Worksheet fun balancing equations

The number of hats that Leah had on Monday, given that half the hats were destroyed and four hats were bought, was, A. 22 hats.

If half the hats that Leah owns were destroyed on Wednesday such that only 13 hats were left, then it means that the total hats before the destruction, was :

= 13 hats x 2

= 26 hats

Seeing as Leah bought four hats on Tuesday, this means that the hats she had on Monday were :

= Total hats - Hats purchased on Tuesday

= 26 - 4

= 22 hats

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Answer:

probably 21

Step-by-step explanation:

The factor of expression 3x² 12xy is 3x². To find the factor, we need to divide 12xy by 3x². We start by dividing the coefficients, 12 divided by 3 is 4. Then we divide the x terms, x divided by x is 1. Finally, we divide the y terms, y divided by y is 1. Therefore, the factor of 3x² 12xy is 3x².

The factor of  expression 3x² 12xy is 3x². To find the factor, we need to divide 12xy by 3x². We start by dividing the coefficients, 12 divided by 3 is 4. Then we divide the x terms, x divided by x is 1. This means that the x part of the factor is 3x. Next, we divide the y terms, y divided by y is 1. This means that the y part of the factor is y. When we combine the two parts, 3x and y, we get the factor of 3x². Therefore, the factor of 3x² 12xy is 3x². This means that 3x² is a factor of 12xy, which can be seen by multiplying 3x² by 4y, which results in 12xy. This shows that 3x² is a factor of 12xy.

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If the horizontal distance between Tyler and the kite is 600 feet then the kite is 80 ft above the ground.

Pythagoras's Theorem is a fundamental result in Euclidean geometry that states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. This can be mathematically represented as:

[tex]c^2 = a^2 + b^2[/tex]

Where c is the length of the hypotenuse, and a and b are the lengths of the legs of the triangle.

The theorem is named after the ancient Greek mathematician Pythagoras, who by tradition is credited with its discovery and proof, although it is often argued that the theorem may have been known to the Babylonians and Indians over a thousand years earlier.

Pythagoras's theorem is widely used in mathematics and physics, especially in trigonometry and in the study of triangles and their properties, and it's also used to find the distance between two points in a two-dimensional space, for example, in cartesian coordinates.

Hypotenuse2 = Perpendicular2 + Base2

c2 = a2 + b2  

We apply the Pythagorean Theorem to determine the kite's height, h

the problem can solve if the kite is 60feet

[tex]h^2 = 100^2 - 60^2\\h^2 = 10000 - 360\\h^2 = 6,400\\h=\sqrt{6400} \\h=80[/tex]

h =80 ft (we take the positive solution since the height can not be negative number)

The kite is 80 ft above the ground.

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Straight line has the equation is, y = 5x - 4.

An endless number of points that are connected on both sides of the point make up a straight line.

The slope of a straight line, "m," is determined by:

m = y2 - y1 / x2 - x1

A linear equation has the expression y = mx + b in slope-intercept form. X and Y are the variables in the equation. The numbers m and b stand for the line's slope (m) and the value of y at x = 0.

The graph's acquired points are (0,-4) and (1,1)

The slope is ,

m = 1-(-4) / 1-0

  = 5/1

  = 5

The line's equation will be as follows since it crosses the y-axis at its intersection point, where C = -4.

⇒ y = mx + c

⇒ y = 5x + (-4)

⇒ y = 5x - 4

As a result, y = 5x - 4 is the equation for the straight line depicted below.

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The distribution has the greatest spread is

The term standard deviation refers to a measurement of the data's dispersion or spread from the mean.

A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed or spread out.

In the given problem the distribution that has a higher value of standard deviation is the one that has the highest spread spread

This is distribution 3 with a standard deviation of 7.2

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Answer:

6-L2

10-hypotenuse

Step-by-step explanation:

Pythagorean theorem

Therefore .as a result the supplied linear equation problem's solution is shown to be a linear equation with two variables.

Any model that meets the algebraic equation y=mx+b is said to be linear. B is the slope, and m is the y-intercept. Since both y and x are distinct factors, the preceding sentence is commonly referred as a "mathematical model with two variables." Two-variable linear equations are referred to as bivariate equations. There are several applications for linear equations, all of which end in zero. If an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept, it is classified as linear. The equation is written as Y=mx+b, where m denotes the slope and b

Here,

Assumed: 2x + 3Y = 0.

