Learning task 2. Complete the following to make a true statements. Then, determine the property applied.
1. 18 + _______ = 6 + 18
2. -40 + ________ = 0
3. ( 10 + 3 ) + 6 = 10 + ______
4. -15 + ________ = -15
5. _______ + 0 = 42
6. -2 ( 5 + 8 ) = ___________ + ( -16 )
7. 30 ( _____ ) = 30
[( 4 )( 6 )] 2 = 4 [ ___________ ]
9. 15 * ______________ = 0
10. ( 12 )(-4 ) = ________ 12

Answer:

[tex]72cm[/tex]

watch the cm sign too

Step-by-step explanation:

[tex]area = s2[/tex]

I think you should find the square root in order to get the length of one side

[tex] \sqrt{64} [/tex]

answer is 8, then you multiply 8 by 9 to get the length of one side of the board

[tex]9 \times 8[/tex]

[tex] = 72cm[/tex]

that should be your final answer

log (24) is each expression as a single logarithm.

A logarithm is defined simply.

Each of the properties of exponential functions has an analog for

logarithmic functions.

logb(x)+logb(y)= logb(xy)

Use this properties

log 8+log 3  = log ( 8 * 3 )

log 8+log 3  = log (24)

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By applying the distributive property, the equivalent expression to 3v - (7.9w - 9.3) is: 3v - 7.9w + 9.3.

Two expressions are equivalent if they both have equal values when simplified or evaluated.

To apply the distributive property, the term or operation sign outside the parentheses is used to multiply each of the terms that are within the parentheses.

Given the expression, 3v - (7.9w - 9.3)

Apply the distributive property to find an equivalent expression

3v - (7.9w - 9.3) = 3v -(7.9w) - (-9.3)

3v - (7.9w - 9.3) = 3v - 7.9w + 9.3

Therefore, by applying the distributive property, the sign "-" is distributed to get the equivalent expression to 3v - (7.9w - 9.3, which is: 3v - 7.9w + 9.3.

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The quadratic equation is an equation of the form ax^2 + bx + c =0. Note that the quadratic equation is a polynomial of degree two. This implies that the highest power of x in the quadratic function is power two.

The quadratic formula is given by x = -b ± √b^2- 4ac/2a. The discriminant can be used to obtain the nature of the roots of a quadratic equation. If the roots are real and positive we would have a positive discriminant. If the value of the discriminant is negative then it implies that the roots of the equation are imaginary.

The discriminant can be given as √b^2 - 4ac. The statements that are true about the quadratic formula are;

x = -b/2a gives the line of symmetry

√b^2- 4ac/2a gives the maximum and the minimum points of the quadratic equation

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The solution to the inequality expression 22 >= -3x + 7 and -3x + 7 >-17 is -5 <= x  < 8

A number line is a  vertical or horizontal line that has endpoints and it is used to represent numbers at a constant interval

The expression is given as

22 >= -3x + 7 and -3x + 7 >-17

The above expression is an inequality expression

As a general rule:

Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal

So, we have

22 >= -3x + 7 and -3x + 7 >-17

Evaluate the like terms

15 >= -3x  and -3x  >-24

Divide through by -3

So, we have

-5 <= x  and x  < 8

Combine the expressions

-5 <= x  < 8

Hence, the solution to the inequality expression 22 >= -3x + 7 and -3x + 7 >-17 is -5 <= x  < 8

See attachment for the number line

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Answer:

Step-by-step explanation: Hope my explanation  made sense

Answer:

Thank you, if you need more clarification on the system of parallelograms, let me know.

The rate of change in gas usage is 34.70 miles per gallon.

The rate of change is the total gallons used for every one mile travelled. To determine the rate of change, divide the miles driven by the gallons used.

Division is the mathematical operation that is used to determine the quotient of a number. It involves grouping a number into equal parts using another number. The sign used to represent division is ÷.

Rate of change = miles driven / gallons used

1041 / 30 = 34.70 miles per gallon

1596. 2 / 46 = 34.70 miles per gallon

1665.6 / 48 = 34.70 miles per gallon

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The result of simplifying each number 1000⁴/₃ / 100³/₂ using the exponent rules is: 10

To solve this exercise we have to resolve algebraic operations following the exponent rules.

