3х – 5y = 15
у = 2х + 4

Answer:

(a, 2a), and (a, -2a)

The constant of proportionality in the equation is 5/4

The constant connecting two given numbers in what is known in a proportional relationship is the constant of proportionality.

The constant of proportionality may also be referred to as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.

In the problem, y = 5/4x

The constant term 5/4 as used in the equation is used t multiply the input x values to get the out put y values

The term helps in relating x to y

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Answer:

\(35x \\ 35 \times 7 = 245\)

Answer:

245

Step-by-step explanation:

All you have to do is replace a with 7.

So, 35a=35*7= 245

Answer:

(4,0)

Step-by-step explanation:

You basically are plotting a point on the positive number 4 on the x line. Since they're only asking for an X and not a Y, you'd leave it as (4,0). Hope this helps!

Answer:

3/8 because 3 is bigger than 2.

3 of anything is bigger than 2 of the same thing.

Answer:

3x-x+2=4

Step-by-step explanation:

i ain readin allat !!

The speed of the slower plane is 325 mph and the speed of the faster plane is 365 mph.

This is a classic problem of relative speed. The two planes are moving toward each other, so their effective speed is the sum of their individual speeds. If we denote the slower plane's speed as x mph, then the faster plane's speed would be x + 40 mph. As they pass each other in 4 hours, we get the equation: 4*(x + x + 40) = 2760.

Solving this equation, we first simplify it to 2x + 40 = 690. Subtracting 40 from both sides gives us 2x = 650. Dividing both sides by 2 yields x = 325 mph, which is the speed of the slower plane, and the faster plane's speed is x + 40 = 365 mph.

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Answer:

Step-by-step explanation:

If cakes of 4 small and 4 large tiers serve 288 guests, and 3 small and 5 large tiers serve 316 guests, you want to know the number of guests served by a tier of each size.

Let 's' and 'l' represent the numbers of guests served by small and large cake tiers, respectively. The first cake serves ...

  4s +4l = 288

And the second cake serves ...

  3s +5l = 316

Subtracting 3/4 of the first equation from the second gives ...

  (3x +5l) -3/4(4s +4l) = (316) -3/4(288)

  2l = 100

  l = 50

  4s +4(50) = 288 . . . substitute for l in the first equation

  4s = 88 . . . . . . . . . . subtract 200

  s = 22 . . . . . . . divide by 4

A small tier will serve 22 guests; a large tier will serve 50 guests.

Answer:

B 2/1

Step-by-step explanation:

2/2=1

3/3=1

4/4=1

and 2/1=2

To find the measure of a side in a right triangle as given (have a angle of 90º) you use the trigonometric function. Use the value of the angle W=31º

The opposite side of angle W is XV and the adjacent side is y:

Use this equation to find the value of side WX (y):

Answer:

Step-by-step explanation:

Given the following complex numbers, we are to expressed them in the form of a+bi where a is the real part and b is the imaginary part of the complex number.

1) (2-6i)+(4+2i)

open the parenthesis

= 2-6i+4+2i

collect like terms

= 2+4-6i+2i

= 6-4i

2)  (6+5i)(9-2i)

= 6(9)-6(2i)+9(5i)-5i(2i)

= 54-12i+45i-10i²

= 54+33i-10i²

In complex number i² = -1

= 54+33i-10(-1)

= 54+33i+10

= 54+10+33i

= 64+33i

3) For the complex number 2/(3-9i), we will rationalize by multiplying by the conjugate of the denominator i.e 3+9i

= 2/3-9i*3+9i/3+9i

=2(3+9i)/(3-9i)(3+9i)

= 6+18i/9-27i+27i-81i²

= 6+18i/9-81(-1)

= 6+18i/9+81

= 6+18i/90

= 6/90 + 18i/90

= 1/15+1/5 i

4) For (3 − 5i)(7 − 2i)

open the parenthesis

= 3(7)-3(2i)-7(5i)-5i(-2i)

