Use the commutative and :or associative properties to simplify 2/5 + 5/12 + (-2/5)

Answer:

Step-by-step explanation:

The f(9) means that the value of x would be 9 in any given equations or functions.

For example:

[tex]f(x) = 2x^{2} + 5\\f(9) = 2(9)^{2} + 5\\f(9) = 2(81) + 5\\f(9) = 162 + 5\\f(9) = 167[/tex]

On the other hand, f(x) = 9 means that the value of a certain function is simply equal to 9.

Answer:

---------------------------------------

Mark's weight is 75 pounds ad his sister's weight is w.

Together, he and his sister weigh 10 pounds more than two times the weight of his sister,

Set up equation:

Solve it for w:

Check the picture below.

so each row has a few gaps, but also has a few surplusses, so we can use the surplusses to fill up the gaps, and that will give us more or less 3 + 5 + 4 + 4 units, namekly 16 units.

1234 in. set A and 1234 in set B and 1234 in set C so the answer is (1234)

The value of the set ( A ∩ C )' = A' ∪ C' = { 4 , 5 , 6 , 7 , 8 }

The set formula is given in general as n(A∪B) = n(A) + n(B) - n(A⋂B), where A and B are two sets and n(A∪B) shows the number of elements present in either A or B and n(A⋂B) shows the number of elements present in both A and B.

Given data ,

Let the universal set be represented as U

The value of U = { 1, 2, 3, 4, 5, 6, 7, 8 }

Let the value of set A = { 1 , 2 , 3 , 4 }

Let the value of set C = { 1 , 2 , 3 , 6 , 8 }

Now , the equation of set is  ( A ∩ C )'

The value of ( A ∩ C )' = A' ∪ C'

Substituting the values in the equation , we get

A' = U - A

A' = { 1, 2, 3, 4, 5, 6, 7, 8 } - { 1 , 2 , 3 , 4 }

A' = { 5 , 6 , 7 , 8 }

And ,

C' = U - C

C' = { 1, 2, 3, 4, 5, 6, 7, 8 } - { 1 , 2 , 3 , 6 , 8 }

C' = { 4 , 5 , 7 }

So , ( A ∩ C )' = A' ∪ C'

Substituting the values in the equation , we get

( A ∩ C )' = { 4 , 5 , 6 , 7 , 8 }

Hence , the set ( A ∩ C )' is { 4 , 5 , 6 , 7 , 8 }

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Answer:

B

Step-by-step explanation:

They put the decimal point in the wrong place.

Answer:

the answer is that 2.5 - 0.8 = 1.7

The intercept, b of the line is 20

It is important to note that the general equation of a line is expressed as;

y = mx + c

Given that;

From the information, we have that;

Now, substitute the values to determine the intercept

50 = 5(6) + c

expand the bracket

50 = 30 + c

collect like terms

c = 50 - 30

c = 20

Hence, the value is 20

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By using the recursive formula, we will see that the sixth term of the sequence is:

A₆ = -1,459

Here we have a sequence where the recursive formula is:

Aₙ = -3Aₙ₋₁ - 4

Where the initial term of the sequence is A₁ = 5

Now we want to find A₆, to do it, we need to find all the previous terms, we will get:

A₂ = -3*A₁ - 4

    =  -3*5 - 4 = -19

A₃ = -3*A₂ - 4

    = -3*-19 - 4

    = 53

A₄ = -3*A₃ - 4

    = -3*53 - 4

    = -163

A₅ = -3*A₄ - 4

    = -3*-163 - 4

    = 485

A₆ = -3*A₅ - 4

    = -3*485 - 4

    = -1,459

The value of the sixth term is -1,459.

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The area of a triangle can be calculated if we know the lengths of all three sides of the triangle or the lengths of two sides and the measure of the included angle. In this case, we are given the lengths of two sides of the triangle (7 yards and 9 yards) and the measure of the included angle (49 degrees).

To find the length of the third side we can use the Law of Cosines. Which states that, in a triangle with sides a, b and c, and an angle C opposite to side c, c² = a² + b² - 2ab * cos(C).

