[tex]4 3/8 + 2 5/12 -3 1/6[/tex]

If the discriminant b² - 4ac = 0 for a quadratic equation ax² + bx + c = 0, it means that the nature of roots of the equation has one real and identical (repeated) root.

When the discriminant is equal to zero, the square root of the discriminant will be zero, and the equation will have one solution for x, regardless of the values of a, b and c.

This can be observed in the quadratic formula, where the square root of the discriminant is used to determine the solutions of x. In this case the equation will be reduced to:

x = -b/2a

It's also possible to observe this by factoring the equation, in this case the equation can be factored as (x - r)^2 = 0, where r is the common root. This means that the graph of the equation will touch the x-axis only once.

In summary, when the discriminant b² - 4ac = 0, the roots of the quadratic equation are real and identical (repeated).

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3/5 is greater than 1/3

What is the fraction?

A fraction is a way of representing a number that is not a whole number. It consists of two parts: a numerator and a denominator. The numerator represents the number of equal parts of a whole, and the denominator represents the total number of parts in the whole.

One way to compare the fractions 1/3 and 3/5 is to find a common denominator between them. In this case, the least common multiple of 3 and 5 is 15. So, you can convert 1/3 to 5/15 and 3/5 to 9/15. Now, you can compare the two fractions by looking at their numerators: 5 and 9. Since 9 is greater than 5, you can say that 3/5 is greater than 1/3.

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The solution for the absolute function is h < 2.

The variable in the absolute value bars makes up an essential algebraic function known as the absolute value function. The most widely used version of the absolute value function is f(x) = |x|, where a = 1 and h = k = 0. The general form of this function is f(x) = a |x - h| + k.

When we extend the absolute value function f(x) = |x|, we can write it as x if x 0 and -x if x 0 since the range of this function, f(x) = |x|, is always non-negative.

The function will be solved as,

| h + 3 | < 5

h + 3 < 5

h < 5 - 3

h < 2

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Yes, because both figures are rectangles and all rectangles are similar.

A rectangle is a four-sided polygon with four right angles. It is one of the most common shapes in both two-dimensional and three-dimensional geometry and can be found in everyday objects such as windows, doors, and tables. Rectangles are also found in nature, like rivers, beaches, and mountains. The area of a rectangle is the product of its length and width, while the perimeter is the sum of its four sides. Rectangles are also special cases of other shapes such as squares and parallelograms, as they are the same shape but with different lengths of sides.

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A collection of values for a variable that simultaneously fulfil each equation is the solution to a system of equations.

A set of two linear equations with two variables is a system of linear equations.

1. Examine the two algebraic methods of substitution and elimination for solving systems of linear equations.

2. Visualize systems of linear equations to better grasp when they have a single solution, none at all, or an unlimited number of solutions.

3. Examine algebraic techniques for determining the quantity of solutions for systems involving two linear equations.

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Answer:

Hmmm, I do not know, but thanks for asking!

Step-by-step explanation:

...

Answer:

11.11 hours

Step-by-step explanation:

Average Bike Speed on Flat Terrain: 18 mph

So Colton can travel 200 miles in 200 / 18 = 11.11 hours

a) The triangles are not similar, as they have different angle measures.

b) The triangles are similar by the SAS theorem.

c) The triangles are similar by the SSS theorem.

Similar triangles are triangle that share these following two features:

For item a, we have that the angle measures are given as follows:

Different angle measures, hence not similar.

For item b, we have that the side lengths are proportional, as:

13.2/6 = 15.4/7

As the angle between these two sides has the same measure of 90º, the SAS theorem proves that these two triangles are congruent.

For item c, the side lengths are proportional, as:

Hence the triangles are similar by the SSS theorem.

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A polynomial function of least degree with a leading coefficient of 1 and zeroes at -2, 3, 6 is given by:  "f(x) = (x + 2)(x - 3)(x - 6) = x^3 - x^2 - 9x - 12)".

According to the Factor Theorem, k is a zero of a given polynomial function f (x), if and only if (x - k) is a factor of the given polynomial function f(x).

Since -2,3 and 6 are zeros to be given of f (x), so

you need to put -2,3 and 6 in (x - k)

such as

f (x) =  { (x - k) (x - k) (x - k) }

     =  { (x - (-2) (x - 3) (x - 6) }

      =  {(x+2) (x-3)(x-6) }

      =  {( x^3 - x^2 - 9x - 12) }

'f(x) = { (x^3 - x^2 - 9x - 12) }' is the required polynomial function.

