When a polygon reflects across the y axis ,how do the coordinates of the points change

Answers

Answer 1

The y coordinate will stay the same. The x coordinate will flip from positive to negative, or vice versa.

Some examples:
(1,2) ----> (-1,2)
(-3,4) ----> (3,4)
(-1.2, 8) ----> (1.2, 8)

The general rule is
(x,y) ----> (-x, y)
indicating that only the x coordinate undergoes a change

Related Questions

Find the equation of the curve that passes through the point 0, 1 6 and whose slope at each point (x, y) is − x 12y .

Answers

The equation is [tex]$x^2 + 12y^2 - 3072 = 0$,[/tex] obtained from integrating [tex]$12y \, dy = -x \, dx$[/tex] with the initial condition.

To find the equation of the curve passing through the point (0, 16) with a slope given by [tex]$ \frac{{dy}}{{dx}} = -\frac{x}{12y} $,[/tex] you can use separation of variables.

Given that [tex]$ \frac{{dy}}{{dx}} = -\frac{x}{12y} $[/tex], we can rewrite it as:

[tex]\[ 12y \, dy = -x \, dx \][/tex]

Now, integrate both sides:

[tex]\[ \int 12y \, dy = \int -x \, dx \]\[ 6y^2 = -\frac{1}{2}x^2 + C \][/tex]

Given that the curve passes through the point (0, 16), substitute these values into the equation:

[tex]\[ 6(16)^2 = -\frac{1}{2}(0)^2 + C \]\[ 6(256) = C \]\[ C = 1536 \][/tex]

Therefore, the equation of the curve is:

[tex]\[ 6y^2 = -\frac{1}{2}x^2 + 1536 \][/tex]

This can also be written in standard form as:

[tex]\[ x^2 + 12y^2 - 3072 = 0 \][/tex]

So, the equation of the curve is [tex]$ x^2 + 12y^2 - 3072 = 0 $.[/tex]

Between 2004 and 2010, the growth rate of the Florida Panther population was approximately 4%. What was the average annual growth rate?

Answers

Hello! So in order to find the annual growth rate, we have to divide the percentage by the number of years. 2004 and 2010 poses a gap of 6 years. We would have to set it up as 4/6. When you divide them, you would get 0.666 or 0.67 when rounded to the nearest hundredth. The average annual growth rate is about 0.67%.

What is the standard form of 14 ten thousands + 12 thousands

Answers

140000 + 12000 = 152000

hope this helps

Is a measure of dispersion that indicates how much scores in a sample vary around the mean of the sample?

Answers

The measure of dispersion that indicates how much scores in a sample vary around the mean of the sample is the standard deviation.

The measure is called STANDARD DEVIATION.
Standard deviation is a mathematical measure that is used to evaluate the difference between the mean value of a set of number and each value in the group. It is calculated as the square root of variance by determining the variation between each data point relative to the mean.

What do March 16, 1948, Feb. 25, 1950, and Aug. 8, 1964 have in common??

Answers

the product of the month and the day is equivalent to the years last two digits

how many times larger is the value of the 8 in 80,351 than the value of the 8 in 95,852

Answers

I believe it is 100 times larger as it is in the hundreds place for one, and the ten thousands place for the other
10000/100= 100

The 8 in 80,351 is 100 times larger than the value of the 8 in 95,852 because the 8 in 95,852 is in the hundreds place and the 8 in 80,351 is in the ten thousands place. 800x100 is 80,000.

Find the derivative of f (x)=(x^2+1)^3 (x^2+2)^6 using chain rule.

