Find an ordered pair (x, y) that is a solution to the equation. -x+5y=8​

Answer:

Given :

The length of a rectangle is 4 cm more than its width

The area of the rectangle is 96 cm²

To Find :

Width of the rectangle.

Solution :

Let the length of the rectangle be x cm.

Let the breadth of the rectangle be y cm.

Case 1:

➣

➣  _____(1)

Case 2 :

We have the formula for area of the rectangle as follows :

Where,

l = length → x cm

b = breadth → y cm.

➣

➣

Substitute, x = 96/y in equation 1,

➣

➣

➣

➣

➣

Divide by minus sign,

➣

➣

➣

➣

➣

➣

➣

As per assumption, y = breadth of the rectangle.

•°• y = -12 is not acceptable.

Substitute, y = 8 in equation 1,

➣

➣

➣

➣

Step-by-step explanation:

Answer: 2

Hope this Helps!

The common difference of the given arithmetic sequence is 2.

The given arithmetic sequence is -17, -15, -13, .....

We need to find the common difference in the given arithmetic sequence.

A common difference is a difference between consecutive numbers in an arithmetic sequence. To find it, simply subtract the first term from the second term, or the second from the third, or so on...

Now, common difference=-15-(-17)=-15+17=2

-13-(-15)=-13+15=2

Therefore, the common difference of the given arithmetic sequence is 2.

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Answer:

x=8-5

Step-by-step explanation:

since we are not given the answer, we write it as x. so we write this expression as x is equal to 8-5

x=8-5

Answer:

Step-by-step explanation:

The number of views make a GP since increase 20% or 1.2 times per day

The first term is t = 1090 and common ratio is r = 1.2

Find the sum of the first 21 terms

Answer: 245278 views

Series built : 1090, 1308, 1569.6, 1883.52, 2260.224, 2712.2688,...

As every term increases by 1.2, This is a geometric progression sequence.

\(\sf Geometric \ Sequence: a_1 \ x \ \dfrac{r^n - 1}{r -1}\)

Identify Variable's:

a1 = 1090

r = second term ÷ first term = 1308 ÷ 1090 = 1.2

n = 21

Explanation:

\(\rightarrow \sf 1090 \ x \ \dfrac{(1.2)^{21} - 1}{(1.2) -1}\)

\(\rightarrow \sf 245277.9035\)

\(\rightarrow \sf 245278 \ \ \ \ \ (rounded \ to \ nearest \ integer)\)

I assume the limit you're asked to copmute is supposed to be

\(\displaystyle \lim_{x\to5} \frac{\sqrt{x+4}-3}{x-5}\)

Rationalize the numerator by multiplying it by its conjugate:

\(\dfrac{\sqrt{x+4}-3}{x-5} \times \dfrac{\sqrt{x+4}+3}{\sqrt{x+4}+3} = \dfrac{\left(\sqrt{x+4}\right)^2-3^2}{(x-5) \left(\sqrt{x+4}+3\right)} = \dfrac{x-5}{(x-5) \left(\sqrt{x+4}+3\right)}\)

Since x is approaching 5, we have x ≠ 5 and can cancel the factors of x - 5 to remove the discontinuity.

Then

\(\displaystyle \lim_{x\to5} \frac{\sqrt{x+4}-3}{x-5} = \lim_{x\to5} \frac1{\sqrt{x+4}+3} = \frac1{\sqrt9+3} = \boxed{\frac16}\)

because the simplified limand is continuous at x = 5.

Answer:

it is C. 1/6th

Step-by-step explanation:

The proof to sow that a differentiable function f(x) has two roots, its derivative f'(x) must have at least one root between those two roots is explained below.

Assume that f(x) has two roots, denoted as r1 and r2, such that f(r1) = 0 and f(r2) = 0.

Since f(x) is differentiable on the real line, it is also continuous on the real line. By the Intermediate Value Theorem, since f(x) is continuous and f(r1) = 0 and f(r2) = 0, there exists at least one point p between r1 and r2 such that f(p) = 0.

Thus, by Rolle's theorem, there exists at least one point d in the open interval (p, r2) such that f'(d) = 0.

Therefore, we have found two distinct points c and d such that f'(c) = f'(d) = 0, showing that the derivative f'(x) must have at least one root between r1 and r2.

Hence, we have proven that if a differentiable function f(x) has two roots, its derivative f'(x) must have at least one root between those two roots.

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Answer:

Step-by-step explanation:

To apply the distributive property to factor out the greatest common factor from the expression 12 + 20, we first need to find the greatest common factor (GCF) of 12 and 20. In this case, the GCF is 4.

Using the distributive property, we can express the expression as follows:

12 + 20 = 4 * 3 + 4 * 5

Now, we can factor out the common factor of 4:

= 4 * (3 + 5)

Simplifying the expression inside the parentheses:

= 4 * 8

Finally, performing the multiplication:

= 32

Therefore, after applying the distributive property and factoring out the greatest common factor of 4, the expression 12 + 20 simplifies to 32.