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Answer:

the common factor is b since it is divisible by both 2b and 5b

Step-by-step explanation:

The expression C(g(m)) represents the total cost of filling the car's gas tank based on the number of miles driven.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

It is given that the car's gas mileage is 25 miles per gallon, then the number of gallons of gas needed to fill the car's tank can be found by dividing the number of miles driven by the gas mileage.

The expression for this is g(m) = m / 25 where m is the number of miles driven.

The total cost of filling the car's gas tank is represented by the expression C(x) where C is the cost in dollars and x is the number of gallons purchased.

So when g(m) is substituted into C(x), C(g(m)) is obtained which represents the total cost of filling the car's gas tank based on the number of miles driven.

Therefore, this expression is the cost of filling the gas tank given the number of miles driven.

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If Phil received £235 in the ratio 3:5, we can use this information to find out how much money was shared in total.

We know that the ratio of Samantha's share to Phil's share is 3:5.

This means that for every 3 parts of the total money that Samantha gets, Phil gets 5 parts.

We can use this information to set up a proportion:

(Samantha's share) / (Phil's share) = (3) / (5)

We know that Phil's share is £235, so we can substitute that into the proportion:

(Samantha's share) / (235) = (3) / (5)

To find the total amount of money shared, we can cross-multiply and divide:

Samantha's share = (3/5) * 235

Samantha's share = 141

To find the total amount of money shared, we can add the amount Samantha received to the amount Phil received:

141 + 235 = £376

Therefore, £376 was shared in total.

Answer: -5/6, none of your choices

Step-by-step explanation:

-(5/6) = -5/6

None of your choices

The values that represent the inverse of the function which is represented in the table above include the following:

x  4    2    1    3   4

y -2   -3   6   7    5

In Mathematics, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).

In order to determine the inverse of any function, you should interchange (swap) both the input value (x-value) and output value (y-value). This ultimately implies that, the inverse relation of any function has its input value (x-value) and output value (y-value) interchanged (swapped) as follows;

x           y

4          -2

2          -3

1           6

3          7

4          5

In conclusion, we can logically deduce that the above inverse relation is not a function because the same input value (4) appears more than once with different output values (-2 and 5).

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Using Algebraic expressions, the original length of the string was 72 feet.

When addition, subtraction, multiplication, division, and other mathematical operations are performed on variables and constants, the result is a mathematical statement known as an algebraic expression.

Let's say James and Natalie were playing with matchsticks when they had the idea to create number patterns with them. James made the number 4 with four matchsticks. In order to create a pattern with two 4s, Natalie added three extra matchsticks.

They understood that they could keep adding three matchsticks each round to make an additional "four" by doing so. They deduced from this that, generally speaking, in order to create a pattern with n number of 4s, you need 4+ 3(n-1) sticks. We refer to 4+ 3(n-1) as an algebraic expression in this case.

Let x be the length of the string,

when it is cut into 4 halves,

the length becomes x/4,

then it is again cut 1/3,

Now, it is given that 1/3 × x/4 = 6

⇒ x = 72

So, the original length of string was 72 feet.

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Each of psychology's subfields or subtypes takes a unique approach to considering issues and topics. Despite the fact that they each have their unique areas of interest, they all strive to understand and research human mind and behavior.

Psychology's subfields are always expanding and changing due to the wide variety of human behavior. Many schools and universities offer courses and degree programs in some of these subfields, which have established themselves as popular subjects of study.

Each category of psychology denotes a distinct field of research centered on a certain subject. Psychologists frequently choose to focus their careers on one of these.

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The product of the sum and difference of two terms can be found using the distributive property and the FOIL (First, Outer, Inner, Last) method.If you have two terms, A and B, the sum and the difference of these terms can be represented as:

Sum: A + B Difference: A - B

To find the product of the sum and difference, you can multiply the sum and the difference together:

(A + B)(A - B)

Using the distributive property, we can expand the product:

AA - AB + AB - BB

Which is equal to:

A^2 - B^2

This is the difference of squares of the terms.

It's worth noting that this is a very common pattern in algebra, and it's called the difference of squares. It is the product of the sum and difference of two terms. The distributive property and FOIL method can be used to expand the product of two binomials, but it's important to recognize patterns, like this one to solve the problem in a faster way.

