show a²-4= (a+ 2)(a-2) in diagram​

Coordinate (-a , b ) belongs to second quadrant.

The axes (x-axis and y-axis) of a two-dimensional Cartesian plane system divide the plane into four infinite regions called quadrants. The horizontal line or x-axis and vertical line or y-axis intersect each other at the right angle.  The intersection of two lines is known to be the reference point. All the measurement is done by taking this point as the reference (or starting point) in the coordinate system.

"A quadrant is simply defined as the region of a cartesian plane formed when the x-axis and y-axis intersect each other."

Given, Coordinate ≡ (-a , b)

1st Quadrant: The upper right-hand corner of the graph is the first quadrant. In this quadrant the values of x and y both are positive.

2nd Quadrant: The upper left-hand corner of the graph is the second quadrant. In this quadrant, the value of x is negative whereas the value of y is positive.

3rd Quadrant: The lower left-hand corner of the graph is the third quadrant. It contains the negative values of both x and y.

4th Quadrant: Finally, the fourth quarter is at the lower right-hand corner, which has a positive value of x and a negative value of y.

Hence, by the above observation, given coordinate (-a, b) belongs to the 2nd quadrant.

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The perimeter of the rectangle is  4y + 6 (cm).

All four side lengths must be added up in order to get the perimeter, or the distance around the rectangle. Since there are two of each side length, it is simple to multiply the total of the length and the breadth by two in order to do this task effectively. The formula for perimeter is perimeter=(length Plus width)2.

The diagram shows a rectangle. All measurements are in centimetres  an expression in terms of y, for the perimeter of the rectangle.

The perimeter of the rectangle is

2(y+3)+24

=2y + 6 + 2y = 4y + 6 (cm)

{ the perimeter:

2 *  width + 2 * Length}

The perimeter of the rectangle is  4y + 6 (cm).

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The discriminant of the given quadratic equation 2x² - 4x + 3 = 0 is -8.

The standard form of quadratic equation is ax² + bx + c = 0

Compare the given equation with its standard form

a = 2, b = -4, c = 3

We know that

D = b² - 4ac

Substitute the values in the formula

D = (-4)² - 4(2)(3)

⇒ D = 16 - 24

⇒ D = -8

Since D < 0

Therefore, the given equation has no real roots.

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The ^ operator in logical mathematics means the OR operation . Therefore , the statement ∧ and ∠means that a or the negation of a is joined by the or operation .

These are known as logical operations as they are based upon logic.The meaning of the term logic is reasoning which means to resonate. The reasoning may be a legal opinion or mathematical confirmation.

We apply logic on expression to check whether they are true of false . Some of the mathematical logics are a negation, conjunction, and disjunction logical operations. The symbols used for them in mathematical logic is, ‘~’ for negation ‘^’ for conjunction and ‘ v ‘ for disjunction.

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Answer:

Jared's groceries = 495

Step-by-step explanation:

We calculate 11% from Jared monthly income:
11% x 4500 = 495

Jared's groceries = 495

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Answer:

R = 144400000/59 [this is a fraction]

The value of the expression is -44 and thus does not depend on the value of x

An algebraic expression can be described as a mathematical expression made up of variables, terms, factors, coefficients and constants.

They are also made up of mathematical or arithmetic operations, which includes;

From the information given, we have that;

(x-5)(x+8)-(x+4)(x-1)

expand the bracket

x² + 8x - 5x - 40 - (x² -x + 4x - 4)

x² + 8x - 5x - 40 - x² + x - 4x + 4

collect like terms

3x - 3x - 40 - 4

add or subtract like terms

0 - 44

Hence, the expression does not depend o x

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Answer:

12?

Step-by-step explanation:

Lowkey don't understand the last part of your q but if it's 4 times then if the original was 12 48 is four times bigger

The two side lengths are congruent, and their opposite angles are congruent, and the hypotenuse is the length of either leg times the square root of two, √2.

A 45° 45° 90° triangle is a special type of isosceles right triangle where the two legs are congruent to one another and the non-right angles are both equal to 45 degrees.

A 45°−45°−90° triangle is a commonly encountered right triangle whose sides are in the proportion 1:1:√2.

properties of 45°-45°-90°:

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Answer:

912 cm²

Step-by-step explanation:

Formula for area of triangle: 1/2bh

So you'll first multiply the base by the height of the triangle

48 x 38 = 1,824

Then you'll multiply 1,824 by 1/2(which is the same as dividing it by 2)

1,824 ÷ 2 = 912

Answer: 4

Step-by-step explanation:

1. Question: 2x+1=9

2. Subtract 1 from the 9

Answer to step 2: 2x=8

3. Divide 8/2 (4x2)

4. Answer: x=4

Answer: X= 4; look below for the explanation of algebra tiles

Step-by-step explanation: First, we need to determine the value of x. We can use the rule of inverse operations. So, the opposite of addition is subtraction, and the opposite of multiplication is division. Now, using that, we start with the inverse operations of 1 + 9. That'd be 9 - 1. So, that's 8. Now, according to the order of inverse operations, we divide the 2 by 8. So, 8 divided by 2 is 4. Therefore x = 4.

Now, using the tiles, we need to get 8 tiles, + 1 tile, which should get you your answer. I hope this helped!

Answer:

[tex]\dfrac{3}{a-6}\quad \textsf{if}\;\;a \neq -6,a \neq 6[/tex]

Step-by-step explanation:

Given expression:

[tex]\dfrac{a}{a-6}-\dfrac{3}{a+6}+\dfrac{a^2}{36-a^2}[/tex]

Rewrite the third fraction:

[tex]\implies \dfrac{a^2}{36-a^2}=\dfrac{-a^2}{-(36-a^2)}=\dfrac{-a^2}{a^2-36}[/tex]

[tex]\boxed{\begin{minipage}{4 cm}\underline{Difference of two squares }\\\\$x^2-y^2=(x-y)(x+y)$\\\end{minipage}}[/tex]

Apply the difference of two squares to the denominator of the third fraction:

[tex]\implies a^2-36=a^2-6^2=(a-6)(a+6)[/tex]

Therefore the expression can be written as:

[tex]\implies \dfrac{a}{a-6}-\dfrac{3}{a+6}+\dfrac{-a^2}{(a-6)(a+6)}[/tex]

[tex]\implies \dfrac{a}{a-6}-\dfrac{3}{a+6}-\dfrac{a^2}{(a-6)(a+6)}[/tex]

The least common multiplier (LCM) of the denominator is (a - 6)(a + 6).

Adjust the fractions based on the LCM:

[tex]\implies \dfrac{a(a+6)}{(a-6)(a+6)}-\dfrac{3(a-6)}{(a-6)(a+6)}-\dfrac{a^2}{(a-6)(a+6)}[/tex]

Simplify:

[tex]\implies \dfrac{a^2+6a}{(a-6)(a+6)}-\dfrac{3a-18}{(a-6)(a+6)}-\dfrac{a^2}{(a-6)(a+6)}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}-\dfrac{b}{c}-\dfrac{d}{c}=\dfrac{a-b-d}{c}:[/tex]

[tex]\implies \dfrac{a^2+6a-(3a-18)-a^2}{(a-6)(a+6)}[/tex]

Simplify:

[tex]\implies \dfrac{3a+18}{(a-6)(a+6)}[/tex]

Factor out 3 from the numerator:

[tex]\implies \dfrac{3(a+6)}{(a-6)(a+6)}[/tex]

Cancel the common factor (a + 6):

[tex]\implies \dfrac{3}{a-6}[/tex]

Therefore:

[tex]\dfrac{a}{a-6}-\dfrac{3}{a+6}+\dfrac{a^2}{36-a^2}=\dfrac{3}{a-6}\quad \textsf{if}\;\;a \neq -6,a \neq 6[/tex]

On solving the provided question, we can say that the quadratic equation is  y = 5x² - 9x + 3 this quadratic equation can not factorized further

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

the quadratic equation is

y = 5x² - 9x + 3

this quadratic equation can not factorized further

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Answer: The answer is 10x2

Step-by-step explanation:

mean of the sampling distribution of the difference in sample proportions is 0.36.

The best method for the random sampling will be to write the students' names on paper and pick them out of a hat, as each student will have an equal chance of being chosen.

22% of the population of eastern grey squirrels weigh more than 0.5 kg.

36% of the population of western grey squirrels weigh more than 0.5 kg.

Eastern grey squirrel sample size is 60.

There were 120 western grey squirrels in the sample.

Required:

The difference in sample proportions' mean of the sampling distribution (eastern minus western)

The difference of the mean yields the mean of the difference.

