Twelve trees are equally spaced along one side of a straight road. The distance from the first tree to the sixth tree is 60 feet. What is the distance in feet between the first and last trees?
Answer:
120 feet
Step-by-step explanation:
because 60 feet x2 is 120
The distance between the first and the last tree is 132 feet.
What is an Arithmetic Progression?An arithmetic progression(A.P.) is a series, where the difference between consecutive numbers is constant.
The first term of an A.P. is denoted by a, and the common difference is denoted by d.
The nth term of an A.P. series is found using the formula:
aₙ = a + (n-1)d.
The sum of n terms of an A.P. series is found using the formula:
Sₙ = (n/2)(2a + (n-1)d)
How do we solve the given question?We are said that every tree is equally spaced. So the distance between the trees is in arithmetic progression.
With the first tree being at 0 feet from itself, our a = 0.
The distance from the first tree to the sixth tree is 60 feet, so we can say that the 6th term is 60
6th term = a + 5d
or, 60 = 0 + 5d
or, d = 60/5 = 12 feet.
To find the distance between the first tree and the last tree(12th tree), we will find the 12th term of the series,
12th term = a + (12-1)d = 0 + 11(12) = 132 feet.
∴ The distance in feet between the first and last tree is 132 feet.
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Factor the following polynomials by finding a GCF
Answer:
Step-by-step explanation:
To factor out a GCF from a polynomial we first need to identify the GCF of all the terms, this is the part that goes in front of the parenthesis, then we divide each term by the GCF, the answer is what is left inside the parenthesis. This is shown in the following examples Example 3. 4x2−20x+16 4x2 −20x16GCF is4, divide each term by4
help hurry! 10 points
The school drama club sold 2,400 tickets to a play and made $9,000 from the ticket sales. Student tickets,
X, were $3 and adult tickets, y, were $5.
Create a system of two equations to represent this situation.
Hi!
Given:
total tickets = 2,400 total profit = 9,000student tickets cost $3adult tickets cost $5x = student ticketsy = adult ticketsThe first equation we can make can use the total number of tickets. The total number of tickets would be equal to the number of student tickets plus the number of adult tickets, correct? Therefore:
[tex]x+y=2400[/tex]
Now, the second one can use the profit and the price of each ticket. The number of student tickets multiplied by 3 (for the price) plus the number of adult tickets multiplied by 5 would be equal to the total profit. Hence:
[tex]3x+5y=9000[/tex]
Therefore, your system of equations is:
[tex]x+y=2400[/tex]
[tex]3x+5y=9000[/tex]
A cylindrical flower vase has a height of 8 inches and a diameter of 4 inches. What is the volume of the vase? Use 3.14 for π
I kept getting the answer 401.92 and says it’s not correct, am I doing something wrong? This is what I did
V= π 4^2(8)
V= π 16(8)
V= π 124
V= 3.14 • 124 = 401.92
Reply with reasoning.
Answer:
v=pie r² ×h
v=3.14×2²×8
v= 100.48
Step-by-step explanation:
you are using diameter as the radius that is why exactly you are not getting it right! divide the diameter by 2 to get radius and use it with the formula
20 emails in 5 minutes……. Unit rate
While on vacation in Colorado, an extended
family consisting of x children and y adults visited a
y
historic gold mine. The tickets to visit the gold mine
cost c dollars for children and a dollars for adults.
What is the best interpretation of the following
equation in everyday language? c = a - 7
Answer: The equation for a straight line is a linear equation. Since linear usually stands for anything straight or in a line, thus the equation for lines in the XY plane is referred to be a linear equation. For example, 2x+3y = 5 is a linear equation in two variables.
Step-by-step explanation:
Which expressions are equivalent to the one below? Check all that apply.
9^x
Answer: B, C, E, and F.
Step-by-step explanation: All these answers I picked all simplify to 9^x. A and D both don't simplify to that as both are 27^x.
Hope this helps! :)
Write a+5 as a difference.
Answer:
+(a-5)
Step-by-step explanation:
Take out the positive sign as a common factor and change the middle positive sign to negative.
Every angle in the polygon is a right angle. The area of the polygon is 426 in2
What is the length of the left side of the polygon? Show your work
Plss help
The length of the missing side of the polygon with an area of 426 inches² is 31 inches.
PolygonPolygon is a 2-dimensional shape. They are made of straight lines.
Therefore,
area of the polygon = 426 inches²
The composite figure can be divided into two rectangle. Therefore,
area = area of rectangle 1 + area of rectangle 2
area of rectangle = lw
where
l = lengthw = widthTherefore,
let
the unknown side = x
426 = 26 × 11 + (26 - 19) (x - 11)
426 = 286 + 7x - 77
426 + 77 - 286 = 7x
7x = 217
x = 217 / 7
x = 31
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If 12 out of 15 people recycle aluminum cans, how many people out of 1 million would you expect to recycle? ( Answer fast please!! Due in 20 minutes thank you !)
Answer:
800,000 people
Step-by-step explanation:
Abdul has a rope that is 6 meters long. He cuts away a piece that is 2.39 meters long. How long is the remaining piece of rope?
6 - 2.39 = 3.61 meteres remaining for the rope
John share one pizza with Alan, If Alan ate 3/5 of the pizza, what fraction was eaten by John? *
Step-by-step explanation:
John = 1-(⅗) = ⅖
hope you are helped.
Answer:
if Allan ate 3/5 and the full is 5/5 then John ate 2/5
Which of the following functions best describes this graph?
We see that the zeros of the function are 4 and 5.
Now lets us write that into the equation
[tex]y=(x-4)(x-5)[/tex]
Now multiply that out
[tex]y = x^2-5x-4x + 20 = x^2-9x+20[/tex]
Hope that helped!
need rn! worth 25 points!!!
~Shoto Todoroki here~
Use the form a cos(bx−c)+d
to find the amplitude, period, phase shift, and vertical shift.
Amplitude: 3/4
Period: 2π/3
Phase Shift: None
Vertical Shift: 4
hope this helps :D
pleseeeeeeeee help meeeeeeee
Answer:
33 feet
Step-by-step explanation:
6 sprinklers
5.5 feet each
6x5.5= 33feet
What are the area and perimeter of the figure? Include the units in your answers (units, square units, or cubic units). The area is . The perimeter is . Skip to navigation
Answer:
howdy, I THINK it's 27
Step-by-step explanation:
because I searched it up
abcdef is a regular hexagon of side 6 cm. Find the area of the shaded region.
Answer:
36√3 cm2 is the answer you should be expected
After years of smoking, the most powerful influence for their continuing to smoke is: Please help for Health and make sure you're right
A. To ease anxiety or stress.
B. To satisfy their desire for the taste of a cigarette.
C. To give their hands something to do.
D. Their addiction to nicotine.
Answer:
D. Their addiction to nicotine.
Explanation:
Nicotine is a type of drug which makes it tough for smokers to stop smoking and this is what makes them attracted most. The more nicotine you inhale, the better you feel - giving pleasure. Nicotine is harmful for the body and increases possibility of heart attack.
Jane made a poster that had a length of feet and a width of feet. What is the perimeter of her poster?.
Answer:
Im not completely sure what this question is asking, however I'll try...
Well, if the length is in feet and the width is in feet, that would conclude that the perimeter would also be in feet. If you're asking for the actual number answer for what the perimeter is, I will not be able to help since there is a lack of information; you can only determine the perimeter when given the exact number of feet, both the width and length are.
Step-by-step explanation:
ILL GIVE BRAINLIEST #20 please, how do I know if it’s similar or not? Is it similar
Answer:
Step-by-step explanation:
20.
itis not similar as ratio of corresponding sides is not equal.
4/2=2
6/4=3/2
8/6=4/3
2≠3/2≠4/3
For a standard normal distribution, find the approximate value of p (negative 0.78 less-than-or-equal-to z less-than-or-equal-to 1.16). use the portion of the standard normal table below to help answer the question. z probability 0.00 0.5000 0.16 0.5636 0.22 0.5871 0.78 0.7823 1.00 0.8413 1.16 0.8770 1.78 0.9625 2.00 0.9772 22% 66% 78% 88%
The z-probability for the condition -0.78 ≤ z ≤ 1.16 is 66%.
What is a z-score?
A z-score is a numerical measurement that describes a value's relationship to the mean of a group of values.
It is given that
-0.78 ≤ z ≤ 1.16
We have to find the p-value corresponding to -0.78 ≤ z ≤ 1.16.
This means, p(-0.78 ≤ z ≤ 1.16)
p(0.78≤ z ≤1.16) can be written as p(z ≤ 1.16) - p(z ≤ -0.78)
p(0.78≤ z ≤1.16) = p(z ≤ 1.16) - (1-p(z ≤ 0.78))
p(0.78≤ z ≤1.16) = p(z ≤ 1.16) -1 + p(z ≤ 0.78)
From the standard normal table,
p(z ≤ 1.16)=0.87698
p(z ≤ 0.78)=0.78230
So, p(0.78≤ z ≤1.16)= 0.87698-1+0.78230
p(0.78≤ z ≤1.16) = 0.65928≈0.66 i.e 66%
Therefore, the z-probability for the condition -0.78 ≤ z ≤ 1.16 is 66%.