In this case, a = 7, b = 9 and C = 49. So, we can calculate the value of c which is the length of the third side. Once we have this value, we can use Heron's formula, which states that the area of the triangle is equal to √(s(s-a)(s-b)(s-c)), where s is the semiperimeter of the triangle (s = (a+b+c)/2).

By using these formulas we can calculate the area of the triangle which is approximately 25.38 square yards.

I hope this helps :)

Therefore , the solution of the given problem of interest comes out to be

A = $3,130.37  is the amount after 15 years.

Simple interest is calculated by dividing the principal by the borrowing cost, the remaining time, and other elements. The simple return formula in marketing is principal + interest plus hours. Utilizing this method is the simplest way to calculate interest. As a percentage of the principle sum is the most frequent way to calculate income. For instance, he will only pay his portion of the 100% cost if he borrows $100 from a friend and agrees to pay the loan back with 5% interest.. You have to pay interest on money you borrow, and you have to charge interest on money you lend.

Here,

Given :  

a ) the equation that can be formed is

2500x - 1.5y = 30

b)

Using compound formula :

=> Then solve the equation for A

A = P(1 + r/n)nt

A = 2,500.00(1 + 0.015/12)(12)(15)

A = 2,500.00(1 + 0.00125)(180)

A = $3,130.37

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The equation that could be used to represent the context if a represents the cost of labor per hour is a = 481/3.25.

An equation is written in the form of variables and constants separated by the operation of multiplication and division,

An equation states that terms in different forms on both sides of the equality sign are equal.

Multiplication and division do not separate the terms of an equation.

Given,  The technician at the store worked on the computer for 3.25 hours and charged him $78 for parts and the total was $484.25.

Therefore, The equation representing the context is,

3.25a + 78 = 484.25.

3.25a = 484.25 - 3.25.

3.25a = 481.

a = 481/3.25.

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Answer: 125

Step-by-step explanation:

Answer: Here it is

1) The range is {y | y ≥ 11.5}. This is true.

2) The domain is all real numbers. This is true.

3) The y-intercept is 4.5. This is False. The y-intercept is 7.

4) There is no X-intercept. This is true.

5) The rate of change is $4.5 per mug. This is true.

C(m) = 4.50m + 7 is a linear function, and the slope of a linear function represents the rate of change (or the unit rate of change) which is 4.5 dollars per mug. The y-intercept represents the cost when no mugs are ordered which is 7 dollars. As the domain is all real numbers this means that Marta can order any number of mugs. And as the range is {y | y ≥ 11.5} this means that the minimum cost for any order will be 11.5 dollars.

And as there is no X-intercept, this means that the function never crosses the x-axis, this means that the function can never have a y value of zero, which confirms that it doesn't have an X-intercept.

The resulting stack of items :

[3,6,9,10,14,16,17].

It is a linear data structure that carries out the operations in a certain order.

Because we can only access the elements on the top of the stack, maintaining the reference to the top of the stack, which is the last element to be placed, is necessary to implement the stack.

Given:

Stack = [3,6,9,10,14,17].

Now we know in Stack elements are added or removed from the rear end of a stack or a queue.

So,

(1)  Add/push a new number : 10

Resulting stack :[3,6,9,10,14,17,10]

(2)  Add/push another number : 16

Resulting Stack :[3,6,9,10,14,17,10,16]

(3)  You remove/pop a number

Resulting stack : [3,6,9,10,14,16,17].

Therefore, resulting stack : [3,6,9,10,14,16,17].

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The required values are ∠B ≈ 59° and ∠C ≈ 31° for the given triangle.

Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.

The triangle is given in the question, as shown

As per the tangent function,

tan ∠B = AC/AB

tan ∠B = 35/21

∠B = tan ⁻¹(35/21)

∠B = tan ⁻¹(1.667)

∠B ≈ 59°

tan ∠C = AB/AC

tan ∠C = 21/35

∠C = tan ⁻¹(21/35)

∠C = tan ⁻¹(0.6)

∠C ≈ 31°

Thus, the required values are ∠B ≈ 59° and ∠C ≈ 31°.

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The expression for the perimeter of the right triangle with hypotenuse 2p + 8 and base p - 5 is: perimeter = (p - 5) + sqrt((2p + 8)^2 - (p - 5)^2) + (2p + 8)

What is triangle ?

Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always 180 degrees.

In a right triangle, the hypotenuse (the longest side) is opposite the right angle, and the other two sides are called the legs. In this case, the hypotenuse is 2p + 8 and one of the legs (the base) is p - 5.

To find the third side (the other leg), we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs. In other words:

(hypotenuse)^2 = (leg 1)^2 + (leg 2)^2

Substituting the given values, we get:

(2p + 8)^2 = (p - 5)^2 + (leg 2)^2

Simplifying and solving for leg 2, we get:

leg 2 = sqrt((2p + 8)^2 - (p - 5)^2)

Now we can use the perimeter formula, which is the sum of the lengths of all the sides of the triangle. In this case, the perimeter of the triangle is:

perimeter = (leg 1) + (leg 2) + (hypotenuse)

Substituting the given values and the expression we found for leg 2, we get:

perimeter = (p - 5) + sqrt((2p + 8)^2 - (p - 5)^2) + (2p + 8)

Therefore, the expression for the perimeter of the right triangle with hypotenuse 2p + 8 and base p - 5 is: perimeter = (p - 5) + sqrt((2p + 8)^2 - (p - 5)^2) + (2p + 8)

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Answer: -2

Step-by-step explanation:

Given, aₙ = aₙ - ₁ - 3

so,

a₂ = a₁ - 3 = 7 - 3 = 4

a₃ = a₂ - 3 = 4 - 3 = 1

a₄ = 1 - 3 = -2

Pls mark as brainliest if possible. Cheers

The vertex form of the equation of the parabola is (y - 6) = - 2 · (x + 6).

Parabolae can be described by quadratic equations, whose forms are standard form and standard form. The vertex form of the equation of the parabola is shown below (please notice that parabolas are parallel to y-axis when its axis of symmetry is a vertical line):

y - k = C · (x - h)²

Where:

If we know h = - 6, k = 6 and (x, y) = (- 5, 4), then the vertex constant is:

C = (y - k) / (x - h)²

C = (4 - 6) / [- 5 - (- 6)]²

C = - 2 / 1²

C = - 2

The equation of the parabola in vertex form is (y - 6) = - 2 · (x + 6).

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Answer:

Step-by-step explanation:

²

a. 72² - 28² = (72 + 28)(72 - 28) = 100 × 44 = 4,400

b. 85² - 25² = (85 + 25)(85 - 25) = 110 × 60 = 6,600

Answer:

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

Step-by-step explanation:

In a 45-45-90 triangle to find the two shorter sides (a and b) are represented as the number n in this case n is [tex]\sqrt{3\\[/tex] . The hypotenuse on the other hand is can be found by doing n[tex]\sqrt{2\\}[/tex] so you multiply [tex]\sqrt{3}(\sqrt{2} )[/tex] to get [tex]\sqrt{6}[/tex]

The solution is

a) The diagram can represent the equation A = 10 ( 4 ) + 10 ( 10 ) = 140 and Andre's explanation is True

b) The diagram cannot represent 410 and Diego's explanation is False

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

The number of small squares = 4 squares

The number of squares in the rectangle = 10 squares

So , the total number of squares = 10 + 4 = 14 squares

Now , the equation will be

a)

Andre's explanation says that diagram can represent 140

So , when A = 140

The total number of squares = 14

when one square = 10 ,

On simplifying the equation , we get

A = 10 ( 10 ) + 4 ( 10 )

The value of A = 100 + 40 = 140

So , each square can have a value of 10

And , Andre's explanation is True

b)

Diego's explanations says that diagram can represent 410

So , when A = 140

The total number of squares = 14

when one square = 10 ,

The value of A = 410 / 14

On simplifying the equation , we get

A = 29.28571..

So , each square cannot have an equal value

And , Diego's explanation is False

Hence , the equations are solved

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Answer:

2.48 x 10⁻² or 2.48 x 10^-2

Step-by-step explanation:

Alr, so 1.24 x 3.6/1.8 = 1.24 x 2 = 2.48

10² x 10⁻³ x 10⁻¹ = 10⁻²

Therefore, your answer is, 2.48 x 10⁻² or 2.48 x 10^-2.

Cheers!

each of the lap is of length 6617.6 miles.

What are Distance and velocity?

a velocity is a unit of measurement for the Distance an object travels in a

the predetermined period of time. Here is a word equation that illustrates the

connection between space, speed, and time: velocity is calculated by

dividing the total Distance traveled by the journey time.

Diane and Douglas both drive at an average rate of 50 miles per hour. So if they travel for the same time they will end up covering the same distance as well.

As we know velocity = rate of change of displacement or

She drove a total distance of 86,028.8 yd on a race track.

He drove 13 laps where each lap was the same lefty.

each lap is 86028.8/13 = 6617.6

Hence each of the lap is of length 6617.6 miles.

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well, the subtotal cost will be 48.30 + 17.75 = 66.05, now let's add the tax to that

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{6\% of 66.05}}{\left( \cfrac{6}{100} \right)66.05} ~~ \approx ~~ 3.96~\hfill \underset{total~cost}{\stackrel{66.05~~ + ~~3.96}{\approx \text{\LARGE 70.01}}}[/tex]

The total cost of the purchase is $70.013.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Set of baseball cleats = $48.30

Baseball gloves = $17.75.

Sales tax = 6%.

This means,

6% of (48.30 + 17.75)

= 6/100 x 66.05

= $3.963

Now,

Total cost.

= 48.30 + 17.75 + 3.963

= $70.013

Thus,

The total cost is $70.013.

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Women literacy rate since five years in Kerala is as follows:

2018 = 65.8%

2019 = 70.30%

2020 = 84.4%

2021 = 92.1%

2022 = 95.2%

The proportion of people in a given age group who are reading and writing proficiently is known as the literacy rate. A person must be at least 15 years old to be considered an adult, 15 to 24 years old to be considered a young person, and 65 years old or older to be considered an elder. The ability to understand a brief, simple statement about daily life is typically used to measure it.

Most of the time, literacy includes numeracy as well, and measurements sometimes include a quick evaluation of arithmetic proficiency. It is important to distinguish between the literacy rate and the total number of literates and functional literacy, a more thorough assessment of literacy conducted over time and allowing for the determination of multiple proficiency levels.

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Answer:

flagpole is sqrt(7h)

Step-by-step explanation:

We can use similar triangles to find the height of the flagpole.

Since Justin can see the top of the pole in the mirror, we can assume that the mirror and the ground form a right angle and the flagpole, mirror and Justin form a right triangle.

We can use the concept of similar triangles to find the height of the flagpole.

Let h be the height of the flagpole.

We can set up a proportion:

(7+h)/h = h/(7)

Cross-multiply and solve for h:

7h + h^2 = 7h

h^2 = 7*h - 7h

h^2 = 7h

h = sqrt(7h)

So the height of the flagpole is sqrt(7h)

It is worth noting that this answer is a square root of a variable and not a numerical value, thus we can't find an exact value of the height of the flagpole.

The number of Cloud cupcakes that each person will be 4.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

I'm on a team of 9 people and we told our teacher that together we could eat 36 Cloud cupcakes.

The number of Cloud cupcakes that each person will be given as,

⇒ 36 / 9

⇒ 4

The number of Cloud cupcakes that each person will be 4.

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The measure of ∠RQP is, 45°

The measure of ∠SPR is, 50°

The measure of ∠PSR is, 50°

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

We have to given that;

In trapezoid PQRS,

PQ is parallel to SR, and diagonal PR is drawn.

And, SP = SR, SRP = 50°, and PRQ = 85°

Here, SP = SR

So, We get;

In Δ PSR; ∠PRS = ∠SPR = 50°

And, PQ is parallel to SR.

Hence, We get;

⇒ ∠SRP = ∠RPQ = 50°

Now, In Δ PQR;

⇒ ∠PRQ + ∠QPR + ∠PQR = 180°

⇒ 85° + 50° + ∠PQR = 180°

⇒ 135° + ∠PQR = 180°

⇒ ∠PQR = 180° - 135°

⇒ ∠PQR = 45°

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The amount invested in the two different bank accounts which has a simple interest of $ 560 is $ 2000 and $ 4000 respectively

Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.

Simple Interest = ( Principal Amount x Rate x Time Period ) / 100

Given data ,

Let the simple interest be represented as SI

The value of SI = $ 560

Now , the total amount A = $ 6000

Let the first bank account be A

Let the second bank account be B

The amount invested in the bank account A be = P

The amount invested in the bank account B be = ( 6000 - P )

The rate of interest of bank account A = 8 %

The rate of interest of bank account B = 10 %

Now ,

The SI of bank account A = ( Principal Amount x Rate x Time Period ) / 100

Substituting the values in the equation , we get

The SI of bank account A = ( P x 8 x 1 ) / 100

The SI of bank account A = 8P/100

And ,

The SI of bank account A = ( Principal Amount x Rate x Time Period ) / 100

Substituting the values in the equation , we get

The SI of bank account A = [ ( 6000 - P ) x 10 x 1 ] / 100

The SI of bank account A = ( 60000 - 10P ) /100

And , the total SI = $ 560

So ,

8P/100 +  ( 60000 - 10P ) /100 = 560

Multiply by 100 on both sides of the equation , we get

8P + 60000 - 10P = 56000

On simplifying the equation , we get

-2P = -4000

Divide by -2 on both sides of the equation , we get

P = $ 4000

So , the amount invested in bank account A = $ 4000

And , the amount invested in bank account B = $ 2000

Hence , the amount invested is $ 4000 and $ 2000 respectively

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Answer:

Step-by-step explanation:

No, the entire population of Turks and Caicos would not be able to fit on the football field. The total area of the football field is 6,480 square yards, which is equivalent to 13,728 square feet. Since each person takes up 2 square feet, this means that only 6,864 people could fit on the field. Therefore, the population of Turks and Caicos is more than double the amount of people that could fit on the football field.

The solution is 9x - 36u + 27.

What is the linear equation?

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line. An example of a linear equation is y=mx + b.

We have given

-9(-×+4u-3)

When you multiply a negative number by another negative number, the result is positive.

So, to solve this problem, we can use the distributive property and simplify:

-9(-x + 4u - 3) = -9(-x) + -9(4u) + -9(-3)

= 9x - 36u + 27

Hence, the solution is 9x - 36u + 27.

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a) When Ozzie Foster deposits $2,000 at the end of each year,

amount in account after 25 years = $126571.43

b) If Ozzie had deposited the $2,000 at the beginning of each year,

amount in account after 25 years = $135431.43

An annuity is a financial product that pays out a fixed stream of payments to an individual, primarily used as an income stream for retirees.

Given,

Value of each payment P = $2000

Rate of interest per period in decimal r = 7% = 0.07 per year

Number of years n = 25

a) future value of ordinary annuity

FV = P×((1+r)ⁿ−1) / r

FV = 2000×((1+0.07)²⁵−1) / 0.07

FV = 2000×((1.07)²⁵−1) / 0.07

FV = 2000×(5.43 - 1 )/ 0.07

FV = 2000×4.43/ 0.07

FV = 8860/0.07

FV = $126571.43

b) future value of annuity due

FV = (1+r)P×((1+r)ⁿ−1) / r

FV = (1+0.07) × $2000((1+0.07)²⁵ - 1)/0.07

FV = 1.07 × 2000×((1.07)²⁵−1) / 0.07

FV = 1.07 × 2000×(5.43 - 1 )/ 0.07

FV = 1.07 × 2000 × 4.43 / 0.07

FV = 2140 × 4.43 / 0.07

FV = 9480.2 / 0.07

FV = $135431.43

Hence,

a) $126571.43 is the amount in the account when Ozzie Foster deposits $2,000 at the end of each year.

b) $135431.43 is the amount in the account If Ozzie had deposited the $2,000 at the beginning of each year.

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