you want to sell 1/lb jars of mixed peanuts and cashews for five dollars . you paid three dollars per pound for peanuts and six dollars per pound of cashews . you plan to combine four parts peanuts and one part cashews to make your mix . you have spent $70 on materials to get started . how many jars must you sell to break even ?

By using the Pythagorean identities we can find the sine of an acute angle.

What is angle ?

An angle is a measure of rotation about a point or a line. It is a geometric concept that describes the amount of rotation between two lines or planes. Angles are typically measured in degrees or radians.

What is acute angle ?

An acute angle is an angle that measures less than 90 degrees. It is an angle that is smaller than a right angle. Acute angles are commonly found in triangles and other geometric shapes. They are represented by the symbol "α" (alpha) in trigonometry.

What is Pythagorean identities?

The Pythagorean identities are a set of trigonometric identities that are based on the Pythagorean theorem. They relate the sine, cosine, and tangent of an angle to the ratios of the sides of a right triangle. The Pythagorean identities can be used to find the sine of an acute angle by relating it to the ratio of the opposite side to the hypotenuse of a right triangle.

Specifically, the identity [tex]sin^2(x) + cos^2(x) = 1[/tex] can be used to find the sine of an acute angle x by first finding the cosine of x and then subtracting it from 1.

The equation becomes [tex]sin(x) = \sqrt{1 - cos^2(x)}[/tex].

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No, a polynomial is not always a binomial. A binomial is a polynomial of two terms, while a polynomial can have any number of terms.

Since polynomials can have more than two terms, they are not all binomials.

For instance

A polynomial but not a binomial is 2x2 + 3x + 4.

A polynomial and a binomial, 2x2 + 6

The assertion thus is false.

For some whole integer n, a polynomial is the sum of n monomials. As a result, polynomials are a general term for monomials, binomials, and trinomials.

You can have as many terms as you like in a polynomial. The exponents of all a monomial's variables are added to determine its degree.

The binomial theorem or, alternatively, Pascal's triangle can be used to extend a binomial raised to the nth power, denoted as (x + y)n.

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The longest side c of an acute triangle is the one opposite the largest angle γ. To determine its length, use the law of cosines: c = √(a²+ b² - 2ab cos(γ)), where a and b are the two shorter sides of the triangle.

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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no idea either

but we are learning the same thing

Answer:

[tex]-2+2\sqrt{7} and -2-2\sqrt{7}[/tex]

Step-by-step explanation:

To find where x intersects x-axis, plug in y=0 and solve for x.

[tex](x+2)^2+(0-3)^2=37[/tex]

[tex](x+2)^2+(-3)^2=37[/tex]

[tex](x+2)^2+9=37[/tex]

[tex](x+2)^2=37-9[/tex]

[tex](x+2)^2=28[/tex]

[tex]x+2=\sqrt{28}[/tex]

x+2=±2[tex]\sqrt{7}[/tex] Simplify square root

x=-2±2[tex]\sqrt{7}[/tex]

A nameless polynomial p(x), or simply "some polynomial p whose variable is x," serves as the foundation of the Remainder Theorem. The Theorem then talks about dividing that polynomial by some linear factor, x a, where an is just a number.

Examples :

Factor 4x² - x - 3 :  (4x + 3 ) (x - 1)

4x² - x - 3

=(4x² + 3x) + (-4x -3)

Factor out x from 4x² + 3x : x(4x + 3 )

Factor Out -1 from -4x -3: -(4x + 3)

=x(4x + 3) - (4x +3)

Factor out common team (4x + 3): (4x + 3) (x - 1)

=(4x + 3) (x - 1).

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If the lines are parallel, then the pair of equations representing parallel lines have no solution.

Parallel lines are straight lines which, existing in the same plane and being produced indefinitely in both directions, do not meet one another in either direction. Another term involved is the "plane". We keep the Plane as an undefined term. The only thing is that we can represent it intuitively or explain it with the help of a physical model.

As the parallel lines never intersect at any point, hence the pair of equations of parallel lines will not have any solution, i.e. they have no solution.

