4. A rectangle is a four-sided flat shape where every interior angle is a right angle.
Therefore, opposite sides are parallel and consecutive sides are perpendicular.
Rae is drawing rectangle PQRS on a coordinate plane. The rectangle has
coordinates P(-1,2), Q(2,4), R(x, y), and S(3,-4).
Answers
Answer:
coordinates of R(x,y) is R(6,-2).
Step-by-step explanation:
A. we know that
The rectangle has coordinates P (-1,2), Q(2,4), R(x,y) and S(3,-4)
using a graph tool
see the attached figure
Step 1
Find the slope of the line PS
the slope is equal to
m=(y2-y1)/(x2-x1)
mPS=(-4-2)/(3+1)=-6/4=-3/2
Step 2
Find the equation of the line QR
we know that
PS and QR are parallel lines
so
their slopes are the same
mQR=-3/2
with mQR and the point Q(2,4) find the equation of the line
y-y1=m*(x-x1)
y-4=(-3/2)*(x-2)
y=(-3/2)*x+3+4--------> y=7-(3/2)*x
Step 3
Find the equation of the line SR
we know that
SR and QR are perpendicular lines
so
the product of their slopes is equal to minus one
mSR*mQR=-1
mSR=2/3
with mSR and the point S(3,-4) find the equation of the line SR
y-y1=m*(x-x1)
y+4=(2/3)*(x-3)
y=(2/3)*x-2-4---------> y=-6+(2/3)*x
Step 4
Find the intersection of the lines QR and SR
we know that
the intersection of the lines QR and SR is the point R
y=7-(3/2)*x------> equation 1
y=-6+(2/3)*x------> equation 2
equate equation 1 and equation 2
7-(3/2)*x=-6+(2/3)*x
7+6=(2/3)*x+(3/2)*x
13=(2/3)*x+(3/2)*x
Multiply by 6 both sides
6*13=4*x+9*x
13*x=6*13
x=6
find the value of y
y=-6+(2/3)*x------> y=-6+(2/3)*6---------> y=-6+4
y=-2
therefore, the coordinates of point R are (6,-2)
Related Questions
I need someone to explain functions and functional symmetry to me. This is very important, so if you do not have a legit answer, you will get reported.
Answers
Symmetrical functions can be about the x and y axis. Essentially, if we reflect the graph across the y or x axis, we get the same graph. Some other graphs can be reflected across both the x and y axis at the same time and be symmetrical. These can be classified as odd and even functions. You can test this by replacing x and y with -x and -y and simplify the equation. If the results comes out to be the same as the original, it is symmetrical across the origin.
Best of Luck!
Answer:
a shape that has reflective symmetry either x or y axis of origin.
in other words... it's a mirror image.
Christina is paid biweekly. Her annual salary is 37,500. What is her biweekly salary, rounded to the nearest cent?
Answers
Answer:
$1,423.08
Step-by-step explanation:
[tex]\frac{37000}{26} = 1,423.076[/tex] rounded to the nearest cent it becomes 1,423.08.
*Remember that there are 26 biweekly periods in a year. Divide her annual salary (37,500) by 26.
The biweekly salary, rounded to the nearest cent is 1,423.08.
It is required to find the solution.
What is rounded number?A number that is easily multiplied, divided, etc., and especially a number that ends in zero.
Given :
Christina is paid biweekly. Her annual salary is 37,500.
According to given question we have,
We know that there are 26 biweekly periods in a year. Divide her annual salary (37,500) by 26.
37500/26=1423.076
Rounded to the nearest cent it becomes 1,423.08.
Therefore, the biweekly salary, rounded to the nearest cent is 1,423.08.
Learn more about rounded number here:
brainly.com/question/17561230
#SPJ6
how do i solve for equations that have 2 variables
Answers
Answer:
To solve for an equation with two variables, substitute a zero(0) into the other variable and find one variable.
Step-by-step explanation:
To solve for an equation with two variables, substitute a zero(0) into the other variable and find one variable.
Simple Example:
3x+3y=12
Substitute 0 as y,
3x+0=12
3x=12
12/3=4
x=4
Now substitute 4 into the main equation,
3(4)+3y=12
12+3y=12
-12 -12
3y=0
0/3=0
y=0
So the answer is
3(4)+3(0)=12
12=12
Please 20 points like rn 5 mins left on test
Answers
Answer: counterclockwise rotation of 90° and a reflection over y axis
Step-by-step explanation:
A number y plus 7 is at least 16
Answers
Answer:
yes
Step-by-step explanation:
you are correct
Answer/Step-by-step explanation:
[tex]16-7=9[/tex]
Therefore [tex]y\geq9[/tex]
There was no picture to go off of, but this should be correct anyways!
Please mark Brainliest!!! =Danswer for p=2l+2w for l
Answers
Answer:
[tex]I=\frac{p-2w}{2}[/tex]
Step-by-step explanation:
[tex]p=2I+2w\\\\p-2w=2I+2w-2w\\\\p-2w=2I\\\\\frac{p-2w}{2}= I[/tex]
Pls help I don’t understand
Answers
B) a bisector
B) bisector!!!
I don’t understand this
Answers
Given that f(x) = 2x - 2 and g(x) = 5x. Find the value of f(0) + g(3).
Answers
Step by step explanation:
f(0)=2(0) - 2
=0 - 2
= -2
g(3) = 5(3)
= 15
f(0) + g(3)
= -2 + 15
=13
Tanya is 6 times younger than her great-grandfather. If a zero is placed between the digits of her age, it will read as the age of her great-grandfather. How old is Tanya?
Answers
Answer:
Tanya is 18 years old.
Step-by-step explanation:
In order to determine this, we assume the following
x = tens digit of the age of Tanya, and also the hundreds digit of Tanya's great-grandfather age
y = units digit of the age of Tanya, and also the units digit of Tanya's great-grandfather age
Therefore, we have:
10x + y = (1 / 6) * (100x + y)
Multiply both sides by 6, we have:
[10x + y] * 6 = [(1 / 6) * (100x + y)] * 6
60x + 6y = 100x + y
Collect the like terms, we have:
6y - y = 100x - 60x
5y = 40x
Divide through by 5, we have:
y = 8x
That is,
8x = y
Note that x and y has to be single digits. This can only be obtained only when x = 1 and y = 8. And given how x and y is defined above, we have:
The age of Tanya = 18
This can be verified as follows:
18 = 108 / 6
18 * 6 = 108
108 = 108
Therefore, Tanya is 18 years old.
X/2-5=25???????
HELP!!!!
Answers
Answer:
x = 60
Step-by-step explanation:
X/2-5=25
Add 5 to each side
X/2-5+5=25+5
x/2 = 30
Multiply each side by 2
x/2*2 = 30*2
x = 60
Answer:
60
Step-by-step explanation:
x/2 - 5 =25 /×2
x - 10 =50
x=50 +10
x=60
When they ask, for example "What is the value of √100?" are they asking what is the square root of 100?
Answers
Answer: I need help on this tooooooo
Step-by-step explanation:
Answer:
Yes. The term [tex]\sqrt{}[/tex] means "square root".
If there is a number beside the symbol, for example [tex]\sqrt[3]{}[/tex], this means to cube root. But if there is no number, it just simply means square root.
Use the commutative property to write an equivalent expression to 4g + 13, and show that they are equivalent for g = 10 and g = 2. Complete the statements. If you change the order of the terms you can create the equivalent expression . After substituting 10 for g, the expressions are and . After substituting 2 for g, the expressions are 4(2) + 13 and 13 + 4(2). The expressions are equivalent because they both have a value of when g = 10 and a value of when g = 2.
Answers
Answer: 1= ( 13 + 4g )
2= ( 4(10) + 13 )
3= ( 13 + 4(10) )
4= ( 53 )
5= ( 21 )
Step-by-step explanation:
The equivalent expression by cumulative property is,
[tex]4g+13=13+4g[/tex]
Commutative property :The commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer.
