How to solve systems of linear equation in two variables by substitution?.

The roots of the quadratic equation are x and if they are the values of x that fulfill the quadratic equation. The equation (-b(b2-4ac))/2a yields roots. The discriminant determines the kind of roots.

Mathematical algebra includes solving quadratic equations. The equations that have at least one term that is squared or in square form are known as quadratic equations. The equation of the second degree is another name for quadratic equations.

The standard form of the quadratic equation is ax2 + bx + c = 0, where a, b, and c are real numbers or constants that do not equal 0, and x is an unknown variable whose value can only be determined by solving the equation using a variety of methods for solving quadratic equations. The two powers of x are equal to the square on x, and the nature of the roots can be real, estimated, or assumed.

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The missing length is 14 yards from the given figure.

What is Quadrilateral ?

A quadrilateral is a closed form and a form of polygon that has 4 sides, 4 vertices and 4 angles. it's miles formed via joining four non-collinear points. The sum of indoors angles of quadrilaterals is continually identical to 360 tiers.

The word quadrilateral is derived from the Latin phrases ‘Quadra’ which means four and ‘Latus’ means ‘sides’. It is not essential that every one the four aspects of a quadrilateral are equal in length. therefore, we are able to have distinct kinds of quadrilaterals primarily based on aspects and angles.

Given ,

from the figure,

It was mentioned to find the missing length

As when we add up two sides we get the missing length from the given figure.

missing length = 9 + 5

missing length = 14 yards.

So, missing length is 14 yards

Therefore, the missing length is 14 yards from the given figure.

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The reflection and after that the dilation of triangle ABC is correctly represented by,

⇒ Triangle ABC is reflected across line m and then is dilated to form smaller triangle A double-prime B double-prime C double-prime.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

Triangle ABC was reflected over line m, then dilated by a scale factor between 0 and 1.

Now, After the reflection, the triangle will be inverted and the measure of angle: A should be equal to A", B should be equal to B", and C should be equal to C".

Now, The dilation factor is less than 1 and greater than 0. So, the reflected triangle should shrink its size.

Therefore, The reflection and after that the dilation of triangle ABC is correctly represented by,

⇒ Triangle ABC is reflected across line m and then is dilated to form smaller triangle A double-prime B double-prime C double-prime.

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A horizontal line at y=4 has the following formula: Nothing slopes. The y-intercept is at 4.0.

What are the intercepts and slopes?

The slope or gradient of a line in mathematics is a numerical representation of the steepness and direction of the line.

The slope conveys how quickly the dependent variable shifts in response to changes in the independent variable. Mathematicians and economists frequently use the Greek capital D or D to denote change. The change in the horizontal axis, x, is contrasted with the change in the vertical axis, y.

Negative values are below the origin on the x-axis and to the left of the origin on the y-axis. If the y-coordinate is negative, go downhill; if the x-value is negative, start at the origin and travel to the left.

Line graphs, often referred to as XY graphs, are used to graphically display data (the results of an experiment) to show how multiple aspects, such as time and the severity of the disease, are related.

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Answer: $22.5

Step-by-step explanation:

refer to the image to see the steps and explanation

A formula with just one phrase where the unknown is squared and no terms where the unknown is raised to a power greater than 2 assumed: 3x* + 2kx+ 3= when compared to the quadratic equation ax2 + bx + c = 0, a = 3 b= 2kc= 3.

Given that the equation's roots are genuine and equal D=0 Discriminant, hence D = b2 - 4ac = 0 (2k) - 4.3.3 = 0 4k -36 = 0 4k -36 = 0 4k2 = 36 k'=9 taking square root on both sides k=3 or k=-3 as a result, the roots of the quadratic equation are real and equal for the values of k of 3, and -3.

When a polynomial is evaluated at x=2, the outcome is zero if the polynomial is divisible by (x-2). Therefore, we can substitute x = 2 into the polynomial 2kx-kx-8 and solve for k to find the value of k.

2k(2)^-k(2)-8 = 0 2

k(0.25) - 8 =0\s

k(0.25) = 8\sk=32 = 4

Therefore, k must be equal to 4 for the polynomial 2kx-kx-8 to be divisible by (x-2).

Complete question:

What is the value of K in the polynomial 3x2 2kx 3 The roots of the quadratic equation 3x2 2kx 27 are real and equivalent.