Answers

[tex]\bf f(x)=(x^2)^3(x^2+2)^6\impliedby \textit{product rule on the factors} \\\\\\ \cfrac{df}{dx}=[ 3(x^2+1)^2(2x)][(x^2+2)^6]~+~(x^2+1)^3[6(x^2+2)^5(2x)] \\\\\\ \cfrac{df}{dx}=[6x(x^2+1)^2(x^2+2)^6]~+~[12x(x^2+1)^3(x^2+2)^5] \\\\\\ \cfrac{df}{dx}=\stackrel{\textit{common factor}}{6x(x^2+1)^2(x^2+2)^5}[(x^2+2)+2(x^2+1)] \\\\\\ \cfrac{df}{dx}=6x(x^2+1)^2(x^2+2)^5[3x^2+4][/tex]

Find y'' by implicit differentiation. 5x3 + 2y3 = 1

Answers

[tex]\bf 5x^3+2y^3=1\implies 15x^2+\stackrel{chain-rule}{6y^2\cfrac{dy}{dx}}=0\implies 6y^2\cfrac{dy}{dx}=-15x^2 \\\\\\ \cfrac{dy}{dx}=\cfrac{-15x^2}{6y^2}\implies \cfrac{dy}{dx}=\cfrac{-5x^2}{2y^2}[/tex]

The value of y'' will be (- 5x/y² - 25x⁴/2y⁵).

What is implicit differentiation?

In implicit differentiation, we differentiate each side of an equation with two variables by treating one of the variable as a function of other.

Given that;

The equation is;

5x³ + 2y³ = 1

Now, Apply implicit differentiation rule we get;

5x³ + 2y³ = 1

After differentiation;

15x² + 6y² dy/dx = 0

dy/dx = - 15x² / 6y²

dy/dx = -5x²/2y²

Again differentiation;

d²y/dx² = -5/2 (y² × 2x - x² × 2y dy/dx) / y⁴

d²y/dx² = -5/2 (2xy² - 2x²y dy/dx) / y⁴

Substitute value of dy/dx;

d²y/dx² = - 5/2 (2xy² - 2x²y × -5x²/2y²) / y⁴

d²y/dx² = - 5/2 (2xy² + 5x⁴/y) / y⁴

d²y/dx² = - 5x/y² - 25x⁴/2y⁵

y'' = - 5x/y² - 25x⁴/2y⁵

Thus, The value of y'' will be (- 5x/y² - 25x⁴/2y⁵).

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Find the degree of the term -5x squared

Answers

The polynomial degree is 33, the leading term is 4x34x3, and the leading coefficient is 44.Polynomial Degree: 33Leading Term: 4x34x3Leading Coefficient: 4

-5x²

The degree of the term is 2, or quadratic

hope this helps

Let a be a rational number and b be an irrational number. Which of the following are true statements?

A. The sum of a and b is never rational
B. The product of a and b is rational
C. b^2 is sometimes rational
D. a^2 is always rational
E. √a is never rational
F. √b is never rational

Answers

a and b would be correct

How many gallons of a 80% antifreeze solution must be mixed with 60 gallons of 30% antifreeze to get a mixture that is 70% antifreeze?

Answers

Let x be the number of gallons.

(x)(80%) + (60)(30%) = (x+60)((70%)

0.8x + 18 = 0.7x +42

0.8x - 0.7x = 42-18

0.1x = 24

and x = 240 Gal.

how many gallons will it take to mow a lawn if you maintain the rate of 1/2 gallon of gasoline per 1/4 mowed

Answers

recall that one whole is 1, or in this case since the denominator is 4, then 4/4 is 1 whole, so the whole lawn is 4/4.

[tex]\bf \begin{array}{ccll} gallons&mowed\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ \frac{1}{2}&\frac{1}{4}\\\\ g&\frac{4}{4} \end{array}\implies \cfrac{\frac{1}{2}}{g}=\cfrac{\frac{1}{4}}{\frac{4}{4}}\implies \cfrac{\frac{1}{2}}{\frac{g}{1}}=\cfrac{\frac{1}{4}}{\frac{4}{4}}\implies \cfrac{1}{2}\cdot \cfrac{1}{g}=\cfrac{1}{4}\cdot \cfrac{4}{4} \\\\\\ \cfrac{1}{2g}=\cfrac{1}{4}\implies 4=2g\implies \cfrac{4}{2}=g\implies 2=g[/tex]

Write the number 63 in four different ways

Answers

63 in four different ways
1) 63 ones
2) 6 tens and 3 ones
3) 3 tens and 33 ones
4) 4 tens and 23 ones

Solution:

we have been asked to write the number 63 in four different ways. It can be done as follows

[tex]63=60+3[/tex]

Here we are just adding 3 to 60 and finally we get 63.

