In 1992, jason bought a gallon of gas for $1.23. yesterday, he bought a gallon of gas for $2.19. what is the percentage increase of the price of a gallon of gas from 1992 to yesterday? if necessary, round to the nearest tenth of a percent.

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Final answer:

To solve a quadratic equation using the quadratic formula, put the equation in ax² + bx + c = 0 form, identify a, b, and c, plug them into the formula x = (-b ± √(b² - 4ac)) / (2a), calculate the discriminant, and find the two possible values for x.

Explanation:

To solve a quadratic equation by using the quadratic formula, you should follow these steps:

First, make sure that the equation is in the standard quadratic form, which is ax² + bx + c = 0.Identify the coefficients a, b, and c from the equation.Plug these values into the quadratic formula, which is x = (-b ± √(b² - 4ac)) / (2a).Calculate the discriminant D, which is the part under the square root: b² - 4ac.The discriminant tells you the nature of the roots:
If D is positive, there are two real and distinct solutions.If D is zero, there is one real solution.If D is negative, there are two complex solutions.Finally, calculate the two possible values for x using the plus and minus signs in the formula and simplify as needed.

For example, if we have the equation t² + 10t - 200 = 0, by identifying a=1, b=10, and c=-200, and plugging them into the quadratic formula, we can solve for t.

Answer:

171 degrees

Step-by-step explanation:

40-sided polygon has an interior angle equal to:

(40 - 2) (180) /40 = 171 degrees

The length of the rectangle is 10 cm and the width of the rectangle is 5 cm because 2(10)+2(5)=30

I hope this helps you




p^2+13p-30=0


p +15


p -2


(p+15)(p-2)=0


p= -15


p=2

Answer:

The correct option is D.

Step-by-step explanation:

The given quadratic equation is

[tex]p^2+13p-30=0[/tex]

First find two numbers whose sum is 13 and whose product is -30.

The two numbers are 15 and -2.

[tex]p^2+(15-2)p-30=0[/tex]

[tex]p^2+15p-2p-30=0[/tex]

[tex]p(p+15)-2(p+15)=0[/tex]

[tex](p+15)(p-2)=0[/tex]

By using zero product property, equate each factor equal to 0.

[tex]p+15=0[/tex]

[tex]p=-15[/tex]

[tex]p-2=0[/tex]

[tex]p=2[/tex]

Therefore the values of p are -15 and 2. Option D is correct.

Final answer:

The function rule representing a worker's earnings e as a function of hours n worked at a rate of $8.75 per hour is e(n) = 8.75 × n. This formula is used to calculate the worker's pay based on their hours worked.

Explanation:

To represent a worker's earnings e as a function of the number of hours n worked at a rate of $8.75 per hour, you would write the function rule as:

e(n) = 8.75 × n

Here, n represents the number of hours worked and e(n) represents the earnings for those hours.

For example, if a worker puts in 8 hours of work, their earnings would be calculated as:

e(8) = 8.75 × 8

      = $70

This means the worker would earn $70 for an 8-hour workday.

The Factor theorem states that  for any polynomial f(x) if f(c)=0 then x-c is a factor of the polynomial f(x).

If any polynomial f(x) is divided by x-a and remainder is 0 that means f(a)= 0 .In other words we can say x-a is a factor of the polynomial f(x).So the statement :If a polynomial is divided by (x-a) and the remainder equals zero then (x -a) is a factor of the polynomial is True.

It is true that (x -a) is a factor of the polynomial.

How to determine the true statement?

Let the polynomial function be f(x)

When divided by x -a, we have:

f(x)/(x - a) = Some polynomial remainder 0

The above can be represented as

f(a) = 0

This means that it is true that (x -a) is a factor of the polynomial.

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Answer:

Option 4). Machine with $8 per hour operating cost, producing 14 pounds of candy per hour.

Step-by-step explanation:

We have to find the most profitable investment for a candy shop that earns $1 per pound of candy.

We will take up each option one by one.

Option 1).

Producing eight pounds of candy per hours means profit = $1×8 = $8

But workers take $10 per hours so expenditure = $8 - $10 = -$2

There is a loss of $2 in this investment.

Option 2).

Production of 16 pounds candy per hour will make the profit = $1 × 16 = $16

But workers take $12 per hour so profit earned = 16 - 12 = $4

Option 3).

Machine produces 10 pound of candy per hour so profit will be = $1 ×10 = $10

Operating cost of the machine = $5 per hour

So profit generated = profit - Operating cost of machine

                                 = 10 - 5 = $5

Option 4).

Profit earned by production of 14 pounds of candy per hour = $1 × 14 = $14

Operating cost of the machine = $8 per hour

Therefore, Total profit per hour = 14 - 8 = $6

Finally we can say that the maximum profit will be generated in option 4.

Therefore, Option 4) will be the best option to invest.

Final answer:

The most profitable investment for a candy shop is the machine with an $8 per hour operating cost, producing 14 pounds of candy per hour, yielding a net profit of $6 per hour.

Explanation:

The task is to determine the most profitable investment for a candy shop that makes $1 profit per pound of candy. To calculate the profitability of each option, we need to figure out the net profit per hour for each.

Worker at $10 per hour, producing eight pounds of candy per hour:

Profit = 8 pounds * $1 profit per pound - $10 wage per hour = $8 - $10 = -$2 per hour.

Worker at $12 per hour, producing 16 pounds of candy per hour:

Profit = 16 pounds * $1 profit per pound - $12 wage per hour = $16 - $12 = $4 per hour.

Machine with $5 per hour operating cost, producing 10 pounds of candy per hour:

Profit = 10 pounds * $1 profit per pound - $5 operating cost per hour = $10 - $5 = $5 per hour.

Machine with $8 per hour operating cost, producing 14 pounds of candy per hour:

Profit = 14 pounds * $1 profit per pound - $8 operating cost per hour = $14 - $8 = $6 per hour.

Comparing the net profit per hour for each option, the Machine with $8 per hour operating cost, producing 14 pounds of candy per hour, is the most profitable investment.

The apparent solution is (1,2) because it moves over 1 on the x axis and 2 up on the y axis.

Solution for system of 2 equations of lines is coordinates of point at which those 2 lines intercept. The reason for is that those coordinates fit in both equations. IF you implement coordinates of that point in either of those equations of 2 lines you will see that left side is equal to right side which means that that point belongs to that line. 

This method here is graphical method of solving system of equations. Other method is, of course, solving system of equations using math...

Answer is (1,2)

When you ask "what do you add to A to get B, you solve it by subtracting.
For example, what do you add to 5 to get 13?
Subtract 13 - 5 = 8
The answer is you add 8 to 5 to get 13.

Now you need to do the same with your polynomials.
What do you add to x^2 - 2x + 6 to get 3x^2 + 7x?

To find the answer, subtract

(3x^2 + 7x) - (x^2 - 2x + 6)

Explanation is given step by step just below:
tan(theta(t))=y(t)/x(t)

differentiate
sec^2(theta(t))*theta'(t)=y'(t)x(t)-y(t)x'(t)/x^2(t)
thus
theta'(t)=(y'(t)x(t)-y(t)x'(t))
divided by (x^2(t)*sec^2(θ(t))

Answer:

dθ/dt = [(cos^2 θ)*(dy/dt * x - y * dx/dt)]/(x^2)

Step-by-step explanation:

Given that x and y are the lengths of the sides adjacent and opposite θ, then they are related by:

tan θ = y/x

Differentiating respect to t, we get:

sec^2 θ * dθ/dt = (dy/dt * x - y * dx/dt)/(x^2)

dθ/dt = [(cos^2 θ)*(dy/dt * x - y * dx/dt)]/(x^2)

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y = 7x - 4x² 

7x - 4x² = 0 

x(7 - 4x) = 0 

x = 0, 7/4 

Find the area of the bounded region... 

A = ∫ 7x - 4x² dx |(0 to 7/4) 

A = 7/2 x² - 4/3 x³ |(0 to 7/4) 

A = 7/2(7/4)² - 4/3(7/4)³ - 0 = 3.573 

Half of this area is 1.786, now set up an integral that is equal to this area but bounded by the parabola and the line going through the origin... 

y = mx + c 

c = 0 since it goes through the origin 

The point where the line intersects the parabola we shall call (a, b) 

y = mx ===> b = m(a) 

Slope = m = b/a 

Now we need to integrate from 0 to a to find the area bounded by the parabola and the line... 

1.786 = ∫ 7x - 4x² - (b/a)x dx |(0 to a) 

1.786 = (7/2)x² - (4/3)x³ - (b/2a)x² |(0 to a) 

1.786 = (7/2)a² - (4/3)a³ - (b/2a)a² - 0 

1.786 = (7/2)a² - (4/3)a³ - b(a/2) 

Remember that (a, b) is also a point on the parabola so y = 7x - 4x² ==> b = 7a - 4a² 
Substitute... 

1.786 = (7/2)a² - (4/3)a³ - (7a - 4a²)(a/2) 

1.786 = (7/2)a² - (4/3)a³ - (7/2)a² + 2a³ 

(2/3)a³ = 1.786 

a = ∛[(3/2)(1.786)] 

a = 1.39 

b = 7(1.39) - 4(1.39)² = 2.00 

Slope = m = b/a = 2.00 / 1.39 = 1.44

Final answer:

The slope of the line that divides the region bounded by the parabola y=2x-4x^2 and the x-axis into two regions with equal area is -2.

Explanation:

To find the slope of the line that divides the region bounded by the parabola y=2x-4x^2 and the x-axis into two regions with equal area, we need to set up an integral to find the area under the parabola. The equation of the line will be in the form y = mx, where m is the slope we need to find. Setting up the integral, we get:

Solve the integral to find:

Substituting the limits of integration and solving, we get:

Therefore, the slope of the line that divides the region into two equal areas is -2.

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Ix-4I=3 
The supreme esteem condition above implies that x-4 is equivalent to 3, OR, that x-4 is equivalent to - 3. 
On the off chance that x-4=3, then x=7. On the off chance that x-4=-3, then x=1. 
Presently envision the number line with the numbers 1 and 7 set apart with a dab. 
The number 4 is in the focal point of that fragment. What's more, the numbers 1 and 7 are at a separation of precisely 3 units of the number 4 which is at the middle. 
That is precisely what the outright esteem condition is requesting that you discover. Which numbers are inside a separation of 3 units of 4. Also, your answer is x=1 and x=7.

I hope this helps you




y=2/3x+7.3/3.1


y=2x+21/3


3y=2x+21


3y-2x=21

The answer is: [A]: -2x + 3y = 21 .
___________________
Note that "standard form" refers to:
_______________________________
→  Ax +By =C ;
      in which "x" and "y" are variables; "A" and "B" represent the coefficients before those variables, respectively; and "C" is a number (not a variable).
_______________________________
I shall demonstrate 2 (two) methods to convert the equation given:
________________________________________
→  y = (⅔) x + 7 ;   to "standard form".).
_____________________ 
Method 1:
_______________________
→ Given: y = (⅔)x + 7 ; 
______________________
→ Subtract "y" from EACH SIDE of the equation; and subtract "7" from EACH SIDE of the equation. Doing so: 1) puts the "x" and "y' values on one side of the equation; 2) removes a numeric value from the side of the equation with the "x" and "y" values; and 3) puts a numeric value on a side of the equation that does not have any "x" or "y" values — all three of which help to convert to equation to "standard form"—that is, " Ax + By = C " ;
____________
→ y = (⅔)x + 7 ;  → y − y − 7 = (⅔)x + 7 − y − 7 ; To get:
____________
→  -7 = (⅔)x − y  ↔ Rewrite as: (⅔)x − y = -7 ;
________________________
Note:  While this very would could be an answer in"standard form"; 
 "Ax + By = C", in which A = ⅔ , B = -1; and C = -7; 
                     (Note: There is an implied "1" before the "y", since  "1*y = y; 
                                    since: y*1 = y; (anything * 1 = said number); 
                                     and the coefficient is "-1" (NEGATIVE 1); since the                                               "standard form" is: "Ax + By = C; and we have: 

                                                                             (⅔)x − y = -7 ; so the:
"− y" functions as a: PLUS "negative 1y"; in this circumstance.
_________________________________________________
However, this equation—as written—does NOT match any of the answer choices given.
___________________
→So, now we should multiply our ENTIRE equation (BOTH SIDES) by "-3"; for the sake of:  
___________________
1) getting an answer choice that matches one of the answer choices given;
AND: 
2) for the general sake of simplicity—which would include getting the "-7" changed to a "positive 21" ;
_______________________.
 → {Note: A non-zero, negative integer, when multiplied by another non-zero, negative integer; will result in a non-zero POSITIVE integer.
 As such: -7 *-3 = 21}.
_________________
We have:  (⅔)x − y = -7 ; We shall multiply EACH SIDE of the equation by "-3";     → -3 * {(⅔)x − y = -7} ;
______________________
→  Note: Start with:
   →"(-3 * (⅔)x =  -3 * ⅔ * x ;
   →   -3 * ⅔  = [tex] \frac{-3}{1} [/tex] * [tex] \frac{2}{3} [/tex]  =(-3*2)/(1*3)
= -6 / 3 = -2 ;  → Don't forget to bring down the "x":  -2 * x = -2x ; 
→ So: - 3 *(⅔)x = - 2x ;
_________________
The next term: -3 *-1y = +3y ; (Note: -3 *-1y = (-3* -1)*y = 3*y = +3y ;
____________________
The next term: -3*(-7) = +21 ;
_______________________________________
→ to get:  → -2x + 3y = 21 ; which is: 'Answer choice: [A]'.
___________________________________________________________
Method 2:
____________
Given: y = (⅔)x + 7 ; write in standard form:
_________________________
 →  Given:    y = (⅔)x + 7 ; Multiply EACH SIDE of the equation by "3", to get rid of the fraction, "(⅔)" ; 
___________________________
 → 3* { y = (⅔)x + 7 } ;  to get:
____________________________
First term: 3*y  = 3y;  

Second term: 3*((⅔)x)) = 3 * (⅔) * x ;  3 * (⅔) = (3/1)*(2/3) =(3*2)/(1*3) =
6/3 = 2; → Don't forget the "x" → 2 * x
    = 2x;
___________________
Third term: 3*7 = 21;
__________________
→To get: → 3y = 2x + 21 ; 
____________________________
 → Now, subtract "3y" and subtract "21" from EACH SIDE of the equation:
____________________________
→ 3y = 2x + 21 ;   →  3y − 21 − 3y = 2x + 21 − 3y − 21 ;
_____________________________________________
to get: →  -21 = 2x − 3y ; → Rewrite as: → 2x − 3y = -21 ;

______________________________
Note:  This would appear in "standard form" equation; "Ax + By = C"; 
                       in which A = 2; B = 3; C = -21;
___________________________________________
However,  " 2x − 3y = -21 " ;  is NOT an answer choice given.
______________________________
However, there are answer choices given with "21" {note: "positive 21"} representing the number for "C" within the "standard form" equation: 
________
→ "Ax + By = C"
_________________
 So, given our equation:
________________________
→ 2x − 3y = -21 ;
          → We can multiply the ENTIRE equation (BOTH sides) by "-1" ; to                 change the "-21" value to "21" (positive 21); and see if the equation matches any of the answer choices:
______________
→  -1 * {2x − 3y = -21} ; 
______________
First term:  -1* 2x = -2x ; 

Second term: -1 * -3y = -1 * -3 * y = +3y ; 

Third term: -1 * -21 = + 21
___________________________
→  -2x + 3y = 21 ; which is:   'Answer choice: [A]'.

The correct answer is $6000.00

The original cost of the mink coats was $6,000. This is determined by dividing the markup amount of $3,000 by the markup percentage, which is 50% or 0.50 in decimal form.

A 50% markup on cost means that the extra amount added to the cost price of the coats is 50% of that original cost price. Since the markup on the mink coats is given as $3,000, we can set up the equation as follows to find the original cost price (C):

Markup = 50% of Cost
3000 = 0.50  imes C

To find the cost (C), we divide the markup by the percentage, which in decimal form is 0.50:

C = $3,000 / 0.50
C = $6,000

Hence, the original cost of the mink coats was $6,000.

306!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

LCM of 9,17 and 51 is 153

Answer:16( 3+2)

Step-by-step explanation:

Another way of expressing 48 + 32 are:

32 + 48 and 80.

Addition is a basic mathematical operation that combines two numbers to give a total or sum.

The given expression is:

48 + 32

The commutative property is:

A+B  = B+A

Since Addition always holds the commutative property

Therefore, we can write the given expression as,

32 + 48

We can also express it by direct sum,

   3 2

+  4 8

_______

   8 0

_______

So, the sum of 32 and 48 is 80.

Hence,

We can express the given expression as 32 + 48 and 80.

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1. A. (-1,2) 
2. Sorry but i cant help you with this one
3. C. (3,2)

Hope this help! Need anything else just ask! :)

Sometimes systems of equations with different slopes and different y-intercepts have more than one solution. This is, for the most part true but should be answered sometimes.

y=mx+b
4y=5x-12
y=5/4x-3
so you change your y intercept (-3) to your other y intercept (15)
y=5/4x+15

i know this is late but the answer is 8 because your doing common factors so you you so 16 over 24 and see what number can go into both of those numbers which is 8 because 8 times 2=16 and 8 times 3= 24 so the answer is 8 again sorry i was late

Answer:

Maximum number of packets made = 8

Step-by-step explanation:

Number of pencils Rosy has = 16

Number of erasers Rosy has = 24

Now, it is given all the packets made contain equal number of pencils and erasers in each packet.

Therefore, to find the maximum number of packets : We find the HCF of both 16 and 24

16 = 2 × 2 × 2 × 2

24 = 2 × 2 × 2 × 3

Common factors are : 2, 2 and 2

⇒ HCF = 2 × 2 × 2

            = 8

So, 8 packets can be made from 16 pencils and 24 erasers so that each packet will contain 2 pencils and 3 erasers each.

Hence, Maximum number of packets made = 8

The following statement is true about the 2 (two) triangles shown in the image:
_________________________________________________
Triangle ABC is similar to Triangle FDE because:

AB  =   AC 
FD       FE
_________________________________________________

So here is how you determine the values of x that cause the polynomial function to be positive. 
Set each one greater than zero:x+2>0x+1>0x−5>0

Then, solve for x on all three:
 x > -2 x > -1 x > 5
 so in order for the polynomial to be positive the answer is x > 5.
Hope this is the answer that you are looking for. 

A = P(1+rt)
A (Future) = 450(2) = 900
P (Principal) = 450
R (Rate) = 14% = .14
T (Time) = Unknown

Create the equation:
900=450(1+.14t)

Distribute the 450:
900=450 + 450(.14t)

Multiply the 450(.14t)
900=450 + 63t

Subtract the 450:
450 = 63t

Divide by 63:
t=7.142857

Answer:
It will take 7.1 years.

2p=p(1+0.14t),,2=1+0.14t,,1=0.14t,,t==7.14 years or 7 years

the number 5 is prime

Answer:

5

It's easy.

5 has only 2 factors: 1 and itself.

Therefore, it is prime:)

Step-by-step explanation:

the distance between any 2 points on a number line when the 2 points are x and y is
|x-y|

|-2-3|=|-5|=5
the distance is 5

or
it take 2 units to get to 0 from -2
it takes 3 units to get from 0 to 3
2+3=5

x - y

4 - 5 = -1

The difference between x and y is -1.

8 - 1 = 7

The answer for when y = 8, x = 7.

y = kx,,5=4k,,k=5/4,,8=(5/4)x,,x=6.4

The function n^3/1000 - 100n^2 - 100n + 3. The big-Theta notation represents a function that can sandwich the given function for sufficiently large n. Formally, Theta(g(n): k1*g(n) < f(n) < k2*g(n). Sometimes, it is just as easy as removing the lower order terms and dropping the coefficient of the highest degree term. Thus, the function can be represented as Theta(n^3).

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The answer to this is 36.

Each year has 12 months so you just need to use the formula 12 * 4 = x to get the answer. The answer is 48

2x+3y-5=0
substitute (4,-1) where x=4 and y=-1
2*4+3*(-1)-5 = 0
8-3-5=0
0=0
correct! 
this point belongs to this line



test point (-2,3) where x = -2 and y=3
2x+3y-5 = 0
substitute
2*(-2)  + 3*3 - 5  = 0
-4+9-5=0
0=0
belongs!