Answer:
Slope of this line is given by:
Aaron’s rate for mowing lawns is 0.5 acres per hour
Step-by-step explanation:
It is given that time is tracked by Aaron related to x coordinate.
and the area of land mowed in acres is related to y coordinate.
Two of his points are given as:
(3, 1.5) and (5,2.5)
We know that the coordinates are represented in the form of (x,y)
i.e. first coordinate represents x coordinate and
second coordinate represents y coordinate.
So, it can be observed that:
[tex]x_1=3, y_1=1.5\\x_2=5, y_2=2.5[/tex]
Change in x coordinate = [tex]x_2-x_1=5-3 = 2[/tex]
i.e. total time taken is 2 hours.
Change in y coordinate = [tex]y_2-y_1=2.5-1.5 = 1[/tex]
i.e. total land mowed taken is 1 acre.
In other words, it takes 2 hours for Aaron to mow 1 acre of land.
So, "option 1) It takes Aaron about 1 hour to mow 2 acres." is incorrect.
Rate of mowing lawn is the land mowed by Aaron in 1 hour.
Land mowed in 2 hours = 1 acre
Land mowed in 1 hours = [tex]\frac{1}{2}[/tex] acre i.e. 0.5 acre
Also, slope of a line is given as:
[tex]m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]
Here [tex]y_2 - y_1 = 1[/tex]
[tex]x_2 - x_1 = 2[/tex]
As per formula:
[tex]m = \dfrac{1}{2} = 0.5[/tex]
So, option 2) Aaron’s rate for mowing lawns is 0.5 acres per hour.
Using the slope concept, it is found that the correct option is:
Aaron’s rate for mowing lawns is 0.5 acres per hour.
---------------------------
A linear function has the following format:
[tex]y = mx + b[/tex]
The slope is m, which is the rate of change, that is, by how much the output y changes when the input changes by 1.---------------------------
In this question, the input is the time in hours and the output is the area of land mowed, thus the slope represented the rate of area mowed per hour.Two points, (3, 1.5) and (5, 2.5). The slope is change in y divided by the change in x, thus:[tex]m = \frac{2.5 - 1.5}{5 - 3} = \frac{1}{2} = 0.5[/tex]
Thus, the correct option is:
Aaron’s rate for mowing lawns is 0.5 acres per hour.
A similar problem is given at https://brainly.com/question/17460142
Find the area of the regular polygon. Round your answer to the nearest tenth.
Answer:
43.30 km^2
Step-by-step explanation:
Since the shape is a regular polygon, the sides of the triangle are equal (10km) now find the area on the triangle using herons formula
Working:
Side is 10
Perimeter= 30km
Semiperimeter (s) = 15km
Formula= √s(s-a)(s-b)(s-c)
= √15(15-10)(15-10)(15-10)
= √15*5*5*5
=5√5*15
=5√75
= 5*8.66
= 43.3 km^2
Answer:
43.3
Step-by-step explanation:
since it is a regular polygon thus it is a equilateral triangle where all sides are the same and all angles are 60
use formula 1/2 x a x b x sin C where a and b are sides and C is the angle
1/2 x 10 x 10 x sin 60 = 43.30
or method 2 is using Pythagoras theorem by drawing a perpendicular height to length 10km
h = [tex]\sqrt{10^{2} - (10/2)^{2} } = \sqrt{75} \\[/tex]
area of triangle = 1/2 x 10 x [tex]\sqrt{75}[/tex] = 43.30
A right triangle has an area of 50 square inches. Part 1 out of 2 If the triangle is an isosceles triangle, what are the lengths of the legs of the triangle? The length of each leg is____ inches.
Answer: The length of each leg is 10 inches.
Step-by-step explanation: The triangle in question has been described as a right angled triangle, which implies that one side measures 90 degrees. It ia also described as an isosceles triangle. An isosceles triangle has two sides being equal, and also the two angles facing the two equal sides also measure the same.
If a right angled triangle is given as isosceles, then it means the hypotenuse (which is the side facing the right angle) is not one of the equal sides. The other two sides apart from the hypotenuse are the sides with equal measurement.
The area of a triangle is given as
Area of triangle = 1/2 (b*h)
Where b (the base) is one of the equal legs, and h (the vertical height) is the other leg equal to b.
