Given: [tex]cosec[/tex] [tex]A[/tex] [tex]=\sqrt{2}[/tex]
∴ [tex]A=\frac{\pi }{4} =45^{0}[/tex]
[tex]sin[/tex] [tex]A[/tex] [tex]=sin[/tex] [tex]45^{0}[/tex] = [tex]\frac{1}\sqrt{2}[/tex]
[tex]cot[/tex] [tex]A[/tex] [tex]=cot[/tex] [tex]45^{0}[/tex] [tex]=1,[/tex]
[tex]tan[/tex] [tex]A[/tex] [tex]=[/tex] [tex]tan[/tex] [tex]45^{0}[/tex] [tex]=1[/tex]
[tex]cos[/tex] [tex]A[/tex] [tex]=[/tex] [tex]cot[/tex] [tex]45^{0}[/tex] [tex]=\frac{1}{\sqrt{2} }[/tex]
∴ [tex]=2[/tex]
[tex]\large\underline{\sf{Solution-}}[/tex]
METHOD 1: Using Trigonometric values.
We have given that,
[tex]\sf\cosec\theta=\sqrt2[/tex]
So,
[tex]\sf\theta=45^{\circ}[/tex]
We need to find:
[tex]\sf\dfrac{1+\sin^2\theta+\cos^2\theta}{1+\sec^2\theta-\tan^2\theta}[/tex]
So,
[tex]\sf\longmapsto\dfrac{1+\sin^2(45^{\circ})+\cos^2(45^{\circ})}{1+\sec^2(45^{\circ})-\tan^2(45^{\circ})}[/tex]
[tex]\sf\longmapsto\dfrac{1+\left(\frac{1}{\sqrt2}\right)^2+\left(\frac{1}{\sqrt2}\right)^2}{1+(\sqrt2)^2-(1)^2}[/tex]
[tex]\sf\longmapsto\dfrac{1+\frac{1}{2}+\frac{1}{2}}{1+2-1}[/tex]
[tex]\sf\longmapsto\dfrac{1+1}{2}[/tex]
[tex]\sf\longmapsto\dfrac{2}{2}[/tex]
[tex]\sf\longmapsto\bf1[/tex]
METHOD 2: Using Trigonometric Identities
We need to find:
[tex]\implies\dfrac{1+\sin^2\theta+\cos^2\theta}{1+\sec^2\theta-\tan^2\theta}[/tex]
But, we know that,
[tex]\sf\red⇛ \sin^2\phi+\cos^2\phi=1[/tex]
And,
[tex]\sf\red⇛ \sec^2\phi-\tan^2\phi=1[/tex]
So,
[tex]\sf\longmapsto\dfrac{1+(\sin^2\theta+\cos^2\theta)}{1+(\sec^2\theta-\tan^2\theta)}[/tex]
[tex]\sf\longmapsto\dfrac{1+1}{1+1}[/tex]
[tex]\sf\longmapsto\dfrac{2}{2}[/tex]
[tex]\sf\longmapsto\bf1[/tex]
Therefore, by both methods the answer is 1.
Learn more:
Similar questions
Prove that:
\cos( \frac{3\pi}{2} + \theta) \cos(2\pi + \theta) [ \cot( \frac{3\pi}{2} - \theta) + \cot(2\pi + \theta) ] = 1...
https://brainly.com/question/25207676
Four different stores are offering incentives to purchase headphones as shown below. Noisy Music Regular Price $250 Clearance Special - 15% off Loud N Sharp Regular Price $200 $5 off for every $100 spent Music Mart Regular Price $300 Mail-in rebate for $115 Head Jamz Regular Price $225 Manager special – 25% off Which store offers the lowest price?
Answer:
Head Jamz
Step-by-step explanation:
Noisy Music Regular Price $250 Clearance Special - 15% off
If 15% is off then we pay only 100-15 =85% from the original price.
$250 / 100 % = x / 85%
x= 250*85/100 = $ 212.5
Loud N Sharp Regular Price $200 $5 off for every $100 spent
If the price is 200 then will get $5+$5 =$10 discount
Final price will be 200-10 = $ 180
Music Mart Regular Price $300 Mail-in rebate for $115
$300-$115 = $ 185
Head Jamz Regular Price $225 Manager special – 25% off
If 25% is off we only pay 75% of the original price
$225/ 100% = x / 75%
x= 225*75/ 100 = $168.75 is the lowest price
Can someone pls help me
9 is your answer
................................
