PLEASE HELP!!!!! Sometimes two transformations, one performed after the other, have a nice description as a single transformation. For example, instead of translating 2 units up followed by translating 3 units up, we could simply translate 5 units up. Instead of rotating 20 degrees counterclockwise around the origin followed by rotating 80 degrees clockwise around the origin, we could simply rotate 60 degrees clockwise around the origin. Can you find a simple description of reflecting across the x-axis followed by reflecting across the y-axis?
Answer: A rotation of 180° around the origin.
Step-by-step explanation:
When we have a point (x, y) and we want to reflect it over a given line, the distance between the point and the line remains invariant under the transformation.
This is equivalent as a rotation around a point, the "radius" of the circle that we are creating when we do a rotation is constant.
Now, let's analyze our case:
First a reflection over x-axis, and then a reflection over the y-axis.
This means that if our point starts in quadrant 1 then:
-The reflection over the x-axis will leave our point in quadrant 4.
-The reflection over the y-axis will leave our point in quadrant 3.
Now, if our point stated on quadrant 2.
-The reflection over the x-axis will leave our point in quadrant 3.
-The reflection over the y-axis will leave our point in quadrant 4.
So essentially, these transformations "move" our point to the opposite quadrant, such that the rules of the reflection are applied.
This means that:
The distance between our point and the x-axis does not change.
The distance between our point and the y-axis does not change.
But if the distances to both axes do not change, then the distance between our point and the origin also does not change.
This means that we can find a rotation that is equivalent to this transformation.
So we must look at a rotation that moves our point 2 quadrants.
a rotation that moves our point 2 quadrants will be:
A rotation of 180° around the origin.
find the value of x that makes the lines parallel 3x-9 2x-1
Answer:
x=8
Step-by-step explanation:
set the equations equal to themselves and solve
3x-9=2x-1
+9 and -2x
x=8
Check:
3(8)-9=2(8)-1
24-9=16-1
15=15
On a windmill, the tip of one blade moves in a circular motion. The maximum height is 18 feet and the minimum height is 4 feet. The height of the tip of the blade (in feet) can be modeled by the function h(x)=−14sinx+18 h(x)=−14sinx+18 where x is time in seconds. Use the inverse function to determine how many seconds it will take to make a full rotation for one blade.
A 0.3 second
B 0.6 second
C 1.6 seconds
D 3.2 seconds
Answer:
The correction is D
Step-by-step explanation:
From the question we are told that
The maximum height is [tex]h_m = 18 ft[/tex]
The minimum height is [tex]h_i = 4 ft[/tex]
The function that models the height of the blade is [tex]h(x) =- 14 sin(x) + 18[/tex] here x is time in seconds
Now at maximum height
[tex]18 = - 14 sin(x) + 18[/tex]
=> [tex]-14 sin(x) =0[/tex]
=> [tex]sin(x) =0[/tex]
=> [tex]x =sin^{-1}[0][/tex]
=> [tex]x =0 \ s[/tex]
Now at minimum height
[tex]4 = -14 sin(x) + 18[/tex]
=> [tex]-14 = -14 sin(x)[/tex]
=> [tex]sin (x) = 1[/tex]
=> [tex](x) = sin^{-1}[1][/tex]
=> [tex]x = 1.6 \ s[/tex]
Now this values is the time taken to move from the higher position of the blade to the lower position of the blade
Now it will take this same amount of time to complete the circle
So the total time take is
[tex]x_t = 2 * |x|[/tex]
=> [tex]x_t = 2 * 1.6[/tex]
=> [tex]x_t = 3.2 \ s[/tex]
Which fractions are equivalent to
-? Check all that apply.
12
Answer:
2/3
24/36
32/48
are all equivalent to 8/12
Answer:
32/48
Step-by-step explanation:
32 divided by 4 is 8
48 divided by 4 is 12
Solve for a: u = 3b - 2a + 2
If a=2 then you would have u=3b-2(2) or u=3b-4 :)
Answer:
Step-by-step explanation:
B= 2/3a-2//3+1/3u, u equals R, A equals r
A=3/2b+1-1/2u, u equals R b equals R
What is the measure
of ZA, in degrees?
20
3xsquared +13x-10
HELPP PLEASE
Answer:
(x + 5)(3x - 2)
Step-by-step explanation:
Assuming you require the expression factorised.
