Write (5-√5) (5-√5) in the form a+b√5, where a and b are integers.

a)The cost of 480 gallons =  $1248

b)Expression to represent the new yearly cost of gasoline =  $ 31200/ (25+x)

c)total savings on gasoline per year =$1248x/ 25+ x

d)miles per gallon does the new car​ get = 36.79 miles

Unitary method Technique to solve a problem by first finding the value of a single unit , and then finding the necessary value by multiplying the single unit value.

Given :

drive an average of = 12000miles per year

one gallon consumed = after every  25 miles

cost per gallon of gasoline = $ 2.60

a)  25 miles consume = 1 gallon of gasoline

      12000 mile will consume = (1/ 25)* 12000 =480 gallons

     cost of one gallon = $ 2.60

     cost of 480 gallons = $ 2.60 * 480=  $1248

b) another car gives x more miles per gallon :

       25 + x miles consume = 1 gallon

       12000 miles will consume = 1/ (25+x) * 12000 gallons

       cost of one gallon = $ 2.60

       cost of 1/ (25+x) * 12000 gallons=  2.60 * (1/ (25+x) * 12000)

                                                            =  $ 31200/ 25+x

c)Total savings will be = cost  spent in initial case - cost in 2nd case

                                     =   1248 - 31200/(25+x)

                                     = (31200 + 1248 x - 31200)/ (25+x)

                                     = $1248x/ 25+ x        equation 1

d) let saving = $ 400  (given )     equation 2

    savings calculated in previous part =$1288x/ 25+ x

    equating both the equations 1 and 2

   1248x/ 25+x = 400

    1248x = 10000 + 400x

    1248x -400x = 10000

    x = 11 .79 miles

Total miles covered per gallon = 25 + x = 25 + 11.79 = 36.79 miles

learn more about unitary method :

https://brainly.com/question/14793162?referrer=searchResults

#SPJ2

r

sin

θ

=

−

3

Explanation:

Imagine we have a point  

P

with Rectangular (also called Cartesian) coordinates  

(

x

,

y

)

and Polar coordinates  

(

r

,

θ

)

.

The following diagram will help us visualise the situation better:

https://keisan.casio.com/exec/system/1223526375

https://keisan.casio.com/exec/system/1223526375

We can see that a right triangle is formed with sides  

x

,  

y

and  

r

, as well as an angle  

θ

.

We have to find the relation between the Cartesian and Polar coordinates, respectively.

By Pythagora's theorem, we get the result

r

2

=

x

2

+

y

2

The only properties we can say about  

θ

are its trigonometric functions:

sin

θ

=

y

/

r

⇒

y

=

r

sin

θ

cos

θ

=

x

/

r

⇒

x

=

r

cos

θ

So we have the following relations:

⎧

⎪

⎨

⎪

⎩

r

2

=

x

2

+

y

2

y

=

r

sin

θ

x

=

r

cos

θ

Now, we can see that saying  

y

=

−

3

in the Rectangular system is equivalent to say

r

sin

θ

=

−

3

Answer link

Jim G.

May 19, 2018

r

=

−

3

sin

θ

Explanation:

to convert from  

cartesian to polar

∙

x

x

=

r

cos

θ

and  

y

=

r

sin

θ

⇒

r

sin

θ

=

−

3

⇒

r

=

−

3

sin

θ

Answer: I say 4/3 the fraction so your answer is D

Explanation: Because its white cars to blue cars the problem is whats equivalent to the ratio 40 to 30, 4:1 is not the same as 40 to 30 neither

is 1:4 or 3 to 4 So its D. :)

Siama and Wills used different methods to find the differences between (5x + 6x) and (2x - 1) but they both arrived at the same answer.

I prefer Wills method because it is easier and less complicated.

Wills method:

(5x + 6x) - (2x - 1)

Subtract both 2x and -1

5x + 6x - 2x - - 1

5x + 4x + 1

In conclusion, Wills method is preferred when both methods are compared.

Read more on difference of numbers:

https://brainly.com/question/17301989

#SPJ1

Answer:

987

Step-by-step explanation:



57√56259= 987

Answer:

987

Step-by-step explanation:

56259 ÷ 57 = 987

Answer:

  2 +4√2

Step-by-step explanation:

Perhaps you want the simplified form of (6-√8)/(√2 -1).

The denominator can be rationalized by multiplying numerator and denominator by the conjugate of the denominator:

  \(\dfrac{6-\sqrt{8}}{\sqrt{2}-1}=\dfrac{(6-\sqrt{8})(\sqrt{2}+1)}{(\sqrt{2}-1)(\sqrt{2}+1)}=\dfrac{6\sqrt{2}+6-\sqrt{16}-\sqrt{8}}{2-1}=\boxed{2+4\sqrt{2}}\)

__

Additional comment

The conjugate of the denominator is the same pair of terms with the sign between them changed. The product of the binomial and its conjugate is then the difference of squares. Since the square of a square root eliminates the radical, multiplying by the conjugate has the effect of removing the radical from the denominator.

