What are the slope, m, and y-intercept, b, of a line that passes through the points
(3,-1) and (7,-5)?

Answer:

6610

Step-by-step explanation:

We have tan(X) = opposite/ adjacent

tan(QBP) = PQ/BQ

tan(35) = PQ/BQ    ---eq(1)

tan(QAP) = PQ/AQ

tan(20) = \(\frac{PQ}{AB +BQ}\)

\(=\frac{1}{\frac{AB+BQ}{PQ} } \\\\=\frac{1}{\frac{AB}{PQ} +\frac{BQ}{PQ} } \\\\= \frac{1}{\frac{230}{PQ} + tan(35)} \;\;\;(from\;eq(1))\\\\= \frac{1}{\frac{230 + PQ tan(35)}{PQ} } \\\\= \frac{PQ}{230+PQ tan(35)}\)

230*tan(20) + PQ*tan(20)*tan(35) = PQ

⇒ 230 tan(20) = PQ - PQ*tan(20)*tan(35)

⇒ 230 tan(20) = PQ[1 - tan(20)*tan(35)]

\(PQ = \frac{230 tan(20)}{1 - tan(20)tan(35)}\)

\(= \frac{230*0.36}{1 - 0.36*0.7}\\\\= \frac{82.8}{1-0.25} \\\\=\frac{82.8}{0.75} \\\\= 110.4\)

PQ = 110.4

≈110

Height above sea level = 6500 + PQ

6500 + 110

= 6610

The equivalent expression to  4√3 is  √48 or 6.928.

An equivalent expression is an expression that has equal value to the original given expression.

From the given expression, we can determine its equivalent expression as follows;

The given expression = 4√3

We can square 4 and multiply it by 3 and enclose all with the square root.

4√3 = √(4² x 3 )

= √ ( 16 x 3 )

= √ ( 48 )

= 6.928

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Answer:

b

Step-by-step explanation:

sum of two lengths=9+18=27 inches

45-27≤x≤60-27

18≤x≤33

The possible range for x is 18≤x≤33 (option b).

Given that the sum of three fence lengths ranges from 45 to 60 inches, and two side lengths are 9 and 18 inches, the possible range for the third side's length, x, can be derived by considering that the sum of any two sides of a triangle must be greater than the third side.

So, the inequalities can be set up as:

9 + 18 + x ≥ 45 (Minimum total length must be 45 inches)

9+18+x≤60 (Maximum total length must be 60 inches)

Solving for x in each inequality:

x≥18 (Minimum value for x)

x≤33 (Maximum value for x)

Combining these inequalities, the possible range for x is:

18≤x≤33

So, the correct answer is:

18 ≤ x ≤ 33

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Answer:

Expected Value = -1(999/1000) + 499(1/1000) = -500/1000 = -50 cents

Step-by-step explanation:

The solution to the system of inequalities in interval notation is [-2, 1].

Based on the information provided in the image below, we have the following system of inequalities;

-12 < 3x - 6

-3 ≥ 3x - 6

By adding 6 to both sides of the equation (inequality), we have;

-12 < 3x - 6

-12 + 6 < 3x - 6 + 6

-6 < 3x

-2 < x

x > -2 (flip)

-3 ≥ 3x - 6

-3 + 6 ≥ 3x - 6 + 6

3 ≥ 3x

1 ≥ x

x ≤ 1

Therefore, the solution to the system of inequalities is given by:

-2 < x ≤ 1

In interval notation, we have [-2, 1].

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x:

2x² - x - 10 = 0

This equation can be factored as:

(2x + 5)(x - 2) = 0

Setting each factor equal to zero, we get:

2x + 5 = 0 => 2x = -5 => x = -5/2

x - 2 = 0 => x = 2

Therefore, the x-intercepts of the graph of f(x) are x = -5/2 and x = 2.

Part B: The vertex of the graph of f(x) can be determined using the formula x = -b/2a, where a and b are the coefficients of the quadratic equation in standard form (ax² + bx + c = 0).

In this case, a = 2 and b = -1. Plugging these values into the formula, we have:

x = -(-1) / (2 * 2) = 1/4

To determine if the vertex is a maximum or a minimum, we can examine the coefficient of the x² term. Since the coefficient a is positive (a = 2), the parabola opens upwards, and the vertex represents a minimum point

Therefore, the vertex of the graph of f(x) is (1/4, f(1/4)), where f(1/4) can be obtained by substituting x = 1/4 into the equation f(x).