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The number 120 symbolizes  the restaurant that has been open for 120 months.

Use Slope-intercept form

The equation of the straight line is provided by:

y =mx+ b

m stands the slope of the line

b stands for the initial value or y-intercept.

As per the information:

The scatter plot displays the association between the average number of nightly consumers and the number of months since a restaurant opened.

The equation describes the linear standard for these details

y = 5x + 120

Where,

y denotes the number of months since a restaurant opened and,

x denotes the average number of nightly customers.

We have to discover the number 120 in the equation indicate in this context.

On analogizing provided equation with  we have;

m=5

b= 120

means y(0) = 120

and

Thus, The number 120 symbolizes  the restaurant that has been open for 120 months.

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The solution of the system of linear inequalities is the intersection of both graphs and the coordinates of the intersection are neither at pair 1 nor at pair 2.

According to the mathematical definition of inequality, neither side is equal. When a relationship leads to a non-equal comparison between two expressions or numbers, it is known as an inequality in mathematics. The equal sign "=" in this statement can be replaced with any of the inequality symbols, such as greater than (>), less than (<), greater than or equal to (≥), less than or equal to (≤), or not equal to (≠).

Given the graph for a system of linear inequalities,

the shaded region for the inequalities is below the dashed line,

for the solution of the system of linear inequalities,

the point where both the pair of lines intersect is the solution of the equations,

the equation for a dashed line from the graph is y < - x - 2

and the equation for the second line is y ≤ x/2 + 5

from the graph, the intersection point does not lie on any of the given pairs.

Hence the solution of  the system of linear inequalities neither at Pair 1 nor at Pair 2

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The inverse of y = 3x is f⁻¹(x) = 1/3x.

The inverse is a function or an operation which reverses the order of operation of another function or an operation”.

There are a few steps to find the inverse of a number:

We will be using the concept of inverse function to solve this.

Given that, y=3x

Let f(x) =y=3x

Switch x and y

x=3y

Express y in terms of x.

y = 1/3x

From the definition of the inverse function. f(x)=y⇒x=f⁻¹(y)

⇒ f⁻¹(y)=1/3x

Thus, the inverse of y = 3x is f⁻¹(x)=1/3x.

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A point (x1, y1) is said to satisfy the inequality ax + by ≤ c if a(x1) + b(y1) ≤ c. The graph of a linear inequality is the set of all points in the plane which satisfy the inequality.

Now, the given equation is 2x + 3y ≥ 6

We can find multiple points (x, y) that satisfy the given inequality. For now, we can take the point (1,2).

To check if (1,2) satisfies the inequality, put x = 1, y = 2 in the inequality.

2 + 6 ≥ 6

8 ≥ 6, which is true.

This line cuts the plane in half. One half contains all points (x, y) with 2x + 3y > 6 and the other half contains all points with 2x + 3y < 6.

To find which half is which, we need only check one point on one side of the line. (if the line does not cut through (0, 0), we can check that point easily.) In this case we find that 2(0) + 3(0) < 6.

Therefore the solution to the inequality 2x + 3y ≥ 6 is the half plane not containing (0, 0) shaded below. We can also represent it with arrows as in the diagram on the right.

Since the region includes the points along the line 2x + 3y = 6, we draw a

solid line. We use a dotted line when we want to indicate strict inequality as in the solution set to 2x + 3y > 6 shown in the diagram.

Thus, this is the boundary line for the given inequality.

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Answer:

Option 3 [tex]f(x) = 1,000 x (1.12)^{x}[/tex]

Step-by-step explanation:

The Product of two mixed fractions is always greater than 1.

Now, According to the question;

1. Convert the mixed number into an improper fraction.

2: Multiply the numerators of the fraction and multiply the denominators of the fraction.

3: Convert it into simplified form if required.

A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.

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The expression can be simplified to:

(m^2 + 1 - m^2 - 2m + m^2 + 2m + 1) / (m^2 + 1) + 4m / (m^2 + 1)

= (4m) / (m^2 + 1)

So the final simplified form of the expression is (4m) / (m^2 + 1)

Answer:

the picture is blurry I can not see the question to help you!

The equation that relates the number of coins, y, in Janice's collection x months since she started adding to her collection is y = 26 + 5/3 x In the context of this problem, the y-intercept is the initial number of coins that Janice had in her collection while the slope is the rate at which Janice is adding to her collection which is 5/3.