The same "difference of squares" relation can be used to remove a complex number from the denominator.

  (a -b)(a +b) = a² -b²

In general, the differences of terms of the same power can be factored. This means that denominators with this form can be "rationalized" by taking advantage of that factoring.

<95141404393>

Answer:

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

Simplify the expression in steps:

\(\cfrac{6-\sqrt{8} }{\sqrt{2}-1 } =\)

\(\cfrac{6-2\sqrt{2} }{\sqrt{2}-1 } =\)

\(\cfrac{2(3-\sqrt{2} )(\sqrt{2} +1)}{(\sqrt{2}-1)(\sqrt{2}+1) } =\)

\(\cfrac{2(3\sqrt{2}+3-(\sqrt{2}^2) -\sqrt{2} )}{(\sqrt{2})^2-1 } =\)

\(\cfrac{2(2\sqrt{2}+3-2) }{2-1} =\)

\(\cfrac{2(2\sqrt{2}+1) }{1} =\)

\(4\sqrt{2}+2\)

Answer: Eva made 40 sand art bottles

Step-by-step explanation:

1 kilogram =1000 grams
she bought 4000 grams
4000/100 =40
she filled 40 bottles

Answer:

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

A and C are congruent angles opposite to congruent sides of the isosceles triangle.

Find the measure of ∠A

Answer:

The angle A is 55°.

Step-by-step explanation:

We know that,

→ <A = <C

Now the value of x will be,

→ 3x + 40 = x + 50

→ 3x - x = 50 - 40

→ 2x = 10

→ x = 10/2

→ [ x = 5 ]

Then the value of m<A is,

→ A = 3x + 40

→ A = 3(5) + 40

→ A = 15 + 40

→ [ A = 55° ]

Hence, the answer is 55°.

Answer:

- Banking Operations salary in India with less than 1 year of experience to 10 years ranges from ₹ 1.4 Lakhs to ₹ 7 Lakhs with an average annual salary of ₹ 3.1 Lakhs based on 261 latest salaries

Answer:

I think it is D

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(x + 9 < 4\)

Subtract 9 from both sides

\(x + 9 - 9 < 4 - 9\)

Simplify

\(x < - 5\)

Answer:

Step-by-step explanation:

first add the ratio together

3+1+2=6

Malachy=3/6 x$18

              =9

Gavyn=1/6 x $18

           = 3

for the last person you can either add the result for malachy and gavyn the subtract it from the original amount

18-(9+3)

18-12

6

or

2/6 x 18

6

Lavage Rapide's total cost per car washed is $19.05.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

Fixed costs are expenses that do not change based on the number of units produced or sold. Variable costs, on the other hand, change with the level of production or sales. Here, the fixed costs are cleaning supplies, electricity, maintenance, wages and salaries, depreciation, rent, and administrative expenses.

The variable cost is the cost per car washed, which includes wages and salaries and administrative expenses.

To calculate the total cost per car washed, we need to add fixed costs to the variable cost per car. So, the total cost per car washed for Lavage Rapide would be:

Total Cost per Car Washed = Fixed Costs + Variable Cost per Car Washed

Total Cost per Car Washed =\(($0.80 + $1,400 + $0.20 + $4,700 + $8,000 + $2,100 + $1,400) + ($0.40 + $0.05)\)

Total Cost per Car Washed = $18,620 + $0.45

Total Cost per Car Washed = $19.05

Therefore, Lavage Rapide's total cost per car washed is $19.05.

To know more about equation visit:

brainly.com/question/649785

#SPJ1

complete question:

Fixed Cost per Month Cost per Car Washed

Cleaning supplies $ 0.80

Electricity $ 1,400 $ 0.08

Maintenance $ 0.20

Wages and salaries $ 4,700 $ 0.40

Depreciation $ 8,000

Rent $ 2,100

Administrative expenses $ 1,400 $ 0.05

The expression that could be used to calculate the amount Trina was charged in interest for the billing cycle is  (APR / 365) x 30 days x adjusted balance.

The adjusted balance method is one of the methods for computing the finance charge (interest and other fees) for credit cards.

The adjusted balance is the ending balance determined after adjusting the opening balance with purchases and payments.

Credit card interest method = adjusted balance method

Beginning balance = $780

Purchase = $170

Payment = $210

Adjusted balance, AB = $740 ($780 + $170 - $210)

APR = 17% = 0.17 (17/100)

The interest charged = (APR / 365) x 30 days x adjusted balance

= $10.34 [(0.17/365) x 30 x $740]

Learn more about the adjusted balance method at https://brainly.com/question/14351468.

#SPJ1

Answer: ∠16 and ∠11

Step-by-step explanation:

      All of these answer options include ∠16, so we know we're looking for an angle that is corresponding to ∠16. A corresponding angle is an angle that is in the same relative position. We will look at ∠9, ∠11, ∠2, and ∠12 since those are the given answer options, and see which is corresponding.