Hence, the area can be re-written as follows;
Area of a triangle = 1/2 (b*h)
50 = 1/2 (b*h)
By cross multiplication, you now have
50 *2 = b*h
100 = b*h
Having already determined that b equals h,
100 = h²
Alternatively
100 = b²
Therefore, adding the square root sign to both sides of the equation, you now have
√100 = √h²
10 = h
Therefore, the length of each leg, both base and height is 10 inches
if 11x+5y = 9
11x +3y=1
.
[tex]the \: value \: of \: x \: is \: - 1. \\ the \: value \: of \: y \: is \: 4 \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps[/tex]
6. Classify this kind of triangle:
Answer:
Number 3
Step-by-step explanation:
It is an acute isosceles because all the angles are acute and two sides are congruent.
Answer:
Acute and isosceles
Step-by-step explanation:
All the angles are less than 90
2 sides are equal
find the volume with the explanation if possible <3
Answer: 905 cu. in.
Step-by-step explanation:
volume = (4/3) * π * r³
= (4/3) * π * 216
Please help ASAP! Correct answer only! This assignment is due today.
A student has to choose an elective class for the last semester of high school. His counselor suggested 8 electives, 5 of which were dance classes.
If the student randomly chose to read about 4 of the electives, what is the probability that all of them are dance classes?
Write your answer as a decimal rounded to four decimal places.
Answer:
Probability ≈ 0.0714
Step-by-step explanation:
Consider permutation and combination;
[tex]Total Combinations - 8C4,\\8C4 = 8! / 4! * ( 8 - 4 )!,\\8 * 7 * 6 * 5 / 4!,\\\\Total Combinations = 70,\\\\Combinations of Dance Classes - 5C4,\\5C4 = 5! / 4! * ( 5 - 4 )!,\\5 * 4 * 3 * 2 * 1 / 4 * 3 * 2 * 1,\\\\Dance Classes = 5,\\\\Probability - 5 / 70 = 0.0714,\\Conclusion; Probability = ( About ) 0.0714[/tex]
Help center of circle
Answer:
Center = (7, - 5)
Radius = 3
Step-by-step explanation:
[tex] {x}^{2} + {y}^{2} + 14x - 10y + 65 = 0 \\ {x}^{2} + 14x + {y}^{2} - 10 + 65 = 0 \\ ( {x}^{2} + 14x + {7}^{2}) - {7}^{2} + ({y}^{2} - 10y + {5}^{2}) \\- {5}^{2} + 65 = 0 \\ (x + 7)^{2} + (y - 5)^{2} - 49 - 25 + 65 = 0 \\ (x + 7)^{2} + (y - 5)^{2} - 49 + 40= 0 \\ (x + 7)^{2} + (y - 5)^{2} - 9= 0 \\ (x + 7)^{2} + (y - 5)^{2} = 9 \\ (x + 7)^{2} + (y - 5)^{2} = {3}^{2} \\ equating \: it \: with \: \\ (x - h)^{2} + (y - k)^{2} = {r}^{2} \\ - h = 7 \implies \: h = - 7 \\ - k = - 5 \implies \: k = 5 \\ center = ( - h, \: - k) = (7, \: \: - 5) \\ \\ radius \: r = 3[/tex]
Which value of f 3f+5=32 a true statement
Choose 1 answer
A
f=6
B
f=8
C
f=9
D
f=12
Answer:
C. f = 9
Step-by-step explanation:
→Subtract 5 from both sides:
3f + 5 = 32
- 5 - 5
_________
3f = 27
→Divide both sides by 3:
f = 9
Answer:
C f=9
Step-by-step explanation:
Trust me, I got the answer right.
I need help ASAP I shall give brainlyist (idk how to spell)
Answer:
[tex]5cm[/tex]
Step-by-step explanation:
[tex]r=\sqrt{\frac{V}{\pi h} } \\=\sqrt{\frac{225.5}{\pi *3} } \\=5cm[/tex]
will award most brainliest need help pls (due today)
Answer:
m∠A = 24°
Step-by-step explanation:
m∠A = m∠B
3x-12 = 2x
-2x. -2x
x-12 = 0
x = 12
3(12)-12 = 24
2(12) = 24
11 (12) = 132
132 + 24 +24 = 180
Probability Race game
Read the whole thing even the scenario
Question 2: Why is picking horse 1 a really bad idea? What is its probability of winning?
