If sin θ +cosec θ = 2 then sin2θ+ cosec2θ is equal to
a) 1 b) 4
c) 2 c) 9
Answer:
C
Step-by-step explanation:
We are given that:
[tex]\sin \theta +\csc \theta = 2[/tex]
And we want to find the value of:
[tex]\sin^2\theta + \csc^2\theta[/tex]
From the first equation, we can square both sides:
[tex](\sin \theta + \csc \theta)^2=(2)^2[/tex]
Square:
[tex]\sin ^2\theta +2\sin\theta\csc\theta +\csc^2\theta =4[/tex]
Let csc(θ) = 1 / sin(θ):
[tex]\displaystyle \sin ^2\theta +2\sin\theta\left(\frac{1}{\sin \theta}\right) +\csc^2\theta =4[/tex]
Simplify:
[tex]\displaystyle \sin ^2\theta +2(1) +\csc^2\theta =4[/tex]
Therefore:
[tex]\sin ^2\theta + \csc^2\theta =2[/tex]
Our answer is C.
What is the solution of the equation x2 − 2x + 4 = 0?
Answer:
No real solution
Step-by-step explanation:
This leads to a square root of a negative number, which is not possible without imaginary numbers
Tony sold t-shirts and hats at the festival. He made a $4 profit for each t-shirt he sold. He also made a profit of $34 from selling hats. If he made a total profit of $106, how many t-shirts did he sell?
Answer:
18 T-shirts
Step-by-step explanation:
$4×18= $72 $72+$34=$106
A line's y-intercept is 1, and its slope is -5. What is its equation in
slope-intercept form?
help please
Cylinder A has a radius of 12 inches and a height of 6 inches. Cylinder B has a volume of 648π. What is the percent change in volume between cylinders A and B? (5 points)
Question 6 options:
1)
Cylinder B is 50% smaller than cylinder A.
2)
Cylinder B is 25% smaller than cylinder A.
3)
Cylinder B is 150% bigger than cylinder A.
4)
Cylinder B is 200% bigger than cylinder A.
Answer: 2) Cylinder B is 25% smaller than cylinder
The angle of elevation to a nearby tree from a point on the ground is measured to be
31°. How tall is the tree if the point on the ground is 62 feet from the tree? Round
your answer to the nearest tenth of a foot if necessary.
Answer:
37.3 ft
Step-by-step explanation:
tan A = opp/adj
tan 31° = x/62
x = 62 * tan 31°
x = 37.3 ft
The height of the tree is 37.25 ft if the point on the ground is 62 feet from the tree.
What is the right triangle?A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.
Trigonometric ratios are used to demonstrate the connection between the sides and angles of a right-angled triangle.
Let h denote the tree if the point on the ground is 62 feet from the tree.
The angle of elevation = 31°. Hence:
tan 31° = h/62
h = 62 × tan 31°
h = 37.25 ft
Thus, the height of the tree is 37.25 ft if the point on the ground is 62 feet from the tree.
Learn more about the right triangle here:
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Which expression is equal to 2sin(pi/10)cos(pi/10)?
Answer:
sin pi/5,
Step-by-step explanation:
In the system of equations , x represents .... ( please answer 12a and 12b )
Answer:
x = cost of each t-shirt
y = cost of each sweatshirt
Step-by-step explanation:
Given equation:
2x + 2y = 26 (1)
x + 3y = 33 (2)
From (2)
x = 33 - 3y
Substitute x = 33 - 3y into (1)
2x + 2y = 26 (1)
2(33 - 3y) + 2y = 26
66 - 6y + 2y = 26
- 6y + 2y = 26 - 66
-4y = -40
y = -40/-4
y = 10
Substitute y = 10 into (2)
x + 3y = 33 (2)
x + 3(10) = 33
x + 30 = 33
x = 33 - 30
x = 3
Where,
x = cost of each t-shirt = $3
y = cost of each sweatshirt = $10
Enriques bathroom measures 6 ft. Long by 5 ft. Wide His shower is 3 feet square The title he wants to buy for the floor is sold in square feet. What is the area of the floor that he has to title
Answer:
Area of the floor is 30 square ft.
Step-by-step explanation:
Length of the floor, L = 6 ft
width of the floor, W = 5 ft
The floor is in the shape of rectangle.