= 21-6i-35i+10i²

= 21-6i-35i+10(-1)

= 21-41i-10

= 11-41i

  Simplified form of the given expressions will be,

1). 6 - 4i

2). 64 + 33i

3). \(\frac{1}{15}+\frac{1}{5}i\)

4). \(\frac{31}{53}-\frac{31}{53}i\)

1). In a complex number (a + bi),

    a = Real part of the complex number

   bi = Imaginary part

     Expression given in the question → (2 - 6i) + (4 + 2i)

Rule to solve the given expression,

"Add real part and imaginary part of two complex numbers separately"

(2 - 6i) + (4 + 2i) = (2 + 4) + (-6i + 2i)

                         = 6 + (-4i)

                         = 6 - 4i

  Therefore, simplified form of the given expression will be (6 - 4i).

2). Given expression → (6 + 5i)(9 - 2i)

Rule to solve the expression → i² = -1

(6 + 5i)(9 - 2i) = 6(9 - 2i) + 5i(9 - 2i)

                       = 54 - 12i + 45i - 10i²

                       = 54 - 12i + 45i + 10 [Since, i² = -1]

                       = (54 + 10) + (45i - 12i)

                       = 64 + 33i

     Therefore, simplified form of the given expression will be (64 + 33i).

3). Given expression → \(\frac{2}{3-9i}\)

Multiply numerator and denominator with the conjugate of (3 - 9i) to convert the expression into (a + bi).

\(\frac{2}{3-9i}= \frac{2(3+9i)}{(3-9i)(3+9i)}\)

       \(=\frac{2(3+9i)}{3^2-(9i)^2}\)

       \(=\frac{6+18i}{9-81(-1)}\)

       \(=\frac{6+18i}{9+81}\)

       \(=\frac{6+18i}{90}\)

       \(=\frac{6(1+3i)}{90}\)

       \(=\frac{1}{15}+\frac{1}{5}i\)

    Therefore, simplified form of the given expression will be \(\frac{1}{15}+\frac{1}{5}i\)

4). Given expression → \(\frac{(3-5i)}{(7-2i)}\)

Multiply numerator and denominator with the conjugate of the denominator.

\(\frac{(3-5i)}{(7-2i)}=\frac{(3-5i)(7+2i)}{(7-2i)(7+2i)}\)

         \(=\frac{3(7+2i)-5i(7+2i)}{7^2-(2i)^2}\)

         \(=\frac{21+4i-35i-10i^2}{49-4(-1)}\)

         \(=\frac{21-31i+10}{53}\)

         \(=\frac{31-31i}{53}\)

         \(=\frac{31}{53}-\frac{31}{53}i\)

  Therefore, simplified form of the given expression will be \(\frac{31}{53}-\frac{31}{53}i\).

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Answer:

$202.5

Step-by-step explanation:

13.5 sqyd area

13.5 x 15= $202.5

Optimizing function describes the minimum or maximum output from the function.

The factory should make 3 David statues and 4.5 Liberty statues

The constraints and the objective function are given as:

\(\mathbf{18L + 27 D \le 162}\)

\(\mathbf{36L + 18 D\le 216}\)

\(\mathbf{7L + 7D \le 49}\)

\(\mathbf{Objective:\ Income = 63L+ 96D}\)

We start by plotting the graphs of the inequalities, where L is represented on the vertical axis, and D on the horizontal axis

From the graph, the only optimal point is: D = 3 and L = 4.5

Hence, the factory should make 3 David statues and 4.5 Liberty statues

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The quotient is 3x + 7, and the remainder is (28x + 9) / (x^2 - 3x).

A division is a process of splitting a specific amount into equal parts.

We have to find 3x³-2x²+7x+9 divided by x²-3x

3x³-2x²+7x+9 is the dividend and x²-3x is the divisor.

The steps to solve this are given below.

