Jason's living room has 210 square feet of wall. How much wall is left to paint?

The length of the vegetable garden as a function of its length will be given as: y = 3x + 2

The expression of the garden width in terms of the width of the tomato patch is given as:

y = x + 5

Let the length of the garden be y

Let the length of the tomato patch be x

If Melissa wants the length of  the garden to exceed three times the length of the tomato patch by 2 feet, the length of the vegetable garden as a function of its length will be given as:

y = 3x + 2

Therefore, If she also wants the garden's width  to exceed the width of the tomato patch by 5 feet,  the expression of the garden width in terms of the width of the tomato patch is given as:

y = x + 5

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As per the given tax percentage, the sales tax is $3 and the total amount paid by the group including the tip is $47.25

Here we have given that the bill before sale tax and tip is $37.50.

Here we have know that there was a tax of 8%.

And the there was a tip of 18%.

As we all know that the tip is after the tax, then it's not going to affect it, and we can essentially ignore it.

Therefore here the real question here is just what is 8% of $37.50.

Now, here we have to find the percent of something, then first you need to put the percent as a decimal.

Then we get the 8% in decimal form is 0.08 where as 18% as 0.18

Now, we have to multiply the percent in decimal form by the number.

Then we get,

=> 37.50 dollars × 0.08 = 3 dollars.

=> 37.50 dollars × 0.18 = 6.75 dollars.

And the total amount pair is calculated as,

=> 37.50 + 3 + 6.75

=> 47.25

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The two main types of coordinate systems used in mathematics and physics are Cartesian and Polar Coordinates.

A coordinate system is a system used to identify and locate a point in space. It is the basis for maps, navigation and surveying. Coordinate systems can be two-dimensional or three-dimensional, and can use a variety of units such as latitude, longitude, and feet. Coordinate systems are used in a variety of fields such as engineering, architecture, geology, and navigation. Coordinate systems help to identify and locate points in space and are essential for charting and mapping the physical world.

Cartesian Coordinates, named after the French mathematician and philosopher René Descartes, use a two-dimensional plane to represent points with an x-axis and a y-axis. These coordinates are expressed as ordered pairs (x,y) and represent points in relation to the origin (0,0). This can be used to plot graphs and equations, and is the most commonly used coordinate system.

Polar Coordinates are based on a two-dimensional plane centered on a pole. Points are expressed as ordered pairs (r,θ) where r is the distance from the pole and θ is the angle from the polar axis. This coordinate system is useful for finding distances and angles in a circle. It is used frequently in physics and astronomy.

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A unbiased estimator is a statistic that accurately reflects the population mean, μ. A statistic is unbiased when the mean of its sampling distribution is equal to μ.

Mathematically, this can be expressed as:

E(x) = μ

Where E(x) is the expected value of x and μ is the population mean.

This means that if we take a sample from a population and calculate the mean from that sample, the expected value of that mean should be equal to the population mean. This can be seen in the following example:

Let's say we have a population with a mean of 30. We take a sample of size 5 from this population and calculate the sample mean, x. The expected value of x should be equal to 30. We can calculate this using the formula:

E(x) = ∑xi/n

Where xi are the values in the sample and n is the sample size.

For our example, E(x) = (30 + 30 + 30 + 30 + 30) / 5 = 30

This shows that x is an unbiased estimator of μ.

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Answer:

12,800

Step-by-step explanation:

20% of 20000 is 4000

20000-4000=16000

20% of 16000 is 3200

16000-3200=12,800

The slope of a line perpendicular to the line whose equation is x - 2y = 14 is -2

What is the equation of straight line ?

The equation of straight line is

y = mx + b

where m is slope of the straight line .

Given ,

The equation is x - 2y = 14 .

So, the equation in slope-intercept form would be 2y = x -14,

which then becomes y = 0.5x - 7

giving a slope of -0.5.

The slope of the perpendicular line is a negative reciprocal,

so 0.5 is the same as (1/2), so the positive reciprocal of that is -2,

meaning the slope of the perpendicular line will be -2.

Hence, The slope of a line perpendicular to the line whose equation is x - 2y = 14 is -2

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The lengths 5, 13 and 12 can form a right angled triangle as they follow Pythagoras theorem.

The lengths can form a right triangle if they follow Pythagoras theorem. The longest side will be hypotenuse which is 13. Remaining will be base and height.

Pythagoras theorem -

Perpendicular² = Base² + Height²

Keep the values in formula

13² = 12² + 5²

Taking square on each side of the equation

169 = 144 + 25

Performing addition on Right Hand Side of the equation

169 = 169

Thus, the righ triangle can be formed based on the mentioned dimensions.

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Note that the expression that is equivalent to 8x² ∛375x + 2∛3x⁷, if x ≠ 0 is:  42x²∛3x (Option B). Even if x = 0, then none of the answers would apply because the expression would automatically = 0.

To prove the above lets us factor and rewrite the radicand in exponential form as follows:

8x² ∛(5³ * 3x) + 2∛(3x⁶ * x)

Rework the expression using

ⁿ√ab = ⁿ√a * ⁿ√b:8x² * ∛5³ * ∛3x + 2∛x⁶ * ∛3x

Simplify the expression 8x² * 5∛3x + 2x² ∛3x

Multiply the monomials to get:
40x² ∛3x+2x²∛3x; Taking the coefficients for the like terms we have:

(40 + 2)x² ∛3x

Calculate the sum to get 42x²∛3x

Thus the simplified version of  8x² ∛375x + 2∛3x⁷, if x ≠ 0 is: 42x²∛3x

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Full Question:

Select the correct answer. Which expression is equivalent to 8x² ∛375x + 2∛3x⁷, if x ≠ 0

A) 42x³

B) 42x²∛3x

C) 10x⁴∛125x

D) 10x²∛125x³

=================================================

Explanation:

Matrix C has 3 rows and 2 columns. The size or dimensions can be written in shorthand as 3x2.

Matrix D has dimensions 2x1, aka 2 rows and 1 column.

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

Write "3x2" and "2x1" side by side in that exact order.

Notice the inner '2's match up. This is important. We need the inner numbers to match so that matrix multiplication is possible. The outer values '3' and '1' will help form the dimensions of the final answer matrix. The final answer matrix will have dimensions 3x1

Luckily we don't need to compute the value of CD. We just need to use the justification mentioned in the previous paragraphs to conclude that matrix CD is possible.

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

Something like BC is not possible because B is 3x2 and C is 3x2. We don't have a match of inner values this time. We can then rule out the answer choice "BC". The answer choices "DC" and "CB" are ruled out for similar reasoning.

Therefore , the solution to the given problem of equation comes out to be4x-3y = 6 as a standard equation in all the above options.

An equation is a representation of two identical variables in mathematics, one on either side of an equals sign. Common difficulties can be solved using equations. We frequently seek pre algebra help when faced with obstacles in real life. Lessons in pre-algebra cover the basics of mathematics.

Here,

Given : 4x-3y = 6

-4x + 2y =8

=> y = 4/5x + 4

=> 4/5x + 2y = 6

Thus ,

From the above following equations we get ,

4x-3y = 6

as a standard equation in all the above options.

Therefore , the solution to the given problem of equation comes out to be 4x-3y = 6 as a standard equation in all the above options.

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On solving the provided question, we can say that the equation that cab be formed the data is as 8 > 3x => x>2.6666666667

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

the equation that cab be formed the data is as

eight more than three times the sum of a number

let the number be x.

8 > 3x

x> 8/3

x>2.6666666667

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value of x is greater than or equal to half.

A mathematical expression shows the unequal comparison between two or more terms.

Inequalities can be greater than, less than, greater than or equal and less than or equal.

The difference of x and one third is greater than or equal to one third of x.

The statement can be written as x -1/3 ≥ x1/3

                                                 x -1/3 ≥ x/3

                              x - x/3 - 1/3 ≥ x/3- x/3 [ subtract x/3 from both parts]

                         2x/3 - 1/3 ≥ 0

             now add 1/3 on both parts

        we get, 2x/3 -1/3 + 1/3 ≥1/3

                      2x/3 ≥ 1/3

                   2x ≥ 1

                     x ≥1/2

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Centroid​, Incenter, Circumcenter,Orthocenter are the name of its center

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1. The statement that is false is: If two figures have the same shape, then they are congruent.

2. The dashed line appears to be a line of symmetry.

When two or more shapes have their length of sides and measure of internal angles to be equal, then it can be inferred that they are congruent. But shapes can be similar, but not congruent.

A line of symmetry is a straight line drawn in such a way that it divides a given shape into two equal parts. So that a shape may have more than one line of symmetry.

From the given questions, we can deduce that;

1. If two figures are similar, they may not be congruent. So that the statement that is false among the given option is A. If two figures have the same shape, then they are congruent.

2. Considering the dashed line drawn through the shape, it appears that it is a line of symmetry.

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The concept of the oldest prime numbers is an ancient one and has been known since ancient times. The ancient Greeks were the first to systematically study prime numbers

The largest and oldest data collection in mathematics is prime numbers. What is it about them that has intrigued mathematicians for millennia?

They were very much aware of the existence of prime numbers and the fundamental theorem of arithmetic, the statement that every positive integer greater than 1 can be represented uniquely as the product of primes. So, it is hard to determine the oldest prime number known, but it's been studied throughout human history.

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The number of solutions for the system of equations x - 2y = 0 and 3x + 4y = 20 is one.

For the given pair of equations x − 2y = 0 and 3x + 4y = 20;

a₁/a₂ = 1/3

b₁/b₂ = -2/4 = -1/2

c₁/c₂ = 0/-20 = 0

As the given pair of linear equation satisfies a₁/a₂ ≠ b₁/b₂​​,

The graph of these equations will be a pair of lines intersecting at a unique point, which is the solution of the given pair of equations.

Let's verify this by calculating the solution of the given system

x = 2y     eqn(1)

3x + 4y = 20     eqn(2)

Now, put the value of x in eqn(2), we get

3 × 2y + 4y = 20

10y = 20

y = 2

Now, put the value of y in eqn(1), and we get

x = 2 × 2 = 4

Thus, the solution is x = 4, y = 2.

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Therefore , the solution of probability problem In the absence of digit usage restrictions, 1000000 postcodes are possible, as are 900000 when the first integer cannot be 9.

The ratio of all possible outcomes to all outcomes in a large group of equally as likely alternatives that result in a specific event determines how likely it is for that event to occur. A branch of mathematics that studies probability a situation or occurrence that is likely to occur the characteristic or state of just being likely of range 0 to 1.

Here ,

1) If there aren't any digit restrictions, there are 1000000 zip codes, or 10*10*10*10*10.

2) 9*10*10*10*10=900000 is the maximum number of postal codes that could exist if the initial number is not 7.

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The graph which could be the graph of the polynomial f( x) with roots-8,-5, 1, and 2 is Graph 4.

What is Polynomial function?

A polynomial function is a function that involves onlynon-negative integer powers or only positive integer expounders of a variable in an equation like the quadratic equation, boxy equation, etc. For illustration, 2x 5 is a polynomial that has exponent equal to 1.

Given that;

Root of polynomial = 4.

This means that the polynomial f( x) has 4 roots.

Now, when f( x) = 0, we're told that the 4 roots are;

x = -8

x = -5

x = 1

x = 2

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The measure of the same side interior angle made by track T and track U is; 79 degrees

Same side interior angles are defined as two angles that are on the interior of or between the two lines and particularly on the same side of the transversal. The same-side interior angles usually sum up to 180 degrees. Finally, when two parallel lines are intersected by a transversal line they will form 4 interior angles.

Now, we are told that the train track U creates an interior angle of 101 with track S.

Thus, using same side interior angles definition, the measure of the same side interior angle made by track T and track U is;

same side interior angle = 180 - 101

= 79 degrees

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A perpendicular line is one that is perpendicular or 90 degrees to another line. In order to draw a perpendicular line in Class 7, it is important to understand the formula and calculation associated with it.

The formula associated with perpendicular lines is that the product of the slope of the two lines must be equal to -1. This means that if one line has a slope of m1, then the slope of the perpendicular line must be -1/m1.

In order to calculate the slope of a line, we must use the formula m = (y2-y1)/(x2-x1), where m is the slope, (x1,y1) is the first point, and (x2,y2) is the second point. With this information, we can use the formula to calculate the slope of the line we want to draw a perpendicular line to, and then use the formula m = -1/m1 to calculate the slope of the perpendicular line.

Finally, with the slope of the perpendicular line, we can use the point-slope form of the equation of a line, y-y1=m(x-x1), to plot the equation of the line and draw it on the graph. This formula can be used to draw a perpendicular line in Class 7.

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we can find the total volume of material that makes up the ball by subtracting the volume of the hollow space from the volume of the sphere:

V = 20,834 cm^3 - 19,848.44 cm^3

= 985.56 cm^3

Volume is a measure of the amount of space occupied by an object or a substance. It is typically measured in units such as cubic meters (m^3), cubic centimeters (cm^3), or cubic feet (ft^3).

Diameter is a measure of the distance across the widest part of a circular object, such as a circle or a sphere. It is equal to twice the radius of the object and is typically measured in units such as millimeters (mm), centimeters (cm), or inches (in). It is a linear measurement.

To find the total volume of material that makes up the ball, we need to find the volume of the sphere and then subtract the volume of the hollow space in the center.

We can begin by calculating the volume of the sphere using the formula for the volume of a sphere:

V = (4/3) * pi * r^3

Where V is the volume, pi is approximately 3.14, and r is the radius of the sphere.

The outer diameter of the ball is 50 cm, so the radius of the sphere is (50/2) = 25 cm.

Substituting these values into the formula, we get:

V = (4/3) * 3.14 * (25 cm)^3

= (4/3) * 3.14 * 15,625 cm^3

= 20,834 cm^3

Next, we need to find the volume of the hollow space in the center of the ball, which is the same as the volume of a smaller sphere with a radius of (25 cm - 1.25 cm) = 23.75 cm.

So the volume of the hollow space is :

V = (4/3) * pi * (23.75 cm)^3

= (4/3) * 3.14 * (23.75 cm)^3

= 19,848.44 cm^3

Finally, we can find the total volume of material that makes up the ball by subtracting the volume of the hollow space from the volume of the sphere:

V = 20,834 cm^3 - 19,848.44 cm^3

= 985.56 cm^3

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Therefore , the problem of mathematics comes out to be Algebra , geometry , trigonometry and etc.

In the study of mathematics, a variety of subjects are studied, including numbers, figures, logic, quantity, equations, and arrangements. Through the use of numerical variable computations, math enables students to find answers to issues.

Here,

Thus the 6 main branches of pure mathematics are

1) Algebra

2) Geometry.

3) Trigonometry.

4) Calculus.

5) Probability and

6)statistics.

the solution of the given problem is Algebra , geometry , trigonometry , calculus , probability and statistics.

Therefore , the problem of mathematics comes out to be Algebra , geometry , trigonometry and etc.

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Answer:

Below

Step-by-step explanation:

5 out of ( 5 + 2) vehicles are cars     5 / 7 are cars

5/7 * 56 = 40 cars

1/216 as a power of 6 is 6^-3. The solution has been obtained by using the concept of exponents.

What is an exponent?

A number's exponent demonstrates how many times we are multiplying a given number by itself. For instance, 2^4, indicates that we are multiplying 2 itself by four times. 2*2*2*2 is its expanded form. The power of a number is another name for an exponent. A whole number, fraction, negative number, or decimal are all acceptable.

We are given 1/216 which is to be written as a power of 6.

We know that 216 is the cube of 6.

This means that 216 can be written as 6^3.

Also, 1/n is written as n^-1

So, 1/216 can be written as 6^-3.

Hence, 1/216 as a power of 6 is 6^-3.

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Answer:

[tex]\Huge \boxed{\boxed{\textbf{False}}}[/tex]

Step-by-step explanation:

A quadrilateral must have four right angles in order to be a rectangle, not simply one. A quadrilateral with a single right angle, however, can take on a wide range of shapes, like a right angled triangle or an irregular quadrilateral. A shape having multiple sides and one right angle, for example, could be an irregular quadrilateral.

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________________________________________________________

Answer:

8, 15, 16

Step-by-step explanation:

8, 15, 16 is not a Pythagorean triple because it doesn't satisfy the Pythagorean Theorem:

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

When we plug this set of numbers into the theorem:

[tex]8^2 + 15^2 \stackrel{?}{=} 16^2[/tex]

[tex]289 \neq 256[/tex]

we get an inequality, not an equality which would make this set of numbers a Pythagorean triple.

Note that all of the other given triples satisfy the Pythagorean Theorem.

Frequency distribution graphs, exponential graphs, logarithmic graphs, trigonometric graphs, and statistical graphs are among the six types of graphs (such as bar, pie, and line graphs).

A straightforward two-dimensional graph is created when a vertical and horizontal line join at the origin. The y axis is vertical whereas the x axis is horizontal. In simple line graphs, the x and y axes are split into regularly spaced sections and assigned integer values.

There are eight main categories of graphs: linear, power, quadratic, polynomial, and they are all used to organise how information is presented.

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