1/3x + y =-1
1/3x + 8y=13
solving system of equation by substitution
PLS SHOW WORK

Algebraic expressions and equations are written using mathematical symbols and letters to represent numbers and operations.

Algebraic expressions: An algebraic expression is a mathematical phrase that can contain numbers, variables, and operations. For example, 3x + 2y is an algebraic expression that contains the variables x and y and the operations of addition and multiplication.

Algebraic equations: An algebraic equation is a statement that shows two algebraic expressions are equal. For example, 3x + 2y = 12 is an algebraic equation that shows the left-hand side (3x + 2y) is equal to the right-hand side (12).

To write an algebraic expression or equation, you need to follow these steps:

Identify the numbers and variables in the problem.

Write the problem using mathematical symbols and operations.

Use the correct order of operations (PEMDAS) to simplify the expression or equation.

Use the equal sign (=) to write the equation.

For example, if you are given the problem "Three times a number plus two times another number equals 12", you can write the algebraic equation as:

3x + 2y = 12

In this equation, x and y are the variables and 3 and 2 are the coefficient. The equation represents the relationship between x and y and it can be used to solve for one of the variables if the other one is known.

Therefore, In short, algebraic expressions and equations are written using mathematical symbols and letters to represent numbers and operations. To write an algebraic expression or equation, you need to identify the numbers and variables in the problem, use mathematical symbols and operations, use the correct order of operations and use the equal sign (=) to write the equation.

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the required equation is 5x - 6y + 5z = 7

Given that;

points : (1, 4,4) and (-4, 1,2).

mid point : ( [(1-4)/2], [(4-1)/2], [(4+2)/2]

⇒ midpoint : ( -3/2, 3/2, 3 )  

                       x₀    y₀    z₀

Direction vector n = [-4-(1)], [  1-4], [ 2-4]

⇒ Direction vector n = < -5, -3, -2 >

General equation plane : n(x-x₀, y-y₀, z-z₀) = 0

so we substitute

⇒ (-5,-3,-2) (x-3/2, y-(-2), z-(-5/2) ) = 0

⇒ (-5,-3,-2) (x - 3/2, y + 2, z + 5/2) ) = 0

⇒ 5(x - 3/2) - 6(y + 2 ) + 5(z + 5/2) = 0

⇒ 5x - 15/2 - 6y - 12 + 5z + 25/2 = 0

⇒ 5x - 6y + 5z = 15/2 + 12 - 25/2

⇒ 5x - 6y + 5z = 7

Therefore, the required equation is 5x - 6y + 5z = 7

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From the given proof below, we have shown that AB is parallel to CD.

From the attached diagram showing the triangles inside the circle, we are given that;

<APC = <DQB [ Given]

Now, we know that in cyclic quadrilaterals that Equal angles subtend equal arcs and therefore; Arc(AC = BD)

From the statement above showing that Equal angles subtend equal arcs. we can conclude that AB is parallel to CD

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The tip left by the family at the restaurant is 18.48% of the total bill.

To determine the percentage of the tip, we need to divide the amount of the tip by the total bill, and then multiply by 100 to get the percentage.

The amount of the tip can be calculated by subtracting the cost of the bill from the total amount paid: $49.77 - $42 = $7.77

So the percentage of the tip is:

$7.77 / $42 x 100 = 18.48%

Therefore, the tip left by the family at the restaurant is 18.48% of the total bill.

The percentage is a relative term that expresses a number as a fraction of 100. It is commonly used to express a proportion or rate in terms of a hundred. For example, 45% is equal to 45 out of 100, or 0.45. The percentage can be used to represent any ratio, such as a ratio of two numbers, a fraction of a whole, or a proportion of a total.

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Answer:

f=32

Step-by-step explanation:

11f = 352

11x32=352

Answer:

[tex] \sf \: f = 32[/tex]

Step-by-step explanation:

Now we have to,

→ find the required value of f.

The equation is,

→ 11f = 352

Then the value of f will be,

→ 11f = 352

→ f = 352 ÷ 11

→ [ f = 32 ]

Hence, the value of f is 32.

