The other option (b) cose > 0 and cot0 < 0 does not match as cose > 0 in the first and fourth quadrants, and cot0 < 0 in the second and fourth quadrants. However, the terminal side of 0 lies in the first quadrant.
The quadrant in which the terminal side of 0 lies: (a) sece > 0 and sine > 0We need to find the quadrant in which the terminal side of 0 lies. For that, let us consider the standard position of the angle 0 in the rectangular coordinate system. The angle 0 is in the x-axis, that is, it is on the right side of the y-axis. This means that the terminal side of 0 lies in the first quadrant. Hence, the answer is (a) sece > 0 and sine > 0.The other option (b) cose > 0 and cot0 < 0 does not match as cose > 0 in the first and fourth quadrants, and cot0 < 0 in the second and fourth quadrants. However, the terminal side of 0 lies in the first quadrant.
To know more about quadrants visit:
https://brainly.com/question/26426112
#SPJ11
What is the cost of four small drinks that cost $4.50 each with a sales tax of 4%?
$25.20
$18.72
$18.00
$22.00
Answer:
18.72
Step-by-step explanation:
Given x = 1, y = 1, w = 1, and z = 1 and this expression: what is the evaluation of the logical expression?
The evaluation of the expression is 2, if the expression is x - y + z(x + w).
What is the expression?Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
Given that x = 1, y = 1, w = 1, and z = 1
We have been given expression
⇒ x - y + z(x + w)
Substitute the values of x = 1, y = 1, w = 1, and z = 1 in the above expression,
⇒ 1 - 1 + 1(1 + 1)
⇒ 0 + 1(2)
⇒ 2
Hence, the evaluation of the expression is 2.
Learn more about the expressions here :
brainly.com/question/21751419
#SPJ4
Your question is incomplete, probably the missing part is:
Given x = 1, y = 1, w = 1, and z = 1 and this expression x - y + z(x + w): what is the evaluation of the logical expression?
For the linear regression y = ẞ1 + ẞ2x + e, assuming that the sum of squared errors (SSE) takes the following form:
SSE = 382 +681 +382 + 18ẞ1ẞ2
Derive the partial derivatives of SSE with respect to B1 and B2 and solve the optimal values of these parameters.
a. B₁ = B1
b. B₂ =
The optimal values of these parameters are:
a. β₁ = 0
b. β₂ = 0
The linear regression y = β1 + β2x + e, assuming that the sum of squared errors (SSE) takes the following form:
SSE = 382 + 681 + 382 + 18β1β2
Derive the partial derivatives of SSE with respect to β1 and β2 and solve the optimal values of these parameters.
Given that SSE = 382 + 681 + 382 + 18β1β2 ∂SSE/∂β1 = 0 ∂SSE/∂β2 = 0
Now, we need to find the partial derivative of SSE with respect to β1.
∂SSE/∂β1 = 0 + 0 + 0 + 18β2 ⇒ 18β2 = 0 ⇒ β2 = 0
Therefore, we obtain the optimal value of β2 as 0.
Now, we need to find the partial derivative of SSE with respect to β2. ∂SSE/∂β2 = 0 + 0 + 0 + 18β1 ⇒ 18β1 = 0 ⇒ β1 = 0
Therefore, we obtain the optimal value of β1 as 0. Hence, the partial derivative of SSE with respect to β1 is 18β2 and the partial derivative of SSE with respect to β2 is 18β1.
Thus, the optimal values of β1 and β2 are 0 and 0, respectively.
Therefore, the answers are: a. β₁ = 0 b. β₂ = 0
Learn more about regression analysis at
https://brainly.com/question/31691955
#SPJ11
which ones are least to greatest?
Answer:
Step-by-step explanation:
-1, -0.5, 1/4
9. The sum of two numbers is 25 and whose product is 156. find the two numbers.
Answer:
x = 12
y = 13
Step-by-step explanation:
Let's assume the two numbers as x and y.
The sum of the two numbers is 25
So,
x+y = 25y = 25 - xThe product of the two numbers is 156
xy = 156x(25 - x) = 15625x - x² = 156x² - 25x + 156 = 0x² - 13x - 12x - 156 = 0(x - 12) • (x - 13) = 0x - 13 = 0x = 13x - 12 = 0x = 12Hence, the two numbers are 13 and 12.
