27) Electric vehicles often have been proposed as an environmentally sound alternative to the gasoline engine for transportation. In response to state initiatives, several car manufacturers now include electric vehicles among their available models. In spite of these state initiatives, the penetration of electric vehicles into the transportation sector of the United States, as well as other countries, remains modest. (a) Identify and describe two environmental benefits to using electric vehicles in place of gasoline-powered engines for transportation. (b) Estimate the potential reduction in petroleum consumption (in gallons of gasoline per year) that could be achieved in the United States by introducing electric vehicles under the following assumptions: 1. The mileage rate for the average car is 25 miles per gallon of gasoline. 2. The average car is driven 10,000 miles per year. 3. The United States has 150 million cars. 4. 10 percent of United States cars could be replaced with electric vehicles. (c) Some people have suggested that electric vehicles only shift the emission of air pollutants from dispersed sources to point sources. Explain and defend or refute this statement. (d) Propose two potential new United States government policies that would encourage the widespread use of electric vehicles. Explain.

Therefore 5 + 4 × (14 - 4) - 8 = 37

The extraneous solution is the value of the independent variable for which the problem has no solution. x=3 is an extraneous solution.

An extraneous solution is a solution that develops from the process of addressing the problem but is not a real solution to the problem, such as an equation.

In order to know the extraneous solution, we need to find the value of x in the given equation,

[tex]\rm log_4(x)+log_4(x-3)= log_4(-7x+21)[/tex]

Using the logarithmic property,

[tex]\rm log_4[x(x-3)]= log_4(-7x+21)[/tex]

Taking the anti-log, we will get,

[tex]x(x-3)= -7x+21\\\\x^2-3x=-7x+21\\\\x^2+7x-3x-21=0\\\\x(x+7)-3(x+7)=0\\\\(x-3)(x+7)=0[/tex]

If we substitute the factors with the 0, we will get the value of x as 3 and -7.

We know that extraneous solutions are those solutions, which when substituted in the initial equation, the equation does not return an equation.

x=3

[tex]\rm log_4(x)+log_4(x-3)= log_4(-7x+21)[/tex]

[tex]\rm log_4(x3)+log_4(3-3)= log_4(-21+21)\\\\\rm log_4(x)+log_4(0)= log_4(0)[/tex]

As the value of logₐ(0) is undefined, therefore, x=3 is an extraneous solution.

Learn more about Extraneous solutions:

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Answer:

B. x = -3

Step-by-step explanation:

Answer:

y=-4

Step-by-step explanation:

Answer:

I believe the answer is 1

Step-by-step explanation:

Hope that helps!

Answer:

10 and 11, The square root of 109 is approximately 10.4 and the two consecutive numbers are 10 and 11.

Answer: ?

Step-by-step explanation:

Answer:

it will take the second crocodile 60 seconds

The time it will take the second crocodile to finish it's snack is; 120 s

Let x represent the rate of the first crocodile and let y represent the rate of the second crocodile.

The two crocodiles working together can finish a snack in 40 seconds. Thus;

(1/x + 1/y)40 = 1

It takes one of the crocodiles 60 seconds to finish it's snack. Thus;

(1/x + 1/60)40 = 1

40/x + 2/3 = 1

x = 120 seconds

Read more about rate of work at; https://brainly.com/question/12442233

Answer:

B. [tex]x^2+11x+24\leq 150[/tex]

Step-by-step explanation:

Step 1) Defining Sue and Jeremy's ages using x

Sue is 3 years older than Holly (h):

[tex]h=x+3[/tex]

Jeremy is 5 years older than Sue, or 8 years older than Holly (j):

[tex]j=x+8[/tex]

Product of Jeremy and Sue's ages is less than or equal to 150:

[tex]hj\leq 150[/tex]

Step 2) Simplifying into a single equation

Using the equation above we can substitute Sue and Jeremy's ages:

[tex](x+3)(x+8)\leq 150[/tex]

Now we can simplify this equation. Use the distributive property first:

[tex]x(x+8)=x^2+8x\\3(x+8)=3x+24[/tex]

Now add all the terms together and get the final answer:

[tex]x^2+8x+3x+24\leq 150\\x^2+11x+24\leq 150[/tex]

Final equation: [tex]x^2+11x+24\leq 150[/tex]

We are given with an equation in variable y and we need to solve for y . So , now let's start !!!

