Problem 9
Leon drives a long distance to attend a family reunion. At 12:00 PM, his gas tank is completely filled with
12 gallons of gas. Leon's car uses gas at a constant rate, and after two hours of driving, Leon notices that
his car used five gallons of gas.
Leon will stop to get gas when his tank is one fourth of the way full. If Leon's car continues to use gas at
the same constant rate and Leon makes no other stops on his trip, at what time will Leon stop to get gas?
Be sure to include AM or PM in your answer.

Answer:

w=2  w = -9

Step-by-step explanation:

w^2 + 7w - 18 = 0

We can factor this equation

What 2 numbers multiply to -18 and add to 7

9*-2 = -18

9+-2 = 7

(w-2) (w+9) = 0

Using the zero product property

w-2 = 0    w+9 =0

w=2  w = -9

Answer:

[tex]w_1=2\\w_2=-9[/tex]

Step-by-step explanation:

This is going to be solved using the quadratic formula.

1. Determine the quadratic equation’s coefficient [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex].

Use the standard form, [tex]ax^2+bx+c=0[/tex]  , to find the coefficients of our equation,

[tex]w^2+7w-18=0[/tex]:

a = 1

b = 7

c = -18

2. Plug these coefficients into the quadratic formula

The quadratic formula gives us the roots for  [tex]aw^2+bw+c=0[/tex] , in which [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] are numbers (or coefficients), as follows:

[tex]w=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

7 additional steps:

a = 1

b = 7

c = -18

[tex]w=\frac{-7\pm\sqrt{7^2=4*1*-18} }{2*1}[/tex]

Simplify exponents and square roots

[tex]w=\frac{-7\pm\sqrt{49-4*1*-18} }{2*1}[/tex]

Perform any multiplication or division, from left to right:

[tex]w=\frac{-7\pm\sqrt{49-4*-18}}{2*1}\\w=\frac{-7\pm\sqrt{49--72}}{2*1}\\\\w=\frac{-7\pm\sqrt{49+72}}{2*1}\\w=\frac{-7\pm\sqrt{121}}{2*1}[/tex]

to get the result:

[tex]w=\frac{-7\pm\sqrt{49-4*-18}}{2}[/tex]

3. Simplify square root [tex]\sqrt{121}[/tex]

Simplify 121 by finding its prime factors:

121 ( 11 * 11)

The prime factorization of 121 is 11^2

Write the prime factors:

[tex]\sqrt{121}=\sqrt{11\cdot 11}[/tex]

Group the prime factors into pairs and rewrite them in exponent form:

'[tex]\sqrt{11\cdot 11}=\sqrt{11^2}[/tex]

Use the rule [tex]\sqrt{x^2=x}[/tex]  to simplify further:

[tex]\sqrt{11^2}=11[/tex]

4. Solve the equation for w

[tex]w=\frac{-7\pm11}{2}[/tex]

The ±  means two answers are possible.

Separate the equations:

[tex]w_1=\frac{(-7+11)}{2}[/tex] and [tex]w_2=\frac{-7-11}{2}[/tex]

[tex]w_1=\frac{-7+11}{2}[/tex]

[tex]w_1=\frac{4}{2}[/tex]

[tex]w_1=2[/tex]

[tex]w_2=\frac{-7-11}{2}[/tex]

[tex]w_2=\frac{-18}{2}[/tex]

[tex]w_2=-9[/tex]

---------------------

Why learn this

---------------

Terms and topics

-----------

Learn more:

Answer:

Always include the steps and/or background required to get to the final answer. Let’s help other people understand and solve future problems on their own.

Step-by-step explanation:

Answer:

14.7868 ml are equal to 1 tablespoon

Step-by-step explanation:

1 tablespoon is equivalent to __14.7868___ ml.

Hope This Helped

Answer:

14.7868ml or 15 ml

Step-by-step explanation:

it can be either one since 14.7686 is close to 15

Answer:

28

Step-by-step explanation:

Circumference = 2*pi*r

r = 1/2*diameter = 4.5

pi = 3.14

Circumference = 2*(3.14)*(4.5) = 28.26 = 28

Answer:

The item has a 9% sales tax.

Step-by-step explanation:

Given the following question:

We are given an item that costs 490 dollars before tax, the sales tax of the item is $44.10, which means the item will cost $534.10 in total. Assuming what you are asking is to find the percentage of the sales tax we will use the formula to calculate percentages, and then add that answer to our before cost to confirm our answer.

Formula to calculate percentages:

[tex]\frac{p\times n}{100}[/tex]
[tex]p=9[/tex]
[tex]\frac{9\times490}{100}[/tex]
[tex]9\times490=4410[/tex]
[tex]4410\div100=44.1=44.10[/tex]
[tex]490+44.10=534.10[/tex]
[tex]=534.10[/tex]

Our sales tax percentage is 9%.

Hope this helps.

The value of the diagonal will be equal to 20√2.

Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides.

The value of the diagonal by the Pythagorean theorem.

H²  =  B²  +  P²

H²  =  20²  +   20²

H²  =  400   +  400

H  =  √800

H  =  20√2

Therefore the value of the diagonal will be equal to 20√2.

To know more about the Pythagorean theorem follow

https://brainly.com/question/343682

#SPJ1

The attached graph shows that the system of equation has no solution since there is no point of intersection

Inequalities are expressions not separated by an equal sign

Given the following inequalities

2y < -12x + 4

y <- 6x +4

_________________

2y < -6x + 4

y <- 6x +4.

Find the y-intercept. When x = 0

y < -6(0) + 4

y < 4

Plot the graphs and determine the point of intersection

Learn more on inequality here: https://brainly.com/question/24372553

#SPJ1

Using a dot plot, it is found that the number of dots of each point are given as follows:

The dot plot shows the number of times each measure appears in the data-set.

In this problem, one measure has a value of 1/8, hence:

The value [tex]\frac{1}{8}[/tex] will have one dot above it.

Two measures have a value of 1/4, hence:

The value [tex]\frac{1}{4}[/tex] will have two dots above it.

Three measures have a value of 3/8, hence:

The value [tex]\frac{3}{8}[/tex] will have three dots above it.

Five measures have a value of 1/2, hence:

The value [tex]\frac{1}{2}[/tex] will have five dots above it.

Two measures have a value of 5/8, hence:

The value [tex]\frac{5}{8}[/tex] will have two dots above it.

Three measures have a value of 3/4, hence:

The value [tex]\frac{3}{4}[/tex] will have three dots above it.

More can be learned about dot plots at https://brainly.com/question/27742008

#SPJ1

Answer:

1 2 3 5 2 3

Step-by-step explanation:

Answer:

392

Step-by-step explanation:

hope this helps!!

Answer:

279 miles

Step-by-step explanation:

31 miles/gal  *  9 gallons = 279 miles

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's solve for x ~

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} + 5x + 6 = 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} + 3x + 2x + 6 = 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{}( x+ 3) + 2(x + 3)= 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: {}^{}( x+ 2)(x + 3)= 0[/tex]

[tex] \begin{cases} \sf \: x = - 2 \: \: \: \: \: \: \: \sf if \: (x + 2) = 0 \\ \\ \sf \: x = - 3 \: \: \: \: \: \: \: if \: (x + 3) = 0\end{cases} [/tex]

I hope that helps ~

Answer:

See below

Step-by-step explanation:

The CENTER will de directly between the two given points

h, k   = -1,7

so...so far the circle eq is

  (x+1)^2 + ( y-7)^2

the RADIUS is  1/2 of the distance between the given points

1/2  d = (using distance formula) = 1/2 sqrt 80     = 4.472

then the equation of the circle in standard form

 (x+1)^2  + (y-7)^2 = 20          

Answer:

$0.60 per pound

Step-by-step explanation:

Dollars per pound :

Answer:  93 boxes will be needed

Step-by-step explanation:

     If each box holds 16 paperweights, and 1,486 need to be packaged, we will divide 1,486 by 16.

1,486 / 16 = 92.875

    We will assume you cannot have 0.875 of a box, so we will round up to:

              93 boxes will be needed

Read more about your question here:

https://brainly.com/question/19116511

Answer:

2 733.25 + 7270 = 10 003.25

Step-by-step explanation:

192 * 36 = 6 912 +358 = 7 270

45425 - 36000 ( allowed miles for 3 years )

9 425 * 0.29 = 2 733.25

The points mean that the temperature at 11 am and 7 pm is 6 degree Celsius

The given parameters are:

The points are given as:

(x, y) = (-1,6) and (7,6)

-1 represents 11 am and 7 represents 7 pm.

The points mean that:

The temperature at 11 am and 7 pm is 6 degree Celsius

Read more about coordinate planes at:

https://brainly.com/question/14351004

#SPJ1

The system of equations is consistent and independent and the solutions are x = 4, y = 5, and z = -1 option third is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have three linear equations in three variables:

x - y - z = 0 ..(1)

2x - y + 2z = 1 ..(2)

x - y + z = -2 ..(3)

From the equation (1):

[tex]\rm x=y+z[/tex]

Plug this value in the equation (2) and (3):

[tex]\rm 2\left(y+z\right)-y+2z=1\\\\ y+z-y+z=-2[/tex]

After solving we get:

z = -1

y = 5

Plug the above two values in equation (1) we get:

x = 4

Thus, the system of equations is consistent and independent and the solutions are x = 4, y = 5, and z = -1 option third is correct.

Learn more about the linear equation here:

brainly.com/question/11897796

#SPJ1

Answer:

Step-by-step explanation:

From left to right:

(don't listen to the other ways. this should be correct).

(Just g o o g l e it).

The expressions for (h+g)(x) and (h-g)(x) and evaluate (h-g) (4) is 9x-3 ,  x+3 and 7

A function is defined as the law that build relation between a dependent variable and an independent variable.

It is given that

functions g and h are defined for all real numbers x as follows.

g(x) = 5x

h(x) = 4x-3

the expressions for (h+g)(x)= ?

(h+g)(x)= 5x+4x-3

(h+g)(x)= 9x-3

and (h-g)(x) = ?

(h-g)(x) = 5x - 4x +3

(h-g)(x) = x+3

and evaluate (h-g) (4).

(h-g)(x) = x+3

at x = 4

(h-g)(4) = 4+3 = 7

Therefore the value for the functions have been determined.

To know more about Function

https://brainly.com/question/12431044

#SPJ1

Step-by-step explanation:

this is the problem to sum the numbers 1 ... n.

remember the old trick by adding

n + 1

n-1 + 2 = n + 1

n-2 + 3 = n + 1

...

and doing this n/2 times, giving us a sum

n×(n+1)/2

for n = 30 we get

30×31/2 = 15×31 = 465

so, 465 people will perform.

Inequalities are expression not separated by an equal sign. None of the inequality is correct since there is absence of equal sign.

Inequalities are expression not separated by an equal sign. According to the question, we ned the inequality's graph that will have a dashed boundary line.

An inequality that will have solid boundary line must include only the less than or equal to sign < or greater than or equal to > sign.

From the option given, none of the inequality is correct since there is absence of equal sign.

Learn more on inequality graph here: https://brainly.com/question/24372553

#SPJ1

Answer:

3.5x10^4 is 50 times larger than 7x10^2

Step-by-step explanation:

3.5x10^4 is 35,000 (move decimal 4 places to the right)

7x10^2 is 700 (7.0 move decimal 2 places to the right)

700x50=35,000 which shows that 35,000 is 50 times larger than 700

to get the equation of any straight line, we simply need two points off of it, let's use those two points from the table in the picture below.

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{13})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-17}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-17}-\stackrel{y1}{13}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{(-4)}}} \implies \cfrac{-30}{6 +4} \implies \cfrac{ -30 }{ 10 }\implies -3[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{13}=\stackrel{m}{-3}(x-\stackrel{x_1}{(-4)}) \\\\\\ y-13=-3(x+4)\implies y-13=-3x-12\implies y=-3x+1[/tex]

Answer:

(B

The given system of equations are:

y=x^2+3x+3y=x

2

+3x+3 (1)

and y=x^2+x+2y=x

2

+x+2 (2)

Subtracting equation (2) from (1), we get

0=2x+10=2x+1

⇒2x=-12x=−1

⇒x={\frac{-1}{2}}x=

2

−1

⇒x=-0.5x=−0.5

Now, substituting the value of x=-0.5 in equation (2), we get

y=0.25-0.5+2y=0.25−0.5+2

⇒y=1.7y=1.7

Thus, the values of x and y are -0.5 and 1.7.

Therefore, the approximate solution of the given system of the equation is (-0.5, 1.7).

Hence, option (B) is correct.