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1).  0 + (-3) = = -3 is Additive Inverse

2).2(3-5) = 2(3)3) - 2(5) is Associative Property

3). (-6) + (-7) = (-7) + (-6) is Commutative Property

4).1(-9) = = -9 is Multiplicative Identity

5).(-4) (-1/4) = 1 is Commutative Property

6). 2 (3 x 7) = (2 X 3) x 7 is  Associative Property

7). 10 + (-10) = 0 is Additive Inverse

8). 2(5) 5(2) is Commutative Property

9).1(-1/4)= -1/4 is  Multiplicative Identity

10).  (-3)(4 + 9) = (-3)(4) + (-3)(9) ​ is Distributive Property

What is Additive inverse ?

To get a result equal to 0, add the original number and the additive inverse by simply changing the sign of the integer. On the basis of negation of the original number, the characteristics of additive inverse are listed below. For instance, if x is the starting number, then -x is x's additive inverse.

What is Commutative Property ?

This law merely asserts that while adding and multiplying integers, you can rearrange the numbers in a problem without changing the solution. Division and subtraction do not work interchangeably.

A+B=B+A

What is Multiplicative Identity ?

An element of a set that remains intact after being multiplied by any other element of the set. In the set of real numbers, 1 is a multiplicative identity.

What is  Distributive Property?

The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.

What is  Associative Property?

A mathematical principle known as the associative property states that grouping the factors in a multiplication problem does not affect the solution.

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The directions on a swimming pattern says to cut an extra 15 percent of fabric to account for error, Chloe needs 0.75 yard of fabric to make a skirt and she cuts 0.8625 yards,

Given that the directions on a sewing pattern say to cut an extra 15% of fabric to account for an error, and Chloe needs a 0.75 yard of fabric to make a skirt, so she cuts 0.1125 yard, to determine if Chloe cut the correct amount of fabric the following calculation must be made:

0.75 x 1.15 = X

0.8625 = X

0.8625 - 0.1125 = 0.75

Therefore, the amount of fabric that Chloe cut is correct.

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Hercules got 300 cattle from the King for cleaning out his stable

Multiplying fractions is defined as the product of a fraction with a fraction or with an integer or with the variables. The procedure to multiply the fractions are: Multiply the numerator with numerator. Multiply the denominator with the denominator. Simplify the fractions, if required.

To find how many cattle Hercules got for his work, we can simply multiply 3000 by 1/10 and get the value.

3000 * 1/10 = 300.

He got 300 cattle for his work.

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The following equation is not proportional.

What is equation?

An equation is a formula that uses the equals sign to connect two expressions to show that they are equal.

Main Body:

we now that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form k=y/x  or y= kx.

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

In this problem we have

y= 1/(3x+5)

This is the equation of the line in slope intercept form

where

m= 3

b= 5

The given equation not represent a proportional relationship, because the line not pass through the origin

In a proportional relationship the value of b (y-intercept) is equal to zero

Hence , equation is not proportional.

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The equation that could be used to determine x, the number of seconds, when the two tanks have the same amount of water is 120 - 1/2(x) = 100 - 1/4(x) or x = 80.

An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question. An equation is the equality of expressions.

Let x be the number of seconds at the moment that the two tanks have the same amount of water.

If a tank has 120 gallons of water and is being drained at a rate of 1/2 gallon each second, the the amount of water left after time = x is "120 - 1/2(x)".

If another tank has 100 gallons of water and is being drained at a rate of 1/4 gallon each second, the the amount of water left after time = x is "100 - 1/4(x)".

Equate the two expressions to determine the time, x , at which the two tanks have the same amount of water left.

120 - 1/2(x) = 100 - 1/4(x)

20 = 1/4 x

x = 80

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The 3rd degree equation that is divisible by x, (x − 3), (x+1) is x³ - 2x² - 3x.

A cubic polynomial is a sort of polynomial that is based on the variable's largest exponent, or degree, in mathematical terms. As a result, a cubic polynomial is one in which the degree or maximum power of the variable is 3. An algebraic statement having variables, constants, and exponents that are whole integers is called a polynomial.

The given factors are x, (x - 3), (x + 1)

To find the 3rd-degree polynomial divisible by x, (x - 3), (x + 1) multiply the three expressions.