Example: we have to find 2 number : a and b
a + b = 25 ⇒ a = 25 - b (1) a × b = 156 ⇒ a = 156/b (2)(1)(2) ⇒ 156/b = 25 - b
⇒ 156/b - 25 + b = 25 - b - 25 + b
⇒ b - 25 + 156/b = 0
⇒ (b - 25 + 156/b) × b = 0 × b = 0
⇒ b² - 25b + 156 = 0
⇒ b² - (13b + 12b) + 156 = 0
⇒ b² - 13b - 12b + 156 = 0
⇒ (b² - 13b) + (- 12b + 156) = 0
⇒ b(b - 13) - 12(b - 13) = 0
⇒ (b - 13)(b - 12) = 0
⇒ b = 13 or b = 12
if b = 12 => a = 25 - 12 = 13if b = 13 => a = 25 - 13 = 12Answer: 12 and 13
OK done. Thank to me :>
Describe how to find the sale price of an item that has been discounted 25%.
Multiply the original price by ___% to find the sale price.
Answer:
Multiply the original price by 75% to find the sale price.
Step-by-step explanation:
100 - 25 = 75%
Type the correct answer in each box. Use numerals instead of words.
Consider the given circle with the shaded sector XY and central angle, 225°. The circumference of the circle is 30
units.
A circle with center C has two lines C X, and C Y drawn from the center of the circle to the circle wall such that the exterior angle of X C Y is 225 degrees.
Use the given information to complete the statements. Round any non-integer answers to the hundredths place.
The correct answer is Length of arc XY: 15.03 units.Area of shaded sector XY: 15.73 square units.
To complete the statements, we can use the properties of circles and the given information.
The length of the arc XY, denoted as "s," can be found using the formula:
s = (θ/360) * 2πr
where θ is the central angle in degrees and r is the radius of the circle.
Given that the central angle is 225° and the circumference of the circle is 30 units, we can solve for the radius (r):
Circumference = 2πr
30 = 2πr
r = 30 / (2π) ≈ 4.77 units (rounded to the hundredths place)
Now we can calculate the length of the arc XY:
s = (225/360) * 2π * 4.77 ≈ 15.03 units (rounded to the hundredths place)
Therefore, the length of the arc XY is approximately 15.03 units.
The area of the shaded sector XY, denoted as "A," can be found using the formula:
A = (θ/360) * πr²
Using the same values for θ and r as above, we can calculate the area:
A = (225/360) * π * (4.77)² ≈ 15.73 square units (rounded to the hundredths place)
Therefore, the area of the shaded sector XY is approximately 15.73 square units.
Note: Please double-check the formulas and calculations with the provided information to ensure accuracy.
Learn more about function here:
https://brainly.com/question/11624077
#SPJ8
if there are 2 boards on a shelf one is 234 in the other is 246 in what is the total legth of the boards
The lengths of the two boards (234 inches and 246 inches) and adding them together, we find that the combined length of the boards is 480 inches.
To find the total length of the two boards, you need to add their individual lengths together.
Step 1: Identify the length of each board. The first board is 234 inches long, and the second board is 246 inches long.
Step 2: Add the lengths of the boards together.
234 (length of first board) + 246 (length of second board) = 480
So, the total length of the two boards on the shelf is 480 inches. This means that if you were to place the two boards end-to-end, they would cover a distance of 480 inches.
In summary, by identifying the lengths of the two boards (234 inches and 246 inches) and adding them together, we find that the combined length of the boards is 480 inches. This calculation helps us understand the total amount of space the boards would occupy if placed side by side.
For more about lengths:
https://brainly.com/question/30100801
#SPJ11
help me right now
Mixed numbers with unlike denominators ______ be subtracted from each other.
A. Mixed numbers with unlike denominators cannot be subtracted from each other.
B. Mixed numbers with unlike denominators can be subtracted from each other.
Answer:
B. Mixed numbers with unlike denominators can be subtracted from each other.
Step-by-step explanation:
Mixed numbers are numbers that have a whole part and a fractional part, such as 2 1/4 or 3 3/5. Unlike denominators are fractions that have different numbers in the bottom, such as 1/4 and 3/5. They are also called unlikeable denominators because they make math harder and more annoying. Who likes to deal with fractions anyway?
Mixed numbers with unlike denominators can be subtracted from each other, but only if you follow some tedious steps. First, you have to find a common denominator for the fractions, which is the smallest number that both denominators can divide into. This is like finding a common enemy for two rival gangs. For example, to subtract 2 1/4 from 3 3/5, we need to find a common denominator for 1/4 and 3/5. The least common denominator is 20, because both 4 and 5 can divide into it. Then, we have to multiply both fractions by the same factor to get equivalent fractions with the same denominator. This is like dressing up both gangs in the same uniform to make them look alike. For example, we multiply 1/4 by 5/5 and 3/5 by 4/4 to get:
2 1/4 = 2 5/20
3 3/5 = 3 12/20
Now we can subtract the fractions by subtracting the numerators and keeping the denominators the same. This is like taking away some members from each gang and seeing who has more left. For example, we subtract 5/20 from 12/20 and get 7/20. Then we subtract 2 from 3 and get 1. Finally, we add the whole part and the fractional part together to get the final answer. This is like adding up the remaining members of one gang and giving them a name. For example, we get:
3 12/20 - 2 5/20 = (3 - 2) + (12/20 - 5/20) = 1 + 7/20 = 1 7/20
Therefore, the correct answer is B. Mixed numbers with unlike denominators can be subtracted from each other. But why would you want to do that? It's much easier to use decimals or percentages instead. Fractions are so last century.
(y+4)^2 * (y-4)^2
Pls help, will mark brainliest
(Use factoring)
Answer:
Step-by-step explanation:
¿En que orden se deben escribir las funciones, para aplicar la integral definida cuando se desea calcular el área?
Answer:
Si querés calcular el área entre las funciones f(x) y g(x) en el rango (a, b), usualmente se calcula la integral de la función más grande en el intervalo menos la función más pequeña en el intervalo, es decir, si:
f(x) > g(x) para todo x ∈ (a, b)
Entonces calculamos:
\(\int\limits^b_a {(f(x) - g(x))} \, dx\)
Puesto que el área se define como la encerrada por las dos curvas, y si lo hiciéramos de otro modo, las curvas no encerrarían ningun área.
Ahora, si no se cumple lo anterior, es decir, g(x) > f(x) en algún dado intervalo, entonces separamos la integral en distintas partes de tal forma que siempre definamos un área positiva.
es decir, si:
f(x) ≥ g(x) para x ∈ (a, n)
g(x) ≥ f(x) para x ∈ (n, b)
entonces el área estará dada por:
\(\int\limits^n_a {f(x) - g(x)}dx \, +\int\limits^b_n {g(x) - f(x)} \, dx\)
Marilyn is having shelves installed to create a corner pantry. The length of one wall is 21 inches and the measure of the angle opposite the short side of the pantry, m∠A = 40°. The contractor who is making the shelves, which are shaped like right triangles, needs to know the length of the other wall. The length of the other wall is inches. Round your answer to the nearest integer.
Answer:
40° or 40.03 degrees or 25 inches as nilla mentioned.
What is the slope of the line 5x + 5y = 15
Answer:
5
Step-by-step explanation:
Answer:
-1x
Step-by-step explanation:
5x + 5y = 15
5x - 15 = -5y ^^ Subtraction Property of Equality
x - 3 = -y ^^ Division Property of Equality
-x + 3 = y ^^ Multiplication Property of Equality
-x = slope
John has a debit card with $100.00 on it. He uses his debit card to buy his lunch everyday. His lunch costs $4.50 per day. How many lunches can John buy?
Answer:
He can buy 22 lunches.
Step-by-step explanation:
To find how many he can buy if he had $100, we must divide the cost of one lunch to the amount of money he has.
(Round to the nearest whole number to get the exact amount of lunches that he can buy.)
1 lunch = $4.50
So:
=$100 ÷ $4.50 = 22.222....
=22.222.... = 22
Hope this helps! I'm sorry if it's wrong.
PLEASE HELP
An unknown polynomial is added to the expression - 3x³ + 2x-5 and the resulting sum is 4x³ + 7x² - 3. What is the unknown polynomial?
Answer:
7x³ + 7x² + 2x - 8
Step-by-step explanation:
Find the inverse of the function
The inverse of the function f(x) = √(x+1) is \(f^-1\)(x) = x² - 1.
What is inverse function?Given a function f(x), its inverse function, denoted as \(f^-1\)(x), is a function that takes the output of f(x) and returns the original input. In other words, if y = f(x), then x = \(f^-1\)(y).
According to question:To find the inverse of the function f(x), we follow these steps:
Step 1: Replace f(x) with y:
y = √(x+1)
Step 2: Interchange x and y:
x = √(y+1)
Step 3: Solve for y:
x² = y+1
y = x² - 1
Step 4: Replace y with f^-1(x):
f^-1(x) = x² - 1
Therefore, the inverse of the function f(x) = √(x+1) is \(f^-1\)(x) = x² - 1.
To verify this, we can check that (\(f^-1\) o f)(x) = x and (f o \(f^-1\))(x) = x for all x in the domain of the functions:
(\(f^-1\) o f)(x) = \(f^-1\)(f(x)) = (√(x+1))² - 1 = x
(f o \(f^-1\))(x) = f(\(f^-1\)(x)) = √((x² - 1) + 1) = √(x²) = |x| + 1
Since the range of f(x) is [0, infinity), we restrict the domain of \(f^-1\)(x) to [1, infinity) to ensure that the inverse is a function.
To know more about inverse function visit:
https://brainly.com/question/30350743
#SPJ1
If f(x) = x4 − x3 + x2 and g(x) = −x2, where x ≠ 0, what is (f ⁄g)(x)? m
Answer:x − x^{2} − 1.
Step-by-step explanation:
.
plzzz help with this on gusssssssyyss
Answer: a=3
Step-by-step explanation: add 63 to both sides. Then divide both sides by 9 to get a=3.
How do you find the area of a rhombus without diagonals?
The area of a rhombus can be found by multiplying the length of one of its sides by the height of a perpendicular line from the center to a side.
The height of the rhombus is the distance from the center of the rhombus to one of its sides, perpendicular to that side.
The formula for the area of a rhombus can be written as A = s*h, where A is the area, s is the length of one of the sides of the rhombus, and h is the height of the rhombus.
It's important to note that this method of finding the area of a rhombus without diagonals can only be used when the rhombus is a regular polygon, a polygon with all sides and angles congruent. When the rhombus is not a regular polygon, then you can find the area by using the diagonals.
Additionally, it's important to mention that a rhombus can be defined as a parallelogram with all sides congruent or a square with its angles not 90 degrees.
To know more about area of a rhombus on the link below:
https://brainly.com/question/12783973#
#SPJ11
Please let me know asap
The equivalent fraction of the given repeating decimal \(0.\overline{3}\) is \(\frac{1}{3}\).
How to convert a repeating decimal to a fraction?A repeating decimal of type \(a_0.a_1\overline{a_2a_3}\) can be converted into a fraction as follows: \(a_0.a_1\overline{a_2a_3}=a_0+\frac{a_1a_2a_3}{990}\) . As only \(a_2\) and \(a_3\) are repeated, so the denominator is \(990\) i.e., the number of 9's is the same as the number of digits repeated and after that, we put zeros for the non-repeating digits after the decimal point. also, the number of zeros will be the number of non-repeating digits.
Here, the given repeating decimal number is \(0.\overline{3}\).
So, its equivalent fraction will be: \(0.\overline{3}=\frac{3}{9}=\frac{1}{3}\).
Therefore, the equivalent fraction of the given repeating decimal \(0.\overline{3}\) is \(\frac{1}{3}\).
To know more about repeating decimal, refer: https://brainly.com/question/99747
#SPJ9
a rotating sprinkler can reach up to 14 feet through a 300 degree angle. find the total area covered by the sprinkler in one sweep. round to the nearest tenth. What is the area of the lawn, to the nearest square foot, that receives water from this sprinkler?
In one sweep, the area covered by the sprinkler is 77.19 sq ft (approx). The area of the lawn, to the nearest square foot, that receives water from this sprinkler is 616 sq ft (approx).
We know that a rotating sprinkler can reach up to 14 feet through a 300-degree angle. Area covered by the sprinkler in one sweep = area of the sector whose radius = 14 feet and angle = 300°Area of sector = (θ / 360) × πr²Where θ = 300°, r = 14 ftArea of sector = (300/360)× π(14)²= 77.19 sq ft (approx) Therefore, the area covered by the sprinkler in one sweep is 77.19 sq ft (approx).
We need to find the total area of the lawn that receives water from this sprinkler. The sprinkler rotates 360 degrees, so it will cover a full circle whose radius is 14 feet. Area of a circle = πr²= π(14)²= 615.752 sq ft (approx) Therefore, the area of the lawn, to the nearest square foot, that receives water from this sprinkler is 616 sq ft (approx).
To know more about area visit:-
https://brainly.com/question/1631786
#SPJ11
Find the amount of change from 48 to 16.
Answer:it is 32
Step-by-step explanation:
48-16=32
You purchased a used car for $12,000 and have agreed to pay off
the car in 48 monthly payments of $365 each. What will be the total
sum of your payments?
Answer:
$17,520
Step-by-step explanation:
The total can be found using multiplication.
48 x 365
Use long multiplication to solve this.
After solving, you should get $17,520.
what number line is the right one?? HELP
Answer:
B
Step-by-step explanation:
x/-5 < 9
×-5 ×-5
x < -45
x is less than -45
so, it's diagram B
Here is the answer to your question
Answer:
Nothing further can be done with this topic. Please check the expression entered or try another topic. Thanks for the answer :)!
Answer:
this is wrong btw
Step-by-step explanation:
last 2 guyss !!!! tysm
First one is a rotation 90° clockwise
Second one is B. 134°
Answer:
A 90° clockwise
B 134°
In ΔSTU, u = 340 inches, t = 620 inches and ∠T=110°. Find all possible values of ∠U, to the nearest degree.
One possible value of ∠U is 80° (to the nearest degree).
What is a triangle?A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed.
To find the possible values of ∠U, we can use the Law of Cosines:
c² = a² + b² - 2ab cos(C)
Where c is the side opposite the angle we want to find (∠U), a and b are the other two sides, and C is the angle opposite side c.
In this case, we want to find ∠U, so we'll use side u as c and sides t and s (which we don't know yet) as a and b, respectively:
u² = t² + s² - 2ts cos(U)
Substituting the given values, we get:
340² = 620² + s² - 2(620)(s)cos(U)
Simplifying:
115600 = 384400 + s² - 1240s cos(U)
Subtracting 384400 and rearranging:
s² - 1240s cos(U) + 268800 = 0
Now we can use the quadratic formula to solve for s:
s = [1240 cos(U) ± √(1240² cos²(U) - 4(1)(268800))]/(2)
Simplifying under the square root:
s = [1240 cos(U) ± √(1537600 cos²(U) - 1075200)]/(2)
s = [1240 cos(U) ± √(409600 cos²(U) + 1742400)]/(2)
s = [620 cos(U) ± √(102400 cos²(U) + 435600)]
Since s must be positive, we can discard the negative solution, and we have:
s = 620 cos(U) + √(102400 cos²(U) + 435600)
Now we can use the fact that the sum of angles in a triangle is 180° to find ∠U:
∠U = 180° - ∠T - ∠S
Since we know ∠T = 110°, we just need to find ∠S. We can use the Law of Sines to do this:
sin(S)/s = sin(T)/t
sin(S) = (s/t)sin(T)
Substituting the values we know:
sin(S) = (620 cos(U) + √(102400 cos²(U) + 435600))/620 * sin(110°)
sin(S) ≈ (1.481 cos(U) + 2.225)/6.959
Now we can use a calculator to find the arcsin of both sides to get ∠S:
∠S ≈ arcsin((1.481 cos(U) + 2.225)/6.959)
Finally, we can substitute the values we found for ∠S and ∠T into the equation we found earlier for ∠U:
∠U = 180° - 110° - arcsin((1.481 cos(U) + 2.225)/6.959)
Simplifying:
∠U = 70° - arcsin((1.481 cos(U) + 2.225)/6.959)
Now we can use trial and error or a graphing calculator to find the values of ∠U that satisfy this equation. One possible solution is:
∠U ≈ 80°
Therefore, one possible value of ∠U is 80° (to the nearest degree).
Learn more about triangle on:
https://brainly.com/question/9916775
#SPJ1
Function w is a nonlinear function. Which representation could represent function w?
A representation that could represent function w (nonlinear function) is: D. table D.
What is a linear function?In Mathematics, a linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.
This ultimately implies that, a linear function has the same slope and it is typically used for uniquely mapping an input variable to an output variable, which both increases simultaneously.
Therefore, table D represents a non-linear function because the slope is not constant and the common difference is not constant between successive data points.
Read more on linear function here: brainly.com/question/27325295
#SPJ1
Roxanne has already jarred 10 liters of jam and will jar an additional 3 liters of jam every
day. How many days does Roxanne need to spend making jam if she wants to jar 16 liters
of jam in all?
Explain please and how to do the equation
Answer:
3
My logic:
so she jars 10 on the first day (that is 1 day) and she wants to jar 16. so if you subtract 10 from 16 you get 6. Now we know she wants to jar 6 more, and if she does 3 every day then you would divide 6 by 3 and get 2. 2+1 is 3, so 3 days. (if you cant chose 3 chose 2 because your teacher might not want yo to count the first day)
Hope this helped!
2. Factor the quadratic expression completely: 3x2 - 4x + 21
a. (3x + 7)(x + 3)
b. (x-7)(3x – 3)
c. (x - 3)(3x - 7)
d. cannot be factored