Mathematics College

py+7=6y+q
what is the answer for this question (linear equations with unknown coefficients)?

Answers

Answer 1
Assuming your solving for y:
py+7=6y+q
-6y -7 -6y -7
(p-6)y = q-7
divide both sides by p-6
y=(q-7)/(p-6)
Answer 2

Answer:

The required equation is  [tex]y =\frac{(q-7)}{(p-6)}[/tex].

Step-by-step explanation:

Consider the provided equation.

[tex]py+7=6y+q[/tex]

We need to simplify the equation and convert it into a linear equation with unknown coefficients.

Subtract 6y from both sides.

[tex]py - 6y + 7 = q[/tex]

Subtract 7 from both sides.

[tex]py - 6y = q - 7[/tex]  

Take y common from left side.

[tex]y(p-6) = q-7[/tex]

 Divide both sides by p-6.

 [tex]y =\frac{(q-7)}{(p-6)}[/tex]

Hence, the required equation is  [tex]y =\frac{(q-7)}{(p-6)}[/tex].

Related Questions

On Saturday a local shop shop sold a combine TOTAL of 345 hamburgers and cheeseburgers. The number of cheeseburgers sold was 2 times the number of hamburgers. How many hamburgers were sold on Saturday?

Answers

x = hamburgers

2x = cheeseburgers

x +2x = 345

3x = 345

x = 345/3 = 115

115 hamburgers were sold

Samantha threw an apple out of a window. The equation -16t^(2)+120=y can be used to represent the apple's height above the ground, where t = time in seconds after she threw the apple. how long did it take for the apple to hit the ground. Round to nearest hundredth

Answers

check the picture below, y = 0 when that happens

[tex]\bf -16t^2+120=0\implies 120=16t^2\implies \cfrac{120}{16}=t^2\implies \cfrac{15}{2}=t^2 \\\\\\ \sqrt{\cfrac{15}{2}}=t[/tex]

bear in mind the square root would give us a +/- roots, however, since this is seconds, a negative unit would be unfeasible, thus we only used the positive root from it.

How many positive integers not exceeding 1000 are not divisible by either 4 or 6?

Answers

Final answer:

There are 667 positive integers not exceeding 1000 that are not divisible by either 4 or 6.

Explanation:

This is a question about number theory and involves the comprehension of divisibility. To identify the positive integers that are not divisible by either 4 or 6 and not exceeding 1000 is an application of the principle of inclusion and exclusion.

First, we need to figure out how many numbers up to 1000 are divisible by 4, which is 1000/4 = 250. Then, we look at how many numbers are divisible by 6, which is 1000/6 = about 166 (we only consider the whole numbers).

However, some numbers are divisible by both 4 and 6, so we have over-counted and need to correct for this. These would be the numbers divisible by the least common multiple (LCM) of 4 and 6, which is 12. There are 1000/12 = about 83 such numbers.

Thus, according to the principle of inclusion and exclusion, the total number of numbers divisible by 4 or 6 would be 250 + 166 - 83 = 333. The last step is to subtract this from the total number of integers from 1 to 1000, so the answer would be 1000 - 333 = 667.

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To make the two triangles below similar, what would the values of x and y have to be?

Answers

i dont really remember how to solve this since i done this some time ago the angles must be the same i would say d since 5 the bigger triangle is five times bigger 

~ hope this helps ~
First, y and 40 degrees would have to be the same; thus, y = 40 degrees.

Second, form and solve the ratio (x/25) = (6/30).  30x=25(6)=150.  Thus, x=5.

Determine whether the given differential equation is exact. if it is exact, solve it. (if it is not exact, enter not.) (3x + 6y) dx + (6x − 8y3) dy = 0

Answers

[tex]\underbrace{(3x+6y)}_{M(x,y)}\,\mathrm dx+\underbrace{(6x-8y^3)}_{N(x,y)}\,\mathrm dy=0[/tex]

The ODE is exact if [tex]\dfrac{\partial M}{\partial y}=\dfrac{\partial N}{\partial x}[/tex]. We have

[tex]\dfrac{\partial M}{\partial y}=6[/tex]
[tex]\dfrac{\partial N}{\partial x}=6[/tex]

so the equation is indeed exact.