Part C: To graph f(x), we can follow these steps:

Plot the x-intercepts: Plot the points (-5/2, 0) and (2, 0) on the x-axis.

Plot the vertex: Plot the point (1/4, f(1/4)) as the vertex, where f(1/4) can be obtained by substituting x = 1/4 into the equation f(x).

Determine the direction of the graph: Since the coefficient of the x² term is positive, the graph opens upwards from the vertex.

Determine additional points: Choose a few x-values on either side of the vertex and calculate their corresponding y-values by substituting them into the equation f(x). Plot these points on the graph.

Draw the graph: Connect the plotted points smoothly, following the shape of the parabola. Ensure the graph is symmetrical with respect to the vertex.

The answers obtained in Part A (x-intercepts) and Part B (vertex) provide crucial points to plot on the graph, helping us determine the shape and position of the parabola.

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The x-intercepts from the graph attached are

The vertex  from the graph attached is

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x:

2x² - x - 10 = 0

x = (-b ± √(b² - 4ac)) / (2a)

a = 2, b = -1, c = -10

Plugging these values into the quadratic formula:

x = (-(-1) ± √((-1)² - 4 * 2 * (-10))) / (2 * 2)

x = (1 ± √(1 + 80)) / 4

x = (1 ± √81) / 4

x = (1 ± 9) / 4

x₁ = (1 + 9) / 4 = 10 / 4 = 2.5

x₂ = (1 - 9) / 4 = -8 / 4 = -2

Therefore, the x-intercepts of the graph of f(x) are 2.5 and -2.

Part B

To find the coordinates of the vertex, we can use the formula:

x = -b / (2a)

x = -(-1) / (2 * 2) = 1 / 4 = 0.25

we substitute this value back into the original function:

f(0.25) = 2(0.25)² - 0.25 - 10

f(0.25) = 0.125 - 0.25 - 10

f(0.25) = -10.125

Therefore, the vertex of the graph of f(x) is located at (0.25, -9.125).

Part C: The steps to graph f(x) include:

Plotting the x-intercepts: Based on the results from Part A, we know that the x-intercepts are 2.5 and -2. We mark these points on the x-axis.

Plotting the vertex: Using the coordinates from Part B, we plot the vertex at (0.25, -9.125). This represents the minimum point of the graph.

Drawing the shape of the graph: Since the coefficient of the x² term is positive, the graph opens upward. From the vertex, the graph will curve upward on both sides.

Additional points and smooth curve: To further sketch the graph, we can choose additional x-values and calculate their corresponding y-values using the equation f(x) = 2x² - x - 10. Plotting these points and connecting them smoothly will give us the shape of the graph.

By using the x-intercepts and vertex obtained in Part A and Part B, we have the necessary information to draw the graph accurately and show the key features of the quadratic function f(x)

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Answer:

6x - 18

Step-by-step explanation:

(2x - 6) + 4(x - 3) =

= (2x - 6) + 4x - 12 =

= 2x - 6 + 4x - 12 =

= 2x + 4 - 6 - 12 =

= (2x + 4x) + (-6 - 12) =

= 6x - 18

Answer:

I don't understand your question

Step-by-step explanation:

Answer:

Explanation

There are some activities in Courseware content that report scores and some that just report mastery and/or completion status.

Resolution

Dynamic vs. Non-dynamic mastery tests

Mastery tests give mastery status if the score is 80% or higher, but not all tests report a score. There are two types of mastery tests in Courseware content:

Non-dynamic tests: Those that do report a score, such as those in the Writing Process and Practice titles, in the Grammar and Mechanics modules, give the same number of questions each time; these are non-dynamic tests. For example, Splitting Fused Run-ons: Mastery Test presents ten questions. Even if the Learner answers the first three questions incorrectly and is, at that point, no longer able to answer eight correctly to achieve mastery, the remaining seven questions are presented.

Dynamic tests: Mastery tests from some content titles, such as Essential Reading Skills, however, are dynamic, which means they adapt to the Learner's responses. These tests do not always give the maximum number of questions; instead, they will end sooner if 80% is either achieved or no longer achievable. These tests show mastery if 80% or better was achieved, but do not show a score. For example, in Essential Reading Skills, Pronouns: Mastery Test, the maximum number of questions presented is five; mastery requires four questions are answered correctly. The test will end early if the student answers the first four correctly or two incorrectly out of the first four. Mastery is still based on achieving 80% or better, but the score is not fully determined, so no score is reported, by design.

Step-by-step explanation:

The solution to the equation -2(x + 3) = -6 is x = 0.

To simplify the expression 5t + 7 + 8b, we can combine like terms.

There are two like terms in the expression: 5t and 8b.

Combining the like terms gives us:

5t + 8b + 7

Therefore, the simplified form of the expression 5t + 7 + 8b is 5t + 8b + 7.

Regarding the equation -2(x + 3) = -6:

To solve this equation, we can follow these steps:

Distribute the -2 to the terms inside the parentheses:

-2 * x + (-2) * 3 = -6

This simplifies to:

-2x - 6 = -6

Move the constant term to the right side by adding 6 to both sides of the equation:

-2x = 0

Divide both sides of the equation by -2 to isolate the variable x:

x = 0 / -2

Simplifying the right side of the equation gives us:

x = 0

The solution to the equation -2(x + 3) = -6 is x = 0.

The simplified expression 5t + 7 + 8b remains as 5t + 8b + 7, and the solution to the equation -2(x + 3) = -6 is x = 0.

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The equation of the axis of symmetry is x = 5/8

The axis of symmetry of a parabola is a vertical line that divides the parabola into two symmetric halves.

The equation of the axis of symmetry for a parabola of the form y = ax² + bx + c is given by:

x = -b/(2a)

In the given equation, a = 4 and b = -5. Substituting these values into the formula, we get:

x = -(-5)/(2×4)

x = 5/8

Therefore, the equation of the axis of symmetry is x = 5/8

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A) Completing the table to show the results of the survey is as follows:

                   How do you feel about a longer school year?

                  Very Happy    Unhappy   Neutral   Happy   Very Happy   Total

6th Grade           18                23              20         24               8               93

7th Grade            5                22               14          15               5                61          

8th Grade          24               25               22         12               8                91      

Total                  47                70               56         51              21             245

B) Combining the Very Happy and Unhappy categories into Dislike and the Happy and Very Happy categories into Like to form a new two-way table is as follows:

    How do you feel about a longer school year?

                  Dislikes    Likes

6th Grade      41           32

7th Grade      27          20

8th Grade     49          20

Total             117          72

A two-way table is a frequency table that shows the relative frequency of survey results with two columns.

From the two-way table, the number or frequency of Dislikes or Likes of the longer school year can be easily determined.

To compute the frequency table, the very unhappy and unhappy categories are combined (by addition) just as the very happy and happy categories, while the neutral category was eliminated.

    How do you feel about a longer school year?

                  Dislikes   Neutral   Likes   Total

6th Grade      41             20         32        93

7th Grade      27             14         20         61

8th Grade     49             22        20         91

Total             117             56         72     245

                   How do you feel about a longer school year?

                  Very Happy    Unhappy   Neutral   Happy   Very Happy   Total

6th Grade         18                 23              20         24               8               93

7th Grade            5                22              14          15               5                61          

8th Grade          24               25              22         12               8                91      

Total                  47                70              56        51               21             245

                                    = (23+22+25)                              = 21 (245 - 224)

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Answer:The area would be 108.

Step-by-step explanation:

12 x 9 = 108

Answer:

B

Step-by-step explanation:

Answer:

The formula for finding the area of a circle using its radius is:

The formula for finding the area of a circle using its radius is:A = πr²

The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.

The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:

The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²

The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²where A is the area of the circle and d is its diameter.

The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²where A is the area of the circle and d is its diameter.Note that π (pi) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter and is approximately equal to 3.14

Step-by-step explanation:

Hope it Helps

The formula for finding the area of a circle using its radius is π * r².

The formula for finding the area of a circle using its diameter is (π/4) * d².

The formula for finding the area of a circle using its radius is:

A = π * r²

where:

A represents the area of the circle,

π (pi) is a mathematical constant approximately equal to 3.14159, and

r represents the radius of the circle.

If you have the diameter of the circle instead of the radius, you can use the following formula:

A = (π/4) * d²

where:

A represents the area of the circle,

π (pi) is a mathematical constant approximately equal to 3.14159, and

d is the diameter of the circle.

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Answer:

No solutions

Step-by-step explanation:

To solve systems of inequations with absolute values you need to isolate the items inside of the absolute value brackets then solve for x.

\(|\frac{x}{4}+5|=-7\\\frac{x}{4}+5=-7\\\frac{x}{4}=-12 \\x=-48\)

Therefore our answers would be -48 and 48, however there are no answers to this solution as if you try either it does not equal -7. Furthermore graphing both sides of the equations shows there is no intersection.

Answer:

81 is the scale of drawing.

Step-by-step explanation:

Area of the house in drawing = A =

Let the factor by which scaling is present in the drawing be s.

Area of the house in reality = A' =

Answer:

130 degrees

Step-by-step explanation:

DE+DA=130

Answer:

It's in England

Step-by-step explanation:

England is the furthest west red dot on top (furthest left). England is also known as the United Kingdom or Britain, and it's an island.

Megalithic Site Name: Stonehenge

Nation/Country/State: United Kingdom, England

District/Region/Parish/County: Salisbury, Amesbury

Local Location: Salisbury Plain

GPS: 51°10'44" N, 1°49'35" W

Grid: SU 1224 4218

Step-by-step explanation:

(-1)^2+(5×4)-4

=1+20-4

=17

Answer:

(-2+1)^2+5(12/3)-4

First opening the brackets

(-1)^2+60/3-4

1+60/3-4

1+20-4

21-4

17 is the answer

Step-by-step explanation:

I hope this will help you :)

The expression that represents the perimeter of the given rectangle is 20x + 6 inches.

The perimeter formula for a rectangle is 2l + 2w. We are given that the length is 8x - 1 inches and the width is 2x + 4 inches, so we can substitute those expressions into the formula to get:

Perimeter = 2(8x - 1) + 2(2x + 4)

We distribute the 2 to each term inside the parentheses:

Perimeter = 16x - 2 + 4x + 8

We combine like terms:

Perimeter = (16x + 4x) + (-2 + 8)

Add the like terms together

Perimeter = 20x + 6

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Answer (assuming it can be point-slope form):

\(y-3=6(x-1)\)

Step-by-step explanation:

Use the point-slope formula \(y-y_1 = m (x-x_1)\) to write the equation of the line in point-slope form. Substitute \(m\), \(x_1\), and \(y_1\) for real values.

\(m\) represents the slope, so substitute 6 in its place. \(x_1\) and \(y_1\) represent the x and y values of one point the line intersects, so substitute the x and y values of (1,3) into the equation as well. Substitute 1 for \(x_1\) and 3 for \(y_1\). This gives the equation in point-slope form:

\(y-(3) = 6(x-(1))\\y-3 = 6(x-1)\)

The value of 0.045 × 2.05 / 0.0025 in standard form is 3.69 × 10.

To perform the calculation and express the answer in standard form, follow these steps:

Multiply 0.045 by 2.05:

0.045 × 2.05 = 0.09225

Divide the result by 0.0025:

0.09225 / 0.0025

= 36.9

Convert the answer to standard form by writing it as a decimal multiplied by a power of 10:

36.9 = 3.69 × 10

Therefore, the value of 0.045 × 2.05 / 0.0025 in standard form is 3.69 × 10.

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Answer:

6x^2 - 11x + 8

Step-by-step explanation:

(2x-3)^2 + 2x^2+x-1

You do the square expression

= (2x-3)(2x-3) + 2x^2+x-1

Then you plus or subtract the same variables

= 4x^2 - 12x + 9 + 2x^2 + x - 1

= 6x^2 - 11x + 8

Answer:

8(3+4p)

Step-by-step explanation:

8 goes into 24 and 32, so it can be factored out:

\(24+32p=8(3+4p)\)

Answer:

8(3 + 4p)

Step-by-step explanation:

Factor 24 + 32p

First, factor out the GCF. In this case, the GCF is 8, and we have

8(3 + 4p)

We can't factor anymore so the answer is 8(3 + 4p)

Answer:

A

Step-by-step explanation:

(f-g)(x) means that the 2 functions are being subtracted.

\(3^{x}\) +10x -(5x-3) =\(3^{x}\) +10x-5x+3

simplify!

\(3^{x}\) +5x+3

the answer is A

Answer:

D

Step-by-step explanation: