The required equation of the line is y = 3x which passes through the origin with the slope 3.
What is the slope of the line?The slope of the line is defined as the gradient of the line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
We have to determine the equation of the line that passes through the origin with slope 3.
Let's assume slope-intercept form:
So required line in the slope-intercept form is:
y = mx + b
where m is the slope and b is the y-intercept.
In this case, the slope of line m = 3, and the line passes through the origin
So, therefore equation will be:
y = 3x + 0 or
y = 3x
Thus, the required equation of the line is y = 3x which passes through the origin with the slope 3.
Learn more about the Slope of Line here:
brainly.com/question/14511992
#SPJ5
Which transformations are needed to change the parent cosine function to y=3cos(10(x-pi))
The parent cosine function is transformed [tex]y=3cos(10(x-\pi ))[/tex] by vertically stretching it by a factor of 3 (amplitude), horizontally compressing it by a factor of 10 (frequency), and shifting it to the right by [tex]\pi[/tex] units (horizontal shift or phase shift).
The question asks which transformations are required to alter the parent cosine function to [tex]y=3cos(10(x-\pi ))[/tex]. The transformations involved in this equation are:
Amplitude modification: The coefficient '3' indicates that the amplitude of the cosine function is scaled by a factor of 3.Frequency adjustment: The factor '10' inside the cosine function affects the function's frequency, indicating the function has 10 complete cycles within the interval of [tex]2\pi[/tex] radians. This is a horizontal scaling transformation.Horizontal shift (or phase shift): The subtraction of [tex]\pi[/tex] within the argument of the cosine function translates the function [tex]\pi[/tex] units to the right along the x-axis.No vertical shift is present because there is no addition or subtraction outside the cosine function.
To transform the parent cosine function [tex]\(y = \cos(x)\) to \(y = 3 \cos(10(x-\pi))\)[/tex], apply a vertical stretch by 3, horizontal compression by 1/10, and a right shift by [tex]\(\pi\)[/tex] units.
To transform the parent cosine function[tex]\(y = \cos(x)\)[/tex] to the function [tex]\(y = 3 \cos(10(x-\pi))\)[/tex], we need to apply the following transformations:
1. Amplitude change: Multiply the function by [tex]\(3\)[/tex], which increases the amplitude.
2. Horizontal compression: Multiply the input of the cosine function by [tex]\(10\),[/tex]which compresses the graph horizontally.
3. Phase shift: Shift the graph to the right by [tex]\(\pi\)[/tex]units, indicated by the term [tex]\(x - \pi\).[/tex]
So, the transformations needed are:
- Amplitude change: Vertical stretch by a factor of [tex]\(3\).[/tex]
- Horizontal compression: Compression by a factor of [tex]\(1/10\).[/tex]
- Phase shift: Right shift by [tex]\(\pi\)[/tex] units.
Think about what you have learned about parallel and perpendicular lines. In what profession might a person rely upon this information? Describe how that person would apply these concepts.
Which postulate or theorem can be used to prove that △ABD≅△CBD?
ASA Congruence Postulate
SAS Congruence Postulate
SSS Congruence Postulate
HL Congruence Theorem
Answer:
SAS
Step-by-step explanation:
Please help me with question
Decide which of the two points lies on the graph of the line
X+y=6
A. 2,2
B. 5,1
Jaime had $37 in his bank account on Sunday. The table shows his account activity for the next four days. What was the balance in Jaime’s account after his deposit on Thursday?
Sheldon bought a $20 book at a 35% discount. He wrote an expression to find the discounted price. 20−0.35(20) Which expression is equivalent to discounted price Sheldon paid?
A (1−0.35)20
B (1+0.35)20
C (20−0.35)20
D 20+0.35(20)
The equivalent expression to '20 - 0.35(20)', which represents the discounted price Sheldon paid for a book, is '(1 - 0.35)20', or option A.
Explanation:The expression 20−0.35(20) represents the original price of the book Sheldon bought minus the 35% discount. The expression states that Sheldon is taking 35% of $20, which is the book's original price, then subtracting that amount from $20 to find the discounted price he paid.
This operation can be rewritten as multiplication by factoring out the $20 from the expression. Hence, the equivalent expression is (1−0.35)20, representing 65% of the original cost (or the amount Sheldon pays after the discount). Therefore, the answer is A.
Learn more about Discounted Price here:https://brainly.com/question/40202103
#SPJ2
write a linear factorization of the function. f(x) = x4 + 49x2
Answer:
f(x) = [tex]x^2 (x + 7i)(x - 7i)[/tex]
Step-by-step explanation:
The given function is f(x) = [tex]x^4 + 49x^2[/tex]
Here x^2 is a common factor, so we take out and write the remaining term inside the parenthesis.
f(x) = [tex]x^2 (x^2 + 49)[/tex]
f(x) = [tex]x^2 (x^2 - (7i)^2)[/tex] [Here i^2 = -1]
We know that a^2 - b^2 = (a +b)(a-b) using this identity, we get
f(x) = [tex]x^2 (x + 7i)(x - 7i)[/tex]
Max rented a motorbike at $465 for 5 days. If he rents the same motorbike for a week, he has to pay a total rent of $625.
Write an equation in the standard form (Ax + By = C) to represent the total rent (y) that Max has to pay for renting the motorbike for x days.
The sum of two numbers is 32. the larger number is one less than twice the smaller number. find the numbers.
To find the two numbers, we set up a system of equations and solve for the variables using substitution.
Explanation:To solve this problem, we can set up a system of equations. Let's call the smaller number 'x' and the larger number 'y'. We know that the sum of the two numbers is 32, so our first equation is x + y = 32.
We are also given that the larger number is one less than twice the smaller number. This can be written as y = 2x - 1. Now we have two equations:
x + y = 32y = 2x - 1We can solve this system of equations by substitution or elimination. Let's use substitution:
Starting with the second equation, we can substitute y with its value from the first equation:
2x - 1 = 32 - x
Now we can solve for x:
3x = 33
x = 11
Substituting this back into the first equation, we can find the value of y:
11 + y = 32
y = 21
Therefore, the smaller number is 11 and the larger number is 21.
Learn more about Solving equations here:https://brainly.com/question/18322830
#SPJ3
How many complex roots does the polynomial equation have?
−3x^4−7x+17=0
2
3
4
5
2 people are going to equally share 5 kg, of chocolate. how many kilograms of chocolate should each person get?
5 kilograms divided by 2 is 2.5 kilograms
Which best describes the effect on f (x) = 2x - 5 if the slope changes to 10?
If ST=3x, TU=7x, and SU=10, what is ST?
Final answer:
To find the value of ST, we set up the equation 3x + 7x = 10, solve for x, and then calculate ST as 3(1), which gives us ST = 3.
Explanation:
The student is asking to solve for ST, given that ST=3x, TU=7x, and SU=10. This is a segment addition problem, where ST and TU make up the whole segment SU. To solve it, you would first set up the equation ST + TU = SU. Substituting the given values, we get:
3x + 7x = 1010x = 10x = 1After finding the value of x, we substitute it back into the expression for ST:
ST = 3xST = 3(1)ST = 3So, the segment ST is 3 units long.
A circle with radius 5 and a center at (2, 3) was transformed to a circle with radius 10 and a center of (‒1, 4).
Show that the two circles are similar by describing the transformations that would have to be performed.
Answer:
First of all, remember that all circles are similar to each other regardless of how to twist the cartesian plane.
Let the origin in first case(radius 5) be at (0,0) , so if we shift the origin to (2-(-1),3-(4)) = (3,-1) {shifting origin to shift the first circle to second's place}. So, we arrive at a circle of radius 5 and center (-1,4).
Since similarly has no constraints on size comparison increase the radius to 10 units. Thus we arrive at the circle of radius 10 and center (-1,4).