The correct corresponding angles are ∠16 and ∠11.

Answer:

? = 65°

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ PUV is an exterior angle of the triangle , then

? + 95° = 160° ( subtract 95° from both sides )

? = 65°

Answer: 20

Step-by-step explanation:

Multiply 2.4*10-4

Calculate 24-4

the answer is (12x^10000)/5

Given data:

The first term of geometric series is 4.

The second term of geometric series is 12.

The expression for the common ratio is,

The expression for the 10th term is,

Thus, the 10th term is 78,732.

Answer:

In order to find the number, we will need to set it up in an equation. In total, there are 460 students while 60% of them have pets. Lets set that up.

460(60%)

In order to correctly do this, we will need to transfer 60% into a decimal, which is .6. Now we will rewrite it.

460(.6)

This now can be represented by the number 276.

Since we know that 276 is 60% of 460, The total number of students that have pets will be 276.

Step-by-step explanation:

Answer:

In order to find the number, we will need to set it up in an equation. In total, there are 460 students while 60% of them have pets. Lets set that up.

460(60%)

In order to correctly do this, we will need to transfer 60% into a decimal, which is .6. Now we will rewrite it.

460(.6)

This now can be represented by the number 276.

Since we know that 276 is 60% of 460, The total number of students that have pets will be 276. mark me as branlylist sorry im late

Step-by-step explanation:

True i asked my friend for help though

The values of x and y in the figure are 3√2 and 3, respectively.

The diagram shown is a right triangle with a 45-degree acute angle.

The values of variables x and y must be determined.

Using the trigonometry identity, we get:

opposite/hypotenuse = sin 45

sin45 = 3/x

x = 3/sin45

x = 3(1/√2)

x = 3√2

Likewise,

tan 45 = opposite/adjacent

tan 45 = 3/y

1 = 3/y

y = 3

As a result, the values of x and y in the figure are 32 and 3, respectively.

More information about trigonometric identity may be found at: https://brainly.com/question/7331447

#SPJ1

Answer:

x=1

Step-by-step explanation:

y=3x so just add 1+3=4 then add veriable y=4x

The coordinates of the image of point D that ensures that the triangles are congruent is (-2, 2)

Given the triangle ABC and the incomplete triangle DEF

From the triangle transformation of points B and C, we can see that

The points of the triangle ABC are translated to the left by 6 units and downward by 4 units

Mathematically, this can be represented as

(x, y) = (x - 6, y - 4)

Given that

A = (4, 6)

So, we have

D = (4 - 6, 6 - 4)

Evaluate the difference

D = (-2, 2)

Hence, the position is (-2, 2)

Read more about transformation at

https://brainly.com/question/27224272

#SPJ1

The probability of getting blue or green is 1/3, the probability of getting blue is 3/4 and there are 8 blue marbles.

a) If the probability of getting a yellow marble is 2/3, then the probability of getting a blue or green marble is:

P(blue or green) = 1 - P(yellow) = 1 - 2/3 = 1/3

b) If the probability of getting a green marble is 1/4, then the probability of getting a blue marble is:

P(blue) = 1 - P(green) = 1 - 1/4 = 3/4

c) The total number of marbles in the bag is 24. Let x be the number of blue marbles. Then the number of yellow marbles is 2x, and the number of green marbles is 24 - x - 2x = 24 - 3x. We know that:

2x/24 = 2/3 (probability of getting a yellow marble is 2/3)

=> x = 8

Therefore, there are 8 blue marbles in the bag.

Learn more about probability in https://brainly.com/question/30034780

#SPJ1

When proving the properties of logarithms when exponents must be used, the property that is used in all of these is D. \(log_{b} (b^y) = y\)

When proving any property of logarithms that have to do with exponents, one property that should always be used is  \(log_{b} (b^y) = y\).

Expressing y as a product of \(log_{b} (b^y)\) is the most basic property of using exponents on logs because it has both product, quotient, and power rules of logarithms.

Find out more on logarithmic properties at https://brainly.com/question/15263375.

#SPJ1

Answer:

45

Step-by-step explanation:

You are given only one space. Note that the term 6 shows up on both sides. Therefore, it is implying that you need to multiply the other two terms together. Do so:

9 x 5 = 45

45 is your answer.

~

The value of c in the polynomial is - 7.

The polynomial is given as follows:

p(x) = 2x³ - x² +  cx + 2 . The value of c if x - 2 is a factor of p(x) can be computed as follows:

Therefore,

p(x) = 2x³ - x² +  cx + 2

when x - 2 is a factor, p(x) = 0

Therefore,

0 = 2x³ - x² +  cx + 2

Hence,

2(2)³ - (2)² +  2c + 2 = 0

16 - 4 + 2c + 2 = 0

12 + 2 + 2c  = 0

2c = - 14

divide both sides by 2

c = - 14 / 2

c = - 7

Therefore,

c = -7

learn more on polynomials here: https://brainly.com/question/30127172

#SPJ1