First multiply x, (x - 3)

x × (x - 3)

= x × x - 3 × x

= x² - 3x

Now multiply x² - 3x and (x +1)

(x² - 3x) × (x + 1)

= x²(x) - 3x(x) + x²(1)  - 3x(1)

= x³ - 3x² + x² - 3x
= x³ - 2x² - 3x

So, this is the 3rd-degree equation that is divisible by x, (x − 3), (x+1).

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In a case whereby Carmen has a rope that is 18 meters long. She cuts away a piece that is 8.16 meters long the lenght of the remaining piece of rope is 9.84 metres.

Distance can be described as the space that exist between two or more point, the concept that willbe used in the question is the concept of distance.

The total distance of the rope is 18 meters long , and she cut 8.16 meters long awya which implies that the remaining lenght of the rope will be ( 18 - 8.16)= 9.84 metres

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The measure of the exterior angle to ∠G is 138.9°.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

Given, In triangle EFG, m∠E = 95.2° and m∠F = 43.7°.

We know the sum of all the interior angles in a triangle is 180°.

We also know that the measure of an exterior angle in a triangle is the sum of the two opposite interior angles.

∴ The measure of the exterior angle to m∠G is = m∠E + m∠F.

= 95.2° + 43.7°.

= 138.9°.

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Answer:

3.5 hours

Step-by-step explanation:

74-32=42

42/12=3.5

The length of the shorter side on this plan is 2.8cm.

Based on the information illustrated, let the length of the shorter side on this plan be represented by x.

In this case, the dimensions of a room are 4.2 m by 6 m and on a plan, the longer side is equal to 4cm.

This will be illustrated as:

x/4 = 4.2 / 6

Cross multiply

6x = 4 × 4.2

x = (4 × 4.2) / 6

x = 2.8cm

The length is 2.8 cm.

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The factorized form 16 - [tex](5y-2)^2[/tex] is -1(5y+2)(5y-6)

The expression is

16 - [tex](5y-2)^2[/tex]

The expression is a mathematical statement that consist of different variables, numbers and the arithmetic operators

The expression is

The expression is

16 - [tex](5y-2)^2[/tex]

We know the identity

[tex](a+b)^2= a^2+2ab+b^2[/tex]

Apply this identity on the expression

= 16 -( [tex]25y^2[/tex]- 20y + 4)

Apply the distributive property

= 16 - [tex]25y^2[/tex]+ 20y - 4

Subtract the like terms

= - [tex]25y^2[/tex]+ 20y + 12

Take common term outside

= -1([tex]25y^2[/tex]- 20y - 12)

Split the middle term and apply factorization

= -1 ([tex]25y^2[/tex]+ 10y -30y - 12)

Take common term outside

= -1 ( 5y(5y+ 2) -6(5y +2)

Take common term outside

= -1(5y+2)(5y-6)

Hence, the factorized form 16 - [tex](5y-2)^2[/tex] is -1(5y+2)(5y-6)

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Answer:

5.37/3 = 1.79

Step-by-step explanation:

Given statement,

→ 5.37 divided by 3 equals?

Forming the problem,

→ 5.37/3

Let's solve the problem,

→ 5.37/3

→ (5.37 ÷ 3)

→ 1.79

Hence, the answer is 1.79.

At a local high school, GPA's are normally distributed with a mean of 2.9 and standard deviation of 0.6.

x=4.25 is the GPA highest 2.5% of the students.

We have to find the GPA of the highest 2.5% of the students.

Mean = μ = 2.9

Standard deviation = σ = 0.6

Finding the z value for corresponding area 0.9750

For 95% confidence interval ,

z = 1.96

For 97.5% confidence interval,

We get z = 2.25

From

Z = ( x - μ ) / σ

For 2.5% of the students

To solve for x

x = Z*σ + μ

x = 2.25*0.6 + 2.9

x = 1.35 + 2.9

x = 4.25   GPA of highest 2.5% of students

Hence the answer is, x=4.25 is the GPA highest 2.5% of the students.

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The coordinates of the point that represents the weekly average per run for Week 7 is (7, 3.00).

It is defined as a function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = aˣ

where a is a constant and a>1

It is given that:

Jason decided to begin a workout program. He wants to start running three times a week.

As we know, the exponential function can be represented as:

f(x) = abˣ

The weekly average per run is 1 mi.

He increases his weekly average per run by 17% each week,

The exponential function:

f(x) = 1(1.17)ˣ

Plug x = 7

f(7) = 1(3.0012)

f(7) = 3.00

Thus, the coordinates of the point that represents the weekly average per run for Week 7 is (7, 3.00).

