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3 years ago

Use intercepts to graph the linear equation 5x + 3y = 30.

Mathematics

1 answer:

miv72 [106K]3 years ago

5 0

Answer x=6 and y=10

Explanation:

Replace each variable in turn with 0 and solve

5x+3y=30 Put zero in place of x and solve for y

5(0)+3y=30

$\frac{3y}{3} =\frac{30}{3}$

y=10 The y- intercept is 10

5x+3y=30 Put zero in place of y and solve for x

5x+3(0)=30

$\frac{5x}{5} =\frac{30}{5}$

x=6 The x-intercept is 6

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OlgaM077 [116]

Answer: c = 4.97 and c = -1.97

Step-by-step explanation: <u>Mean Value Theorem</u> states if a function f(x) is continuous on interval [a,b] and differentiable on (a,b), there is at least one value c in the interval (a<c<b) such that:

$f'(c) = \frac{f(b)-f(a)}{b-a}$

So, for the function f(x) = $2x^{3}-9x^{2}-60x+1$ on interval [-4,9]

$f'(x) = 6x^{2}-18x-60$

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Calculating average:

$6c^{2}-18c-60 = \frac{100-113}{9-(-4)}$

$6c^{2}-18c-60 = -1$

$6c^{2}-18c-59 = 0$

Resolving through Bhaskara:

c = $\frac{18+\sqrt{1740} }{12}$

c = $\frac{18+41.71 }{12}$ = 4.97

c = $\frac{18-41.71 }{12}$ = -1.97

<u>Both values of c exist inside the interval [-4,9], so both values are mean slope: c = 4.97 and c = -1.97</u>

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