Answer:
P(1) = 0
Step-by-step explanation:
The sum of 1 is impossible so that horse will never get to move
The probability of winning is zero
Answer:
p(1) = 0
Step-by-step explanation:
The horse can't move at all (why it's a bad idea)
The probability of winning is 0
Hope this helps!
Find the next three terms in the geometric sequence: 72, 36, 18,... (sorry for bothering a lot)
Answer:
18 / 2 = 9
9 / 2 = 4.5
4.5 / 2 = 2.25
The next three terms are 9,4.5,2.25
Hope this helps
Step-by-step explanation:
Please answer correctly !!!!!!! Will mark brainliest answer !!!!!!!!!!!!
Answer:
40
Step-by-step explanation:
To find the maximum we need to find the vertex. We can do this by writing the equation in vertex notation by completing the square.
A(w) = -w(w - 80)
= -w² + 80w
= -(w² - 80w) = -(w - 40)² + 160
The vertex is then (40, 160) and since we are looking for the value of w it will be 40.
Find the length of the hypotenuse. The measure of the hypotenuse?
Answer:
Since it's a right angled triangle
Hypotenuse = h
h² = 7²+24²
h= √49 + 576
h = √625
h= 25
Therefore hypotenuse is 25
Hope this helps.
Answer & Step-by-step explanation:
First, we must know the Pythagorean Theorem.
a² + b² = c²
a = 24
b = 7
Now, let's plug in these numbers into the formula.
24² + 7² = c²
Simplify the exponents.
576 + 49 = c²
Add 576 and 49 together.
625 = c²
Square root the terms on both sides of the equation.
√625 = √c²
Simplify the square roots.
25 = c
The length of the hypotenuse is 25 units.
2x-4=2
what is x=
plz help
Answer:
3
Step-by-step explanation:
2x=2+4
2x=6
x=3
#RAVEN
Given a line segment containing the points A,B, & C, in order, if AB is 4 and BC is 16, then the length of AC would be ____. Select one: a. - 12 b. 12 c. 8 d. 20
The length of AC will be equal to 20 units for the given line.
What is the distance?Distance is defined as the length between the two points here we have a line AC divided into two parts having a length of AB = 4 and BC is 16.
The length of the line AC will be calculated as:-
AC = AB + BC
Ac = 4 + 16
AC = 20 units.
Therefore the length of AC will be equal to 20 units for the given line.
To know more about distance follow
https://brainly.com/question/2854969
#SPJ2
Look at pic plzzzzzz
Answer: 10.35 miles per hour
Step-by-step explanation:
[tex]\dfrac{63,756\ feet}{70\ minutes}\times \dfrac{1\ mile}{5280\ feet}\times \dfrac{60\ minutes}{1\ hour}=\dfrac{(63,756)(60)\ miles}{(70)(5280)\ hour}=\dfrac{10.35\ miles}{hour}[/tex]
What equation is equivalent to 3(a+4)-5(a-2)=22?
Answer:
a = 0
Step-by-step explanation:
=> 3(a+4)-5(a-2) = 22
Opening Brackets
=> 3a+12-5a+10 = 22
=> 3a-5a+12+10 = 22
=> -2a+22 = 22
Subtracting 22 to both sides
=> -2a = 0
Dividing both sides by -2
We get,
=> a = 0
Answer:
a = 0
Step-by-step explanation:
3(a+4)-5(a-2)=22
3a+12-5a+10=22
-2a+22=22
Subtract 22 from both sides
-2a=0
Multiply both sides by -1
2a= -0
2a=0
Divide both sides by 2
a=0
Hey I just realized my answer is really similar to Ujalakhan01's so sorry if it seems like I copied them.
(a) The first term of a sequence is -5
The rule for continuing the sequence.
Multiply by 4
then
Subtract 3
What is the second term of the sequence?
Answer:The second term is -23
Step-by-step explanation:
Step 1- multiply
4x-5=-20
Step 2- subtract
-20 - 3=-23
Please answer correctly !!!! Will mark brainliest !!!!!!!!!!!!!!
Answer:
g(-8) = -62
Step-by-step explanation:
solve for x:
8x +2 = -62 subtract 2 from each side
8x =-64 divide by 8
x =-8
A tennis ball is launched from the ground and follows a parabolic path represented by the equation y=−x2+7x, where x=seconds.At the same time, an arrow is shot from a height of 18 feet and follows a straight path represented by the equation y=−5x+25.Using your graphing calculator, when will the arrow pierce the tennis ball and a what height off of the ground?
