The exact values of the trigonometric functions of the ordered pair are listed below:
sin θ = - 4√65 / 65 sec θ = √65 / 7 cot θ = - 7 / 4What are the exact values of three trigonometric functions associated with an ordered pair?In this problem we find an ordered pair in rectangular form (x, y) that the represents the terminal side of angle θ and from which we must determine the exact values of the sine, secant and cotangent. The definitions for each of the three functions are:
sin θ = y / √(x² + y²)
sec θ = √(x² + y²) / x
cot θ = x / y
If we know that x = 7 and y = - 4, then the exact values of the trigonometric functions are, respectively:
sin θ = (- 4) / √[7² + (- 4)²]
sin θ = - 4√65 / 65
sec θ = √[7² + (- 4)²] / 7
sec θ = √65 / 7
cot θ = 7 / (- 4)
cot θ = - 7 / 4
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A store is having a sale on chocolate chips and walnuts. For 3 pounds of chocolate chips and 2 pounds of walnuts, the total cost is $14. For 5 pounds of
chocolate chips and 6 pounds of walnuts, the total cost is $28. Find the cost for each pound of chocolate chips and each pound of walnuts.
Cost for each pound of chocolate chips: $
Cost for each pound of walnuts: $
Cost for each pound of chocolate chips is equal to $3.5.
Cost for each pound of walnuts is equal to $1.75
How to determine the cost for each pound of chocolate chips and each pound of walnuts?In order to solve this word problem, we would assign variables to the cost for each pound of chocolate chips and each pound of walnuts respectively, and then translate the word problem into algebraic equation as follows:
Let the variable c represent the amount of cost for each pound of chocolate chips.Let the variable w represent the cost for each pound of walnuts.For 3 pounds of chocolate chips and 2 pounds of walnuts, we have:
3c + 2w = 14 .....equation 1.
For 5 pounds of chocolate chips and 6 pounds of walnuts, we have:
5c + 6w = 28 .....equation 2.
Solving the system of equations by using the elimination method, we have:
3 × (3c + 2w = 14) = 9c + 6w = 42
5c + 6w = 28_
4c = 14
c = 14/4
c = $3.5
For the cost for each pound of walnuts, we have:
3c + 2w = 14
3(3.5) + 2w = 14
10.5 + 2w = 14
2w = 14 - 10.5
2w = 3.5
w = 3.5/2
w = $1.75.
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can someone
help with this
Step-by-step explanation:
let angles of a triangle a=86
b= 180-3z , c= 180-4z
a+b+c = 180 {angle sum property}
86 +180+180-3z-4z=180
446 -7z = 180
-7z = -266
[tex]z = \frac{ - 266}{ - 7} = 38[/tex]
so other angle are
3z = 3 x 38 = 114
4z = 4 x 38 = 152
Indicate in standard form the equation of the line passing through the given points, writing the answer in the equation box below. E(–2, 2), F(5, 1)
Answer:
dd
Step-by-step explanation:d
Answer:
Step-by-step explanation:
a0 - x-y=3
Find the y-coordinate of the y-intercept of the polynomial function defined below.
f(x) = 3 + 5x² + 4x^4 - 3x³ - 6x
Answer:
3
Step-by-step explanation:
When you substitute 0 in for x in the equation. You are left with f(0) = 3.
IXL Please Help Fast!
The lines which are skewed in the rectangular prisms shown are Line QT (↔QT) and Line WX(↔WX).
What is skew in geometry?
This refers to two lines that do not cut across (intersect) each other and are not parallel to each other. the pair of lines must also be opposite edges of the shape. The lines are not also lying or acting in the same plane. i.e non-coplanar.
How to identify skew lines?
a) Locate lines that do not intersect each other.
b)Find out if these pairs of lines are also not parallel to each other.
c) Examine if these non-intersecting and non-parallel lines are non-coplanar.
If yes then the chosen pair of lines are skew lines.
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log 4(x+8) + log 4(x+5) = 1
rewrite the equation
According to the product rule of logarithms, the given equation is written as, log₄(x² + 13x + 40) = 1
Product rule of logarithm
Basically, the product rule states that the sum of two logarithms is equal to the product of the logarithms.
