Answers
Answer:
Solution given:
Sin[tex]\theta_{1}=\frac{1}{4}[/tex]
[tex]\frac{opposite}{hypotenuse}=\frac{1}{4}[/tex]
equating corresponding value
opposite=1
hypotenuse=4
adjacent=x
By using Pythagoras law
hypotenuse²=opposite²+adjacent²
4²=1²+x²
16=1+x²
x²=16-1
x=[tex]\sqrt{15}[/tex]
In II quadrant
Cos angle is negative
Cos[tex]\theta_{1}=\frac{-adjacent}{hypotenuse}[/tex]
Cos[tex]\theta_{1}=\frac{-\sqrt{15}}{4}[/tex]Answer:
[tex]\displaystyle \cos ( \theta _{1} ) = - \frac{ \sqrt{15}}{ 4 }[/tex]
Step-by-step explanation:
on a unit circle there're 4 Quadrant. on Q:I sin and cos both are positive,on Q:II cos is negative and sin positive, on Q:III both sin and cos are negative and on Q:IV cos is positive and sin negative.
actually a unit circle is a coordinate plane but
there's (cos,sin) instead of (x,y)it'll be required later
well to solve the problem we can consider Pythagorean theorem which states that the square of sin and cos is equal to 1. therefore,
[tex] \displaystyle \sin ^{2} ( \theta) + \cos ^{2} ( \theta) = 1[/tex]
[tex] \rm \displaystyle \implies \boxed{\cos ^{} ( \theta) = \sqrt{1 - \sin ^{2} ( \theta) }}[/tex]
in this case,
[tex] \rm \theta \: \: is \: \: \theta_{1}[/tex]sin[tex]\theta[/tex] is ¼Thus substitute:
[tex]\displaystyle \cos ( \theta _{1} ) = \sqrt{1 - \left( \frac{1}{4} \right) ^{2} }[/tex]
simplify square:
[tex]\displaystyle \cos ( \theta _{1} ) = \sqrt{1 - \frac{1}{16} }[/tex]
simplify substraction:
[tex]\displaystyle \cos ( \theta _{1} ) = \sqrt{ \frac{16 - 1}{16} }[/tex]
simplify numerator:
[tex]\displaystyle \cos ( \theta _{1} ) = \sqrt{ \frac{15}{16} }[/tex]
recall redical rule:
[tex]\displaystyle \cos ( \theta _{1} ) = \frac{ \sqrt{15}}{ \sqrt {16} }[/tex]
simplify square root:
[tex]\displaystyle \cos ( \theta _{1} ) = \frac{ \sqrt{15}}{ 4 }[/tex]
since cos is negative on Q:II hence,
[tex]\displaystyle \cos ( \theta _{1} ) = \boxed{- \frac{ \sqrt{15}}{ 4 }}[/tex]
and we're done!
Related Questions
The sides of an equilateral triangle measure 0.2(10x+90)cm each. If the perimeter of the triangle is 612.6 cm, what is the side length?
Write the equation to solve the problem.
Solve for x
Find the side of the triangle
Answers
Answer:
204.2 cm
Step-by-step explanation:
equilateral means all sides are of equal length.
the perimeter of such a triangle is simply 3 times one of these sides.
so,
612.6 = 3×0.2×(10x + 90) = 0.6×(10x+90) = 6x + 54
6x = 558.6
x = 93.1
so, a single side is
0.2×(10×93.1 +90) = 0.2×(931 + 90) = 0.2×1021 = 204.2 cm
to check
3×204.2 = 612.6 = the original perimeter.
so, correct.
Rotate the vector 3,-2 90 degrees clockwise about the origin.
Answers
Answer:
-2,-3
Step-by-step explanation:
Answer:
-2 -3
It worked for me on acellus
Step-by-step explanation:
Suppose that a sales person observes that if an item is priced at $9 per item then 6 items are sold. If 4 items are sold for $11 per item then find a linear equation to model the number y of items sold for x dollars per item. Find the slope-intercept form of the equation of the line.
Answers
Answer:
y = -x + 15
Step-by-step explanation:
if an item is priced at $9 per item then 6 items are sold.
Thus, the input is 9 while the output is 6.
Thus, we can say; x, y = (9, 6)
4 items are sold for $11 per item. Thus, the coordinate is; (11, 4)
Now,slope is;
m = (y2 - y1)/(x2 - x1)
m = (4 - 6)/(11 - 9)
m = -2/2
m = -1
We know that slope intercept form is;
y = mx + c
Let's try the first point.
Thus;
6 = -1(9) + c
6 + 9 = c
c = 15
Thus, equation of line is;
y = -x + 15
Write an inequality and show on a number line all numbers:
less than 4 but greater than or equal to 0
Answers
Answer:
the inequality is 0<x<4
Step-by-step explanation:
(0,4)
I don't understand this one
Answers
Answer:
9/8 = n
Step-by-step explanation:
9 = 8n
Divide each side by 8
9/8 = 8n/8
9/8 = n
Find two fractions, when multiplied together make 3/4
Answers
Answer:
3/1 times 1/4, 3/2 times 1/2, 9/8 times 2/3
Answer:
1/2 & 3/2
Step-by-step explanation:
1/2 X 3/2 = 3/4
To get this answer, you need to think of two numbers which we can multiply to get 3 and two numbers which we can multiply to get 4.
