a^2 + 6=

a=5


Evaluate

Part (a)

Multiply both sides by 2, then add 9 to both sides.

z > 2

2z > 2*2

2z > 4

2z+9 > 4+9

2z+9 > 13 is the final answer for part (a)

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

Part (b)

We'll start with subtracting 4 from both sides, and then triple each side.

z > 2

z-4 > 2-4

z-4 > -2

3(z-4) > 3*(-2)

3(z-4) > -6 is the final answer for part (b)

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

Part (c)

Follow similar steps to that of part (a).

z > 2

2z > 2*2

2z > 4

2z+4 > 4+4

2z+4 > 8 is the final answer to part (c)

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

Part (d)

For now let's ignore the 5 out front and focus on 3z-2

z > 2

3z > 3*2

3z > 6

3z-2 > 6-2

3z-2 > 4

Now multiply each side by 5.

5(3z-2) > 5*4

5(3z-2) > 20 is the final answer to part (d)

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

Side note: The inequality signs did not flip when multiplying both sides by a positive number. The flip would only happen if we multiplied both sides by a negative number.

The solution set of the following equation (- 8x +  x + 15) = ( - 7x + 12) is zero i.e this equation does not have any solution.

Equation is (- 8x + x + 15) = (-7x + 12)

Now solving

(-8x + x  + 7x ) = ( 12 - 15 )

( - 7x +7x) = (-3)

( 0 )= ( - 3)

Since 0 = -3 is not correct, therefore, the equation does not have any solution.

So it is stated that the equation (- 8x +  x + 15) = ( - 7x + 12) does not have any solution in its solution set.

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By setting each factor to 0, you can get the roots, or solutions, of the polynomial equation P(x) = 0 by figuring out what x is. Factor the polynomial equation to find the solution.

Constants and indeterminates are parts of polynomial algebraic expressions.

One could consider polynomials to be a subset of mathematics.

They are used to express numbers in almost all areas of mathematics, and calculus is one of those areas where they are particularly important.

A polynomial is a specific sort of expression.

An expression is a mathematical statement that does not contain the equals sign (=). Let's look at the following descriptions of polynomials' definition and applications.

All the exponents of an algebraic expression called a polynomial must be whole numbers.

Any polynomial must have non-negative integer variable exponents. We cannot divide a polynomial by a variable even though it contains variables and constants.

Hence, By setting each factor to 0, you can get the roots, or solutions, of the polynomial equation P(x) = 0 by figuring out what x is. Factor the polynomial equation to find the solution.

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Answer:  x [tex]\leq[/tex] 52 inches.

Step-by-step explanation:

Answer:

How can you tell if a function is an exponential function? If your function can be written in the form y = a b x , where and are constants, a ≠ 0 , b > 0 , and b ≠ 1 , then it must be exponential. In quadratic equations, your functions were always to the 2nd power. In exponential functions, the exponent is a variable.

The solution of the given inequality is x < –5 or x > 2

Equations are not always balanced on both sides using an "equal to" symbol in mathematics. Sometimes it can be about a "not equal to" relationship, meaning that something is greater than or lower than another.

In mathematics, an inequality is a relationship between two numbers or other mathematical expressions that results in an unequal comparison. Inequalities are the name given to certain algebraic mathematical expressions.

Here we have

|2x + 3| < 7  

=> 2x + 3 > 7  or 2x + 3 < - 7

Take 2x + 3 > 7

Add  - 3 on both sides    

=> 2x + 3 - 3  > 7 - 3

=> 2x  > 4

Divide by 2 into both sides

=>  2x/2 > 4/2

=> x > 2

Take 2x + 3 < - 7  

Add  - 3 on both sides  

=> 2x + 3 - 3  < - 7 - 3

=> 2x  < -10

Divide by 2 into both sides

=> 2x/2 < -10/2

=> x < -5    

Therefore,

The solution of the given inequality is x < –5 or x > 2

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Answer:

BY = 9.90 cm

Step-by-step explanation:

AY = 7cm

AB = 7cm

BY = ?

