Is a coordinate plane 2 dimensional?

The length of each leg from the given triangle is  13 [tex]\sqrt{2}[/tex], 13 [tex]\sqrt{2}[/tex]  respectively.

What is triangle ?

triangle can be defined as figure which contains three sides and three angles and the sum of three angles could be 180 degrees.

Given triangle is right angled triangle,

with given hypothenuse 26.

let other two sides be x and y.

so,

tan45 = x/y

1= x/y

x = y.

from the figure we can say that ,

[tex]\sqrt{ x^{2} + y^{2} }[/tex] =  26

[tex]\sqrt{x^{2} +x^{2}}[/tex]  = 26

2[tex]x^{2}[/tex] = 26*26

[tex]x^{2}[/tex] = 13*13*2

x = 13 [tex]\sqrt{2}[/tex]

Hence the other two sides be 13 [tex]\sqrt{2}[/tex], 13 [tex]\sqrt{2}[/tex] respectively .

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The equations can be used to solve for y, the length of the room are  y2 – 5y = 750 , (y + 25)(y – 30) = 0,  – y(y – 5) = 0

The formula for calculating the area of a rectangle is expressed as;

A = wl

Given that the parameters are;

From the information given, we have that;

Now, substitute the values, we get;

750 = (y-5)y

expand the bracket

750 = y² - 5y

This can also be written as;

y² - 5y -750 = 0

Hence, the correct option for the expression is  y2 – 5y = 750

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A system whose answer is (6, -8).

Elimination, substitution, and graphing are the three techniques for resolving equation systems.

Graphing the provided equations and identifying the point(s) at which they all meet is all that is required to solve a system by graphing. You can get the values of the variables you're solving for by finding this point's coordinate.

Elimination, substitution, and graphing are the three techniques for resolving equation systems.

Y = 1/3x - 10 and 2x + y = 4 together form a system whose answer is (6, -8).

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The solution to the system of equations y is x = -5, y = 4

Elimination, substitution, and graphing are the three techniques for resolving equation systems.

Graphing the provided equations and identifying the point(s) at which they all meet is all that is required to solve a system by graphing. You can get the values of the variables you're solving for by finding this point's coordinate.

To solve the system of equations y = 1/3x + 10 - 2x and y = 4,  we can use following method:

We can begin by isolating the variable y in the first equation: y = 1/3x + 10 - 2x.

Next, we can substitute the value of y from the second equation into the first equation: 4 = 1/3x + 10 - 2x

Now we can solve for x by combining like terms and isolating x: 4 = 1/3x + 10 - 2x => 4 = -4x + 10 => x = -5

Substitute x = -5 back into either of the equations to find y:

For example, y = 1/3x + 10 - 2x => y = 1/3(-5) + 10 - 2(-5) => y = 4

So the solution is x = -5, y = 4

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The linear regression model is the model that you would have to use when analyzing the data in a scatter plot.

A scatterplot is a graphical representation of two sets of numerical data, where the values of one set are plotted on the x-axis and the values of the other set are plotted on the y-axis.

Each point on the plot represents a pair of (x, y) values. Scatterplots are often used to visualize the relationship between two variables and to identify any patterns or trends in the data.

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The population of the down represent by the equation  P = 53800 [tex](1-\frac{2.5}{100})^3[/tex] and the population after 3 years is 49865.

What is rate of decrease in population?

The rate of decrease calculates a decline as a percentage of the initial sum. To determine how quickly a population is dwindling or how much money is being lost on an investment, you may want to know the rate of decrease . Knowing the initial and final amounts is necessary to compute the rate of decrease.

Here the initial population of the town is [tex]P_0[/tex] = 53800.

Population shrink rate R = 2.5%

Number of years = 3.

Now using decrease in population formula then,

P = [tex]P_0(1-\frac{R}{100})^n[/tex]

=> P = 53800 [tex](1-\frac{2.5}{100})^3[/tex]

=> P = 53800(0.975×0.975×0.975)

=> P = 49865.

Hence the population of the down represent by the equation  P = 53800 [tex](1-\frac{2.5}{100})^3[/tex] and the population after 3 years is 49865.

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A mirror is a surface that virtually always reflects the incident light that strikes it. Both flat and curved surfaces are possible for mirrors. The terms "plane mirror" and "spherical mirror" are used to describe mirrors with flat surfaces and curved surfaces, respectively.

An image is either produced in real time or virtually in a mirror, which is a reflecting surface that reflects light. An object's reflection may be seen in a mirror when it is positioned in front of one. The incident rays are coming from the item, and the reflected rays are what create the image. The classification of the pictures as real or virtual depends on where the light beams cross. Real images happen when light rays truly cross, but virtual images happen when rays of light from a point appear to diverge.

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Taking the subject A and solving the equation, the resultant value of A will be 1,150.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

So, we have the equation:

4/5*A=920

Now, calculate the equation taking A as the subject:

4/5 * A = 920

4A  = 920 * 5

4A = 4,600

A = 4,600/4

A = 1,150

Therefore, taking the subject A and solving the equation, the resultant value of A will be 1,150.

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the value of t is found to be 16.

What is probability?

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

Li has t toy bricks only red and blue She picks two bricks one after the other If the first is red the probability of the second brick being red 2/3.

If the first is blue the probability the second brick is red is 7/10.

Let the number of red bricks be x.

So, the number of blue bricks would be t - x

We have 6x-6 = 5x

x =6

and we get t-1 =15

t =16.

Hence the value of t is found to be 16.

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To represent 2 is greater than 1 in math is presented as 2 > 1.

In math, there is a certain symbol to describe a certain condition of comparison. Here some of them:

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In slope-intercept form, the equation of a line is represented as y = mx + b. So the equation in slope-intercept form is y = (1/2)x + 2

Slope is a measure of the steepness of a line or a linear function. It is often represented by the letter "m" and is calculated as the ratio of the change in the y-coordinates of two points divided by the change in the x-coordinates of those same two points. In other words, it is the ratio of the "rise" to the "run" of the line. The slope of a line can be positive, negative, zero, or undefined.

The slope-intercept form of a linear equation is a way to represent the equation of a line in the form of y = mx + b, where m is the slope and b is the y-intercept of the line. The y-intercept is the point where the line crosses the y-axis, and it is represented by the value of b. This form of the equation is useful because it allows us to easily identify the slope and y-intercept of a line, as well as to graph the line using these values.

The first step is to add 12y to both sides:

6x - 12y + 12y + 24 = 12y

6x + 24 = 12y

The next step is to divide both sides by 12 to get y by itself on one side:

y = (6/12)x + (24/12)

y = (1/2)x + 2

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Answer:

5 is what the answer will end up being

because a it's is adding a negative to a positive

On the plan  student are seated in following manner

A-  Emily

B-   Ben

C-  Cath
D-  Adam

E-   Darren

Direction is a particular way to move one place to another place, Commonly we have four directions like, North, South, East, West.

Given information,

Ben is North-East of Adam

Cath is East of Ben

Darren is South-East of Emily

After following instructions given in problem,

we can draw the conclusion,

Sitting arrangement is like this,

A-  Emily, B-   Ben, C-  Cath, D-  Adam, E-   Darren

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The 7th term of the sequence is 48.

Sequence is an ordered arrangement of elements. It is often used to refer to a series of related events, or occurrences, which take place in a logical order. This order can be used to describe a process, a set of instructions, or a mathematical pattern. In mathematics, a sequence is a collection of numbers or other objects that follow a certain pattern or order. Common examples of sequences include the Fibonacci sequence, the prime numbers, and the geometric sequence.

This can be found by calculating the difference between each pair of terms, which is 6, and then adding 6 to each successive term.

Therefore, the 7th term is 27 + 6 = 33, and 33 + 6 = 39, and 39 + 6 = 45, and 45 + 6 = 51, and 51 + 6 = 57, and 57 + 6 = 63, and 63 + 6 = 69. Rounded to the nearest integer, the 7th term is 48.

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Answer:

Step-by-step explanation:

It is not possible to determine which system of inequalities is shown without a graph or more information about the inequalities. Without a graph, it is not possible to determine the region that is being represented by the system of inequalities. Additionally, without more information about the inequalities, it is not possible to determine which inequality is the upper bound and which is the lower bound. Therefore, the answer is "not enough information."

The solution of the system of inequalities is,

y > x and y > 2

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The graph of inequality is shown.

Now, We get;

The first graph is, y > x

And, The second graph is, y > 2

Thus, The solution of the system of inequalities is,

y > x and y > 2

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The perimeter of the square is 16√5 inches.

A square is a quadrilateral with 4 sides equal to each other. The opposite sides of a square is parallel to each other.

The perimeter of a square is the sum of the whole sides of the square.

Let's find the length of the square using the length of the diagonal.

Using Pythagoras's theorem,

c² = a² + b²

where

Therefore,

x² + x² = (4√10)²

2x² = 160

x² = 160 / 2

x = √80

Hence,

perimeter of a square = 4l

where

perimeter of the square = 4 × √80

perimeter of the square = 4 × 4√5

perimeter of the square = 16√5 inches

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A. Another method for finding the slope of the linear function is by using the formula, slope = (y2-y1)/(x2-x1).

B. Sarah's method will not work for every linear function because not every linear function pass through the origin.

The slope of a linear function that can be determined using the formula:

Slope = (y2-y1)/(x2-x1)

Where (x1, y1) and (x2, y2) are two points on the line

A. Another method for finding the slope of the linear function is by using the formula above.

x1 = 4, y1 = 22 and x2 = 12 , y2 = 66

Slope = (66-22)/(12-4) = 44/8 = 11/2

B. Sarah's method will not work for every linear function because not every linear function pass through the origin.

Example:

x y

2 5

3 9

Sarah's method:

slope = 5/2 = 2.5 or slope = 9/3 = 3.

This will not work because the values of y/x are not the same.

Using the formula:

x1 = 2, y1 = 5 and x2 = 3 , y2 = 9

Slope = (9-5)/(3-2) = 4/1 = 4

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The linear equation 5x - y = -5 have x - intercept is at x = -1 and y - intercept is at y = 5.

The x-intercept of a linear equation is the point at which the line crosses the x-axis. It can be found by setting y equal to 0 and solving for x. The y-intercept of a linear equation is the point at which the line crosses the y-axis. It can be found by setting x equal to 0 and solving for y.

x - intercept is when y = 0 and;

5x - 0 = -5

5x = -5

x = -5/5 {divide through by 5}

x = -1

y - intercept is when x = 0 and;

5(0) - y = -5

-y = -5

y = -5/-1 {divide through by -1}

y = 5

Therefore, the linear equation 5x - y = -5 have x - intercept is at x = -1 and y - intercept is at y = 5.

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A substitution is a mathematical strategy where alphabets in a formula are replaced by numbers.

We know that the substitution is a method or strategy for solving systems of equations.

In this method we solve for one variable and using that solution to find the other variable.

When letters (or alphabets) in a formula are replaced by numbers, it is known as substitution.

As we know the formula is a rule or principle written with mathematical symbols.

A substitution in formula is nothing but we replace the variables in the formula by its value (numerical value)

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By trigonometry x is equal to 2 radian. An area of mathematics that researches connections between triangle side lengths and angles.

The Greek mathematician Hipparchus created the first chord chart sometime around 140 BC. Hipparchus is said to have authored twelve books of chord tables, yet none of these tables have survived. Thus, Hipparchus is credited as the discovery of trigonometry. A subfield of mathematics known as trigonometry studies how angles and length ratios relate to one another. Applications of geometry to astronomical research led to the field's emergence in the Hellenistic civilization during the third century BC.

tanx = 29/14

tanx = 0.036

x= tan¯1(0.036)

x = 2

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The college graduate's new net worth is $12,057. The Option A is correct.

The net worth of an entity (i.e company or person) is given by the sum of the values of all assets of the person subtracted by the sum of the values of all debts (liability) of the person.

The assets of the student are given as follows:

Signing bonus: $10,000.

Furniture: $3,865.

Savings Account Balance: $571.

Car Value: $19,250.

Electronic: $2,160.

Total = $35,846

The liabilities of the student are given as follows:

Car Loan: $12,500.

Credit Card Balances: $2,468.

Student Loans: $33,821 - $25,000 = $8821.

Total = $23,789

The student's net worth is calculated as follows:

= $35,846 - $23,789

= $12,057.

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The length of CE is 22. The measurement of ∠EAD = 34°.

What is a diagonal?

The diagonal is the line that runs through the centre of the figure from one corner of the square or rectangle to the opposite corner. Any square with two diagonals that are the same length.

Given that AE = 2x+2 and BD=3x+14, ∠BEC=112°.

The diagonals of a rectangle equal and bisect each other.

Thus BD = AC.....(i)

The diagonal AC bisect at E.

AE = EC = 1/2 AC

Rewrite equation:

BD = 2AE

3x+14 = 2(2x+2)

3x+14 = 4x+4

4x-3x = 14-4

x = 10

Putting x=10 in AE = EC :

EC = 2(10)+2

EC = 22

Vertical angle theorem: The Vertical opposite angles are equal.

∠AED = ∠BEC =112° (vertical opposite angles)

Consider △ADE:

Since AE = ED, thus ∠EAD = ∠EDC.

The sum all interior angle of a traingle is 180°

∠EAD + ∠EDC + ∠AED = 180°

2∠EAD + ∠AED = 180°

2∠EAD + 112° = 180°

2∠EAD  = 180° - 112°

2∠EAD  = 68°

∠EAD  = 34°

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To find the distance between two points in a plane, you can use the distance formula. The distance formula is:

d = √((x2 - x1)^2 + (y2 - y1)^2)

Where (x1, y1) and (x2, y2) are the coordinates of the two points, and d is the distance between the points.

For example, if you have two points (3, 4) and (7, 10), you can use the distance formula to find the distance between them:

d = √((7 - 3)^2 + (10 - 4)^2)

d = √((4)^2 + (6)^2)

d = √(16 + 36)

d = √52

d = 2√13

To find the midpoint of two points, you can use the midpoint formula. The midpoint formula is:

(x,y) = ((x1 + x2) / 2, (y1 + y2) / 2)

Where (x1, y1) and (x2, y2) are the coordinates of the two points, and (x,y) are the coordinates of the midpoint.

For example, if you have two points (3, 4) and (7, 10), you can use the midpoint formula to find their midpoint of them:

(x,y) = ((3 + 7) / 2, (4 + 10) / 2)

(x,y) = (5, 7)

The midpoint of points (3,4) and (7,10) is (5,7).

It's worth noting that both distance and midpoint formulas can be adapted for three-dimensional points, where the distance formula would be:

d = √((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)

and the midpoint formula would be

((x1 + x2)/2, (y1 + y2)/2, (z1 + z2)/2)

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The percentage of melon in Salma's and Luke's fruit salads will be roughly 57% and 58%, respectively. Luke's fruit salad will consequently taste more melon-like.

This technique allows us to calculate both the value of multiple units from the value of a single unit and the value of single unit from the value of multiple units.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique.

We typically utilize this technique for math calculations.

This approach will be helpful to you while tackling problems involving ratio and proportion, algebra, geometry, etc.

According to our question-

Out of the 7 cups of fruit, Salma uses 4 cups of melons. 4/7 is around 57%.

Out of the 12 cups of fruit, Luke uses 7 cups of melons. Around 58 percent is 7/12.

Hence, The percentage of melon in Salma's and Luke's fruit salads will be roughly 57% and 58%, respectively. Luke's fruit salad will consequently taste more melon-like.

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The meaning of the term 2² is number 2 is squared:

2*2 = 4.

Examples:

1 * 1 = 1.

One is a square number therefore.

2 * 2 = 4.

Four is the following square number, so. You can probably guess how to determine the following square number.

Let's multiply 3 by itself:.

3 * 3 = 9.

and so on.

Thus, for the stated question:

The number 2 is squared.

= 2*2 = 4.

Therefore, the result of the expression comes as 4.

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If the hypotenuse is c = astartroot 2 endroot, then 6 = astartroot 2 endroot then the value of a in inches would be 3.

What is right triangle ?

A right triangle is a triangle in which one angle is a right angle (90 degrees). The side opposite the right angle is called the hypotenuse, and the two other sides are called the legs. The Pythagorean Theorem states that the square of the hypotenuse is equal to the sum of the squares of the legs.

The given information is that the hypotenuse, represented by c, is equal to the square root of 2. If we set c = √2 and 6 = √2, we can solve for the value of the other side of the right triangle, represented by a.

To solve for a, we can square both sides of the equation 6 = √2:

[tex]6^{2}[/tex] = [tex](\sqrt{2} )^{2}[/tex]

36 = 2

So a = 6/√2 = 6/√2 = 3,

If the hypotenuse is c = astartroot 2 endroot, then 6 = astartroot 2 endroot then the value of a in inches would be 3.

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Answer: The correct answer to this question is 3 square root 2

Step-by-step explanation: Lincoln Edge 2023

For monthly use of phone calls more than 170 minutes, plan a will cost more than plan b.

In plan a, the customer pays 7 cents per minute of use with no monthly fee.

So, the cost of x minutes call is given by, y = 0.07x ............. (1)

Again, in plan b, there is a charge of 5 cents per minute of use and in addition, the customer pays a monthly fee of 3.40.

So, the cost for x minutes call is given by, y = 3.4 + 0.05x  ........... (2)

Now, we have to find the value of x for which plan a costs plan b will be

0.07x > 3.4 + 0.05x

⇒ 0.02x > 3.4

⇒ x > 170 minutes.

So, for monthly use of phone calls more than 170 minutes, plan a will cost more than plan b.

The complete question is,|
A phone company offers two monthly charge plans. In plan a, there is no monthly fee, but the customer pays 7 cents per minute of use. In plan b, the customer pays a monthly fee of 3.40 and then an additional 5 cents per minute of use. For what amounts of monthly phone use will plan a cost more than plan b

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The trigonometric function cotθ is undefined for B)0.

What is trigonometric functions?

The simplest definition of a trigonometric function is the function of an angle in a triangle, often known as a circular function. It implies that these trigonometric functions can be used to determine the relationship between a triangle's angles and sides.

Now given trigonometric function is cotangent.

This function is undefined for infinitely many points in the real number system, specifically any time sin(x)=0 which occurs for any integer n at

x = nπ.

If n is 0 you get x=0 so yes that is one value where cot(x) is undefined. Big question is what domain you are restricted to.

For example, if on [0,π), zero is the only value in that interval where cot(x) is undefined.

Hence the correct option is B) 0.

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Approximately after 6 days there will be fewer than 40 bugs remaining at the farm.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given exponential function is f(x)=500(0.67)ˣ.

Part A: To complete table

Put x=0

f(0)=500(0.67)⁰

f(0)=500

Put x=1

f(1)=500(0.67)¹

f(1)=335

Put x=2

f(2)=500(0.67)²

f(2)=224.45

Put x=3

f(3)=500(0.67)³

f(3)=150.3815

Part B:

Percentage of the bugs are eaten

= 335/500 ×100

= 335/5

= 67%

Part C:

Percentage of the bugs are remain 33%

Part D: Number of days after there will be fewer than 40 bugs remaining at the farm.

40=500(0.67)ˣ

(0.67)ˣ =40/500

(0.67)ˣ =0.08

Take the logarithm of both sides of the equation to remove the variable from the exponent.

Exact Form: ln (0.08)/ln(0.67)

x=6.306

x≈6

Therefore, approximately after 6 days there will be fewer than 40 bugs remaining at the farm.

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