How do you solve an algebraic equation with 3 variables?.

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

The markup percentage for the clarinet is 33.33%

The store buys a guitar at the price of $45

The price tag on the trumpet in the store is $104.

30% in decimal value is approximately 1.3 and so the price should either be multiplied or divided by it to know the store markup and margin.

The store's selling price for the guitar would be $45 x 1.3 = $58.50.

The store paid $104 / 1.3 = $80 for the trumpet.

The store marked up the clarinet by $100 - $75 = $25.

The markup percentage for the clarinet is ($25 / $75) x 100 = 33.33%.

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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

Answer:dddjdvjd

Step-by-step explanation:

mb i just need points\

Answer:

d = 63 degree

e = 96 degree

f = 21 degrees

Step-by-step explanation:

The angle d is the vertical angle theorem with 63 degrees; that is why d is 63 degrees.

The angle e is the vertical angle theorem with 96 degrees; that is why d is 63 degrees.

96 + 63 = 159 degrees

180 - 159 = 21 degrees

So, f = 21 degrees

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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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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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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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]

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

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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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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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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Answer:

E

Step-by-step explanation:

Answer:

1. 6

2. $14.27

3. 36

4. $691.70

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: To answer your question, since they played 35 games, that means that there were 12 wins, 14 draws, and they lost 9 games. I hope this helps! Sorry for the previous person, they just like to get points.

Step-by-step explanation:

P = 3W + D

50 = 3W + 14  subtract the 14 from both sides

36 = 3W divide both sides by 3

12 = W

The equation y = -2x + 5 is already in the standard slope intercept form.

The slope-intercept form is a way of expressing the equation of a straight line in algebraic terms. The equation of a line in slope-intercept form is typically written as:

y = mx + b

Where m represents the slope of the line and b represents the y-intercept, which is the point at which the line crosses the y-axis. The slope-intercept form is useful because it allows you to quickly identify the slope and y-intercept of a line, given its equation. The slope represents the rate of change of y with respect to x, and the y-intercept represents the initial value of y when x is equal to 0. By using slope-intercept form we can easily graph the line and also can find the equation of the line from the graph.

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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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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

Answer: The equation of a line can be written in the slope-intercept form y = mx + b, where m is the slope of the line and b is the y-intercept.

To find the equation of a line that passes through the point (3, 2) and cuts off equal intercepts on the x and y axes, we can use the following steps:

First, we need to find the slope of the line using the point (3, 2) and the fact that the line cuts off equal intercepts on the x and y axes. Since the line cuts off equal intercepts on the x and y axes, it means that it is a line of symmetry, which means that the slope of the line is zero.

Now we can use the point-slope form of a linear equation which is y-y1 = m(x-x1) and substitute the point (3,2) and the slope (0)

The equation of the line will be y = b where b is the y-intercept.

So the equation of the line which passes through the point (3, 2) and cuts off equal intercepts on the axes is y = 2

The line is a horizontal line passing through the point (3,2) and it cuts the x-axis at y = 2.

Step-by-step explanation:

Multiplication: Decimal point moves right for every 10^n.

Division: Decimal point moves left for every 10^n.

When you multiply a number by a power of 10, the placement of the decimal point shifts to the right by the number of zeroes in the power of 10. For example, if you multiply 2.34 by 100 (102), the result would be 234.0, with the decimal point shifting two places to the right.

When you divide a number by a power of 10, the placement of the decimal point shifts to the left by the number of zeroes in the power of 10. For example, if you divide 234.0 by 100 (102), the result would be 2.34, with the decimal point shifting two places to the left.

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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.

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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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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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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Answer:

2

Step-by-step explanation:

Since this is all raise to the -1, we put it under 1.

[tex]\frac{1}{5^{-2}a^{3}b^{-4} }[/tex]  Pull the [tex]5^{-2}[/tex] and [tex]b^{-4}[/tex] from the bottom and put them on top to make them positive [tex]5^{2}[/tex] mean 5x5 or 25

[tex]\frac{25b^{4} }{a^{3} }[/tex]

Answer:

Option 2

Step-by-step explanation:

[tex]=(\frac{a^{3} }{5^{2} b^{4} } )^{-1}[/tex]

[tex]=\frac{1}{\frac{a^{3} }{5^{2} b^{4} } }[/tex]

[tex]=\frac{5^{2} b^{4} }{a^{3} }[/tex]

[tex]=\frac{25b^{4} }{a^{3} }[/tex]

Hope this helps

Using the same method, determine the histogram's total area: divide it into rectangles and use the calculation for a rectangle's area to arrive at a total area of 100.The answer 40.

The area below the 40 to 55 line in the histogram must first be located.By using the area of a rectangle, one can determine the area: side side.

This will reveal a 60-square-foot space.

Then, using the same method, determine the histogram's total area: divide it into rectangles and use the calculation for a rectangle's area to arrive at a total area of 100.

You must now apply the rule of three:

The number of people between the ages of 40 and 55 is 25, and that age range corresponds to 60, as indicated by the question's sentence, so:

60 ———- 24

100 ———- x

60•x = 24•100

60x = 2400

x = 2400/60

x = 40

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In the given question of inequality, the greater than symbol makes the statement true, 14 > 5/6​.

A relationship between two expressions or values that is not equal to each other is known as inequality in mathematics. So inequality emerges from an imbalance.

"Less than or equal to," "less than," or "not equal to" are all ways to describe an inequality, which is a mathematical relationship between two expressions.

Both equations and inequalities are mathematical phrases created by connecting two expressions. The equal sign (=) in an equation denotes that the two expressions are regarded as equal. In contrast, an inequality indicates that the two phrases are not always equal by using the symbols >, <, or =.

Less than or equal to, larger than, less than, and more than or equal to are the four fundamental inequalities.

Therefore, the correct answer is option b) >.

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The complete question is:

Which sign makes the statement true?

-2 / 5  ___  -3 / 8

a) <

b) >

c) =