[tex]a+b=b+a[/tex]
Given expression is, [tex]4g+13[/tex]
The equivalent expression by cumulative property is,
[tex]4g+13=13+4g[/tex]
For [tex]g=10[/tex],
[tex]4(10)+13=13+4(10)\\\\40+13=13+40\\\\53=53[/tex]
Learn more about the commutative property here
https://brainly.com/question/2475734
Find the values of x for which f(x) = g(x).
f(x) = x2 + 2x + 1,
g(x) = 5x + 19
Answers
Can someone help with this
Answers
Answer:
[tex]GH=2\sqrt{10}[/tex]
Step-by-step explanation:
Considering each is square is 1x1.
We have the points G(-2, -3) and H(0, 3).
Using the distance formula:
[tex]$d=\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$[/tex]
[tex]$d=\sqrt{(-2 - 0)^2 + (-3 - 3)^2}$[/tex]
[tex]$d=\sqrt{(-2 )^2 + (-6)^2}$[/tex]
[tex]$d=\sqrt{4 +36}$[/tex]
[tex]d=\sqrt{40}=2\sqrt{10}[/tex]
Also, using the Pythagorean theorem:
[tex]a^2+b^2=c^2[/tex]
[tex]2^2+6^2=c^2[/tex]
[tex]4+36=c^2[/tex]
[tex]c=GH=\sqrt{40}=2\sqrt{10}[/tex]
a pound of chocolates costs 6 dollars. chris buys p pounds. write an equation to represent the total cost c that chris pays.
Answers
Answer:
y=6x+p
Step-by-step explanation:
Answer:
6p= c bc each pound cost $6 so if u have p pounds, 6p would equal to the cost or c
Kyle ran 150 feet and 15 seconds how many hours would it take him to run 30 miles
Answers
Answer:
b. 4.4 hours
Step-by-step explanation:
We can use the conversion factor 1 mi/h = 22/15 ft/s. The required relation is ...
time = distance/speed
[tex]\dfrac{30\text{ mi}}{\left(\dfrac{150\text{ ft}}{15\text{ s}}\right)}\times\dfrac{\left(\dfrac{22\text{ ft}}{15\text{ s}}\right)}{\left(\dfrac{1\text{ mi}}{1\text{ h}}\right)}=\dfrac{(30)(22)\text{\h}}{150}\text{ h}=4.4\text{ h}[/tex]
Assuming Kyle can keep up the pace for that distance, it would take him 4.4 hours to run 30 miles.
Help please, I need it
Answers
Answer:
2) c) (x-3)² + (y+2)² = 25
5) x^2 +y^2 -8x -16y +54 = 0
6) x^2 +y^2 -10x -12y +36 = 0
Step-by-step explanation:
2) The standard form equation for a circle is ...
(x -h)^2 +(y -k)^2 = r^2
You are given the center: (h, k) = (3, -2) and a point on the circle. So, the equation will be ...
(x -3)^2 +(y +2)^2 = r^2
Since we know a point on the circle we know that ...
(7 -3)^2 +(1 +2)^2 = r^2 = 16 +9 = 25
So, the circle's equation is ...
(x -3)^2 +(y +2)^2 = 25 . . . . . matches choice C
__
5) As in the previous problem, the standard form equation is ...
(x -4)^2 +(y -8)^2 = (-1-4)^2 +(7-8)^2 = 25+1 = 26
To put this in general form, we need to subtract 26 and eliminate parentheses.
x^2 -8x +16 +y^2 -16y +64 -26 = 0
x^2 +y^2 -8x -16y +54 = 0
__
6) A circle tangent to the y-axis will have a radius equal to the x-value of the center point.
