Reuben rented a truck for one day. There was a base fee of $14.95, and there was an additional charge of 80 cents for each mile driven. Reuben had to pay
$135.75 when he returned the truck. For how many miles did he drive the truck?

Step-by-step explanation:

1) zeros of the given function:

6x²-3=0; ⇔ 6(x²-0.5)=0; ⇔ x²=0.5; ⇔

[tex]\left[\begin{array}{ccc}x=-\sqrt{0.5} \\x=\sqrt{0.5} \end{array}[/tex]

2) relationship:

if to see the equation x²-0.5=0 (ax²+bx+c=0 is standart form!), then the sum of the zeros is '0' (it is 'b' of the standart form), the product of equation roots is '-0.5' (it is 'c' of the standart form).

[tex]{\large{\textsf{\textbf{\underline{\underline{Given :}}}}}}[/tex]

★ The polynomial

f(x) = 6x² - 3

[tex]{\large{\textsf{\textbf{\underline{\underline{To \: find :}}}}}}[/tex]

★ Zeroes of the polynomial f(x) = 6x² - 3

[tex]{\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}[/tex]

We have,

[tex]f(x) = \tt 6 {x}^{2} - 3[/tex]

Which can also be written as

[tex] \implies f(x) = \tt {(\sqrt{6} x)}^{2} - { (\sqrt{3}) }^{2} [/tex]

Using a² - b² = (a - b) (a + b)

[tex] \implies f(x) = \tt ( \sqrt{6} x - \sqrt{3} )( \sqrt{6} x + \sqrt{3} )[/tex]

To find the zeroes, solve f(x) = 0

[tex] \longrightarrow \tt ( \sqrt{6} x - \sqrt{3} )( \sqrt{6} x + \sqrt{3} ) = 0[/tex]

either [tex] \tt \sqrt{6} x - \sqrt{3} = 0 \: or \: \sqrt{6} x + \sqrt{3} = 0[/tex]

[tex] \implies \tt \sqrt{6} x = \sqrt{3 \: } \: or \: \: \sqrt{6} x = - \sqrt{3}[/tex]

[tex] \implies \tt x = \dfrac{ \sqrt{3} }{ \sqrt{6} } \: or \: x = - \dfrac{ \sqrt{3} }{ \sqrt{6} }[/tex]

[tex] \implies \tt x = \dfrac{ \sqrt{3} }{ \sqrt{2 \times 3} } \: or \: x = - \dfrac{ \sqrt{3} }{ \sqrt{2 \times 3} }[/tex]

[tex]\implies \tt x = \dfrac{ \cancel{ \sqrt{3} }}{ \sqrt{2} \: \cancel{\sqrt{3}} } \: or \: x = - \dfrac{ \cancel{ \sqrt{3} }}{ \sqrt{2} \: \cancel{\sqrt{3}} }[/tex]

[tex]\implies \tt x = \dfrac{1}{ \sqrt{2} } \: \: or \: \: - \dfrac{1}{ \sqrt{2} }[/tex]

Hence, the zeroes of f(x) = 6x² - 3 are:

[tex] \tt \alpha =\sf \boxed {{ \red{ \dfrac{1}{ \sqrt{2} } } }}\: \: and \: \: \beta =\sf \boxed {{ \red{ - \dfrac{1}{ \sqrt{2} } } }}[/tex]

• Verification

Sum of zeroes = [tex] ( \alpha + \beta )[/tex]

[tex] = \tt \dfrac{1}{ \sqrt{2} } + \bigg(- \dfrac{1}{ \sqrt{2} } \bigg)[/tex]

[tex] = \tt \dfrac{1}{ \sqrt{2} } + - \dfrac{1}{ \sqrt{2} } [/tex]

[tex]= \tt 0[/tex]

and, [tex]\tt - \dfrac{Coefficient \: of \: x}{Coefficient \: of \: {x}^{2} }[/tex]

[tex] \tt = - \dfrac{0}{6} [/tex]

[tex] \tt = 0[/tex]

[tex] \therefore \tt \: Sum \: of \: zeroes = {\boxed{ \red{\dfrac{ \tt Coefficient \: of \: x}{ \tt Coefficient \: of \: {x}^{2}}}}}[/tex]

Also,

Product of zeroes = [tex] \alpha \beta [/tex]

[tex] = \dfrac{1}{ \sqrt{2} } \times - \dfrac{1}{ \sqrt{2} } [/tex]

[tex] = - \dfrac{1}{ 2 } [/tex]

and, [tex]\tt - \dfrac{Constant \: term}{Coefficient \: of \: {x}^{2} }[/tex]

[tex] \tt = \dfrac{ - 3}{6} [/tex]

[tex] \tt = \dfrac{ - 1}{2} [/tex]

[tex] \therefore \tt \: Product \: of \: zeroes = {\boxed{ \red{\dfrac{ \tt Constant \: term}{ \tt Coefficient \: of \: {x}^{2}}}}}[/tex]

[tex]\rule{280pt}{2pt}[/tex]

The probability that 5 would not be working is 0.18665, the probability that at least one machine would be working is 0.00602 and the probability that all would be working is 1.

Given a company has 200 machines. Each machine has a 12% probability of not working.

If we working pick 40 machines randomly then we have to find the probability that 5 would not be working, the probability that at least one machine would be working, and the probability that all would be working.

So

1) probability that 5 would not be working

C(40,5)·0.12⁵·0.88³⁵= 40!/(5!(40-5)!)·0.12⁵·0.88³⁵

                                ≈ 0.18665

2)  probability that at least one machine would be working

0.88⁴⁰ ≈ 0.00602

3) probability that all would be working

1 - 0.12⁴⁰ ≈ 1.0000

Learn more about probability here: https://brainly.com/question/24756209

#SPJ10

The total amount due on the electricity bill is $55.64.

Here given that the last month's electricity consumption is 354 kWh

According to my contract with the electricity company, I agree to pay 11.3 cents per kWh.

So for 354 kWh of last month, I have to pay [tex]=11.3\times354=4000.2[/tex] cents

Now we know that 1 dollar = 100 cents

100 cents = $1

1 cent = [tex]\$\frac{1}{100}[/tex]

4000.2 cents [tex]=\$\frac{4000.2}{100}=\$40.002[/tex]

also, I have to pay a fixed charge of $15.63

So the total bill for last month will be [tex]=\$40.002+\$15.63=\$55.632\approx\$55.64[/tex]

Hence the total due amount on the electricity bill is $55.64 approximating the amount to the next two decimal place number.

Learn more about cent-dollar here -

https://brainly.com/question/1597365

#SPJ10

The odds of jimmy winning a free lunch is 0.066.

Probability is the likeliness of an event to happen.

It is given that

A restaurant will select 1 card from a bowl to win a free lunch,

jimmy puts 10 cards in the bowl.

The bowl has a total of 150 cards in it

The odds of jimmy winning a free lunch is given by

= No. of chances / Total Outcomes

= 10/150

= 1/15

= 0.066

Therefore the odds of jimmy winning a free lunch is 0.066.

To know more about Probability

https://brainly.com/question/11234923

#SPJ1

Answer:

Step-by-step explanation:

1/1

Answer:

9

Step-by-step explanation:

This problem is represented below.

=3(4+2)-9

=3(6)-9

=18-9

=9

The interest which has to be paid is $28.

Simple Interest amount can be estimated by the product of principal amount, rate of interest, and time in year.

Simple Interest= S.I. =p*t*r/100

where p is the principal amount,

r: interest rate (%)

t: the time (in year).

Here, given,

Margo has taken borrowed $600 with an annual interest of 7% which has to be paid within 8 months.

principal amount P = $600

rate of interest= r=7%

time=t=8 months= 2/3 year

using the above-mentioned formula,

Simple Interest S.I.= p*t*r/100= (600*(2/3)*7)/100= $28

Therefore the interest which has to be paid is $28.

Learn more about Simple interests

here: https://brainly.com/question/12918571

#SPJ10

The width of the pool is 10 feet.

The area of rectangle is product of length and breadth.

Let the width be x.

length = 24 + 2x. and breadth =  12 + 2x

We know, area= 1408 ft².

(12 + 2x)(24 + 2x) = 1408

12*24 + 12*2x + 24*2x + (2x)² = 1408

288 + 72x + 4x² = 1408

4x² + 72x + 288 - 1408 = 0

4x² + 72x - 1120 = 0

x² + 18x - 280 = 0

x² - 10x + 28x - 280 = 0

x(x - 10) + 28(x - 10) = 0

(x - 10)(x + 28) = 0

So, x=10, -28.

Hence, the width be 10 feet.

Learn more about this concept here:

https://brainly.com/question/26638297

#SPJ1

There are 25773 foxes in the region in the year 2008

The given parameters are:

Let the number of years after 2000 be x.

So, the function is

f(x) = a * (1 + r)^x

This gives

f(x) = 15000 * (1 + 0.07)^x

In 2008, we have:

x = 8

So, the equation becomes

f(8) = 15000 * (1 + 0.07)^8

Evaluate

f(8) = 25773

Hence, there are 25773 foxes in the region in the year 2008

Read more about exponential functions at:

https://brainly.com/question/2456547

#SPJ1

Last option: (50, 30); 50 adult tickets and 30 child tickets

A linear equation is an equation in which the highest power of the variable is always 1.

We have the system of equations:

x + y = 80

6x + 4y = 420

We will use elimination method to solve it:  

Multiply the first equation by -6 and then add the equations:

- 6x - 6y = -480

6x + 4y = 420  

We get:

-2y = -60

After dividing both sides by -2 we get:

y = 30

then plugging 30 in place of y into the original first equation we get:

x+30=80

Then subtracting 30 from both sides we get:

x = 50

The solution to the system is (50, 30)

Then notice the second equation 6x+4y=420 clear indicates that x represents the tickets for adults since the price for adults $6 is the coefficient of the x-term, while the price for children which is $4 is attached as coefficient in front of the y.

Thus, x=50 means there were sold 50 adult tickets. And y=30 that there were sold 30 child tickets.

Learn more about Linear equation from:

https://brainly.com/question/2263981

#SPJ1

Answer:

( 50, 30)

Step-by-step explanation:

Step-by-step explanation:

please mark me as brainlest

Answer:

-x^2-2

Step-by-step explanation:

So by looking at the two curves it appears that g(x) is simply a reflection of f(x) over the x-axis and then shifted 2 units down. So to reflect the parabola you simply make the x^2 negative to get -x^2 and then to go 2 units down you subtract 2 from the -x^2. This gives you the equation

[tex]g(x)=-x^2-2[/tex]

[tex]\large\orange\implies \rm \large \:f(x) \: = \: 2x[/tex]

We have to find x when f(x) is 8

[tex]\large\orange\implies \rm \large \:8 = \: 2x[/tex]

[tex]\large\orange\implies \rm \large \: \cancel\frac{8}{2} \: = \: x \\ [/tex]

[tex]\large\orange\implies \rm \large \: \: 4 \: = \: x[/tex]

[tex]f(x) \: = \: 2x[/tex]

We have to find x when f(x) is 8

[tex]8 = \: 2x[/tex]

[tex]x = \frac{8}{2} \\ \\ x = 1.[/tex]

The value of x is 4 when f(x) is 8 .

Answer:

34.562

Step-by-step explanation:

To find the perimeter of a circle, it's 2 * the radius * pi. In this case, we have a semicircle, so it would be the circle's perimeter divided by 2, or just the radius * pi.

The radius, 11, times pi (3.142), is 34.562.

Brainliest, please :)

Step-by-step explanation:

please mark me as brainlest

The correct answer is option C which is the ratio of the difference in the means of the two teams to the mean absolute deviation of Team B will be 0.25.

Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data.

The difference between the mean times is about 16 times the mean absolute deviation of the data set.

59.32 - 59.1 = 0.22

2.4 - 1.5 = 0.9

0.22 / 0.9 = 0.25

Therefore the correct answer is option C which is the ratio of the difference in the means of the two teams to the mean absolute deviation of Team B will be 0.25.

To know more about mean follow

https://brainly.com/question/968894

#SPJ1

Answer:

[tex]\frac{3}{32}[/tex]

Step-by-step explanation:

-> Simplify

[tex]\frac{6}{64} =\frac{6/2}{64/2} =\frac{3}{32}[/tex]

6/64 simplified.

Answer:

5√2, 5

Step-by-step explanation:

in a 90 45 45 triangle, each leg is the same legnth

the hypotenuse of a 90 45 45 triangle is x√2

x being the measure of the leg

Answer:

? = 12

Step-by-step explanation:

[tex]\frac{7}{12} +\frac{10}{12} =\frac{7+10}{12} =\frac{17}{12}[/tex]

[tex]\frac{17}{12} =\frac{12}{12} +\frac{5}{12} =1+\frac{5}{12} =1\frac{5}{12}[/tex]

Hope this helps

Answer:

g(f(x)) = 1x² + 1

Step-by-step explanation:

We are given:
f(x) = x² - 1

g(x) = x + 2

And we want to find g(f(x)).

To do this, we substitute f(x) as x in x+2 (the expression that is equal to g(x)), as g(f(x)) is saying that f(x) is the value of x in g(x).

So, this will be:

g(f(x)) = x² - 1 + 2

Simplify

g(f(x)) = x² + 1

In your system, place 1 in front of x² - this is the coefficient of x², and also 1 after that - this is a constant.

Answer:

below

Step-by-step explanation:

Measure of each angle is 27 and 63 degrees.

Answer:

C

Step-by-step explanation:

A reflection of a graph on the x axis simply adds the opposite sign to the x^2, in this case, since f(x) = x^2 is positive, a reflection would mean that g(x) would be -x^2. As g(x) is also vertically translated down 2 units, the equation would then become g(x) = -x^2 - 2 and the correct answer would be C.

The reflection over the line y = x - 3 will take figure M onto its congruent image, figure N.

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

As we can see in the graph there are two shapes are shown.

Figure M and Figure N

The sequence of transformations that will take figure M onto its congruent image, figure N is:

First, we need to draw a line that passes through (3, 0) and (0, -3)

The equation of the line is:

[tex]\rm y+3=\dfrac{\left(-3\right)}{-3}\left(x\right)[/tex]

y + 3 = x

y = x - 3

The reflection over the above line will take figure M onto its congruent image, figure N.

Thus, the reflection over the line y = x - 3 will take figure M onto its congruent image, figure N.

Learn more about the geometric transformation here:

brainly.com/question/16156895

#SPJ1

The volume of the given figure is 210 cubic in..

We need to find the volume of the given figure.

Volume is a scalar quantity expressing the amount of three-dimensional space enclosed by a closed surface.

Divide the given figure into two convenient cuboids. That is one with dimensions length=4 in., breadth=2 in. and height=3 in. Another with length=4 in., breadth=4 in. and height=12 in.

We know that, the volume of cuboid =l×b×h cubic units.

Now, the volume of the cuboid=4×2×3=18 cubic in. and the volume of another

cuboid=4×4×12=192 cubic in.

The volume of the given figure=18+192=210 cubic in.

Therefore, the volume of the given figure is 210 cubic in.

To learn more about the volume visit:

https://brainly.com/question/1578538.

#SPJ1

The ordered pairs are ( -2,0),( -1,-3),( 0,-4),(1,-3),(-2,0).

A coordinate plane is a 2D plane which is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.

The ordered pairs will be calculated as:-

y = x² − 4

At  x = -2

y = ( -2)² - 4 = 4 - 4 = 0

At x = -1

y = (-1)² - 4 = -3

At x = 0

Y = 0² - 4 = -4

At x = 1

Y = 1 ² - 4 = -3

At x = 2

Y = (2)² - 4 = 0

Therefore ordered pairs are ( -2,0),( -1,-3),( 0,-4),(1,-3),(-2,0).

To know more about Coordinate geometry follow

brainly.com/question/18269861

#SPJ1

Answer:

5.0

Step-by-step explanation:

0.16÷0.03220=4.9689

=5.0

Answer:

The answer is A. 21

i hope this can help you! :)

Answer:

a)21

-step explanation:

The ratio is given by 98:0.34.

The ratio of (1/5 of 245ml) to (0.2 of 0.84ml).

The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.

we have  (1/5 of 245ml) to (0.2 of 0.84ml).

⇒ [tex]\frac{1}{5} 245 :0.2*0.84[/tex]

⇒[tex]98:0.34[/tex]

Thus, the required ratio is 98:0.34.

Learn more about Ratio here:
https://brainly.com/question/13419413

#SPJ1