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The value of k when x = (-1/2) is a solution of the quadratic polynomial 3x² + 2kx - 3 = 0 is -2.

To find the value of k, we can substitute the value of x = (-1/2) into the equation and solve for k. So, we have:

3 * (-1/2)² + 2k * (-1/2) - 3 = 0

Expanding the square and substituting the value of x gives us:

-3/4 + k * (-1/2) - 3 = 0

Simplifying the left-hand side of the equation gives us:

k * (-1/2) = 3/4 + 3

Finally, solving for k by dividing both sides by -1/2 and simplifying gives us:

k = -2

Hence, the value of k when x = (-1/2) is a solution of the quadratic equation 3x² + 2kx - 3 = 0 is -2.

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Complete Question:

If x=(− 1/2), is a solution of the quadratic equation 3x^2 +2kx−3=0, find the value of k.?

Answer:  I think that the answer for that is fh

Step-by-step explanation:

Polynomials can be simplified by applying the distributive property to multiply the term outside the parentheses by everything inside the parentheses.

The highest degree of terms is written first, followed by the next degree, and so on, to represent a polynomial in standard form. The standard form of the polynomial is f(x) = anxn + an-1xn-1+an-2xn-2+.....+a1x+a0

An expression made up of variables, constants, and exponents that are joined together via mathematical operations is referred to as a polynomial.

A polynomial must be simplified in two ways: Firstly, combine similarities, and secondly, rewrite the terms in descending order of exponent. A polynomial can be written in standard form. To write any polynomial in standard form, consider the degree of each term. Then, from highest to lowest, left to right, you write each term in order of degree.

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The equation to determine the length and width of the rug is

28 = w² + 12w

Since, the shape of the rug is rectangle, therefore area of rectangle has been used to obtain the solution.

What is a rectangle?

Rectangle is a flat, two-dimensional shape, having four sides and vertices with opposite sides being equal and parallel. We may easily represent a rectangle in an XY plane by using its length and breadth as the arms of the x and y axes, respectively.

Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.

We are given a rectangular rug with an area of 28 square feet.

Also, the rug is 12 feet longer than it is wide.

So,

Let 'l' be the length of the rug and 'w' be the width of the rug

As given, Length is 12 feet longer than its width

Therefore, l = w + 12

We know Area of rectangle = Length * Width and area is given to be 28 square feet.

So,

⇒28 = (w + 12)w

⇒28 = w² + 12w

Hence, the equation to determine the length and width of the rug is

28 = w² + 12w.

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Question: Tammy has a rectangular rug with an area of 28 square feet. The rug is 12 feet longer than it is wide.

Create an equation to determine the length and the width of the rug.

The number that represents Six times a number is at least four less than eight times the number is the expression 6x ≥ 8x - 4.

What is system of equations?

A system of equations, also referred to as a set of simultaneous equations or an equation system, is a finite set of equations for which we searched for the common solutions. Similar to single equations, a system of equations can also be categorised. In everyday life, systems of equations are used to model situations where the unknown values can be represented by variables.

A system of equations is made up of two or more equations with the same variables. A solution to an equation system is the point at which the lines intersect.

According to given question, x represents the number

So, The number would be 6x ≥ 8x - 4

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In summary, the upper and lower bounds for the volume of the box are:

Upper bound: 382.125cm³

Lower bound: 238.375cm³

The volume of the box is calculated by multiplying the length, width, and height together. In this case, the measurements of the box are given as 10cm x 7cm x 4cm, so the volume of the box is:

volume = 10cm x 7cm x 4cm = 280cm³

However, since the measurements are given to the nearest centimeter, there is a slight degree of uncertainty in the exact measurements of the box. To calculate the upper and lower bounds for the volume of the box, we need to consider the possible variations in the measurements.

The upper bound for the volume would be calculated by taking the highest possible measurements for each dimension. So, if the length could be as much as 10.5cm, the width could be as much as 7.5cm and the height could be as much as 4.5cm. Then the upper bound for the volume would be:

Upper bound = 10.5cm x 7.5cm x 4.5cm = 382.125cm³

The lower bound for the volume would be calculated by taking the lowest possible measurements for each dimension. So, if the length could be as little as 9.5cm, the width could be as little as 6.5cm and the height could be as little as 3.5cm. Then the lower bound for the volume would be:

Lower bound = 9.5cm x 6.5cm x 3.5cm = 238.375cm³

In summary, the upper and lower bounds for the volume of the box are:

Upper bound: 382.125cm³

Lower bound: 238.375cm³

And the exact volume is 280cm³

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The dot plot that represents the data for pulse rate of some cattle at a farm is shown in the image below.

