The common denominator of
5/6-2/7

Answer:

y = - 2x

Step-by-step explanation:

Given that x and y vary directly then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition x = - 5, y = 10, thus

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{10}{-5}[/tex] = - 2, hence

y = - 2x ← is the equation relating them

Answer: a) 70%

b) 6%

c) 24%

d) and: 6%

   or: 66%

e) 46.2%

Step-by-step explanation:

Living on campus = 30%

Living off Campus = 70%

Living on campus with car = 20% of 30% = 0.2 x 0.3 = 0.06 = 6%

Living on campus w/o car = 80% of 30% = 0.8 x 0.3 = 0.24 = 24%

Living off campus with car = 60% of 70% = 0.6 x 0.7 = 0.42 = 42%

Living off campus w/o car = 40% of 70% = 0.4 x 0.7 = 0.28 = 28%

a) 70%

b) 6%

c) 24%

d) Student lives on campus and has an automobile: 6%

   Student lives on campus or has an automobile = 66%

living on campus 30%

students with car = 6% (on campus)  42% (off campus)

30 - 6 + 42 = 66

e) P (living on campus/not have a car) = P(living on campus w/o a car)/P(not have a car)

P(living on campus w/o a car) = 24

P(not have a car) = 24+28 = 52

P (living on campus/not have a car) = 24/52 = 0.462 = 46.2%

Answer:

12 1/2

1/2

6 1/4

Step-by-step explanation:

hope this helps ya

To estimate Martin's friend's purchase of grapes, convert 12 3/5 to an improper fraction and multiply it by 3/8. The estimate is 9/40 pounds of grapes.

To estimate how many pounds of grapes Martin's friend bought, we can use compatible fractions. Martin bought 12 3/5 pounds of grapes. His friend bought 3/8 of that amount.

Step 1: Convert 12 3/5 to an improper fraction.

12 3/5 = (5 * 12 + 3)/5 = 63/5

Step 2: Multiply the improper fraction by 3/8.

(63/5) * (3/8) = (63 * 3)/(5 * 8) = 9/40

Therefore, Martin's friend estimated about 9/40 pounds of grapes.

Answer:

3x+5y-16=0

Step-by-step explanation:

See it in the pic.

Equation of tangent line to the curve is

[tex]y=-\frac{3}{5}x+\frac{16}{5}[/tex]

Equation of tangent line is in the form of y=mx+b

where m is the slope and b is the y intercept

Derivative of a given function is the slope. To find slope at the given point , we find out f'(2)

we are given with function

[tex]f(x)= \frac{5x}{1+x^2} \\Apply \; quotient \; rule \\5\frac{\frac{d}{dx}\left(x\right)\left(1+x^2\right)-\frac{d}{dx}\left(1+x^2\right)x}{\left(1+x^2\right)^2}\\5\cdot \frac{1\cdot \left(1+x^2\right)-2xx}{\left(1+x^2\right)^2}\\\frac{5\left(1-x^2\right)}{\left(1+x^2\right)^2}\\[/tex]

Now we find f'(2) by replacing 2 for x

[tex]f'(x)=\frac{5\left(1-x^2\right)}{\left(1+x^2\right)^2}\\f'(2)=\frac{5\left(1-2^2\right)}{\left(1+2^2\right)^2}\\f'(2)=\frac{-15}{25} \\f'(2)=-\frac{3}{5}[/tex]

Now we use the given point and the  slope to get the equation of tangent line

[tex]m=-\frac{3}{5} and (2,2)\\y-y_1=m(x-x_1)\\y-2=-\frac{3}{5}(x-2)\\y-2=-\frac{3}{5}x+\frac{6}{5}\\y=-\frac{3}{5}x+\frac{6}{5}+2\\y=-\frac{3}{5}x+\frac{16}{5}[/tex]

Equation of tangent line to the curve is

[tex]y=-\frac{3}{5}x+\frac{16}{5}[/tex]

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Final answer:

The factorization of x² + 3x - 4 is (x + 4)(x - 1), which can be verified using algebra tiles that represent these factors and the product.

Explanation:

The factors of x² + 3x - 4 can be determined by looking for two numbers that multiply to -4 (the constant term) and add up to +3 (the coefficient of the middle term x). Through factor pairs of -4 (e.g., -1 and 4, or 2 and -2), we notice that (+4) and (-1) are the numbers that meet the criteria because 4 × (-1) = -4 and 4 + (-1) = 3. Therefore, the factorization is (x + 4)(x - 1). To use algebra tiles, you would arrange them into a rectangle where the length and width represent the factors of the quadratic expression, and the product area represents the entire expression.

Answer:

  $2300

Step-by-step explanation:

The commission earned by the representative is ...

  commission = 0.02 × $15,000 = $300

so the total to be paid to the sales representative is ...

  salary + commission

  = $2000 +300 = $2300

Answer:

[tex]\frac{9x}{40}[/tex] is the answer.

Step-by-step explanation:

The question has some typo errors.

Rashid and Mikhail submitted a total of x pastries to a baking competition.

Suppose say :

Mikhail made x pastries .

Hence Rashid made [tex]\frac{2x}{3}[/tex] pastries.

And in total they made [tex]\frac{5x}{3}[/tex] pastries.

Now we have that out of x, [tex]\frac{5}{8}[/tex] of x were brushed with olive oil.

So, [tex]\frac{3}{8}[/tex] of x that is [tex]\frac{3x}{8}[/tex] are brushed by butter.

So, it becomes [tex](\frac{3}{8}) / ( \frac{5x}{3} )[/tex]

= [tex]\frac{3}{8} \times\frac{3x}{5}[/tex] = [tex]\frac{9x}{40}[/tex]

Hence, answer is option B.

Answer:

PQ = 6 and QR = 7.5

Step-by-step explanation:

The lengths of the sides of two similar triangles are proportional. That is, if Δ ABC is similar to Δ PQR, then the following equation is established.

[tex]\frac{AC}{PR}=\frac{AB}{PQ}=\frac{BC}{QR}[/tex]

[tex]\frac{6}{9} = \frac{4}{PQ} = \frac{5}{QR}[/tex]

[tex]\frac{6}{9} = \frac{4}{PQ}[/tex]

PQ = 6

[tex]\frac{6}{9} = \frac{5}{QR}[/tex]

QR = 7.5

Answer:

See explanation

Step-by-step explanation:

Let [tex](x,y)[/tex] be the coordinates of the point which has to be dilated with the scale factor of [tex]k[/tex] with the center of dilation at point [tex](0,0)[/tex] (the origin).

The dilation with the scale factor [tex]k[/tex] and the center of dilation at the origin has the rule

[tex](x,y)\rightarrow (kx,ky)[/tex]

So, you have simply to multiply each coordinate of the point by [tex]k[/tex] to get the image's coordinates.

Answer:

The initial population P0 is 7500

Step-by-step explanation:

First of all, we are told that the population is proportional to time. This means that as time goes by, the population will increase. This type of relationship between two variables has the form of a linear equation expressed as:

y = mx + b,

where m is the slope of the curve and b is the intercept of it.

In this case we can state the following equation:

P = mt + P0

Where P is the population at a certain time "t", "m" is the slope of the curve, "t" is the time (this is the independent variable) and P0 is the intercept of the curve and represents the initial population.

Once we state the equation, let's see what we know:

If t = 0, then P = P0

If t = 3, then P = 12000 just as we are told

and if t = 5, then P = 2 P0 because after five years the population has doubled compared to the initial population (P0).

From the definition of the slope of the curve:

(Y2 - Y1)/(X2-X1) = m

and using the data described before we can formulate the slope value:

m = (2P0 - P0)/(5-0)

m = (2P0 - P0)/5

m = P0/5

Then, let's replace the value of m in the following equation:

P = mt + P0

12000 = (P0/5) × 3 + P0 → This is the equation presented when 3 years has gone by and we now have a population of 12000.

12000 = (3/5) P0 + P0

12000 = (8/5) P0

12000×5/8 = P0 = 7500

Then we can calculate the value of the slope m:

m = P0/5

m = 7500/5 = 1500

Now, knowing the value of m and the initial population P0 we are able to calculate the population at any value of "t".

Answer:

quotient = 4x + 3 + (3/x+6)

Step-by-step explanation:

To solve this, we conduct polynomial division. We divide the first term of the divisor into the first term of the polynomial.

Step 1: Divide the first term of the polynomial, 4x^2, by the first term in the divisor, x, to obtain 4x. This is the first term of our quotient.

Step 2: Keep the divisor, x+6, as it is and multiply it by the first term of the quotient, 4x.  We obtain 4x^2 + 24x.

Step 3: Subtract this result from the original polynomial. The difference is 3x+22.

Step 4: The divisor x+6 is then divided into the first term of the new polynomial, 3x, to obtain 3.  Add this to the quotient, making the quotient 4x+3.

Step 5: Multiply the divisor, x+6, by the new term in the quotient, +3, obtaining 3x+18.

Step 6: Subtract this result from the last polynomial, 3x+22, to get the remainder, 4

So when we divide 4x^2 +27x+22 by x+6, we get the quotient is 4x+3 and the remainder is 4.

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Answer:

Step-by-step explanation:

Finding the slope is perhaps easiest done by solving for y.

  5x -6 = -3y . . . . subtract 3

  y = -5/3x +2 . . . divide by -3

This is slope-intercept form, so we can see both the slope (the coefficient of x, -5/3) and the y-intercept (the constant, +2).

__

To find the x-intercept, we set y=0 and solve for x. This might be most easily done using the original equation:

  5x -3 = 0 +3 . . . . set y = 0

  5x = 6 . . . . . . . . . add 3 to get the x-term by itself

  x = 6/5 = 1.2 . . . . divide by the coefficient of x. This is the x-intercept.

__

Slope = -5/3

y-intercept = 2

x-intercept = 6/5

Answer:

The answer to your question is:   F = (-6, -4)

Step-by-step explanation:

Segment = EF

mpM = (-2, 2)

first point = E = (2, 8)

second point = F = (x, y)

Formula

      Xmp = (x1 + x2) / 2                         Ymp = (y1 + y2) / 2

      x2 = 2xmp - x1                                y2 = 2ymp - y1

Process

     x2 = 2(-2) - 2                                   y2 = 2(2) - 8

     x2 = -4 - 2                                       y2 = 4 - 8

     x2 = -6                                            y2 = -4

                     F = (-6, -4)

The coordinates of the other endpoint of the line segment EF, given that the midpoint M is (-2,2) and the endpoint E is (2,8), are (-6,-4). This is determined by using the midpoint formula and solving for the remaining variables.

To find the coordinates of the other endpoint F, we apply the midpoint formula which is M ( (x₁ + x₂) / 2, (y₁ + y₂) / 2 ). Here, we have the midpoint M(-2,2) and one endpoint E(2,8).

It's like saying: (-2,2) = ( (2 + x₂) / 2, (8 + y₂) / 2 ).

To solve for x₂ (the x-coordinate of point F) and y₂ (the y-coordinate of point F), we will set up two separate equations based on the x and y coordinates.

For the x-coordinate, (-2) = (2 + x₂) / 2. Solve for x₂ gives x₂ = -2*2 - 2 = -6.

For the y-coordinate, 2 = (8 + y₂) / 2. Solve for y₂ gives y₂ = 2*2 - 8 = -4.

So, point F, the other endpoint of the line segment EF, has the coordinates (-6,-4).

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Answer:

  ₹30/cap

Step-by-step explanation:

To gain 15%, the dealer must have total revenue of ...

  ₹1500 × 1.15 = ₹1725

His revenue so far is ...

  15 × ₹35 +15 × ₹40 = ₹1125

There are 50 -15 -15 = 20 caps remaining, and the dealer wants additional revenue of ₹1725 -1125 = ₹600. He must sell them at a price of ...

  ₹600/(20 caps) = ₹30/cap

Answer: 175760000

Step-by-step explanation:

We know that the total number of digits in the number system is 10  [0,1,2,3,4,5,6,7,8,9]

The total number of letters in English Alphabet = 26

Now, if standard automobile license plates in a country display 2 numbers, followed by 3 letters, followed by 2 numbers, then the number of different standard plates are possible in this system (if repetition of letters and numbers is allowed)will be :_

[tex]= 10\times10\times26\times26\times26\times10\times10\\\\=175760000[/tex]

Hence, the number of different standard plates are possible in this system = [tex]175760000[/tex]

In the given license plate system, there are 175,760,000 possible combinations by calculating the combinations for each segment (2 numbers, 3 letters, 2 numbers) and multiplying them together.

A standard automobile license plate in this system consists of 2 numbers, followed by 3 letters, followed by 2 numbers. To determine the number of different plates possible, we calculate the combinations for each part separately and then multiply them together.

To find the total number of different standard license plates possible, we multiply the combinations for each part:

Total Plates = 100 x 17,576 x 100 = 175,760,000

Therefore, there are 175,760,000 different possible license plates in this system.

The remaining factor of the given polynomial x^3 + 25x^2 + 50x - 1000, knowing that (x-5) and (x+10) are factors, is 'x - 20'. This is calculated by dividing the original polynomial by the known factors.

In the polynomial

x^3 + 25x^2 + 50x - 1000

, you have expressed that (x-5) and (x+10) serve as factors. Thus, to find the remaining factor, we need to divide the polynomial by these two known factors. We'll begin with dividing the original polynomial by (x-5). This yields a quotient of x^2 +  20x - 200. Subsequently, we divide this quotient by the second known factor (x+10), which ultimately gives us the final factor, being

x - 20

. Hence, x - 20 is the remaining factor of the polynomial.

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10(x/2 + 9) = 13

5x + 90 = 13

5x = 13 - 90

Can you do the rest?

Answer:

Tax due on the property : $ 960

Step-by-step explanation:

We know that the property is assessed at the 40% of it's current value.

First we are going to find the value assessed.

40% of $40,000 = 0.4 * 40,000 = $ 16,000

Now, at the value, we are aplying a factor of 1.5. This equalization factor is the multiplier we use to calculate the value of a property that is in line with statewide tax assessments

So, we do, 1.5* $16,000 = $24,000

Now we got that we the tax rate is $4 per $100 assessed.

So we got $24,000 * $4  / $100 = $ 960

Answer:

$1.91

Step-by-step explanation:

This means the cost of the item to you is $1.91. You will pay $1.91 for a item with original price of $2.25 when discounted 15%. In this example, if you buy an item at $2.25 with 15% discount, you will pay 2.25 - 0.3375 = 1.91 dollars.

Answer:

1.91

Step-by-step explanation:

1- 2.25

2- 2.25÷100= 0.0225 find 1 percent

3- 0.0225×15=0.3375 find the 15 percent

4- 2.25-0.3375=1.9125 subtract the discount of the original price

5- 1.91 round off to two decimals

Answer:

G = (9.4, 9,4)

Step-by-step explanation:

The ratio is applied in the x-distance and the y-distance. The ratio is 2:3 so you have to divide the distances by 5 and 2/5 correspond to FG and 3/5 to GH

x-distance:

x2 - x1 = 16 - 5 = 11

11/5 = 2.2

y-distance:

y2 - y1 = 13 - 7 = 6

6/5 = 1.2

Point G = Point F + (2.2*2, 1.2*2)

Point G = (5, 7) + (4.4, 2.4)

= (9.4, 9.4)

Answer:

[tex]\frac{2}{5}*\frac{3}{5} +\frac{2}{5}*\frac{2}{5}+\frac{3}{5} *\frac{3}{5}  = \frac{19}{25}[/tex]

Step-by-step explanation:

We must remember that in order to get one even number we need to multiply one even number times one odd number or two even numbers. So, the first term tells the probability of having an even number from A and an even number from B, the next would be even from A and odd from B and the last one tells the likelihood of having odd from A and even from B

Answer:

Option E.

Step-by-step explanation:

Let the intended length of Rebecca's swimming is = x units

and we assume the length of the pool = l units

Now it is given in the question that " She covers one fifth of her intended distance "

That means distance covered = [tex]\frac{x}{5}[/tex]

" After swimming six more lengths of the pool she had covered one quarter of her intended distance"

So [tex]\frac{x}{5}+6(l)=\frac{x}{4}[/tex]

[tex]6l=\frac{x}{4}-\frac{x}{5}[/tex]

[tex]6l=\frac{x}{20}[/tex]

x = 20×(6l)

x = 120l

Therefore, Rebecca has to complete 120 lengths of the pool.

Option E is the answer.

Answer:

The answer to your question is:    Y = (13, -14)

Step-by-step explanation:

Data

midpoint = mp = (6, -3)

one endpoint = X = (-1, 8)

second endpoint = Y = (x, y)

Formula

Xmp = (x1 + x2) / 2

Ymp = (y1 + y2) / 2

Process

                    x2 = 2xmp - x1

                    y2 = 2ymp - y1

                   x2 = 2(6) - (-1)                     y2 = 2(-3) - 8

                   x2 = 12 + 1                          y2 = -6 - 8

                   x2 = 13                               y2 = - 14

                   Y = (13, -14)

Answer:

The answer is c. $48,000

Step-by-step explanation:

To find the free cash flow, we need to take into account the money that is entering the company and the money that is being used.  Money that we are earning is possitive, and money being spend goes with a minus.

The net cash, the $50,000 is our sales column. And is money entering the company.

The Investment would be our CAPEX or directly we can use it as investment. And this money is being spended.

The dividends, are the payments that we are doing to the board of directors or the share holders. Since we are paying others, we know this money is being used.

The equation here is:

Sales - Investment - Dividends = Free Cash Flow

So it $50,000 - $1,000 - $1,000 = $48,000

Answer:

Step-by-step explanation:

Well, there are several  relationships you can describe.  As time increases how does number of pages  react?  Like does it increase or decrease.  Is it always increasing or decreasing by the same amount?  If it's not all the same how do different parts look different.  

There aren't any actual numbers, so you can't say specifically how they relate, like you can't say she read 5 pages a minute or something.

There is no smooth increase or decrease of the graph thus it reperesnts a non linear relationship.

Typically, when a graph increases or decreases abruptly, the data or function it represents is showing some sort of discontinuity or sudden change in behavior.

In other words, there are areas or locations on the graph where values or the slope abruptly shift rather than gradually and constantly changing.

Thus, the slope of the graph is constantly changing and the relationship that is depicted is non linear.

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Answer:

180h + 15h²

Step-by-step explanation:

Since both have same function i.e. function of f, so we simply put 6 + h and 6 in place of x in f(x)

Here,

f(x) = 15x² + 6

Then, f(6+h) - f(6)

= [15(6 + h )² + 6] - [15(6 )² + 6]

⇒ [15 (36 + 12h + h²) + 6] - [15 × 36 + 6]

⇒ [ 15 × 36 + 15 × 12h + 15h² + 6 - 15 × 36 - 6 ]

⇒ 15 × 12h + 15h²

⇒ 180h + 15h²

Answer:

What we know is that 30% of the group have brown hair and are girls. It means that in the other 70% we have the boys with brown hair, the other boys and the other girls.

In the case all the girls have brown hair, the 70% remaining would be boys. So 70% of then would have brown hair. (0.7*0.7=0.49 -> 49% of the children would be brown hair) so 49% (boys) and 30% (girls) are more than 50%..

Now, let's suppouse that 90% of the group are girls. It means 10% are boys and 70% of that 10% (=7%) are the boys in the group that have brown hair. Now 7% + 30% of the children have brown hair, wich isn't more than the half.

We have explained with two extreme cases that the information is not enough for making a precise answer

Yes, the average speed for the entire trip from A to C is equal to 80 km/h.

Given

You travel from point A to point B in a car moving at a constant speed of 70 km/h.

You travel the same distance from point B to another point C, moving at a constant speed of 90 km/h.

The average speed is defined as the change in displacement and change in a time interval.

The formula is used to calculate average speed;

[tex]\rm Average \ speed= \dfrac{V_1+V_2}{2}[/tex]

Where [tex]\rm V_1[/tex] is 70 and [tex]\rm V_2[/tex] is 90.

Substitute all the values in the formula

[tex]\rm Average \ speed= \dfrac{V_1+V_2}{2}\\\\\rm Average \ speed= \dfrac{70+90}{2}\\\\\rm Average \ speed= \dfrac{160}{2}\\\\\rm Average \ speed= 80[/tex]

Hence, the average speed for the entire trip from A to C is equal to 80 km/h.

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Answer:

[tex]2 = x[/tex]

Step-by-step explanation:

THIS IS CORRECT! These two angles are somewhat linear pairs, so you set both expressions equal to 180°:

[tex]180° = 52° + (2^{3x + 1})°[/tex]

- 52° - 52°

______________________

128° = [tex](2^{3x + 1})°[/tex]

7 = 3x + 1

-1 - 1

_______

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

[tex]128° = [2^7]°[/tex]

I am joyous to assist you anytime.

The expression (4 + 5i)(4 - 5i) simplifies to 41, as the multiplication of complex conjugates yields a real number.

The expression (4 + 5i)(4 - 5i) is a product of two complex conjugates. When multiplied, the product of complex conjugates results in a real number because the imaginary parts cancel out. The multiplication proceeds as follows:

Multiplying the real parts: 4 * 4 = 16.

Multiplying the outer terms: 4 * (-5i) = -20i (but this will cancel out with the next step).

Multiplying the inner terms: 5i*4 = 20i (which cancels out the -20i from the outer multiplication).

Multiplying the imaginary parts: 5i * -5i = -25[tex]i^2[/tex]. Remembering that i^2 = -1, we simplify this to -25 * -1 = 25.

Adding the results from steps 1 and 4, we get 16 + 25 = 41.

Therefore, the simplified expression is 41.