HELP I NEED TO COMPLEYE THSISJI toDay
Answer: A. 7x(2x + 5)
Step-by-step explanation:
7x * 2x = 14x^2
7x * 5 = 35x
Write the expression for the amount of wallpaper in square feet you need to cover the living room, which is the same height and width as the family room, but it has a length that is 5 times greater than the height. The living room has 2 doors.
Answer:
The expression for the amount of wallpaper needed is [tex]20b^{2}- 2d[/tex]
Step-by-step explanation:
The necessary dimensions of the living room we need are the length and the height. We will not be needing the width because we will not be covering the floors with any wallpaper.
We will now assign variables to represent the surface areas of some features of the rooms.
Let the length of one wall of the living room be = l cm
Let the breadth of one wall of the living room be = b cm
Let the surface area of the doors be = d [tex]cm^{2}[/tex]
From the problem, we know that l = 5b
The area to be covered on one wall of the living room will be = length X breadth.
l X b
recall l = 5b
[tex]5b \times b = 5b^{2}[/tex]
this is the area to be covered on one wall.
For the four walls, we would have [tex]4 \times 5b^{2}= 20b^{2}[/tex]
Let us remember that the living room has two doors each covering a surface area of [tex]d cm^{2}[/tex] we will have to subtract these out since hey won't be covered.
[tex]20b^{2}- 2d[/tex]
Therefore, the expression for the amount of wallpaper needed is [tex]20b^{2}- 2d[/tex]
Can someone help me with this please
URGENT!!!!! LAST TWO QUESTIONS!!!!!!! WILL GIVE BRANLIEST!!!AT LEAST TAKE A LOOK!!!!!! PLS HELP!!!
6. What must be true in order for two triangles to be similar?
11. What is the measure of angle y?
A) 130°
B) 50°
C) 40°
D) 90°
Answer:
50
Step-by-step explanation:
The sum of angles in a triangle is 180 so the answer is 180 - 90 - 40 = 50.
Also, for your first question, 2 corresponding angles of the triangles must be congruent.
Answer:
B. 50°
Step-by-step explanation:
40°+90°+y = 180°
130°+y°=180°
y° =180°-130°
y = 50° (sum of the interior angles in a triangle=180°)
can you do this for me 3x+y=10, 2x^2+y^2=19
Answer:
1 , 29/11
Step-by-step explanation:
3x+y = 10 ....(1)
2x² +y² = 19 ....(2)
3x+y= 10
y = 10-3x
substituting the value of y in 2nd equation
2x² + y² = 19
2x² + (10-3x)² = 19
2x² + 100 + 9x² - 60x -19 = 0
11x² - 60x +81 = 0
11x² - 33x - 27x + 81 = 0
11x( x-3) - 27(x-3) = 0
(x-3)(11x-27) = 0
x = 3, 27/11
substituting x value on first equation
x= 3 x= 27/11
y= 10-3(3) y= 10 - 81/11
= 10-9 = (110-81)/11
= 1 = 29/11
Hope it helps...
one x intercept for a parabola is at the point (1,0). use the factor method to find the other x intercept for the parabola defined by y=-5x^2+15x-10
First simplify the equation of parabola y=-5x^2+15x-10 in the following way:
D=(15)^2-4\cdot (-5) \cdot (-10)=225-200=25, \\ \sqrt{D}=5, \\ x_{1,2} = \dfrac{-15\pm 5}{2\cdot(-5)} = 2, 1 \\ -5x^2+15x-10=-5(x-1)(x-2), \\ y=-5(x-1)(x-2).
You can see that if x=1 or x=2, then y=0. Two points of intersection with x-axis are (1,0) and (2,0).
Some amount of marbles were arranged in an equilateral triangle. And 2 marbles were extra. When the same set of marbles were arranged into triangle in which each side has one more marble than in the first arrangement there were 13 marbles shortage. How many marbles were in the set?
