Warm-Up
Identifying Shaded Regions
Analyze the linear inequalities and determine if the solution set is the shaded region above or below the boundary
line.
y> -1.4x+7
y> 3x-2
y<19-5x
y>-x-42
y<3x
y<-3.5x+2.8
(Solution Set Shaded Above)
(Solution Set Shaded Below)

An example of a pattern rule is "add 3" which means that to find the next term in a sequence, you add 3 to the previous term.

To write a rule for a sequence, you need to identify the pattern. This involves looking at the differences between the numbers and seeing if there is a pattern of increasing or decreasing numbers. Once you have identified the pattern, you can then write a rule that expresses that pattern.

Examples of pattern sequences include the Fibonacci sequence (1,1,2,3,5,8,13,21,34, etc.), the even numbers (2,4,6,8,10, etc.), and the multiples of 3 (3,6,9,12,15, etc.).

To describe the pattern of a sequence, you need to look at the differences between the numbers and the pattern of increases or decreases. For example, in the Fibonacci sequence, the pattern is that each number is the sum of the two numbers before it so 1+1=2, 1+2=3, 2+3=5, etc.

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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°

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

After simplification, the formula 4 (2x - 1) + 3 (2x + 5) becomes 14x + 11.

A number's arithmetic value for each digit can be expressed using the expanding form. Expanded numbers are numerical expressions that consist of the place value of each digit added to the total of the digits. To improve place value comprehension, expanded form is an excellent strategy.

It is given that,

4 (2x - 1) + 3 (2x + 5)

We have to expand and simplify the expression,

= 4 (2x - 1) + 3 (2x + 5)

Multiply the term out of the bracket into the bracket as

= 8x - 4 + 6x + 15

Add comparable terms together so that we can execute mathematical operations like addition and subtraction on the result.

= 14x + 11

As a result, the simplified expression for 4 (2x - 1) + 3 (2x + 5) will be 14x + 11.

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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]

Answer:1111

Step-by-step explanation:

11111

Answer:3/4

Step-by-step explanation:

1/4 multiplied 3/1 =3/4

The volume of the chamber follows a pattern. The formula that represents the volume of the nth chamber is 6.3% of the previous chamber.

What is a pattern?

A pattern is a repeated arrangement of numbers, shapes, colours, or other elements. The Pattern can be associated with any kind of event or object. A pattern is defined as a set of numbers that are related to one another in a specific way. Patterns are sometimes referred to as sequences.

Given that:

Chamber 7: 1.207 cm³

Chamber 6: 1.135 cm³

Chamber 5: 1.068 cm³

Chamber 4: 1.005 cm³

Chamber 3: 0.945 cm³

Chamber 2: 0.889 cm³

Chamber 2: 0.836 cm³

                          1.207     1.135     1.068   1.005     0.945      0.889      0.836

First difference:        .072        0.067    0.063   0.060    0.056      0.053

Second difference:            0.005     0.004    0.003     0.004    0.003

Since the difference is not the same, thus the volume is not in a linear pattern. Then find the ratio consecutive volume:

1.207/1.135 ≈ 1.063

1.135/1.068 ≈ 1.063

1.068/1.005 ≈ 1.063

1.005/0.945 ≈ 1.063

0.945/0.889 ≈ 1.063

0.889/0.836 ≈ 1.063

Each chamber is 6.3% greater than the previous chamber. The pattern is exponential functions.

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Marsha and Kristen will be at the same elevation of -72 feet after 4 minutes.

How to find their elevation?

To find out after how many minutes Marsha and Kristen will be at the same elevation, we can set their elevation equations equal to each other:

-24 - 12t = -8 - 16t

Then, we can solve for t by adding 8 to both sides and dividing by 4:

t = 4

So, Marsha and Kristen will be at the same elevation after 4 minutes.

To find out what elevation they will be at that time, we can substitute 4 into either one of the elevation equations and solve for the elevation:

-24 - 12(4) = -24 - 48 = -72

So, Marsha and Kristen will be at the same elevation of -72 feet after 4 minutes.

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The angle when the secant intersect is as follows:

A secant is a line that intersects a circle in exactly two points.

If two secants or chords intersect in the interior of a circle, then the measure of each angle formed is half the sum of the measures of its intercepted arcs.

Therefore,

m ∠GPE = 1 / 2 ( mGE -  mHF)

mGE = 99°

mHF = 41°

m ∠GPE = 1 / 2 (99 - 41)

m ∠GPE = 1 / 2 (58)

Therefore,

m ∠GPE = 29 degrees

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The proper method of filling a table with a function has been explained below.

Tables are helpful when we have to plot a function or we have to interpolate a function using given data points. A table usually consists of 2 or more 2 variables whose values are arranged either in a row or in a column. For filling a table with the help of a function, firstly we have to define the values of independent variables which we will input into the function to get the dependent variable's values.

When we get the value of independent data we will be inputting one of one those values in the function we will get the values of the function at the given point and hence the function will be filled by the output values.

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The coordinates of the points after the translation are:

All the points are translated on the same way, so let's analyze the translation of P to P'.

The coordinates of Pare (5, 8), and P' is at (3, 4)

Then the translation is:

(3, 4) - (5, 8) = (3 - 5, 4 - 8) = (-2, -4)

So we just need to subtract 2 to the x-value and 4 to the y-value.

The coordinates of Q and R are:

Q = (7, 8)

R = (8, 5)

Then the translated points are:

Q' = (7 - 2,8 - 4) = (5, 4)

R' = (8 - 2, 5 - 4) = (6, 1)

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The transformations that apply are Horizontal stretch or compression by a factor of 3, Vertical shift up by 24 units, Reflection over the x-axis, The leading coefficient of 1/3 is a vertical compression and The exponent of 2 on x is a parabola.

Vertical Stretch/Compression by a factor of 3: The coefficient in front of the x^2 term is 1/3, which stretches or compresses the graph vertically by a factor of 3.

Horizontal Stretch/Compression by a factor of 24: The exponent on the x term is 24, which stretches or compresses the graph horizontally by a factor of 24.

Reflect over the x-axis: The coefficient in front of the x^2 term is positive, so the graph is reflected over the x-axis.

Shift up or down: The constant term is not present, so the graph does not shift up or down.

Shift left or right: The constant term is not present, so the graph does not shift left or right.

Rotation: The graph does not rotate as it is a parabola in the standard form y=ax^2 + bx + c, it does not have any trigonometric function in it.

Therefore, The transformations that apply are Horizontal stretch or compression by a factor of 3, Vertical shift up by 24 units, Reflection over the x-axis, The leading coefficient of 1/3 is a vertical compression and The exponent of 2 on x is a parabola.

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Answer:N= 10 fo sho m -14 maybe

Step-by-step explanation:

this triangle is an isosceles triangle because of the 90 45 45 angles. This means that the two side lengths are equal and 10 is equal to n. to calculate m is maybe square root of 2 times 10 because this image.

The balanced equation is:

CCl₄ --> C + 2Cl₂

The law of conservation of mass states that when a chemical reaction takes place, the mass of the reactants and products should be equal.

Here is an equation that describes a chemical reaction:

CCl₄ --> C + 2Cl₂

Thus, add 2 atoms of Cl to balance the equation.

Then,

The balanced equation is:

CCl₄ --> C + 2Cl₂

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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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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.

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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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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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.

Answer: 6 in each batch

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

Answer:

x=3

Step-by-step explanation:

An equation's omitted factors are the values of x for which the result is unknown. This indicates that if the denominator or x(x-3) equals 0, your solution is undefined.

Set up this equation and solve for the potential possibilities of x to find these numbers: x(x-3)=0

Divide both sides by (x-3) to find one of the values:

x(x-3)/(x-3)=0(x-3)

Because (x-3) cancels on the left side of the equation and everything divided by 0 is zero on the right, you should get: x=0.

Now that you've determined one of the excluded values, work out the other:

To begin, split both sides by x:

x(x-3)=0

x-3=0

Finally, multiply both sides by -3 to get: x=3

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: area: 1/2 length * width, perimeter: add the three sides

Step-by-step explanation:

Answer:

[tex]I'(-0.5,0.25), J'(0.5,0.5), K'(0.5, -0.25)[/tex]

Step-by-step explanation:

Assuming the dilation is centered at the origin, we can use the rule that:

In this case, the highest power on any variable is 2. As a result, the degree of polynomial is 2.

The degree of a polynomial in mathematics is the highest of the degrees of the polynomial's monomials with non-zero coefficients. A term's degree is the sum of the exponents of the variables in it, and it is thus a non-negative integer. The degree of a polynomial is the greatest or maximum power of a variable in a polynomial equation. A degree represents the polynomial with the greatest exponential power. Finding the degree of a polynomial. 2 x 2 + 2 x - 364 = 0. The maximum degree of the polynomial in the preceding equation.

Here,

Given : 2x^2

Degree of polynomial = Highest power of a variable.

Here, 2 is the highest power on any variable. So, degree of polynomial is 2.

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