And it is the first law and it can be represented as;
logₐ(x) + logₐ(y) = logₐ(xy)
Given,
Here we have the logarithmic equation log 4(x+8) + log 4(x+5) = 1
And we have to rewrite the equation.
Here we have the logarithmic equation,
=> log₄(x+8) + log₄(x+5) = 1
By using the product property of logarithms,
We have to rewrite the equation as,
=> log₄(x+8)(x+5) = 1
Now, we have to expand (x+8)(x+3) using the FOIL Method.
Then we get,
=> log₄(x² + 5x + 8x + 40) = 1
=> log₄(x² + 13x + 40) = 1
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If the function f(x) is thje absolute value of 3 more than the value of x. Select all the true statements. A. The x-intercept of the function is 3.
The absolute value function is represented by f(x) = |x+3| and the
x-intercept of the function is -3.
The function is represented as absolute value of 3 more than x.
hence the function 3 more than x is given by
f(x)=x+3
Now for absolute function:
f(x)=|x+3|
The graph of the function will have no negative value for f(x).
The graph will pass through the point (0,3) which is the y-intercept.
The x-intercept is at (-3,0) .
The domain of the function is all real vales of x.
The range of the function is (0,∞)
The parent function is given by y=|x| .
An procedure that establishes the absolute value of a number or variable is known as a modulus function. It produces the variable count's size.
It is also known as an absolute value function. No matter what input was given to this function, a positive result is always the result.
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1.3 x 10 to the power of negative 3
Answer:
The answer to this problem is 0.0013.
55555555555555555555555555555555555555555555555555555555555555555555555555x0
Answer:
Step-by-step explanation:
Ok:
1. Anything times zero always equals zero.
So: 55555555555555555555555555555555555555555555555555555555555555555555555555x0=
Answer:0
f(x)=−x 2 −2x+3 \text{Find }f(1) Find f(1)
An entry level architect's annual pay is $47,008 based on 52 weeks per year. Due to the economy, his company is having to cut back on the number of weeks that it employs its architects. If the firm cuts the work year to 48 weeks but keeps the same rate of pay, how much should the architect expect his annual pay to decrease? Round your answer to the nearest dollar.
After the firm work year reduced to 48 weeks at the same rate, the architect annual pay decrease to 43,392 dollars.
How to find the annual pay decrease?An entry level architect's annual pay is $47,008 based on 52 weeks per year. Due to the economy, his company is having to cut back on the number of weeks that it employs its architects
The company cuts the work year to 48 weeks but keeps the same rate of pay. The amount the architect should expect his annual pay to decrease can be calculated as follows:
Let's find the rate.
Therefore,
52 weeks = 47008
1 week = ?
cross multiply
rate = 47008 / 52
rate = 904 dollars per weeks
He collects the same rate after the company cuts the work year to 48 weeks.
Therefore,
annual pay of the architect after the cut = 48 × 904
annual pay of the architect after the cut = 43,392 dollars
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What is the equation of a circle with a center at (-4, 0)
that passes through the point (-2, 1)?
O x² + (y + 4)² = √√5
O (x-1)² + (y + 2)² = 5
O (x + 4)² + y² = 5
O (x + 2)2 + (y - 1)² = √5
The equation of a circle with a center at (-4, 0) that passes through the point (-2, 1) is (x + 4)² + y² = 5. Option C is correct.
The standard equation of a circle is given by:
(x – h)² + (y – k)² = r²
Where (h, k) is the center of the circle and r is the radius.
We are given:
The circle has a center at (–4, 0) and passes through the point (–2, 1).
Substitute (h, k) with (–4, 0) in the above equation, we will get;
(x – (-4))² + (y – 0)² = r²
(x + 4)² + y² = r²
Substitute (x, y) with (–2, 1) in the above equation to get the value of r:
(-2 + 4)² + 1² = r²
(2)² + 1² = r²
r² = 5
Put the value r² = 5 in (x + 4)² + y² = r², we will get;
(x + 4)² + y² = 5
So, the equation of the circle is (x + 4)² + y² = 5.