The complete question is:

Jason decided to begin a workout program. He wants to start running three times a week. At the beginning of the workout program, his weekly average per run is 1 mi. He increases his weekly average per run by 17% each week, according to an exponential growth model. Jason makes a sketch of the graph for this situation. He plots the point containing the y-intercept, (0,1) . He then plots the point representing the weekly average per run for Week 7 and rounds the coordinates of the point to the nearest tenth. What are the coordinates of the point that represents the weekly average per run for Week 7?

options:

A. (7, 3.2)

B. (7, 2.7)

C. (7, 3.0)

D. (7, 4.6)

E. (7, 4.1)

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Answer:

7,3,0

Step-by-step explanation:

The name of the function that matches each equation on the blank is,

-|x-7|= h(x)

0.5|x-3|= g(x)

|x-3|-2= f(x)

-5|x-7|=j(x)

A function from a set X to a set Y in mathematics assigns to each element of X exactly one element of Y. The domain of the function is the set X, and the codomain of the function is the set Y.

The first known approximation to the concept of function is attributed to the Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were originally idealistic representations of how one variable quantity depended on another. The location of a planet, for example, changes throughout time. Historically, the concept was formed with infinitesimal calculus near the end of the 17th century, and the functions that were analyzed were differentiable until the 19th century.

The name of the function that matches each equation on the blank is,

-|x-7|= h(x)

0.5|x-3|= g(x)

|x-3|-2= f(x)

-5|x-7|=j(x)

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The amount owed at the end of the 6 years duration is $10865

The given parameters about the compound interest are

Principal Amount, P = $5300

Interest Rate, R = 8%

Time, t = 6 years

To calculate the amount owed, we make use of the following formula

A = P + CI

Where

Compound interest, CI = P(1 + R)^t - P

So, the equation becomes

A = P + P(1 + R)^t - P

Evaluate the like terms

A = P(1 + R)^t

In this question, the formula is given as

A = P(1 + r/n)^nt

Where

n = 12, i.e compounded monthly

Substitute the known values in the above equation

A = 5300 * (1 + 8%/12)^(6*12)

Express 8% as decimal

A = 5300 * (1 + 0.08/12)^(6*12)

Evaluate the sum

A = 5300 * (1.01)^(6*12)

Evaluate the exponent

A = 5300 * 2.05

Evaluate the product

A = 10865

Hence, the value of the amount after 6 years is $10865

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The best line fit go through to represent the data is (3,8) and (5,12)

The correct option is Option c)

What is best fit line?

A straight line that minimises the gap between it and some data is called a line of best fit. In a scatter plot containing various data points, a relationship is expressed using the line of best fit. It is a result of regression analysis and a tool for forecasting indicators and price changes.

We are given some points we will plot the graph on the points

From that if we plot the line through the point (3,8) and (5,12)

That will leave 2 points above the line and 2 point below the line

Hence it is the best fit line

The correct option is option C)

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Step-by-step explanation:

(1 + i)¹⁴ = (1 + i)²×(1 + i)¹² = ((1 + i)²)⁷

(1 + i)² = 1 + 2i - 1 = 2i

((1 + i)²)⁷ = (2i)⁷ = 2⁷×i⁷ = 128×i²×i²×i²×i =

= 128×-1×-1×-1×i = -128i

The rounded value of x² = 521/73 is ± 2.67 and already rounded to the nearest hundred.

A perfect square number when taken the square root of it results in an integer.

Numbers that are not perfect squares when taken the square root of it are irrational numbers.

One method of obtaining square roots for perfect squares is prime factorization.

Given, x² = 521/73.

∴ x² = 7.13.

x = ± √7.13.

x = ± 2.67.

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Answer:

55 cars

Step-by-step explanation:

x + (x-14) = 96

The new coordinates for point S are (84,24), for a dilation centered around the origin,  

Dk (x,y) = (kx, ky) ,

K is the dilated scale factor that is multiplied by points vertices of a rectangle,

then rectangle QPRS where vertices were,

P = (1,1)

Q = (1,3)

R = (5,2)

S = (7,2)  

To get the dilation of this QPRS to Q'P'R'S' with a scale factor of 12 you have to multiply each and every coordinate of its vertices by 12.  

Q' = (12,12)

P' = (12,36)

R' = (60,24)

S' = (84,24)

Hence, The new coordinates for point S are (84,24)

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The expression 2x + 1 = y and y = 2x + 1 has no solution.

Expression:

The expression means a mathematical statements that have two terms at least that contain variables, numbers, or both connected by the arithmetic operators.

Given,

Here we have the expressions 2x + 1 = y and y = 2x + 1.

Now, we have to find the number of solution for this expression.

When we try to find the solution(s) graphically, you would plot both of the equations as straight lines. The solution(s) lies where the lines intersect.

But here we looking into the given equation both are equal.

And if we plot these on the graph then it will simply present the straight line. And there is no intersection in it.

Which also states that there is no solution for this expression.

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Answer:

x=2

y=-4

Step-by-step explanation:

a) we isolate y

18=7x-y

+y.     +y

y+18=7x

-18.  -18

y=7x-18

b) now fill this in

3x+(7x-18)=2

10x-18=2

    +18. +18

10x=20

/10.  /10

x=2

Now fill in X to find y

3(2)+y=2

6+y=2

-6.  -6

y=-4

Hopes this helps

Answer:

20 slices

Step-by-step explanation:

2 3/5 = 13/5

13/5 / 1/8

(13/5)(8/1) = 20.8

about 20 slices

Answer:

===========================

Correct choice is C

Answer:

c) 196.2 minutes

Step-by-step explanation:

Forming the equation,

→ y = (4.5/5) × 218

Now required value of y will be,

→ y = (4.5/5) × 218

→ y = 981/5

→ [ y = 196.2 min ]

Hence, the value of y is 196.2.

The equations in quadratic will be:

a) x⁴ – 6x² – 27 = 0

d) 6(2x + 4)² = (2x + 4) + 2

e) 6x⁴ = -x² + 5.

The quadratic equation au² +bu + c=0 can be written as a formula. where u is an algebraic expression. In each of these examples, doubling the exponent of the middle term equals doubling the exponent of the leading term.

The quadratic function f(x) = a(x - h)² + k is said to be in standard form if an is not equal to zero. If an is positive, the graph will open upward; if an is negative, it will open downward. The vertical line x = h is the line of symmetry, and the point is the vertex (h,k)

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The scale of reading that the chef needs to see for this spice when preparing the specialty for 19 people would be = 4.5 ounce.

A chef is a trained individual in various aspects of preparation of dishes, who has the knowledge of combination of food products to achieve an adequate meal.

The quantity of spice per serving= 1/20 ounce.( For an individual)

The quantity of people to prepare specialty for = 90 people

The quantity of spice that would be used to prepare specialty for 90 people would be;

= 1/20 × 90

= 90/20

= 4.5 ounce.

Therefore, the scale reading the chef needs to see for preparing of specialty for 90 people would be = 4.5 ounce.

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Answer:

slope: 6

y-intercept: -4

easy: y = 6x -4

Answer:

  P(basketball or baseball) = 11/24

Step-by-step explanation:

You want the probability that a randomly chosen student plays either sport, given the probability that 13 of the 24 students plays neither sport.

The probability that a student plays at least one (of the two) sports is the complement of the probability they play neither sport. If 13 of 24 students play neither sport, then (24-13)/24 = 11/24 must play at least one of the two sports.

  P(basketball or baseball) = 11/24

__

Additional comment

6+7-11 = 2 students play both sports.

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The division of the fraction 27/22 will result to 1.22 rounded to the nearest hundredth.

To divide the fraction using long division, we first divide the dividend with the divisor, write the whole number result, and then multiply it by the divisor, subtract the result from the dividend to get a new dividend. Repeat the process for the new dividend until you arrive at a remainder of zero, or continue to a given place value.

27/22 = 1 whole number and a remainder of 5

1 × 22 = 22

27 - 22 = 5

drop the value for the tenth digit of 27.00 which is 0 to yeild 50{ new dividend}

50/22 = 2 whole number and a remainder of 6

2 × 22 = 44

50 - 44 = 6

drop the value for the hundredth digit of 27.00 which is 0 to yeild 60{ new dividend}

60/22 = 2 whole number and a remainder of 16

2 × 22 = 44

69 - 44 = 16

we are rounding up to the nearest hundredth, we stop with the quotient of 1.222.

Hence, the fraction 27/22 is equal 1.22 rounded up to the nearest hundredth using the long division process.

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