Mean = p1 - p2 is the sampling distribution's average for the difference in the sampling proportion from two populations.

Where;

p1 = 22% of the eastern grey squirrel, which equals 0.22.

p2 = 36% of the western grey squirrel, which equals 0.36.

Therefore;

p1 - p2 = 0.22 - 0.36 is the mean.

The right answer is (E) 0.22 - 0.36.

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Answer: you will need 8 cars. 4 can go into 7 evenly so you will have to left over. So 8 cars will be necessary.

Step-by-step explanation: divide 30 by four which equals 7.5 so we can just round up and say we need 8 cars

To determine how many cars are needed to transport 38 students, we need to divide the total number of students by the number of students that can fit in each car.

According to the problem, each car can hold 4 students and a driver. Therefore, the total number of people that can fit in one car is 4+1 = 5.

To transport 38 students, we need to divide 38 by 4 to find the number of cars needed to transport all the students.

38 ÷ 4 = 9 remainder 2

This means that 9 cars can transport 36 students (9 cars x 4 students per car), but we still have 2 students left.

Therefore, we need an additional car to transport the remaining 2 students.

In total, we need 10 cars to transport all 38 students.

You had a better score relative to the rest of your class.

To compare the scores of you and your friend relative to the rest of their classes, we need to calculate the standard deviation of your score and your friend's score from the average of their respective classes.

A standard deviation of 2 means that 68% of the scores in the class fall within 1 standard deviation of the mean, or between 84 and 88 in the case of Mrs. Wilson's class. Since 88 is greater than 86 (the mean) and less than 2 standard deviations away (88-86 < 2*2=4) , so your score of 88 is better than the average score in your class.

On the other hand, 85 is less than 82 (the mean) and more than 1 standard deviation away (85-82 > 2) so your friend's score of 85 is less than the average score in their class.

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Answer:

Step-by-step explanation:

These are the tests for similar triangles:

AA - if 2 pairs of corresponding angles are equal.  

SSS - if corresponding sides have the same ratio.

SAS - if 2 pairs of corresponding sides have the same ratio and the included angles are equal.

This diagram does not indicate any of these relationships exist.

Therefore the triangles are not similar.

The total cost for Ben to buy 1 binder and P pencils is 2.25 + 0.75 P.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

Cost of a binder = 2.25

Cost of a pencil = 0.75

We have to find the total cost for Ben to buy 1 binder and P pencils.

Cost of 1 binder = 2.25

Cost of P pencils = 0.75 × P = 0.75 P

Total cost of 1 binder and P pencils = 2.25 + 0.75 P

Hence the total cost for Ben to buy 1 binder and P pencils is 2.25 + 0.75 P.

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Answer:

a)  10

b)  Number of hours of phone support (per month).

c)  Total bill (per month).

d)  y = 35x + 10

e)  2.5 hours

Step-by-step explanation:

The company bills you at a rate of:

The fixed cost (the constant) is the cost per month ⇒ $10.

The independent variable is the variable that is not affected by any other variables.

Therefore, the independent value (variable x) is the number of hours of phone support per month.

A dependent variable is the variable that is affected by the other variable.

Therefore, the dependent value (variable y) is the total bill (in dollars) per month.

The equation that describes the given situation is:

To calculate how many hours of phone support was needed for a bill of $97.50, substitute y = 97.5 into the equation from part d and solve for x.

[tex]\implies 35x+10=97.5[/tex]

[tex]\implies 35x+10-10=97.5-10[/tex]

[tex]\implies 35x=87.5[/tex]

[tex]\implies \dfrac{35x}{35}=\dfrac{87.5}{35}[/tex]

[tex]\implies x=2.5[/tex]

Therefore, 2.5 hours of phone support was needed last month.

Exponential equation in the form y = a(b)* that can model the value of the pizza oven, y, x years after purchase is y = 16000(0.985625)ˣ.

The formula for an exponential function is f (x) = ax, where x is a variable and an is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.

The development of bacteria is an illustration of an exponential function. Some germs multiply by two per hour. After x hours, you will have twice as much germs if you start with one and it doubles every hour. F(x) = 2x can be used to express this.

The exponential equation is y = a(b)ˣ

The value of y = 15770, a = 16000 and x = 1

b = 0.985625

y = 16000(0.985625)ˣ

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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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The expression represents a polynomial with three terms.

A polynomial is an expression consisting of variables (often denoted by x, y, z, etc.) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. Polynomials can be used to express a wide range of algebraic equations, from simple linear equations to more complex equations. Polynomials can also be used to construct functions with properties that are useful for solving real-world problems.

The expression represents a polynomial with three terms.

The constant term is -1, and the leading coefficient is 8. The leading term is 8x³.

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Answer:

Hey there! So the square root of 38 can be simplified by breaking it down into simpler parts. We can use a technique called prime factorization. We need to find the largest perfect square that is a factor of 38 and extract it from the square root. So, we can express 38 as 219 and that means we have 2^2=4 as the largest perfect square. Therefore, we can simplify the square root of 38 as 2sqrt(19).

It can't be simplified anymore, but it gives us a more manageable form. Let me know if you have any more questions, I'm happy to help!

________________________________________________________

A perfect square is a number that can be written in the form of n^2 (n raised to the power of 2) for some whole number n. For example 4, 9, 16, 25 and 36 are perfect squares. A way to determine if a number is a perfect square is by taking the square root of that number, if the result is a whole number it's a perfect square. Also, you can check it by finding the prime factorization of the number, if each of the prime factors appears in even power, it's a perfect square.

There are a few techniques that can make simplifying square roots quicker and easier:

Recognizing perfect squares (as described above) and extracting them from the square root

Using prime factorization to simplify the square root

Recognizing when the square root can be written as a rational number (a fraction of two integers)

Another way to approach is to factorise the radicand and combine any pairs of identical factors out from the square root.

Please let me know if you have any other questions on this topic or any other topic I could help with.

√38 is the simplest representation of the square root of 38.

The square root of a number is a value that, when multiplied by itself, gives the original number.

In the case of √38, we are looking for a number that, when multiplied by itself, equals 38.

Since 6 multiplied by itself is 36 and 7 multiplied by itself is 49, we can conclude that the square root of 38 lies between 6 and 7.

We cannot find a whole number that satisfies the equation √38 = x, where x is an integer.

Therefore, we express the square root of 38 as an irrational number, meaning it cannot be expressed as a simple fraction or a terminating or repeating decimal.

Hence, √38 is the simplest representation of the square root of 38.

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Answer:218

explanation: 162 divided by 9 = 18 and 18 multiplied by 12 =218

Number of students that do two subjects are 12.

Number of students that do only exactly one subject are;

For Art;

⇒ 14

For Chemistry;

⇒ 11

For Bio;

⇒ 8

Number of students that do at least two of the subjects are 15.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

In a class of 48 students, 24 of them do Arts, 22 do Chemistry and 20 do Biology.

All the students do at least one of the three subjects.

3 do all three subjects while 4 do Arts and Biology only, 3 do Arts and Chemistry only and 5 do Chemistry and Biology only.

Here,

Total students = 48

So, Number of students that do two subjects are = 4 + 3 + 5

                                                                            = 12

And, Number of students that do only exactly one subject are;

For Art;

⇒ 24 - (3 + 4 + 3)

⇒ 14

For Chemistry;

⇒ 22 - (3 + 5 + 3)

⇒ 11

For Bio;

⇒ 20 - (3 + 4 + 5)

⇒ 8

Number of students that do at least two of the subjects are;

⇒ 3 + 3 + 4 + 5

⇒ 15

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The length of the median = 6[tex]\sqrt{3}[/tex]

If we call the longer base "a" and the shorter base "b", then we know that:

a:b = 2:1

Since the ratio of the four sides is 1:1:1:1, we know that the height, median and the longer base are all equal.

We can use that information to determine the area of the trapezoid. The formula for the area of a trapezoid is:

Area = (a + b) * h / 2

We know that the area is  27[tex]\sqrt{3}[/tex] and the height and median are equal, so we can set up the equation:

(a + b) * h / 2 = 27[tex]\sqrt{3}[/tex]

We also know that a:b = 2:1, so we can substitute that in:

(2b + b) * b / 2 = 27[tex]\sqrt{3}[/tex]

Simplifying, we get:

3b^2 = 54 * [tex]\sqrt{3}[/tex]

So the length of the median (h) is b

= [tex]\sqrt{(54 * \sqrt{3} / 3) }[/tex]

= 6[tex]\sqrt{3}[/tex]

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