3x² + 13x - 10
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 3 × - 10 = - 30 and sum = + 13
The factors are + 15 and - 2
Use these factors to split the x- term
3x² + 15x - 2x - 10 ( factor the first/second and third/fourth terms )
= 3x(x + 5) - 2(x + 5) ← factor out (x + 5) from each term
= (x + 5)(3x - 2) ← in factored form
PLZ need serious HELP! No fake or dumb answers
Find the intersection point for the following linear functions.
f(x) = 2x + 3
g(x) = -4x − 27
A. (5,-7)
B. (5,13)
C. (-5,-10)
D. (-5,-7)
Answer:
D) (-5, - 7)
Step-by-step explanation:
Because both lines intersect, they must share a point (have same x and y coordinates).
[tex]2x + 3 = - 4x - 27[/tex]
[tex]2x = - 4x - 30[/tex]
[tex]6x = - 30[/tex]
[tex]x = - 5[/tex]
Substite x for - 5 in any of the equations to find the y coordinate.
[tex]y = 2( - 5) + 3 [/tex]
[tex]y = - 10 + 3[/tex]
[tex]y = - 7[/tex]
The x coordinate for the intersection point is - 5 and the y coordinate is - 7. The intersection point is (-5, - 7)
What is the value of the expression 5(X+3) when X=-3?
Answer:
0
Step-by-step explanation:
5(x+3) replace x with -3
5(-3+3)
5(0)
0
HURRY PLEASE!! I’ll mark you as brainliest
Evan has agreed to mow his neighbor's lawn each week. His neighbor will pay him $15 each week. Evan will
also baby-sit some hours each week for $10 per hour. Evan needs to make at least $100 per week to save for
his own car, but if he makes $200 or more each week his parents will charge him rent. How many hours h
should Evan agree to baby-sit each week to avoid paying rent but still be able to save for his car?
Non example of complex fraction.
Answer:
42/6
Step-by-step explanation:
:P
Joyce paid $31.50 for an item at the store that was 55 percent off the original price. What was the original price?
Give your answer to the nearest cent.
The original price of the item was $70 if Joyce paid $31.50 for an item at the store that was 55 percent off the original price.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
Let x be the original price of the item. Then, we can write the equation:
x - 0.55x = 31.50
from the given expression we need to solve the value of x to get the original price if Joyce paid $31.50 for an item at the store that was 55 percent off the original price
Simplifying the given equation, we get:
0.45x = 31.50
Dividing both sides by 0.45, we get:
x = 70
Therefore, the original price of the item was $70.
To learn more about Algebraic expression from given link.
https://brainly.com/question/28884894
#SPJ1
Can someone help please ??
Answer:
a)1 , 5 , 9 , 13 , 17, 21 , 25
Find the product.
[tex](b-9)(b+9)[/tex]
Suzy's Sculpting gym charges a $10 application fee and $12 per month for membership. Tami's Toning does not charge an application fee, but charges $14 per month for membership. After how many months will the total cost of membership be the same for both gyms?
Answer:
Total cost of membership will be the same for both gyms after 5 months.
Step-by-step explanation:
Given: Suzy's Sculpting gym charges a $10 application fee and $12 per month for membership.
Tami's Toning does not charge an application fee, but charges $14 per month for membership.
To find: After how many months will the total cost of membership be the same for both gyms
Solution:
Let [tex]t[/tex] denotes number of months after which total cost of membership will be the same for both gyms
For Suzy's Sculpting gym,
Total charges [tex]= 10+12t[/tex]
For Tami's Toning,
Total charges [tex]=14t[/tex]
Now solve [tex]10+12t=14t[/tex]
[tex]10+12t=14t\\10=14t-12t\\10=2t\\t=\frac{10}{2}\\ t=5[/tex]
So, total cost of membership will be the same for both gyms after 5 months.
HELP PLS HOW DO U DO THIS
Answer:
10
Step-by-step explanation:
1/3 of 24 is 8, and 1/4 is 6. 8+6=14, and 24-14=10. So I think that 10 people brought chips.
Answer:
10
Step-by-step explanation:
24 ÷ 3 = 8 so one third is 8
24 ÷ 4 = 6 so one fourth is 6
8 + 6 = 14 (14 people brought drinks or dessert)
24 - 14 = 10
ten people brought chips.
Find an ordered pair (x, y) that is a solution to the equation.
5x + y=9
Answer:
Some points are: (1, 4), (0, 9), and (3, -6), just to name a few.
Step-by-step explanation:
We can find out an ordered pair for this equation by plotting the line 5x + y = 9 on a graph. If you graph 5x + y = 9, then we see that the point (1, 4) is a point that the line intersects. Let's substitute that values:
5(1) + 4 = 9
Order of operations, multiply first...
5(1) = 5
Then it becomes...
5 + 4 = 9
We can see that 5 plus 4 actually does equal 9, so the point (1, 4) works. Let's try a different point. We can see the point (0, 9) is another point that the line intersects. Same process for this point too.
