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Bookwork code: M56
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a) What is the y-intercept of this line?
b) What is the gradient of this line?

For each 45-45-90 triangle, the period of the hypotenuse equals the length of the leg expanded via the square root of 2. That is the 45-45-90 Triangle Theorem.

A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is greater than thousand years vintage, having been described at the very first web page of Euclid's elements.

In Euclidean geometry, any 3 elements, at the same time as non-collinear, determine a very precise triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean area). In special words, there's exceptional one plane that includes that triangle, and each triangle is contained in some plane. If the complete geometry is best the Euclidean plane, there is the fine one aircraft and all triangles are contained in it; however, in better-dimensional Euclidean areas, this isn't actual. this text is prepared triangles in Euclidean geometry, and specifically, the Euclidean plane, besides in which otherwise said.

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Answer:

u = -69

Step-by-step explanation:

Now we have to,

→ find the required value of u.

The equation is,

→ -11u = 759

Then the value of u will be,

→ -11u = 759

→ u = 759/-11

→ u = -(759/11)

→ [ u = -69 ]

Hence, the value of u is -69.

The amount of neurotransmitter released from the parasympathetic ganglion is acetylcholine.

The parasympathetic nervous system is part of the autonomic nervous system which helps to regulate involuntary bodily functions such as heart rate, digestion and other processes.

The parasympathetic nervous system is responsible for calming the body and restoring it to its resting state. Parasympathetic ganglia are clusters of neurons that receive and transmit nerve signals from the brain to the organs and muscles.

The amount of neurotransmitter released from these ganglia is acetylcholine, which helps to slow the heart rate and promote relaxation.

The parasympathetic nervous system is part of the autonomic nervous system which helps to regulate involuntary bodily functions such as heart rate, digestion and other processes.

The parasympathetic nervous system is responsible for calming the body and restoring it to its resting state. Parasympathetic ganglia are clusters of neurons that receive and transmit  signals from the brain to the organs and muscles.

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The order of operations is a collection of rules that gives the correct sequence of steps for doing a calculation. BIDMAS is an acronym used to tell you the correct order to complete a calculation when there are different operations . It stands for Brackets, Indices , Division, Multiplication, Addition and Subtraction.

Thus solving the expression;

we first solve all the multiplication parts:

7 x 6 - 5 x 4 + 1 x 3

Now addition:

= 42 - 20 + 3

Lastly subtraction:

= 42 - 23

= 19

There are 198 passengers in each car.

What is division?

The division is one of the four basic mathematical operations of arithmetic, along with addition, subtraction, and multiplication. It is the inverse operation of multiplication.

To determine the number of passengers in each car, we need to divide the total number of passengers by the total number of cars.

We know that:

There are 4,752 passengers in total

There are 8 cars per train and 3 trains

So, the total number of cars is 8 cars/train x 3 trains = 24 cars

To find the number of passengers per car, we divide the total number of passengers by the total number of cars:

4,752 passengers / 24 cars = 198 passengers per car.

Hence, there are 198 passengers in each car.

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The expression which represents the amount Gabe spent at the mall will be 18.58k + 52.

The amount that Gabe spent if he bought 3 items will be $107.74.

From the information, Gabe goes to the mall. If k is the number of items he bought, the expression 18.58k+30 gives the amount he spent in dollars at one store and he spent 22 dollars at another store.

The expression which represents the amount Gabe spent at the mall will be:

= 18.58k + 30 + 22

= 18.58k + 52

The amount that Gabe spent if he bought 3 items will be:

= 18.58k + 52

= 18.58(3) + 52

= $107.74

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Julie is approximately 40.6 ft away from the base of the tower.

Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles. One of the main uses of trigonometry is to calculate distances in a triangle when the lengths of two sides and the measure of the angle between them are known.

We can calculate this by using the formula:

Distance = (tower height) / (tan(angle of depression))

Distance = (83 ft) / (tan(49))

Distance = 40.6 ft (rounded to the nearest tenth)

Therefore, Julie is approximately 40.6 ft away from the base of the tower.

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Answer:

Step-by-step explanation:

a+b=7 and ab= 6 find a^2+b^2

( a + b )² = a² + b² + 2ab =

7² = a² + b² + 2 × 6 =

49 = a² + b² + 12 =

a² + b² = 49 - 12 =

a² + b² = 37

Two different methods used to solve the system of linear equation is given by :

a. Elimination method.

b. Substitution method

As given in the question,

Let us consider system of linear equation  be :

2x + 5y = 3  __(1)

3x + 4y = 1  __(2)

a. Elimination method :

Multiply (1) by 3 and ( 2) by -2 and add them we get,

6x + 15y = 9

-6x -8y = -2

     7y  = 7

⇒ y = 1

b. Substitution method :

Substitute the value of y = 1 in any one equation we get,

2x + 5(1) = 3

⇒ 2x = 3 - 5

⇒ x = -1

While solving two equation substitute the value of one variable from one equation into the other.

Therefore, the two methods used to solve the system of linear equation is equal to :

a. Elimination method.

b. Substitution method

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On simplifying the given quadratic equation , we get that the solution of the quadratic equation  3x² -14x -5 = 0 are x = -1/3 and  x = 5     .

The Quadratic Equation are given as : 3x² -14x -5 = 0 ;

to find the solutions of this equation , we use the split the middle term method ;

⇒ 3x² -14x -5 = 0 ;

we split "-14" as the sum of -15 and 1 .

⇒ 3x² -15x + x -5 = 0 ;

⇒ 3x(x - 5) +1(x - 5) = 0;

⇒ (3x + 1)(x - 5) = 0  ;

Solving the factors separately ,

we have ;

⇒ 3x + 1 = 0    and   x - 5 = 0  ;

⇒  x = -1/3    and  x = 5  ;

Therefore , the solutions of given quadratic are x = -1/3    and  x = 5 .

The given question is incomplete , the complete question is

What are the solutions of the quadratic equation 3x² -14x -5=0 ?

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Answer:

210

Step-by-step explanation:

70

14 booths

ratio = 70/14 =5

42 booths

by the same ratio = 42*5 = 210

Answer:

They are perpendicular!

Step-by-step explanation:

Get 7x-3y=-21 into y=mx+b format.

7x-3y=-21           Bring 7x to the other side

-3y=7x-21          Divide -3 by both sides, it cancels out on the y's side.

y=-7/3x+7       Two negatives equal a positive, that it why 7 is positive.

y=-7/3x+7 is the line, the other is y=-3/7x+5

The slope of this line is -7/3 , the slope of the given line is -3/7.

Lines are perpendicular if the slopes are opposite reciprocals, such as this.

So, while they intercept at different points on the y-axis, they will intersect at some point! This makes them perpendicular.

The second transformation that is applied to rectangle A B C D is a translation.

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Answer: [tex]x-\frac{x}{9}[/tex]

Step-by-step explanation:

1) quotient is the answer of a division problem

with that in mind and letting "a number" = x . . .

"The quotient of a number and nine..." would be [tex]\frac{x}{9}\\[/tex]

2) "is less than" always means you but the previous statement BEHIND . . .

[tex]x-\frac{x}{9}[/tex]

Answer:

(3, 8 )

Step-by-step explanation:

given 2 points (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

here (x₁, y₁ ) = P (1, 6 ) and (x₂, y₂ ) = Q (5, 10 ) , then

midpoint = ( [tex]\frac{1+5}{2}[/tex], [tex]\frac{6+10}{2}[/tex] ) = ( [tex]\frac{6}{2}[/tex] , [tex]\frac{16}{2}[/tex] ) = (3, 8 )

The expression $(4 - 5i) - (-2i - 8) + (-1 + 8i) is simplified to $5i -11

Algebraic expressions are defined as expressions that are  composed of variables, coefficients, factors, constants and terms.

These expressions are likely to consist of some arithmetic operations, such as;

From the information given, we have that;

$(4 - 5i) - (-2i - 8) + (-1 + 8i)

expand the bracket

$4 - 5i + 2i +8 - 1 + 8i

Now, collect like terms

$-5i +2i + 8i +4 +8 - 1

Add or subtract the like terms

$5i -11

Hence, the expression is $5i -11

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663.

i found out what 35% of 1020 is and then subtracted that by 1020.

Answer:

24 inches.

Step-by-step explanation:

In order for a triangle to be obtuse, one of its angles must be greater than 90 degrees. In a right triangle, the angle opposite the hypotenuse is always 90 degrees, so in order for the triangle to be obtuse, the hypotenuse must be the longest side.

To find the lowest whole number side length in inches that would ensure that the triangle is obtuse, we can use the Pythagorean theorem. The Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

a^2 + b^2 < c^2

If we take the base 48cm and convert it to inches, 48cm = 48*0.393701 = 18.897638 inches

So the base is 18.897638 inches.

Now we have to find the lowest whole number side length of c so that:

18.897638^2 + b^2 < c^2

358.565744 + b^2 < c^2

We can see that the lowest whole number of c is 24 inches.

So, the lowest whole number side length in inches that would ensure that the triangle is obtuse is 24 inches.

The difference between the greatest 6-digit and smallest 6-digit numbers is 899999.

The aim is to find the smallest and largest 6-digit numbers, and then we need to find how many numbers are between these two values.

Let's start by finding the smallest 6-digit number.

We know that 0 is the smallest digit that can not be used in the highest place value, so we will consider the next smallest digit; that is, 1 and 1 can be used in the highest place value.

Thus, we can create the required 6-digit smallest number with 0 and 1.

Hence, the smallest 6-digit number is 100000.

Now, we will discover the largest 6-digit number.

As we know, the largest digit is 9, which can be used anywhere. So, we will form the largest 6-digit number with the digit 9.

Thus, the largest 6-digit number is 999999.

Next, we need to find the difference between these two values.

So, we can determine the difference between the smallest 6-digit number and the largest 6-digit number by subtracting the smallest from the largest.

Thus, we get,

⇒999999−100000

⇒899999

Hence, 899999 is the difference between the smallest 6-digit and the largest 6-digit numbers.

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The factor of 9x² 24xy 16y² is (3x−4y)²

A number or other mathematical object is factorized or factored when it is written as the product of numerous factors, usually smaller or simpler things of the same kind.

Factorization in mathematics is the method of dividing a large number into tiny ones that, when multiplied together, give you the original number. Factorization is the split of a number into its factors or divisors.

9x²−24xy+16y²

=(3x)²−24xy+(4y)²

=(3x)²−2(3x)(4y)+(4y)²

Using (a−b)²=a²−2ab+b², we get

=(3x−4y)²

Factorization, also known as factoring, is the process of dividing or decomposing a thing into factors that, when multiplied together, form the original number, matrix, etc.

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1) Triangle Midsegment Theorem will be used to solve the given problem.

2) The value of x would be 10.

What is Triangle Midsegment Theorem?

A triangle midsegment is a segment that links the midpoints of two triangle sides. A midsegment joining two triangle sides is parallel to the third side and half the length.

1) Triangle Midsegment Theorem will be used to solve the given problem.

2) Here M is the midpoint of AB, and P is the midpoint of BC. So, PM is a midsegment.

Therefore by the Triangle Midsegment Theorem,

      [tex]PM=\frac{1}{2} AC\\\\(x+5)=\frac{1}{2} 3x\\\\x=10[/tex]

 Hence, The value of x would be 10.

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The three types of multiplication properties are given by :

1. Commutative property : a × b = b × a , a, b ∈R

2. Identity property : a × 1 = a , a ∈ R

3. Distributive property : a × ( b + c ) = a × b + a × c , a, b, c ∈R.

As given in the question,

Three types of multiplication property is given by :

Let us consider variable a, b, c belongs to real number R.

1. Commutative property :

Order of the multiplication having no affect on the final outcome.

a × b = b × a

Example : 5 × 4 = 20

4 × 5 = 20

2. identity property :

Multiplying one to any real number always gives the same number.

a × 1 = a

Example : 3 × 1 = 3

3. Distributive property :

Adding first two numbers and then multiplying or first multiplying each pair and then adding result remain same.

a × ( b + c ) = a × b + a × c

Example:

5 × ( 2 + 1 )  = 5 × 2 + 5 × 1

Therefore, the three types of multiplication property are given by :

1. Commutative property

2. Identity property

3. Distributive property

The above question is incomplete , the complete question is :

What are the 3 types of multiplication properties ?.

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Answer: 4,000 people live in condominiums.

Step-by-step explanation:

First add 55%+25%=80%

Then subtract 100%-80%=20%

Then turn 20% to 0.2.

Last, multiply 0.2x20,000= 4,000

Different types of multiplication method is given by :

a. Addition method

b. Vertical method

c. Box method

d. Partial multiplication method

As given in the question,

Different types of the multiplication method are as follow :

a. Addition method :

In addition method if 4 × 3 it means add 4 three times.

4 + 4 + 4 = 12

b. Vertical method :

It is traditional way of multiplying the given numbers . Example : 12 × 4

1 2

×4

48

c. Box method :

In this box was formed as per the given numbers . Example 42 × 13

           10          3

40     400         120

2       20           6

Add : 400 + 120 + 20 + 6 = 546

d. Partial multiplication method :

This method is based on distributive property to make the calculation easy.

45 × 6

= ( 40 + 5 ) × 6

= 40 × 6 + 5 × 6

= 240 + 30

= 270

Therefore, the different types of multiplication methods are:

a. Addition method

b. Vertical method

c. Box method

d. Partial multiplication method

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Answer:

  9xy² -6x²y +5x³

Step-by-step explanation:

You want the additive inverse of –9xy² + 6x²y – 5x³.

The additive inverse is the value that gives zero when added to the original. It can be formed by changing the signs of the terms in the sum:

  9xy² -6x²y +5x³

Answer:

that even a complete problem?

Answer: A

Step-by-step explanation:

when you have a number to a negative power, putting it as a fraction under 1 will turn the negative power positive

The slope of y = -3x + 3 is -3, it's the coefficient of the x variable.

What is slope ?

Slope, also known as gradient, is a measure of the steepness of a line. It is the ratio of the change in the y-coordinate to the change in the x-coordinate between any two distinct points on the line. It is represented by the letter "m" in the slope-intercept form equation of a line y = mx + b, where m is the slope, x is the independent variable, y is the dependent variable and b is the y-intercept, the point where the line crosses the y-axis.

The slope of a line is a measure of its steepness or incline. It is the ratio of the change in the y-coordinate (rise) to the change in the x-coordinate (run) between two points on the line. The slope is represented by the letter "m" and it is the coefficient of the x variable in the equation of the line y = mx + b, where b is the y-intercept.

In this case, the equation of the line is y = -3x + 3,

The slope of y = -3x + 3 is -3, it's the coefficient of the x variable.

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Answer:c

Step-by-step explanation: