a vehicle covers a distance of 524/25 kilometers on 7/8 liters of petrol. How much distance will it cover 2 liters of petrol

Answer:

[tex]1) \:\:\: \dfrac{14x}{y}[/tex]

[tex]2) \:\:\:\dfrac{16x^2}{9y^2}[/tex]

[tex]3)\:\:\:10[/tex]

[tex]4)\:\:\:\dfrac{x-2}{x+4}[/tex]

Step-by-step explanation:

I will provide detailed explanation for the first problem and quicker steps to solve the others. You should be able to figure them out

Dividing a number(integer or fraction) by a fraction is equivalent to multiplying that number by the reciprocal of the divisor fraction

So if you have an expression
[tex]\dfrac{a}{b} \div \dfrac{c}{d}\\\\\implies \dfrac{a}{b} \times \dfrac{d}{c}[/tex]

Question 1

[tex]\dfrac{14x^5}{5y^2}\:\div \dfrac{2x^4}{10y}\\\\= \dfrac{14x^5}{5y^2} \times \dfrac{10y}{2x^4}\\\\[/tex]

[tex]=\dfrac{14x^5\cdot \:10y}{10y^2x^4}[/tex]

10 in the numerator and 10 in the denominator cancel:

[tex]=\dfrac{14x^5y}{y^2x^4}[/tex]

[tex]\dfrac{x^5}{x^4} = x^{5-4} = x \;\;\;\;\;\;\text{Since }\dfrac{x^a}{x^b}=x^{a-b}}[/tex]

Likewise

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

Therefore
[tex]=\dfrac{14x^5\cdot \:10y}{10y^2x^4} = 14 \dfrac{x}{y} = \dfrac{14x}{y}[/tex]
Answer: Question 1

Question 2

[tex]\left(\dfrac{x}{y}\right)\left(\dfrac{4y}{3x}\right)\:\div \dfrac{6y^2}{8x^2}[/tex]

[tex]\dfrac{x}{y} \cdot \dfrac{4y}{3x} = \dfrac{4}{3}[/tex]

[tex]\dfrac{6y^2}{8x^2} = \dfrac{4y^2}{3x^2}[/tex]'

[tex]\left(\dfrac{x}{y}\right)\left(\dfrac{4y}{3x}\right)\:\div \dfrac{6y^2}{8x^2} \\\\= \dfrac{4}{3} \times \dfrac{3x^2}{4y^2}\\\\= \dfrac{16x^2}{9y^2}[/tex]

Question 3

[tex]\dfrac{\left(5\left(y+6\right)\right)}{2\left(xy-3\right)}\:\div \dfrac{\left(y\:+\:6\right)}{4\left(xy\:-\:3\right)}\\\\\\\dfrac{5(y + 6)}{2(xy-3)} \times \dfrac{4(xy-3)}{y+ 6}\\\\[/tex]

The y + 6 terms cancel out from numerator and denominator as do the xy - 3terms

[tex]= \dfrac{5}{2} \times \dfrac{4}{1}\\\\= \dfrac{20}{2} \\\\= 10[/tex]

Question 4

[tex]\dfrac{x^2-4}{x^2+5x+4}\:\div \dfrac{x+2}{x+1}\\\\=\dfrac{x^2-4}{x^2+5x+4}\:\times \dfrac{x+1}{x+2}[/tex]

[tex]x^2-4 = (x + 2)(x-2) \;\;\;\; \text{Since $a^2-b^2 = (a +b)(a-b)$}[/tex]

[tex]x^2 + 5x + 4\;\;\; \text{can be factored as: }\\\\(x + 1)(x + 4)[/tex]

Therefore
[tex]\dfrac{x^2-4}{x^2+5x+4}\:\div \dfrac{x+2}{x+1}\\\\\\=\dfrac{x^2-4}{x^2+5x+4}\:\times \dfrac{x+1}{x+2}\\\\\\= \dfrac{(x+2)(x-2)}{(x+1)(x+4)} \times \dfrac{x+1}{x+2}\\\\\\\\[/tex]

The x+2 terms cancel out as do the x + 1 terms giving the result
[tex]\dfrac{x-2}{x+4}[/tex]

Answer:

[tex]\textsf{1. \quad $\dfrac{14x}{y}$}[/tex]

[tex]\textsf{2. \quad $\dfrac{16x^3}{9y^2}$}[/tex]

[tex]\textsf{3. \quad $10$}[/tex]

[tex]\textsf{4. \quad $\dfrac{x-2}{x+4}$}[/tex]

Step-by-step explanation:

When dividing two fractions, multiply the first fraction by the reciprocal of the second fraction.  

The reciprocal of a fraction is its inverse (swap the numerator and denominator).

[tex]\boxed{\begin{minipage}{3 cm}\underline{Exponent Rules}\\\\$\dfrac{a^b}{a^c}=a^{b-c}$\\\\$a^{-n}=\dfrac{1}{a^n}$\\\end{minipage}}[/tex]

[tex]\begin{aligned}\dfrac{14x^5}{5y^2} \div \dfrac{2x^4}{10y} & = \dfrac{14x^5}{5y^2} \times \dfrac{10y}{2x^4}\\\\& = \dfrac{14x^5 \times 10y}{5y^2\times 2x^4}\\\\& = \dfrac{140x^5y}{10x^4y^2}\\\\& = \dfrac{14x^5y}{x^4y^2}\\\\& = 14x^{5-4}y^{1-2}\\\\& = 14x^1y^{-1}\\\\& = \dfrac{14x}{y}\end{aligned}[/tex]

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

[tex]\begin{aligned}\left(\dfrac{x}{y} \right)\left(\dfrac{4y}{3x} \right) \div \dfrac{6y^2}{8x^3}&=\dfrac{4xy}{3xy} \div \dfrac{6y^2}{8x^3}\\\\&=\dfrac{4}{3} \div \dfrac{6y^2}{8x^3}\\\\&=\dfrac{4}{3} \times \dfrac{8x^3}{6y^2}\\\\&=\dfrac{4 \times 8x^3}{3 \times 6y^2}\\\\&=\dfrac{32x^3}{18y^2}\\\\&=\dfrac{16x^3}{9y^2}\end{aligned}[/tex]

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

[tex]\begin{aligned}\left[\dfrac{5(y+6)}{2(xy-3)} \right] \div \left(\dfrac{y+6}{4(xy-3)}\right) & = \left[\dfrac{5(y+6)}{2(xy-3)} \right] \times \left(\dfrac{4(xy-3)}{y+6}\right)\\\\& = \dfrac{5(y+6) \times 4(xy-3)}{2(xy-3) \times (y+6)}\\\\& = \dfrac{20(y+6)(xy-3)}{2(xy-3)(y+6)}\\\\& = \dfrac{20}{2}\\\\&=10\end{aligned}[/tex]

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

Factor the numerator and denominator of the first fraction.

Apply the Difference of Two Squares to the numerator:

[tex]\implies x^2-4=x^2-2^2=(x-2)(x+2)[/tex]

Factor the denominator:

[tex]\begin{aligned}\implies x^2+5x+4 & =x^2+x+4x+4\\ & =x(x+1)+4(x+1)\\ & =(x+1)(x+4)\end{aligned}[/tex]

Therefore:

[tex]\begin{aligned}\left(\dfrac{x^2-4}{x^2+5x+4}\right) \div \left( \dfrac{x+2}{x+1} \right) & = \left(\dfrac{x^2-4}{x^2+5x+4}\right) \times \left( \dfrac{x+1}{x+2} \right)\\\\& = \left( \dfrac{(x-2)(x+2)}{(x+1)(x+4)} \right) \times \left( \dfrac{x+1}{x+2} \right)\\\\& = \dfrac{(x-2)(x+2)(x+1)}{(x+1)(x+4)(x+2)}\\\\& = \dfrac{x-2}{x+4}\\\\\end{aligned}[/tex]

Answer:

20% off is better and it is the only offer which is under the budget.

20% off of the $1,500 dining set is $300, and the dining set price will be 1500 - 300 = $1200.

And by applying the $150 coupon, the dining set price will be $1500 - $150 = $1350.

Therefore 20% off is better and it is the only offer which is under the budget.

Step-by-step explanation:

Answer:

22

Step-by-step explanation:

Answer:

There isn't an image to go with your question. repost this question with an image to be able to receive an answer.

Have a nice day :)

Answer:

Step-by-step explanation: You don't have an picture for me to explain add a picture and I'll be able to help you.

Given the equation of a parabola:

• You can rewrite it in Standard Form by following these steps:

1. Add the y-term to both sides of the equation:

2. Subtract the Constant Term from both sides of the equation:

3. Divide both sides of the equation by 5 (the leading coefficient)

4. The coefficient of the x-term is:

Then, you need to add this value to both sides:

Therefore.

5. Rewrite the equation as follows:

• Having the equation written in Standard Form:

You can identify that:

Solving for "p", you get:

• You can identify that:

Therefore, the Vertex is:

• By definition, the Focus of a parabola that opens upward is given by:

Then, in this case, this is:

• By definition, the Directrix for a parabola that opens upward is given by:

Then, in this case, you get:

Hence, the answers are:

• Standard Form:

• Value for "p":

• Vertex:

• Focus:

• Directrix:

The foci of the given ellipse are (D) (0, 5) and (0, -5).

So, the foci of the ellipse are:

(Refer to the graph attached below)

Therefore, the foci of the given ellipse are (D) (0, 5) and (0, -5).

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The correct question is shown below:

Which are the foci of the ellipse represented by 25x² + 16y² = 400?

A. (-3,0) and (3, 0)

B. (-5, 0) and (5, 0)

C. (0, 3) and (0, -3)

D. (0, 5) and (0, -5)

The total amount of money collected if Anya and Lauren sold their mangoes at $15 is $10,350

= 575 mangoes

Total number of mangoes = Number of mangoes Anya has + Number of mangoes Lauren has

= 115 + 575

= 690 mangoes

Amount each mangoes was sold = $15

Total amount of money collected = Total number of mangoes × Amount each mangoes was sold

= 690 × 15

= $10,350

So therefore, Anya and Lauren sold their total mangoes for $10,350

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The equality of the respective angles and the proportionality of the corresponding sides determine if two triangles are comparable.

Triangle A: 53, 71, Triangle B: 53, 71; Similar

Triangle C: 90, 37, Triangle D: 90, 53; Similar

Triangle E: 63, 45 Triangle F:14, 71; Not similar

Triangle G, 121, Triangles H: 70, Not similar

If two of one triangle's angles are congruent with two of the

angles of a different triangle, then the two triangles are comparable.

Similarity hypothesis, angle, and AA

Given that: The interior product of the AA similarity hypothesis

The angle sum property of a triangle states that the angles of a triangle are 180°,

Consequently, the third angle is also congruent when two angles are

congruent

53, 71 in Triangle A and 53, 71 in Triangle B; similar

Based on the AA similarity postulate, the triangles are similar.

Triangles C (90, 37) and D (90, 53) have similar angles.

Supplied that the given angles are identical to each of their complimentary angles, the triangle is similar.

Triangle F: 14, 71 Triangle E: 63, 45; not comparable

There are no parallel triangles.

Triangles H: 70, not identical to Triangle G's 121,

The details are insufficient.

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Answer:

x < 7/3

Step-by-step explanation:

[tex] - 5 < 9 - 6x[/tex]

[tex] - 14 < - 6x[/tex]

[tex] \frac{7}{3} > x[/tex]

[tex]x < \frac{7}{3} [/tex]

Answer:

(x-2)(x+8)

Step-by-step explanation:

Answer:

I think it's 171.5 in^3 but not sure :)

Step-by-step explanation:

Using algebra, we know that the total number of bees in her hive is 540.

So,

Then,

(A) Work out an estimate for the total number of bees in her hive

The estimated total no. of bees will be 540 bees.

Therefore, using algebra, we know that the total number of bees in her hive is 540.

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An expression is a collection of variables and constants that are bound by some mathematical operation the value for w for the given expression w -5.36=10+w/6 is 18.432.

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

A statement expressing the equality of two mathematical expressions is known as an equation.

As per the given expression,

w - 5.36 = 10 + w/6

Subtract w/6 both sides,

w - w/6 - 5.36 = 10 + w/6 - w/6

5w/6 = 10 + 5.36

w = 18.432

Hence "The value for w for the given expression w -5.36=10+w/6 is 18.432".

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[tex]|x-4|[/tex] is non-negative, and vanishes when [tex]x=4[/tex].

For all [tex]x\in[-2,1][/tex], we have [tex]x<4[/tex], so by definition of absolute value,

[tex]g(x) = |x-4| + 8 = -(x-4)+8 = -x+4[/tex]

which is strictly decreasing on [-2, 1] since [tex]g'(x)=-1<0[/tex]. Then the minimum value of [tex]g[/tex] on [-2, 1] occurs at the endpoint [tex]x=1[/tex], so that

[tex]\min\left\{g(x) \mid -2\le x\le1\right\} = g(1) = |1-4| + 8 = \boxed{11}[/tex]

[tex] \frac{v}{8} - 4 = - 12 \\ \frac{v}{8} = - 12 + 4 \\ \frac{v}{8} = - 8[/tex]

Now I will use CROSS MULTIPLICATION

[tex]v = 8( - 8) \\ v = -6 4[/tex]

ATTACHED IS THE SOLUTION

Answer: v/8 - 4 = (-12)

-12 + 4 = (-8)

what divided by 8 is 8?

8/8 = 1 so 8 x 8 = 64

this means v = -64

64/8 - 4 = -12

- 64/8 is -8 and that minus 4 is -12

3,058.08 cubic yards

radius = 9 yd

π = 3.14

Volume of a sphere = 4/3 πr³

Volume of sphere = 4/3 × 3.14 × 9³

Volume of sphere = 3052.08

To the nearest hundredth, the volume 3,058.08 cubic yards

The original price of the jacket before sale amount is $45.

Original price of the jacket will be calculated by forming the expression relating mentioned price. Let us assume the original price of the jacket to be x.