Step-by-step explanation:
First of all, remember that all circles are similar to each other regardless of how to twist the cartesian plane.
rewrite the expression as a multiple of a sum of two numbers with no common factor 15+24 _____
To rewrite the expression as a multiple of a sum of two numbers with no common factor, find the prime factorizations of the given numbers and then multiply them together which brings the result as 39.
Explanation:To rewrite the expression as a multiple of a sum of two numbers with no common factor, we need to find two numbers that have no common factors and multiply them together. Let's find the prime factorizations of 15 and 24:
15: 3 × 524: 2 × 2 × 2 × 3Now we can rewrite the expression as:
15 + 24 = (3 × 5) + (2 × 2 × 2 × 3) = 3 × (5 + 8) = 3 × 13 = 39
So, 15 + 24 can be written as a multiple of 3 × 13, which is 39.
Hi can I find the missing coordinates of this parallelogram ?
There are 180 pages in the book Diana is reading. Diana has read 90 pages. What percent of the book has she read?
EXPERTS/ACE OR PEOPLE THAT KNOW IT QUICK PLZ. !!
The product of 19 and a number , subtracted from the reciprocal of the number cubed
Final answer:
The expression for the product of 19 and a number, subtracted from the reciprocal of the number cubed, is represented as (1/x)³ - 19x. It involves finding the product of 19 and a variable, taking the reciprocal of the variable, cubing it, and then performing the subtraction.
Explanation:
The original question is asking for the expression of a mathematical operation involving a variable and its reciprocal raised to a power. Specifically, the operation is the product of 19 and a number, subtracted from the reciprocal of the number cubed. When constructing this expression, we denote the unknown number as x and perform the following steps:
Identify the product of 19 and x, which is 19x.
Find the reciprocal of x, which is 1/x.
Cube the reciprocal of x to get (1/x)³.
Subtract the product of 19 and x from the cubed reciprocal to get the final expression (1/x)³ - 19x.
This expression represents the mathematical relationship detailed in the question. To simplify or evaluate this expression, additional information about the value of x would be required.
A painter uses 1.2 liters of the paint to cover 1m2 of the wall. How many square meters he can cover with (1)12 liters; (2)6.6 liters; (3)4.8 liters of paint?
Answer:
He can cover 10 sq. meters using 12 liters, 5.5 sq. meters using 6.6 liters, and 4 sq. meters using 4.8 liters of paint.
Step-by-step explanation:
1. 12 LITERS/ 1.2 LITERS = 10 SQ. METERS
2. 6.6 LITERS/ 1.2 LITERS = 5.5 SQ. METERS
3. 4.8 ITERS/ 1.2 LITERS = 4 SQ. METERS
Find an equation for the horizontal line that passes through the point (10 , -13 )
A red candle is 8 inches tall and burns at a rate of 710 inch per hour. a blue candle is 6 inches tall and burns at a rate of 15 inch per hour. after how many hours will both candles be the same height? enter your answer in the box.
Answer:
5 hour
Step-by-step explanation:
what number must you add to complete the square? x^2+6x=15
Final answer:
To complete the square for the equation [tex]x^2 + 6x = 15,[/tex] you must add 9 to both sides to form the perfect square [tex]trinomial (x + 3)^2 = 24.[/tex]
Explanation:
To complete the square for the equation [tex]x^2 + 6x = 15,[/tex]we need to add a number to both sides of the equation to form a perfect square trinomial on the left side.
Completing the square involves taking half of the linear coefficient (6), squaring it, and adding that value to both sides. Since half of 6 is 3, and 3 squared is 9, we must add 9 to both sides of the equation.