[tex]63=6\times10+3[/tex]

This one of the many way of writing 63.

[tex]63=70-7[/tex]

Here we have used the concept of subtraction to write 63.

[tex]63=7\times10-7[/tex]

Concept of subtraction and multiplication to write the number 63.

Hence the four ways have been written.

Why is it impossible to list the set of rational numbers using the roster method?

Answers

It is impossible to list the set of rational numbers using the roster method because the set of rational numbers is uncountable/inumerable.

There is no way to list all the members of the set of rational numbers.

solve the following equation for 2 + √4y -3 = 11

Answers

2+√4y-3=11
2+√4y=11+3=14
√4y=14-2=12
root 4y=2y
2y=12,divide both side by 2
y=6

Final answer:

To solve the equation 2 + √(4y - 3) = 11 for y, subtract 2 from both sides, square both sides to remove the square root, then solve for y to find that y = 21.

Explanation:

The question asks to solve the equation 2 + √(4y - 3) = 11 for y. To solve for y, follow the steps below:

First, subtract 2 from both sides of the equation to isolate the square root term: √(4y - 3) = 9.

Now, square both sides of the equation to eliminate the square root: (√(4y - 3))^2 = 9^2, which simplifies to 4y - 3 = 81.

Add 3 to both sides of the equation to isolate the term with y: 4y = 84.

Finally, divide both sides by 4 to solve for y: y = 21.

Therefore, the solution to the equation is y = 21.

translate into an algebraic expression: the difference of six times a number and 8

Answers

6x-8 is the answer to the question

Estimate sin pi/3 if sin pi/2 = 1 and sin 0 = 0 and sin pi = 0

Answers

hello :
sin(π/3) = √3 / 2

Final answer:

To estimate the value of sin pi/3, which is roughly 1.047 or 60 degrees, we can use standard trigonometric values. Since pi/3 is closer to pi/2 than pi, where sin achieves its maximum of 1, the value of sin pi/3 should be closer to 1 than 0. Standard trigonometric values confirm that sin pi/3 = sqrt(3)/2 = 0.866.

Explanation:

To estimate sin pi/3, we can make use of some standard values in trigonometry. Pi is roughly 3.14, hence pi/3 is roughly 1.047. The sin function gives a result of 1 at pi/2 (or 90 degrees), 0 at 0, and again 0 at pi (or 180 degrees). Thus, it achieves its maximum at pi/2 and then decreases to 0 at pi. Intuitively, since pi/3 (or 60 degrees) is closer to pi/2 than to pi, the sin value at pi/3 should be closer to 1 than to 0. From the standard trigonometric values, we know that sin pi/3 = sqrt(3)/2 which is roughly 0.866.

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Lean wants to giftwrap a present she got for her little brother. how many square inches of giftwrap will be needed to cover a box that is 5in × 7in × 3in?

Answers

check the picture below.

so.. notice, the box for the gift is really just a rectangular prism, which is really just 6 rectangles stacked up to each other at the edges.

the front and back are two 5x3 rectangles

the left and right are just two 3x7 rectangles

and the top and bottom are just two 5x7 rectangles

so, just get the area of each, sum them up, and that's the area of the rectangular prism and thus of the box, and that's how many in² she will need.

subtract the quotient of 15/3 from the sum of 33 and 7

Answers

quotient is division

so 15/3 = 5

sum is addition so 33+7 = 40

40-5 = 35

A car travels 182 miles in 3 hours and 15 minutes. How many miles does it travel per hour?

