Answer:
sinθ = -5/√61
secθ = √61/6
tanθ = -5/6
Step-by-step explanation:
From the given coordinate (6, -5), x = 6 and y = -5. This shows that the point lies in the 4th quadrant. In the fourth quadrant, only cos θ is positive, both sin θ and tan θ are negative.
Let us get the value of the radius 'r' first before calculating the trigonometry identities.
Using the Pythagoras theorem;
[tex]r^2 = x^2 + y^2\\r^2 = 6^2 + (-5)^2\\r^2 = 36+25\\r^2 = 61\\r = \sqrt{61}[/tex]
Using SOH, CAH, TOA to get the trigonometry identities;
Given x = 6, y =5 and r = √61
[tex]sin \theta = opp/hyp = y/r\\sin \theta = 5/\sqrt{61} \\[/tex]
Since sin θ, is negative in the fourth quadrant, [tex]sin \theta = -5/\sqrt{61} \\[/tex]
[tex]cos \theta = adj/hyp = x/r\\cos \theta = 6/\sqrt{61} \\[/tex]
[tex]sec \theta = \frac{1}{cos \theta} \\sec \theta = \frac{1}{6/\sqrt{61} } \\sec \theta = \frac{\sqrt{61} }{6}[/tex]
For tanθ:
[tex]tan \theta = \frac{opp}{adj} = \frac{y}{x} \\tan \theta = \frac{5}{6}\\[/tex]
Since tan θ, is negative in the fourth quadrant, [tex]tan \theta = -5/6[/tex]
[tex]SIN\Theta=\frac{-5}{\sqrt{61} }[/tex],
[tex]SEC\Theta=\frac{\sqrt{61} }{6}[/tex]
[tex]TAN\Theta=\frac{-5}{6}[/tex].
Given coordinate of point be (6, -5).
So the point lies in the 4th quadrant. In the fourth quadrant, only cos θ is positive, both sin θ and tan θ are negative.
Since (6, -5) is on the terminal side that puts us in the fourth quadrant. If we plot that point and draw a diagonal to it from the origin, we will be able to draw a right triangle with that diagonal as the hypotenuse.That means the adjacent side is 6 and opposite side it -5.
By Pythagorean theorem, we find that the hypotenuse
[tex]H=\sqrt{6^{2} +(-5)^{2} }[/tex]
[tex]H=\sqrt{61}[/tex]
We know from trigonometric ratios,
[tex]SIN\Theta=\frac{Perpendicular}{hypotenuse} \\[/tex]
[tex]SIN\Theta=\frac{5}{\sqrt{61} }[/tex]
Since [tex]SIN\Theta[/tex] is negative in 4th quadrant,
so,
[tex]SIN\Theta=\frac{-5}{\sqrt{61} }[/tex]
Similarly,
[tex]SEC\Theta=\frac{hypotenuse}{base}[/tex]
[tex]SEC\Theta=\frac{\sqrt{61} }{6}[/tex]
And,
[tex]TAN\Theta=\frac{perpendicular}{base}[/tex]
[tex]TAN\Theta=\frac{-5}{6}[/tex]
Hence, [tex]SIN\Theta=\frac{-5}{\sqrt{61} }[/tex], [tex]SEC\Theta=\frac{\sqrt{61} }{6}[/tex] and [tex]TAN\Theta=\frac{-5}{6}[/tex].
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Draw a square with side-length x. Write an expression that represents the perimeter.
Answer:
4x
Step-by-step explanation:
Length of square = x cm
Perimeter; p = 4 × length of square
p = 4x
A line segment (DE) joining the midpoints of two sides of a triangle is
parallel
to the third sid
Answer:
Given = A △ABC in which D and E are the mid-points of side AB and AC respectively. DE is joined .
To Prove : DE || BC and DE = 1 / 2 BC.
Const. : Produce the line segment DE to F , such that DE = EF. Join FC .