Thus, the equation of a circle with a center at (-4, 0) that passes through the point (-2, 1) is (x + 4)² + y² = 5. Option C is correct.
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2 market women shared a basket full of oranges in order to sell them.the share of the first woman is twice the other if the are 300 oranges in the basket what is the share of each women
Answer:
Step-by-step explanation:
no idea
The number of oranges with first women are 200 and the number of oranges with other women are 100.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, 2 market women shared 300 oranges.
The share of first woman is twice the other.
Let the number of oranges with other women be x.
Then, the number of oranges with first women will be 2x.
Now, x+2x=300
3x=300
x=100
So, 2x=200
Therefore, the number of oranges with first women are 200 and the number of oranges with other women are 100.
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Joseph invested $7,850 in an account that pays 7.5% interest per year. How much interest will Juan have earned at the end of 36 months?
Juan have earned of interest after 36 months at the rate of 7.5% interest per year.
What is Simple Interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest. The formula of simple interest is as follows:
S.I = p×r×t
Where p is principle value, r is rate and t is time in years.
Here, the principle amount is $7,850 and rate is 7.5% i.e [tex]\frac{7.5}{100}=0.075[/tex] and time is 36 months i.e 3 years.
Now, putting the values,
SI = 7850×0.075×3
= $ 1766
Therefore, the interest Juan have earned in 36 months is $1,766.
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The equation y – 4 = 6(x + 7) represents a linear function. What is the y-intercept of the graph of the equation?
Step-by-step explanation:
In general equation, y = mx+c, c represents y-intercept.
So, y-4 = 6x+42
y = 6x+46
So, y intercept will be 46
What is the value of x?
Thank you.
Answer:
x would be 3 by 2
I am 90% sure but I hope this helps!
4
The height of a cone is two times its base diameter. What is the volume of the cone in terms of its base radius r
The volume of cone will be [tex]\frac{88r^{3} }{21}[/tex]
Cone:
A cone is a three-dimensional geometric shape that tapers smoothly from a flat base.
Given,
The height of a cone is two times its base diameter.
we have to find the volume of cone in terms of base radius.
let us assume the base radius of cone is equal to r units
so diameter(d) of cone will be, d= 2r units
so,
height(h) of cone will be equal to, h = 2d units
h = 2x2r units
h = 4r units
We know,
Volume of the cone(V) = [tex]\pi r^{2} h/3[/tex]
Where,
r = radius of base
h = height of cone
π = 22/7
Thus by using formula,
Volume of cone(V) = [tex]\pi r^{2} h/3[/tex]
= 22/7 * [tex]r^{2}[/tex] * 4r/3
= 88[tex]r^{3}[/tex]/21
= [tex]\frac{88r^{3} }{21}[/tex]
Hence,
The volume of cone will be [tex]\frac{88r^{3} }{21}[/tex]
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for any integer p, show that p^3+11p will always be a multiple of 6
By the principle of mathematical induction, it has been proved that
[tex]p^3 + 11p[/tex] is divisible by 6
What is Principle of mathematical induction?
Let the statement be given by P(n). At first P(n) is proved to be true for 1. Then it is assumed that P(n) is true for all n. If P(n) is true for (n+1) then by Principle of Mathematical induction, P(n) is true for all natural numbers
The given expression is [tex]p^3 + 11p[/tex]
For p = 1
[tex](1)^3 + 11 \times 1\\12[/tex]
which is a multiple of 6
Let it be true for p = m
[tex]m^3 + 11m[/tex] is a multiple of 6
[tex]m^3 + 11m = 6k[/tex], where k is any integer
For p = m + 1
[tex](m+1)^3 + 11(m+1) \\m^3+3m^2+ 3m +1+11m+11\\m^3+11m +3m^2+3m+12\\m^3+11m + 3m(m+1) + 12[/tex]
Now,
[tex]m^3 + 11m[/tex] is divisible by 6
We know that the product of two consecutive integers are divisible by 6
[tex]3m(m+1)[/tex] is divisible by 6
12 is divisible by 6
[tex](m+1)^3 + 11(m+1)[/tex] is divisible by 6
So it is true for p = m + 1
By the principle of Mathematical induction, it is true for all natural numbers and eventually for all integers
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The radius of a hula hoop is 15in what is the area of a hula hoop in terms of pi
The area of the hula hoop is equal to 450π square inches.