We are given with ;

[tex]{:\implies \quad \sf \dfrac{33}{2}+\dfrac{3y}{5}=\dfrac{7y}{10}+15}[/tex]

Take LCM on both sides :

[tex]{:\implies \quad \sf \dfrac{165+6y}{10}=\dfrac{7y+150}{10}}[/tex]

Multiplying both sides by 10 ;

[tex]{:\implies \quad \sf \cancel{10}\times \dfrac{165+6y}{\cancel{10}}=\cancel{10}\times \dfrac{7y+150}{\cancel{10}}}[/tex]

[tex]{:\implies \quad \sf 165+6y=7y+150}[/tex]

Can be further written as ;

[tex]{:\implies \quad \sf 7y+150=165+6y}[/tex]

Transposing 6y to LHS and 150 to RHS

[tex]{:\implies \quad \sf 7y-6y=165-150}[/tex]

[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{y=15}}}[/tex]

Answer:

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Step-by-step explanation:

Answer: 2

Step-by-step explanation:

1/4 ÷ 1/8 = 1/4 x 8 = 8/4 = 2

Answer:

This is a parallelogram.

Step-by-step explanation:

This figure has two pairs of paralel sides with completely different angles.

Using compound interest, it is found that:

a) $1,270.70 will be in the account after 6 years.

b) It will take 17.53 years for the $1000 to double.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

In this problem, the parameters are given as follows:

[tex]A(0) = 1000, r = 0.04, n = 12[/tex]

Item a:

Over 6 years, that is t = 6, thus:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]A(t) = 1000\left(1 + \frac{0.04}{12}\right)^{12 \times 6}[/tex]

[tex]A(t) = 1270.7[/tex]

$1,270.70 will be in the account after 6 years.

Item b:

This is t for which A(t) = 2P = 2000, hence:

[tex]2000 = 1000\left(1 + \frac{0.04}{12}\right)^{12t}[/tex]

[tex](1.0033)^{12t} = 2[/tex]

[tex]\log{(1.0033)^{12t}} = \log{2}[/tex]

[tex]12\log{(1.0033)} = \log{2}[/tex]

[tex]t = \frac{\log{2}}{12\log{1.0033}}[/tex]

[tex]t = 17.53[/tex]

It will take 17.53 years for the $1000 to double.

More can be learned about compound interest at https://brainly.com/question/25781328

Answer:

the fourth

Step-by-step explanation:

Complementary means that the sum of two angels equals to 90°

so LKM and MKN because they're both 45° and the sum is 90°

Answer:

okay look at the diagram and try to draw it to help you. Then look carefully at the equation and then solve it.

Step-by-step explanation:

Draw it

Label it

solve it

Let me know if u need help with other problems :)

If the value of x increases then the value of y decreases. Then the correct option is B.

The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.

For the inverse variation function

[tex]\rm y = \dfrac{k}{x}[/tex]    (where x, k > 0),

We know that the y is inversely proportional to the x.

Thus, if the value of x increases then the value of y decreases.

Therefore, the correct option is B.

More about the function link is given below.

