arthur benjamin says that the current top of the pyramid of mathematics curriculum is

When there is no solution to a system called an inconsistent system of equations.

A linear equation in two variables is in the form ax + by + c = 0 where a, b, c ∈ R, a, and b ≠ 0. An inconsistent pair of linear equations is named a linear equation system with no solution. When we think of a system of linear equations, we are able to compare the coefficients of the equations and find whether it is a system of equations with no solution.

Assume the pair of linear equations in two variables, x and y.

a₁x + b₁y + c₁ = 0

a₂x + b₂y + c₂ = 0

Where a₁, b₁, c₁, a₂, b₂, c₂ stand real numbers.

Note that, a₁² + b₁² ≠ 0, a₂² + b₂² ≠ 0

If (a₁/a₂) = (b₁/b₂) ≠ (c₁/c₂), then there will be no solution.

--The given question is incorrect; the correct question is

"When there is no solution of a system called _____ system of equations."--

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The solutions to the nonlinear system of equations are (x₁, y₁) = (1 + √14 / 7, - 1 + 3√14 / 7) and (x₂, y₂) = (1 - √14 / 7, - 1 - 3√14 / 7).

In this problem we find the case of a system of two equations formed by a linear equation and a quadratic equation that can be solved by means of algebra properties. First, write the entire system of equations:

3 · x - y = 4

2 · x² + y² + x · y = 6

Second, clear y in the first equation:

y = 3 · x - 4

Third, substitute in the second equation:

2 · x² + (3 · x - 4)²  + x · (3 · x - 4) = 6

2 · x² + 9 · x² - 24 · x + 16 + 3 · x² - 4 · x = 6

14 · x² - 28 · x + 10 = 0

By quadratic formula:

x₁ = 1 + √14 / 7 or x₂ = 1 - √14 / 7

Fourth, find the possible values for y:

y₁ = 3 · x₁ - 4

y₁ = 3 · (1 + √14 / 7) - 4

y₁ = - 1 + 3√14 / 7

y₂ = 3 · x₂ - 4

y₂ = 3 · (1 - √14 / 7) - 4

y₂ = - 1 - 3√14 / 7

Fifth, write the solutions:

(x₁, y₁) = (1 + √14 / 7, - 1 + 3√14 / 7), (x₂, y₂) = (1 - √14 / 7, - 1 - 3√14 / 7)

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Answer: D.

x^2/8 + (y-2)^2/4 = 1

Step-by-step explanation:

Hope this helps.

The profit percent for the pencils is equal to 10%.

If C is the cost and P is the price, then the formula for the profit percent is:

p = 100%*(P - C)/C

Here we know that the selling price of 10 pencils is equal to the cost price of 11 pencils, then we can write the eqation:

10*P = 11*C

We can solve this for P.

P = (11/10)*C = 1.1*C

Replacing that in the given formula we will get:

p = 100%*(1.1*C - C)/C

p = 100%*(1.1 - 1)*C/C

P = 10%

The profit percent is 10%.

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[tex] = \frac{3}{5} - \frac{1}{10} \\ [/tex]

[tex] = \frac{3}{5} \times \frac{2}{2} - \frac{1}{10} \\ [/tex]

[tex] = \frac{6}{10} - \frac{1}{10} \\ [/tex]

[tex] = \frac{6 - 1}{10} \\ [/tex]

[tex] = \frac{5}{10} \\ [/tex]

Change in lowest term

answer [tex] = \frac{1}{2} \\ [/tex]

A system of equations is a set of two or more equations with two or more variables. The number of solutions to a system of equations depends on the number of equations and the number of variables.

It's important to note that the number of solutions is not determined by the number of equations, but by the relationship between the equations and the variables.

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By applying the distributive property to open the parentheses and then combining like terms, the answers above are gotten when each expressions are simplified.

To simplify an expression that as parentheses, we can apply the distributive property to get the answer.

Given the expression, 2(4 + 3(x - 5)), to get the answer in simple form. apply the distributive property to open the parentheses:

2(4 + 3x - 15)

Combine like terms:

2(3x - 11)

Apply the distributive property:

6x - 22

Also, follow the same process to simplify -3(9 - 2(k + 3) + 5k):

-3(9 - 2(k + 3) + 5k)

Apply the distributive property:

-3(9 - 2k - 6 + 5k)

Combine like terms:

-3(3k + 3)

Apply the distributive property:

-9k - 9

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The percentage of Venus's year to mercury's year is 39.1%

A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction - three for the price of one! To change the percentage to a fraction, just put the percentage number in the numerator and 100 in the denominator.

Venus year is 88 earth days and mercury is 225 earth days.

To find the percentage of venus's year to mercury's we divide the Venus's year by mercury and multiply by 100

Then , 88/225 ×100 = 39.1 %

Therefore Venus length of year is 39% of mercury's year.

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Quantitative variables provide numerical measures of individuals. the measures can be added or​ subtracted, and provide meaningful results.

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O₂ is two moles.

The molecular mass of an element is described as the sum of the masses of all the atoms present in the molecule.

Molecular mass is acquired by adding the atomic masses of all atoms with the number of atoms in the molecule.

O₂ has two atoms, so a mole of O₂ would have 1 mole of O₂ molecules, and when broken down into atoms, 2 moles of atoms.

Think about it like pairs of shoes. If you have 6 pairs of shoes, you have 12 pairs of shoes.

CO₂ has 3 atoms, 2N₂0 has 3 atoms, and there are already 2 moles, so that would be 6 moles of atoms; 2NaCl has 2 atoms but again, that 2 indicates that you'd have 4 moles of atoms, and H₂SO₄ has 7 atoms.

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Answer:

p = t - a - b

Step-by-step explanation:

T = a + p + b

- p + T = a + b

- p = - T + a + b

p = T - a - b

Answer:

The variable that belongs in the green box is T

(p=T-a-b)

Step-by-step explanation:

The total amount of fruit (T) minus the apples (a) and minus the bananas (b) would leave us with just the pears (p).

Writing this out mathematically, we have : T - a - b = p

Answer:21

Step-by-step explanation:

L'effectif total de l'équipage est donc de 10 personnes. L'âge moyen des équipiers de ce voilier est donc de 22 ans. le milieu de 20 et 22 est 21. La médiane des âges des équipiers est donc de 21.

The four parts of a quadrant are upper right, upper left, lower right, lower left.

The upper right quadrant of the coordinate plane, sometimes known as quadrant 1, has only positive coordinates (QI). Quadrant two is the upper left-fourth of the coordinate plane (QII). Quadrant three is at the bottom left (QIII). Located in the bottom right corner is quadrant number four (QIV). In quadrant I, the x- and y-coordinates are both positive. In quadrant II, the x-coordinate is negative while the y-coordinate is positive. In quadrant III, the x- and y-coordinates are positive. In quadrant IV, the x-coordinate is positive while the y-coordinate is negative. The area enclosed by the x and y axes is referred to as a quadrant in a coordinate system. The quadrants are formed by the 90-degree intersection of the x- and y-axes.

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Product rule example is f(x) = (3x - 2x2)(5 + 4x).

Following the Product rule we have

f ' (x) = (3x - 2x2)(0 + 4) + (5 + 4x) (3 - 4x)

       = 12x - 8x2 + 15 + 12x - 20x - 16x2

       = - 24x2 +4x + 15

Simply put, a product is the outcome of multiplying two functions. This rule, which was developed by Gottfried Leibniz, enables us to compute derivatives that we don't want (or are unable to) multiply quickly. In other words, by combining our understanding of the power rule with the sum and difference rule for derivatives, we can use the product rule to obtain the derivative of two differentiable functions that are being multiplied together.

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By evaluating the system of inequalities we will see that the point (0, 1) is not a solution.

Here we know that a student says that (0, 1) is a solution to the system of inequalities below:

y > x

y > 2x + 1

A point (x, y) is a solution of the system of eqations if, when we replace both values, both inequalties are true.

Replacing the values of the point (0, 1) we will get:

1 > 0

1 > 2*0 + 1  → 1 > 1

The second inequality is false, then the point (0, 1) is not a solution of the system.

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Answer:

Look at my image:

Left 4, down 2

M = A + |B| is the function's highest possible value. When sin or cos x equals 1, this maximum value is reached. m = A |B| is the function's lowest possible value. If either cos x or sin x is equal to 1, this minimum will be reached.

Example :

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Answer: 6

Step-by-step explanation:

When solving this problem, it is important to remember the rules for when we add a negative and subtract a negative. When we add a negative (+ -), we are essentially going to keep the sign attached to the number. In this case, we would still subtract. When subtracting a negative (- -), the signs cancel out, so will add the number instead. With that in mind, we can rewrite the equation and solve it as follows:

13 - 12 + 5

1 + 5

6

Hope this helps!

The graph of f(x) = 2x + 3 is a linear function and its y-intercept is y = 2x + 3.

Any function is referred to as linear if it represents a straight line on the coordinate plane. For instance, the linear function represented by the equation y = 3x – 2 looks like a straight line on a coordinate plane. Due to the fact that f(x) can substitute for y, this function can be written as f(x) = 3x - 2.