Answer from Gauthmath
Anyone please help me
Answers
Standard form of a quadratic equation: ax^2 + bx + c = 0
4x^2 - 5x + 10 = 2x
4x^2 - 7x + 10 = 0
Hope this helps!
I NEEDDDD HELPPPP ITSSSS URGENTTTT!!!!!
Answers
Answer: 75.4
Step-by-step explanation:
The equation for the circumference for a circle is diameter times pi. 24 times pi is 75.3982236862. Rounded to the nearest tenth would make it 75.4.
Divide $128 in the ratio 2:3:7
Answers
Answer:
21.33: 32: 74.67
Step-by-step explanation:
2:3:7
The total is 2+3+7 = 12
Divide 128 by 12
128/12 = 32/3
Multiply each number by 32/2
2*32/3 : 3*32/3 :7*32/3
64/3 : 32 : 224/3
Rounding to the nearest cent
21.33: 32: 74.67
What is the range of the function$$f(x) = \frac{1}{1-x}~?$$Express your answer in interval notation.
Answers
I think you tried copy pasting the thing in here. usually written equations on tests or whatever don't copy paste well
Rewrite the following polynomial in standard form.
1
23
+
04
+8
Answers
Answer:
1/2 x^4 +x^3 +8
Step-by-step explanation:
Standard form means highest power of x to lowest power of x
1/2 x^4 +x^3 +8
Please help !!!!!!!!!!!
Answers
Answer:
98°+62°+6x = 180
160+6x = 180
6x = 180 - 160
6x = 20
x= 20/6
x= 3.33
therefor your answer is 3.33
helpppp: write the rule that describes the composition of transformations
Answers
Which equation is in slope-y-intercept form?
Question 1 options:
a) 3x + 4y = 7
b) x = 4y - 2
c) y = 3x -1
d) x + 4y -2
Answers
Answer:
C = y - 3x-1
Step-by-step explanation:
Slope intercept form is
y = mx+b where m is the slope and b is the y intercept
C = y - 3x-1 is in slope intercept form
The answer is A.
I took the test.
Translate the sentence into an equation.
Three more than the quotient of a number and 6 is equal to 5.
Use the variable b for the unknown number.
Answers
Answer:
3 + b/6 = 5
solve it too?
b/6 = 2
b = 12
Answer:
is it like
3x+6=5
to solve this
3x+6=5
collect like terms
3x= -6+5
3x= -1
divide both side by 3
3x/3=-1/3
x= -0.3
I don't understand need help?
Answers
9514 1404 393
Answer:
2. (only)
Step-by-step explanation:
The Pythagorean theorem tells you the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. To determine if these are right triangles, determine if that condition is met.
1. 3^2 +5^2 = 9 + 25 = 34 ≠ (√35)^2 . . . . not a right triangle
2. 5^2 +4^2 = 25 +16 = 41 = (√41)^2 . . . a right triangle
3. 6^2 +8^2 = 36 +64 = 100 ≠ (√10)^2 . . . . not a right triangle
4. 3^2 +3^2 = 9 +9 = 18 ≠ (3√3)^2 = 27 . . . . not a right triangle
Help needed ASAP rocky!
Answers
Answer:
C. {x | x < [tex]\frac{10}{7}[/tex]}
Step-by-step explanation:
x must be less than 10/7
I hope this helps!
Does this graph show a function? Explain how you know.
Answers
Answer:
yes because the graph passes the vertical line test
A spinner numbered 1 to 6 is spun ten times, giving the results : 2, 5, 3, 5, 1, 2, 3, 3, 4, 6. The experimental probability of getting a 2 is:
Answers
Answer:
1 / 5
Step-by-step explanation:
Given the outcome of number cube spin : 2, 5, 3, 5, 1, 2, 3, 3, 4, 6
The experimental probability of an event, A is given as :
P(A) = number of times A occurs / total number of trials
Therefore, the experimental probability of getting 2 ;
P(getting 2) = Number of times 2 occurs / total number of trials
P(getting 2) = 2 / 10 = 1/5
Could someone help me out?
Answers
Answers:
DE = 1.1DF = 1.6BC = 4.8===========================================================
Explanation:
I recommend drawing the two triangles as shown below. The diagram isn't to scale, but all that matters is that we get the general idea down.
Your teacher gave you this info:
angle A = angle E (red angles)angle C = angle F (blue angles)These two pieces of info are enough to prove that triangle ABC is similar to triangle EDF. Use the angle angle (AA) similarity theorem to do this proof. The order of the lettering matters because it helps us see how the letters pair up.