(1000⁴/₃) / (100³/₂)

Base: 1000 = 10³

Base: 100 = 10²

As 1000 is the same as 10³ and 100 is the same as 10², we get:

(10³)⁴/₃ / (10²)³/₂

Using the power of a power rule that indicates that: the exponent result will be the multiplication of these exponents, we have:

10³*⁴/₃ / 10²*³/₂

10¹²/₃ / 10⁶/₂

10⁴ / 10³

Using the quotient rule that indicates that: the exponent result will be the subtraction of these exponents, we have:

10⁽⁴⁻³⁾

10

In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.

Example: 3² = 3*3 = 9

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Answer:

Arrow

Because I used a word calc that took me like 5 mins to find lol

Answer:

50.28 m²

Step-by-step explanation:

Area of a circle = pi r²

= 22/7 × 4 × 4

= 50.28 m²

Answer:

52 is the answer to that question

Answer:

que aa que quiere uste puntos yo tmbb ayuda

Yes. The Law of Detachment dictates that Catalina employ Speedy. The conclusion should come naturally if the hypothesis is correct.

According to the Law of Detachment, in order for our desires to manifest in the physical reality, we must dissociate ourselves from the outcome or result. For things to happen after we have done our part, we must learn to let go of the result. And when we do let go, things start to happen. They might not arrive in the manner we anticipated, but they do. Why is letting go so difficult? The most potent and difficult law is the Law of Detachment. The ability to accept things as they come, when they arrive, and in whatever form they take and to learn to be happy no matter what is closely tied to the law of detachment.

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When 4 nightstands are sold the profit is $1800 since the number of nightstands sold is directly proportional to the profit.

The profit is defined as difference between the cost price and sell price for a product.

A directly proportional relationship means that if two variables x and y are proportional to one another then there exist a constant k such that x = y × k .

The graph of a directly proportional equations is a straight line passing through the origin.

Given that the profit is $900 for 2 sold nightstands, $3600 for 8 night stands and $4500 for 10 sold nightstands.

Now this relationship is directly proportional.

So the constant is given by k=900/2=4500/10=3600/8=450

Hence the profit for selling 4 night stands is 450 × 4 =$1800

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The measure of variability easiest to compute, but seldom used as the only measure, is the range.

The range is the term that is used to refer to the difference that lies between the highest value and the lowest value in a data set while computing a statistical data.

The measures of variability are 4 in number. These are

Hence we can conclude that The measure of variability easiest to compute, but seldom used as the only measure, is the range.

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The numeric values for the function are given as follows:

A. f(a) = 9a - 9.

B. f(a + h) = 9a + 9h - 9.

C. f(a + h) - f(a) = 9h.

D. (f(a + h) - f(a))/h = 9.

To find the numeric value of a function, we replace each instance of the variable by the desired value.

For this problem, the function is given by:

f(x) = 9x - 9.

At x = a, the numeric value is given by:

f(a) = 9(a) - 9 = 9a - 9.

Hence:

f(a) = 9a - 9.

At x = a + h, the numeric value is given by:

f(a + h) = 9(a + h) - 9 = 9a + 9h - 9.

Hence:

f(a + h) = 9a + 9h - 9.

Subtracting these values, we have that:

f(a + h) - f(a) = 9a + 9h - 9 - 9a + 9 = 9h.

Hence:

f(a + h) - f(a) = 9h.

Dividing by h, we have that:

(f(a + h) - f(a))/h = 9h/h = 9.

Hence:

(f(a + h) - f(a))/h = 9.

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The answer of the given expression is 77 .

We have given an expression 68-5-(13-27)=77

First simplify LHS = 68-5-(13-27)            ...(1)    

According to BODMAS first solve the bracket term .

On solving the bracket term , we get

13 - 27 = - 14

Now put this value in equation (1) , we get

   [tex]LHS = 68-5-(-14) \\LHS=68-5+14\\[/tex]

Now , apply addition and subtraction operation

    [tex]LHS = 63+14\\LHS=77[/tex]

as RHS = 77 = LHS

Hence , the evalution is correct.

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Answer:

n = (f + w)/b

Step-by-step explanation:

bn - w = f

Rearrange the equation so that the subject is on its own, in the format Ax = B

bn - w + w = f + w

bn = f + w

Isolate the subject, so that it's in the format x = C

bn = f + w

bn/b = (f + w)/b

n = (f + w)/b

Using long division 2/3 is found to be 0.6667, the value is discontinued by approximating a 6 to 7

3 | 2 =

3 | 2 = 0.

3 | 20 = 0.

3 | 20 = 0.6        20 - 3 * 6 = 20 - 18 = 2

3 | 2 = 0.6

3 | 20 = 0.6

3 | 20 = 0.66      20 - 3 * 6 = 20 - 18 = 2

3 | 2 = 0.66

3 | 20 = 0.66

3 | 20 = 0.666      20 - 3 * 6 = 20 - 18 = 2

The procedure continues unending to get 0.666666666.........

Hence we say that 2/3 = 0.6666...≅ 0.6667

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Answer:

6 (r + 9)

Step-by-step explanation:

6 times the sum of r and 9 means 6 (r + 9)

The total length between the two fences is 136 ft, and the total cost is 164.56 dollars.

We have a square garden with a perimeter of 60ft. Then if the sidelength of the square is S, we have that:

60ft = 4*S

S = 60ft/4 = 15ft

We know that the first fence is around the perimeter of the garden, so the length of the first fence is exactly 60ft.

Now, the other fence is 2ft away from the first fence, so it forms a square of sidelength of:

15ft + 2*2ft = 19ft

Then the perimeter of this square is:

P = 4*19ft = 76ft

This means that the length of the second fence is 76 ft.

So the total length of fence is 76ft + 60ft = 136ft

And the cost is $1.21 per ft, then the total cost for the fence is:

C = 136*$1.21 = $164.56

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The isolated value of h is found to be V/πr²

The three-dimensional solid shape of a cylinder is made up of two parallel bases connected by a curved surface. These bases have the shape of a spherical disc. The axis of the cylinder is a line drawn through the centre or connecting the centres of two circular bases. The density of a cylinder is determined by its volume, which represents how much material may be immersed in it or carried inside of it. The formula πr²h, where r is the radius of the circular base and h is the height of the cylinder, determines the volume of a cylinder. Any substance that can fill the cylinder consistently with liquid or another material may be used as the component.

According to given formulae:

V=πr²h

On dividing both side with πr² we get

⇒V/πr²=πr²h/πr²

(Solving R.H.S)

⇒h=V/πr²

Therefore, the value of h in the given question is V/πr²

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Part A: Expression to represent the total amount of juice left in the jar : (0.25 +0.30 + 0.75) - 0.20

Part B: Simplifying above expression using properties of addition and subtraction gives that total amount of juice left is  1.1 liter.

An expression is a group of terms consisting of numbers and mathematical operators ( +, -,*,/) and "=" is not there.

Given that a  jar contains 0.25 liter of apple juice, 0.30 liter of grape juice, 0.75 liter of pineapple. Melissa then drank 0.20 liter of the mixture.

Therefore, total juice in the jar before Melissa drank it = quantity of (apple juice + grape juice + pineapple juice ) = (0.25+ 0.30+0.75) liters

After Melissa drank 0.20 liter juice left = total  juice before - 0.20

Thus, Expression to represent the total amount of juice left in the jar is: (0.25 +0.30 + 0.75) - 0.20

And it can be solved as (0.25 +0.30 + 0.75) - 0.20 = (0.55+0.75)-0.20

                                                                                   = 1.30-0.20 = 1.1 liter

Thus, after simplifying expression we get that the left juice in the jar is 1.1 liter.

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If you have applied for two jobs a and b and the probability that you get an offer for the job a is 0.25 and the probability of being offered job b is 0.20, then the probability that you will be offered both jobs is 0.05.

Probability is a term used in mathematics that is concerned with the numerical illustration of the possibility of an event to take place. Its value is between 0 and 1 where 0 illustrates the impossibility of the event to take place while 1 illustrates the certainty of an event to take place.

As the probability of both the jobs are not dependent on each other, the probability that both jobs will be offered can be calculated by the formula;

P(A∩B) = P(A) × P(B)

Here, P(A∩B) represents the probability of both the events to take place together

As P(A) is equal to 0.25

P(B) is equal to 0.20

P(A∩B) = (0.25)(0.20)

P(A∩B) = 0.05

Therefore, 0.05 is the probability that both jobs will be offered.

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There will be a 6% rise using the 0.9646 multiplier, then a 9% reduction.

Simply said, a multiplier is a factor that increases the basic value of another object. For example, a 2x multiplier would double the initial value. On the other hand, a multiplier of 0.5x would actually cut the basic amount in half. In finance and economics, multipliers come in a wide variety.

Say that Number is 100N.

growth of 6%

= (6/100)100N

= 6N

Number following reduction: 100N + 6N = 106N

9% lessening

= (9/100)106N

=954N/100

= 9.54N

Final result after reduction = 106N - 9.54N

=96.46N

=9646N/100

= 9646 * 100N/100 * 100

= 9646 * 100N/10000

= 0.9646 * 100N

There will be a 6% rise using the 0.9646 multiplier, then a 9% reduction.

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Naomi's burger shack sold a total of 484 hamburgers today .Then  121 cheeseburgers were sold and 363 hamburgers were sold

Naomi's burger shack sold a total of 484 hamburgers today.

three times as many hamburgers were sold without cheese as were sold with cheeseburgers

how many cheeseburgers were sold?

according to the question

Hamburgers (H) + cheeseburgers (C) = 484

C + H =  484

H = 3C

we can solve these equation

C+ 3C = 484

4 C= 484

C = 121

then we can find H by putting the value of C

H = 3* 121 = 363

So, 121 cheeseburgers were sold and 363 hamburgers were sold

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According to the solving Mrs. Weatherford spends 15 percent of each weekday  25 hours and 20 minutes in her car.

A % is a relative figure that represents the hundredth part of any amount. One percent (symbolized 1%) is one hundredth part; consequently, 100 percent denotes the complete amount and 200 percent defines twice the supplied amount.

The most fundamental use of percentages is really to compare one number to another, with the second number rebased to 100. Assume we want to know the number among employed females as both a percentage of all employees.

Mrs. Weatherford drives 15% of the time during the week.

We know that:

1 week  = 7days

1day  = 24 hours

So 7 days  = 7 x 24

                  = 168 hours

Mrs. Weatherford drives 15% of the time during the week.

So,

(168/100) * 15

1.68 * 15

25.2 hours

According to the solving Mrs. Weatherford spends 25 hours and 20 minutes in her car.

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If the expression is log a², then the expansion of this expression looks like 2 log a.

Given that the expression is log a².

We are required to find the expansion of the expression.

The change of base formula gives the way to re-write a logarithm operation as a fraction of logarithms with a new base.

We know that log [tex]a^{b}[/tex]=b log a.

The expression is log a². So,

log a²=2 log a   (Power of a will come in front of log)

Hence if the expression is log a², then the expansion of this expression looks like 2 log a.

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The fractions 16/20, 12/15, and 8/10 are equivalent fractions to 4/5.

When writing equivalent fractions, the numerator and denominator should be multiplied or divided by the same number. This is the reason why when these fractions are simplified, they are reduced to the same value.

Let us understand the two ways in which we can make equivalent fractions:

Now, Divide the denominator or numerator by the same number or multiply the denominator and the numerator by the same number.

So, the equivalent fractions for 4/5 are:

(4/5) × (2/2) = (4 × 2) / (5 × 2) = 8/10

(4/5) × (3/3) = (4 × 3) / (5 × 3) = 12/15

(4/5) × (4/4) = (4 × 4) / (5 × 4) = 16/20

After simplifying, 16/20, 12/15, and 8/10 equal 4/5, indicating that they are identical in nature.

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