A dot plot, also known as a strip plot or dot chart, is a simple form of data visualization that consists of data points plotted as dots on a graph with an x- and y-axis

How to Construct a Dot Plot?

Given the data as: 65, 68, 69, 67, 69, 68, 65, 69, 65, 68, 67, 69, 68, 67, 67, 69, find the frequency of each data point in the data set as shown below:

65 - 3

67 - 4

68 - 4

69 - 5

Use dots to represent the frequency of each data point.

Thus, the dot plot that represents the data is shown in the image below.

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The most are $13.75 if she wants to give all of her friends a gift.

Ryan has an $800 present budget. She had already made up her mind to use $25 to buy her granny a vehicle. The remaining funds will be used to buy gifts for her four friends. She will invest the same sum of money in each present for a buddy.

Okay, so she would have 55 dollars left over after spending 25 of her 80 dollars.

She will distribute her 55 bucks among her four buddies equally now that she has them.

55/4 = 13.75

She could only afford to offer them a maximum of $13.75

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Answer:

Father:42

Son:18

Step-by-step explanation:

Present ages are father 48–6= 42

son = 24 ‘6 = 18

The solution of |( 2x-3 )|= 7 is 5.

|(2x – 3)| = 7

2x = 7+3

2x = 10

x=5

In arithmetic, an equation is a system that expresses the equality of two expressions, by connecting them with the equals signal =. The phrase equation and its cognates in different languages may additionally have subtly one-of-a-kind meanings; as an example, in French, an équation is defined as containing one or more variables, whilst in English, any well-formed method together with expressions associated with an equals signal is an equation.

solving an equation containing variables includes figuring out which values of the variables make the equality real. The variables for which the equation must be solved are also called unknowns, and the values of the unknowns that fulfill the equality are called answers to the equation. There are kinds of equations: identities and conditional equations. An identity is real for all values of the variables. A conditional equation is handiest authentic for particular values of the variables.

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Complete Question:

What is the solution of |( 2x-3 )|= 7?

Answer: option 1

Step-by-step explanation: as when you try to simplify you get the values in option 1

Answer: 1

Step-by-step explanation:

In  such cases, the median may give a better idea about the central part of the distribution. In case of a skewed distribution like seen in case of wage distribution ,

income distribution, wealth assessment, mean loses its representation of the data.

Moreover, in case of qualitative data or for any ordinal data where the variable under question is not directly measurable, say when you are trying to measure intelligence, honesty, color, median would be a good choice to represent that data.

We can find the median of class 10 through class frequency C.f. (CUMULATIVE FREQUENCY)

0to10. 3. 3

10 to 20. 7 10

20to 30. 10 20

30 to 40 8 28

40 to 50. 6. 34

Total. 34

N=34

N/2 = 34/2 =17

MEDIAN class=20 to 30

C =10

L lower boundary of MEDIAN class =20

f=10

m=10

MEDIAN =L +( N/2 -- m) ×c) /F

=20+ (17-10)×10. /10

= 20+ 7=27

MEDIAN=27

It is known that median is a positional average such that you consider the number of observations above and below are almost equal hence it is not damaged by extreme values unlike in the case of mean where it is damaged the most.

In brief, for any qualitative data or in case of numerical data where the distribution is skewed, Median is the most taken average.

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Answer:

Step-by-step explanation:

In  such cases, the median may give a better idea about the central part of the distribution. In case of a skewed distribution like seen in case of wage distribution , income distribution, wealth assessment, mean loses its representation of the data.

Moreover, in case of qualitative data or for any ordinal data where the variable under question is not directly measurable, say when you are trying to measure intelligence, honesty, color, median would be a good choice to represent that data.

We can find the median of class 10 through class frequency C.f. (CUMULATIVE FREQUENCY)

0to10. 3. 3

10 to 20. 7 10

20to 30. 10 20

30 to 40 8 28

40 to 50. 6. 34

Total. 34

N=34

N/2 = 34/2 =17

MEDIAN class=20 to 30

C =10

L lower boundary of MEDIAN class =20

f=10

m=10

MEDIAN =L +( N/2 -- m) ×c) /F

=20+ (17-10)×10. /10

= 20+ 7=27

MEDIAN=27

It is known that median is a positional average such that you consider the number of observations above and below are almost equal hence it is not damaged by extreme values unlike in the case of mean where it is damaged the most.

In brief, for any qualitative data or in case of numerical data where the distribution is skewed, Median is the most taken average.

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Answer:

  1/5

Step-by-step explanation:

You want the slope of line AB, given A(-2, 2) and B(3, 3).

The slope is given by the formula ...

  m = (y2 -y1)/(x2 -x1)

  m = (3 -2)/(3 -(-2)) = 1/5

The slope of the line AB is 1/5.

__

Additional comment

You can also find the slope by counting the grid squares. Point B is 1 up and 5 over from point A, so the slope is rise/run = 1/5.

The statue of the cat is 14 meters tall.

If the ladder is 6 meters tall and it casts a shadow that is 3 meters long and the statue of a cat casts a shadow that is 7 meters long, then we can use the concept of similar triangles to determine the height of the statue of the cat.

The ratio of the height of the ladder to the length of its shadow is 6/3 = 2.

We can also assume that the ratio of the height of the statue of the cat to the length of its shadow is also 2.

so, the height of the statue of the cat can be calculated by:

height of statue of the cat = (2 * shadow length of the statue of the cat) = (2 * 7) = 14 meters

Therefore the statue of the cat is 14 meters tall.

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Answer:

We can use the chain rule to find the derivative of y with respect to x.

The chain rule states that if y = f(u) and u = g(x), then dy/dx = dy/du * du/dx

y =sin x sec (90-x)

dy/dx = cos x sec (90-x) * d/dx(sec (90-x)) - sin x tan (90-x) sec (90-x) * d/dx(90-x)

let us calculate the second derivative

du/dx = -cos(90-x)

d²y/dx² = -sin x sec (90-x) * cos (90-x) - cos x tan (90-x) sec (90-x) * cos (90-x) - cos x sec (90-x) * (-sin (90-x))

= -sin x sec (90-x) * cos (90-x) - cos x tan (90-x) sec (90-x) * cos (90-x) + cos x sec (90-x) * sin (90-x)

= -sin x sec (90-x) * cos (90-x) + cos x tan (90-x) sec (90-x) * sin (90-x)

= -(sin^2 x + cos^2 x) sec (90-x) tan (90-x)

= -sec^2 (90-x) tan (90-x)

So, the value of the second derivative of y with respect to x is -sec^2 (90-x) tan (90-x)

Step-by-step explanation:

The 45-45-90 triangle has two congruent sides and one right angle, with each angle measuring 45°. The sides are perpendicular to each other and the length of the hypotenuse is equal to the square root of 2 times the length of a leg.

The 30-60-90 triangle has one right angle and two sides that are proportional. The shortest side is half the length of the hypotenuse and the middle side is equal to the shortest side times the square root of 3. The two acute angles in the triangle measure 30° and 60°, respectively.

In conclusion, both 45-45-90 and 30-60-90 triangles are special right triangles with distinct relationships between their sides and angles.

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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Answer:

a) Tandeka will be in the middle of a circuit as the time runs out.

b) Tandeka began the last circuit after 7 minutes.

c) Lerato played 2 more games than Tandeka.

Explanation:

a) To determine which player will be in the middle of a circuit when the 12 minutes are up, we need to figure out which player completes the most circuits in 12 minutes. We can use the formula: time available / time per circuit = number of circuits completed. In this case: 12 minutes / 2 minutes per circuit = 6 circuits for Lerato, 12 minutes / 3 minutes per circuit = 4 circuits for Jarrod, 12 minutes / 4 minutes per circuit = 3 circuits for Ian, 12 minutes / 5 minutes per circuit = 2.4 circuits for Tandeka. Tandeka completes 2 full circuits, and starts the third one, hence she will be in the middle of a circuit when the time runs out.

b) To determine when Tandeka began the last circuit, we need to figure out how many minutes were left when she completed the second circuit. We know that Tandeka completes 2 full circuits in 10 minutes (2 x 5 minutes). So, the last circuit starts after 12 minutes - 10 minutes = 2 minutes

c) To determine how many more games Lerato played than Tandeka, we can subtract the number of games Tandeka played from the number of games Lerato played: 6 games - 4 games = 2 games.

Step-by-step explanation:

The ounces of the watermelon sugar scrub per dollars is 1.1 ounces per dollars.

The store charges $12.65 for a 14 oz container of watermelon sugar scrub. The amount in ounces of watermelon sugar scrub per dollars can be calculated as follows:

12.65 dollars = 14 ounces

1 dollars = ?

cross multiply

Hence,

amount of ounces of watermelon sugar scrub per dollars  = 14 × 1 / 12.65

amount of ounces of watermelon sugar scrub per dollars  = 14/ 12.65

amount of ounces of watermelon sugar scrub per dollars  = 1.10671936759

amount of ounces of watermelon sugar scrub per dollars  = 1.1 ounces per dollars

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Answer:

side length of square C is 5 ft

Step-by-step explanation:

A, B andC are the areas of the sides of a right triangle.

C is the square on the hypotenuse of the right triangle.

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

C² = A² + B² = 9 + 16 = 25 ft²

the area of a square is  s² , where s is the side length, then

s² = 25 ( take square root of both sides )

s = [tex]\sqrt{25}[/tex] = 5 ft

The one-to-one function is also called the injective function.

The one-to-one function is a special function that maps every element of the range to exactly one element of its domain.

we can define one to one function as:

function g: D -> F is said to be one-to-one if

g(x₁) = g(x₂)

⇒ x₁=x₂

for all elements x₁ and x₂ ∈ D., A one-to-one function is also considered an injection, a function is injective only if it is one-to-one.

There are some examples of injective functions:

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The factors of 50 are the natural numbers that divide the original number, evenly. They are 1,2,5,10,25 and 50.

Herbal numbers are a set of fine integers, frequently used for counting and ordering. They consist of the numbers 1, 2, 3, four, 5, and so on. The set of natural numbers is denoted by way of the symbol N. they are also called counting numbers. natural numbers are used in lots of regions of arithmetic, inclusive of number concepts and combinatorics.

They play a critical function in the look at algorithms and information structures. moreover, herbal numbers are used in lots of areas of physics and engineering, inclusive of the look at vibrations and waves. They may be also used in laptop technological know-how and programming, where they are regularly used to symbolize the number of objects in a listing or array. natural numbers are an essential idea in arithmetic, and they may be used in many areas of technological know-how, technology, and normal existence.

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The expression that represents the height of the cylinder in terms of its radius is 3r - 5.

The cylinder's radius is specified in "r" units.

So, In comparison to its radius, r, a cylinder's height, h, is five units less.

The radius times three will be denoted by the unit "3r."

and

The radius reduced by 5 units will be shown as "3r - 5" units.

The height "h" of the cylinder is equal to 5 units less than 3 times the radius, hence the final equation is,

h = 3r-5

Thus, the expression representing the height of the cylinder in terms of the radius is h = 3r-5

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The solution set of the inequality x - 2 × + 3 > 0 is (-Infinity,3) U (-2,infinity).

What is inequality?

An inequality is a mathematical statement that represents a relationship between two values that are not equal. It uses symbols such as < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), to describe the relationship between the values.

Isolate the variable x:

x - 2 × + 3 > 0

x - 2 × + 3 - 3 > 0 - 3

x - 2 × > -3

Divide both sides by -2 and reverse the inequality sign:

(x - 2 ×)/(-2) < (-3)/(-2)

x - 2 × < 3

x > 2 × + 3

Test values of x to see which ones make the inequality true:

If x is less than -2, the inequality is false.

If x is between -2 and 3, the inequality is true.

If x is greater than 3, the inequality is false.

So the solution set of the inequality x - 2 × + 3 > 0 is (-Infinity,3) U (-2,infinity).

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The equivalent function when the number of bacteria in a lab experiment can be modeled by the function is P(t) = 1161(9)^t

A function illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the situation.

Here, we are given that the number of bacteria in a lab experiment can be modeled by the function given as P(t) = 43(39^(2t + 3)

This will be:

= 43 × 3³ × 3(^2t)

= 1161 × 3²^t.

P(t) = 1161(9)^t

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