Use the graph to write a linear function that relates y to x

For k=6 the system of equations have a no unique solution

So,we have given 2 equations from the question:

kx+2y=5…(1)
3x+y=1 …(2)

First multiply the second equation by 2
We get:
6x+2y=2

Now subtracting (2) from (1), we get:

kx+2y−6x−2y=5−2
(k−6)x=3
x= 3/K-6

​So, here if we put any value in k, then we will get a corresponding value of x but if we put k=6, then we will not get any value of x.

So, for k=6 this equation has no unique solution.

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Answer:

Step-by-step explanation:  Hello!

I don't remember all of the postulates to these, but I hope this will help you! Vertical angles are congruent, so both angles SRT and PRQ are congruent.  This also means that line segments PQ and ST are congruent.  You also know that angles Q and S are congruent which is given.  By the ASA Theorem, when two angles and a side are congruent, then the triangles are congruent.

Finn would run 18 miles after 6 track practices.

Generally, A unit rate is a ratio of two measurements with a denominator of 1. To find the number of miles Finn would run after 6 track practices, we can use the unit rate of miles per practice to multiply by the number of practices.

Unit rate: 6 miles / 2 practices = 3 miles per practice

To find the total number of miles Finn would run after 6 practices, we can multiply the unit rate of 3 miles per practice by the number of practices, 6.

Total miles: 3 miles/practice * 6 practices = 18 miles

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Solving a system of 3 equations with 3 variables using a scientific calculator can be done by using matrix operations. The method is called Gaussian elimination or Gauss-Jordan elimination. Here is an overview of the steps you can follow:

Write the system of equations in matrix form. For example, if the equations are

a₁x + b₁y + c₁z = d₁

a₂x + b₂y + c₂z = d₂

a₃x + b₃y + c₃z = d₃

the matrix form would be:

| a₁ b₁ c₁ | |x| |d₁|

| a₂ b₂ c₂ | |y| = |d₂|

| a₃ b₃ c₃ | |z| = |d₃|

Enter the matrix of coefficients (on the left side of the equations) into your calculator, usually by using the matrix function or the linear equation solver function.

Enter the constant terms of the equations (on the right side of the equations) into your calculator as a column matrix or vector.

Perform row operations to make the matrix of coefficients into an upper-triangular matrix.

Solve the system by back-substitution using the values of x, y, z in the matrix of coefficients and the matrix of constant terms.

The calculator will give you the solution of the system in terms of x, y, z.

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The quadratic equation that matches the graph is f(x) = (x - 2)² + 4.

The correct option is B.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

The graph shows the function.

The graph is given in the attached image.

In the interval, [x = 0, x = 2],

we have a line that passes through the points (0, 8) and (2, 4).

That means, the points satisfies then function.

Let the f(x) = (x - 2)² + 4.

That means,

f(0) = 8

And f(2) = 4

Therefore, the quadratic function is f(x) = (x - 2)² + 4.

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Answer:

i tried to solve it and the solution is : x=3/2 or 1.5 so ig its neither

Not quite, but really close. All you need to do is switch -4/3 and -0.2, because -4/3 is about -1.3, and negative numbers get greater as they get closer to 0

The multiplication formula in maths is given as follows Multiplier × Multiplicand = Product.

The product meaning in maths is a number you get to by multiplying two or more other numbers. For example, if you multiply 3 and 5 together, you get a product of 15.

Multiplication is an important part of maths. Learning and understanding how to find the product in maths is an important basis for developing their skills in maths.

You can help children learn the maths definition of the product by reminding them that it is produced when two or more numbers are multiplied together.

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The figure in which two rays intersect at a single location known as the vertex is referred to as an angle. The symbol "" is used to indicate an angle.

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The area of a 45-45-90 triangle, with a hypotenuse of 8mm in length is [tex]4mm^{2}[/tex]

This is a 45-45-90 triangle the base of the triangle and the height of the triangle are equal. So we simply need to find the values of the two sides and plug them into the formula.

