The graph of a function h is shown below use the graph of the function to find its average rate of change from x=5 to x=7

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answer:

main types of numbers used in mathematics are listed below:

• natural numbers   also called positive integers, counting numbers, or natural numbers); they are the numbers {1, 2, 3, 4, 5, …}

• whole numbers- this is the set of   natural numbers, plus zero, i.e., {0, 1, 2, 3, 4, 5, …}.

• integers   -this is the set of all whole numbers plus all the negatives (or opposites) of the natural numbers, i.e., {… , ⁻2, ⁻1, 0, 1, 2, …}

• rational numbers   -this is all the fractions where the top and bottom numbers are integers; e.g., 1/2, 3/4, 7/2, ⁻4/3, 4/1 [note: the denominator cannot be 0, but the numerator can be].

• real numbers - (also called measuring numbers or measurement numbers). this includes all numbers that can be written as a decimal. this includes fractions written in decimal form e.g., 0.5, 0.75 2.35, ⁻0.073, 0., or 2.142857. it also includes all the irrational numbers such as π, √2 etc. every real number corresponds to a point on the number line.

read the details about numbers in

: given:   3.111 + 3.11 + 3.1

  = 9321/1000

=9.321

there are four fundamental operation used in mathematics to solve the given problem.   read the details of the symbol of operation in mathematics in

1. addition

adding two (or more) numbers means to find their sum (or total).   the symbol used for addition is '+'.

for example, 10 + 10 = 20

this is read as ten plus ten is equal to twenty or simply, ten plus ten is twenty.

example 1

find the sum of 10 and 8.

solution:

10 + 8 = 18

addition of large numbers

to add large numbers, list them in columns and then add only those digits that have the same place value.

2. subtraction

subtracting one number from another number is to find the difference between them.   the symbol used for subtraction is '–'.   this is known as the minus sign.

for example, 17 – 8 = 9

this is read as seventeen take away eight is equal to nine (or seventeen take away eight is nine).   also, we can say that 17 minus 8 is 9.

3.multiplication

multiplication means times (or repeated addition).   the symbol used for multiplication is '×'.

for example, 7 × 2 = 14

this is read as seven times two is equal to fourteen or simply, seven times two is fourteen.

to multiply a large number with another number, we write the numbers vertically and generally multiply the larger number with the smaller number.

note:

a product is the result of the multiplication of two (or more) numbers.

remember:

• to multiply two large numbers, write the numbers vertically with the larger number generally being multiplied by the smaller number which is called the multiplier.

• we use the 'times table' to find the product of the larger number with each digit in the multiplier, adding the results.

• remember to add a zero for every place value after the multiplying digit.   for example, if the multiplying digit is in the hundreds column, add two zeros for the tens column and for the units column.

4. division

division 'undoes' multiplication and involves a number called the dividend being 'divided' by another number called the divisor.   the symbol used for division is '÷'.

note:

• as division is the inverse of multiplication, start by dividing 4 into the column furthest to the left.

• 6 ÷ 4 = 1 and 2 is the remainder.

• clearly, the remainder 2 is 200 (i.e. 20 tens); and we can carry this into the tens column to make 29.

• now, 29 ÷ 4 = 7 with a remainder of 1.   clearly, the remainder of 1 is 10 (i.e. 10 units) and we carry this into the units column to make 12.

• finally, 12 ÷ 4 = 3.

summary

• the four basic mathematical operations are:

• adding two (or more) numbers means to find their sum (or total).

• subtracting one number from another number is to find the difference between them.

• multiplication means times (or repeated addition).   a product is the result of the multiplication of two (or more) numbers.

• division 'undoes' multiplication.

read the details about why mathematics is important in

The average rate of change from x=-7 to x=-5 is -3

Step-by-step explanation:

In order to calculate average rate of change we would have to make the following calculation:

According to the given data we have the following:

x=-7 so, f(-7) is to be calculated in the graph y

x=-5 so, f(-5) is to be calculated in the graph y

Therefore, average rate of change=f(-5)-f(-7)/-5-(-7)

average rate of change=3-9/2

average rate of change=-6/2

average rate of change=-3

The average rate of change from x=-7 to x=-5 is -3



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