Proof : In △s AED and CEF, we have
AE = CE [∵E is the mid point of AC]
∠AED = ∠CEF[vert. opp.∠s]
and DE = EF [by construction]
∴ △AED ≅ △CEF [by SAS congruence axiom]
⇒ AD = CF ---(i)[c.p.c.t.]
and ∠ADE and ∠CEF ---(ii) [c.p.c.t.]
Now, D is the mid point of AB.
⇒ AD = DB ---(iii)
From (i) and (iii), CF = DB ---(iv)
Also, from (ii)
⇒ AD = || FC [if a pair of alt. int. ∠s are equal then lines are parallel]
⇒ DB || BC ---(v)
From (iv) and (v), we find that DBCF is a quadrilateral such that one pair of opposite sides are equal and parallel.
∴ DBCF is a ||gm
⇒ DF || BC and DF = BC [∵opp side of ||gm are equal and parallel]
Also, DE = EF [by construction]
Hence, DE || BC and DE = 1 / 2 BC
Numbers 2-4 Will choose brainliest
Answer:
2. 9, 8+9
3. 17-8=9, 17, 8, 9
4. 13-7=6
Step-by-step explanation:
Tan45degree - 10cos60degree
Answer:
- 4
Step-by-step explanation:
Tan(45°) - 10 * cos (60°) = - 4
Let f(x) = 1/x+2 and g (x) = 1/x-3. Find (f/g) (x). Assume all appropriate restrictions to the domain. help!!!!
Answer:(f/g)(x)=(1+2x)/(1-3x) where x<>0
Step-by-step explanation:
f(x)= 1/x+2= (1+2x)/x , x<>0
g(x)=1/x-3=(1-3x)/x , x<>0
=>f(x)/g(x)= (1+2x)/(1-3x) , x<>0
What are the explicit equation and domain for a geometric sequence with a first term of 5 and a second term of −10? an = 5(−2)n − 1; all integers where n ≥ 1 an = 5(−2)n − 1; all integers where n ≥ 0 an = 5(−15)n − 1; all integers where n ≥ 1 an = 5(−15)n − 1; all integers where n ≥ 0
Answer:
A
Step-by-step explanation:
The standard form of an explicit formula for a geometric sequence is given by:
[tex]x_n=a(r)^{n-1}[/tex]
Where n is the nth term, a is the initial term, and r is the common ratio.
We are given that the first term is 5. Hence, a = 5.
Also, we are given that the second term is -10. Therefore, the common ratio r is -2, because we multiply the first term by -2 to acquire -10.
Substituting yields:
[tex]x_n=5(-2)^{n-1}, n\geq 1, n\in\mathbb{Z}[/tex]
(Note: Z means the set of all integers. This is required because the term number can only be positive starting from one. For instance, we can't have the 0th term or the 1.5th term.)
In conclusion, the answer is A.
Evaluate the expression when x= -3 X^2+8x-7
arrange the following fraction in ascending order 2/3 1/6 3/5
Answer:
2/3 3/5 1/6
Step-by-step explanation:
look at the denominators and arrange from least to greater
when the polynomial f(x)=2x^3+ax^2+b is divisible by (x+1) and that there is a remainder of 16 when it is divided by (x-3) find the values of a and b
Answer:
hjgyjgyjyjhhh
Step-by-step explanation:
ygjyjygyjjg
rounds the capacity of a 1.85 liter jug to the tenth
Answer:
1.9 liters.
Step-by-step explanation:
The hundredths digit is 5 so we add 1 to the tenths digit.
Answer: 1.9 liter
Step-by-step explanation: the tenth is the first digit after the decimal point. Anything greater than it equal to 5 will be rounded up. So 1.85 is rounded up to 1.9
Solve -4r + 18= 6 I need this equation
Answer:
r = 3Step-by-step explanation:
[tex]-4r + 18= 6\\\\\mathrm{Subtract\:}18\mathrm{\:from\:both\:sides}\\\\-4r+18-18=6-18\\\\\mathrm{Simplify}\\\\-4r=-12\\\\\mathrm{Divide\:both\:sides\:by\:}-4\\\\\frac{-4r}{-4}=\frac{-12}{-4}\\\\\mathrm{Simplify}\\\\r=3[/tex]
(3+4i)+(8+2i) complex number in standard form
Answer:
(3 + 4i) + (8 + 2i) = 3 + 4i + 8 + 2i
(3 + 4i) + (8 + 2i) = (3 + 8) + (4i + 2i)
(3 + 4i) + (8 + 2i) = 11 + 6i
hope it helps if yes mark me BRAINLIEST!
Tysm!
:)
Answer:
11 + 6i
Step-by-step explanation:
Well, by the looks of it, you're combining like terms. Just add numbers that have the same variable or jut add coefficients:
(3 + 4i) + (8 + 2i)
= 3 + 4i + 8 + 2i
= (3 + 8) + (4i + 2i)
= 11 + 6i
What the answer S4• s8 •s3
Answer:
s^15
Step-by-step explanation:
When multiplying exponents with the same base, add the exponents
double the sum of x and 5
Answer:
2(x+5) = 2x+10
Step-by-step explanation:
2(x+5)
= 2*x + 2*5
= 2x+10
Which expression is the simplest form of...
Answer:
The answer is option A
Step-by-step explanation:
[tex]( {x}^{ - \frac{4}{7} } )^{7} [/tex]Using the rules of indices
That's
[tex]( { {a}^{x} })^{y} = {a}^{x \times y} [/tex]Simplify the expression
We have
[tex]( { {x}^{ - \frac{4}{7} } })^{7} = {x}^{ - \frac{4}{7} \times 7 } \\ = {x}^{ - 4} [/tex]Again using the rules of indices
That's
[tex] {x}^{ - y} = \frac{1}{ {x}^{y} } [/tex]The final answer is
[tex] \frac{1}{ {x}^{4} } [/tex]Hope this helps you
the ratio of Encik Arif's mass to his sons mass is 3:2 . If his son's mass is 42 kg, find Encik Arif's mass.
Answer:
Encik Arif's mass is 63kgStep-by-step explanation:
Let Encik Arif's mass be x
the ratio of Encik Arif's mass to his son's mass is 3:2
That's
[tex] \frac{3}{2} [/tex]The son's mass is 42, so the ratio of Encik Arif's mass to his son's is
x : 42
That's
[tex] \frac{x}{42} [/tex]Now equate the two fractions
That's
[tex] \frac{3}{2} = \frac{x}{42} [/tex]Cross multiply
3(42) = 2x
126 = 2x
Divide both sides by 2
We have the final answer as
x = 63Hope this helps you
if you bought a stock last year for $59 and it risen 13% how much is the stock worth now
Answer:
$ [tex] \underline{ \underline { \sf{ \bold{66.67}}}}[/tex]Step-by-step explanation:
Price of stock bought = $ 59
% rise = 13%
Price of stock rise :
⇒[tex] \sf{13\% \: of \: 59}[/tex]
⇒[tex] \sf{ \frac{13}{100} \times 59}[/tex]
⇒$ [tex] \sf{7.67}[/tex]
New price is 13% more than $ 59
Hence, New price = $ 57 + $ 7.67
= $ 66.67
Hope I helped!
Best regards!!
I need help with #66 and #68
Step-by-step explanation:
66. Δy = -3.4 Δx
Δy/Δx = -3.4
The slope of the line is -3.4. Slope-intercept equation of the line is:
y = -3.4x + b
Plug in the given point to find b:
2 = -3.4(4) + b
b = 15.6
Therefore, the equation is y = -3.4x + 15.6.
Use the equation to find the y coordinates.
[tex]\left[\begin{array}{cc}x&y\\-4&29.2\\4&2\\6&-4.8\\18&-45.6\end{array}\right][/tex]
68. Repeat the same steps as 66.
Δy = -1.7 Δx
Δy/Δx = -1.7
The slope of the line is -1.7. Slope-intercept equation of the line is:
y = -1.7x + b
Plug in the given point to find b:
3 = -1.7(-7) + b
b = -8.9
Therefore, the equation is y = -1.7x − 8.9.
Use the equation to find the x or y coordinates.
[tex]\left[\begin{array}{cc}x&y\\-19&23.4\\-7&3\\-2.412&-4.8\\3.2&-14.34\\9.1&-24.37\end{array}\right][/tex]
Calculate the total surface area of a rectangular box 10cm long, 8cm wide and 6cm tall.
Answer:
The answer is
376 cm²Step-by-step explanation:
Since the rectangular box is a cuboid,
Total surface area of a cuboid is given by
2( lw + wh + lh)Where
l is the length
w is the width
h is the height
From the question
l = 10 cm
w = 8cm
h = 6cm
Substitute the values into the above formula
That's
Total surface area of the rectangular box is
2 [ (10)(8) + (8)(6) + (10)(6) ]
2 [ 80 + 48 + 60 ]
2( 188)
We have the final answer as
Total surface area = 376 cm²Hope this helps you
Binomial (-x + 3) and trinomial (-2x2 + 5x + 6) are the factors of what polynomial? (Hint: 4 and 2 are factors of 8. Multiply.)Binomial (-x + 3) and trinomial (-2x2 + 5x + 6) are the factors of what polynomial? (Hint: 4 and 2 are factors of 8. Multiply.)Binomial (-x + 3) and trinomial (-2x2 + 5x + 6) are the factors of what polynomial? (Hint: 4 and 2 are factors of 8. Multiply.)
Answer:
2x^3-11x^2+9x+18
Step-by-step explanation:
By multiplying both the binomial and the trinomial given, we obtain a polynomial which contains both as factors. We notice as well that the given trinomial doesn't have 3 as a root (so there is no multiple root x = 3 in the product we obtain:
[tex](-x+3)\,(-2x^2+5x+6)=2\,x^3-5x^2-6x-6x^2+15x+18=2x^3-11x^2+9x+18[/tex]
Then, this new polynomial
[tex]2x^3-11x^2+9x+18[/tex]
has both given polynomials as factors.
19. If the polynomial P(x) = 27x^3 + 9x^2 – 3x – 10 is divided by 3x – 2, the remainder will be
options:
A) 1
B) 2
C) 3
D) 0
Answer:
D) 0
Step-by-step explanation:
Remainder is zero as 10 is fully divisible by 2.
Proof:
27x^3 + 9x^2 – 3x – 10 = (3x -2) (9x^ 2 +9x+5)Correct choice is D) 0
You need a total of 60 pounds of two commodities costing $1.35 and $2.85 per pound.
A) Verify that the total cost is y = 1.35x + 2.85(60 - x), where x is the number of pounds of the less expensive commodity.
Let x be the number of pounds of the commodity costing $1.35 per pound. Because there are_____pounds total, the amount of the second commodity is______. The total cost, in dollars, is y = 1.35x + 2.85(60 - x).
B) Find the inverse function of the cost function.
What does each variable represent in the inverse function?
1) X represents the commodity costing $1.35 per pound and Y represents the commodity costing $2.85 per pound.
2) X represents pounds and Y represents cost.
3) X represents the commodity costing $2.85 per pound and Y represents the commodity costing $1.35 per pound.
4) X represents cost and Y represents pounds.
5) X represents the commodity costing $1.35 per pound and Y represents cost.
C) What is the domain of the inverse function?
Validate or explain your answer using the context of the problem.
1. The domain of the inverse function is equal to the range of the original function.
2. The domain of the inverse function is equal to the domain of the original function.
3. The domain of an inverse function is always R.
D) Determine the number of pounds of the less expensive commodity purchased when the total cost is $78.
Answer: provided in the explanation section
Step-by-step explanation:
We will take this problem step by step to ensure we have easy understanding of the problem at hand.
(a). taking x as the number of pounds of the commodity costing $1.35 per pound.