Writing the equation representing original price, percentage and price after sale

80%×x = 36

Converting percentage to fraction

80/100×x = 36

Shifting the fraction to Right Hand Side of the equation

x = 36×100/80

Cancelling zero as it is common in numerator and denominator and performing division

x = 45

Therefore, according to the sale price, the original price of jacket is $45.

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Answer:

Sometimes, Never, and Always.

(Sounds like a good movie title).

Step-by-step explanation:

See attached image.

Out of 400 students, 120 students would pick math as their favorite subject.

Data provided to us

fav subject       students

 Math                  6

 Science             3

 English              4

 History              7

Hence the total becomes 20 students

we have to calculate students whose favorite subject is math from 400 students

students with math as fav subject out of 20 students = 6

students with math as fav subject out of 400 students = (6 / 20) x 400

                                                                                          = 120 students

we can verify it as

%age of students out of 20 , who like math = 6/20 x 100

                                                                                   = 30 %

similarly, %age of students out of 400, who like math= 120/400 x 100

                                                                                        = 30 %

As we can see both the percentages are same. and the answer is verified .

So 120 students would pick math as their favorite subject out of 400 students.

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Given: A table that shows the result of a survey from 35 randomly selected students at Courtney's school.

Required: To determine the number of votes Rockzilla is expected to receive from a population of 115 students at Courtney's school.

This is achieved thus:

First, we determine the probability of Rockzilla's votes as follows:

Next, we determine the number of votes Rockzilla is expected to receive as follows:

Hence, the answer is:

The expression as an exponent is 21^1

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

(23) - 2

Open the bracket in the above expression

So, we have the following equation

(23) - 2 = 23 - 2

Evaluate the difference in the above expression

So, we have the following equation

(23) - 2 = 21

The above expression can be rewritten as

(23) - 2 = 21^1

Hence, the equivalent expression is 21^1

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Equivalent ratios are the ratios that are the same when we compare them. Three equivalent ratios are 1/2, 4/8, 3/6 in digits from 1 to 9.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other

Equivalent ratios are the ratios that are the same when we compare them.

The digits from 1 to 9 include 1,2,3,4,5,6,7,8,9.

Ratios are nothing but fractions.

Let 1/2 (one by two) is the first ratio.

Now 3/6 (three by six) is the second ratio

4/8 (four by eight) is the third ratio.

If we calculate the value of 1/2 = 0.5

The value of  3/6=1/2=0.5

The value of 4/8= 1/2=0.5

we get the same answer for all the ratios 1/2, 4/8 and 3/6 that is 0.5

That is 0.5 or 1/2.

Hence the three equivalent ratios are 1/2, 4/8, 3/6.

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Answer:

-15x - 3

I hope this helps :)

The change in the price level from the first to the second month is 106.4

Price index: Price index, measure of relative price changes, consisting of a series of numbers arranged so that a comparison between the values for any two periods or places will show the average change in prices between periods or the average difference in prices between places.

A college student purchases 4 movie tickets for $7 each, 2 CDs for $13 each, and 20 gallons of gasoline at $2 a gallon during the base period.

Gas will cost $2.25 per gallon in the upcoming month, CDs will cost $12.50 each, and cinema tickets will cost $7.50

The price index

=(price in current year/price in last year) x 100

=100/94 x 100

=106.38 or 106.4

The change in the price level from the first to the second month is 106.4

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Answer:  36 copies per minute

Step-by-step explanation:

126 copies in 3.5 minutes

We want x number of copies per 1 minute

[tex]\frac{126copies}{3.5minutes} = \frac{xcopies}{1minute}[/tex]

Cross multiply and we get

126 = 3.5x

Solve for x.

x = 126/3.5

x = 36

36 copies per minute

Answer:

D. 9x² - 12x - 1

Explanation:

To find f(g(x)), we need to replace x by g(x) as follows:

f(x) = x² - 5

f(g(x)) = (g(x))² - 5

Then, g(x) is equal to -3x + 2, so replacing g(x) by (-3x + 2), we get:

f(g(x)) = (g(x))² - 5

f(g(x)) = (-3x + 2)² - 5

f(g(x)) = (-3x)² + 2(-3x)(2) + 2² - 5

f(g(x)) = 9x² - 12x + 4 - 5

f(g(x)) = 9x² - 12x - 1

Therefore, the answer is D. 9x² - 12x - 1

Answer:

The answer is 5(30+2)!

Answer:

m∠1 = 140 by the Alternate Interior Angles Theorem

m∠2 = 40 by the Consecutive Interior Angles Theorem

Step-by-step explanation:

Lawn care is kind of model do you think best represents the profit for each business.

What is profit?

Dog walker = 5 + 12 + 23 + 50 + 62 + 82  = $234

House sitter = 11 + 19 + 29 + 38 + 50 + 73  = $220

Lawn care = 142 + 150 + 165 + 141 + 120 + 91  = $809

Lawn care is kind of model do you think best represents the profit for each business.

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