[tex]a^{2} +b^{2} = 8^{2}[/tex]

[tex]a=b[/tex]

[tex]a^{4} =16[/tex]

[tex]a^{2} =8[/tex]

[tex]a=\sqrt{8}[/tex]

[tex]Area = 1/2 *base.height[/tex]

[tex]area=1/2*\sqrt{8} .\sqrt{8}[/tex]

[tex]Area= 4mm^{2}[/tex]

A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.

In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.

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Complete Question:

What is the area of a 45-45-90 triangle, with a hypotenuse of 8mm in length?

The inverse of a logarithmic function is an

The inverse of the inverse logarithmic function is simply the exponential function.

The inverse logarithmic function (also known as the logarithm or log) takes as input a number x and returns the power to which a fixed number (usually 10 or e) must be raised to produce x. The inverse of the logarithmic function is the exponential function, which takes as input a power and returns the number that would result from raising a fixed number to that power. In other words, if log_b(x) = y, then b^y = x, where b is the fixed number.

In other words, the exponential function is the inverse of the inverse logarithmic function.

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A circle's arc length can be determined from its radius and central angle using the formula Length of an Arc = r, where is in radians.

Length of an Arc = r, where is in radians, is a formula that may be used to calculate the arc length of a circle given its radius and central angle. A circle's length is equal to (r/180)r, where r is the radius and is the angle. The length of the arc on a circle of radius r intercepted by a central angle is S = r.

Multiply the radius (6 in) by the central angle's measurement in radians to determine the length of the arc. Remember that the angle must be expressed in radians in order to employ the calculation s = r.

Assuming that is measured in radians, the formula for the length s of the arc that is intercepted on a circle with radius r by a central angle is: s = r.

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The percentage increase in the price of a gallon of gas is 80.84 %.

Given,

Jason bought a gallon of gas in 1992 = $1.20

He bought a gallon of gas yesterday = $2.17

Using the formula for the percentage increase in the price,

= ( New Price - Old Price) / Old Price × 100

= ( 2.17 - 1.20) / 1.20 × 100

= 80.84%

Therefore, the percentage increase in the price of a gallon of gas from 1992 to yesterday is 80.84 %.

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Answer: What you chose was correct :>

Answer:

  see attached

Step-by-step explanation:

You want the given diagram annotated with an arrow to show the direction of acceleration.

Acceleration is a result of a net force on an object. It is in the direction of that net force.

Here, the forces to the left and right are equal and opposite, so have a sum of zero.

The forces up and down are opposite, but unequal. The downward force is larger, so the direction of the net force is downward. (+5 +(-10) = -5)

The object will be accelerated downward in the direction of the 10 N force.

When you substitute a value into an equation and the result is a true statement it means solution to an equation is a value of a variable.

The substitution method is a quick and easy way to algebraically solve a set of linear equations and determine the variables' solutions. According to what the name implies, this method entails determining the value of the x-variable in terms of the y-variable from the first equation and then substituting or replacing the value of the x-variable in the second equation.

We can solve and determine the value of the y-variable in this method. Finally, we may use any of the above equations to obtain x by substituting the value of y. This procedure can also be switched around so that we first solve for x before solving for y.

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The amount of money left for the 5 other employees is 0.75x dollars.

From the question, we have the following parameters that can be used in our computation:

Employees = 5

Salary = 25%

If the manager's salary is 25% of the company's salary budget, and the company's salary budget is x dollars, we can represent the manager's salary as 0.25x.

To find the amount of money left for the 5 other employees, we need to subtract the manager's salary from the total salary budget.

We can represent this using the following expression: x - 0.25x

Simplifying this further, we get

x(1-0.25) = 0.75x dollars

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Answer:

Step-by-step explanation:

cp of first tricycle=100/(P%+100)*sp

cp=100/10+100*2200

=100/110*2200

CP=Rs 2000

Cp of second tricycle=100/(100-L%)*SP

=100/100-12*2200

100/88*2200

CP=2500

Thanks for the question

The probability of each individual dying in the pair explains the higher variability in the total outcome of the roll of each pair because there are more possible combinations of outcomes.

