What is it called when you substitute a number for each variable and simplify?.

Step-by-step explanation:

if x and y vary directly, they are defined as

y = kx

with k being a constant for all x.

now, if they vary inversely, they are defined as

y = k/x

so,

6/5 = k/4

24/5 = k

y = f(x) = 24/5 / x = 24/(5x)

f(7) = 24/(5×7) = 24/35

when x = 7, y = 24/35

When x and y vary inversely, their product is always a constant, k. In this case, we know that x = 4 and y = 6/5, so we can use this information to find the value of k:

k = xy = (4)(6/5) = 24/5

The function that models this inverse variation is:

xy = k

We can find y when x = 7 by substituting this value into the equation and solving for y:

xy = k

(7)y = 24/5

y = 24/5*(1/7)

y=24/35

So when x = 7, y = 24/35.

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The four methods of solving a quadratic equation are Factoring, Completing the square, Quadratic formula, Graphing.

A quadratic equation is a type of polynomial equation that can be written in the form of ax^2 + bx + c = 0, where x is the variable, and a, b, and c are constants. The degree of the equation is 2, and it creates a parabolic shape when graphed. The solutions of a quadratic equation are also known as roots, and there can be zero, one or two distinct solutions. The solutions can be real or complex numbers. The most common method to find the roots of quadratic equation is using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a

The four 4 methods of solving quadratic equation are :

Factoring: This method involves factoring the quadratic equation into the product of two binomials. Once factored, you can set each binomial equal to zero and solve for the roots (x-values) of the equation.

Completing the square: This method involves rearranging the equation into a perfect square trinomial and then solving for the roots. The basic idea is to add and subtract the square of half the coefficient of the x^2 term to both sides of the equation.

Quadratic formula: This method utilizes the quadratic formula to find the roots of the equation. The formula is: x = (-b ± √(b^2 - 4ac)) / 2a

Graphing: This method involves plotting the equation on a coordinate plane and finding the x-values (roots) of the equation by observing where the graph intersects the x-axis.

All four method are used to find the x-intercepts(root) of the quadratic equation, which is the main goal of solving the quadratic equation.

Hence, The four methods of solving a quadratic equation are Factoring, Completing the square, Quadratic formula, Graphing.

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If the x coordinate is positive and the y coordinate is zero, the location of the point is in positive x- axis.

The position of a point or a shape in a specific space is determined by coordinates, which are numbers (a map or a graph).

Cartesian coordinates are introduced to students in Year 4 and are taught in primary school. The x axis, which is the horizontal axis, and the y axis, which is the vertical axis, are used to identify points (the vertical axis).

Coordinates are always written with two numbers separated by commas and enclosed in brackets. Coordinates are ordered pairs of numbers, where the first number represents the point on the x axis and the second, the point on the y axis.

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If you are worried about your future in math and want to improve your mathematical abilities, the best way to do so is to practice regularly and seek out additional resources to help you understand the material.

Here are some specific things you can do:

Practice problems: Work through a variety of different types of problems to build your skills and confidence.

Find a study group: Join a study group with other students who are also taking the same math class. This can be a great way to get extra help and support.

Use online resources: There are many online resources, such as videos and tutorials, that can help you understand mathematical concepts.

Seek extra help: Don't be afraid to ask your teacher or a tutor for extra help if you are struggling with a particular topic.

Stay motivated: Keep in mind the importance of math in many fields and how it will be useful in future, and set realistic and challenging goals for yourself.

Make connections between different topics: Try to understand how different mathematical concepts are related and how they can be applied in real-world situations.

Remember, learning math takes time and practice, so be patient and persistent.

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The equation of the graphed function is given as follows:

f(x) = x³ + 2x² - 5x - 6.

The equation of the function is obtained considering the Factor Theorem, as a product of the linear factors of the function.

From the graph, the zeros of the function are:

Hence the function is:

f(x) = a(x + 3)(x + 1)(x - 2).

In which a is the leading coefficient.

Expanding the product, we have that:

f(x) = a(x² + 4x + 3)(x - 2)

f(x) = a(x³ + 2x² - 5x - 6).