As a result, the following equation can be used to determine whether it is linear in two variables.

As x is the sole variable, as can be seen.

Therefore, it is a two-variable linear equation.

As a result, the supplied linear equation problem's solution is shown to be a linear equation with two variables.

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If you solve the equation and get the same number as yourself, there are infinite solutions, and if you get the wrong equation, there is no solution.

You can see that both slopes are the same (-3). This shows that the lines are parallel without creating a graph. Therefore, the system of equations cannot be solved.

What distinguishes infinitely many solutions from zero? If the equation is wrong, the system has no solution. If the equation statement is true, there are infinitely many solutions.

A linear algebra problem is a linear system of n equations with n unknown variables. A system may have one solution, no solution, or an infinite number of solutions.

solution - all linear equations intersect or intersect at some point in space

No Solution - System is inconsistent and not all linear equations intersect or intersect.

Infinitely many solutions - some linear equations are the same line in space, some variables are unbounded.

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The coefficient of the variable x² in the expression 3x+5 is 0

Given that,

The expression is 3x+5

To find : The coefficient of the variable x² in the expression

Coefficient is the number that is beside the variable in the equation.

The coefficient of x in 3x+5  is 0

A number multiplied by a variable is referred to as the coefficient of a number. For instance, the x2 coefficient in the formula 6x2+99 is 6

As we can see that the term that is in multiplication with x²  is 3.

Hence, the coefficient of x²  in the equation 3x+5  is 0.

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The area of rectangle with side whole number = ab sq. units,

and area of rectangle with fraction side = ac/bd sq. units.

A quadrilateral with four right angles is a rectangle. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal (360°/4 = 90°). A square is a rectangle with four equally long sides.

Given  to find the area of rectangle,

Area of rectangle is given by product of length and width.

A = l x b

Let the dimensions of a rectangle are all whole numbers, a by b

Area = a x b

A = ab sq. units

another rectangle with dimensions all fractions say, a/b by c/d .

Area = a/b x c/d

A = ac/bd sq. units

In all situations, the area of the rectangle must be calculated by multiplying its length and breadth.

Hence the area of rectangle is product of length to width in both cases.

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Answer:

Degree: 4

Number of terms: 4

Leading Coefficient: 4

Constant: -20

Step-by-step explanation:

1) Expand (x+3)(x-4) into x^2 - x - 12

2) Combine like terms; equation becomes 4x^4 + x^2 + 4x - 20

3) Degree is looking for the highest exponent; in this case, it's 4

4) Number of terms is looking for how many terms there are in this equation; there are 4 terms

5) Leading Coefficient is looking for the coefficient of the term with the highest exponent, so the answer is 4

6) Constant is looking for the term without a variable

Hope this helps!

The student population in the school can be modeled using an exponential function of the form:

P(t) = 2,035 * 1.03^t

where P(t) is the student population t years from now, and 1.03 is the factor by which the population increases each year.

To predict the number of students in the school after five years, we can substitute t = 5 into the function:

P(5) = 2,035 * 1.03^5

= 2,035 * 1.1895

= 2,408.76

Thus, there will be approximately 2,408.76 students in the school after five years.

The work done on the toy car is 164.4 J.

The formula for work is:

Work = force * distance

In this case, given that:

Force = 5.2 N

Distance = 32 m

So, the work is:

Work = force * distance

Work = 5.2 * 32

Work = 166.4 J

Hence, the work done is 164.4 J.

Force is described as the rate of change of momentum with respect to time, in which momentum is mass multiplied by velocity. Work is the product of displacement and the component of force in the direction of displacement. When work is done, then the kinetic energy of an object changes.

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Comparing the volume of the paints used and analyzing the proportions, The answer is Tina's shade is more blueish and Tyler's shade is more greenish.

A ratio is a way to compare two or more numbers or amounts. It tells you how much bigger or smaller one number is compared to the other. It is often written as two or more numbers separated by a colon, such as "3:5" or "2:4:6". For example, if a recipe calls for 2 cups of sugar to 4 cups of flour, the ratio would be 2:4. This means for every 2 cups of sugar, there are 4 cups of flour. It's a way to express a relationship between values or quantities and it helps to understand the proportion of one value to the other values.

Proportion is a relationship between two or more values or quantities that compares their sizes. It's a way of saying that two or more values are equal in some way. It can be written as an equation, such as "a/b = c/d", which means that the ratio of a to b is equal to the ratio of c to d. In other words, the proportion states that two or more ratios are equal to each other. For example, if a cake recipe calls for 2 cups of sugar to 4 cups of flour, the proportion would be 2/4 = 1/2. This means that for every 2 parts of sugar, there are 4 parts of flour, which can be written as a ratio 2:4 .

Tina's ratio of blue paint to green paint = 777:555

Tyler's favorite shade has a ratio =  555:777.

The ratio for Tina's shade is greater than 1 .

while the ratio for Tyler's shade is less than 1.

So Tina's shade is more blueish and Tyler's shade is more greenish.

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Answer:

y = 2x

Step-by-step explanation:

y = mx + b

m = 2

y-intercept = b = 0

y = 2x + 0

y = 2x

An interval in math is measured in terms of numbers. An interval includes all the numbers that come between two particular numbers.

An interval in math is measured in terms of numbers. An interval includes all the numbers that come between two particular numbers.

Interval notation is a simplified way of describing a particular interval. Let’s see how it’s done.

Step 1: We write the first and last number of the interval, which are the endpoints of the interval. For example, if the interval is from 6 to 20, we write 6, 20.

Step 2: We use a round or square bracket on each side of the two numbers. We use:

A square bracket [ ], if we want to include the endpoints

A round bracket ( ), if we don’t want to include the endpoints

So in this example, we use:

So, we can see that some intervals include the endpoints, some partially include them, and some do not include them. Based on this, there are three types of intervals

These are:

This type of interval does not include the endpoints. For example, (5, 10) does not include endpoints 5 and 10.

This type of interval includes the endpoints. For example, [4, 9] includes the endpoints 4 and 9.

This type of interval includes only one of the endpoints.

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You can differentiate best time, worst time and average time of an algorithm like this:

Best time = fastest completion time with optimal inputs.

Worst time = slowest completion time, with pessimistic inputs.

Average time = arithmetic mean

The average-case complexity of an algorithm is the amount of a computational resource (typically time) used by the algorithm, averaged over all potential inputs, according to computational complexity theory. The worst-case complexity, which takes into account the algorithm's maximum complexity given all potential inputs, is frequently contrasted with it.

There are three main reasons to investigate average-case complexity. First off, while some problems may be insurmountable in the worst case, the inputs that cause this behaviour may only occasionally occur in practise, so the average-case complexity may be a better indicator of an algorithm's performance.

Second, tools and techniques to create challenging problems are provided by average-case complexity analysis. These tools and techniques can be used in fields like derandomization and cryptography.

Third, average-case complexity enables the most effective algorithm in practise to be distinguished from algorithms with equivalent best case complexity.

What is average case complexity

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On solving the provided question, we can say that -  here in graph we have on solving equation [tex]x^2+ 3y^2 \\[/tex]  =  [tex]4+3 = 7[/tex]

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

here-

from graph, x= 2

y = 1

[tex]x^2+ 3y^2 \\[/tex]

[tex]4+3 = 7[/tex]

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Answer:

isosceles triangles have two congruent acute angles

Answer:

16.74

Step-by-step explanation:

-1.8 times -9.3 will have a positive answer because 2 negative numbers will have a positive sum

  -1.8

x -9.3

---------

    5 4

1 6 2 0

---------

1 6 7 4 ||| add two decimal spaces

16.74

The equation that represents the relationship of x number of badges to y dollars is y = 9x.

What is an equation?

A mathematical statement called an equation displays the equality of two mathematical expressions. Variables, coefficients, exponents, arithmetic operators, equal signs, and constants are some of the components that make up an equation.

 An equation is said to be linear if the maximum power of the variable is consistently 1.

Let the number of badges be x and the cost of x number of badges be y.

From the question, we know that for 48 badges, the cost is $432.

So the cost of one badge = 432/48 = $9

Now the cost of x number of badges = $(9x)

We mentioned in the beginning that the cost of x number of badges is y

Therefore the equation that represent the relationship of x badge to y dollars is,

        y = 9x

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y=0 is the linear equation to denote the x - axis, as all the points on the x- axis, have their y co-ordinate =0.

What is linear equation ?

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

Because the equation y=0 has a slope of 0, the resulting graph must be a straight horizontal line. This is true for all equations with a slope of 0.

Hence , y=0 is the linear equation to denote the x - axis, as all the points on the x- axis, have their y co-ordinate =0.

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The answers to each part is mentioned below.

The general equation of a straight line is -

y = mx + c

{m} - slope.

{c} - intercept along the y - axis.

Given is a straight line problem as shown in the question.

(a) -

Now, 12 oz of honey will cost $5.4. So, we can write that -

1 ounce of honey will cost - (5.4/12)

Cost of 1 oz honey will be - $(0.45)

(b) -

Now, 12 oz of honey will cost $5.4. So, we can write that -

For $1, you can buy - (12/5.4) oz of honey.

Amount of honey bought in 1 dollar - 2.22 ounces

(c) -

We can write the equation as -

c = 0.45h

(d) -

The graph for this function is attached with the answer.

Therefore, the answers to each part is mentioned above.

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The augmented matrix, however, is a two-by-four matrix because it also contains the constants.

The augmented matrix will always include one additional column for every additional variable, and the same number of rows as there are equations. An easier technique to write a set of linear equations is to utilize enhanced matrices.

In an augmented matrix, two sides of the matrix are separated by a vertical line that serves as a representation of a succession of equal signs. The collection of linear equations, for instance, would be represented by the matrix. There is only ever one pivot in a column.

For (c): Three rows and four columns make up the augmented matrix of this system. As a result, it only has three pivot points at most. Thus, a pivot column cannot be represented by a single variable.

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Answer:

What is the size of the augmented matrix for the linear system?

B) 2x3

Identify the values for the elements in the augmented matrix:

a11 =  3

a12 =  7

a13 =  20

a21 =  1

a22 =  -4

a23 = 9

Step-by-step explanation:

Answer:

4 prime numbers all divisible by 3

Step-by-step explanation:

there are 4 prime numbers between 20 and 40 23, 29, 31, 37 all divisible by 3

Answer:

7 integers

Step-by-step explanation:

We can find how many integers between 20 and 40 are divisible by 3 by looking at the multiples of 3 that lie between 20 and 40.

1: 3 * 7 = 21

2: 3 * 8 =24

3: 3 * 9 = 27

4: 3 * 10 = 30

5: 3 * 11 = 33

6: 3 * 12 = 36

7: 3 * 13 = 39

On solving the provided question, we can say that By percentage, the amount that will be covered in the insurance = $749

A percentage in mathematics is a figure or ratio that is stated as a the fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

By percentage.,

35% 0f 2140 =

35/100 X 2140 = 0.35*2140 = $749

the amount that will be covered in the insurance = $749

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Answer:

1/3 + 1/3 = (1+1)/3 = 2/3

1) 2/3

5/7 - 2/7 = (5-2)/7 = 3/7

2) 3/7

so all you have to do is add or sub the fractions together.

1/3 + 1/3 = 2/3

5/7 - 2/7 = 3/7

for the first box is 2/3

Second box is 3/7

GOODLUCK

No, Both will not have the same amount of comic books because they add the same number each month.

Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

Adrian started with 12 comic books and buys 4 more each month.

Rory started with 8 comic books and buys 4 more each month.

let x be the number of books.

A(x) = 4x+12

Rory starts with 8 comic books and add 4 comic books each month.

R(x) = 4x+8

Hence, Both will not have the same amount of comic books because they add the same number each month. There will be 4 additional comic books for Adrian.

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Answer:

x = 16/9

Step-by-step explanation:

9x -16 = 0

9x = 16

x = 16/9

Let's check

9(16/9) -16 = 0

144/9 - 16 = 0

16 - 16 = 0

0 = 0

So, x = 16/9 is correct!

Answer:

Step-by-step explanation:

9x = 16

x = 16/9