Therefore, our new equation would be[tex]x^2 + 6x + 9 = 15 + 9[/tex] , which simplified to [tex](x + 3)^2 = 24.[/tex]
the table shows the sales of admission tickets to a science museum. A table labeled Science Museum Admission Revenue. It contains a row for Tickets Sold with the amounts 128, 264, 308, 514, 520, 650, 722, and a row for Sales with the amounts 1088, 2244, 2618, 4369, 5525, and 6137. The equation y = 9.75x represents the number of dollars, y, earned by an art museum for selling x tickets. Which statements about the costs of the admission tickets at the museums are true? Select each correct answer. It costs $9.75 per ticket for admission to the art museum. It costs $8.75 per ticket for admission to the science museum. Art museum tickets are more expensive than science museum tickets. Given the same number of ticket sales, the science museum earns more revenue. 1 2 3 4 5
Answer: It costs $9.75 per ticket for admission to the art museum.
Art museum tickets are more expensive than science museum tickets.
Step-by-step explanation:
From the given table of Science Museum Admission Revenue, we can see that the sales amount by selling 128 tickets = $1088
Therefore, the cost of each ticket for science museum =[tex]\frac{1088}{128}=\$8.5[/tex]
∴ It costs $8.5 (not 8.75) per ticket for admission to the science museum.
Also,The equation [tex]y = 9.75x[/tex] represents the number of dollars, y, earned by an art museum for selling x tickets.
At x=1, y=9.75
∴ It costs $9.75 per ticket for admission to the art museum.
Clearly, 9.75>8.5
∴ Art museum tickets are more expensive than science museum tickets.
If the number of ticket sales will be same then art museum will earn more revenue.
Since the price of one ticket to an art museum ($9.75) is higher than the price per ticket for science museum ($8.5), therefore the following statements about the cost at both museums would be true:
Price per ticket for admission to the art museum cost $9.75 (Option A)
Art Museum tickets cost more than that of science (Option C).
Price per ticket to a science museum:
Given the table showing the sales of admission tickets to a science museum:
Thus,
The unit rate/price per ticket sold at the science museum using a pair of values from the table, say, (128, 1088) is: y/x
Thus:
unit rate/price per ticket = [tex]\frac{1088}{128} = 8.5[/tex]That is, a ticket to a science museum costs $8.5.
Price per ticket to an art museum:
The equation, y = 9.75x is given as the equation modelling the situation.
Where x = number of tickets soldy = amount in dollarsThus, this means that the price per ticket to the art museum is: $9.75.
Therefore, since the price of one ticket to an art museum ($9.75) is higher than the price per ticket for science museum ($8.5), therefore the following statements about the cost at both museums would be true:
Price per ticket for admission to the art museum cost $9.75 (Option A)
Art Museum tickets cost more than that of science (Option C).
Learn more here:
https://brainly.com/question/19330987
Which of the following has the ability to turn light energy into chemical energy? A. a generator B. an automobile C. a tree D. water
Explain how the common difference in an arithmetic sequence is like the slope of a linear function. read more >>
What percent of 95 equals 76
____ regular polygons are symmetrical.
A) Even- sided
B) Odd- sided
C) Rectangular
D) All
Answer:
Step-by-step explanation:
We have to find which type of Regular Polygons are symmetrical.
Regular Polygons are the polygons whose all sides and angles are equal.
For ex:- Equilateral triangle is a regular triangle as its all sides are equal and all angles are equal to 60°.
Square is a regular quadrilateral whose all sides are equal and all angles are equal to 90°.
Option A:
Even-sided regular polygons are the polygons whose no of sides is an even no.
ex, quadrilateral with 4 side, hexagon with 6 sides.
They are symmetrical which no of line of symmetry equal to no of side.
Option B:
Odd-sided regular polygons are the polygons whose no of sides is an Odd no.
ex, Triangle with 3 side, pentagon with 5 sides.
They are symmetrical which only 1 line of symmetry.
Option C:
Rectangular regular polygons are also symmetrical.
Therefore, Option D is correct .i.e., ALL regular polygons are symmetrical.
What is the significance of the mean of a probability distribution? choose the correct answer below.
a. it gives information about how the outcomes vary.
b. it represents the most likely possible outcome.
c. it is the expected value of a discrete random variable.
d. it can never be negative?
Answer:
Step-by-step explanation:
ANSWER C : It is the expected value of a discrete random variable