A and E go firstB and D in the middleC and F go lastSince the triangles are similar, the scale factor to go from ABC to EDF is EF/AC = 2/6 = 1/3
In other words, the side lengths of triangle EDF are exactly 1/3 that of the corresponding lengths of ABC. Or we can reverse things to say the sides of ABC are 3 times longer than the sides of EDF.
----------------------
Use this scale factor to help determine the missing length ED.
(ED)/(AB) = scale factor
(ED)/(AB) = 1/3
(ED)/(3.3) = 1/3
ED = (1/3)*(3.3)
ED = 1.1
Note how ED/AB = (1.1)/(3.3) = 11/33 = 1/3
----------------------
While we don't know how long sides BC or DF are, we are told that DF is 3.2 units shorter compared to BC.
This means
DF = BC - 3.2
DF = x - 3.2
Then we can say,
(DF)/(BC) = scale factor
(x-3.2)/(x) = 1/3
3(x - 3.2) = x*1
3x - 9.6 = x
3x - x = 9.6
2x = 9.6
x = (9.6)/2
x = 4.8
So BC is x = 4.8 units long and DF is x-3.2 = 4.8-3.2 = 1.6 units long
What is the value of the expression 53.5-5? please explain
Answers
Reason- an expression is an equation without an equal sign and this expression is saying 53.5 - 5.
Answer:
48.5
Step-by-step explanation:
53.5
- 5.0
48.5
5 tenths - 0 tenths = 5 tenths (.5)
3 minus 5, three smaller than 5 so BORROW 10 13 -5 = 8 (8)
the 5 in the tens position becomes a four because one got "borrowed"
4 - 0 = 4 (4)
48.5 is the result
1+1+5+8+6+45+6+4+34+423
Answers
Answer:
answer is 533 because we add all the no.
y' = (x+1/[tex]\sqrt{x^{2} +1[/tex]
Answers
Answer:
Solving for x (rearranging) you get:
(x^3+x+(x^2+1)^1/2)/x^2+1=y
Step-by-step explanation:
Solve for x by simplifying both sides of the equation and solving for y by isolating y
NEED HELP! What is the equation of the axis of symmetry?
A) x=-4
B) x=4
C) y=4
D) y= -4
Answers
if you look at the vertex (4,-1) and draw an imaginary line going through that point, you will see that it goes through x when it equals 4.
HELP ME PLS ITS URGENT
Answers
Answer: -3 (option D) is the answer.
(-8)-(-5)= -8+5 = -3
-3
Explanation:
= (-8)-(-5)
= -8+5 (- and - is equal to +)
= -3
So the correct answer is D)-3
YOUR WELCOME☺️⭐️
DOES A TRANSLATION PRESERVE ITS LENGTH, SHAPE, SIZE, AND ORIENTATION? EXPLAIN.
Answers
Step-by-step explanation:
Yes. A translations preserve it's. length, shape,size and orientation. WHY?
, A translation is a rigid transformation so it preserve it physical features of the shape( both pre image and current image).A translation can be used to show if two figures are congruent so it preserve it shape.E) Natasha's parents want to support Natasha by saving $5000 for her college. They searched up for some investment options and came up with two best ones o 4.8% simple interest for 2 years o 4.1 % / year compounded semi- annually for 2 years Compare both the plans and find out which is the best to choose
Answers
Answer:
Amount she would have in 2 years at a simple interest of is
$5000 + ($5000 x 0.048 x 2) = $5480
Amount she would have in 2 years at a 4.1 % / year compounded semi- annually is :
$5000 x ( 1 +0.041/2)^4 = $5422.78
the first option yields a higher value in two years when compared with the second option. Thus, the first option is the best one to choose
Step-by-step explanation:
Future value with simple interest = principal + interest
Interest = principal x interest rate x time
0.048 x 5000 x 2 = 480
future value = $480 + 5000 = $5480
The formula for calculating future value with compounding:
FV = P (1 + r)^nm
FV = Future value
P = Present value
R = interest rate
m = number of compounding
N = number of years
5000 x ( 1 + 0.041 / 2)^(2 x 2) = $5422.78
Christina buys 3 DVDs . 2 of the DVDs cost X+Y . Write an expression that shows the amount the 3 DVDs cost
Answers
Answer:
3/2(x+y)
Step-by-step explanation:
The cost of 2 DVD is x+y
Divide by 2 to get the cost of one DVD
(x+y) /2
Multiply by 3 to get the cost of 3
3/2(x+y)
Answer:
= 3(x + y)/2
Step-by-step explanation:
Cost of two DVD's is shown as :-
= x + y
If we divide by 2 we'll get the cost of each DVD
= (x + y)/2
Then, multiplying by 3 gives us the total amount.
= 3(x + y)/2
Help me with this anyone
Answers
Answer:
1/4
Step-by-step explanation:
b+-sqrt b^2-4ac all over 2a
Find the interior angle sum for the following polygon
Answers
Answer:
360/ 5 is the answer
Step-by-step explanation:
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