So I have some confusion and I'm having a hard time following the logic of how you convert a linear equation from slope intercept form to standard form.

Here is an example

How is it when you are converting from slope intercept form to standard form:

1.) When you are subtracting 3x from both sides in this example, I could see that both 3xs cancel out but I'm confused about how you can subtract it from y ( a different variable) and also end up with 3x on the side underneath y (How do they switch places)

2.) Also how does the variable y end up right next to -3x? Also, how is 3x negative? is it just dragged down or something?

The area of the tulip border, or the shaded region, of this figure in square feet is 32

The formula that is used for calculating the area of a rectangle is expressed as;

A = lw

Such that the parameters are;

From the information given, we have that the tulip is in a 3 -foot border from the larger rectangle

Then, we have  that;

Length = 10 - 6 = 4

Width = 14 - 6 = 8

Substitute the values

Area = 4(8) = 32 ft²

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The wallet is about 12.8 feets away from the base of the platform.

using trigonometric function , the angle of depression can be obtained using the tangent relationship.

The tangent can be mathematically related using the ratio of the opposite and adjacent side.

Tan(A) = opposite/Adjacent

tan(32°) = 8/x

Solving for x, we get:

x = 8/tan(32°)

x = 12.8 feet

Hence , the wallet is about 12.8 feet away from the base of the platform.

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Answer:

D: 18i + 8b ≤ 100

Step-by-step explanation:

The correct inequality that represents the scenario is option D: 18i + 8b ≤ 100.

Explanation:

Let's break down the components of the inequality based on the given information:

8i represents the cost of ink bottles (i) at $8 each.

8b represents the cost of brushes (b) at $18 each.

18i + 8b represents the total cost of ink bottles and brushes combined.

The scenario states that Emily has $100 extra to spend, which means the total cost of ink bottles and brushes should be less than or equal to $100. Therefore, the correct inequality is 18i + 8b ≤ 100.

Answer:

Step-by-step explanation:

20% of 60 is equal to_____% of 100

20% of 60 =

60 : 100 × 20 =

0.6 × 20 =

12

Answer:  x=72

Step-by-step explanation:

All of the angles of a triangle add up to 180

32+x+x=180             >combine x's

32+2x=180              >subtract 32 from both sides

2x=148                    >Divide both sides by 2

x=74

Answer:

Step-by-step explanation:

We know that,

sum of 3 side of triangle is 180°

So,

→ 32° + x + x = 180°

→ 32° + 2x = 180°

→ 2x = 180° -32°

→2x = 148

→ x = 148/2

→ x = 74

Thus, x = 74°

There is no day when the Number of cupcakes sold at Location 1 is equal to the number of cupcakes sold at Location 2. on Day 5, Location 2 sold 850 cupcakes.

(a) To determine the number of cupcakes sold at each location on Day 5, we substitute x = 5 into the equations:

For Location 1:

y = 150x + 200

y = 150(5) + 200

y = 750 + 200

y = 950

Therefore, on Day 5, Location 1 sold 950 cupcakes.

For Location 2:

y = 150x + 100

y = 150(5) + 100

y = 750 + 100

y = 850

Therefore, on Day 5, Location 2 sold 850 cupcakes.

(b) To find the day when the number of cupcakes sold at Location 1 is equal to the number of cupcakes sold at Location 2, we set the two equations equal to each other:

150x + 200 = 150x + 100

We can see that the variable x cancels out, which means the value of x doesn't matter in this case. The equation simplifies to:

200 = 100

However, this equation is not true. It implies that the number of cupcakes sold at Location 1 can never be equal to the number of cupcakes sold at Location 2.

Therefore, there is no day when the number of cupcakes sold at Location 1 is equal to the number of cupcakes sold at Location 2.

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Note the full question may be :

A local bakery keeps track of the number of cupcakes sold each day at two different locations. At Location 1, the number of cupcakes sold is represented by the equation y = 150x + 200, where x represents the number of days and y represents the number of cupcakes sold. At Location 2, the number of cupcakes sold is represented by the equation y = 150x + 100.

(a) Determine the number of cupcakes sold at each location on Day 5.

(b) On which day will the number of cupcakes sold at Location 1 be equal to the number of cupcakes sold at Location 2?            

The probability of winning the lottery in this case is 1 in 3,645,280.