Also since we have 60 pounds as total
The amount of second commodity is 60 - x
then the total cost (in dollars) is
y = 1.35x + 2.85(60 - x)
(b). since we have that;
y = 1.35x + 2.85(60 - x)
solving for y gives
y = 1.35x + 171 - 2.85x
y = 171 - 1.5x
doing exchange of variables y and x we have;
x = 171 - 1.5y
where;
1.5y = 171 - x
y = 171 - x / 1.5
f(x) = y and y = f⁻¹(x)f⁻¹(x) = 2/3 [171 - x] ------------- (1)
Here x represents the cost and y represents the pounds
(c). Given that less commodity is purchased, the Cost will be at its lowest and will be 60 (1.35) = $81.
Also, if only the more expensive commodity is purchased, the Cost will be at its maximum and will be 60(2.85) = $171
Therefore the domain of inverse becomes [81,171]That is to say that the domain of inverse function is equal to the range of original function.
(d). plug in x = $78 in the inverse function
where y = 2/3 [171-78]
y = 2/3[93] = 2[31]
y = 62
The number of pounds of the less expensive commodity purchased when the total cost is $78 is given as
y = 62
cheeers i hope this solution was helpful
A bottle of hot sauce is 3/4 full. Leigh uses 2/9 of the contents of the hot sauce bottle for lunch. How much of a full bottle of hot sauce did Leigh use for lunch?
Leigh uses [tex]\frac{1}{6}[/tex] of full bottle of hot sauce
What is Unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given,
A bottle of hot sauce is 3/4 full.
Leigh uses 2/9 of the contents of the hot sauce bottle for lunch.
Therefore
How much of a full bottle of hot sauce did Leigh use for lunch = [tex](\frac{3}{4}).(\frac{2}{9})[/tex]
= [tex]\frac{1}{6}[/tex]
Hence, Leigh uses [tex]\frac{1}{6}[/tex] of full bottle of hot sauce
Learn more about Unitary method here
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Solve the following:
2x – 7 > 9
a
3> 8
b
x > 1
C
3 < 8
d
x>-1
Answer: x > 8
2x - 7 > 9
2x > 9+7
2x > 16
2x / 2 > 16 / 2
x > 8
What is the value of 4 in the number 45?
Answer:
40
Step-by-step explanation:
The 4 in 45 is 40 because it is in the tens place, 4 times 10= 40. The 5 is 5 becasue it's in the ones place. :)
It's just place value:
Answer:
The first digit i.e. 4 is called the tens' place. Here, there are 4 tens. The last or right digit i.e. 5 is called the ones' place. Therefore, in the number 45 = 4 tens plus 5 ones = 40 + 5 = 45
How many times larger than the number (1 − 8 /15 ) is the number (1.2 + 2/ 3 )?
Answer:
1- 8/15= 7/15 = 0.4(6)
1.2 + 2/3 = 28/15 = 1.8 (6)
-13+(-4)÷2-3[-{(-3)×(-7)-(3+5)}]
If y varies inversely with x and y=11 when x=3, find the equation that relates x and y.
Answer:
y = [tex]\frac{33}{x}[/tex]
Step-by-step explanation:
Use the inverse relationship equation, y = [tex]\frac{k}{x}[/tex]
Plug in what we know to solve for k:
11 = [tex]\frac{k}{3}[/tex]
33 = k
Plug 33 in as k to find the equation:
The equation will be y = [tex]\frac{33}{x}[/tex]
A wall Of a building is 34 inches wide, 14 inches is concrete, 12 inches is brick, and 8 inches is limestone. what fraction of the wall is brick?
Step-by-step explanation:
It is given that,
A building is 34 inches wide. Its 14 inches is concrete, 12 inches is brick, and 8 inches is limestone. We need to find the fraction of the wall is brick.
A fraction is in the form of x/y. y is total value and x is a part of y.
Here, 12 inches is brick. So, its fraction is :
[tex]F=\dfrac{12}{34}=\dfrac{6}{17}[/tex]
So, fraction of [tex]\dfrac{6}{17}[/tex] is the wall which is brick.
A. 3/4=a/36
B.4/9=b/36
Answer:
A. = 27 B. = 16
Step-by-step explanation:
A. 36/4 = 9 3X9 = 27
B. 36/9 = 4 4X4 =16