Answer: You multiply the 2 given numbers together

Step-by-step explanation: I hope this helped!

The intensity of an earthquake decided on the Richter scale by the following formula,

10ᴬ⁻ᴮ , where A and B are magnitude of earthquake recorded by Richter Scale.

The Richter magnitude scale was developed in 1935 by Charles F. Richter of the California Institute of Technology as a mathematical device for comparing the magnitude of earthquakes. The size of an earthquake is determined from the logarithm of the amplitude of the waves recorded by seismographs. Adjustments are included for the change in distance between different seismographs and the epicenter of the earthquake. The Richter scale is a logarithmic scale with a base of 10, meaning that each order is 10 times more intense than the previous one. In other words, a two is 10 times more intense than a one, and a three is 100 times greater. In the case of the Richter scale, there is an increase in the amplitude of the wave.The Formula used to measured the intensity of an earthquake is A is x times intense than B, x = 10ᴬ⁻ᴮ.

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No, 45 and 36 are not a Co-prime numbers, because the two numbers have a common prime factor i.e., 9 .

A co-prime number is a number that has exactly one common divisor, which is 1. This means that a pair of numbers is co-prime if their greatest common divisor is 1. Consider x and y are two positive integers, they are called relatively prime if and only if their only common divisor is 1, so gcd(x, y) = 1. There are two numbers 45 and 36. First we determine the divisors of both numbers, then check the greatest common divisor. So, the factors of 45 are 1,3,5,9,15,45.

=> 45 = 1× 3×3× 5

and factors of 36 are 1, 3,2,4,6,9,12,36

=> 36 = 1×2×2×3×3

Now, greatest commen factor between 45 and 36 is 9, i.e., gcd(45,36) = 9 ≠ 1. Therefore, 45 and 36 are not co-prime numbers.

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Complete question:

Are 45 and 36 a Coprime number?.

The formula for the sum of an arithmetic sequence is [tex]S_n[/tex]=[tex]n/2[/tex][2a+(n−1)d], [tex]S_n[/tex] = [tex]n/2[/tex] [2a +( n − 1 )d ], where: n = the number of terms to be added. a = the first term in the sequence. d = the constant value between terms.

In arithmetic, a chain is an enumerated series of gadgets in which repetitions are allowed and order matters. Like a hard and fast, it consists of contributors (additionally referred to as elements, or terms). The quantity of elements (possibly endless) is called the duration of the series.

Unlike a fixed, the same factors can appear a couple of times at distinct positions in a chain, and unlike a fixed, the order does be counted. formally, a chain can be described as a function from herbal numbers (the positions of elements inside the collection) to the factors at each position. The belief of a sequence may be generalized to a listed family, defined as a character from an arbitrary index set.

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Answer:

A, C, E

Step-by-step explanation:

Answer:

£1885.71

Step-by-step explanation:

Reducing by 30% is doing this: 100% - 30% = 70% = 0.7

Reducing a price by 30% is the same as multiplying the price by 0.7

Adding 17.5% is doing this: 100% + 17.5% = 117.5% = 1.175

Adding 17.5% to a price is the same as multiplying the price by 1.175

Let the original price be x.

1.175 × 0.7 × x = £1551

x = £1551/(1.175 × 0.7)

x = 1885.71

Answer: £1885.71

Answer:

y = 4

Step-by-step explanation:

21/3 = 7

7 - 3 = 4

A triangle with a right angle is a 3 4 5 triangle.

A right triangle is a particular kind of triangle that only has one right (90°) angle.A mathematical formula for determining the length of the third side of a right triangle given the lengths of the other two sides was developed by the Greek mathematician Pythagoras.

The sides of variables a and b make up the right angle of the triangle. Any side may make use of any variable. The variable c stands for the left side, or the side that leans away from the right angle. The longest side, or side c, is always present and is known as the hypotenuse.

So the right angle triangle is a triangle with sides of 3, 4, and 5.