When x = 0, y = -6, hence the leading coefficient a is obtained as follows:

-6a = -6

a = 1.

Hence the function is:

f(x) = x³ + 2x² - 5x - 6.

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Answer: 1 1/4 mile

Step-by-step explanation:

Answer: liner

Step-by-step explanation:

Answer:

Step-by-step explanation:

linear, because the slope intercept fomat is y=mx+b it's just that the y intercept is zero so they just excluded it. So the equation would be y=8.75x+0 but they just removed the zero to simplify. So yes, it is linear

Answer:

comparing (x+2) with (x-a) we get a=-2

Using factor theorem

p(x)=0

p(-2)=0

(-2)⁴-(-2)³+c×(-2)²+3×-2-2=0

-16+8+4c+12=0

4+4c=0

4c=-4

c=-4/4

c=-1

Explanation:

When going from A(-2,-3) to A '(-6,-9), we multiplied both coordinates by the scale factor 3. In other words, we tripled the coordinates.

Do the same thing to the coordinates of point B.

Therefore we arrive at (12, 0) as the final answer. This is choice C.

The var() function in R is used to calculate sample variance. In those uncommon situations where you want a populace change, utilize the populace mean to work out the example difference and duplicate.

The outcome by (n-1)/n; Take note of the fact that sample variance converges on population variance as sample size increases.

R's sample variance and standard deviation are specified by var(y), which tells R to calculate the sample variance of Y by employing n-1 "degrees of freedom," where n is the number of observations in Y. On the other hand, sd(y) tells R to return the sample standard deviation of y by employing n-1 degrees of freedom. sqrt(var(y)) equals sd(y).

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Any alternative for the variable in a function that results in a zero answer is said to as the zero of a function.

The x-intercept(s) of the function's graph, or the real zero of a function, is where the function's graph hits the x-axis graphically.

The values of the variable in a function that allow the function to equal zero are termed the zeros of the function. The places on the x-axis where the graph crosses the x-axis are referred to as a function's zeros graphically. In other respects, we can say that the zeros of something like a function are the x-intercepts of the graph.

Finding the values of the variable that correspond to the function's zeros can be achieved by equating the function to 0. By calculating the polynomial and then equating it to 0, we can discover the zeros for polynomials.

Example:

Find the zeros of the function f(x) = ex - 1. Answer: Zero of function f(x) = ex - 1 is x = 0.

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Answer:

7/9

Step-by-step explanation:

Multiply [tex]\frac{2}{3}[/tex] by 3 to get the common denominator of 9. Whatever you do to the top, you do to the bottom too.

So you would do [tex]\frac{2}{3}[/tex] x [tex]\frac{3}{3}[/tex]  to get [tex]\frac{6}{9}[/tex]

Add [tex]\frac{1}{9}[/tex] to [tex]\frac{6}{9}[/tex] to then get [tex]\frac{7}{9}[/tex]

So your answer would be [tex]\frac{7}{9}[/tex]

So, the given system will have a unique solution when k=,1

A system of linear equations in two variables will have a unique solution when the equations are consistent and independent.

In this case, the system of equations is kx + 3y = k and 3x + ky = k.

One way to check for consistency and independence is by using the determinant of the coefficient matrix and comparing it to the determinant of the system. The determinant of the coefficient matrix is (kk) - (3ky) = k^2 - 3ky and the determinant of the system is k^2 - k.

For the system to have a unique solution, the determinant of the coefficient matrix must be non-zero and equal to the determinant of the system.

Therefore, the system will have a unique solution when k^2 - 3ky = k^2 - k.

Which means that k=1.

This system will have a unique solution when k=1, and the pair of linear equations will be 1x + 3y = 1 and 3x + ky = 1.

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After solving, the solution of the pair of equation is (2, 1).

In the given question, we have to find the solution of pair of equation 2x + y = 5 and 3x - 2y = 4.

The given equation are:

2x + y = 5.........(1)

3x - 2y = 4.........(2)

Multiply equation 1 by 2 then add by equation 2.