We're looking for a solution of the form

[tex]\Psi(x,y)=C[/tex]

By the chain rule, we have

[tex]\dfrac{\partial\Psi}{\partial x}+\dfrac{\partial\Psi}{\partial y}\dfrac{\mathrm dy}{\mathrm dx}=0[/tex]
[tex]\iff\dfrac{\partial\Psi}{\partial x}\,\mathrm dx+\dfrac{\partial\Psi}{\partial y}\,\mathrm dy=0[/tex]

which means [tex]\dfrac{\partial\Psi}{\partial x}=M[/tex] and [tex]\dfrac{\partial\Psi}{\partial y}=N[/tex].

Now

[tex]\dfrac{\partial\Psi}{\partial x}=M\implies\displaystyle\int\frac{\partial\Psi}{\partial x}\,\mathrm dx=\int M\,\mathrm dx[/tex]
[tex]\implies\Psi(x,y)=\dfrac32x^2+6xy+f(y)[/tex]

Differentiating with respect to [tex]y[/tex] yields

[tex]\dfrac{\partial\Psi}{\partial y}=N\implies 6x+f'(y)=6x-8y^3[/tex]
[tex]\implies f'(y)=-8y^3\implies f(y)=\displaystyle\int(-8y^3)\,\mathrm dy=-2y^4+C[/tex]

and so the general solution is

[tex]\Psi(x,y)=\dfrac32x^2+6xy-2y^4+C=C[/tex]
[tex]\implies\Psi(x,y)=\dfrac32x^2+6xy-2y^4=C[/tex]
Final answer:

The given differential equation (3x + 6y) dx + (6x − 8y3) dy = 0 is exact because its mixed partial derivatives are equal. To solve it, first integrate M with respect to x to get a function involving an unknown function of y, then compare it with N to determine the unknown function.

Explanation:

To determine if the given differential equation is exact, we need to check if the partial derivative of M with respect to y is the same as the partial derivative of N with respect to x. In this given differential equation (3x + 6y) dx + (6x − 8y3) dy = 0, M = 3x + 6y and N = 6x - 8y3. First, compute the partial derivative of M with respect to y (∂M/∂y) which is 6, then the partial derivative of N with respect to x (∂N/∂x), which is 6 as well. Since ∂M/∂y=∂N/∂x, the given differential equation is exact.

To solve this exact differential equation, we integrate M dx, i.e., ∫M dx, to get ψ(x,y) =1.5x^2+6xy+h(y), where h(y) is an arbitrary function of y. Next, differentiate ψ(x,y) with respect to y, then compare the result with N: ψy=6x+dh/dy=6x-8y³. Solving for dh/dy gives dh/dy=-8y³, so integrating this gives h(y)=-2y⁴+C, where C is a constant. Therefore, the solution to the differential equation is ψ(x,y)=1.5x²+6xy-2y⁴=C.

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palace help me solve these two equations 14, 15

Answers

14)

check the picture below... so.. is just a semi-circle and a rectangle, nothing fancy, get their area, sum them up.

15)

so... the voter turnout, is referring to, what's the percentage that voted, which year has the highest percentage... well, we simply check the percentage of the value provided from the total eligible voters, keeping in mind that, all eligible voters are the 100%

so.. for 1944

[tex]\bf \begin{array}{ccllll} amount&\%\\ ------&----\\ 86,607,000&100\\ 47,976,670&x\\ \end{array}\implies \cfrac{86,607,000}{47,976,670}=\cfrac{100}{x} \\\\\\ x=\cfrac{100\cdot 47,976,670}{86,607,000}\implies x\approx 55.39583405498[/tex]

for 1984

[tex]\bf \begin{array}{ccllll} amount&\%\\ -----&-----\\ 167,727,000&100\\ 92,659,000&x \end{array}\implies \cfrac{167,727,000}{92,659,000}=\cfrac{100}{x} \\\\\\ x=\cfrac{100\cdot 92,659,000}{167,727,000}\implies x\approx 55.2439380660239[/tex]

Three times a number added to seven is 22

Answers

3x+7=22

3x=15

x=5

 the number is 5

a soccar team spent $55 dollars on supplies for a car wash then earned $275 whats their total after paying for supplies

Answers

To find what profit they made, subtract what they earned from what they spent money on. 275-55=220. They made a total of $220 after paying for supplies. I hope this helps! :)


John has taken out a loan for college. He started paying off the loan with a first payment of $100. Each month he pays, he wants to pay back 1.1 times the amount he paid the month before. Explain to John how to represent his first 20 payments in sequence notation. Then explain how to find the sum of his first 20 payments, using complete sentences.