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These concepts can be used in many buildings like skyscrapers because they may fall over if they are not parallel to the ground. In the case of a cabinet, you need the sides to be perpendicular to each other and to the top and bottom. Otherwise, the door may not open and close accurately.

The characteristics of parallel lines are;

1. The shortest distance between the lines that are parallel is the same at all points along the lines.

2. The lines are on the same plane.

3. As the plane is extended indefinitely, the lines do not intersect.

The characteristics of perpendicular lines are;

1. Perpendicular lines are lines that intersect at a point.

2. Where two lines are perpendicular, the slope of one line is the negative reciprocal of the other, such that the product of the slopes of two lines that are perpendicular is -1.

3. The angle formed at the intersection of perpendicular lines is 90°.

4. A horizontal and a vertical line on the same plane are perpendicular to each other.

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The value of input is -8 when the output is -10.

A function is a mathematical relation between a set of inputs (also called independent variables) and a set of outputs (also called dependent variables). It assigns a unique output to each input in its domain. Functions are often represented by mathematical expressions, graphs, or tables. In computer science, functions are used to organize and structure code by breaking it down into smaller, more manageable tasks.

The function describes that the value of function is  6 more than 2 times tha input

so f(x)  = 2x + 6

so this is required function according to the description.

given that output of the function is -10

so f(x) = -10

=> 2x+6 = -10

=> 2x = -16

=> x = -16/2

=> x = -8

so the value of input is -8 for which the output is 10.

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Answer:

KS24 add K27ab4 6b3r1b olps

i have the awnser in the box

Work Shown:

11 = 10+1

27*11 = 27*(10+1) = 27*10 + 27*1 = 270+27 = 297

I used the distribution rule a(b+c) = ab+ac

The 11 was broken up into 10+1 since 10 is easy to work with.

If cosine of x degrees equals three-fifths and angle L measures x degrees, LN measures 20 units, and LM measures 3b units. The value of b is 11.

Value of angle b can be determine by dividing the LN measures by the LM measures.

Given data:

LN measures 20 units

LM measures 3b units

Using this formula to find the value of b

Cosine(x°) = LN/NM

3/5 = 20/(3b)

b = 20×5/ (3×3)

b = 100 /9

b  = 11

Therefore we can conclude that the value of b is 11.

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Answer:

b = 4

Step-by-step explanation:

cos x = 3/5 = 3b/20

20/5 = 4

b/4 = 3

4 x 3 = 12

12/20 = 3/5

So, b = 4

Difference in the measures of two angles is 48°.

Linear pair of angles are the pair of angles formed when two lines are intersected at a point.

Sum of the measures of angles of linear pair is supplementary or 180°.

Given that ∠1 and ∠2 form a linear pair.

m∠1 + m∠2 = 180°

Also, m∠1 is eighteen less than twice m∠2.

m∠1 = (2 × m∠2) - 18

Substituting second equation in first equation,

(2 × m∠2) - 18 + m∠2 = 180°

3 × m∠2 - 18 = 180

3 × m∠2 = 198

m∠2 = 198 / 3

m∠2 = 66°

m∠1 = (2 × 66) - 18 = 114°

Difference of the angles = m∠1 - m∠2 = 114° - 66° = 48°

Hence there is 48° difference in the measures of angles.

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The system of equations does not have a solution.

Generally, These are three equations with three variables (a, b, and c). To find the solution, you can use a method such as substitution, elimination, or graphing.

This is a system of linear equations. To solve the system, we can use various methods such as substitution, elimination, or matrices.

One way to solve this system is by using the elimination method. We can start by adding the first and second equations, which will cancel out the b and -2c terms, leaving us with 3a = 6. Therefore, a = 2.

Next, we can substitute this value of a into the other equations and solve for b and c.

For example, using the first equation we can get:

a + b - 2c = 5

2 + b - 2c = 5

b - 2c = 3

Thus, b = 3 + 2c

Using the last equation we can get:

2a - b + 2c = 3

2(2) - (3 + 2c) + 2c = 3

4 - 3 - 2c + 2c = 3

1 = 3

This is a contradiction, so the system of equations does not have a solution.