What is the area of a hula hoop?
A hula hoop is a toy with the form of a circle, whose area (A), in square inches, has to be found. The area of a circle is described by the following formula:
A = 2π · R²
Where R is the radius of the hula hoop, in inches.
If we know that R = 15 inches, then the area covered by the hula hoop is:
A = 2π · (15 in)²
A = 450π in²
The area is equal to 450π square inches.
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y is directly proportional to x3 When x = 10, y = 250
(a) Find a formula for y in terms of x.
The formula for y in terms of x is a cubic equation:
y = 0.25*x³
How to find the relation between x and y?We know that y is directly proportional to x³, then we can write the equation:
y = k*x³
Where k is the constant of proportionality.
In this case, we know that when x = 10, the value of y is 250, then we can replace these values in the above equation to find the value of x:
250 = k*10³
250 = k*1,000
Dividing both sides by 1,000 we get:
250/1,000 = k
0.25 = k
Then the equation is:
y = 0.25*10³
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Ashley and Laura are 60 miles apart, traveling towards each other. If Laura travels 12 mph
and Ashley travels 8 mph how long until they meet?
hours
The time taken by Ashley and Laura to meet each other is 3 hrs
Relationship Between Time, Speed & Distance:The speed of an object tells us how slow or fast an object moves. The formula for speed is given below
Speed = Distance/TimeThe speed of an object is directly proportional to Distance and Inversely proportional to Time. Hence,
Distance = Speed X TimeHere we have,
Ashley and Laura are 60 miles apart, traveling toward each other
This means the distance between Ashley and Laura is 60 miles
Speed of Laura = 12 mph
Speed of Ashley = 8 mph
Let us assume that Both Ashley and Laura meet after t hours
Then
The distance traveled by Laura in t hours = 12 mph × t hrs = 12t m
The distance traveled by Ashley in t hours = 8 mph × t hrs = 8t m
As we know the distance between Laura and Ashley is 60 miles
=> 12t m + 8t m = 60 miles
=> 20t miles = 60 miles
=> t = 60/20
=> t = 3hrs
Therefore,
The time taken by Ashley and Laura to meet each other is 3 hrs
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what is the equation and solution please?
Answer:
y=3x+1
y=-17
Step-by-step explanation:
y=3x+1
7=3(2)+1
7=6+1
7=7
y=3(-6)+1
y=-18+1
y=-17
Hopes this helps please mark brainliest
Determine which set of side measurements could be used to form a triangle.
8, 14, 20
7, 8, 15
2, 19, 22
1, 4, 8
The set of side measurements that could be used to form a triangle are 8, 14, 20.
How can the set of side measurements be identified?The concept that will be used is the concept of triangle inequality theorem.
To know if the given 3 side lengths are a triangle, then the use of the triangle inequality theorem comes into play.
This rule tells us that when we sum 2 sides of a triangle the value must be greater than the third side.
Then this rule can be applied as
The first option; 8, 14, 20
a+b>c = 8+14>20
a+c>b = 8+20>14
b+c>a = 20+14>8
Therefore, first option is correct.
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A rectangular garden has an area of 72 square yards. The dimensions of the
garden are not prime numbers. What are the possible dimensions of the
garden
Answers:
1 yard by 72 yards
4 yards by 18 yards
6 yards by 12 yards
8 yards by 9 yards
==========================================================
Explanation:
Let's list out all the ways to multiply to 72 using two values
1*72
2*36
3*24
4*18
6*12
8*9
Then cross off something like 2*36 since 2 is prime. We also cross off 3*24 since 3 is prime.
