 D 7.50 + p = 9.50
Answer:
The answer is D: 7.50 + p = 9.5
Step-by-step explanation:
The cost of the book(7.5) plus the cost of the pen(p) equals the total cost which was 9.5
yes i need help anyone please give me the answer
Answer:
x = 25
y = 65
Step-by-step explanation:
I'm not sure if I'm right but..
To solve x:
Since there is a 90 degree angle with 65 degrees and x, the total should sum up to 90. (ofc)
90 - 65 = 25 <--- the missing angle (x)
To solve y:
I'm pretty sure that it is also a 90 degree angle because there is a 90 degree across from you, so they should have the same angles. Since you know x=25, You would do this:
90 - 25 = 65 <--- y
Your welcome!!
Is 1/10 a rational number
Answer:
yes i believe so
Step-by-step explanation:
a rational number is a number that can be written as a fraction, and 1/10 is a fraction. hope this helps
Answer: yes.
Step-by-step explanation:
a rational number is any number which can be expressed as a fraction p/q where p and q are integers and q is not equal to zero. In this fraction both numerator and denominator are natural numbers so 1/10 is a rational number!
A glass is 2/3 full. Then 40cm^3 of orange juice is poured in. The glass is now 4/5 full What is the total volume of the glass?
Answer:
The total volume of the glass is 300 cm^3.
Step-by-step explanation:
Let V represent the total glass volume.
Then (4/5)V - (2/3)V = 40 cm^3. The LCD here is 15, so we rewrite this equation as
(12/15)V - (10/15)V = 40 cm^3, or
(2/15)V = 40 cm^3.
Solve for V by multiplying both sides of this equation by (15/2):
(15/2)(2/15)V = (15/2)(40 = 300 cm^3
The total volume of the glass is 300 cm^3.
Grade 7 Imagine math i will give brainlist who ever gives me the right answers. plz help me
-9-(-12)=-9+12
=3
-9-12=-9+(-12)
=-21
Solve the system by graphing.
y=2x+6
y=−2x−4
Answer:
(-5/2, 1)
Step-by-step explanation:
i hope this helps :)
6.
Find the slope of the line.
A. –3
B. [tex]-\frac{1}{3}[/tex]
C. 3
D. [tex]\frac{1}{3}[/tex]
Answer:
The slope is 1/3. Goes 1 up and 3 to the right.
What are sin 0 and cos 0 for each value of 0?
Answer:
a. sin 300 = -∛3/2, cos 300 = 1/2
b. sin -225 = √2/2, cos -225 = √2/2
c. sin 5π/6 = 1/2, cos 5π/6 = -3√2
d. sin -4π/3 = √3/2, cos -4π/3 = -1/2
Step-by-step explanation:
See unit circle