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Step-by-step explanation:

a function with a single input variable x is usually defined like

y = f(x) = expression in x

to "solve" it means either to have a value for x and then calculate y.

or to have a value for y and find the corresponding value for x, so that f(x) = y. this usually involves finding and using the inverse function of f(x).

the details depend on the functions and operations used in the function expression.

a) The amount in the account at the end of this year after the interest is paid will be 1.04x.

b) The amount in the account at the end of this year after the interest is paid will be 1.08x.

c) The expression for the amount in the account after N years will be x + 0.04xn.

a) From the information, Mybankaccount pays 4% interest at the end of each year. The person has $x in the bank account at the start of this year. The amount in the account at the end of this year after the interest is paid will be:

= x + (x*0.04*1)

= x + 0.04x

= 1.04x

b) The amount in the account at the end of 2 years after the interest is paid will be:

= x + (x*0.04*2)

= x + 0.08x

= 1.08x

c) The expression for the amount in the account after N years will:

= x + (x*0.04*n)

= x + 0.04xn

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The sum of terms with the notation kxn, where k is any number and n is a positive integer, is referred to as a polynomial.

The following expressions are polynomials:

A. 6y^2 + 5x

D. (7y^2 + 9x) / 4

Describe polynomials.

An algebraic expression known as a polynomial requires that all of its exponents be whole numbers.

Any polynomial must have variable exponents that are non-negative integers.

Although a polynomial contains variables and constants, we are unable to divide a polynomial by a variable.

These expressions are now:

A. 6y^2 + 5x

B. (7x^2 + 8) / 4x

C. (y^2 + 3x ^1/3) / 4

D. (7y^2 + 9x) / 4

Here, we can observe that there are just two polynomial expressions.

A. 6y^2 + 5x

D. (7y^2 + 9x) / 4

The non-polynomial expressions include,

B. (7x2 + 8/ 4x) contains a variable in the numerator.

C. (y2 + 3x 1/3) / 4 - This exponent has a fractional exponent.

Consequently, the polynomial expressions are,

A. 6y^2 + 5x

D. (7y^2 + 9x) / 4

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The formula for finding the axis of symmetry for a quadratic function in standard form is y = a (x-h)² + k

The term axis of symmetry in math is defined as an imaginary straight line that divides a shape into two identical parts hereby creating one part as the mirror image of the other part.

Here we need to identify the formula for finding the axis of symmetry for a quadratic function in standard form.

According to the definition of axis of symmetry, the general formula is written as

Here the quadratic equation in vertex form is written as,

=> y = a (x-h)² + k

Here the values (h, k) refers the vertex of the parabola.

And here we have also given that the axis of symmetry formula is x = h.

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Checkpoint 4 will be higher than Checkpoint 3 by 108.

In our question, it is given that the Checkpoint 4 value is -99 and the Checkpoint 3 value is -207.

We will use Subtraction. What is Subtraction?

The process of subtracting one number from another is called subtraction. The way to calculate the difference between two numbers is by using the basic arithmetic operation of subtraction, which is represented by the symbol (-).

The operation of subtraction is used to calculate the difference between two numbers. If you have an object group and remove a couple of them, the object group gets smaller. For instance, your friends consumed 7 of the 9 cupcakes you purchased for your birthday party. You are now down to two cupcakes. This can be expressed as a subtraction formula: 9 - 7 = 2, which means "nine less seven equals two." The result of subtracting 7 from 9 is 2, or (9 - 7) Here, we divided two numbers, 9, and 7, by one another to get the difference of 2.

Subtracting the value of Checkpoint 3 from Checkpoint 4, we get:

Checkpoint  - Checkpoint 3 = -207 -(-99)

= -207 + 99 = 108.

Therefore Checkpoint 4 will be higher than Checkpoint 3 by 108.

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Step-by-step explanation:

the area of a rectangle is

length × width.

so, it's simply a problem of multiplying 2 fractions.

it is

2 3/5 × 3 1/4

first we need to convert the numbers into true fractions.