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The relationship is proportional because the equation graphs to a straight line that goes through the origin.

The y-value at x = 1 is 1/5, and this value serves as the proportionality constant.

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(a). The values of x for which f(x) = 8, are x = (-1 + √17) / 2 and x = (-1 - √17) / 2.

(b). The equation has no real roots, and f(x) never equals 5.

(c). The equation has no real roots, and f(x) never equals -5.

(d). The graph will confirm that there are two x-intercepts corresponding to the two solutions found.

What is algebraic value?

A general rule is that the algebraic expression should take any of the following forms: addition, subtraction, multiplication, and division. Bring the variable to the left side and the other values to the right side in order to find the value of x.

a.

To find the values of x for which f(x) = 8,

we need to solve the equation x² +10x +32 / x+5 = 8.

We can start by multiplying both sides of the equation by (x+5) to get rid of the fraction:

x² + 10x + 32 = 8(x + 5)

Expanding the right side:

x²  + 10x + 32 = 8x + 40

Subtracting 8x from both sides:

x²  + 2x + 32 = 40

Subtracting 32 from both sides:

x² + 2x = 8

Dividing both sides by 2:

x² + x = 4

Subtracting 4 from both sides:

x² + x - 4 = 0

We can use the quadratic formula to solve this equation:

x = (-b ± √(b² - 4ac)) / 2a

where a = 1, b = 1, and c = -4.

So,

x = (-1 ± √(1² - 4 * 1 * -4)) / 2 * 1

x = (-1 ± √(1 + 16)) / 2

x = (-1 ± √17) / 2

Thus, the two solutions are x = (-1 + √17) / 2 and x = (-1 - √17) / 2. These are the values of x for which f(x) = 8.

b. To show that f(x) never equals 5, we need to show that there is no solution to the equation (x² + 10x + 32)/(x + 5) = 5.

Suppose there is such a solution, say x = a.

Then,

5(x + 5) = x² + 10x + 32

5x + 25 = x² + 10x + 32

-x² + 5x - 7 = 0

This is a quadratic equation and can be solved using the quadratic formula. However, we can see that the equation has no real solutions because the discriminant, b² - 4ac, is negative. Therefore, the equation has no real roots, and f(x) never equals 5.

c. To determine whether f(x) ever equals -5, we can follow a similar approach as in part b.

Suppose there is a solution to the equation (x² + 10x + 32)/(x + 5) = -5. Then,

-5(x + 5) = x² + 10x + 32

-5x - 25 = x² + 10x + 32

x² - 15x + -57 = 0

This is a quadratic equation and can be solved using the quadratic formula. However, we can see that the equation has no real solutions because the discriminant, b² - 4ac, is negative. Therefore, the equation has no real roots, and f(x) never equals -5.

d. To confirm the results of parts a, b, and c, we can plot the graph of the function f(x) = (x² + 10x + 32)/(x + 5) and sketch the result.

The graph of the function will show the x-intercepts and the y-intercepts and will also show any asymptotes.

The graph will confirm that there are two x-intercepts corresponding to the two solutions found.

Hence, (a). The values of x for which f(x) = 8, are x = (-1 + √17) / 2 and x = (-1 - √17) / 2.

(b). The equation has no real roots, and f(x) never equals 5.

(c). The equation has no real roots, and f(x) never equals -5.

(d). The graph will confirm that there are two x-intercepts corresponding to the two solutions found.

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The value of {b} is equivalent to 4.

Geometry is a branch of mathematics that deals with shapes, sizes, angles, and dimensions of objects.

Given are two intersecting lines.

The two intersect to create two pairs of vertically opposite angles. We can write -

(5b + 16)° = (b + 32)°

5b - b = 32 - 16

4b = 16

b = 4

Therefore, the value of {b} is equivalent to 4.

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{Question in english is given below -

The figure shows two lines cut by a transversal. (5b + 16)° (b + 32)°.​}

The degree of the polynomial of 7x ³ 5x 4x ³ 2x ² is 3.

The largest power of a component in a polynomial expression is the polynomial's degree.

Just to clarify your position, a polynomial is an expression with more than two algebraic terms, typically the sum (or difference) of various terms with various powers of the same or distinct variables (s). It is a monomial linear combination.

The polynomial can be divided into those with single value and those with many variables (multivariable polynomial).

As was previously said, the higher power of the polynomial expression is the degree of the polynomial with one variable.

However, if a polynomial comprises more than one variable, the degree of the polynomial can be calculated by multiplying the powers of the additional variables by the terms in the polynomial expression.

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In class 8, students typically learn the following formulas in algebraic expressions:

The distributive property: This formula states that a(b + c) = ab + ac. This formula is used to simplify expressions by breaking down a product of a sum into separate products.

The commutative property: This formula states that a + b = b + a and a x b = b x a. This formula is used to change the order of the terms in an expression without changing its value.

The associative property: This formula states that (a + b) + c = a + (b + c) and (a x b) x c = a x (b x c). This formula is used to group the terms in an expression in a different way without changing its value.

The identity property: This formula states that a + 0 = a and a x 1 = a. This formula is used to simplify expressions by canceling out certain terms.

The inverse property: This formula states that a + (-a) = 0 and a x (1/a) = 1. This formula is used to simplify expressions by canceling out certain terms.

The order of operations: This formula, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), is used to determine the order in which mathematical operations should be performed.

Therefore, These are some of the basic formulas in algebraic expressions that students learn in class 8, they are important to understand and apply in solving algebraic equations and problems.

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The Required Equations are y=2(x+3) and y=3x-2

Given:

'y' represents the larger number and

'x' represents the smaller number

Consequently, a greater number is double the sum of three, and a smaller number is larger no = double of ( 3 and smaller number)

The necessary equation for the first condition is y=2(x+3).

The bigger figure is now two less than three times the smaller one.

For the first condition, the equation is larger number Equals three times smaller number and two less, or y=3x-2.

Therefore, y=2(x+3) and y=3x-2 are the Required Equations.

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Answer:

24

Step-by-step explanation:

Let x be the original number of people who entered the room

Since 2/3 of the people leave, 1/3 of the people remain = (1/3)x

If 2 more people leave, number of people remaining in the room = (1/3)x - 2

We know this to be 1/4 of the original number = (1/4)x

[tex]\rm{So\;\dfrac{1}{3}x - 2 = \dfrac{1}{4}x\\\\[/tex]

Multiply throughout by 12 to get rid of the denominator

[tex]\rm{So\;12 \left(\dfrac{1}{3}x - 2\right) = 12\left(\dfrac{1}{4}x\right)\\\\[/tex]

[tex]4x - 24 = 3x\\\\\implies x = 24\\\\[/tex]

Original number of people who entered the empty room = 24

Answer:

t=3

Step-by-step explanation:

8t=24

8x3=24

Answer:t=3 I hope this helps good luck

Step-by-step explanation:

8t=24

Divide both sides of the equation by 8

8t divide by 8 = 24 divided by 8

Any expression divided by itself equals 1

t=24 divided by 8

then do this

Calculate the quotient which is

T=3

To solve the equation 6 - square root of x-2 = x + 4, you can follow these steps:

Start by isolating the square root term on one side of the equation. Subtract x + 4 from both sides to get:

6 - x - 4 - square root of x-2 = 0

Next, combine like terms:

2 - square root of x-2 = 0

Add square root of x-2 to both sides to get:

2 = square root of x-2

Now square both sides of the equation:

4 = x - 2

Finally, add 2 to both sides:

x = 6

So the solution is x = 6

Since 3* + 4x + 2k equals the value of k= -2, the polynomial's zero is 2. A polynomial is an equation with variables, constants, and other terms.

A polynomial is a mathematical expression made up of variables (also known as indeterminates) and coefficients. It can be expressed using only the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. A polynomial is an equation that contains variables, constants, and exponents and is based on the operations of addition, subtraction, multiplication, and division of numbers (No division operation by a variable).