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According to the given match the following:

A. discriminant

B. standard form of a polynomial

C. complex solution

D. quadratic formula

The conventional form of a quadratic equation is written as ax2 + bx + c = 0. It's imperative to confirm that the equation is in this form before utilising the Quadratic Formula to solve it. If you don't, the formula may produce inaccurate results because you used the wrong numbers for a, b, or c.

In 1594, Simon Stevin discovered the quadratic formula that applies to all situations. The quadratic formula in its modern version was first presented in René Descartes' La Géométrie in 1637.

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Answer:

\(\huge\boxed{50}\)

Step-by-step explanation:

In order to solve for this number, we have to create a percentage proportion.

We know that 24 is 48% of something, so we can create a ratio like this:

\(\frac{24}{x}=\frac{48}{100}\)

We can then cross multiply and then divide to find the value of x.

\(24 \cdot 100 = 2400\)

\(2400 \div 48 = 50\)

So 24 is 48% of 50.

Hope this helped!

48 percentage of the number 50 is 24.

To find the number, you can set up an equation where 48% of that number is equal to 24.

Let's represent the unknown number as "x."

48% of x is written as 0.48x.

Setting up the equation:

0.48x = 24

To solve for x, divide both sides of the equation by 0.48:

x = 24/0.48

Evaluating this expression:

x = 50

Therefore, 48% of 50 is 24.

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Answer:

A. 0.824 x 3=2.472

Step-by-step explanation:

hope this helps

Answer:

The answer is 0.01, 0.1, 0.1, 0.11, 1 and 1.11

Step-by-step explanation:

Answer:

I hope this helps : ) !!!!

Step-by-step explanation:

0.01 , 0.1, 0.1, 0.11, 1, 1.11

Answer:

x<-3

Step-by-step explanation

2x+5<x-1/4

in x-1/4 you should remove 4 so you should multiply 4 from both side

8x+20<x-1

subtract x from both side

8x-x<-1-20

7x<-21

divided by 7 from both side

x<-3 answer is x<-3

In the parallelogram DEFG, value of x is,

⇒ x = - 31

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Given that;

The parallelogram DEFG is shown,

And, m ∠FHG = 58° , m ∠DHE=(−2x−4)°

Now, By figure we get;

⇒ m ∠FHG = m ∠DHE

⇒ 58° = (- 2x - 4)°

⇒ 58 = - 2x - 4

⇒ 58 + 4 = - 2x

⇒ 62 = - 2x

⇒ x = - 31

Thus, In the parallelogram DEFG, value of x is,

⇒ x = - 31

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The equation is solved and the distributive property is used

Given data ,

a)

If you use the distributive property to solve the equation first, either addition or subtraction will need to be done last, depending on the equation. This is so that you may isolate the variable on one side of the equation or combine like terms after applying the distributive principle, which usually requires addition or subtraction as the last step.

b)

Instead, if you divide first to answer the problem, you would need to apply multiplication as the last operation. This is because, in order to "undo" the division operation and find the variable, you would need to multiply by the reciprocal of the value by which you had divided to isolate the variable. As the inverse operation of division, multiplication would be utilized as the last step in the equation's solution.

Hence , the equations are solved

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The optimal solution using the two-phase simplex method for the given linear programming problem, we first need to convert it into standard form by introducing slack and surplus variables.

The problem can be rewritten as follows: Minimize Z = 2x1 + 3x2
subject to: 2x1 + 4x2 + s1 = 4
-x1 - 3x2 - s2 = -36
x1 + x2 = 10
x1, x2, s1, s2 ≥ 0

In the first phase of the simplex method, we introduce artificial variables and solve the problem to obtain an initial feasible solution. The initial tableau is constructed with the objective row as [0, 0, -M, -M, 0] and the constraint rows corresponding to the coefficients of the variables and artificial variables. Here, M represents a large positive number.

Next, we perform the simplex iterations to improve the solution. At each iteration, we pivot to select the entering and leaving variables until the optimal solution is reached. The iterations involve calculating the ratios of the right-hand side to the pivot column elements and selecting the minimum ratio as the pivot row.

In the second phase, we remove the artificial variables and proceed with the simplex iterations using the revised tableau. The iterations continue until the optimal solution is obtained, and the objective function value is minimized.

Unfortunately, I cannot generate the detailed steps and iterations of the two-phase simplex method in this text-based format. It requires a series of calculations and tabular representation. However, by following the steps of the two-phase simplex method, including initializing the tableau, performing simplex iterations, and removing the artificial variables in the second phase, you can find the optimal solution for the given problem.