5(0) + 9 = 9
Then...
5(0) = 0
0 + 9 = 9
We see that 0 plus 9 ALSO works, but let's try one more time. Another point that works is the point (3, -6) Again, same process.
5(3) + -6 = 9
That is equal to:
5(3) - 6 = 9
Simplify...
5(3) = 15
15 - 6 = 9
15 minus 6 works as well! Any point that the line intersects will be a solution for the equation. I hope this helps!
What is the quotient of -32/8?
Answer:
Hope it help you
Stayhomestaysafe
Plz mark my answer brainliest✍️✍️
Step-by-step explanation:
[tex] - 32 \div8 = - 4[/tex]Answer is -4
REAL NAME - SHRESTH DUBEY
-4 is the Answer.
-32/8 would be -4
I need an answer for this ASAP thanks.
Answer:
ll
Step-by-step explanation:
A line has a slope of
1/4
and passes through the point (0.2,
4/5
Find the value of b, the y-intercept.
b = ???
Answer:
b = 3/4
Step-by-step explanation:
Using point slope: y - y1 = m(x - x1).
Substitute your given slope, given point, and subsitute 0 in for x and solve for y since the y intercept is the y value when x = 0.
0.2 = 1/5, so 1/5 * 1/4 = 1/20
Therefore: y - 4/5 = 1/4(0 - 0.2) → y - 4/5 = -1/20 → y = 4/5 - 1/20 → 15/20 → 3/4
b = 3/4
Using point slope: y - y1 = m(x - x1).
Substitute your given slope, given point, and subsitute 0 in for x and solve for y since the y intercept is the y value when x = 0.
0.2 = 1/5, so 1/5 * 1/4 = 1/20
Therefore: y - 4/5 = 1/4(0 - 0.2) → y - 4/5 = -1/20 → y = 4/5 - 1/20 → 15/20 → 3/4
Match the correct scenario with the correct unit rate format.
1. meters/second
2. $/pound
3. $/ tire
4. people/class
5. miles/gallons
6. calories/serving
Some helppppp!!!!! I’m having trouble
Help me ASAP major grade
Answer:
$5.58
Step-by-step explanation:
Because divide 12 by 67:
67 ÷ 12 = 5.58
5.58 is the answer
Hope this helped! Pls Brainliest!
Answer:
$5.58
Step-by-step explanation:
$67.00÷12=$5.58
Hope this helps!
Coming in at lunch for extra math help has really paid off! You started out scoring
18 points on each quiz, but your number of points has been increasing 36% per
month for the last 5 months. How many points are you now earning per quiz?
Answer:
83 points.
Step-by-step explanation:
A football team scored a total of 41 points in a Sunday game. They scored 7 points in the first quarter, 10 points in the second quarter, and 7 points in the third quarter. How many points did the team score in the fourth quarter?
41 - 7 - 10 - 7 = 41 - 24 = 17.
The team scored 17 points in the last quarter.
There are 90 people in a group.
A sixth of the people in the group are men.
The number of women in the group is 2 times the number of men in the group
The rest of the people in the group are children.
the number of children in the group : the number of men in the group = n: 1
Work out the value of n.
You must show how you get your answer.
Answer:
n=3
Step-by-step explanation:
90×1/6=15 men
15*2=30 women
90-15-30=45 children
45 children: 15 men
3:1 ratio of children to men
n=3
Question 2 (1 point)
Explain how you used the distribute property to find an equivalent expression for
4 (3+x)
ANYONE ITS WORTH 10 POINTS PLEASE???
Please help me with this.
Answer:
y = (-1/2)x + 4
Step-by-step explanation:
Slope (m): (-1/2)
down one, right two
y-intercept (b): 4
y = mx + b
The slope-intercept equation if the line is [tex]y=-\frac{1}{2}x+4[/tex]
To find the slope, you must put the 2 points into the slope equation.
[tex]\frac{3-4}{2-0}=\frac{-1}{2}[/tex]
And to find the y-intercept, you must find where the line crosses the y-axis.
(0,4)
HELP!!!!!!!!!!!!!!!!!!
Answer:
it is an acute angle
Step-by-step explanation:
less then 90° is a acute and above 90° angle is an obtuse
writing equations of lines
Step-by-step explanation:
Equation of straight line is y=mx+c
choose any two points on straight line
for me I choose:(-3,11) and (3,-1)
use these two points to find gradient,m.
m= (-1-11)/(3-(-3))
m= -2
now, y=-2x+c
choose any point on the straight line
I choose point (3,-1)
sub the point into the equation to find c
-1=-2(3)+c
c=5
equation: y=-2x+5