First find the slope of the line

y - y₁ = m(x - x₁)

0 - 3 = m(-1.5 - 0)

m = 2

From the graph, we can take any of the two points i.e.(0, 3) and put it in slope formula

y - y₁ = m(x - x₁)

So,

y - 3 = 2(x - 0)

y = 2x + 3 (y-intercept)

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Full question:

Graph each function determine which of the functions are linear. find the y-intercept of each function and the slope.

f(x) = 2x + 3

The dependent and independent variables ,C is 3 + 1(X) (X)

where, C is the price of gift-wrapping, X is the quantity of wrapped goods.

The number of goods that were wrapped is the independent variable for this function, and the price paid to wrap the presents is the dependent variable.

The number of goods that were wrapped is the independent variable for this function, and the price paid to wrap the presents is the dependent variable.

As opposed to the dependent variable, which is the function's output, the independent variable refers to the function's input. The function in this instance is written as follows:

C = 3 + 1(X) (X)

where,

C is the price of gift-wrapping.

X is the quantity of wrapped goods.

The complete question is,

An order will cost $3 plus $1 for each item that will be wrapped as a present. What are the dependent and independent variables?

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Answer:

(2,-5)

Step-by-step explanation:

find the coordinates which forms rectangle with othe given points

The coordinates of the fourth vertex of the rectangle are (2, -5).

A rectangle is defined as a four-sided shape with opposite sides that are equal in length and parallel to each other.

We have to determine the fourth vertex of the rectangle.

As we know that the opposite sides of a rectangle are equal.

The x-coordinate of the second vertex (2,4) is equal to the x-coordinate of the fourth vertex.

So, the x-coordinate of the fourth vertex = 2

The y-coordinate of the third vertex (-2,-5) is equal to the y-coordinate of the fourth vertex.

So, the y-coordinate of the fourth vertex = -5

Therefore, the coordinates of the fourth vertex of the rectangle are (2, -5).

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Answer: C). Yes, by HL

Step-by-step explanation:

The two lines in the system of equations will be parallel when the value of k is 15/4.

Let 2 equations of the line be,

ax+by=c1

dx+ey=c2

for lines to be parallel it is necessary that their slopes are equal

we can easily find the slopes of these equations by re-arranging them in the standard equation of a line i.e, y=mx+c

after rearranging we'll get the following equations,

y=(-a/b)x+c1/b

y=(-d/e)x+c2/e

and it should satisfy the given condition,

-a/b=-d/e≠c1/c2

as, if the ratio of the slope is the same as the constants it will become the same line. So, according to the given question

-3/2k must be equal to -2/5

k must be 15/4.

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The cosine of a right-angled triangle is defined by the trigonometric word “cos” meaning.The neighboring base-to-hypotenuse ratio is known as the cos function in a right-angled triangle.

It aids in determining the triangle's side lengths regardless of the provided angle. If the angle between the neighboring side and the hypotenuse of a right triangle is, we can write this using the cos function.

In a right triangle, the ratio between an angle's adjacent side and the hypotenuse is known as the cosine of the angle. It is written as:

Cos = Base of the right-angled triangle/ Hypotenuse of the right-angled triangle.

The cosine function takes up different values depending upon the value of

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The slope of y=-10x is -10.

The slope of a linear equation in the form of y = mx + b is represented by the coefficient of x, which is also known as the "slope" or "rate of change." In this case, the coefficient of x is -10.

This means that for every unit increase in x, there is a corresponding decrease of 10 units in y. In other words, the line represented by this equation has a negative slope, meaning it slopes downwards as it goes from left to right.

A linear equation is an equation that can be written in the form of y = mx + b, where m is the slope (or rate of change) and b is the y-intercept (the point where the line crosses the y-axis). Linear equations represent straight lines on a graph, and their slope and y-intercept can be used to determine the characteristics of the line, such as its direction and position.

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Answer:

s >= 18 and s <= -18

Step-by-step explanation:

-|s| <= -18

|s| >= 18

The value inside the module can be either positive or negative:

positive:

s >= 18

negative:

-s >= 18

s ≤ -18

Step 1: Find the important numbers. The roots of a quadratic inequality in standard form are the critical numbers. Therefore, solve by setting the function to zero.

Using inverse operations to isolate the x2 squared is the first step in solving quadratic equations by finding square roots. Step 1: Utilize inverse operations to isolate the x2 squared. Step 2: To isolate x, square root both sides.

The quadratic formula, factoring, using the square roots, and completing the square are the four methods for solving a quadratic equation. As a result, I want to go over a general discussion of the various approaches to solving quadratic equations at this point.

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