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Answer:

so i don't  know  the answanswer

Step-by-step explanation:

i son't  know  go  learn

Answer:

r = sqrt(16/pi)

Step-by-step explanation:

Cylinder formula = r^2 x pi x height

176 pi/11pi = 16

16 = r^2 x pi

16/ pi = r^2

r = sqrt(16/pi)

~Shoto Todoroki here~

Y=(x+4)(−x+6)

Hope this helps :D

Answer:

Simplify   —

           3

Equation at the end of step

1

:

                        5    

 (((6 • (x2)) -  7x) -  —) -  x

                        3    

STEP

2

:

Equation at the end of step

2

:

                     5    

 (((2•3x2) -  7x) -  —) -  x

                     3    

STEP

3

:

Rewriting the whole as an Equivalent Fraction

3.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  3  as the denominator :

                6x2 - 7x     (6x2 - 7x) • 3

    6x2 - 7x =  ————————  =  ——————————————

                   1               3      

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

STEP

4

:

Pulling out like terms

4.1     Pull out like factors :

  6x2 - 7x  =   x • (6x - 7)

Adding fractions that have a common denominator :

4.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

x • (6x-7) • 3 - (5)     18x2 - 21x - 5

————————————————————  =  ——————————————

         3                     3      

Equation at the end of step

4

:

 (18x2 - 21x - 5)    

 ———————————————— -  x

        3            

STEP

5

:

Rewriting the whole as an Equivalent Fraction :

5.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  3  as the denominator :

        x     x • 3

   x =  —  =  —————

        1       3  

Trying to factor by splitting the middle term

5.2     Factoring  18x2 - 21x - 5

The first term is,  18x2  its coefficient is  18 .

The middle term is,  -21x  its coefficient is  -21 .

The last term, "the constant", is  -5

Step-1 : Multiply the coefficient of the first term by the constant   18 • -5 = -90

Step-2 : Find two factors of  -90  whose sum equals the coefficient of the middle term, which is   -21 .

     -90    +    1    =    -89

     -45    +    2    =    -43

     -30    +    3    =    -27

     -18    +    5    =    -13

     -15    +    6    =    -9

     -10    +    9    =    -1

     -9    +    10    =    1

     -6    +    15    =    9

     -5    +    18    =    13

     -3    +    30    =    27

     -2    +    45    =    43

     -1    +    90    =    89

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Adding fractions that have a common denominator :

5.3       Adding up the two equivalent fractions

(18x2-21x-5) - (x • 3)     18x2 - 24x - 5

——————————————————————  =  ——————————————

          3                      3      

Trying to factor by splitting the middle term

5.4     Factoring  18x2 - 24x - 5

The first term is,  18x2  its coefficient is  18 .

The middle term is,  -24x  its coefficient is  -24 .

The last term, "the constant", is  -5

Step-1 : Multiply the coefficient of the first term by the constant   18 • -5 = -90

Step-2 : Find two factors of  -90  whose sum equals the coefficient of the middle term, which is   -24 .

     -90    +    1    =    -89

     -45    +    2    =    -43

     -30    +    3    =    -27

     -18    +    5    =    -13

     -15    +    6    =    -9

     -10    +    9    =    -1

     -9    +    10    =    1

     -6    +    15    =    9

     -5    +    18    =    13

     -3    +    30    =    27

     -2    +    45    =    43

     -1    +    90    =    89

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Final result :

 18x2 - 24x - 5

 ——————————————

       3      

Step-by-step explanation:

Answer:

I believe the answer is x • y = ?

Answer:

25.

Step-by-step explanation:

the ratio from even to odd is equal. a half chance of getting even 3:6 & 4:8 [ theres 3 even #s on the cube, 3 odds #s on the cube] vice VERSA!! for either even or odd roll. so out of 50, half of 50 is 25. there's a 1:2 chance of even(or in whatever case) 1:2 = 25:50

Answer:

a

Step-by-step explanation:

Answer:

Width: x - 5

Step-by-step explanation:

x² - 25

x² - 5²

(x - 5)(x + 5)

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

Solve the question in steps

(8+36)/11

44/11=4

Now you have 4+7x2

You do multiplication first

4+14=18

Answer:

Step-by-step explanation:

Answer: B

Step-by-step explanation:

JK = 6.08

JL = 5.83

using distance formula is √[(x2 – x1)^2 + (y2 – y1)^2].