Answers

Let a_0 = 100, the first payment. Every subsequent payment is the prior payment, times 1.1. In order to represent that, let a_n be the term in question. The term before it is a_n-1. So a_n = 1.1 * a_n-1. This means that a_19 = 1.1*a_18, a_18 = 1.1*a_17, etc. To find the sum of your first 20 payments, this sum is equal to a_0+a_1+a_2+...+a_19. a_1 = 1.1*a_0, so a_2 = 1.1*(1.1*a_0) = (1.1)^2 * a_0, a_3 = 1.1*a_2 = (1.1)^3*a_3, and so on. So the sum can be reduced to S = a_0 * (1+ 1.1 + 1.1^2 + 1.1^3 + ... + 1.1^19) which is approximately $5727.50

what is the area of a circle with a radius of 7 inches

Answers

Area formula is A=πr2 
A=3.1416(radius)2 (radius is 7)
A=3.1416(49) 
A=153.94 
The area is 153.94 inches.
Hope that was helpful :)

Answer is provided in the image attached.

What are the X intercepts of a parabola with vertex (6,27) and y intercept of (0,-81)?

Answers

so hmm let's see if we can get the parabola's equation

if we assume a vertical parabola, "y" in x-terms.... then

[tex]\bf \begin{array}{llll} \boxed{y=a(x-{{ h}})^2+{{ k}}}\\\\ x=a(y-{{ k}})^2+{{ h}} \end{array} \qquad\qquad vertex\ ({{ h}},{{ k}})\\\\ -------------------------------\\\\[/tex]

[tex]\bf \textit{we know that } \begin{cases} h=6\\ k=27 \end{cases}\implies y=a(x-6)^2+27 \\\\\\ \textit{we also know the y-intercept } \begin{cases} x=-81\\ y=0 \end{cases}\implies 0=a(-81-6)^2+27 \\\\\\ -27=a(-87)^2\implies \cfrac{-27}{(-87)^2}=a\implies -\cfrac{3}{841}=a\\\\ -------------------------------\\\\ \boxed{y=-\cfrac{3}{841}(x-6)^2+27}[/tex]

now, to get the x-intercepts, we simply set y = 0

[tex]\bf 0=-\cfrac{3}{841}(x-6)^2+27\implies -27=-\cfrac{3}{841}(x-6)^2 \\\\\\ \cfrac{-27\cdot 841}{-3}=(x-6)^2\implies 7569=(x-6)^2\implies \pm\sqrt{7569}=x-6 \\\\\\ \pm 87=x-6\implies \pm 87+6=x\implies x= \begin{cases} 93\\ -81 \end{cases}[/tex]

and... since the y = 0, then (93, 0) and (-81, 0)

A store is selling two mixtures of coffee beans in one-pound bags. The first mixture has 12 ounces of Sumatra combined with 44 ounces of Celebes Kalossi, and costs $42. The second mixture has 44 ounces of Sumatra and 12ounces of Celebes Kalossi, and costs $30. How much does one ounce of Sumatra and one ounce of Celebes Kalossi cost?