Answer:
The total number of marbles in the set is 107 marbles
Step-by-step explanation:
The parameters given are;
Let the size of the marbles be 1 unit
The marbles are arranged to form the equilateral triangle as follows;
1st row = 1 marble
2nd row = 2 marbles and so on so that the total number of marbles for an arithmetic series as follows;
Total number of marbles, t = 1 + 2 + 3 + ... + n
Therefore;
[tex]t = \dfrac{1 + n}{2} \times n[/tex]
Since there are 2 marbles left in forming the first equilateral triangle, we have the total number of marbles in the set, t₁, is given as follows;
[tex]t_1 = \dfrac{1 + n}{2} \times n + 2[/tex]
When the same marble set are arranged into a triangle in which each side has one more marble than in the first arrangement, there where 13 marble shortage, hence, the total number of marbles is given as follows;
[tex]t_1 = \dfrac{1 + (n+1)}{2} \times (n+1) -13[/tex]
We therefore have;
[tex]t_1 = \dfrac{1 + n}{2} \times n + 2 = \dfrac{1 + (n+1)}{2} \times (n+1) -13[/tex]
Which gives;
[tex]\dfrac{n^{2}+n+4}{2}=\dfrac{n^{2}+3\cdot n-24}{2}[/tex]
Therefore;
n² + n + 4 = n² + 3·n - 24
2·n = 24 + 4 = 28
n = 14
From which we have;
[tex]t_1 = \dfrac{1 + 14}{2} \times 14 + 2 = 107[/tex]
Therefore, the total number of marbles in the set, t₁ = 107 marbles.
The number of marbles in the set would be as follows:
[tex]107[/tex] marbles
Arrangement
Given that,
After arranging the marbles in an equilateral Δ, 2 marbles would be left
The size of marble being 1 unit,
So,
The first row of the equilateral Δ will consist of 1 marble,
while
The second row comprises of 2 marbles.
The process goes so on and on.
Therefore,
Total marbles [tex]t = 1 + 2 + 3 + ... + n[/tex]
Hence,
[tex]t = (1 + n)/2[/tex] × n
Because 2 marbles are extra,
[tex]t = (1 + n)/2[/tex] × n [tex]+ 2[/tex]
In case,
The same marble set are framed into a triangle, every side would contain 1 marble exceeding the previous one where 13 marbles would be felt short.
Thus,
Total marbles = [tex]\frac{1 + (n + 1)}{2}[/tex] × [tex](n + 1) - 13[/tex]
by putting the values, we get
[tex]n^2 + n + 4 = n^2 + 3n - 24\\2n = 24 + 4 = 28\\n = 14[/tex]
∵ Total marbles [tex]= (1+ 14)/2[/tex] × [tex]14 + 2[/tex]
[tex]= 107[/tex]
Thus, 107 marbles are the correct answer.
Learn more about "Probability" here:
brainly.com/question/8069952
I have been asking for assistance for an hour and a half now, I will greaty appreciate anyone that can help with this..Find the Slopes,and for the third one find Mid-point
Answer:
1st graph: m = -1/2. (m is the slope)
2nd graph: m = 3/2.
3rd graph: Midpoint = (1/2, 1/2)
Step-by-step explanation:
1st graph:
Find the slope by looking for two points on the line. Use the formula [tex]m = \frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]
We can derive the points (-3, 0) and (1, -2). Plug these into the equation above.
[tex]m= \frac{-2-0}{1-(-3)}[/tex]
Simplify this, giving you: m = -1/2.
2nd graph:
Use the same formula as stated above. From this graph, you can plug in the points (-1, 1) and (1, 4)
[tex]m = \frac{4-1}{1-(-1)}[/tex]
Simplifying gets you: m = 3/2.
3rd graph:
To find the midpoint, use the formula: [tex](\frac{x_{1}+x_{2} }{2} , \frac{y_{1} +y_{2} }{2} )[/tex]
Plug in the end-points of the graph, or (-3, 2) and (4, -1).
You get:
[tex](\frac{-3+4}{2}, \frac{2-1}{2})[/tex]
Simplify:
Midpoint = (1/2, 1/2)
What is the value of x?
The line is 7 units long. Add the two equations together and set equal to 7:
7x-1 + 2x-1 = 7
Combine like terms:
9x-2= 7
Add 2 to both sides:
9x= 9
Divide both sides by 9:
X= 1
Answer:
For 2x -1, X = 3 (2 x 3 = 6 - 1 = 5)
For 7x -1, X = 1/7 or 0.142857.
Step-by-step explanation: