A parking lot is 20 feet long. One tortoise starts at the edge of the parking lot and moves at a rate of 6 feet per minute. Another tortoise starts 4 feet from the edge of the parking lot and moves 2 feet per minute. Write an equation to represent when they will be in the same spot.
Answer:
Kindly check explanation
Step-by-step explanation:
Length of parking lot = 20 feets
Speed of tortoise which starts at the edge = 6 feets per minute
Speed of tortoise which starts 4 feets from the edge = 2 feets per minute
Equation to represent when they will be in the same spot.
Distance = speed * time
Distance of Tortoise at edge = 6ft/min * t = 6t - - (1)
Distance of the other tortoise = (4 + 2t) - - - (2)
Equating both (1) and (2)
6t = 4 + 2t
6t - 2t = 4
4t = 4
t = 4/4
t = 1
Hence, they'll be at the same spot after 1 minute.
Which transformation is shown by the coordinates below? L (-1, 9) M (-8, 8) N (-3, 5) L '(- 9, -1) M' (- 8, -8) N '(- 5, -3) A. Reflection over the x-axis / B. Translation 8 units left and 8 units down / C. Rotation 90 degrees clockwise / D. Rotation 270 degrees clockwise
Answer:
D. Rotation 270 degrees clockwise.
Step-by-step explanation:
The transformation used in the coordinates below was a rotation 270 degrees clockwise, whose definition is:
[tex](x', y') = (r\cdot \cos (\theta - 270^{\circ}), r\cdot \sin (\theta -270^{\circ}))[/tex]
Please note that clockwise rotation is represented by the minus sign.
Where [tex]r[/tex] is the norm of original point, defined as:
[tex]r =\sqrt{x^{2}+y^{2}}[/tex], [tex]\forall \,x,y\in \mathbb{R}[/tex]
And [tex]\theta[/tex] is the direction of the point centered at origin and with respect to +x semiaxis, measured in sexagesimal degrees:
[tex]\theta = \tan^{-1} \frac{y}{x}[/tex]
Now we proceed to prove the statement:
[tex]L (x, y) = (-1, 9) \longrightarrow L'(x,y)[/tex]
Norm
[tex]r = \sqrt{(-1)^{2}+9^{2}}[/tex]
[tex]r = \sqrt{82}[/tex]
Direction
The point is located on 2nd quadrant, which means that [tex]90^{\circ} \leq \theta \leq 180^{\circ}[/tex]. Then:
[tex]\theta = \tan^{-1}\left(\frac{9}{-1} \right)[/tex]
[tex]\theta = 96.340^{\circ}[/tex]
Rotation
[tex]L'(x,y) = (\sqrt{82}\cdot \cos (96.340^{\circ}-270^{\circ}),\sqrt{82}\cdot \sin (96.340^{\circ}-270^{\circ}))[/tex]
[tex]L'(x,y) = (-9, -1)[/tex]
[tex]M(x,y) = (-8,8) \longrightarrow M'(x,y)[/tex]
Norm
[tex]r = \sqrt{(-8)^{2}+8^{2}}[/tex]
[tex]r = \sqrt{128}[/tex]
Direction
The point is located on 2nd quadrant, which means that [tex]90^{\circ} \leq \theta \leq 180^{\circ}[/tex]. Then:
[tex]\theta = \tan^{-1}\left(\frac{8}{-8} \right)[/tex]
[tex]\theta = 135^{\circ}[/tex]
Rotation
[tex]M'(x,y) = (\sqrt{128}\cdot \cos (135^{\circ}-270^{\circ}),\sqrt{128}\cdot \sin (135^{\circ}-270^{\circ}))[/tex]
[tex]M'(x,y) = (-8, -8)[/tex]
[tex]N(x,y) = (-3,5)\longrightarrow N'(x,y)[/tex]
Norm
[tex]r = \sqrt{(-3)^{2}+5^{2}}[/tex]
[tex]r =\sqrt{34}[/tex]
Direction
The point is located on 2nd quadrant, which means that [tex]90^{\circ} \leq \theta \leq 180^{\circ}[/tex]. Then:
[tex]\theta = \tan^{-1}\left(\frac{5}{-3} \right)[/tex]
[tex]\theta = 120.964^{\circ}[/tex]
Rotation
[tex]N'(x,y) = (\sqrt{34}\cdot \cos (120.964^{\circ}-270^{\circ}), \sqrt{34}\cdot \cos (120.964^{\circ}-270^{\circ}))[/tex]
[tex]N'(x,y) = (-5, -3)[/tex]
Hence, the correct answer is D.
-5r - 10 = 10
HELP ASAP
Answer:
r equals -4
Step-by-step explanation:
there's your help
6W - 12x + 7w - 8x =
How can we find out whether or not a point is on the line?
Answer:
Plug the points into an equation
Step-by-step explanation:
To find out if a point is on a line, you can plug the points back into an equation. If the values equal one another, then the point must be on a line.
Answer:
To determine if a point is on a line you can subsitute the x and y coordinates into the equation.. If the values equal one another, then the point must be on a line.
Step-by-step explanation:
For example if the x - 3y = 11 and the point is (2, -3) plug in
2 - 3(-3) = 11
2 + 9 = 11
11 = 11
will give branlest for any help that is right
Answer:
7x+3=2x-6 #4
Step-by-step explanation:
Answer:B
Step-by-step explanation:
ava's turtle is half as old as her parrot. in 10 years her turtle will be ¾ as old as her parrot. write an equation to represent this situation. how old is ava's turtle
Answer:I’m not sure but I think the answer is 19
Step-by-step explanation:
Help Asap ! Find The Measure Of Angle A In The Triangle.
Answer: m<A = 35
Step-by-step explanation: The sum of the measures
of the interior angles of a triangle is 180°.
So we can setup the equation 3x + 5 + 8x + 65 = 180.
Combining our numbers and variables on the left, we have 11x + 70 = 180.
Now subtract 70 from both sides to get 11x = 110.
Dividing both sides by 11, we find that x = 10.
In the diagram, the m<A is represented as 3x + 5.
Plugging a 10 in for x, we have 3(10) + 5 or 30 + 5 which is 35.
So the m<A = 35.
Solve for x: 3x + 11 = 41
Answer:
x=10
Step-by-step explanation:
move all terms that don't contain x to the right side and solve.
I need help. What is m
Answer:
A
Step-by-step explanation:
(8x + 4) = (10x-6)
If you solve this you find x = 5, plug that into one and you get 44 degrees
Open GeoGebra, and follow the steps below to create and compare triangles using the side-angle-side criterion.
Question 1
Create a triangle of your choice on the grid. Measure two of the sides on the triangle and the angle between the two sides. Record the measurements in the table.
Answer:
Answers will vary but might resemble this answer based on a triangle called ∆ABC.
A 16-ounce can of carrots for $1.29 OR a 20-ounce can of carrots for $1.49
Answer: 20 ounce
Step-by-step explanation: 1.29/16=0.080625 1.49/20=0.0745
Answer:
20 ounce, its 20 cents more and it has more carrot.
Step-by-step explanation:
Plz help fast I’ll mark Brainiest. Don’t answer just for points.
Sum of interior angles in quadlateral (trapezoid) is 360 degrees.
[tex]5y+2+8y+73+2y=360[/tex].
Simplify by collecting y terms and subtracting 73 on the other side.
[tex]15y+75=360\implies y=285/15=\boxed{19}[/tex].
Hope this helps.
STAY UP LATE TONIGHT!!!
MARS WILL BE VISIBLE FROM EARTH!!!
IT WON'T BE LIKE THIS AGAIN, UNTIL 15 YEARS!!!
Answer:
You sure this true
Step-by-step explanation:
How you know
Answer:
OOOOOOOO THANK YOU!!!!!!
What letter would this be?
Answer:
A
Step-by-step explanation:
Show work please 100 points plus brainliest
Answer:
10. :)
Step-by-step explanation:
the theatre has 4 chairs in a row. there are 5 rows. how many chairs are there in total.