We're left with this list
1*72
4*18
6*12
8*9
which represent the possible dimensions of this rectangle.
Keep in mind that 1 is not prime.
How long will Suban need to leave a $10 000 investment in the bank at 5% per
year simple interest for it to grow to $15 000?
a. 10 years c. 5 years
b. 100 years d. 50 years
Suban need to leave $10000 investment in the bank at 5% per year simple interest for 10 years so that it grows to $15000
According to question,
Principal (P) = 10,000
Rate of interest (I) = 5%
Interest = Amount - Principal
= 15000 - 10000
= 5000
We need to find the number of years
T = ?
Interest = P * R * T / 100
5000 = 10000 * 5 * T / 100
T = 10 years
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I really do not understand these questions at all watched a video and attempted it still got it wrong
Answer:
540 cm₂
Step-by-step explanation:
Area of right triangular prism:[tex]\sf \boxed{Area = (b_1+b_2+b_3)*l + bh}\\\\[/tex]
[tex]\sf \text{where $b_1$, $b_2$ and $b_3$ are the sides of the triangle l is the length of the rectangle}\\\\ \text{and b is the base of the triangle and h is the altitude of the triangle}[/tex]
b₁ = 12 cm ; b₂ = 5 cm ; b₃ = 13 cm
l = 16 cm ; b = 12 cm and h = 5 cm
Area = (12 + 5 + 13)*16 + (12*5)
= 30*16 + 60
= 480 + 60
= 540 cm²
Does anyone know what the Answer is...
45 ÷ ? = 8
Answer:
Step-by-step explanation:
Instead you do 45 divided by 8
And you will get 5.625
Suppose you are designing a cardboard box that must have a volume of 18 cubic feet. The cost of the cardboard is $6 per square foot. How much will the material for each box cost?
Answer:
I think its 108 each Box is going to cost 108
Determine the domain and range of the following parabola. f(x)=−3x2−30x−74
Step-by-step explanation:
1. if to rewrite the given equation, then
y= -3(x+5)²+1;
2. the vertex of the parabola is (-5;1) and it is the highest point. Then
3. domain: x is any value, x∈(-∞;+∞);
range: y not greater than 1, y∈(-∞;1].
For the parabola f(x) = -3x² - 30x - 74, the domain is all real numbers (-∞, ∞), and the range is also all real numbers (-∞, ∞).
To determine the domain and range of the given parabola f(x) = -3x² - 30x - 74, we need to understand the behavior of parabolas.
The domain of a function represents all the possible x-values for which the function is defined. In this case, there are no restrictions on the x-values for the given quadratic function. Therefore, the domain is all real numbers, expressed as (-∞, ∞).
The range of a function represents all the possible y-values that the function can produce. For a parabola, if the coefficient of the squared term (in this case, -3) is negative, the parabola opens downward. Since the coefficient is negative, the parabola will have a maximum value. In this example, there is no minimum or maximum specified; thus, the range will also be all real numbers.
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Michelle sells new and used kayaks. She makes a 10.5% commission on every kayak she sells and she also gets paid $495.50 per week.
a) Develop an equation for the way Michelle is paid.
b) Last month, the total value of the kayaks she sold was $19 425. Use the equation you’ve developed to find out how much Michelle was paid for that month.
Part a
The equation for the way Michelle is paid is
Total weekly payment y = 495.50 + 0.105x
Part b
The total payment in a month = $4021.625
She makes a 10.5% commission on every kayak she sells
Consider the total value of kayaks she sold = x
The rate of commission = 10.5%
The amount of commission = x × (10.5/100)
= 0.105x
The weekly fixed payment = $495.50
Total weekly payment y = 495.50 + 0.105x
Part b
The total value of the kayaks she sold = $19425
Total number of weeks in a month = 4
Then the total payment in a month = (4 × 495.50) + (0.105×19425)
= 1982 + 2039.625
= $4021.625
Hence,
part a
The equation for the way Michelle is paid is
Total weekly payment y = 495.50 + 0.105x
Part b
The total payment in a month = $4021.625
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