Using properties of parallelograms, RSTU is a parallelogram that has vertices R (-3,1), S (3,4), and T( 6,2(. What are the coordinates of point U.
Answers
Answer:
(0, -1)
Step-by-step explanation:
A parallelogram is a quadrilateral (has four sides) in which opposite sides are parallel to each other. Also for a parallelogram, the opposite sides and angles are equal to each other.
Hence for parallelogram RSTU, RS // TU and RU // ST
Let the coordinate of U be (x , y). Two lines are parallel to each other if their slopes are equal, hence:
Slope of RS = (4 - 1) /[3 - (-3)] = 3/6 = 0.5
Slope of ST = (2 - 4) /[6 - 3] = -2/3
Slope of RU = (y - 1) /[x - (-3)] = (y - 1) / (x + 3)
Slope of TU = (y - 2) /[x - 6]
Slope of RU = Slope of ST
(y - 1) / (x + 3) = -2/3
3y - 3 = -2x -6
2x + 3y = -6 + 3
2x + 3y = -3 (1)
Slope of RS = Slope of TU
0.5 = (y - 2) /[x - 6]
0.5x - 3 = y - 2
0.5x - y = 1 (2)
Solving 1 and 2 simultaneously gives:
x = 0, y = -1
Therefore the coordinates of U = (0, -1)
Related Questions
Which number is 1/10 the value of 600?
Answers
Answer:
60
Step-by-step explanation:
Simply multiply to find your answer:
Answer = 600 x 1/10
Simplify. Divide:
600 x 1/10 = 600/10 = 60
60 is your answer.
~
Answer:
[tex] \frac{1}{10} th \: of \: the \: value \: 600 \\ \frac{1}{10} \times 600 \\ 60 \: is \: the \: required \: number.[/tex]
order 9%, 0.03, 0.7% and 0.004 from least
to greatest
Answers
What is the solution to the inequality 5.25- b
6.5?
Answers
-b > 6.5 - 5.25
b < 1.25
Hope this helps!
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three-fourths of the sum of six times a number and twelve distribute
Answers
Answer:
Step-by-step explanation:
Let x be the number.
6 times the number = 6*x = 6x
Sum of 6 times of a number and twelve = 6x + 12
Three-fourths of the sum of 6 times of a number and twelve = [tex]\frac{3}{4}(6x +12)[/tex]
[tex]\frac{3}{4} ( 6x + 12) = \frac{3}{4}*6x + \frac{3}{4}*12\\\\[/tex]
[tex]= \frac{3}{2}*3x + 3*3\\\\=\frac{9}{2}x + 9[/tex]
A bird leaves its nest and travels 18 miles per hour downwind for x hours. On the return trip, the bird travels 3 miles per hour slower and has 5 miles left after x hours.
a. What is the distance of the entire trip? (In miles)
b. How long does the entire trip take? (In hours and minutes and seconds)
Answers
9514 1404 393
Answer:
60 miles3 hours 40 minutes 0 secondsStep-by-step explanation:
The relation between speed, distance, and time is ...
distance = speed × time
a) The distance the bird traveled downwind is ...
(18 miles/hour)(x hours) = 18x miles
3 miles per hour slower than 18 miles per hour is 15 miles per hour. So the distance in miles the bird traveled after x hours on the return trip is ...
15x = 18x -5
5 = 3x . . . . . . add 5 -15x
x = 5/3 . . . . . .divide by 3
Then the distance traveled downwind is ...
18x = 18(5/3) = 30 . . . . miles
and the time for the return trip is ...
(30 mi)/(15 mi/h) = 2 h . . . . . for the entire return trip
So, the entire round trip is 2×30 miles = 60 miles.
__
b) The time for the entire trip is ...
5/3 h downwind + 2 h return = 3 2/3 h = 3 hours 40 minutes 0 seconds
Dan invests £1600 into his bank account. He receives 3.5% per year simple
interest. How much will Dan have after 2 years? Give your answer to the
nearest penny where appropriate.
Answers
Answer:
171200 pennies
Step-by-step explanation:
Amount after 2 years = Principal + Interest
Given
Principal = £1600
Rate = 3.5%
Time = 2years
Get the interest
Interest = PRT/100
Interest = 1600*3.5*2/100
Interest = 32 * 3.5
Interest = £112
Get the amount after 2 years;
Recall that:
Amount after 2 years = Principal + Interest
Amount after 2 years = 1600 + 112
Amount after 2 years = £1712
Hence the amount Dan will have after 2 years is £1712
1712 pounds = (1712 * 100)penny
1712 pounds = 171200 pennies
Find the length of XY.
Answers
Answer:
XY = 50
Step-by-step explanation:
Triangle given in the picture,
Point B, C and D are the midpoints of the sides of the triangle.
By applying midsegment theorem in the given triangle,
"Segment joining the midpoints of two sides of a triangle is parallel and half of the length of the third side"
CD = [tex]\frac{1}{2}(XY)[/tex]
25 = [tex]\frac{1}{2}(XY)[/tex]
XY = 50
Therefore, XY = 50 is the answer.
if there is one store and they are selling 10 pens for 8.99 and they are selling 25 pens for 19.75 witch one is better explian
Answers
25 pens is better because if you see the cost of one it will be cheaper
All of the following would make a formal proof incomplete except what?
A) A lack of justifications
B) Incomplete sentences
C) Errors in logic
D) Incorrect reasons for statements
Urgent I need this for tonight please!!!
Answers
Answer:
b incorrect sentences
Step-by-step explanation:
got it right on my test
HELP HELP HELP
The function t relates the age of a plant fossil in years to the percentage c of carbon remaining in the fossil relative to when it was alive.
t(c)=-3970.9(ln c)
Use function t to complete the statements.
A fossil with 47% of its carbon remaining is approximately how old
1. 2998
2 11,910
3 7550
A fossil that is 7000 years old will have approximately
1. .2%
2. 57%
3 17%
Of its carbon remaining.
Select the correct answers
Answers
Answer:
2998 ; 17%
Step-by-step explanation:
Given the function:
t(c)=-3970.9(ln c)
c = % of carbon remaining ; t = time
1.) c = 47% = 47/100 = 0.47
t(0.47) = - 3970.9(In 0.47)
t = - 3970.9 * −0.755022
t = 2998.119
t = 2998
B.)
t = 7000
t(c)=-3970.9(ln c)
7000 = - 3970.9(In c)
7000 / - 3970.9 = In c
−1.762824 = In c
c = exp(−1.762824)
c = 0.1715596
c = 0.1715596 * 100%
c = 17.156% ; c = 17%
Answer: For plato family
The function t relates the age of a plant fossil, in years, to the percentage, c, of carbon-14 remaining in the fossil relative to when it was alive.
Use function t to complete the statements.
A fossil with 47% of its carbon-14 remaining is approximately
years old.
A fossil that is 7,000 years old will have approximately
17% of its carbon-14 remaining.
Step-by-step explanation:
The first box is 2,998
The second box is 17%
Will give Brainly
Find the measure of b.
Answers
Answer:
b= 90 degrees
Step-by-step explanation:
opposite sides
1 A farmer needs to plow a 8-acre field. She starts by plowing – of the field. 6 How many acres does the farmer plow?
Answers
What is the slope of a line that is perpendicular to the graph ofy = 7x+1?
Answers
Answer: 4pi , second part is 5pi/2 + 4npi and third part is 7pi/2 + 4npi
Step-by-step explanation: Edge 2021
Which of the following statements are true?
The value of the 5 in 592,841 is 10 times the value of the 5 in 358,764.
The value of the 6 in 861,257 is 10 times the value of the 6 in 651,042.
The value of the 8 in 358,764 is 10 times the value of the 8 in 592,841.
The value of the 5 in 592,841 is in of the value of the 5 in 358,764.
The value of the 6 in 861,257 is in of the value of the 6 in 651,042.
The value of the 8 in 358,764 is id of the value of the 8 in 592,841.
Answers
Answer:
5/6 is eaqual to 2.5/3
Step-by-step explanation:
Find the area of the structure.
Answers
Answer:
8/9 in squared
Step-by-step explanation:
because one block is 1/9, and there are 8
Sally goes to the store and buys a camera for $65. The store is
running a discount of 10%. What is the price of the camera after the
discount?
Answers
Answer:
58.50
Step-by-step explanation:
10.12 ÷ 4.4 =
A
0.23
B
2.3
C
5.72
D
57.2
Answers
Answer:
The answer is 2.3 B It is just by dividing
Answer:
B. 2.3
Step-by-step explanation:
Change the divisor 4.4 to a whole number by moving the decimal point 1 place to the right. Then move the decimal point in the dividend the same, 1 place to the right.
We then have the equations:
101.2 ÷ 44 = 2.3
and therefore:
10.12 ÷ 4.4 = 2.3
out of 800 cards in a album each page of the album holds 8 cards if 66% of the album is empty how many pages are filled with cards
Answers
Answer:
ummm you are going to do terrible on on your test jk
Step-by-step explanation:
Write an equation of the line that has a slope of -5 and a y intercept of 4 in slope intercept form.
PLEASE HELP!!!
Answers
Hope this helps:)
m = slope
b = y-intercept
Ans: y = -5x + 4
Compare the values.
9 × 10^2 is _____ times as much as 3 x 10^-2.
A) 6 x 10^4
B) 3 x 10^-4
C) 3 x 10^4
D) 6 x 10^0
please i need help **Will mark BRAINLIEST**
Answers
k I need help again the last part says triangles
Answers
C
One side is 3, another is 6, and the last side is 9
Hope this helps :)
Pls give me BRAINLIEST
What is the equation of the line that has a slope of 14
and goes through the point (8,−3)?
y=1/4x−5
y=1/4x+5
y=1/4x−11
y=1/4x+1
Answers
Answer:
y=1/4x+1
please mark as brainliest
Find the local maximum and minimum values of f(x)=x^3-6x^2+5
Answers
Answer:
Local maxima at x=0
Local minima at x=4
Step-by-step explanation:
47 + 34 - 3k ТІЗk + Зk
solve for k show your work
Answers
Answer:
47+34= 3k + 3k + 3k + 3k
Step-by-step explanation:
6¾
Solve each of the following equations.
(4b + 11)(3b - 7) = 0
Answers
Answer:
4b = 4(11/4)
3b = 3(7/3)
I need help with this word problem please
Answers
Answer:
Step-by-step explanation:
Given function is,
f(x) = [tex]x\sqrt{x}[/tex]
We can rewrite this function as,
f(x) = [tex]x^{\frac{3}{2}}[/tex]
a). Domain of the function is [0, ∞)
Derivative of the function in this domain,
f'(x) = [tex]\frac{3}{2}x^{(\frac{3}{2}-1)}[/tex]
= [tex]\frac{3}{2}x^{\frac{1}{2}}[/tex]
Since, f'(x) > 0 in the interval [0, ∞)
Function is increasing in the interval [0, ∞)
b). For local maxima and local minima,
Second derivative of the function,
f"(x) = [tex]\frac{3}{2}(\frac{1}{2})x^{\frac{1}{2}-1}[/tex]
= [tex]\frac{3}{4}x^{-\frac{1}{2}}[/tex] > 0
So the function should have a local minima.
But the function is continuous in the interval x ≥ 0,
There is no local minima (only absolute minima).
c). Since, second derivative is undefined at x = 0,
There are no inflection points.
d). Since, f"(x) > 0 in the interval [0, ∞)
Concavity of the curve is UPWARDS.
There are 100 classes at Sun Valley Magnet School. 45% of the classes are Math and Science. How many classrooms are not Math and Science?
Answers
what is the equation
Answers
[tex]y - y_1 = m(x - x_1)[/tex]
[tex]y_1 = y - coordinate \: \: point \\ x_1 = x - coordinate \: \: point[/tex]
From the given equation.[tex]y + 8 = 4(x - 5)[/tex]
[tex]y - ( - 8) = 4(x - ( + 5))[/tex]
Answer[tex] \large \boxed{( - 8,5)}[/tex]
can someone please help meeee
Answers
97^2 = 9409
65^2 = 4225
4225 + b^2 = 9409
b^2 = 5184
b = 72
then you need to add 65 and 72 to get 137
137 - 95 = 42
42 kilometers closer
Part 1: Determine the domain.
DOMAIN:
Answers
Answer:
The domain is -2 to positive 2.