BY = [tex]\sqrt{7^2+7^2}[/tex]

BY = [tex]\sqrt{98}[/tex]

BY = 9.89cm (round to 9.90cm)

Answer:

[tex]c+d=\langle-3,9\rangle[/tex]

Step-by-step explanation:

We simply add the respective horizontal and vertical components:

[tex]c+d=\langle 6,2 \rangle+\langle-9,7\rangle=\langle6+(-9),2+7\rangle=\langle6-9,9\rangle=\langle-3,9\rangle[/tex]

A rate is a ratio comparing quantities of different items. A unit rate is a rate with 1 in the denominator.

A rate is a ratio comparing quantities of different items. A unit rate is a rate with 1 in the denominator. If you have a rate, such as price per some number of items, and the quantity in the denominator is not 1, you can calculate unit rate or price per unit by completing the division operation: numerator divided by denominator.

Examples of How to Find Unit Rate or Unit Price

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Due to the fact that the solutions lie where the parabola crosses the x-axis, quadratic equations frequently have two solutions.

Any equation in algebra that can be written in standard form as

ax^2+bx+c=0,

where x stands for an unknown integer and a, b, and c are known quantities, where a 0, is considered a quadratic equation.

The coefficients of the equation are the numbers a, b, and c, which can be separated by naming them, respectively, the quadratic coefficient, the linear coefficient, and the constant coefficient or free term.

Due to the fact that the solutions lie where the parabola crosses the x-axis, quadratic equations frequently have two solutions. The graph will cross twice if the vertex is below the x-axis and the parabola opens up, and it will cross twice again if the vertex is above the x-axis and the parabola opens down.

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Answer: MMDCCLXXXIX

Step-by-step explanation:

Answer:

Step-by-step explanation:

we can see that the function C(x) = 25x + 75 represents the labor cost (in dollars) for Bob's Auto Repair to replace your alternator, where x is the number of hours. We can use this function to find the cost of replacing an alternator that is estimated to take 5 hours of labor.

C(5) = 25(5) + 75 = 125 + 75 = 200

We also have the labor cost for the main competitor, Budget Auto Repair, in a table format.

Hours Cost

1          $90

2         $130

3         $170

We can see that the cost of labor increases as the number of hours increases. From the information provided it's hard to say which company would be cheaper to hire, however the company with the function C(x) = 25x + 75 would be cheaper if the alternator takes more than 4 hours of labor, otherwise Budget Auto Repair would be cheaper.

It's important to check the warranty, prices of parts, and reputation of both companies. If a company has a good reputation and a good warranty, it may be worth paying a little more for labor.

It's also a good idea to get a second opinion or ask for a quote from both companies before making a decision.

In conclusion, it's hard to say which company would be cheaper to hire based on the information provided, but it's recommended to check the warranty, prices of parts, and reputation of both companies, and to get a second opinion or quote from both companies before making a decision.

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Answer: To find the length of the hypotenuse of a right triangle, you can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs).

So, if the legs of the right triangle measure 2 cm and 5 cm, the hypotenuse c can be calculated as follows:

c² = a² + b²

c² = 2² + 5²

c² = 4 + 25

c² = 29

Therefore, the length of the hypotenuse c is the square root of 29.

c = √29

The answer is c = √29 which is the only one that is not squared, So the answer is (C) 29.

Step-by-step explanation:

A statement of an order relationship between two numbers or algebraic expressions is known as an inequality in mathematics. It can be greater than, greater than or equal to, less than, or less than or equal to.

Using the inequality symbol, a mathematical statement known as an inequality depicts the relationship between two expressions. An inequality symbol denotes that the terms on each side are not equal.

It indicates that the expressions on the left and right should be bigger or less than one another, or vice versa. Literal inequalities are those where the relationship between two algebraic expressions is described by the inequality symbols.

According to the definition, a relationship is considered to be an inequality if it involves two real numbers or algebraic expressions and uses the symbols “>”, “<”, “≥”, “≤”.

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The number of rentals would  be 20 so that both plans cost the same amount.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

It costs $30 to join and each video game rental for members costs $2.

Non-members pay a rental fee of $3.50 per rental.

let the number of rentals they both pay same amount be x.

So, 30 + 2x = 3.5x

30 = 3.5x - 2x

30 = 1.5x

x= 30/1.5

x = 20

Hence, number of rentals should be 20.

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The pattern shown by the erosion data measurements for the Western Beach is that the width decreases over time, with a steady decrease of about 10 feet per year. The pattern for the Dunes Beach is that the width increases over time, with an increase of about 5 feet per year.

Based on the data, it appears that the beaches will have approximately the same width around year 20. At this point, the Western Beach will have a width of approximately 50 feet and the Dunes Beach will have a width of approximately 90 feet.

To get a better approximation of when the two beaches will have the same width, it would be necessary to gather more data points over a longer period of time and to take into account other factors that may affect the beaches' widths such as the strength of the waves, the composition of the beach, and human interventions that may be taking place.

The measures of the missing angles are given as follows:

First we consider that when two angles form a ray, they are supplementary, meaning that the sum of their measures is of 180º.

Then the measures of angles 3 and 5 are given as follows:

The sum of the internal angles of triangle is of:

S(3) = (3 - 2) x 180º = 180º.

Hence the measure of angle 4 is obtained as follows:

m < 4 + 36 + 56 = 180

m < 4 = 180 - (36 + 56)

m < 4 = 88º.

Angles 2 and 4 are congruent, hence the measure of angle 2 is given as follows:

m < 2 = m < 4 = 88º.

The sum of the internal angles of a quadrilateral is of:

S(4) = (4 - 2) x 180º = 360º.

Hence the measure of angle 1 is obtained as follows:

m < 1 + 88 + 144 + 124 = 360

m < 1 = 360 - (88 + 144 + 124)

m < 1 = 4º.

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Answer:

∠S = 105°

∠T = 95°

Step-by-step explanation:

Cyclic quadrilateral:

   Quadrilateral MNST is a cyclic quadrilateral. In cyclic quadrilateral, the opposite angles are supplementary.

     m∠S + m∠M = 180°

 3x + 2x +  5 = 180

        5x  + 5  = 180           {Combine like terms}

                 5x = 180 - 5     {Subtract 5 from both sides}

                 5x = 175

                    x = 175 ÷ 5  {Divide both sides by 5}

                    x = 35°

∠S = 3x

    = 3 * 35

    = 105°

∠T = 3x - 10

     = (3*35) - 10

     = 105 - 10

     = 95°

Substitution refers to the process of replacing one group with another. We can say that it refers to replacing a variable with another given value.

For example, given that x = 17, we can substitute the value of 17 in for x and evaluate the obtained expression to get the value of x.

We can name the expression: F (x) = 17 + 3x - 4.

here , let's say x = 2

then , F (x) = 17 + 6 + 2 = 25

The algebraic method which is used for solving simultaneous linear equations is known as the substitution method. The value of one variable from one equation is substituted in the second equation, as the name implies.

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Answer:

B. 7

Step-by-step explanation:

[tex]I=Prt \\ \\ 196=700(0.04)t \\ \\ 196=28t \\ \\ t=7[/tex]

The length of the side WX of the rectangle WXYZ, which is similar to the rectangle ABCD, is 40 inches.

According to the information provided, the rectangles ABCD and WXYZ are very similar to one another, which means they have the same ratio or proportional. If the ratio between two amounts is directly proportional, then as one quantity increases, the other amount also increases, and when one amount decreases, the other amount also decreases.

In this case, we are given that:

AB = 50 inches

BC = 40 inches

XY = 32 inches

To calculate the length of WX, we may apply the formula that is as follows =

AB/WX = BC/XY

50/WX = 40/32

40WX = 50x32

WX = 40

As a result, the length of WX in rectangle WXYZ is 40 inches

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Answer: 6 in each batch

Step-by-step explanation: 54/9 = 6

Answer:

[tex]\huge\boxed{\sf Yes.}[/tex]

Step-by-step explanation:

y = 6x - 9 ---------------(1)

y = 2x + 3 --------------(2)

So,

x = 3, y = 9

Put this in Eq. (1) to verify.

9 = 6(3) - 9

9 = 18 - 9

9 = 9 [Equation satisfied]

Now, put x = 3, y = 9 in Eq. (2)

9 = 2(3) + 3

9 = 6 + 3

9 = 9 [Equation satisfied]

Since, both the equations are satisfied by the values of x and y, we can say that x = 3 and y = 9 is the solution to the system.

[tex]\rule[225]{225}{2}[/tex]

Answer: Yes, it is a solution

Step-by-step explanation:

Plug (x,y) values into the equations.

Plug in (3,9)

y=6x-9  ---->.  (9)=6(3)-9 ----> 9=18-9 ----->   9=9

y=2x+3 ------>.  (9)=2(3)+3 ----> 9=6+3 ----> 9=9

When know (3,9) is a solution because each side has the same value.

Example:

8=9 Not a solution

5=5 A solution

Answer:

f(x)=a(b)^x

Step-by-step explanation:

exponential functions are usually growth or decay,

a represents the base, b is the change, and x is how much time (depending on the question). if b is larger than 1 ex: 1.08, it is growth. if it is less than 1 ex: 0.4, it is decay

The exponential form formula is a^b = c, where a is the base, b is the exponent, and c is the result. In this formula, a is raised to the power of b, resulting in the value c.

all are statement except shut the window because sets are statement

square is a rectangle .The sun is a star is a statement

Describe finite set using an example.

What is the set in math?

Sets, in mathematics, are an organized collection of objects and can be represented in set-builder form or roster form. Usually, sets are represented in curly braces {}, for example, A = {1,2,3,4} is a set.

 A1 = { 1}   A2 = { 2 }  A3 = { 3 }..

  U  Ai = { 1 , 2 , ,,}

           = N is not a finite set

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The magnified length of the objects is 0.01 meters in decimal form, based on the height of object and magnification power.

The formula to find magnified length is -

Magnification = image height ÷ object height. Here image height is magnified length.

Keep the values in formula -

Image height = 10⁵ × [tex] {10}^{-7} [/tex]

Performing multiplication on Right Hand Side of the equation. Note that power of products will be used to find the magnified length. The exponents will be added.

Image height = [tex] {10}^{5 + (-7)} [/tex]

Performing addition of exponents to find the image height

Image height = [tex] {10}^{-2} [/tex] meters

Writing the image height in decimal form - 0.01 meters

Therefore, the height of image or magnified length is 0.01 meters.

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Both statement by Lorene and Maria is correct because it has a common factor is "1/4".

Both fraction are called proper fraction. Basically, a fractions represent the parts of a whole or collection of objects.

Under fraction, proper fraction is one in which the numerator is less than the denominator. It is in contrast to improper fraction, that numerator equals or exceeds the denominator. Proper fractions are 3/4, 2/11, and 7/19, while improper fractions are 5/2, 8/5, and 12/11.

The statements of Laurie and Maria can be compared as follows:

It can be written as,

3/12 = (3 ÷ 3)/(12 ÷ 3)

= 1/4

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The linear equation for the relationship between the weight and number of months is y = 5.55x + 78.95.

First-order equations include linear equations. In the coordinate system, linear equations are defined for lines. A linear equation in one variable is one in which there is a homogeneous variable of degree 1 (i.e., just one variable). Multiple variables may be present in a linear equation. Linear equations with two variables, for example, are used when a linear equation contains two variables.

We know that the sumo wrestler's weight is 140 kilograms after 11 months and he gained weight at a rate of 5.55 kilograms per month.

The equation for the relationship between the weight and number of months can be represented as:

y = 5.55x + b

Where y is the sumo wrestler's weight (in kilogram) after x month, 5.55 is the rate at which he gained weight per month, x is the number of months and b is the y-intercept.

To find the value of b, we can use the point (11, 140) which represents that after 11 months the sumo wrestler's weight is 140 kg, and substitute it into the equation:

y = 5.55x + b

140 = 5.55(11) + b

Solving for b:

b = 140 - (5.55 * 11)

b = 140 - 61.05

b = 78.95

So the complete equation is:

y = 5.55x + 78.95

Where y is the sumo wrestler's weight (in kilogram) after x months.

Therefore, The linear equation for the relationship between the weight and number of months is y = 5.55x + 78.95.

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Answer:

4a + 25.2.

Step-by-step explanation:

2/3(6a+9)+19.2

= 2/3 * 6a + 2/3 * 9 + 19.2

= 4a + 6 + 19.2

= 4a + 25.2.