(x -5)^2 +(y -6)^2 = 5^2
x^2 -10x +25 +y^2 -12y +36 = 25
x^2 +y^2 -10x -12y +36 = 0
2. Deena drove 585 miles in 9 hours. How fast did she drive in 1 hour?
Answers
Answer:
Deena drove 65 miles in 1 hour
Step-by-step explanation:
hope it helps
Adriana earned a gross income of $46,250 last year. She made $569.10 in IRA contributions, donated $841 to her favorite charity and paid $1,399.03 in home mortgage interest. If Adriana claims a standard deduction of $5,700 and her exemption is $3,650, what is her taxable income?
a.) $34,090.87
b.) $36,330.90
c.) $39,790.87
d.) $34,931.87
Answers
Answer:
B
Step-by-step explanation:
Patrick left an $8 tip on a $50 restaurant bill. What percent tip is that?
Answers
It would give you .16 which is 16%.
If 3x + 2 = 6, what is the value of x?
Answers
Answer:
x = [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
Given
3x + 2 = 6 ( subtract 2 from both sides )
3x = 4 ( divide both sides by 3 )
x = [tex]\frac{4}{3}[/tex]
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = 1.33}}}}}[/tex]
Step-by-step explanation:
[tex] \star \sf \: \: {3x + 2 = 6}[/tex]
[tex] \text{ \sf{ Step 1}}[/tex] : Move 2 to right hand side and change it's sign
[tex] \longmapsto{ \sf{3x = 6 - 2}}[/tex]
[tex] \text{ \sf{ Step \: 2 \: }}[/tex] : Subtract 2 from 6
[tex] \longmapsto{ \sf{3x = 4}}[/tex]
[tex] \text{ \sf{ Step \: 3}}[/tex] : Divide both sides by 3
[tex] \longmapsto{ \sf{ \frac{3x}{3} = \frac{4}{3} }}[/tex]
[tex] \text{ \sf{ Step \: 4 \: }}[/tex] : Calculate
[tex] \longmapsto{ \sf{x = 1.33}}[/tex]
The value of x is 1.33
Hope I helped!
Best regards! :D
~TheAnimeGirl
Solve the equation for x
3x + 5 = 14
Answers
Answer:
[tex]x=3[/tex]
Step-by-step explanation:
[tex]3x+5=14[/tex]
Subtract 5 from both sides:
[tex]3x+5-5=14-5[/tex]
[tex]3x=9[/tex]
Divide both sides by 3:
[tex]\frac{3x}{3}=\frac{9}{3}[/tex]
[tex]x=3[/tex]
help me for a kith please
Answers
Answer:
Kith means becoz i am from India
Compare an angle having a measure of 120° With that of an angle whose measure is five pi over 6 rad explain your reasoning
Answers
Answer:
Step-by-step explanation:
et A=120°
and B=5Pi /6
Pi radians ---------> 180°
x<----------------------- 120°
so x =120 x Pi / 180 = 12 xPi / 18 = 2 Pi/3
so A = 2Pi / 3 radian
let 's compare A and B
we know that 5Pi /6 = 0.8 Pi and 2P/3= 0.6 Pi, 0.8>0.6,
finally 5Pi /6 > 2P/3
so B>A
what is the square root of 5
Answers
Answer:
The square root of 5 is 2.2360679775
Graph y=-2x+5 only please help quickly
I’ll give brainliest to the quickest person
Answers
Answer:Slope: − 2 y-intercept: ( 0 , 5)x 0 5/2 y 5,0
Step-by-step explanation:
Given the formula C = 5(f-32)/9, find the value of C if F is 68
Answers
Answer:
Step-by-step explanation:
C = 5(68 - 32)/9
= 5(36)/9
= 180/9 = 20
C = 20
tyrone walked 8 miles in a walkathon at a speed of 2 mph how long was he walking
Answers
Answer:
4 hours
Step-by-step explanation:
Distance / Velocity = Time
In this case, 8 / 2 = 4
Please 20 points ASAP
Answers
b. (2, 7)
c. (1, -1)
hope this helps :)
Answer:
a. -1, 1
b. 2, 7
c. 1, 1