Answer:
20
Step-by-step explanation:
1111 <--- 1st row
1111 <---- 2nd row
1111 <--- 3rd row
1111 <----- 4th row
1111 <----- 5th row
use multiplication
WRITE AN SLOPE INTERCEPT FORM
I need help 1-10 or as much as you can I don’t care just answer pleaseee
Use the vertex formula to find the vertex of the quadratic function f(x) = - x2 + 2x - 6.
What is the value of 2|6 + p| - 3p^3 when p = -2?
Answer:p
=
2
,
−
8
7
Decimal Form:
p
=
2
,
−
1.
¯¯¯¯¯¯¯¯¯¯¯¯
142857
Mixed Number Form:
p
=
2
,
−
1
1
7
Step-by-step explanation:
Use the table below to determine the approximate height of the flag pole.
Help pls due tomorrow
Answer:
its b
Step-by-step explanation:
...........................
Answer:
B 17.5 ft
Step-by-step explanation:
tangent = opposite / adjacent
tan 35° = h / 25
multiply both sides by 25
h = 25 (tan 35°)
tan 35° = 0.70 (from your calculator)
h = 25 (0.70)
h = 17.51 ft.
If x+5=20, what does X+10 equal?
Let's find the value of x
x + 5 = 20
Subtract 5 from both sides
x = 15
x + 10 = 15 + 10 = 25
What single transformation was applied to triangle AAA to get triangle BBB?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Translation
(Choice B)
B
Rotation
(Choice C)
C
Reflection
(Choice D)
D
Dilation
Answer:
the answer is D
Step-by-step explanation:
Answer:
answer
Step-by-step explanation:
answer is step 5 choice a
pleaaase help me, it'll give you 50 points and i'll mark you as brainliest or whatever it's called.
Answer:
3/16
Step-by-step explanation:
How long is this line segment?
help for this qestion and extra point
Answer:
12.15
Step-by-step explanation:
how old is molly and simba
rjpiejigdorihegourehguhreoghreoghoreghoregregre
The graph shows a reflection.
True or false: The pre-image and the image are not congruent.
Answer:
False
Step-by-step explanation:
That is false
If the pre-image is reflected over any axis, the image will still be congruent to it
For
the function pictured below. Fill in the following values.
a.Domain:
b. Range:
e increasing Interval:
d. Decreasing Interval:
e. Positive Interval(s]
f. Negative Interval (s:
g.Max:
h.min. i.Rate of Change (Slope) [2. 4]:
Answer:
1. (-∞, ∞), [-4, ∞), (2, ∞), (-∞, 2), (-∞, 0) ∪ (4, ∞), (0, 4), DNE, -4, 2
2. y = -|x -4| -2
Step-by-step explanation:
1.
a. the domain is the horizontal extent, (-∞, ∞)
b. the range is the vertical extent, [-4, ∞)
c. the function is increasing where it goes up to the right, (2, ∞)
d. the function is decreasing where it goes down to the right, (-∞, 2)
e. the function is positive where it is above the x-axis, (-∞, 0) ∪ (4, ∞)
f. the function is negative where it is below the x-axis, (0, 4)
g. the function extends to ∞, so has no maximum value
h. the vertex is the low point, or minimum value, -4
i. the function increases from -4 to 0 on the interval [2, 4] so has an average rate of change of (0 -(-4))/(4 -2) = 4/2 = 2
__
2. Reflection across the x-axis negates every y-value. Multiply the given function by -1:
y = -|x-4| -2
Able has a younger sister and an older brother. - Able’s age can be represented by x. - Able’s sister is 4 years younger than him. - Able’s older brother is twice as old as he is. - The combined age of all three siblings is 32. How old is Able’s younger sister?
Answer:9
Step-by-step explanation:
I did the math
Given:
Able's age can be represented by x.
Able's sister is 4 years younger than him.
Able's older brother is twice as old as he is.
The combined age of all three siblings is 32.
To find:
The age of Able's younger sister.
Solution:
Able's age can be represented by x.
Able's sister is 4 years younger than him.
Age of Able's sister = (x-4)
Able's older brother is twice as old as he is.
Age of Able's older brother = 2x
The combined age of all three siblings is 32.
Add 4 on both sides.
Divide both sides by 4.
The age of Able is 9 years. So, age of his younger sister is
Therefore, the age of Able's sister is 5 years.
