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GuDViN [60]
3 years ago
13

On a two-week job, a repairman works a total of 70 hours,He charges 75$ plus 40$ per hour. An equation shows this relationship,

where x is the number of hours and y is the total fee. 3.Which number is the slope of the line shown by the equation? A .14 C .70 B. 40 D.75 4.Which number is the y-intercept A. 14 C. 70 B.40 D.75
Mathematics
1 answer:
statuscvo [17]3 years ago
4 0

Answer:

Which number is the slope of the line shown by the equation?

B. 40

Which number is the y-intercept

D.75

Step-by-step explanation:

The formula for the Equation of a line =

y = mx+b

where:

m is the slope and b is the y-intercept.

Hence, interpreting the above question:

On a two-week job, a repairman works a total of 70 hours,He charges 75$ plus 40$ per hour.

x is the number of hours and y is the total fee.

Hence, the Equation we have is:

y = $40 × x + 75

y = 40x + 75

Comparing with the Equation of a line formula

= y = mx+b

Therefore:

The slope of the line = 40

The y intercept = 75

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3 years ago
Read 2 more answers
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katovenus [111]

1. Let a and b be coefficients such that

\dfrac1{x(2x+3)} = \dfrac ax + \dfrac b{2x+3}

Combining the fractions on the right gives

\dfrac1{x(2x+3)} = \dfrac{a(2x+3) + bx}{x(2x+3)}

\implies 1 = (2a+b)x + 3a

\implies \begin{cases}3a=1 \\ 2a+b=0\end{cases} \implies a=\dfrac13, b = -\dfrac23

so that

\dfrac1{x(2x+3)} = \boxed{\dfrac13 \left(\dfrac1x - \dfrac2{2x+3}\right)}

2. a. The given ODE is separable as

x(2x+3) \dfrac{dy}dx} = y \implies \dfrac{dy}y = \dfrac{dx}{x(2x+3)}

Using the result of part (1), integrating both sides gives

\ln|y| = \dfrac13 \left(\ln|x| - \ln|2x+3|\right) + C

Given that y = 1 when x = 1, we find

\ln|1| = \dfrac13 \left(\ln|1| - \ln|5|\right) + C \implies C = \dfrac13\ln(5)

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We can solve this explicitly for y :

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\ln|y| = \ln\left|\sqrt[3]{\dfrac{5x}{2x+3}}\right|

\boxed{y = \sqrt[3]{\dfrac{5x}{2x+3}}}

2. b. When x = 9, we get

y = \sqrt[3]{\dfrac{45}{21}} = \sqrt[3]{\dfrac{15}7} \approx \boxed{1.29}

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