2 3/5 = (2×5 + 3)/5 = 13/5

3 1/4 = (3×4 + 1)/4 = 13/4

the beauty of a multiplication (compared to addition) is that we don't need to bring the fractions to the same denominator. we can simply calculate with what they are.

you remember,

a/b × c/d = (a×c)/(b×d)

therefore,

13/5 × 13/4 = (13×13)/(5×4) = 169/20 =

= (8×20 + 9)/20 = 8 9/20

the area of the rectangle is 8 9/20 in²

The initial value of b = $3.50 represents the cost of renting skates, while the rate of change m = $3.0 represents the rate per hour.

The initial value, b = $3.50 is the skate rental fee

The rate of change, 'm' is $3.0 is the hourly rate charged by the roller skating rink based on the query we have;

The roller skating rink's fees are comprised of a skate rental fee and an hourly rate.

Skating for two hours will cost you a total of $9.50.

Five hours of skating will cost you $18.50 in total.

Skating's overall cost and its duration in hours are related in a linear fashion.Let 'x' be the number of hours spent skating, and 'y' denote the overall cost;

The equation has the form y = mx + b.

Where;

m = The linear relationship's rate of change

b = The starting point (y-intercept)

X = 2 and Y = 9.50

Consequently, we can write;

9.50 = 2·m + b..(1) (1)

X = 5 and Y = 18.50

Consequently, we can write;

18.50 = 5·m + b..(2) (2)

Equation (1) minus equation (2) results in;

18.50 - 9.50 = 5·m - 2·m + b - b = 3·m

9.0 = 3 × m

∴ m = 9.0/3 = 3.0

m = 3.0 is the rate of change.

Likewise, we have;

We obtain from equation (1);

9.50 = 2·m + b = 2 × 3.0 + b = 6.0 + b

9.50 = 6.0 + b

∴ b = 9.50 - 6.0 = 3.50

The starting point is 3.50.

As a result, the initial value of b = $3.50 represents the cost of renting skates, while the rate of change m = $3.0 represents the rate per hour.

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The inequality that represents the maximum amount of apples and grapes they can buy will be 5a + 3.99 ≤ 11.

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

Therefore, the inequality that represents the maximum amount of apples and grapes they can buy will be 5a + 3.99g ≤ 11.

where a= Apple

g = grape.

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A possible tape diagram that shows the proportion of muffins with and without chocolate is one that displays 1/4 or 10 flavors with chocolate and 30 flavors without chocolate.

This is a simple diagram that uses segments of a tape to illustrate fractions.

It is known 25% of the flavors have chocolate, but let's calculate the exact number:

40/100 = 0.4 x 25= 10 flavors have chocolate and therefore 30 flavors do not have chocolate.  

Based on this, here is the diagram (green shows the chocolate flavors):

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Left Column: AC bisects ZBCA ZDCA. Right Column: Angle ZBAC = Angle ZDCA (Angle Bisector Theorem).

Angle bisector theorem states that in any triangle, the line that bisects an angle also divides the opposite side into two segments that are proportional to the other two sides of the triangle. This theorem can be used to prove that the angle bisector of any triangle is the perpendicular bisector of the opposite side. In other words, the line that bisects the angle of a triangle will also divide the opposite side into two segments with lengths that are equal to the ratio of the other two sides of the triangle.

Left Column                                           Right Column

1. AC bisects ZBAD                                    1. AC bisects ZBCA ZDCA

2. ZBAD = ZBCA + ZDCA                                 2. Angle ZBAC = Angle ZDCA (Angle Bisector Theorem)

3. Angle ZBAC = Angle ZBCA + Angle ZDCA               3. BC = DC (Congruent Sides of Congruent Triangles)

4. Angle ZBCA = Angle ZDCA                            

5. BC = DC (Congruent Sides of Congruent Triangles)  

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The equation -3p + (1/8) = (- 1/4) holds true for p = 0.125.

The equation is as follows:

-3p + ( 1/8 ) = ( - 1/4 )

The denominators of the two terms are different on the left-hand side of the equation.

The LCM of 1 and 8 is therefore 8.

Therefore,

- 3p × ( 8 / 8 ) + ( 1 / 8 ) × ( 1 / 1 ) = ( - 1 /4 )

- 24p / 8 + 1 / 8 = - 1 / 4

( - 24p + 1 ) / 8 = - 1 / 4

Add 8 to both sides of the equation now.

We get,

[ ( - 24p + 1 ) / 8 ]

× 8 = ( - 1 / 4 ) × 8

- 24p + 1 = - 8 / 4

- 24p + 1 = - 2

Add 1 to each side of the equation, then

- 24p + 1 - 1 = - 2 - 1

-24p = - 3

Subtract 24 from each side of the equation now.

- 24p / 24 = - 3 / 24

- p = ( - 1 / 8 )

On each side of the equation, multiply by -1.

( - p ) × ( - 1 ) = ( - 1 / 8 ) × ( - 1 ) ( - 1 )

p = 1 / 8

p = 0.125

The equation will be true for p = 0.125.

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The standard deviation of the sampling distribution of a sample proportion using the formula σ^p=√p(1−p)N σ p ^ = p ( 1 − p ) N. The standard deviation of the sampling distribution of a sample proportion is about 0.054.

In information, the standard deviation is a degree of the quantity of variation or dispersion of a fixed of values. A low standard deviation indicates that the values tend to be near the implied (additionally called the predicted price) of the set, whilst an excessive preferred deviation suggests that the values are spread out over a wider variety.

Popular deviation can be abbreviated SD, and is maximum commonly represented in mathematical texts and equations by means of the decrease case Greek letter σ (sigma), for the population standard deviation, or the Latin letter s, for the sample general deviation.

The standard deviation of a random variable, pattern, statistical population, statistics set, or possibility distribution is the square root of its variance. it's miles algebraically easier, even though in exercise less sturdy, than the common absolute deviation.

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Since a square is either positive or zero, negative numbers don't have real square roots.

No, we are unable to compute the negative number's square root. Positive is always the result of adding two numbers with the same sign.

Theorem: Square Roots of a Negative Number Simplifying an expression involving the square root of a negative number by simplifying the number as if it were a positive number and putting an i in front of it as a coefficient is one method. To put it another way, x=ix x = i x for every x where x is a positive number and where x is a negative number.

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The following ordered pair is given as {(1, -1), (2,0), (3,1)} for the given data of movement of arrow.

A set comprises elements or members that can be mathematical objects of any sort, including numbers, symbols, points in space, lines, other geometric forms, variables, or even other sets. A set is the mathematical model for a collection of various things.

An ordered pair consists of two items. The order of the objects in the pair matters because, unless a = b, the ordered pair differs from the ordered pair. Ordered pairs are also known as 2-tuples, or 2-length sequences.

An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence. In order to understand a point visually, it might be helpful to position it on the Cartesian plane. An ordered pair's numerical values may be fractions or integers.

The following ordered pair is given as {(1, -1), (2,0), (3,1)} for the given data of movement of arrow.

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Answer:

D

Step-by-step explanation:

The required number of Peppermint candies in each bag is 8.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Let the number of peppermint candies be x in each bag,
Butterscotch candies in 5 bags = 5 × 4 = 20 candies
Peppermint candies in 5 bags = x × 4 = 4x candies

According to the quesiton, Altogether, the bags contain 52 candies.
20 + 4x = 52
x = 8

Thus, the required number of Peppermint candies in each bag is 8.

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Yes, Y = -3x + 10 is a linear function.

A linear function is a function 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). The equation Y = -3x + 10 can be written in this form, with m = -3 (the coefficient of x) and b = 10 (the constant term).

Linear functions 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. In this case, the slope of the function is -3, which means that for every unit increase in x, there is a corresponding decrease of 3 units in y. The y-intercept of this function is (0,10), which means that the line crosses the y-axis at the point (0, 10)

In summary, Y = -3x + 10 is a linear function because it can be written in the form of y = mx + b, and it represents a straight line on a graph.

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