Part A

The equation for the number of coins, y, in Janice's collection x months since she started adding to her collection is the total amount of coins she has and can be expressed as

y = 26 + 5/3 x

where y is the total number of coins, and x is the number of months.

Part B

The y-intercept of the equation is the point where the line of the equation crosses the y-axis. In this case, the y-intercept is the point (0,26) which means that when x = 0, the number of coins in Janice's collection is 26. This is the initial number of coins that Janice had in her collection before she started adding to it.

The slope of the equation is the rate of change of the dependent variable (y) with respect to the independent variable (x). In this case, the slope of the equation is 5/3, which means that for every 3 months that pass, the number of coins in Janice's collection increases by 5. So the slope is the rate at which Janice is adding to her collection.

The problem seems incomplete. It must have been

"Janice has a coin collection that began with 26 coins. Since then, she has been adding to her collection at a rate of 5 coins every 3 months. Part A Write an equation that relates the number of coins, y, in Janice's collection x months since she started adding to her collection. ​ ​ ​Part B ​ ​In the context of this problem, interpret and explain the y-intercept and slope of the graph of the equation."

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5. 70

6. not sure sorry :/

45 is not a perfectly square, its square root is irrational. Because it cannot be written as the product of two integers of equal value, 45 is not a perfect square number.

Let's learn what the square root means before we get started. The mathematical concept of the square root is represented by the symbol. Any square root-related problem can be solved once you understand the fundamentals of the process. We will learn about the square root of 45 in this brief lesson. Methods like prime factorization and division will be used to accomplish this, as will the square root of 45.

45/square root: 45 x 6.708 is the square of 45: 452 = 2025

We are aware that the opposite of addition is subtraction, and the opposite of division is multiplication. Similar to squaring, finding the square root is the opposite of squaring. The number that is obtained when 45 is multiplied by itself is the square root of 45. Therefore, we must choose a number whose square is 45. As can be seen, there is no integer whose square is greater than 45. The number that is multiplied by itself to yield the original number is known as its square root. The number 6.7082039325 is 45 times squared.

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If ∡DAB and ∡DCB are right angles and m∡ABD = 42°, then the measure of arc ACB is 264°.

What is an arc?

An "arc" in mathematics is a straight line that connects two endpoints. An arc is typically one of a circle's parts. In essence, it is a portion of a circle's circumference. A curve's arc is a component.

The angles ∡DAB and ∡DCB are right angles.

The measure of ∡ABD = 42°

It can be seen that ∠ABD is inscribed angle of arc AD, so the measure of arc AD is two times the measure of ∠ABD.

AD = 42° × 2 = 84°

It can also be seen that segment DB is diameter of given circle as inscribed angle of diameter is a right angle.

Since segment DB is diameter of given circle, so measure of arc DCB would be equal to half the measure of 360 degrees.

DAB = 360°/2

DAB = 180°

ACB = AD + DCB

ACB = 84° + 180°

ACB = 264°

Therefore, the measure of arc ACB is 264°.

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On solving the linear equations 2x + y = 5 and 3x - 2y = 4 we get x = 2 and y = 1.

Linear equations are the equations of degree 1. It is the equation for the straight line. The standard form of linear equation is ax+by+c =0, where a ≠ 0 and b ≠ 0.

The set of equations given are linear equations that can be solved simultaneously to find the values of variables x and y.

2x + y = 5------->(1)

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

Multiply equation (1) by 2 and add to equation (2)

4x + 2y = 10

3x -  2y =   4

7x + 0  = 14

7x = 14

x = 2

Substituting x = 2 in (1) we get

2(2) + y = 5

y = 5 - 4 = 1

y = 1

Therefore on solving the system of linear equations simultaneously the values of x and y obtained are 2 and 1 respectively.

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9 types of solution are gas in gas, liquid in liquid, solid in liquid, solid in solid, gas in liquid, liquid in gas, solid in gas, gas in solid and supercritical fluid.

There are many different types of solutions, but here are 9 common types with examples:

Gas in gas: air (a mixture of gases)

Liquid in liquid: oil and vinegar salad dressing

Solid in liquid: sugar in water

Solid in solid: alloy of gold and silver

Gas in liquid: carbonated water

Liquid in gas: fog (water droplets in air)

Solid in gas: smoke (solid particles in air)

Gas in solid: a gas bubble in a solid piece of plastic

Supercritical fluid: carbon dioxide in a supercritical state (above its critical temperature and pressure)

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