Given that -2 is a zero in the equation

f(x)=3a*+4x+2

k, f(-2)=0 :3(-2) +4 (-2) +2k=0\s

=>12-8+2k=0\s

=>2k=-4\s

=>k=-2

Since 3z + 4x + 2k is the value of k = -2, the polynomial's zero is 2.

Complete question:

What is the value of k in the quadratic polynomial 3x². The polynomial 3x2 4x 2k has a zero for what value of k(-2).

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The quadratic polynomial 3x² does not include a term with the variable k.

The expression 3x² is a second degree polynomial, also known as a quadratic, but it does not include a term with the variable k. The general form of a quadratic polynomial is ax² + bx + c, where a, b, and c are coefficients and x is the variable.

In this case, the coefficient of x² is 3, the coefficient of x is 0, and the constant term is 0. The variable k is not present in the expression 3x², so it is not possible to determine its value.

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Complete Question:

What is the value of k in the quadratic polynomial 3x²?.

Explanation:

1 hat = 45 dollars

6 hats = 6*45 = 270 dollars

1 phone = 40 dollars

4 phones = 4*40 = 160 dollars

total = $270 + $160 = $430

Felicia spent a total of $430. Since this amount of money leaves her account, this means we write a negative sign out front to end up with the final answer of -430

In other words, her account balance went down by $430 which is why we use a negative. If someone gave her $430, then the answer would be positive.

The rules of multiplication are Associative Property, Commutative Property, Distributive Property, and Identity Property, and the rules of addition are Addition of two positive numbers is always positive, and the addition of two negative numbers is always negative.

The properties of multiplication are particular rules that are used while multiplying numbers. These properties help simplify expressions easily and, hence, have a significant role in solving all kinds of mathematical expressions, whether algebraic expressions, fractions, or integers.

Associative Property: (P × Q) × R = P × (Q × R)

For example, (4 × 5) × 3 = 4 × (5 × 3) = 60.

Commutative Property: P × Q = Q × P

For example, 3 × 4 × 2 = 2 × 3 × 4 = 24.

Distributive Property: P(Q + R) = PQ + PR; P(Q - R) = PQ - PR

For example, 3(2 + 4) = (3 × 2) + (3 × 4) = 6 + 12 = 18.

Identity Property: P × 1 = P

For example, 4 × 1 = 4, or 1 × 27 = 27.

The addition means summing up two or more numbers or values to get another number.

Positive + Positive  Addition (Sign will be Positive)  3 + 4 = 7

Negative + Negative  Addition (Sign will be negative)  – 3 + (-4) = -7

Positive + Negative  Subtraction (Sign of greater number)  3 + (-4) = -1

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A quadratic equation's graph is referred to as a parabola in mathematics. Y = a(x - p)(x - q), where p and q are the parabola's x-intercepts, or the x-values at which the parabola crosses the x-axis.

It is the factored form of a parabola, also known as the intercept form of a parabola. We can locate the function's x-intercepts or zeros with the use of factored form.

It is referred to as being in factored form when a quadratic expression is represented as the sum of two linear factors plus a constant. To establish if a graph reflects a function, use the vertical line test. The graph is a function if a vertical line drawn across it is moved and only ever touches it at one point.

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For greatest integer function,

domain :  set of all real numbers (ℝ)

range : set of all integers (ℤ)

We know that the greatest integer function of any real number n is the integer which is less than or equal to the given number n.

The mathematical definition of greatest integer function is :

f(x) = minimum { p ∈ Z ; p ≤ x }

where Z is the set of integers.

A greatest integer function is also known as the floor function.

The symbol to represent greatest integer function is  ⌊ ⌋.

We can write greatest integer function for x as ⌊x⌋

The for x = 1.98,

⌊1.58⌋ = 1

From above definition of floor function, we can say that the domain of greatest integer function is the set of all real numbers (R) whereas the range of  is the set of all integers (Z).

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