This is because there are 25 possible numbers that can be drawn for each of the four positions, meaning there are 25×25×25×25 (or 25⁴) possible combinations of the four winning numbers.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.

To win, you must select the correct combination of the four winning numbers in the same order in which they were drawn. If you select any other combination, you will not win.

Therefore, the probability of winning the lottery is 1 in 25⁴, which is 1 in 3,645,280.

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The calculated area of the composite figure is 85 cm².

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

The composite figure (see attachment)

Where, we have

Rectangle:

Area = length × width.

Therefore, the area of the rectangle is 10 cm × 6 cm = 60 cm².

Triangle:

Area = (1/2) × base × height.

Therefore, the area of the triangle is (1/2) × 5 cm × 10 cm = 25 cm².

To find the total area of the composite figure, we add the areas of the rectangle and the triangle:

Total Area = Area of Rectangle + Area of Triangle

= 60 cm² + 25 cm²

= 85 cm².

Therefore, the area of the composite figure is 85 cm².

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Answer:Your answer is 106

Step-by-step explanation:

Cos69 rounded to the nearest hundredth is approximately 0.39.

The equation is correct, and the value on both sides of the equation is 40.

To verify if the equation 90 × 4/9 = 40 is true, we can perform the calculation on both sides and compare the results.

On the left side of the equation:

90 × 4/9 = (90 × 4) / 9 = 360 / 9 = 40

On the right side of the equation:

40

Both sides of the equation evaluate to 40, which means they are equal. Therefore, the equation 90 × 4/9 = 40 is indeed true.

In summary, the equation is correct, and the value on both sides of the equation is 40.

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The general form of the equation of the Quadratic function is y = (-1/9) x2-(14/9) x-43/9.

The general form of the equation of the Quadratic function is y = (-1/9) x2-(14/9) x-43/9.    

The general form of the equation of a quadratic function given the vertex and a point on the graph, we can use the vertex form of the quadratic equation  y =  a( x- h) 2 k  where( h, k) represents the vertex of the parabola.  In this case, the vertex is(- 7, 6) and the point is(- 10, 5).  We can substitute these values into the equation to get  5 =  a(- 10-(- 7)) 2 6  Simplifying  farther  5 =  a(- 10 7) 2 6  5 =  a(- 3) 2 6  5 =  9a 6  Now, we can  break for' a'  a =  5- 6  9a = -1  a = -1/ 9  Substituting this value back into the equation, we get  y = (-1/9)( x-(- 7)) 2 6

 Simplifying  farther  y = (-1/9)( x 7) 2 6  Expanding and rearranging, we can write the equation in general form  y = (-1/9)( x2 14x 49) 6  y = (-1/9) x2-(14/9) x-49/9 6  y = (-1/9) x2-(14/9) x-43/9  So, the general form of the equation of the quadratic function is y = (-1/9) x2-(14/9) x-43/9.

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The goat has 113.097 square meters of area to roam within the tethered radius.

The area available to the goat can be calculated using the formula for the area of a circle.

The goat is tethered to a 6 m long chain, which means it can move in a circular area with a radius of 6 meters.

The formula for the area of a circle is given by:

Area = π × r²

The radius of the circular area is 6 meters.

Therefore, the area available to the goat is:

Area = π × 6²

= π ×36

= 113.097 square meters

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The figure shown is a counterexample of the statement, "The diagonals

of a parallelogram bisect opposite angles."

The figure shown is a counterexample of the statement,

"The diagonals of a parallelogram bisect opposite angles."

A counterexample is a specific example that disproves a statement by showing that it doesn't hold in all cases.

In this case, the figure demonstrates a parallelogram where the diagonals bisect opposite angles, thus contradicting the statement.

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The height of the television transmission tower is approximately 1298 feet.

The height of the television transmission tower, we can use trigonometry and the concept of tangent.

Let's denote the height of the tower as h.

We know the length of the shadow is 1130 feet and the angle formed by the ground and the line from the top of the tower to the tip of the shadow is 48.3 degrees.

The tangent of an angle is defined as the ratio of the opposite side to the adjacent side.

The height of the tower is the opposite side and the length of the shadow is the adjacent side.

