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Dvinal [7]
2 years ago
13

22. Write the equation of the line through (3, 4) and (2, 1) in slope-intercept form. (Hint: Find point-slope form first)​

Mathematics
1 answer:
salantis [7]2 years ago
5 0

Answer:

y = 3x - 5

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \frac{y_{2}-y_{1}  }{x_{2}-x_{1}  }

with (x₁, y₁ ) = (3, 4 ) and (x₂, y₂ ) = (2, 1 )

m = \frac{1-4}{2-3} = \frac{-3}{-1} = 3 , then

y = 3x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (2, 1 ) , then

1 = 6 + c ⇒ c = 1 - 6 = - 5

y = 3x - 5 ← equation of line

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A professor pays 25 cents for each blackboard error made in lecture to the student who pointsout the error. In a career ofnyears
arsen [322]

Answer:

The correct answer is "0.0000039110".

Step-by-step explanation:

The given values are:

Y_n\rightarrow N(\mu, \sigma^2)

\mu = 40n

\sigma^2=100n

n=20

then,

The required probability will be:

= P(Y_{20}>1000)

= P(\frac{Y_{20}-\mu}{\sigma} >\frac{1000-40\times 20}{\sqrt{100\times 20} } )

= P(Z>\frac{1000-800}{44.7214} )

= P(Z>\frac{200}{44.7214} )

= P(Z>4.47)

By using the table, we get

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6 0
2 years ago
Grover Elementary School is getting ready for the annual Penny Drive. The table below shows the target goals for the drive at th
Sever21 [200]

The slope of the function is $400.

<h3 /><h3>Definition of slope of a function</h3>

The slope of a function is the rate of change of the dependent variable with respect to the independent variable. The equation that represents a function is: y = mx + b

Where:

  • y = dependent variable
  • m = independent variable
  • x = slope
  • b = constant

Looking at the total money raised, the amount of money increases by 400. This is the slope.

To learn more about slope, please check: brainly.com/question/2491620

7 0
2 years ago
Find a linear second-order differential equation f(x, y, y', y'') = 0 for which y = c1x + c2x3 is a two-parameter family of solu
Alisiya [41]
Let y=C_1x+C_2x^3=C_1y_1+C_2y_2. Then y_1 and y_2 are two fundamental, linearly independent solution that satisfy

f(x,y_1,{y_1}',{y_1}'')=0
f(x,y_2,{y_2}',{y_2}'')=0

Note that {y_1}'=1, so that x{y_1}'-y_1=0. Adding y'' doesn't change this, since {y_1}''=0.

So if we suppose

f(x,y,y',y'')=y''+xy'-y=0

then substituting y=y_2 would give

6x+x(3x^2)-x^3=6x+2x^3\neq0

To make sure everything cancels out, multiply the second degree term by -\dfrac{x^2}3, so that

f(x,y,y',y'')=-\dfrac{x^2}3y''+xy'-y

Then if y=y_1+y_2, we get

-\dfrac{x^2}3(0+6x)+x(1+3x^2)-(x+x^3)=-2x^3+x+3x^3-x-x^3=0

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6 0
3 years ago
For which rational expression is 8 an excluded value ? check all that apply
denis23 [38]

<u>Answer:</u>

The correct answer options are C. \frac{x^2+5}{x-8} and D. \frac{x^2-x-56}{x^2-64}.

<u>Step-by-step explanation:</u>

The values which make the denominator equal to zero are called the excluded values.

Here, we can substitute 8 for x and check if it makes the denominator 0.

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\frac{x^2-x-56}{x^2-64} = \frac{8^2-8-56}{8^2-64} = \frac{0}{0} =0

\frac{8x^2-2}{x^2-16} = \frac{8(8)^2-2}{8^2-16} =\frac{510}{48}

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3 years ago
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The answer is A.
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