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marusya05 [52]
4 years ago
10

Given the equation y − 4 = three fourths(x + 8) in point-slope form, identify the equation of the same line in standard form.

Mathematics
1 answer:
yuradex [85]4 years ago
5 0
The standard form of a line is ax+by=c, so we must get both variables on one side of the equal sign and a constant on the other...

y-4=(3/4)(x+8)  perform indicated multiplication on right side

y-4=(3x+24)/4  multiply both sides by 4

4y-16=2x+24  add 16 to both sides

4y=2x+40  subtract 2x from both sides

-2x+4y=40  (note that by convention, coefficient of x should be positive)  divide both sides by -1

2x-4y=-40
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Find the average rate of change between f(-7) and f(-1) in the function f(x)=x^2+2x -8
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Solve the equation by replacing x with -7 and then -1.

Then subtract the two to find the difference and divide that by the difference between -7 and -1.

f(-7) = -7^2 + 2(-7) -8 = 49 -14 -8 = 27

f(-1) = -1^2 + 2(-1) -8 = 1 -2 - 8 = -9

Difference between 27 and -9 = -36

Difference between -1 and -7 = -6

Rate of change = -36 /-6 = 6

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George is building a large model airplane in his workshop. If the door to his workshop is 3 ft wide and 6 1/2 ft high and the ai
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Suppose that the growth rate of children looks like a straight line if the height of a child is observed at the ages of 24​ mo
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4 years ago
Suppose a normally distributed set of data has a mean of 178 and a standard deviation of 20. Use the 68-95-99.7 Rule to determin
Scilla [17]

Answer:

97.7%

Step-by-step explanation:

For a score below 218 :

P(x < 218)

Standard deviation = 20 ; mean = 178

Obtian the standardized score (Zscore) :

Zscore = (x - mean) / standard deviation

Z = (218 - 178) / 20 = 40 / 20 = 2

P(x < Z) = P(Z < 2) = 0.97725 (Z probability calculator)

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7 0
3 years ago
Match each expression written in standard form to the equivalent expression in factored form
den301095 [7]

Answer:

1. 15x^7y^2 + 4x^3 => x^3(15x^4y^2 + 4)

2. 15x^7y^2 + 3x => 3x(5x^6y^2 + 1)

3. 15x^7y^2 + 6xy => 3xy(5x^6y + 2)

4. 15x^7 + 10y^2 => 5(3x^7 + 2y^2)

Step-by-step explanation:

To obtain the answer to the question, first let us factorise each expression. This is illustrated below:

1. 15x^7y^2 + 4x^3

Common factor is x^3, therefore the expression is written as:

x^3(15x^4y^2 + 4)

2. 15x^7y^2 + 3x

Common factor is 3x, therefore the expression is written as:

3x(5x^6y^2 + 1)

3. 15x^7y^2 + 6xy

Common factor is 3xy, therefore the expression is written as:

3xy(5x^6y + 2)

4. 15x^7 + 10y^2

Common factor is 5, therefore the expression can be written as:

5(3x^7 + 2y^2)

4 0
4 years ago
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