Using the tangent function, we can set up the following equation:

tan(48.3°) = h / 1130

To solve for h, we can multiply both sides of the equation by 1130:

1130 × tan(48.3°) = h

Using a calculator, we find:

h ≈ 1130 × 1.1477

≈ 1297.601 feet

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The duration during which the height of the ball is increasing is from 1 second to 2.4 seconds.

To determine the duration during which the height of the ball is increasing, we need to analyze the given data points.

At 0.5 seconds, the height is 27 units.

At 1 second, the height is 31 units.

At 2.4 seconds, the height is 2 units.

We can observe that the height is decreasing between 0.5 seconds and 1 second because the height decreases from 27 to 31. This indicates that the ball is descending during that time interval.

However, between 1 second and 2.4 seconds, the height is increasing because the height goes from 31 to 2 units. This implies that the ball is ascending during that time interval.

Therefore, the duration during which the height of the ball is increasing is from 1 second to 2.4 seconds.

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Answer:

3/8

Step-by-step explanation:

There are 8 outcomes.  Three have exactly two tails.  

The total cost of each health club will be the​ same after the 6 months.

An equation is a statement that the values of two mathematical expressions are equal (indicated by the sign "=".)

There are two health clubs A and B.

To find the total fee of club A:

To find the total fee of club B:

Let us assume that the number of months at which the cost of both clubs A and B is same is 'x'.

Total cost of club A for x months = Total cost of club B for x months

[tex]\rightarrow \sf 17 + 29x = 11 + 30x[/tex]

[tex]\rightarrow \sf 30x - 29x = 17-11[/tex]

[tex]\rightarrow \sf 1x = 6[/tex]

[tex]\rightarrow \sf x=\dfrac{6}{1}[/tex]

[tex]\rightarrow \bold{x = \underline{6 \ months}}[/tex]

Hence, after 6 months, the total cost of each health club will be the​ same.

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Answer:

6

Step-by-step explanation:

Let's assume that the total cost of membership after "m" months for club A is "T(A)" and the total cost of membership after "m" months for club B is "T(B)".

For club A, the total cost of membership after "m" months is given by:

T(A) = 17 + 29m

For club B, the total cost of membership after "m" months is given by:

T(B) = 11 + 30m

To find the number of months when the total cost is the same for both clubs, we need to solve for "m" in the equation:

T(A) = T(B)

Substituting the expressions for T(A) and T(B), we get:

17 + 29m = 11 + 30m

Simplifying and solving for "m", we get:

m = 6

Therefore, the total cost of membership will be the same for both clubs after 6 months. After that point, Club A will be more expensive due to its higher monthly fee.

Answer:

[tex](18,14)[/tex]

Step-by-step explanation:

[tex]\mathrm{Since\ AB=BC=CD,\ we\ may\ say\ that\ B\ is\ midpoint\ of\ AC\ and\ C\ is\ midpoint}\\\mathrm{of\ BD.}\\\mathrm{Let\ the\ coordinates\ of\ C\ be\ (x,y)\ and\ D\ be\ (a,b).}\\\mathrm{Using\ midpoint\ formula,}\\\\\mathrm{(6,6)=(\frac{0+x}{2},\frac{2+y}{2})}\\\\\mathrm{or,\ 6=\frac{x}{2}\ and\ y+2=12}\\\\\mathrm{or,\ x=12\ and\ y=10}\\\mathrm{So,\ coordinates\ of\ C\ is\ (12,10).}[/tex]

[tex]\mathrm{As\ C\ is\ midpoint\ of\ BD,}\\\\\mathrm{(x,y)=(\frac{6+a}{2},\frac{6+b}{2})}\\\\\mathrm{or,\ (12,10)=(\frac{6+a}{2},\frac{6+b}{2})}\\\\\mathrm{or,\ 12=\frac{6+a}{2}\ and\ 10=\frac{6+b}{2}}\\\mathrm{or,\ a=18\ and\ b=14}\\\mathrm{So,\ the\ coordinates\ of\ D\ is\ (18,14).}[/tex]

I remember doing this in 8th grade, this was genuinely fun.

Anyways,

To create an accurate and logical layout of the water park attractions, we can use ordered pairs to represent the location of each attraction. Assuming that the water park is laid out on a rectangular grid, we can use (x, y) coordinates to represent the location of each attraction, where x represents the horizontal position and y represents the vertical position.

Here are some possible ordered pairs that could represent the location of the attractions in the water park:

Help Center: (0,0)

Large Whirlpool: (10,10)

Water Slide #1: (5,20)

Water Slide #2: (15,20)

Water Slide #3: (10,30)

Toddler Area: (20,0)

Lazy River: (30,15)

Concessions: (25,30)

Of course, the actual layout of the water park will depend on various factors such as the size and shape of the park, the available space, and the specific design of each attraction. These ordered pairs are just one example of how the attractions could be laid out on a rectangular grid.

PART 2:

Sure, I can help you with that too. Here's how you can calculate the slope between attractions using the slope formula:

The slope formula is:

m = (y2 - y1)/(x2 - x1)

where m is the slope of the line connecting two points (x1, y1) and (x2, y2).

For example, to calculate the slope between the Help Center and the Large Whirlpool, we can use the ordered pairs (0,0) and (25,25):

m = (25 - 0)/(25 - 0) = 1

Therefore, the slope between the Help Center and the Large Whirlpool is 1.

Similarly, we can calculate the slopes between each pair of attractions using their respective ordered pairs.

To find the midpoint between two attractions, we can use the midpoint formula:

Midpoint formula: ((x1 + x2)/2, (y1 + y2)/2)

For example, to find the midpoint between the Help Center and the Large Whirlpool, we can use the ordered pairs (0,0) and (25,25):

((0 + 25)/2, (0 + 25)/2) = (12.5,12.5)

Therefore, the midpoint between the Help Center and the Large Whirlpool is (12.5,12.5).

Once you have the slope and midpoint for each pair of attractions, you can use them to writethe linear equations for the lines connecting the attractions. The point-slope form of a linear equation is:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is a point on the line.

For example, to write the linear equation for the line connecting the Help Center and the Large Whirlpool, we can use the slope of 1 and the midpoint of (12.5,12.5):

y - 12.5 = 1(x - 12.5)

Simplifying this equation, we get:

y = x

Therefore, the linear equation for the line connecting the Help Center and the Large Whirlpool is y = x.

Similarly, we can write the linear equations for the lines connecting each pair of attractions using their respective slopes and midpoints.

There are no two Real numbers that add up to -2 and multiply to 10.

The numbers that add up to -2 and multiply to 10, we can use algebraic methods. Let's denote the two numbers as x and y. Based on the given conditions, we can set up two equations:

Equation 1: x + y = -2

Equation 2: x * y = 10

To solve this system of equations, we can use substitution or elimination methods. Let's solve it using the substitution method:

1. Solve Equation 1 for x:

  x = -2 - y

2. Substitute the value of x in Equation 2:

  (-2 - y) * y = 10

3. Simplify the equation:

  -2y - y^2 = 10

4. Rearrange the equation to standard form:

  y^2 + 2y + 10 = 0

5. Since the equation is a quadratic equation, we can apply the quadratic formula:

  y = (-b ± √(b^2 - 4ac)) / (2a)

  In this case, a = 1, b = 2, and c = 10.

6. Calculate the discriminant: b^2 - 4ac:

  2^2 - 4(1)(10) = 4 - 40 = -36

7. Since the discriminant is negative, the quadratic equation does not have real solutions. Therefore, there are no real numbers that satisfy both conditions of adding up to -2 and multiplying to 10.

In conclusion, there are no two real numbers that add up to -2 and multiply to 10.

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The system of equations has infinite solutions.

Here we have the system of equations:

y = (-4/5)*x

4x + 5y = 0

We can see that y is already isolated in the first equation, then we can replace that in the second equation so we will get:

4x + 5*(-4/5)*x = 0

4x - 4x = 0

0 = 0

So we have an identity, this means that the system of equations has infinite solutions.

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The number that is not a possible rational zero of the given polynomial is 3/5.

The Correct option is C.

To apply the Rational Root Theorem, we need to consider the possible rational zeros of the polynomial by taking the factors of the constant term (in this case, -8) divided by the factors of the leading coefficient (in this case, 5).

The factors of -8 are: ±1, ±2, ±4, ±8

The factors of 5 are: ±1, ±5

Thus, the possible rational zeros are: ±1, ±2, ±4, ±8, ±1/5, ±2/5, ±4/5, ±8/5

Among these options, the number that is not a possible rational zero of the given polynomial is 3/5.

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The inequalities which satisfy the number line shown is x>2 and x>=2.

We are given that;

The number line showing inequality

Now,

x>2 satisfies the equation by the given number line

x>=2 satisfies the equation by the given number line

x<=-3 does not satisfies the equation by the given number line

x<=-3 does not satisfies the equation by the given number line

Therefore, by the number line the answer will be x>2 and x>=2 .

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The value of x° is 133°.

Given,

Pentagon with angles 107° , 120° , 90° , 90° , x° .

A pentagon is formed by combining three triangles and thus have total of interior angles to be 540°.

Now, to calculate the value of x:

Sum of all interior angles of pentagon = 540°

Put the values of all the angles given in the figure,

120° + 107° + 90° + 90° + x° = 540°

407° + x = 540°

x = 133°

Hence the missing angle is of 133° .

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The base of the prism in this problem is given as follows:

A) 15 m.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

The dimensions in the context of this problem are given as follows:

25 m, 20 m and x.

The volume is given as follows:

7500 m³.

Applying the equation for the volume, the value of x is given as follows:

25 x 20x = 7500

500x = 7500

x = 7500/500

x = 15 m.

The problem is given by the image presented at the end of the answer.

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To find the zeroes of the polynomial 2 + 2√2x - 6, we set the polynomial equal to zero and solve for x:

2 + 2√2x - 6 = 0

Rearranging the terms:

2√2x = 4

Dividing both sides by 2√2:

x = 2/√2

To simplify the expression, we rationalize the denominator:

x = (2/√2) * (√2/√2) = 2√2/2 = √2

Therefore, the zero of the polynomial is x = √2.

To verify the relationship between the zeroes and coefficients of the polynomial, we can use Vieta's formulas. For a quadratic polynomial in the form ax^2 + bx + c = 0, the sum of the zeroes is given by -b/a and the product of the zeroes is given by c/a.

In this case, the polynomial 2 + 2√2x - 6 is not a quadratic polynomial, but rather a linear one. However, we can still apply Vieta's formulas:

The sum of the zeroes is -b/a = -(2√2)/1 = -2√2.

The product of the zeroes is c/a = (-6)/1 = -6.

Therefore, the relationship between the zeroes (√2) and the coefficients (2, 2√2, -6) is that the sum of the zeroes (-2√2) is equal to the negation of the coefficient of the linear term, and the product of the zeroes (-6) is equal to the constant term of the polynomial.

Answer:

increasing, constant, decreasing, constant

Step-by-step explanation:

the first line is going up so it's increasing

the line then goes horizontal which is constant

then the line goes down which is decreasing

then the line again goes horizontal which is constant

Answer:

Approximately 99.7% of housing prices are between a low price of $101,000 and a high price of $149,000.

Step-by-step explanation:

To complete the statement using the empirical rule, we need to determine the range within which approximately 99.7% of housing prices fall.

According to the empirical rule, for a normal distribution:

Approximately 68% of the data falls within one standard deviation of the mean.

Approximately 95% of the data falls within two standard deviations of the mean.

Approximately 99.7% of the data falls within three standard deviations of the mean.

Given that the mean housing price is $125,000 and the standard deviation is $8,000, we can apply these percentages to calculate the range:

One standard deviation:

The low price would be the mean minus one standard deviation:

$125,000 - $8,000 = $117,000

The high price would be the mean plus one standard deviation:

$125,000 + $8,000 = $133,000

So, approximately 68% of housing prices fall between $117,000 and $133,000.

Two standard deviations:

The low price would be the mean minus two standard deviations:

$125,000 - 2 * $8,000 = $109,000

The high price would be the mean plus two standard deviations:

$125,000 + 2 * $8,000 = $141,000

So, approximately 95% of housing prices fall between $109,000 and $141,000.

Three standard deviations:

The low price would be the mean minus three standard deviations:

$125,000 - 3 * $8,000 = $101,000

The high price would be the mean plus three standard deviations:

$125,000 + 3 * $8,000 = $149,000

So, approximately 99.7% of housing prices fall between $101,000 and $149,000.

In conclusion, approximately 99.7% of housing prices are between a low price of $101,000 and a high price of $149,000.

Hope this helps!