Step 1: Take the first digit of the dividend from the left. Check if this digit is greater than or equal to the divisor.

Step 2: Then divide it by the divisor and write the answer on top as the quotient.

Step 3: Subtract the result from the digit and write the difference below.

Step 4: Bring down the next digit of the dividend (if present).

Step 5: Repeat the same process.

Hence, the quotient is 3x + 7, and the remainder is (28x + 9) / (x^2 - 3x).

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The solution of the inequalities is x ≥ 2 or x > -6. The interval notation of the solution of the following inequality is (-6,  ∞).

In mathematics, a range can be conceived of as an interval. It describes a collection of real numbers that starts at one and ends at another. This interval could or might not have its beginning and ending points. Interval notation is a method of representing an interval technically. Interval notation, as its name indicates, is a way to mark or depict an interval that contains a subset of real numbers. A continuous interval of one subset of real numbers or the union of two subsets of real numbers can both be expressed using interval notation. Whether the endpoints are included (a closed interval) or omitted is also indicated by the notation (an open interval).

Given that,

x + 1 ≥ 3 or

4/3x > -8

The solution of the inequalities are:

x + 1 ≥ 3 or 4/3x > -8

x ≥ 2 or x > -6

The system thus consists of all the elements that are present in the system of the equations.

The interval notation of the solution of the following inequality is (-6,  ∞).

To graph the equation equate different values of x and obtain values of y and plot them on the graph.

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Answer:

Amount on 11% note = $106,666.67

Amount on 8% note = $43,333.33

Step-by-step explanation:

Let the amount for the ​short-term note at ​11% interest be x.

Thus, the amount for the ​short-term note at ​8% interest will be (150000 - x)

Now we are told that the total interest paid is $15,200.

Thus;

0.11x + 0.08(150000 - x) = 15200

0.11x + 12000 - 0.08x = 15200

Rearranging gives;

0.03x = 15200 - 12000

0.03x = 3200

x = 3200/0.03

x = $106666.67

Thus, amount for 8% note = $150000 - $106666.67 = $43,333.33

The total 'x' number of cups of trail mix  Orly uses c cups of raisins, she will make 10c / 3 cups of trail mix.

Orly uses 3 cups of raisins for every 10 cups of trail mix,

Which means that the ratio of cups of raisins to cups of trail mix is 3:10.

let us consider x be the number of cups of trail mix

and c be the number of cups of raisins.

We can set up a proportion to solve for the number of cups of trail mix,

⇒ 3/10 = c/x

To solve for x, we can cross-multiply and simplify,

⇒ 3x = 10c

⇒ x = 10c / 3

Therefore, if Orly uses c cups of raisins, she will make 10c / 3 cups of trail mix.

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Answer:

the cost per or per liter,one kilogram,one pound e.t c is called pricing in mathematics

Answer:

Definition: Price is the value that is put to a product or service and is the result of a complex set of calculations, research and understanding and risk taking ability. A pricing strategy takes into account segments, ability to pay, market conditions, competitor actions, trade margins and input costs, amongst others.

The distance between the tops of the buildings is 28.5 meters.

To find the distance between the top of the buildings, we can use the concept of similar triangles.

Let's denote the height of the shorter building as "a" (12 m) and the height of the taller building as "b" (19 m). The distance between the buildings can be denoted as "c" (18 m), and the distance between the top of the buildings as "x" (which we need to find).

We can set up a proportion based on the similar triangles formed by the buildings:

a/c = b/x

Substituting the known values:

12/18 = 19/x

To find "x," we can cross-multiply and solve for "x":

12x = 18 * 19

12x = 342

x = 342/12

x = 28.5 m

Therefore, the distance between the tops of the buildings is 28.5 meters.