The concepts of permutations and combinations apply to this example by showing the different ways the dice can be rolled to achieve a specific total outcome. Each die in a pair of dice has a probability of 1/6 of rolling any number between 1 and 6.

When rolling two dice, there are 36 different possible outcomes (6x6) and each one has a different probability of happening. This is where the concepts of permutations and combinations apply, as each possible combination of dice rolls will result in a different total outcome.

The notion of degree of freedom can be used to illustrate the accumulating results of a set of dice rolls by showing how the total outcome is affected by the roll of each individual die.

For example, if the first die rolls a 4, the second die has 5 degrees of freedom as it can roll any number between 1 and 6 (except for 4) and still achieve a total outcome of 9. As the number of dice being rolled increases, the degree of freedom decreases, making the probability of rolling a specific total outcome less likely.

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a) Graham's employer contributes $561.60 per year towards his coverage.

b) Claudia contributes 28.2% towards the total coverage cost.

What is percentage?

Percentage is a way of expressing a number as a fraction of 100. It is typically represented by the symbol "%", and is often used to express a change or a part of a whole.

a) Graham makes $62,800 per year, which is less than $65,000, so he pays $52 per month for individual coverage. His yearly contribution is 10% of the total cost, so his employer contributes 90% of the total cost. To find the total cost, we can multiply the monthly cost by 12: $52/month * 12 months/year = $624/year. So Graham's employer contributes $624 * 90% = $561.60 per year towards his coverage.

b) Claudia's annual salary is $75,400, which is at least $65,000, so she pays $122 per month for family coverage. Her employer contributes $1,052 per month towards her total coverage cost. To find the total cost, we can multiply the monthly cost by 12: $122/month * 12 months/year = $1,464/year. To find the percentage Claudia contributes, we divide her contribution by the total cost and multiply by 100: $1,464-$1,052 / $1,464 * 100 = 28.2%. So Claudia contributes 28.2% towards the total coverage cost.

Hence,

a) Graham's employer contributes $561.60 per year towards his coverage.

b) Claudia contributes 28.2% towards the total coverage cost.

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Answer:

Theoretical.

Step-by-step explanation:

120/400 = 30/100 = 3/10

She is correct.

It is the theoretical probability since it is based on calculations alone.

The y-intercept of line 2x - 3y = -6 is (0,2).

The y-intercept of a line is the point where the line intersects the y-axis. It can be found by setting x to 0 and solving for y. In this case, we have the equation 2x - 3y = -6.

By setting x to 0, we get:

2(0) - 3y = -6

Which simplifies to: -3y = -6

And finally, by dividing both sides by -3, we get the value of y: y = 2

It means the line will intersect the y-axis at point (0,2) which means

when x =0 the line will be at y = 2.

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The concept is Inverse function. The answer is, the inverse of a convex differentiable function with a non-zero derivative is strictly concave.

In mathematics, an inverse function is a function used to "cancel" another function.  In other words, if f(x) yields y, then setting y to be the inverse of f yields x.

A convex function is a continuous function whose value at the middle of each interval of its domain does not exceed the arithmetic mean of its values ​​at the ends of the interval.

The convex function has an increasing first derivative, making it appear curved upwards. Conversely, the concave function has a decreasing first derivative, so it curves down.

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The number 256 can be written as products of its prime numbers in index notation as 256 = 2⁸

Prime factorization is a way of expressing a number as a product of its prime factors. A prime number is a number that has exactly two factors, which includes 1 and the number.

The first five prime numbers are 2, 3, 5, and 7. We shall divide the number 256 with prime numbers that are factors beginning with 2;

256/2 = 128

128/2 = 64

64/2 = 32

32/2 = 16

16/2 = 8

8/2 = 4

4/2 = 2

2/2 =1

so; 256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

Therefore, the number 256 expressed as product of its prime factors in index notation is written as 256 = 2⁸

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Two of the ways that we can factor the cubes are the addition of cubes and subtraction of the cubes.