Answers

Create 2 equations for the given problem

12s + 44c = 42
44s + 12c = 30

Take either equation and solve for either s or c.
12s + 44c = 42
12s = 42 - 44c
s = (42 - 44c) / 12
s = (21 - 22c) / 6

Substitute into 2nd equation

44s + 12c = 30
22((21 - 22c) / 3) + 12c = 30
22(21 - 22c) + 36c = 90
-448c +462  = 90
-448c = -372
c = -372/-448
c = 93/112
c = 0.83

Substitute into the 2nd equation

44s + 12c = 30
44s = 30 - 12c
s = (30 - 12 (93/112)) / 44
s = (30 - 279 / 28) / 44)
s = (30 - 9 27/28) / 44
s = 0.46

Prove
12s + 44c = 42
12(0.46) + 44(0.83) = 42
5.52 + 36.52 = 42
42.04 = 42

44s + 12c = 30
44(0.46) + 12(0.83) = 30
20.24 + 9.96 = 30.16

Assuming minor rounding issues this looks accurate.

All of the following expressions are equivalent except _____. -4 - y -4 + y -y - 4 -y + (-4)

Answers

All of the expressions are equivalent except (b) -4 + y.

All the expressions involve adding -4 and - y in various orders, resulting in equivalent expressions due to the commutative property of addition.

However, the expression -4 + y  is different because it combines the positive y term with the negative 4, resulting in - 4 + y.

The other expressions either have y added to -4 ( -4 - y) or have -4 added to y (-y - 4, -y + (-4)).

While addition is commutative, changing the order of the terms can affect the overall expression when dealing with negative terms.

So, while mathematically equivalent, the form of -4 + y stands out due to its structure.

Complete Question:

All of the following expressions are equivalent except _____.

(a) -4 - y

(b) -4 + y

(c) -y - 4

(d) -y + (-4 )

Choose the best definition for the following term: variable (1 point)

Answers

It is something that is not consistent. Having a fixed pattern or liable to be changed. 

Answer:

The Meaning of term Variable is that Quantity Represented by small or Capital Alphabets of English whose value is not fixed.It can vary on different Situations.For example , Human diet can be called Variable.

In morning , you ate total of 0.25 Kg, in Afternoon you ate =0.50 Kg in total, and in the evening you ate total of 1 Kg.

So, if x is a variable of my Diet taken from Morning to evening, it has taken three distinct values, which are, x= 0.25, 0.50,1.

Here, x is a Variable, and 0.25,0.50 and 1 are Constant.

Write 11760825 in word form

Answers

11 million seventy six thousand eight hundred twenty five

If fixed costs are $561,000 and the unit contribution margin is $8.00, what is the break-even point in units if variable costs are decreased by $0.50 a unit?

Answers

Answer:

66,000 units

Step-by-step explanation:

Break-Even Sales (units) = Fixed Costs ÷ Unit Contribution Margin = $561,000 ÷ ($8 + $0.50) = 66,000 units

The break-even point in units after the decrease in variable costs is 66,000 units.

Given that the fixed costs are $561,000 and the original unit contribution margin is $8.00, we first calculate the original break-even point:

[tex]\[ \text{Original Break-even point in units} = \frac{561,000}{8} \][/tex]

[tex]\[ \text{Original Break-even point in units} = 70,125 \text{ units} \][/tex]

Now, since variable costs are decreased by $0.50 a unit, the new unit contribution margin becomes:

[tex]\[ \text{New Unit Contribution Margin} = 8 + 0.50 \][/tex]

[tex]\[ \text{New Unit Contribution Margin} = 8.50 \][/tex]

Using the new unit contribution margin, we calculate the new break-even point:

[tex]\[ \text{New Break-even point in units} = \frac{561,000}{8.50} \][/tex]

[tex]\[ \text{New Break-even point in units} = 66,000 \text{ units} \][/tex]

Therefore, the new break-even point in units, after the decrease in variable costs, is 66,000 units.

you have 5 antiques and want to display 3 on a shelf. how many different 3 antique arrangements are possible

Answers

[tex]\bf _{n}P_{r}=\cfrac{n!}{(n-r)!}\qquad\qquad _{5}P_{3}=\cfrac{5!}{(5-3)!}[/tex]

Use rounding or compatible numbers to estimate sum 198+727

Answers

198 round to 200
727 round to 730
200+ 730 is 930

The answer is 930. Hope this helps!

How many squares with sides that are 6 inches long are needed to cover a square with a side length of 30 inches without overlapping

Answers

5 squares are needed
Final answer:

Twenty-five squares with a side length of 6 inches are required to cover a square with a side length of 30 inches.

Explanation:

To find out how many squares with sides that are 6 inches long are needed to cover a square with a length of 30 inches, you first need to find the area of each square.

The area of a square is found by multiplying the length of one side by itself.

So, the area of the smaller square is 6 * 6 = 36 square inches, and

the area of the larger square is 30 * 30 = 900 square inches.

Then, you divide the area of the larger square by the area of the smaller square:

          900/36 = 25.

Therefore, 25 squares with sides of 6 inches are needed to cover a square with a side length of 30 inches.

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Please help with this

Answers

[tex]VWX\cong KLJ[/tex] means that the triangles are congruent, that is exactly identical.

The order of letters is very important. Form the given congruence we can write the following ratio:

[tex] \frac{VW}{KL} = \frac{WX}{LJ} = \frac{VX}{KJ} =1[/tex]

(notice that we do not mix the order: the first 2 letters of VWX are compared to the first 2 letters of KLJ and so on)

the ratio is one because the corresponding sides are equal.

[tex]\frac{VW}{KL}=1\\\\ \frac{2z-1}{z+2}=1\\\\2z-1=z+2\\\\2z-z=2+1\\\\z=3 [/tex]

[tex]|VW|=2z-1=2.3-1=6-1=5[/tex]


Answer: 5 units


Find all solutions to the equation csc theta +sqrt2 = 0

Answers

Theta = 7pi/4+2pi*n
Theta = 5pi/4+2pi*n

A basket contains five apples and seven peaches. Four of the apples and two of the peaches are rotten. You randomly pick a piece of fruit. It is fresh or it is an apple. Find the probability of this occuring.

Answers

2/35possible outcomes:5*7=35fresh or apple = 22/35

Answer:[tex]\frac{5}{6}[/tex]

Step-by-step explanation:

Given

5 apples and 7 peaches out of which 4 apples and 2 peaches is rotten

i.e. 1 apple and 5 peaches is fresh

probability of fresh fruit is =[tex]\frac{6}{12}[/tex]

probability of apple =[tex]\frac{5}{12}[/tex]

Probability of both =[tex]\frac{1}{12}[/tex]

Probability of fresh or an apple is=[tex] \frac{6}{12}+\frac{5}{12}-\frac{1}{12}[/tex]

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

It is desired to estimate the mean gpa of each undergraduate class at a large university. assume that the variance of the gpas is 1.44. how large a sample is necessary to estimate the mean gpa within 0.25 at the 99% confidence level

Answers

Final answer:

To estimate the mean GPA of each undergraduate class at a large university within a margin of error of 0.25 at a 99% confidence level, approximately 187 samples are needed.

Explanation:

To estimate the mean GPA of each undergraduate class at a large university within a margin of error of 0.25 at a 99% confidence level, we need to determine the required sample size. In this case, we can use the formula for sample size determination, which is:

n = (Z^2 * σ^2) / E^2

Where:

n is the required sample sizeZ is the Z-score associated with the desired confidence level (99% corresponds to a Z-score of approximately 2.58)σ^2 is the variance of the GPAs (given as 1.44)E is the desired margin of error (0.25)

Plugging in the values, we get:

n = (2.58^2 * 1.44) / 0.25^2

n ≈ 186.43

Therefore, we need a sample size of approximately 187 to estimate the mean GPA within a margin of error of 0.25 at a 99% confidence level.

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Allana 3/5 used yard of fabric to make a scarf. Can she make 2 of these scarves with 1 7/10 yards of fabric, and why?
Please Help

Answers

One scarf takes 3/5 of a yard. Two of these takes 6/5 of a yard.  If we put the 1 7/10 into an improper fraction we would get 17/10. So in order to compare the two fractions, the 6/5 and the 17/10, they have to have the same denominator. 6/5 can be rewritten as 12/10.  12/10 is less that the 17/10 you have, so yes you can make two scarves with that amount of fabric.

486 is what percent of 900

Answers

486/900 = .54 = 54%. .......

Darcy kicks a ball that is represented by the function h\left( t \right) = - 16{t^2} + 50t h ( t ) = − 16 t 2 + 50 t where t stands for time and h(t) stands for the height of the ball in feet. How long will it take for the ball to hit the ground?

Answers

check the picture below.

[tex]\bf h(t)=-16t^2+50t\implies 0=-16t^2+50t\implies 0=-t(16t-50) \\\\\\ \begin{cases} 0=-t\implies &0=t\\ ------\\ 0=16t-50\\ 50=16t\\ \frac{50}{16}=t\implies &\frac{25}{8}=t \end{cases}[/tex]

it hits it twice, once at the beginning, 0 seconds, and when it hits the ground at the end.

A domino consists of two congruent squares placed side by side. the perimeter of the domino is 60 units. what is the area of the domino, in square units?

Answers

Suppose that the Domino's short side measures l units. Then it's long side measures 2l  units, and the Domino's total perimeter is 6l=60. Thus l =10 and the Domino's area is 10 x 20=200 square units.

Answer:

200

Step-by-step explanation:

So say the dominoes' short side is x. Then the long side is 2x, so altogether there is 6x. So 6x=60, so x=10. So the area is 10*(10*2), which is 10*20 which is 200.

If 5 workers can pave 10 driveways in 30 days, how many days would it take 20 workers to pave 38 driveways?

Answers

Given that 5 workers can pave 10 driveways in 30 days, then:
let x be the number of days that can take 20 workers to complete 38 drive ways;
therefore:
proportion of work completed by 5 workers will be:
5*30/10
=15
proportion of work completed by 20 workers will be:
20*x/38
The time taken for 20 workers to complete 38 driveways will be:
15=20/38x
x=15*38/20
x=28 1/2
The answer is 28.5 days

You have been offered a project paying $300 at the beginning of each year for the next 20 years. what is the maximum amount of money you would invest in this project if you expect 9 percent rate of return to your investment?

Answers

This is a simple problem with some quick addition and subtraction, and a bit of multiplication.

First we figure out how much money you're spending in total, which is $300 each year, for 20 years, so 300 x 20 = 6,000. Now, since the problem is asking for a maximum amount for percentage rate, this means we find the 9% for all 20 years combined and not individually. 9% of 6,000 is of course 540, so if we subtract 540 from 6,000, we get 5,460.

This means your answer is $5,460

The tables represent two linear functions in a system.

What is the solution to this system?

Answers

The solution to this system is (x, y) = (8, -22).

The y-values get closer together by 2 units for each 2-unit increase in x. The difference at x=2 is 6, so we expect the difference in y-values to be zero when we increase x by 6 (from 2 to 8).

You can extend each table after the same pattern.

In table 1, x-values increase by 2 and y-values decrease by 8.

In table 2, x-values increase by 2 and y-values decrease by 6.

The attachment shows the tables extended to x=10. We note that the y-values are the same (-22) for x=8 (as we predicted above). That means the solution is ...

... (x, y) = (8, -22)

Answer:

(8,-22)

Step-by-step explanation:

Table 1)

To form equation we will use two point slope form

[tex](x_1,y_1)=(-4,26)\\(x_2,y_2)=(-2,18)[/tex]

Formula :[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

Substitute the values :

[tex]y-26=\frac{18-26}{-2+4}(x+4)[/tex]

[tex]y-26=-4(x+4)[/tex]

[tex]y-26=-4x-16[/tex]

[tex]y=-4x-16+26[/tex]

[tex]y=-4x+10[/tex] ---1

Table 2)

To form equation we will use two point slope form

[tex](x_1,y_1)=(-4,14)\\(x_2,y_2)=(-2,8)[/tex]

Formula :[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

Substitute the values :

[tex]y-14=\frac{8-14}{-2+4}(x+4)[/tex]

[tex]y-14=-3(x+4)[/tex]

[tex]y-14=-3x-12[/tex]

[tex]y=-3x+2[/tex] ---2

Now we are supposed to solve 1 and 2

Substitute the value of y from 1 in 2

[tex]-4x+10=-3x+2[/tex]

[tex]8=x[/tex]

Substitute the value of x in 2

[tex]y=-3(8)+2[/tex]

[tex]y=-22[/tex]

Hence the solution to this system is (8,-22)

Other Questions
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