Answer:
There were 35 gallons of gasoline and 500 gallons of kerosene.
Step-by-step explanation:
Step 1: Write data for equation 1
Let gallons of kerosene be x
Let gallons of gasoline be y
Total capacity of truck is 4000
Step 2: Form equation 1
x + y = 4000
Step 3: Write data for equation 2
Profit of total gallons of kerosene is 0.12x
Profit of total gallons of gasoline is 16y
Total profit is $620
Step 4: Form equation 2
0.12x + 16y = 620
Step 5: Find x in terms of y from equation 1
x + y = 4000
x = 4000 - y
Step 6: Substitute value of x in equation 2
0.12x + 16y = 620
0.12 (4000 - y) + 16y = 620
480 - 12y + 16y = 620
4y = 620 - 480
y = 140/4
y = 35
Step 7: Substitute value of y in equation 1 to find x
0.12x + 16y = 620
0.12x + 16 ( 35 ) = 620
0.12x = 60
x = 500
There were 35 gallons of gasoline and 500 gallons of kerosene.
!!
The owner loaded 3500 gallons of gasoline and 500 gallons of kerosene into the 4000-gal oil truck to achieve a profit of $620, by setting up a system of linear equations and solving for both variables.
Explanation:To solve this problem, we can use a system of equations to find out how many gallons of gasoline and kerosene were loaded into the truck. Let's denote gasoline as G and kerosene as K. We know that the total volume of the truck is 4000 gallons, so:
G + K = 4000
Next, considering the profit per gallon, 16e represents 16 cents for gasoline and 12 cents for kerosene. If the total profit is $620, then:
0.16G + 0.12K = 620
To solve this system of equations, we can multiply the second equation by 100 to eliminate the decimals:
16G + 12K = 62000
Now solve one of the equations for a variable, for example:
K = 4000 - G
Substitute K in the profit equation:
16G + 12(4000 - G) = 62000
16G + 48000 - 12G = 62000
4G = 14000
G = 3500
So, we have 3500 gallons of gasoline. Substitute G back into the equation K = 4000 - G:
K = 4000 - 3500
K = 500
Therefore, there were 3500 gallons of gasoline and 500 gallons of kerosene.
what is an irrational number that is between 5.2 and 5.5.
Answer:
The irrational number could be √30
Step-by-step explanation:
An irrational number is a number which can not be written as a ratio between two numbers and it can not be written as a simple fraction. In simple words we can not write it in p/q form.
Find an irrational number that is between 5.2 and 5.5.
Mostly irrational numbers are square root numbers.
So square the both numbers.
(5.2)^2 (5.5)^2.
27.04 , 30.25
It means that the number is between 27.04 and 30.25
We will pick number 30
Square root 30
√30 = 5.48
The irrational number could be √30
It is 5.48 to the hundredth....
The segments shown below could form a triangle.
Answer:
True
Step-by-step explanation:
Answer:
The answer is false.
Step-by-step explanation:
Given line segments are :
AC = 9
CB = 8
AB = 17
As per the triangle inequality theorem the sum of any 2 sides should be greater than the third side. This should be true to all the three combinations.
[tex]AC+CB>AB[/tex] => [tex]9+8>17[/tex] => [tex]17>17[/tex] (not true)
[tex]AC+AB>CB[/tex] => [tex]9+17>8[/tex] => [tex]26>8[/tex] ( true)
[tex]AB+CB>AC[/tex] => [tex]17+8>9[/tex] => [tex]25>9[/tex] (true)
As we can see only two conditions are fulfilled not the third one, so the triangle cannot be formed.
The answer is false.
The perpendicular bisector of a chord...
Choices A and C are both true statements.
But C is trivial. It's CALLED a perpendicular "bisector" of the chord, so OF COURSE it bisects the chord ... otherwise it would be silly to CALL it a "bisector".
The choice that's surprising but true is A .
The perpendicular bisector of a chord passes through the center of the circle.
What is a chord?A chord in plane geometry is a line segment that connects two points on a curve. A line segment whose endpoints are on a circle is frequently described using this phrase. A cycle chord of a graph cycle is an edge that is not in and whose endpoints are in, according to graph theory, which also uses the phrase.
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The description below represents Function A and the table represents Function B:
Function A
The function is 2 more than 5 times x.
Function B
x y
−1 2
0 5
1 8
Which statement is correct about the slope and intercept of the two functions?
A) Their slopes are equal but y-intercepts are not equal.
B) Their slopes are not equal but y-intercepts are equal.
C) Both slopes and y-intercepts are equal.
D) Neither slopes nor y-intercepts are equal.
Answer:
D is correct
Step-by-step explanation:
Step 1 : Find equation of function A in y = mx + c
2 more than 5 times x
f(x) = 2 + 5x or y = 5x + 2
Step 2 : Identify slope and y-intercept of function A
y = mx + c
y = 2 + 5x
Slope = m = 5
Y-intercept = c = 2
Step 3 : Find the equation of function B in y = mx + c
From my understanding, the number given in the question are coordinates
(-1, 2) , (0, 5) , (1, 8)
Slope = y2-y1/x2-x1
Lets take two coordinates : (-1, 2) , (0, 5)
Slope = 5-2/0-(-1)
Slope = 3/1 = 3
For y-intercept
Lets take (1, 8)
y = mx + c
8 = 3(1) + c
c = 5
The equation is f(x) = 3x + 5 or y = 3x + 5
Step 4 : Lets write both equations with their slope and y-intercept and check with the statements
y = 5x + 2
y = 3x + 5
A) Their slopes are equal but y-intercepts are not equal. Incorrect
B) Their slopes are not equal but y-intercepts are equal. Incorrect
C) Both slopes and y-intercepts are equal. Incorrect
D) Neither slopes nor y-intercepts are equal. Correct
!!
Find the missing value in the pair of similar polygons.
x³-64 in prime factored form
[tex]\bf \textit{difference and sum of cubes} \\\\ a^3+b^3 = (a+b)(a^2-ab+b^2) \qquad \qquad a^3-b^3 = (a-b)(a^2+ab+b^2) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ x^3-64\implies x^3-4^3\implies (x-4)(x^2+4x+4^2)\implies (x-4)(x^2+4x+16)[/tex]
the sum of 1/5 and twice a number is equal to 4/5 subtracted from three times the number. find the number.
Answer:
1
Step-by-step explanation:
Your equation may be written as follows:
[tex]\frac{1}{5} +2n=3n-\frac{4}{5}[/tex]
Start by multiplying both sides by 5 to clear your fractions.
[tex]\frac{1}{5} +2n=3n-\frac{4}{5} \\1+10n=15n-4[/tex]
Next, subtract 10n from both sides.
[tex]1+10n=15n-4\\1=5n-4[/tex]
Add 4 to both sides.
[tex]1=5n-4\\5=5n[/tex]
Divide both sides by 5 to solve for n.
[tex]5=5n\\1=n[/tex]
Final answer:
By setting up an equation 1/5 + 2x = 3x - 4/5 and solving for x, we find that the number is 1.
Explanation:
The problem involves finding a number when given a relationship involving fractions and that number. The relationship is: the sum of 1/5 and twice a number is equal to 4/5 subtracted from three times the number. To find the number, we set up an equation and solve for the variable, which represents the number.
Let's denote the number as x. Our equation can be written as:
1/5 + 2x = 3x - 4/5
We bring all the x terms on one side and the constants on the other to solve for x:
2x - 3x = -4/5 - 1/5
-x = -1
x = 1
120 is increased by d % and increased by 25% . What is the result ?
Please see attached image for complete answer and steps in detail.
Answer:
The result is 150 + 1.5d
Step-by-step explanation:
We want to translate the wordings into algebraic expression.
Firstly, we increase 120 by d%
d% = d/100
So increasing 120 by d % means;
120 + (d/100 * 120)
= 120 + 1.2d
Then increase this by 25%
= (120 + 1.2d) + 25/100(120 + 1.2d)
= 120 + 1.2d + (120+1.2d)/4
= 120 + 1.2d + 30 + 0.3d
= 120 + 30 + 1.2d + 0.3d
= 150 + 1.5d
I need help with #17 please and thank you!
Convert -sqrt3 - i to polar form. PLEASE HELP. Photo has more information
Answer:
-√3 - i ⇒ (2 , 7/6 π)
Step-by-step explanation:
* Lets explain how to convert a point in Cartesian form to polar form
- Polar coordinates of a point is (r , θ).
- The origin is called the pole, and the x axis is called the polar axis,
because every angle is dependent on it.
- The angle measurement θ can be expressed in radians or degrees.
- To convert from Cartesian Coordinates (x , y) to Polar
Coordinates (r , θ)
1. r = √( x² + y² )
2. θ = tan^-1 (y/x)
* Lets solve the problem
∵ The point in the Cartesian form is z = -√3 - i, where -√3 is the real
part and -i is the imaginary part
∴ The x-coordinate of the point is -√3
∴ The y-coordinate of the point is -1
∵ Both the coordinates are negative
∴ The point lies on the 3rd quadrant
- To convert it to the polar form find r and Ф
∵ [tex]r=\sqrt{x^{2}+y^{2}}[/tex]
∵ x = -√3 and y = -1
∴ [tex]r=\sqrt{(-\sqrt{3}) ^{2}+(-1)^{2}}=\sqrt{3+1}=\sqrt{4}=2[/tex]
∵ Ф = [tex]tan^{-1}\frac{y}{x}[/tex]
∴ Ф = [tex]\frac{-1}{-\sqrt{3}}=\frac{1}{\sqrt{3}}[/tex]
- The acute angle π/6 has tan^-1 (1/√3)
∵ The point is in the third quadrant
∴ Ф = π + π/6 = 7/6 π
- Lets write it in the polar form
∴ -√3 - i ⇒ (2 , 7/6 π)
Answer:
2cis 7pi/6
Step-by-step explanation:
In the Pythagorean Theorem, what
does the "a" stand for?
a2 + b2 = c2
A. The longest side, or hypotenuse, of a right triangle.
B. One of the sides, or legs, that make up the right
angle.
C. Any unknown side of a right triangle.
Answer:
B. One of the sides, or legs, that make up the right angle.
Step-by-step explanation:
The Pythagoras Theorem applies to the right-angled triangles. It is basically a relationship between the sizes of the all lengths of the triangle. The Pythagoras Theorem is given by:
C^2 = A^2 + B^2; where A and B are perpendicular and base respectively, and C is the hypotenuse. It is interesting to note that A can either be the perpendicular or the base of the right angled triangle. Same goes for B; it can be either the perpendicular or the base. Both the perpendicular and the base intersect at 90 degrees. But both cannot be the hypotenuse. Therefore, the variable A in the Pythagoras Theorem is one of the sides, or legs, that make up the right angle, i.e. Option B is the correct answer!!!
If f(x) = 4 – x2 and g(x) = 6x, which expression is equivalent to (9 - 1)(3)?
Answer:
(g − f) ( 3 ) = 23
Step-by-step explanation:
( g − f ) ( x ) = g ( x ) − f ( x )
= 6 x − ( 4 − x 2 )
= x 2 + 6 x − 4
to evaluate ( g - f ) ( 3 ) substitute x = 3 into ( g − f ) ( x )
( g − f ) = ( 3 ) 2 + ( 6 x 3 ) - 4 =23
For this case we have the following functions:
[tex]f (x) = 4-x ^ 2\\g (x) = 6x[/tex]
By definition we have to:
[tex](f-g) (x) = f (x) -g (x)\\(g-f) (x) = g (x) -f (x)[/tex]
Then, we find [tex](f-g) (x):[/tex]
[tex]f (x) -g (x) = 4-x ^ 2-6x = -x ^ 2-6x 4[/tex]
We evaluate the function in 3:
[tex](f-g) (3) = - (3) ^ 2-6 (3) 4 = -9-18 4 = -27 4 = -23[/tex]
Now we find[tex](g-f) (x):[/tex]
[tex]g (x) -f (x) = 6x- (4-x ^ 2) = 6x-4 x ^ 2 = x ^ 2 6x-4[/tex]
We evaluate the function in 3
[tex](g-f) (3) = 3 ^ 2 6 (3) -4 = 9 18-4 = 23[/tex]
Answer:
[tex](f-g) (3) = - 23\\(g-f) (3) = 23[/tex]
What is the median of this data set?
22, 37, 49, 15, 82
O
<
A. 37
O B. 27
O C. 31
O D. 41
Answer:
A. 37
Step by step explanation:
The median is the middle value with high to low frequency and low to high frequency. How to determine the median is to sort the numbers from the smallest to the big number and the largest number to the smallest number, then count using two hands (one finger left hand and one finger right hand).
Method:
22, 37, 49, 15, 82 then sorted: 82, 49, 37, 22, 15 means the median is 37
-----------------------✨ Awesome ✨-----------------------The median of this data set is 49.
Option A is correct.
What is Median of the Data?The median is the value in the middle of a data set, which means that 50% of the data points have a value less than or equal to the median, and 50% of the data points have a value greater than or equal to the median. Given a small data set, count the number of data points (n) and arrange them in increasing order.
We have the data: 22, 37, 49, 15, 82
Now, arranging the data in Ascending order as
15, 22, 37, 49, 82
Now, the median is the middle term of the data.
Here there are 5 terms.
So, the median of data is 37.
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What is each power of i with its multiplicative inverse.
1. i
2. i ^2
3. i ^3
4. i ^4
Answer:
1) multiplicative inverse of i = -i
2) Multiplicative inverse of i^2 = -1
3) Multiplicative inverse of i^3 = i
4) Multiplicative inverse of i^4 = 1
Step-by-step explanation:
We have to find multiplicative inverse of each of the following.
1) i
The multiplicative inverse is 1/i
if i is in the denominator we find their conjugate
[tex]=1/i * i/i\\=i/i^2\\=We\,\, know\,\, that\,\, i^2 = -1\\=i/(-1)\\= -i[/tex]
So, multiplicative inverse of i = -i
2) i^2
The multiplicative inverse is 1/i^2
We know that i^2 = -1
1/-1 = -1
so, Multiplicative inverse of i^2 = -1
3) i^3
The multiplicative inverse is 1/i^3
We know that i^2 = -1
and i^3 = i.i^2
[tex]1/i^3\\=1/i.i^2 \\=1/i(-1)\\=-1/i * i/i\\=-i/i^2\\= -i/-1\\= i[/tex]
so, Multiplicative inverse of i^3 = i
4) i^4
The multiplicative inverse is 1/i^4
We know that i^2 = -1
and i^4 = i^2.i^2
[tex]=1/i^2.i^2\\=1/(-1)(-1)\\=1/1\\=1[/tex]
so, Multiplicative inverse of i^4 = 1
Amanda owns a clothing store that sells graphic t-shirts. n is the number of shirts she sells each month. the revenue function of her store is r = 15n. the cost function of her store is c = 9n + 450. using your calculator, what is the break-even point of amanda's store?
Answer:
The break- even point is attained when n=75
Step-by-step explanation:
The break-even point is defined as the point where revenue is equal to cost.
We take the equation for revenue r=15n, and set it equal to the equation c=9n+450
15n=9n+450
Subtract 9n from both sides:
6n=450
Divide both sides by 6.
6n/6=450/6
n=75
The break- even point is attained when n=75....
Final answer:
To determine Amanda's store's break-even point, set the revenue equal to the cost function and solve for n to find 75 shirts.
Explanation:
To find the break-even point of Amanda's store:
Set the revenue function equal to the cost function: 15n = 9n + 450
Solve for n: n = 75
Therefore, the break-even point is when Amanda sells 75 graphic t-shirts.
A football team started at the line of scrimmage. On the first play of the drive, the team lost 4 yards. On the second play of the drive, the team gained 45 yards. Taylor calculated |–4 – 45| = |–49| = 49, and said that the team gained a total of 49 yards on the two plays. Which best describes Taylor’s error?
A. Taylor did not find the correct distance between –4 and 45.
B. Taylor did not make an error. The team gained a total of 49 yards on the two plays.
C. Taylor correctly found the distance between –4 and 45, but this number represents the team’s total loss, not the team’s total gain.
D. Taylor correctly found the distance between –4 and 45, but this number represents the total distance the team moved in both directions, not the team’s total gain.
Answer:
D. Taylor correctly found the distance between –4 and 45, but this number represents the total distance the team moved in both directions, not the team’s total gain.
Step-by-step explanation:
The team only ended up gaining the 45 yards on the second play and had gained -4 on the first play. 45-4≠49, but the total distance between -4 and 45 is 49.
Answer:
D.
Step-by-step explanation:
1. If x[tex]y^{2}[/tex] and xy are perfect squares, where x and y are positive integers, what is the smallest value of x + y?
Answer:
8
Step-by-step explanation:
xy^2 = k*k y^2 x = k * k so x has to be a perfect square.
xy is a perfect square which means that since x is a perfect square (see above) then y will have to be as well
There is nothing that prohibits x = 4 and y = 4 as being the answer where x = y.
I think the smallest possible value for x + y is 8.
This excludes any possibility of 1 or 0 in some combination, although I would look into 1.
Evaluate the expression -66/(-3)+(-4)-(-5)
Answer:
-21
Step-by-step explanation:
For this case we must evaluate the following expression:
[tex]\frac {-66} {(- 3)} + (- 4) - (- 5) =[/tex]
We solve the division:
[tex]22 + (- 4) - (- 5) =[/tex]
We eliminate parentheses keeping in mind that:
[tex]+ * - = -\\- * - = +[/tex]
So:
[tex]22-4 + 5 =[/tex]
Different signs are added and the same sign is placed, while different signs are subtracted and the sign of the major is placed:
[tex]18 + 5 =\\23[/tex]
Answer:
23
factor the trinomial below. 4x^2+23-6. which two binomials are factors of the trinomial
Answer:
4x - 1 and x + 6 are the factors of given Trinomial
Step-by-step explanation:
The given Trinomial is:
[tex]4x^{2}+23x-6[/tex]
We can factorize this trinomial by mid-term splitting. The mid-term(23x) can be split up in two terms (24x and -x) such that their sum is 23x and their product(-24x²) is equal to the product of other two terms (4x² and -6)
So, the above expression can be written as:
[tex]4x^{2}+23x-6\\\\ =4x^{2}+24x-x-6\\\\\text{Taking out commons, we get}\\\\=4x(x+6)-1(x+6)\\\\ =(4x-1)(x+6)[/tex]
Therefore, 4x - 1 and x + 6 are the factors of given Trinomial
Answer: 4x-1 and x+6
Step-by-step explanation: a p e x
hat is the approximate area of the circle shown below?
A. 60 in 2
B. 119 in 2
c. 4536 in 2
d. 1134 in 2
Help Me Please!!!!!!!!!!!!!!!!!!!!!!
Answer:
d. 1134 inches squared
Step-by-step explanation:
The formula for the area of a circle is [tex]\pi r^2[/tex]
where r is the radius.
You are given r=19 here so replace r in [tex]\pi r^2[/tex] with 19 giving us:
[tex]\pi (19)^2[/tex]
Then it is to the calculator we go:
1134 inches squared
Write the slope-intercept form of the equation that passes through the point (4,-6) and is parallel to the line y = -3/4x - 5 y = -3/4x - 3 y = -3/4x + 3 y = 4/3x + 2/3 y = 4/3x - 34/3
Answer:
[tex]\large\boxed{y=-\dfrac{3}{4}x-3}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
y = mx + b
m - slope
b - y-intercept
Parallel lines have the same slope.
===========================================
We have the equation of the line: [tex]y=-\dfrac{3}{4}x-5[/tex]
The slope is [tex]m=-\dfrac{3}{4}[/tex].
Put the value of the slope and the coordinates of the point (4, -6) to an equation of a line:
[tex]-6=-\dfrac{3}{4}(4)+b[/tex]
[tex]-6=-3+b[/tex] add 3 to both sides
[tex]-3=b\to b=-3[/tex]
Finally:
[tex]y=-\dfrac{3}{4}x-3[/tex]
Linda is twice the age of Vera.
Tanya is four less than four times the age of Linda.
Their total age is two more than nine times the age of Vera.
How old is Tanya?
Answer:
Tanya is 20 years old
Step-by-step explanation:
Let the age of Vera = x years
The age of Linda is twice the age of Vera = 2x years
Tanya is four less than four times the age of Linda = 4(2x)-4 = 8x-4
Total age of Vera, Linda and Tanya is:
x+2x+8x-4
Combine the like terms:
11x-4
But now their total age is two more than nine times the age of Vera:
11x-4 = 9x+2
Solve the expression
Combine the like terms:
11x-9x=2+4
2x=6
Divide both the sides by 2
2x/2 = 6/2
x= 3
Thus the age of Vera is 3 years.
The age of Linda is 2x= 2*3 = 6 years
The age of Tanya is 8x-4 = 8*3 - 4 = 24-4 = 20years....
What was done to the quadratic parent function F(x) = x2 to get the
function G(x) = x2 - 3? 0)
A.Shifted 3 units to the right
B. Vertically stretched by multiplying by 3
C.Shifted 3 units down
D.Shifted 3 units to the left
ОА ОВ Oc OD
HINT
SUBMIT
Answer:
Option C.
Step-by-step explanation:
If k<0, the function g(x) = f(x) + k represents the function f(x) shifted k units downwards.
In this case, given that k=-3 (k<0). The graph was shifted 3 units down. Therefore, the correct option is Option C.
10x^3 y^-5 z^-2 if x=3 y=2 and z=5 express your answer as a reduced fraction
Answer:
[tex]\large\boxed{\dfrac{27}{80}}[/tex]
Step-by-step explanation:
Put x = 3, y = 2 and z = 5 to the given expression [tex]10x^3y^{-5}z^{-2}[/tex]:
[tex]10(3^3)(2^{-5})(5^{-2})\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=\dfrac{10(27)}{(2^5)(5^2)}=\dfrac{270}{(32)(25)}=\dfrac{270}{800}=\dfrac{27}{80}[/tex]
Francis teaches the piano. He charges each student an enrollment fee of $100 plus $15 per hour of piano lessons. The average cost of lessons for a
student per hour is $25
If h represents the number of hours a student spends in lessons, which equation can be used to find the value of h?
Answer:
The first one should be right. Since the teacher is charging $15 per hour of the piano lesson then it can't be any of the answers of $100h. The answer can't be C, the third one, since you're adding the enrollment fee to the cost of every piano lesson it would be wrong to subtract the $100. Hope that helps!
Step-by-step explanation:
The answer will the answer on the top $25=$100+$15h over h
Answer: The number of hours is 10 hours.
Step-by-step explanation:
Since we have given that
Average cost of lessons = $25
let h be the number of hours a student spends in lessons.
Since each student has fee of $100 plus $15 per hour.
So, According to question, it becomes,
[tex]25=\dfrac{100+15h}{h}\\\\25h=100+15h\\\\25h-15h=100\\\\10h=100\\\\h=\dfrac{100}{10}\\\\h=10[/tex]
Hence, the number of hours is 10 hours.
simplify -(x+5) + 3x completely
Answer:2x-5
Step-by-step explanation:-(x+5)+3x
-x-5+3x=(3x-x) -5
=2x-5
rewrite square root of -49 -4 in complex number notation please help
Note that if [tex]i^2=-1[/tex] than [tex]i=\sqrt{-1}[/tex],
Also note that [tex]\sqrt{ab}=\sqrt{a}\sqrt{b}[/tex]
So we have,
[tex]\sqrt{-49}=\sqrt{-1}\sqrt{49}=\boxed{7i}[/tex]
and,
[tex]\sqrt{-4}=\sqrt{-1}\sqrt{4}=\boxed{2i}[/tex]
Hope this helps.
r3t40
i need help with question 2. i think my answer is incorrect.
Answer:
395
You are 100% right! You go!
Step-by-step explanation:
We are given f(x)=5x^2-2x+8 and are asked to find the value of the function at x=9.
So replace x with (9):
f(9)=5(9)^2-2(9)+8
f(9)=5(81)-18+8 I did the exponent 9^2 and 2(9) in this step:
f(9)=405-18+8 I did 5(81) in this step
f(9)=405-10 I did -18+8 in this step
f(9)=395
the sum of four consecutive odd integers is -72. What is the value of the four intergers
Answer:
let the integers be x, x+2, x+4 and x+6
therefore,
x + x+2 + x+4 + x+6 = -72
=> 4x + 12 = -72
=> 4x = -72 - 12
=> x = -84/4
=> x = -21
therefore the integers are: -21, -19, -17, -15
[tex]\huge\boxed{\text{-21, -19, -17, -15}}[/tex]
Represent this mathematically. [tex]x+(x+2)+(x+4)+(x+6)=-72[/tex]
Combine like terms. [tex]4x+12=-72[/tex]
Subtract 12 from both sides. [tex]4x=-84[/tex]
Divide both sides by 4. [tex]x=-21[/tex]
Find the numbers by adding 2 each time. [tex]-21, -19, -17, -15[/tex]
A train can hold 78 passengers. The train starts out empty and picks up one passenger at the first stop,2 passengers at the second stop,3 passengers at the third stop,and so forth. After how many stops will the train be full.
Answer:
After the 12th Stop
Step-by-step explanation:
2nd stop 1+2=3
3rd 3+3=6
4th 6+4=10
5th 10+5=15
6th 15+6=21
7th 21+7=28
8th 28+8=36
9th 36+9=45
10th 45+10=55
11th 55+11=66
12th 66+12=78
After the 12th stop.
The train will be full after 12 full stops. If we include the 13th stop, the train would exceed its capacity. Therefore, the train can handle 12 full stops if it picks one passenger at the first stop and increases the number of passengers picked by one at each stop.
Explanation:The problem you're describing is a summation problem in mathematics. You're incrementing the number of passengers at each stop starting at one and increasing by one each time. This can be summed up using the formula for the sum of the first n positive integers (including one), which is n*(n+1)/2. To find out after how many stops the train will be full, you'll need to solve this formula for n such that this sum is less than or equal to 78 (the capacity of the train). You can do this by substitution or by solving the quadratic equation, n² + n - 156 = 0. The result is roughly 12.421, which means that after 12 full stops, the train will have 78 passengers (since we can't have a fraction of a stop). After the 13th stop, the train will exceed its capacity.
Learn more about Summation and Quadratic Equation here:https://brainly.com/question/33445956
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