The steps below can be used to determine an expression's GCF.

If there are any variables, list them separately and write each term as the prime factorization of the coefficient or constant. As an illustration, write x. y. as x. y. and x. as x. x. The elements that each phrase has in common should be noted. Add together those typical elements.

The set containing all items found in both sets A and B, or both sets A and B taken together, is referred to as the union of two sets A and B. With the symbol "," you can represent the union of the set.

First, we change the equation's form to read as ax2+bx+c=0, where a, b, and c are the coefficients. As a result, we enter these coefficients into the formula: (-b(b2-4ac))/(2a).

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An example of equivalence class is the equivalence relation Congruence Modulo n. Here, two integers say "a" and "b" are equivalent if they results same remainder after dividing by n.

Equivalence classes are constructed such that elements a and b belong to the same equivalence class if and only if a and b are equivalent. Formally, the set S and the equivalence relation ~ on S, the equivalence class of the element a in S is the set [a] = { x Ε X | and ~ x} = S / ~. Example 1 : If X is the set of all pens and ~ is the "has the same color as" equivalence relation, then one particular equivalence class consists of all black pens.

Example 2: A well-known example is itthe equivalence relation Congruence Modulo n . Two integers "a" and "b" are equivalent if they have the same remainder after division by n. For example, consider the congruence relation modulo 2 on the set of integers,

R ≈ { (a,b) | a ≡ b mod 2}

The possible remainders for n = 2 are 0 and 1. An equivalence class consists of those integers that have the same remainder. Hence, there are 4 equivalence classes in this example:

[0] = { ...........,-8,-6,-4,-2,0,2,4,6,8,......}

[1] = {..........-7, -5, -3,1,3,5,7,........}

Similarly, one can show that the relation of congruence modulo n has (n -1) equivalence classes, [0], [1], ...., [ n - 1].

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Answer: A 4 91/100

Step-by-step explanation:  its 491/100  because the 100  is 1 and 4 is the number 4 and 91/100 is .91

The number of gallons of water that Michael's pool holds for the given condition will be 18,900 gallons.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

If Michael's pool holds 21,000 gallons of water and it is 90 percent full.

The number of gallons of water that Michael's pool holds will be given as,

⇒ 90% of 21,000

⇒ 0.90 x 21,000

⇒ 18,900 gallons

The number of gallons of water that Michael's pool holds for the given condition will be 18,900 gallons.

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The present value of the bond is $3,345.90. This is calculated by taking the future value of the bond ($4,500) and dividing it by the present value factor for 4.25% for 10 years (1.427).

PV = FV / (1 + r)n

PV = $4,500 / (1 + 0.0425)10

PV = $4,500 / 1.427

PV = $3,345.90

The present value of an asset is the value of the asset today, taking into account the time value of money and the interest rate of the investment. In this example, the Exxon Corporation bond will pay $4,500 ten years from now, and the going interest rate on safe 10-year bonds is 4.25%. To calculate the present value of the bond today, we use the present value formula, which is the future value of the bond divided by the present value factor for the given interest rate and number of years. In this case, the present value factor is 1.427, and the present value of the bond is $3,345.90. This means that the bond is worth $3,345.90 today, taking into account the time value of money and the given interest rate.

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A  partial sum is basically a addition of series and adding number upto a partial value.

For example,

635 + 312 is calculated by adding 600 + 300 = 900, 30 + 10 = 40 and 5 + 2 = 7.

These partial sums are then added as 900 + 40 + 7 = 947

A function may get close to two distinct limits. There are two scenarios: one in which the variable approaches its limit by values larger than the limit, and the other by values smaller than the limit.

A partial sum is the total of a limited number of the series' terms. To see how the infinite sum behaves, we can examine a collection of these sums. The index of the final term in the sum is used to denote each of these partial sums.

When a group of numbers, known as addends or summands, are added together in mathematics, the outcome is their sum or total.

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