Using Pythagorean theorem
[tex]\\ \sf\longmapsto B^2=H^2-P^2[/tex]
[tex]\\ \sf\longmapsto B^2=(√97)^2-4^2[/tex]
[tex]\\ \sf\longmapsto B^2=97-16[/tex]
[tex]\\ \sf\longmapsto B^2=81[/tex]
[tex]\\ \sf\longmapsto B=9[/tex]
Slope 5, passing through (-4,1)
Answer:
y=5x+21
Step-by-step explanation:
right now we know y=5x+b, so all we need is b.
graphing it on paper starting at (-4,1), you can go up 5, right 1 because your slope is 5.
you'll get (-4,1) (-3,6) (-2,11) (-1,16) (0,21)
Once you reach x=0, your intecept is 21, completing the slope intercept form, making it y=5x+21.
RJ's soccer team has a record of winning 2 matches for every 3 they lose. If the team lost 15 matches during the season, how many matches did they win?
Answer:
i have no idea
Step-by-step explanation:
Answer:
They won 10 matches
Step-by-step explanation:
Since it's 2/3 if you multiply 3 by 5 you get 15. If you multiply 2 by 5 you get 10. So wit would be 10/15 which is also 2/3.
a) 3x²(5x²-2x-4)
b) xy²(x²y+x³y²+3x²y³)
c) xyz(x²y+3yz²+4xy²z)
Answer:
bobo ka ba
Step-by-step explanation:
name!https://youtu.be/vA3qDEMnB5k
I need help with these 2 problems I cant figure out.
I started by labeling the right angle (Angle C) 90º. Next, I wrote down everything in one equation.
2x + 90 + 3x - 20 = 180º (180 degrees in a triangle)
Next, I add 20 on both sides.
2x + 90 + 3x = 200º
I combine like terms (2x and 3x)
5x + 90 = 200º
I subtract 90 from both sides.
5x = 110º
Divide 110 by 5 to get x.
x = 22
======
For problem two, I label all the angles I know.
49º + 80º + r = 180º
I add 80 and 49.
129º + r = 180º
I subtract 180 and 129 and get 51º, which is your angle for R.
For angle X, you know that angle R plus angle X equals half of a circle, which is 180º
We know from before that 129º is 180º without R, so X is 129º
I hope this helps! Let me know if I'm wrong!
What is the most appropriate method to solve the quadratic equation x²−16=0?
B. By factoring
A. By extracting the square root
C. By completing the square
D. By using the quadratic formula
the function is( -7,1)(-5,3)(-7,-1)(5,13)
Answer:
Not a function
Step-by-step explanation:
The an x-value (the first number in your ordered pair)ca not appear in another ordered pair. It it does, you do not have a function.
( -7,1)(-5,3)(-7,-1)(5,13) -7 appears as the first number in two of your ordered pairs. Not a function!
Select the correct answer.
The graph shows a proportional relationship between the number crates and the number of apples per crate.
What is the constant of proportionality in terms of the number of apples to the number of crates?
A.
30
B.
35
C.
40
D.
50
Answer:
40
Step-by-step explanation:
It is 40 because on the graph it shows that you don't start at the first crate but the 2nd you do and you have to figure out if the crate was one how many apples would their be
You are given a card number that says 9 3 4 3 9 4 8 5 3 1 7 3 2 3 6 x. If this is the credit card number what must x be?
Answer:
7
Step-by-step explanation:
it is a 16 digit credit card number. Therefore, start from the first digit and double alternating digits. Add them and the non doubled digits. should be divisible by 10. For double digits, they are added to make single digit.
9+3+8+3+9+4+7+5+6+1+5+3+4+3+3+x = 73+x
final number should be divisible by 10.
x=7
Which expression is equivalent to m-2m-6m?
Answer:
Which expression is equivalent to m-2m-6m?
if this is correct can i have brainliest
Please help me solve this
Answer:
the answer will be something like 18
Compare the weather on two different days using an inequality. Then see if their comparisons change by finding the absolute value of each.
Day 1:
Day 2:
Inequalities are used to compare unequal expressions.
The actual comparison is:[tex]\mathbf{-3.5 < 5}[/tex] or [tex]\mathbf{5 > -3.5}[/tex]
The temperatures are given as:
[tex]\mathbf{Temperature = -3.5F,\ \ 5F,\ \ 1.5F,\ \ -0.5F,\ \ -2F,\ \ 2.5F,\ \ -4F}[/tex]
From the above list, we have:
[tex]\mathbf{Day \ 1= -3.5F}[/tex]
[tex]\mathbf{Day \ 2= 5F}[/tex]
By comparison,
[tex]\mathbf{-3.5 < 5}[/tex] or [tex]\mathbf{5 > -3.5}[/tex]
Using absolute values, the inequalities are:
[tex]\mathbf{|-3.5| < |5|}[/tex] or [tex]\mathbf{|5| > |-3.5|}[/tex]
Hence, the actual comparison is:
[tex]\mathbf{-3.5 < 5}[/tex] or [tex]\mathbf{5 > -3.5}[/tex]
Read more about inequalities and absolute values at:
https://brainly.com/question/24797699
en un restaurante se usan 70 gramos por cada porción de arroz por persona.Si un día se preparan 4760 gramos de arroz ¿cuántas porciones se obtendrán?
Queremos saber cuantas porciones de arroz se preparan dado que conocemos cuantos gramos de arroz se utilizan.
Se prepararon 68 porciones.
Lo que sabemos en principio es que, por cada porción de arroz, se necesitan 70 gramos de arroz.
Sabemos que en total se utilizan 4,760 gramos de arroz. Para saber cuantas porciones se prepararon, hay que tomar el cociente entre la cantidad total utilizada y lo que se usa para cada porción.
Esto nos da:
4,760g/70g = 68
Es decir, se prepararon 68 porciones.
Sí quieres aprender más, puedes leer
https://brainly.com/question/18070326
HEY THERE!! CORRECT ANSWER+EXPLANATION SHALL BE MARKED BRAINLIEST+43 POINTS
-solve the equation
[tex] \frac{1}{x} + \frac{1}{3x} = 4[/tex]
(pls have your answer as a fraction in its simplest form)
Thanks xx)
[tex]\displaystyle \frac{1}{x} +\frac{1}{3x} =4 \ \ ; \ \ x\neq 0 \\\\\\ \frac{3+1}{3x} =4 \\\\\\12x=4 \\\\ \boxed{x=\frac{1}{3} }[/tex]
Given − 13 x − 23 ≥ 7x + 3,, which property is used below? 3 (−13 x − 23) ≥ 3(7x + 3)
The property used is Division property of equality to get the resulting equation since we divided both sides by 3
Given the inequality expression
3 (−13 x − 23) ≥ 3(7x + 3)
We are to know which of the property is used to arrive at − 13 x − 23 ≥ 7x + 3
We can see that both sides of the expression were divided by 3 as shown:
[tex]\frac{3(-13x-23)}{3} \geq \frac{3(7x+3)}{3}\\-13x-23 \geq 7x+3\\[/tex]
From the division, we will see that the property used is Division property of equality to get the resulting equation since we divided both sides by 3
Learn more here: https://brainly.com/question/15816805
If f(x)= –2x+3 then f(3) – f(4)=
Answer:
2
Step-by-step explanation:
F(3) means that we plug in 3 for the x value of the original equation, and F(4) means that we plug in 4 for the x value of the original equation
F(3) = -2(3) + 3
= -3
F(4) = -2(4) + 3
= -5
- 3 -(-5) = 2
Answer:
2
Step-by-step explanation:
Step 1: Solve for f(3)
[tex]f(3) = -2(3)+3[/tex] [tex]f(3) = -6 + 3[/tex] [tex]f(3) = -3[/tex]Step 2: Solve for f(4)
[tex]f(4) = -2(4) + 3[/tex] [tex]f(4) = -8 + 3[/tex] [tex]f(4) = -5[/tex]Step 3: Subtract f(4) from f(3).
[tex]f(3)-f(4)[/tex] [tex](-3)-(-5)[/tex] [tex]-3 + 5[/tex] [tex]2[/tex]Therefore, the answer is 2.
Mr. and Mrs. Smith's children all play different sports. They want to buy a combination of soccer
training sets, which each cost $149, volleyball training set, which each cost $127, and football
training sets which each cost $275. Let s represent number of soccer sets, v represent number of
volleyball sets and frepresent the number of football sets. Which expression represents the total
amount of money the Smiths will spend, before sales tax, based on the number of sports sets they
buy?
Answer:
149sx+127v+275f =
276
Step-by-step explanation:
multiply all the numbers than add you get the answer 149sx+127v+275f
149s + 127v + 275f is expression represents the total amount of money the Smiths will spend, before sales tax, based on the number of sports sets they buy.
What is Expression?An expression is combination of variables, numbers and operators.
The total amount of money the Smiths will spend on the soccer, volleyball, and football training sets can be represented by the expression:
149s + 127v + 275f
Here, 149s represents the cost of s soccer training sets,
127v represents the cost of v volleyball training sets, and
275f represents the cost of f football training sets.
To find the total amount of money the Smiths will spend based on the number of sports sets they buy, simply substitute the corresponding values of s, v, and f into the expression above and simplify.
Hence, 149s + 127v + 275f is expression represents the total amount of money the Smiths will spend, before sales tax, based on the number of sports sets they buy.
To learn more on Expressions click:
https://brainly.com/question/14083225
#SPJ7
PLEASE ANSWER, 100 POINTS!
(Please read the full question before you answer.)
Complete the table below to solve the equation 2.5x − 10.5 = 64(0.5x).
x f(x) = 2.5x − 10.5 g(x) = 64(0.5x)
2
3
4
5
6
Answer:
x
=
−
0.3559322
Step-by-step explanation:
every evening gloria gives her little sister a bath describe what may have happened
Answer:
I dont know?
Step-by-step explanation:
Not math?
Which of the following represents the distance between x and y on a number line?
A. (x + y)
B. |y - x|
C. (y – x)
D. |x+y|
E. yx
Mellie is playing a bowling game at an arcade. She rolls two balls into the 30 point hole four balls into the 20 point hole and three balls into the 50 point hole. Write and evaluate an expression to find mellies total score.
Answer:
290
Step-by-step explanation:
30x2 + 20x4 + 50x3
Hope this helps. Please mark brainliest if you would. It would really help me out
Answer:
290
Step-by-step explanation:
30x2+4x20+3x50 multiply first and you get 60+80+150=290
What is the slope-intercept form of the linear equation 2x + 3y = 6?
Drag and drop the appropriate number, symbol, or variable to each box.
1. х
2. y
3. 6
4. 3
5. -1
6. 2
7. 3
8. 6
9. +
10. 1
11. 2.
12. 3
13. 4
14. 5
I need the 6 that go in the boxes
Answer:
slope is -2/3
Step-by-step explanation:
[tex]3y = - 2x + 6 \\ y = \frac{ - 2}{3} x + 2[/tex]
What is the geometric mean between 4 and 25. Write the answer in simplified radical form
Plzzz help me asap
Answer:
The geometric mean is the square root of 4*25
=10
Step-by-step explanation:
Please help :)
Find the equation that passes through (2, 2) and is parallel to 2y + 4x = 4.5
Answer:
Line passing through (2,2) is parallel to X - 2Y = 4, so, the slope is same as given line.
m = -a/b = -1/-2 = 1/2
The equation is
(Y - Y1) = m(X - X1) => Y - 2 = 1/2(X - 2) =>
2Y - 4 = X - 2 => | X - 2Y = -2 |
-4 = 20 - 10x
i dont know what to do pls help
Answer:
x = 2.4
Step-by-step explanation:
10x = 24
x = 24 ÷ 10
x = 2.4
Step-by-step explanation:
→ -4 = 20 - 10x
→ -20 - 4 = 10x
→ -24 = 10x
→ x = -24/10
→ x = -2.4
therefore, value of x is -2.4
hope this answer helps you dear!
A package of 5 pairs of insulated socks costs $26.45. What is the unit price of the pairs of socks?
Answer:
$5.29 per pair of socks
Step-by-step explanation:
26.45/5=5.29
From his home, Dan would have to walk due north to get to his friend Samuel's house and due east to get to his friend Cindy's house. It is 3 kilometers from Dan's house to Cindy's house and a straight-line distance of 5 kilometers from Samuel's house to Cindy's house. How far is Dan's house from Samuel's house?
The distance from Dan's house to Samuel's house is 4 km
The distance from Dan to Samuel house, Dan to Cindy house and Samuel to Cindy house forms a right angled triangle.
Distance from Dan to Samuel house = x, Distance from Dan to Cindy house = 3 km and Distance from Cindy to Samuel house = 5 km
Pythagoras theorem shows the relationship between the lengths of a right angled triangle.
Using Pythagoras theorem:
5² = x² + 3²
25 = x² + 9
x² = 16
x = 4 km
Hence the distance from Dan's house to Samuel's house is 4 km
Find out more at: https://brainly.com/question/21846482
Amab deposited Rs.200 in a bank.The banker promised 4% interest per annum. How much money will he get by end of one year?
Answer: $208
Step-by-step explanation:
200 x .04 = 208
Giving right answer branleist
Answer:
...probably
Step-by-step explanation:
since it's square units and this is a right triangle
area = (width * height) / 2
area = 6 * 3 / 2
area = 18 / 2
area = 9 square units²
Answer:
9 [tex]units^{2}[/tex]
Step-by-step explanation:
The formula to find the area of a triangle is [tex]A=\frac{1}{2}b*h[/tex] where b is the base or bottom of the triangle and h is the height of the triangle.
The base of the triangle in the picture is 6 units.
The height of the triangle in the picture is 3 units.
Substituting these values into the area formula:
[tex]A=\frac{1}{2}(6*3)=\frac{1}{2}(18)=9[/tex]
So the area of the triangle is 9 [tex]units^{2}[/tex]