The area of the rectangle is
A = Length x width
So, the area of the floor is
A = L x W
A = 6 x 5
A = 30 ft^2
(HELP) A glass jar contains 5 red, 7 green, 9 blue and 11 yellow marbles. If a single marble is picked at random from the jar, what is the probability of it being a blue marble? *
1/11
5/18
9/32
5/12
Answer:
Find the volume of this prism.
25 POINTS Find the slope of the line khan academy
Answer:
-8/5
Step-by-step explanation:
Using the points given ( -1,4) and (4,-4)
We can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( -4 -4)/(4- -1)
= (-4 -4)/(4+1)
= -8/5
Determine whether the parallelogram is a rhombus, rectangle, square, or none. Explain.
Q(1,5), R(3,8), S(5,5), T(3,2)
Help ASAP
Oof, I'm to tired to remember how to do this T-T
Can anyone help asap? This is timed. Brainliest for best answer!!
Answer:
D
Step-by-step explanation:
Equation of the line
y - y1 = m(x - x1)
y - (-4) = 1/3 (x - 3)
y + 4 = 1/3x - 1
y = 1/3 x - 5
the graph that intercept y axis in -5 is the graph D
Answer:
i can't remember how to do this rn because its like 2:30am
C seems like most accurate answer, if this is wrong im really sorry :C
Step-by-step explanation:
To find the slope of the trend line below Reilly chose the points (1,80) and (2,30). explain whether the points she chose will help her write the correct equation of the line and find the equation of a trend line
Answer:
We can't see the graph
Step-by-step explanation:
Circle D is shown. Angles F A E, F D E, and F B E intercept arc F E. ∠FAE measures 72°. What other angle must measure 72°? ∠BFD ∠DEA ∠EDF ∠FBE
Answer:
Option D, ∠FBE
Step-by-step explanation:
The image for the question is attached herewith
Solution
As per the property of arc, angles subtended by the same arc (chord) on the circumference of a circle have equal measures.
∠FAE is an angle subtended by the arc FE that touches the circle at point 'A'.
∠FBE is also subtended by the arc FE at the point 'B'.
Therefore, we must have
m∠FAE = m∠FBE.
Since, m∠FAE = 72°, so m∠FBE = 72°.
Hence, option D, ∠FBE
Answer:
Its D
Step-by-step explanation:
Give him brainlest.
The area of a square is 81 cm squared find its perimeter
Answer:
the answer is 36
Step-by-step explanation:
The equation of a line is 5x + 10y = 15
Answer:
c
Step-by-step explanation:
I don't think I understand this one try graphs n diagram
Erica took out a loan to buy her new motorcycle. The purchase price of the motorcycle was $11349.00 plus 5% GST and 7% PST. She pays $409.00 per month on her loan, which has a term of 3 years. How much more is she paying than the purchase price? a. $2415.74 b. $1610.50 c. $2254.69 d. $2013.12
Answer:
The correct answer is D. $2,013.12.
Step-by-step explanation:
Since Erica took out a loan to buy her new motorcycle, and the purchase price of the motorcycle was $ 11349.00 plus 5% GST and 7% PST, and she pays $ 409.00 per month on her loan, which has a term of 3 years, for To determine how much more is she paying than the purchase price, the following calculation must be performed:
11,349 + (11349 x 0.12) = X
11,349 + 1,361.88 = X
12,710.88 = X
409 x 12 x 3 = X
4,908 x 3 = X
14.724 = X
14,724 - 12,710.88 = X
2,013.12 = X
Therefore, Erica is paying $ 2,013.12 more than the purchase price.
Solve for all values of x by factoring x² + 6x = 0
Answer:
Solution given;
x² + 6x = 0
taking x common
x(x+6)=0
either
x=0
or
x+6=0
x=-6
:.x=0 or -6.
Answer:
0 and -6
Step-by-step explanation:
Factor and find the zeros of the equation or graph the line to find the x-intercepts.
somebody help me out asap
Answer:
the first one doesn't represent function
Step-by-step explanation:
in the domain, x can only be once.
