Alice walks along a road which can be modeled by the equation y=6x, where (0,0) represents her starting point. When she reaches a certain point A, she turns right, so that she is traveling perpendicular to the original road, until she stops at the point (333,0). What was the point A where Alice turned?
Answers
9514 1404 393
Answer:
(9, 54)
Step-by-step explanation:
The first road has a slope of 6 on its graph. So, the perpendicular road will have a slope of -1/6, the negative reciprocal of the slope of the original road. Translating that from y=-1/6x the the right by 333 units, the equation of the second road is ...
y = -1/6(x -333)
The point where Alice turned is the point of intersection of these two equations:
y = 6xy = -1/6(x -333)Substituting for y, we have ...
6x = -1/6(x -333)
36x = -x +333 . . . . . multiply by 6, eliminate parentheses
37x = 333 . . . . . . . . add x
x = 9 . . . . . . . divide by 37
So, the point where Alice turned is ...
(x, y) = (9, 6·9)
(x, y) = (9, 54)
Related Questions
Could this set of ordered pairs have been generated by a linear function (-3,0),(-2,4),(-1,8),(0,12),(1,16),(2,20)
Answers
Answer:yes because the input and the output don’t repeat
Step-by-step explanation:
9514 1404 393
Answer:
yes
Step-by-step explanation:
Each increment of 1 in x produces an increment of 4 in y. When the increments have the same ratio like that (4:1), the function is linear. The equation for it is ...
y = 4x +12 . . . a linear function
The midpoint of a line segment is (−3,2). One endpoint of the line segment is (4,−7).
What are the coordinates of the other endpoint of the line segment?
Answers
Answer:
The other endpoint is (9, −6)
Step-by-step explanation:
(x1,y1)=(3,2) and M=(6,−2)
x1+x22=x and y1+y22=y
3+x22=6 and 2+y22=−2 ←×2
3+x2=12 and 2+y2=−4
x2=9 and y2=−6
The coordinates of the other endpoint of the line segment are [tex]Y(x,y) = (-10, 11)[/tex].
Vectorially speaking, the midpoint of a line segment is determined by the following expression:
[tex]M(x,y) = \frac{1}{2}\cdot X(x,y) + \frac{1}{2}\cdot Y(x,y)[/tex] (1)
Where:
[tex]M(x,y)[/tex] - Midpoint.[tex]X(x,y)[/tex], [tex]Y(x,y)[/tex] - Endpoints of the line segment.If we know that [tex]M(x,y) = (-3, 2)[/tex] and [tex]X(x,y) = (4, -7)[/tex], then the coordinates of the other endpoint is:
[tex]\frac{1}{2}\cdot Y(x,y) = M(x,y) -\frac{1}{2}\cdot X(x,y)[/tex]
[tex]Y(x,y) = 2\cdot M(x,y) -X(x,y)[/tex]
[tex]Y(x,y) = 2\cdot (-3,2)-(4,-7)[/tex]
[tex]Y(x,y) = (-6, 4) - (4, -7)[/tex]
[tex]Y(x,y) = (-10, 11)[/tex]
The coordinates of the other endpoint of the line segment are [tex]Y(x,y) = (-10, 11)[/tex].
We kindly invite to check this question on midpoints: https://brainly.com/question/17506315
7. Identify the reason for each step in the solution.
-
3(x+2) = 2x+3
3x + 6 = 2x + 3
3x + 6 - 2x = 2x +3 - 2x
X+6 = 3
X+6 - 6 = 3-6
x = -3
Answers
Answer:
Distribution is used from steps 1-2
They eliminate 2x by subtracting it on both sides (steps 3-4)
They eliminated 6 by subtracting it from both sides (steps 5-6)
(steps 3-6 is eliminating like-terms)
Thus this leaves the answer being x=-3
Step-by-step explanation:
Equation 3(x+2) = 2x+3 solved using distributive property and simplification, final solution is x = -3.
Let's identify the reason for each step in the solution to the equation 3(x+2) = 2x+3:
Distributive Property
The first step applies the Distributive Property,
which states that multiplying a number outside the parentheses by the terms inside the parentheses.