4x + 2y + (3x - 2y) = 10 + 4

Now simplifying

4x + 2y + 3x - 2y = 14

7x = 14

Divide by 7 on both side, we get

x = 2

Now putting the value of x in equation 1

2(2) + y = 5

4 + y = 5

Subtract 4 on both side, we get

y = 1

Hence, the solution of the pair of equation is (2, 1).

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The complete question is:

What is the solution of pair of equation 2x + y = 5 and 3x - 2y = 4?

The 4 types of symmetry in biology is spherical, radial, biradical, and bilateral.

The term symmetry is defined as the balanced arrangement of body parts or shapes around a central point or axis

As we all know that the 4 types of symmetry in biology is defined as the size, shape, and relative location on one side of a dividing line mirrors the size, shape, and relative location on the other side.

Here we have also know that animals can be categorized on the basis of their symmetry.

And the basic classification includes Levels of organization, Symmetry, Diploblastic and Triploblastic Organization, Coelom, Segmentation, and Notochord in biology.

Therefore all these categories must be kept in mind while classifying an animal.

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Solving 3 equations with 3 variables using substitution involves using one equation to solve for one variable in terms of the other variables, and then substituting that expression into the other equations. Here is the general process:

   1. Choose one of the equations and solve for one of the variables in terms of the other variables. For example, if the equation is 2x + 3y - z = 5, you can solve for x by isolating it on one side of the equation: x = (5 + z - 3y)/2

  2.Substitute the expression for the solved variable into the other equations. For example, if you have the equations 2x + 3y - z = 5, x + y + z = 7, and 3x - 2y + z = 6, you would substitute x = (5 + z - 3y)/2 into the other equations.

  3.For the remaining variables, solve the resulting equations. For instance, you would obtain y + z = 7 - (5 + z - 3y)/2 and 3(5 + z - 3y)/2 - 2y + z = 6 after inserting x = (5 + z - 3y)/2 into the other equations.

  4.By putting the remaining variables on one side of the equation, you can solve for them. After that, you can solve for the variable's value.

 5.Check to see if the solution is valid by substituting it back into the original equation.

It's crucial to remember that this approach could not always result in a singular solution; in certain circumstances, you might discover that the system has neither a solution nor an unlimited number of solutions.

  therefore, using these 5 steps we can solve the equations using substitution .

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Answer:

3p-g-10

Step-by-step explanation:

3(p-3)-g-1

3p-9-g-1

3p-g-9-1

3p-g-10

Answer:

9/12 + 4/12

Step-by-step explanation:

Find the lowest common denominator. 12 is divisible by 4 and 6.

4 x 3 =12 and 6x2 =12

3/4 x 3/3 =9/12

2/6 x 2/2= 4/12

No. of hours, hourly employee need to work to get earnings as the standard employee = 50 hours.

What is an equation?

An equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”. For example, 2x – 5 = 13.

Here,

2x – 5 and 13 are expressions

The sign that connects these two expressions is “=”.

Given, weekly salary of an employee = $500

Hourly earning of another employee = $10

Let the hourly employee work for x hours to earn the same earnings as weekly employee

By the question,

$10 x = $500

x = $500/$10

x = 50 hrs.

Hence, the hourly employee has to work around 50 hours make same weekly earnings as the standard employee.

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The value of x would be 1496 m.

What is trigonometry?

Trigonometry is based on the study of the six basic trigonometric functions: sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). These functions are defined in terms of the ratios of the sides of a right triangle. For example, the sine of an angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.

In the given figure, we can apply the trigonometric ratio, we get

sin22 = x/4000

0.374 = x/ 4000

x = 0.374 * 4000

x = 1496m

Hence, the value of x would be 1496 m.

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A dot serves to depict a point, which is a place in any space (.). Nothing about it is long, tall, shaped, or big.Therefore, the snail finally arrives at the point (6,5).

What is a point and line?

To indicate an accurate location in space, a point is denoted by a dot (.). It has no height, width, or any dimension. It is hence sizeless.

The simplest basic object in geometry is a point. A dot and a capital letter are used to identify it. Only position is represented by a point, which has no size (that is, zero length, zero width, and zero height).

A dot serves as a visual representation of a point, which is a place in any space (.). It lacks all dimensions—length, height, shape, and size. With capital letters, it denotes the start of drawing any figure or shape. Line. a collection of points together along a straight path.

The snail moves 1 unit North, 2 units East, 3 units South, 4 units West, 5 units North, 6 units East, 7 units South, 8 units West, 9 units North, and 10 units East.

Starting at (0,0), the snail moves:

Therefore, the snail finally arrives at the point (6,5).

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1260

Just as 12 is to 72. 210 is to x

setup ratio, cross multiply, and solve for x:

Answer is 1260

The polynomial f(x) = x³ + 9x² + 23x + 15 has a factor of x + 3

An equation is an expression showing the relationship between numbers and variables.

The degree of a polynomial is the power is the highest exponent. The cubic polynomial have a degree of 2.

Given that the linear function x + 3 is a factor of f(x), hence f(-3) = 0. Therefore:

f(-3) = 0

f(-3) = (-3)³ + 9(-3)² + a(-3) + 15 = 0

(-3)³ + 9(-3)² + a(-3) + 15 = 0

-27 + 81 - 3a + 15 = 0

69 - 3a = 0

3a = 69

a = 23

The value of a is 23

The polynomial becomes f(x) = x³ + 9x² + 23x + 15

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Total number of outcomes (n) = 2

Let E be the event of getting a yellow colored side of the coin.

Therefore, n(E) = 1

Therefore, P(E) = n(E)/n = 1/2

Answer:

1/2

Hope it helps.

If you have any query, feel free to ask.

The quotient is the quantity we arrive at when dividing two numbers.

When a number is divided, the result is the quotient. The mathematical symbol (÷) stands for division, which is a technique for allocating items equally among groups. In mathematics, the quotient is the outcome of dividing an integer by any divisor. It is the quantity of times the dividend contains the divisor.

An integer or a decimal number can be the quotient.

A whole number is the quotient when a number is entirely divisible by another integer. The quotient is a decimal number when a number cannot be divided by another number entirely.

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They sell 21 pizzas for $321 in one evening.

A word problem is a few phrases that describe a real-life scenario in which an issue must be solved using a mathematical computation. It is a mathematical problem expressed entirely in words typically used as an educational tool.

Word problems are regarded as an important aspect of the basic curriculum because they require students to apply their understanding of various concepts to real-life settings.

Let us assume that,

small size pizza =x

medium size pizza =y

large size pizza =z

so, x+y+z=21

6x+9y+10z= 321

y=z+1

x+y+z=21

6x+9y+10z= 321

y-z=1

6x+9y+10z= 321

y+4z=31

5z=30

z=6

y=z+1

y=7

x+y+z=21, x=8

{8,7,6}

8*$6=$48

7*$9=$56

6*$10=$60

Thus, they sell 21 pizzas for $321 in one evening.

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Answer:

Step-by-step explanation:

Her displacement is 9.43 miles, and her office is 5 miles west and 8 miles north from her house

Let's use the notation (x, y) to denote Beth's position, we assume she starts at the point (0, 0).

First she travels 9 miles west and 9 miles north, so the new position is:

(0 - 9, 0 + 9) = (-9, 9)

Then travels 6 miles west and 6 miles nort

(-9 - 6, 9 + 6) = (-15, 15)

then travel 10 miles east and 7 miles south to their office

(-15 + 10, 15 - 7) = (-5, 8)

So the office is 5 miles west and 8 miles north from her house, and the displacement is equal as the absolute value of that point.

dispacement = √( (-5)² + 8²) = 9.43

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Answer:

-------------------

Use slope equation:

Substitute coordinates and solve for n:

The images are formed when two plane mirrors are placed at 36 is 9

The term plane in math defined as a two-dimensional doubly ruled surface spanned by two linearly independent vectors.

Here we need to find the number of images are formed when two plane mirrors are placed at 36.

Here we have given that the generalization of the plane to higher dimensions is called a hyperplane.

And here we also know that the angle between two intersecting planes is known as the dihedral angle.

The by using the formula we have calculated as,

=> n = (360 / 36) - 1

=> n = 10 - 1

=> n = 9

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