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Answer:
66%
Step-by-step explanation:
hopes this helps!! have an amazing day <3
Kyle has a notebook for each of his 13 classes he puts 5 stickers on each notebook there are 10 stickers on each sheet how many sheets of stickers will Kyle need?
[tex][Hello,BrainlyUser][/tex]
[tex]\left[Here\; your \;Answer\; below}\right][/tex]
Answer:
7
Step-by-step explanation:
Given;
Kyle has 13 notebooks (1 for each class) and he puts 5 stickers on each one
Solve;
If Kyle wants to put 5 stickers on each of his 13 classroom notebooks, then we simply multiply 5*13 to find out how many stickers he will use in total.
5 * 13 =65
Kyle used 65 stickers total.
Then, to find out how many sheets he used, we will simply divide the total amount of stickers (T) by the amount of stickers on a sheet (S).
T = 65
S = 10
65/10 = 6.5
Thus, He will need 7 sheets, but will only use 6 and a half sheets.
[CloudBreeze]
can someone pls help
Answer 48°
l hope na tama ang sagut ko
help pls don’t know what i’m doing
Step-by-step explanation:
since the polynomial is in the form
+x² - nx - m
we know that we are looking for 2 factors of x (to create x²).
and they must be in the form of
(x + a)(x - b)
to create the negative "m" at the end.
and "b" must be larger than "a" to create the negative "n" in the middle.
let's do the multiplication and compare the parts with our actual expression :
(x + a)(x - b) = x² - bx + ax - ab = x² + (a - b)x - ab
so, we know now in numbers that
-ab = -44
ab = 44
and
a - b = -7
a = b - 7
the short solution here is trial and error with the factors of 44 :
44 = 1×44 = 2×22 = 4×11
ah, only one combination has a difference of the factors of 7 or -7 : 4 and 11.
since b has to be larger (as a - b = -7), we have a = 4 and b = 11
and the factorization of our original expression is
f(x) = (x + 4)(x - 11)
FYI
if there is not such a short list of options to try, we can also go the full formal way :
we can use the second equation as identity in the first equation and get
(b - 7)b = 44
b² - 7b = 44
b² - 7b - 44 = 0
by the way, it is not surprising that it looks the same way as the original expression in x, because the factorization uses exactly the zero solutions for the original expression.
anyway, the formal solution to a quadratic equation of
ax² + bx + c = 0 is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = b (the variable of our equation above)
a = 1
b = -7
c = -44
b = (7 ± sqrt((-7)² - 4×1×-44))/(2×1) =
= (7 ± sqrt(49 + 176))/2 = (7 ± sqrt(225))/2 =
= (7 ± 15)/2
b1 = (7 + 15) / 2 = 22/2 = 11
b2 = (7 - 15) / 2 = 8/2 = 4
based again on the original equations and the fact that b has to be the larger number, we get again (of course) that b1 is the valid solution and
b = 11 and a = 4
The population of Adamsville grew from 10,000 to 18,000 in 6 years. Assuming uninhibited exponential growth, what is the expected population in additional 3 years?
Answer:
22,000
Step-by-step explanation:
If f(1) = 0, what are all the roots of the function f (x) = x cubed 3 x squared minus x minus 3? Use the Remainder Theorem. X = –1, x = 1, or x = 3 x = –3, x = –1, or x = 1 x = –3 or x = 1 x = –1 or x = 3.
All the roots of the provided function If f(1) is equal to the zero are -3, -1 and 1.
What is polynomial?
Polynomial equations is the expression in which the highest power of the unknown variable is n (n is real number).
The function given in the problem is,
[tex]f(x)=x^3+3x^2-x-3[/tex]
If f(1) = 0
[tex]f(1)=(1)^3+3(1)^2-(1)-3\\f(1)=1+3-1-3\\f(1)=0[/tex]
Thus, (x-1) is one of the factor of polynomial. Equate the polynomial equal to the zero, to find other roots as,'
[tex]x^3+3x^2-x-3=0\\x^2(x+3)-1(x+3)=0\\(x+3)(x^2-1)\\(x+3)(x+1)(x-1)=0[/tex]
Equate all the groups to zero to find the roots as,
[tex]x+3=0, x=-3\\x+1=0, x=-1\\x-1=0, x=1[/tex]
Hence, all the roots of the provided function If f(1) is equal to the zero are -3, -1 and 1.
Learn more about polynomial here;
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Answer: B
Step-by-step explanation:
What is the multiple of 7 that are between 44 and 54
Answer:
49 is your only answer........
Step-by-step explanation:
The cafeteria sold 15 more turkey sandwiches than ham sandwiches. They sold 63 sandwiches in all. How many ham sandwiches did the cafeteria sell?
Answer:
48
:)
Step-by-step explanation:
63-15 = 48
48+15= 63
find the volume of the solid