Here, we multiply 3 by (x+2),
3(x+2)
= 3 × x + 3 ×2
= 3x + 6
Combining Like Terms
In the second step, combine like terms on both sides of the equation.
On the left side, we have 3x, and on the right side, we have 2x.
We also have constants 6 on the left side and 3 on the right side.
3x + 6 = 2x + 3
Move Variables to One Side
To solve for 'x', we want all the terms with 'x' on one side of the equation.
Here, move the term with 2x to the left side by subtracting 2x from both sides of the equation:
3x + 6 - 2x = 2x + 3 - 2x
Simplify
On the left side, the term 2x cancels out with the 2x on the right side, leaving us with:
x + 6 = 3
Move Constants to the Other Side
To isolate 'x', we need to get rid of the constant term on the left side.
Subtracting 6 from both sides of the equation:
x + 6 - 6 = 3 - 6
Simplify
On the left side, the +6 and -6 cancel out, leaving us with:
x = -3
Final Solution
After simplifying, find that the value of 'x' that satisfies the original equation is x = -3.
This means that if we replace 'x' with -3 in the equation, it will hold true:
3(-3 + 2) = 2(-3) + 3
-3 = -6 + 3
-3 = -3
And that's why the solution to the equation is x = -3.
Therefore, the reason required for solving the equation are distributive property and simplification which gives solution is x = -3
learn more about simplification here
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Kelly and Mitchell work together. Kelly works 9 hours. Mitchell works 15 hours. How many years of experience could each person have?
Answers
Answer:
You don't know
Step-by-step explanation:
They don't mention any part of experience. Kelly and Mitchell just worked. Plus, you don't know how much experience of years.
write an equation to solve for x. what is the value of x none of this makes any sense to me at all so if y'all get it right amen will mark brainiest this is so hard ty so much
Answers
Answer:
equation: 3x - 2 + 4x - 9 + 3x - 9 = 180 x = 20Step-by-step explanation:
add all internal angles
∠H + ∠I + ∠J = 180
equation: 3x - 2 + 4x - 9 + 3x - 9 = 180
combine similar terms: 3x + 3x + 4x = 180 + 2 + 9 + 9
simplify: 10x = 200
divide 10 both sides: x = 20
Help me solve this 2(q +r)
Answers
I think the answer is 2q+2r
please help it’s due in a couple of min
Answers
Answer:
C
I have done this.
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
The first 3 answer is wrong so Its d
Evaluate the distance from -4 to 8.
Answers
Answer:
12
Step-by-step explanation:
-4 + 4 = 0
0 + 8 = 8
4 + 8 = 12
Emma wants to stain a circular deck that has a diameter of 12 m. The cost of the wood stain is $3.25
per square meter.
To the nearest dollar, how much will it cost Emma to stain the entire deck?
Use 3.14 for
Answers
Answer:
$1469
Step-by-step explanation:
diameter of deck = 12 m
diameter = 2*radius
thus
12 m = 2*radius
radius = 12m / 2 = 6 m
area of circle is given by [tex]\pi r^{2}[/tex]
where r is the radius
thus, area of given deck with radius = 12 m
[tex]\pi r^{2} = 3.14*12^{2} \\=> 3.14*144 = 452.16[/tex]
Thus, area of given deck is 452.16 meter square
given
The cost of the wood stain is $3.25 per square meter
cost of 1 meter square wood stain = $3.25
since we have to find to stain the entire deck which has area 452.16 meter square , we multiply both side of equation by 452.16
cost of 452.16 meter square wood stain = $3.25*452.16 = $1469.25
Thus,
it will cost $1469 to the nearest dollar for Emma to stain the entire deck
What is the constant in the equation
7
x
+
5
=
y
?
Answers
Answer:
7,and 5
Step-by-step explanation:
Bc a constant is the part of equation that contains a proper value.
Answer: 5
find the measure of angle L this is the last question mark brainest ty so much xx
Answers
Answer:
∠L = 50°
Step-by-step explanation:
∠R = 109°
∠U is supplementary to ∠R
This means ∠R + ∠U = 180°
109° + ∠U = 180°
Subtract ∠R from 180° to get ∠U
∠U = 81°
A triangle's angles must add up to 180, so if we take ∠U + ∠E, we figure out what 2 of the 3 angles add up to, we can then subtract this sum from 180 to figure out ∠L
81° (This is ∠U) + 49° (This is ∠E) = 130°
180° (Sum of all of a triangle's angles) - 130° (Sum of ∠U and ∠E) = 50° (∠L)
Answer:
∠L = 60°Step-by-step explanation:
see attached image.
add all internal angles and equal to 180
∠U + ∠L + ∠E = 180
∠U = 180 - 109
= 71
plug in values from equation:
∠U + ∠L + ∠E = 180
71 + ∠L + 49 = 180
∠L = 180 - 49 - 71
∠L = 60
5. Wnte a rational number
between 6 and 7.
Answers
Answer:
6.2
Step-by-step explanation:
decimals are rational numbers so you could do 6.2
What do you multiply 6 by in order to get -3
Answers
Answer:
-1/2
Step-by-step explanation:
Anna is a wildlife photographer. She wants to photograph woodpeckers, snowy owls, and hawks. In which biome can Anna find these birds? O A desert O B. tundra OC temperate deciduous forest O D. rainforest
Answers
Answer:
I think B but you should post this in geography not mathematics for a better answer.
Step-by-step explanation:
Answer:
B. Tundra
Step-by-step explanation:
Anna can find these birds in the tundra biome. Snowy owls habitats are in the tundra and do migrate to the northernmost regions of Canada, Europe, Asia and Alaska. Woodpeckers and hawks can also live in the tundra.
Please help me answer this
Answers
Answer:
a) 10:10 a.m.
b) 10:20 a.m.
c) 10:50 a.m.
d) math class is 60 minutes (1 hour) long
Step-by-step explanation:
Help pls
According to a food label on a box of cookies, each box has 16 servings and each serving contains 4 cookies. The weight of the box of cookies is 1/2 kilograms. What is the weight of each cookie?
Answers
Answer:
7.8125 grams
Step-by-step explanation:
As per the food label on the box of cookies, there are 16 servings in each box and each serving contains 4 cookies.
Therefore, each box of cookies contains (16 × 4) = 64 cookies.
If a box of cookies weighs kg i.e. 500 gram, then the weight of each cookies will be grams. (Answer)
At 1:00 p.m., Kahlil hops in his car and drives at a constant speed of 35 mph for 12 minutes to the grocery store. After 15
minutes at the grocery store, he realizes he is late and drives at a constant speed of 40 mph to the school, arriving at 1:42 p.m.
He then spends 20 minutes at school, buying tickets for the game.
Answers
Answer:
Uh? What's the question?
PLZ HELP FASTTTTTTTT
Answers
1. 0
2. 4
3. 8
4. 12
5. 16
hope this helps!
Please include an explanation.
"a" varies directly as the square of "b" and inversely as the cube of "c". If a=171 when b=8 and c=9, find a if b=9 and c=6. Round your answer to two decimal places if necessary.
Answers
Answer:
a = 730.43
Step-by-step explanation:
The formula for this type of problem is [ a = kb²/c³ ].
We are given a = 171, b = 8 and c = 9.
Solve for k.
171 = k(8)²/(9)³
k = 1947.80
Solve for a since we found k using b = 9 and c = 6.
a = (1947.80)(9)²/6³
a = 730.425
Round to the nearest hundredth.
730.425 → 730.43
Best of Luck!
Answer:
730.42
Step-by-step explanation:
a varies directly with the square of b, and inversely with the cube of c. Therefore:
a = k b² / c³
where k is the constant of proportionality.
a = 171 when b = 8 and c = 9. So the value of k is:
171 = k (8)² / (9)³
k ≈ 1947.8
So the value of a when b = 9 and c = 6 is:
a = 1947.8 (9)² / (6)³
a ≈ 730.42
What are the coordinates of the point (−1, 6) after a reflection across the x-axis
Answers
Answer:
(-1,-6)
Step-by-step explanation:
Because it is reflecting across the x-axis, the x value remains the same but the y value moves down the axis the same distance it was, meaning that the y part of the coordinate becomes the opposite.
For example, if (1,2) was reflected across the x-axis, it becomes (1,-2).
There was a 6 square foot piece of wrapping paper for a birthday present
Answers
where's the rest of question so I can help?
choose the fraction that has not been reduced to simplest form
Answers
Answer: What are the fractions
Step-by-step explanation:
Answer:
um what are the fractions???
Step-by-step explanation:
A certain shade of green paint is made by mixing blue and yellow paint. The relationship between the number of quarts of blue paint in the mix, xx, and the number of quarts of yellow paint, yy, is represented by the graph below.
What does the ordered pair (2,102,10) indicate?
Answers
Answer:
2 quartz of the blue paint for every 10 quartz of yellow paint
Step-by-step explanation:
The graph shows the possible different amount of yellow paint and blue paint, in quartz, that can be mixed to obtain a shade of green paint.
On the graph, at the point with the coordinates pair of (2, 10), it means for we would require 2 quartz of blue paints to be mixed with every 10 quartz of yellow paint in order to get the shade of the green paint that we are looking for.
Answer: 2 quartz of the blue paint for every 10 quartz of yellow paint
Step-by-step explanation: good luck
Drag the tiles to go the boxes to form correct pairs
Answers
Answer:
math
Step-by-step explanation:
Answer: For Edmentum Multiply the sets of numbers and match them with their products.
(-3/4)(7/8)= -21/32
(5/16)(-2)(-4)(-4/5)= -2
(2/3)(-4)(9)= -24
(2 3/5) (7/9)= 91/45
Step-by-step explanation:
If an investment account starts with $3900, and grows with 2.1% interest, compounded continuously. How much is the account worth after 10 years? Round your answer to the nearest dollar. Do NOT round until you have calculated the final answer.
Answers
Answer:
If they are asking amount it is $4800.893013; $4800 (nearest dollar)
If they are asking the amount for interest is $900.8930129; $900 (nearest dollar)
Step-by-step explanation:
Compound interest Formula:
Amount = principle( 1+ rate/100)^n
Information from the question.
-So how you put it is the principle is $3900; the rate is 2.1%; the n is 10.
How to apply it?
- Just substitute in the values;
Amount=3900(1+2.1/100)^10
=4800.893013
~4800 ( nearest dollar)
》That is for amount.
Interest=4800.893013-3900
=900.893013
~900 ( nearest dollar)
》That is for interest.
Hope it helps!!!!:))
Answer:
Step-by-step explanation:
A=Pert=3900e(0.021)(10)≈4811.34
The account is worth $4811 after 10 years.
Consider this simplified algebraic expression:
12y - 5x + 15
Which of the following could be the original expression? Check all that apply.
12y – 20x + 15x + 15
U 10 – 5x + 5+ 6g - 6g
O 15x + 12y - 10x + 15
2xy + 10y - 7x + 15
14 - 4x + 15y - x +1-3y
Answers
Answer:
it is the first one and the last one
Step-by-step explanation:
Multiply or divide as Indicated.
x^-8 divided by x^-7
Answers
Answer:
x^1
Step-by-step explanation:
if you divide exponents with the same coefficients, you subtract the two exponents
SOMEONE PLEASE HELP ILL GIVE BRAINLIEST
Answers
Answer: Its E,F, and H
Step-by-step explanation: There no way its not E,F, and H . C is a right angle so I believe the questions asking what other ones are right angles and that answer would be E,F and H.
Logan thinks he can bring the baseball bat home in his suitcase. Is he correct? Use your understanding of the Pythagorean Theorem to explain your answer.
Answers
Answer:
Step-by-step explanation:
Write an expression for the perimeter of the rectangle. Make sure you expression is as simple as possible. 5x+9 , 3x+12
Answers
Answer:
6x+42
Step-by-step explanation:
So by, "5x+9 , 3x+12" I'm assuming you mean the length and the width.
The perimeter of a rectangle is 2(l+w), so if you put the values in, you get...
2(5x+9+3x+12)
2(8x+21)
6x+42, which is your answer.