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The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Answer:

1 ; 1.25 ; 0.25 ; - 0.75 ; - 1.25 ;- 0.5

Step-by-step explanation:

Given the sample observations : 15, 16, 12, 8, 6, 9

Zscore for each sample Observation :

Zscore = (x - mean) / standard deviation

(15 + 16 + 12 + 8 + 6 + 9) / 6 = 11

Mean value (m) = 11

Standard deviation (s) = 5

Sqrt[(x - m)^2 / (n - 1)]

[(15-11)^2 + (16-11)^2 + (12-11)^2 + (8-11)^2 + (6-11)^2 + (9-11)^2] / (6 - 1)

= 80/5 = 16

Sqrt(16) = 4

Zscore = (x - mean) / standard deviation

x = 15

Zscore = (15 - 11) / 4 = 1

x = 16

Zscore = (16 - 11) / 4 = 1.25

x = 12

Zscore = (12 - 11) / 4 = 0.25

x = 8

Zscore = (8 - 11) / 4 = - 0.75

x = 6

Zscore = (6 - 11) / 4 = - 1.25

x = 9

Zscore = (9 - 11) / 4 = - 0.5

We will have the following:

From this, we can see that the function has no solution in the real numbers and the solutions are:

Answer:

The salary of a paramedic can vary depending on several factors such as location, experience, and employer. According to the Bureau of Labor Statistics, the median annual wage for paramedics and EMTs was $36,650 in May 2020.

Assuming a constant annual income of $36,650 over 30 years, the estimated total income for a paramedic would be:

$36,650 x 30 = $1,099,500

However, it is important to note that this is just an estimate and does not take into account potential salary increases, promotions, or changes in the job market.

Answer:

it takes the bears 12 days to eat honey together.

Step-by-step explanation:

1/x+9+1/x+16=1/x

(solve this using cross multiplication)

= x^2 = 144

x=12

The number of days that it takes for both of the considered bears to eat a barrel of honey together is 12 days.

More people to do a task means less time it will take.

Less people to do a task means more time it will take.

Thus, they are inversely related.

We can define a constant as "Manpower" needed for doing that specific work.

Each worker has his/her own strength. That strength is applied per unit of time.

Let we define:

Manpower needed for a work = time taken for that work  × strength used for that work per unit of time

(we used multiplication as it represents linear use of strength to finish the task, so using that strength for a finite units of time means you stacked up your strengths that many times to finish that work)

Here, we have:

Assume that:

Then, we get:

Manpower needed for a work = time taken for that work  × strength used for that work per unit of time

\(M = x \times S\\M = y \times T\)

If bear A and bear B both do the work together, then their strenghts will add up.

That means, the combined strength would be S + T per day

The manpower the work needs is still M, therefore, the time needed is:

\(M = \text{Time needed} \times (S + T)\\\\\text{Time needed} = \dfrac{M}{S+T}\)

This is the time needed for both bears to do the work together.

Also, it is given that:

It takes a bear 9 more days to eat a barrel of honey alone than it takes the bear and a second bear to eat the barrel of honey together.

or

Time needed by bear A to do work = 9 + time needed by both bears to do the work

or

\(x = 9 + \dfrac{M}{S + T}\)

Also, it is given that:

It takes the first bear 7 fewer days to eat a barrel of honey alone than it takes the second bear to eat a barrel of honey alone.

or

Time taken by bear A to do the work = Time taken by bear B for that work - 7 days

or

\(x = y - 7\)

Thus, we got these equations:

\(M = S \times x\\M = T \times y\\\\x = \dfrac{M}{S + T} +9\\\\x = y - 7\)

call them first, second, third and fourth equation as per their ordering.

From the first and second equation, we get:

\(S = \dfrac{M}{x}\\\\T = \dfrac{M}{y}\)

Putting these values in the third equation, we get:

\(x = \dfrac{M}{M/x + M/y} + 9\\\\\\x = \dfrac{xy}{x+y} + 9\\\\(x-9)(x+y) = xy\\x^2 -9x -9y + xy = xy\\x^2 -9x = 9y\)

From the fourth equation, we know that:

\(x = y - 7\)

or \(y = x +7\)

Putting this value of y in the  equation \(x^2 -9x = 9y\), we get:
\(x^2 -9x = 9(x+7)\\x^2 -9x = 9x + 63\\x^2 -18x -63 =0\\\\x^2 -21x + 3x -63 = 0\\x(x-21) + 3(x - 21) = 0\\(x+3)(x-21) = 0\\(x+3) = 0, (x-21) = 0\\x = -3, x = 21\)

'x' represents time in number of days. So it cannot be negative.

Thus, the value of x obtained is 21.

Also, we need: Time needed for both the bears to do the work together.

This time is the value of \(\dfrac{M}{S+T}\), which is equal to \(x - 9\) days (from the third equation)

Thus, the time needed  for both the bears to do the work together = \(x-9 = 21-9 = 12 \; \rm days\)

Thus, the number of days that it takes for both of the considered bears to eat a barrel of honey together is 12 days.

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Answer:   5/8

Step-by-step explanation:

Answer:

The probability is 5/8

Step-by-step explanation:

First, we must add all the numbers together. 5 + 8 + 7 + 4 = 24. Now, let's add the white balls and green balls. 5 + 4 = 9. Therefore, the probability of choosing a white or green ball is 9/24 which also equals 3/8. To find out the probability of NOT choosing white or green, we must subtract 9 from 24. 24 - 9 = 15. So, the probability of choosing neither the white or green balls equals 15/24 which also equals 5/8.

Hope this helps!!

9514 1404 393

Answer:

  20, 31, 42, 53, 64, 75, 86, 97

Step-by-step explanation:

The difference of 18 means the difference of digits is 18/9 = 2. Since the number you seek is the larger number, the 10s digit will be 2 more than the 1s digit. Possible numbers are ...

  20, 31, 42, 53, 64, 75, 86, 97

_____

If t and o are the tens and ones digits respectively, the relation you seek is ...

  (10t +o) -(10o +t) = 18

  9(t -o) = 18

  t - o = 2 . . . . as above

Since both t and o must be single digits, the minimum will be t=2, o=0, and the maximum will be t=9, o=7.

Answer:

10a+b=10b+a-18

9a+9b = -18

9(a+b) = -18

a+b = 18/9

a + b =2

Step-by-step explanation:

Answer:so what is the question

Step-by-step explanation:

The present value of the annuity is approximately `7032.08. The correct answer is option (d) None of these.

To find the present value of an annuity, we can use the formula:

PV = PMT * (1 - (1 + r)^(-n)) / r

Where PV is the present value, PMT is the periodic payment, r is the interest rate per period, and n is the number of periods.

In this case, the periodic payment is `200, the interest rate is 5% (or 0.05) converted quarterly, and the number of periods is 10 years, which equals 40 quarters.

Plugging in these values into the formula, we get:

PV = 200 * (1 - (1 + 0.05)^(-40)) / 0.05

Simplifying the equation, we find:

PV ≈ 200 * (1 - 0.12198) / 0.05

PV ≈ 200 * 0.87802 / 0.05

PV ≈ 35160.4 / 0.05

PV ≈ 7032.08

Therefore, the present value of the annuity is approximately `7032.08.

None of the provided answer options (a), (b), or (c) match this result. The correct answer is (d) None of these.

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The class mark of the modal class is: 25

From the given histogram, the following Frequency Distribution is obtained:

Class Interval Mid point Frequency

625-675 650 3

676-726 701 5

727 - 777 752 7

778 - 828 803 8

829 - 879 854 6

880 - 930 905 2

931 - 981 956 0

982 - 1032 1007 1

b. To find the lower class limit of the first class:

First class: 625

c. The upper limit of the first class is:

First class: 676

The class mark of the modal class is:

The modal class is: 803

The class mark is upper limit + lower limit/2

Thus, 828-778/2

=> 50/2

The class mark of the modal class is: 25

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