What is 100 ÷ 5 × 4 + 43
A. 69
B. 144
C. 0.3
D. 1.2
Answer:
123
Step-by-step explanation:
100 ÷ 5 x 4 + 43
20 x 4 + 43
80 + 43
123
in which graph does the slope of the line l lequal zero
Answer:
wait can you make the same question with a picture or you don't have any pictures that comes with the problem?
What's the surface area of the pyramid?
The Answer is C 226.8 ft
I remember doing this not to long ago
Em uma competição esportiva uma equipe ganhou 80 medalhas sendo que 25% de ouro 35% de prata e o restante de blusa e qual o número de medalhas de bronze que essa equipe ganhou
Answer:
32 medals
Step-by-step explanation:
Given that
The team wons 80 medals
out of which 25% is gold
35% is silver
and rest is bronze
we need to find out the number of bronze medals that win by the team
The total percentage is 100
So, the remaining percentage is
= 100 - 25 - 35
= 40%
So, the number of bronze medal should be
= 40% of 80 medals
= 32 medals
pls help me answer this question and plsss do not send link
QUESTION:
The angled of a triangle are (x-40), (x-20), (1/2- 10), find x
Answer:
x=124.75
Step-by-step explanation:
Sum of angles of a triangle=180°
(x-40)+(x-20)+(1/2- 10)=180°
(x-40)+(x-20)+(−9.5)=180°
x-40+x-20−9.5=180°
x+x-40-20-9.5=180°
2x−69.5=180°
2x=180°+69.5
2x=249.5
2x/2=249.5/2
x=124.75
There are 120 students in class 7. It is known that
2/3
out of them like Maths, out of which 35
are girls. Also, out of total students,
3/5
are boys. (3)
(a) What is the number of girls in the class?
(b) How many students like Maths?
(c) How many boys like Maths?
Multiply total students by 2/3 to find how many like math:
Like math = 120 x 2/3 = 240/3 = 80 total students like math
Multiply total students by 3/5 to find number of boys:
120 x 3/5 = 360/5 = 72 boys
A) number of girls = total students - boys = 120 -72 = 48 girls
B) from above 80 students like math
C) number of boys that like math = number of students that like math minus girls that like math: 80- 35 = 35 boys like math
which of the following is equivalent to (i+3)+i(2i-4)
a. -5i + 1
b. -3i + 1
c. i-3
d. -i + 3
Answer:
answer is b
Step-by-step explanation:
i+3 -2 -4i = 1-3i
The expression that is equivalent to (i+3)+i(2i-4) is -3i + 1
Option B is correct
The given expression is:
(i+3)+i(2i-4)
Open the parenthesis by expanding the expression using the distributive rule
i + 3 + 2i² - 4i
Note that i² = -1
The expression, therefore, becomes:
i + 3 + 2(-1) - 4i
i + 3 - 2 - 4i
Collect like terms by bring the real parts together and the imaginary parts together
i - 4i + 3 - 2
Simplify to get the final expression
-3i + 1
Therefore, the expression that is equivalent to (i+3)+i(2i-4) is -3i + 1
Learn more here: https://brainly.com/question/12375854
Which expression is equivalent to (x^4/3 x^2/3)^1/3
?
x^2/9
x^2/3
x^8/27
x^7/3
Answer:
X^2/3
Step-by-step explanation:
If Kiri has 17 part-time members this month, how many full-time members does she need according to your equation?
Answer:
5050 = 225f + 125p
If p = 17 this month, then, f = 13
Step-by-step explanation:
Kiri owns a coworking space that has two primary types of memberships, full time and part-time. In order to pay her bills each month (rent on the building, electricity, internet, and so on) she needs to make $5050. Full-time memberships (f) cost $225 per month, and part-time memberships (p) cost $125 per month.
If Kiri has 17 part-time members this month, how many full-time members does she need according to your equation?
Total cost = $5050
cost of full-time memberships = $225
number of full time members = f
cost of part-time memberships = $125
number of part-time members = p
Total cost = cost of full-time memberships * number of full time members + cost of part-time memberships * number of part-time members
5050 = 225f + 125p
If p = 17 this month,
5050 = 225f + 125p
5050 = 225f + 125(17)
5050 = 225f + 2,125
5050 - 2,125 = 225f
2,925 = 225f
f = 2,925/225
f = 13
number of full time members = f = 13
If p = 17 this month, then, f = 13
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP ASAP