Answers

To solve this, we'll use the formula distance=rate*time. There's just one problem here: we need all of our time to be in the same units. Let's convert the 15 minutes into hours:
[tex]15min*\frac{1hour}{60min}=0.25hr[/tex]

Then we just use the formula:
[tex]d=182*0.25[/tex]

15 minutes = 15/60 = 0.25 hrs + the 3 hrs = 3.25 hrs

182 / 3.25 = 56 miles per hr

Generate a process that would generate random numbers between –1 and 1 for x and y positions of 10000 points and count how many points fall with the circle, then determine an estimated version of π. (see below to generate floating point random numbers. this generation is not needed to describe the process, but to implement the process)

Answers

#!/usr/bin/env python

import random
import math
count_inside = 0
for count in range(0, 10000): d = math.hypot(random.random(), random.random())
if d < 1: count_inside += 1
count += 1
print 4.0 * count_inside / count

Final answer:

The question is about using the Monte Carlo method to estimate the value of π, by generating random points in a square, counting how many fall inside a unit circle, and finally using this count to calculate π.

Explanation:

This question involves the implementation of a famous problem in computational mathematics known as the Monte Carlo method for estimating the value of π:

First, initialize a variable, say 'count', to 0. This variable will keep track of the number of points falling within the circle.Next, carry out a 'for' loop to generate 10000 points. Each point will have x and y coordinates, each a random floating point number between -1 and 1.For each generated point (x, y), calculate the distance from the point to the origin (0,0), which is sqrt(x^2 + y^2). If this distance is less than or equal to 1, it means that the point lies within the unit circle, so increment the 'count' variable by one.After all 10000 points have been generated and tested, 'count' will hold the total number of points lying within the circle. To determine an estimation of π, use the formula 4 * (count / total_number_of_points).

This process is based on the mathematical fact that the ratio of the area of a unit circle to the square it is inscribed in is π/4.

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1.4t-0.4(t-3.1)=5.8

What is T?

Answers

1.4t-.4t+1.24=5.80

t+1.24=5.80

t=4.56

Solve for W

A=2Lw+2Lh+2wh

Answers

A = 2LW + 2LH + 2WH....subtract 2LH from both sides
A - 2LH = 2LW + 2WH...factor out w on the left side
A - 2LH = W(2L + 2H) ....divide both sides by (2L + 2H)
(A - 2LH) / (2L + 2H) = W

The sum of three consecutive numbers is 72. What is the largest of these numbers?

Answers

3 consecutive numbers....x, x + 1 and x + 2

x + x + 1 + x + 2 = 72
3x + 3 = 72
3x = 72 - 3
3x = 69
x = 69/3
x = 23

x + 1 = 23 + 1 = 24
x + 2 = 23 + 2 = 25

so ur numbers are 23,24,25 with 25 being the largest

25 Is the largest number too add up to the sum.

How many elements are in the set (A,B,C)

Answers

The answer is:
A has 25 elements
B has 30 elements
C has 35 elements

the answer to this question is 1 I believe

Suppose John opens a savings account with $1,000 that compounds interest daily. The APR at the time John deposits the account is 3.5%. He makes no withdrawals or deposits. What is his APY to the nearest hundredth of a percent after 1 year?

Answers

[tex]\bf \qquad \qquad \textit{Annual Yield Formula} \\\\ \left. \qquad \qquad \right.\left(1+\frac{r}{n}\right)^{n}-1 \\\\ \begin{cases} r=rate\to 3.5\%\to \frac{3.5}{100}\to &0.035\\ n= \begin{array}{llll} \textit{times it compounds per year} \end{array}\to &365 \end{cases} \\\\\\ \left(1+\frac{0.035}{365}\right)^{365}-1[/tex]

A restaurant uses 44 pounds of potatoes for a party of 1212 people. If they are cooking potatoes for a party of 60 people, what should they do?

Answers

use 5 times more potatoes

Can the sum of two negative numbers ever be positive?

Answers

no
two negatives equal positive, and one negative and one positive is i think negative

there can be a negative sum

is a integer a rational number

Answers

yes. it is. a rational number includes whole,natural and integers

Yes, it is. Integers, whole numbers, and natural numbers are all rational numbers.

The equation 22 + 0.15p =c

Answers

You have inadvertently left out some of the instructions for this problem.

22 + 0.15p =c could be solved for p; that's one thing you could do now.

Subtracting 22 from both sides, 0.15p = c - 22

Dividing both sides by 0.15, p = (c-22)/0.15 , or p = (20/3)(c-22).

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