Use the definition of continuity and the properties of limits to show that the function is continuous at x = 3.

A linear equation is an equation in which each term has at max one degree. The table that represents a linear function is Table 1. Thus, the correct option is A.

A linear equation is an equation in which each term has at max one degree. Linear equation in variable x and y can be written in the form y = mx + c

Linear equation with two variables, when graphed on a cartesian plane with axes of those variables, give a straight line.

For the table to represent a linear function, the function must have a constant slope between any two points.

For the first table, the slope between the first two points is,

m = (7-3)/(2-1) = 4

The slope between the last two points is,

m = (15-11)/(4-3)

Hence, the table that represents a linear function is Table 1. Thus, the correct option is A.

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The required, 180 items rentals were tubes or rafts of 300 items.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,

The circle graph shows that tubes and rafts made up 60% of the total rentals. If there were 300 items rented in June, then 60% of those rentals were tubes or rafts:

300 items × 60% = 180 items

So the answer is A. 180.

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The length of segment AB is determined as 13 units.

The distance between two points is the length of the line segment that connects the two points in a plane.

here, we have,

The length of segment AB is the distance between point A and point B, which is calculated as follows;

|AB| = √[(x₂ - x₁)² + (y₂ - y₁)²]

where;

x₁ is the x - component of point A

x₂ is the x - component of point B

y₁ is the y - component of point A

y₂ is the y- component of the point B

|AB| = √[(x₂ - x₁)² + (y₂ - y₁)²]

|AB| = √[(-5 - 7)² + (5 - 10)²]

|AB| = √[144+25]

|AB| = 13 units

Thus, the length of segment AB is the distance between point A and B.

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Answer:

see below

Step-by-step explanation:

60+75=135

BOC =180 -135 =45

DOE = BOA =60

AOE =180-DOE =120

The division expression is (5x³ - 22x² - 17x + 11)/(x - 5) = 5x² + 3x -  2 + (2/(x - 5))

From the question, we have the following parameters that can be used in our computation:

(5x³ - 22x² - 17x + 11)/(x - 5)

Using a synthetic setup, we have

x - 5 = 0

This gives

x = 5

So, the set up becomes

5 | 5   -22   -17   11

The synthetic division is then carried out as follows

5 | 5   -22   -17   11

           25   15   -10

     5     3     -2   1

So, we have

Quotient = 5   3   -2

Remainder = 1

Introduce the variable

Quotient = 5x² + 3x -  2

Remainder = 2

Hence, the quotient is 5x² + 3x -  2 and the remainder is 2

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The value of the expression is q^6 + q^4r^2 + q^2r^4s^2 - q^4r^2s - q^2r^4s + r^6s^3

From the question, we have the following parameters that can be used in our computation:

(blankq^2-r^2s)(blankq^4+blankq^2r^2+blankr^4s^2)

Express properly

So, we have

(q^2-r^2s)(q^4+ q^2r^2 + r^4s^2)

Open the brackets

q^6 + q^4r^2 + q^2r^4s^2 - q^4r^2s - q^2r^4s + r^6s^3

There are no like terms in the expression

So, the solution is q^6 + q^4r^2 + q^2r^4s^2 - q^4r^2s - q^2r^4s + r^6s^3

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The expression without absolute value bars is 3.84.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

|√10 - 7 |

= | 3.16 - 7 |

= | -3.84 |

= 3.84

Thus,

The value of the expression is 3.84.

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Answer:

3 millimeters

Step-by-step explanation:

The formula for finding perimeter: 2W+2L=P

W= width

L= length

P= Permiter

So just substitute the numbers in the equation

4 millimeters is the width

14 millimeters is the perimeter

So this is your equation

2*4+2L=14

8+2L=14

Subtract 8 from both sides

2L=6

Divide both sides by 2

L=3

So your length is 3 millimeters

To check:

(2*4)+(2*3)=14

8+6=14

14=14

Answer:

x = - 3.5 , y = - 5.5

Step-by-step explanation:

y = x - 2 → (1)

y = 3x + 5 → (2)

substitute y = 3x + 5 into (1)

3x + 5 = x - 2 ( subtract x from both sides )

2x + 5 = - 2 ( subtract 5 from both sides )

2x = - 7 ( divide both sides by 2 )

x = - 3.5

substitute x = - 3.5 into either of the 2 equations for y

substituting into (1)

y = x - 2 = - 3.5 - 2 = - 5.5

then x = - 3.5 and y = - 5.5

In geometry, an equilateral triangle is one with three equal-length sides. In the traditional Euclidean geometry, an equilateral triangle is also equiangular, which means that each of the three internal angles is 60 degrees and that they are all congruent with one another.

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The design using three equilateral triangles and two isosceles triangles is shown using the vertices.

Any triangle with three equal sides is said to be equilateral. The third side of this particular isosceles triangle is also equal. ABC has the formula AB = BC = CA. An equilateral triangle has the following qualities:

It has three equal sides. The three angles are equal. Every angle of an equilateral triangle is 60 degrees since the sum of the interior angles is 180 degrees.

It has three regular sides and is a polygon.

Regardless of which way the triangle's apex points, an isosceles triangle is one that has two equal sides. Angle determination can be done using isosceles triangles. AB Equals AC in the isosceles triangle ABC. Likewise, PQ Equals PR in the triangle PQR. The isosceles triangle's base is represented by the uneven sides BC and QR, while vertices A and P are regarded as the triangle's peaks. Among its attributes are:

There are equal sides on it. The basis angles are two equal angles that make up the object. A triangle is referred to as a right isosceles triangle when the third angle is 90 degrees.

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Answer: The diagonals of a parallelogram bisect each other, then. QM = PQ = 21. Explore all similar answers.

Step-by-step explanation: got do the d

Answer: It's the fourth option; f^-1(x)=x^3/125 -7

The solution to the system of equations is ( 1 , -1 )

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 first equation be represented as A

Now , the value of A is

y = -6x + 5   be equation (1)

Let the second equation be represented as B

Now , the value of B is

y = x - 2   be equation (2)

On simplifying the equations , we get

Substitute the value of y from equation (2) in equation (1) , we get

x - 2 = -6x + 5

Adding 6x on both sides of the equation , we get

7x - 2 = 5

Adding 2 on both sides of the equation , we get

7x = 7

Divide by 7 on both sides of the equation , we get

x = 1

Substitute the value of x in equation (2) , we get

y = 1 - 2

y = -1

Hence , the value of x and y is 1 and -1 respectively

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Answer:

68

Step-by-step explanation:

170/5=34 34*2=68

The scale factor for the given quadrilateral would be 1.5.

A scale factor is a numerical value that is used to represent an object's enlarged or shrunk shape. It is a number that can be used to alter the size of any geometric figure or shape in relation to its original size. It aids in altering the figure's size but not its shape.

Given that the two quadrilaterals are similar to each other and are dilated by some scale factor.

The scale factor will be calculated as:-

Scale factor = 15 / 10

Scale factor = 1.5

Hence, the scale factor will be 1.5.

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Answer: D

Step-by-step explanation:

Think about it this way, 3 squared is 3x3 correct? that equals 9. 4 squared is 16 so there you go. Sorry if this isn't answered clearly.I'm trying my best to help

The linear function for the population in t years after 2000 is given as follows:

P(t) = 2200t + 44000.

The estimate for the population in 2010 is given as follows:

66,000.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

Two points for the function are given as follows:

(5, 55000) and (8, 61600).

Dividing the change in the output by the change in the input, the slope m is given as follows:

m = (61600 - 55000)/(8 - 5)

m = 2200.

Hence:

P(t) = 2200t + b.

When x = 5, y = 55000, hence the intercept b is given as follows:

55000 = 2200(5) + b

b = 55000 - 2200(5)

b = 44000.

Hence the function is:

P(t) = 2200t + 44000.

2010 is 10 years after 2000, hence the estimate is given as follows:

P(10) = 2200(10) + 40000

P(10) = 66,000.

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The set {10,17,27} does not represent the three sides of a triangle,

Having three edges and three vertices, a triangle is a three-sided polygon. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.

Given  the sets for the triangles,

property of triangles says that,

The length of a triangle's two longest sides added together is longer than the third side.

Similarly to this, the length of the third side of a triangle third side is shorter than the difference between its two sides.

1: given sides are 10, 17, 27

according to the property sum of 10 and 17 should be greater than  27 but sum  is equal to 27,

10 + 17 = 27,

so the sides do not represent the triangle

2: sides are 9, 22, 30

here 9 + 22 > 30

the set represents the triangle.

3: sides 6, 16, 19

6 + 16 > 19

the set represents the triangle.

4: sides 4, 7, 9

4 + 7 > 9

set represents the triangle.

Hence option A is correct.

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The domain is the second option:

(2, 8]

For a function y = f(x), we define the domain as the set of the possible inputs for the function.

Here we have a piecewise function that is defined in the 3 regions:

2 < x  ≤ 4

4 < x < 8

x ≥ 8

So the domain is the set of any value larger than 2, and we can write that as:

(2, 8]

We end it at "8" becase is the last defined value and that is the only option that makes sense.

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Answer:

A

Step-by-step explanation:

Answer: a) To make apple crumble for 16 people, Farid will need to double the ingredients as compared to serving 8 people. Hence, he will need:

700g * 2 = 1400g of apples

240g * 2 = 480g of sugar

180g * 2 = 360g of flour

So, Farid needs 360g of flour to make apple crumble for 16 people.

b) To make apple crumble for 2 people, Amal will need to use 1/8 of the ingredients as compared to serving 8 people. Hence, she will need:

700g / 8 = 87.5g of apples

240g / 8 = 30g of sugar

So, Amal needs 30g of sugar to make apple crumble for 2 people.

c) To make apple crumble for 6 people, Shahina will need to adjust the ingredients based on the apples she has available. To calculate the amount of sugar and flour required, she can use the ratio of sugar and flour to apples as follows:

Sugar: 700g / 8 = 87.5g per serving * 6 people = 525g

Flour: 700g / 8 = 87.5g per serving * 6 people = 525g

Since Shahina has plenty of the other ingredients, including butter, she can make apple crumble for 6 people with the amount of apples she has available. So, the answer is Yes, Shahina can make apple crumble for 6 people.

Step-by-step explanation:

Answer:

Step-by-step explanation:  https://flexbooks.ck12.org/cbook/ck-12-middle-school-math-concepts-grade-6/section/6.15/primary/lesson/elapsed-time-msm6/

The solution is Option D.

The derivative of the function is given by the equation f' ( x ) = -x / ( √5-x² )

In mathematics, differentiation is the process of determining the derivative, or rate of change, of a function. Differentiation is a technique for determining a function's derivative. Differentiation is a mathematical procedure that determines the instantaneous rate of change of a function based on one of its variables. The process of finding the derivative of dependent variable in an implicit function by differentiating each term separately

Given data ,

Let the function be represented as f ( x )

Substituting the values in the equation , we get

f ( x ) = √ ( 5 - x² )

Now , the derivative of the function is f' ( x )

f' ( x ) = ( 1/2 ) 1 / √( 5 - x² ) ( d/dx ) ( -x² )

On simplifying the equation , we get

f' ( x ) = ( 1/2 ) 1 / √( 5 - x² ) ( -2x )

On further simplification , we get

f' ( x ) = ( -2x/2 ) 1 / √( 5 - x² )

f' ( x ) = -x / ( √5-x² )

Hence , the derivative of the function is f' ( x ) = -x / ( √5-x² )

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The answers to all parts shown below.

A set of numbers arranged in rows and columns so as to form a rectangular array. The numbers are called the elements, or entries, of the matrix.

Given:

a) The system of linear equations

3A + 2B + 6C = 71, 000

3A + 2B +4C = 81, 000

5A + 7B + 0C= 92, 000

B) The equation for the system of linear equations

Y = [tex]\left[\begin{array}{ccc}3&2&6\\3&2&4\\5&7&0\end{array}\right][/tex] , Z = [tex]\left[\begin{array}{ccc}71000\\81000\\92000\end{array}\right][/tex]

So, YX = Z

X = Z[tex]Y^{-1[/tex]

C) The inverse matrix method

               14/11  21/11   -2/11

= 1/22    10/11  -15/11   3/11

        1/2   -1/2      0

= 7/ 121   21/ 242   -1/121

  5/121    -15/242    3/242

  1/44        -1/44         0

and, X = Z[tex]Y^{-1[/tex]

X  =  [tex]\left[\begin{array}{ccc}71000\\81000\\92000\end{array}\right][/tex]  [tex]\left[\begin{array}{ccc}7/ 121 &21/ 242& -1/121\\ 5/121&-15/242&3/242\\1/44&-1/44&0\end{array}\right] \\[/tex]

A= 10,376.03

B = 946.28

C= 227.72

d) The production for A = RM 7,263.221

The production for B = RM 473.14

The production for C = RM 204.948

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Answer:

Step-by-step explanation: A rectangle's perimeter formula is P=2(l+w), therefore,

P=2(21.9+18.3)

P=2(40,2)

P=80,4

You will need 80,4 inches of fondant to cover all the edges of the cake

The unit circle has the co-ordinates (-√2/2, -√2/2)

In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.

Given here: The unit circle and the point makes an angle of 225

we know the co-ordinates of any point on the unit circle is given by

x=cost and y=sint where t is the angle that line passing through the origin containing the point makes with x-axis

Thus x=cos225

           =-√2/2

and y=sin225

        =-√2/2

Hence, The required point is given by co-ordinates (-√2/2, -√2/2)

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Answer: D)12 units

Step-by-step explanation:

Because, your y axis travels from 34 to 22, in that case you have to take away 22 from 34 which you get 12.

The required number of Barnes & Noble stores in 2009 is 725.28.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

To determine the number of Barnes & Noble stores in 2009, we need to evaluate the piecewise function for t = 2009.

Since 2009 is between the interval 6 ≤ t < 12, the number of stores is given by the first piece of the function:

y = -3.692 × x² + 65.28 × x + 437.30

put x = 9 for the year 2009

y = -3.692 × 9² + 65.28 × 9 + 437.30 = 725.28

So, there were 725.28 Barnes & Noble stores in 2009.

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