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Answer: 17 yards

Step-by-step explanation:

well first you do $30 - $27.62 and you get $2.38 then you take the decimal out then divide it like this 238/14 you get 17 and that is how many yards you have !!! Hope that helps!!

The given vector field is not conservative.

Given: f(x, y) = (2xy y^(-2))i + (x^2-2xy^(-3))j. y > 0

We have to determine whether or not f is a conservative vector field. If it is, find a function f such that f = ∇f.

The vector field is called conservative if it is a gradient of a scalar function, called a potential function. The potential function of a conservative field is not unique; it is determined only up to a constant function.

Let's find the curl of vector field f, If curl f = 0, then f is conservative. Suppose curl f ≠ 0, then f is not conservative. We have,

curl f = (d/dx)i + (d/dy)j((x^2 - 2xy^(-3)) - (2xy y^(-2)))

= (d/dx)i + (d/dy)j(x^2 - 2xy^(-3) - 2xy^(-2))

= (d/dx)i + (d/dy)j(x^2 - 2xy^(-2)(y+1))

Now, The curl of the vector field is not zero, i.e., curl f ≠ 0. Therefore, the given vector field f is not conservative.

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The demand function for good X is Qx = m - 3Px + 2Py, where Qx is the quantity demanded of X, m is income, Px is the price of X, and Py is the price of a related good Y. The equation shows that the demand for X is inversely related to its price and directly related to the price of Y. Income, price of X, and price of Y collectively affect the overall demand for X.


The demand function for good X is given by Qx = m - 3Px + 2Py, where Qx represents the quantity demanded of good X, m is the income, Px is the price of good X, and Py is the price of a related good Y. In this equation, the income and prices are assumed to be positive.

To determine the demand for good X, we can analyze the equation. The coefficient -3 in front of Px indicates that the demand for good X is inversely related to its price. As the price of X increases, the quantity demanded of X decreases, assuming other factors remain constant. On the other hand, the coefficient 2 in front of Py indicates that the demand for good X is directly related to the price of the related good Y. If the price of Y increases, the quantity demanded of X also increases, assuming other factors remain constant.

Furthermore, the term (m - 3Px + 2Py) represents the overall effect of income, price of X, and price of Y on the quantity demanded of X. If income (m) increases, the quantity demanded of X increases. If the price of X (Px) increases, the quantity demanded of X decreases. If the price of Y (Py) increases, the quantity demanded of X increases.

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Solving the equation 4x + 7 = 9 will give value of x = 1/2

To solve we will use the equation

4x + 7 = 9

By subtracting 7 from both side we get

4x + 7 -7 = 9 -7

4x = 2

By diving 4 from both sides we get

4x/4 = 2/4

x = 1/2

To check we put the value of x in the equation we get

4(1/2) + 7 = 9

2 + 7  = 9

9 = 9

Hence the value of x is satisfying the equation

Therefore, the value of x is 1/2

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The amount you could save per month would be 25% of your discretionary money.

Discretionary income is the money you have left over after paying taxes and necessary cost-of-living expenses.

The formula for discretionary money is: Discretionary money = Realized income - Fixed expenses. Inputting data, we have: Discretionary money = $3,543.22 - Fixed expenses

Amount to be saved = 25% of discretionary money

Amount to be saved = 0.25 * (Realized income - Fixed expenses)

Therefore, the amount savable is calculated as 0.25 times the difference between your realized income and fixed expenses.

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Answer:

The answer to your question is 22.0 rounded to the nearest tenth.

Step-by-step explanation:

Area=LW, L=W in square so 479=L^2, square root both sides, L=W=21.88=22 rounded

I hope this helps and have a wonderful day!

Answer:

22.0

Step-by-step explanation:

Took the test but best of luck

Answer:

An irrational number is any number than cannot be written in the form p/q, where q is 0 Ex. pi, non-perfect squares

Step-by-step explanation:

In this case D. isn't rational but is irrational

a. U'(ct) = β(1 + r)U'(ct+1). This equation is known as the Euler equation, which represents the intertemporal marginal rate of substitution between consumption at time t and consumption at time t+1.

b. U'(c1) = β(1 + r)^2U'(c3). This relationship shows that the marginal utility of consumption at time 1 is equal to the discounted marginal utility of consumption at time 3.

c. C0 = ∑t=0[infinity]​(β(1 + r))^tct. This equation represents the sum of the discounted values of consumption at each period, where the discount factor β(1 + r) accounts for the diminishing value of future consumption.

d.  U0 = ∑t=0[infinity]​(β(1 + r))^tln(ct). This equation represents the sum of the discounted values of utility at each period, where the discount factor β(1 + r) reflects the time preference and the logarithmic utility function captures the agent's preference for consumption.

Y0 = y0 + (1 + γ)y1 + (1 + γ)^2y2 + ..., where γ represents the growth rate of income.

a. The optimization problem of the representative agent involves maximizing the present discounted value of utility subject to the period-by-period budget constraint. The Euler equation is derived as follows:

At each period t, the agent maximizes the utility function U(ct) = ln(ct) subject to the budget constraint ct = (1 + r)wt + yt, where wt is the agent's wealth at time t. Taking the derivative of U(ct) with respect to ct and applying the chain rule, we obtain: U'(ct) = β(1 + r)U'(ct+1). This equation is known as the Euler equation, which represents the intertemporal marginal rate of substitution between consumption at time t and consumption at time t+1.

b. The Euler equation between time 1 and time 3 can be written as U'(c1) = β(1 + r)U'(c2), where c1 and c2 represent consumption at time 1 and time 2, respectively.

Similarly, we can write the Euler equation between time 2 and time 3 as U'(c2) = β(1 + r)U'(c3). Combining these two equations, we fin

d U'(c1) = β(1 + r)^2U'(c3). This relationship shows that the marginal utility of consumption at time 1 is equal to the discounted marginal utility of consumption at time 3.

c. The present discounted value of optimal lifetime consumption can be written as C0 = ∑t=0[infinity]​(β(1 + r))^tct. This equation represents the sum of the discounted values of consumption at each period, where the discount factor β(1 + r) accounts for the diminishing value of future consumption.

d. The present discounted value of optimal lifetime utility can be written as U0 = ∑t=0[infinity]​(β(1 + r))^tln(ct).

This equation represents the sum of the discounted values of utility at each period, where the discount factor β(1 + r) reflects the time preference and the logarithmic utility function captures the agent's preference for consumption.

e. The present discounted value of lifetime income, denoted as Y0, can be expressed as Y0 = y0 + (1 + γ)y1 + (1 + γ)^2y2 + ..., where γ represents the growth rate of income. The income in each period is multiplied by (1 + γ) to account for the increasing income over time.

This assumption of income growth allows for a more realistic representation of the agent's economic environment, where income tends to increase over time due to factors such as productivity growth or wage increases.

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Solving a linear equation we can see that the correct option is C, she must sell at least 32 pairs.

We know that she earns a fixed fee of $185 plus a comission of $10 for each pair of shoes that she sells.

So, if she sells x pairs of shoes, then the amount that she earns is:

f(x) = 185 + x*10

And we know that she wants to make a minimum of $500, then we can solve the linear equation:

500 = 185 + 10x

500 - 185 = 10x

315 = 10x

315/10 = x

31.5 = x

So she must sell 32 pairs of shoes or more, thus, the correct option is C.

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The area A(x) of a square tile is given by the formula A(x) = x^2, where x represents the length of a side of the square.

This function rule tells us that the area of a square tile is equal to the square of its side length.
To find A(8), we simply substitute x = 8 into the function rule. A(8) = 8^2 = 64. This means that the area of a square tile with a side length of 8 units is 64 square units. In interpretation, A(8) means that if we have a square tile with a side length of 8 units, its area would be 64 square units.

This information could be useful, for example, if we need to calculate the number of tiles needed to cover a given area. We can simply divide the total area by the area of one tile (in this case, 64) to get the number of tiles needed.

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- 17x = -37 - 7y

10x = 16 + 7y

then now add both equations , to eliminate y

(-17x + 10x) = -37 + 16 + (-7y+7y)

then

-7x = -21 + 0

. x = -21/-7

. x = 3

Now find y = ?

y = (10x - 16)/7

. = (10•3 - 16)/7

. = (30-16)/7

. = 14/7 = 2

Then, answers are

x= 3

y= 2

Answer:

4c=12

Step-by-step explanation:

In the chart, it shows 12 and 4 c. Since they equal the same thing, the equation is 4c=12.

Answer:

x=7/5

Step-by-step explanation:

Answer:

100x = 140 or 100x -140 = 0

Step-by-step explanation:

(80 + 20) = 100 - they both have x so they can be added together

you can either subtract 10 from 150 or 150 from ten to get 140 or -140 depending if you want the equation to be on the left side or spilt

Answer:

Find the exact value using trigonometric identities.

Exact Form: x=34

Decimal Form: x=0.75

Step-by-step explanation:

The value of x is 3.

Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols.

Given:

\(9^{-1/2} = 27^{1/4}\)÷\(3^{x +1}\)

\([3^{2}]^{{-1/2}} = [(3)^{4}]^{1/4}\) ÷\(3^{x +1}\)

\(3^{-1}\) = 3 ÷\(3^{x +1}\)

\(3^{-1}\)= \(\frac{3}{3^{x+1}}\)

\(3^{-1}= 3^{1-x+1}\)

\(3^{-1}= 3^{2-x}\)

On comparing we get,

-1=2-x

x= 3

Hence, the value of x is 3.

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