What number between 250 and 260 that is divisible by 9

Use slope-intercept form, y = mx + b to find the equation of the line that passes through the points (−6, 1) and (3, 4).

Mnenie [13.5K]

Answer:

y = one-third x + 3

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

Slope Formula: $m=\frac{y_2-y_1}{x_2-x_1}$

Step 1: Find slope m

m = (4 - 1)/(3 + 6)

m = 3/9

m = 1/3

y = 1/3x + b

Step 2: Find b

4 = 1/3(3) + b

4 = 1 + b

b = 3

Step 3: Rewrite

y = 1/3x + 3

6 0

3 years ago

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Which phrase represents the algebraic expression StartFraction 3 p + 6 Over 7 p minus 9 End Fraction?

Anarel [89]

Answer:

Step-by-step explanation:

(3p+6)/(7p-9)

4 0

2 years ago

Show that d^2y/dx^2=-2x/y^5, if x^3 + y^3=1

aalyn [17]

Answer:

y³ + x³ = 1

First, differentiate the first time, term by term:

${3y^{2}.\frac{dy}{dx} + 3x^{2}} = 0 \\\\{3y^{2}.\frac{dy}{dx} = -3x^{2}} \\\\\frac{dy}{dx} = \frac{-3x^{2}}{3y^{2}} \\\\\frac{dy}{dx} = \frac{-x^{2}}{y^{2}}$

↑ we'll substitute this later (4th step onwards)

Differentiate the second time:

$3y^{2}.\frac{dy}{dx} + 3x^{2} = 0 \\\\3y^{2}.\frac{d^{2} y}{dx^{2}} + 6y(\frac{dy}{dx})^{2} + 6x = 0 \\\\3y^{2}.\frac{d^{2} y}{dx^{2}} + 6y(\frac{dy}{dx})^{2} = - 6x \\\\3y^{2}.\frac{d^{2} y}{dx^{2}} + 6y(\frac{-x^{2} }{y^{2} })^{2} = - 6x \\\\3y^{2}.\frac{d^{2} y}{dx^{2}} + 6y(\frac{x^{4} }{y^{4} }) = - 6x \\\\3y^{2}.\frac{d^{2} y}{dx^{2}} + \frac{6x^{4} }{y^{3} } = - 6x \\\\3y^{2}.\frac{d^{2} y}{dx^{2}} = - 6x - \frac{6x^{4} }{y^{3} } \\\\$

$3y^{2}.\frac{d^{2} y}{dx^{2}} = - \frac{- 6xy^{3} - 6x^{4} }{y^{3}} \\\\\frac{d^{2} y}{dx^{2}} = - \frac{- 6xy^{3} - 6x^{4} }{3y^{2}. y^{3}} \\\\\frac{d^{2} y}{dx^{2}} = - \frac{- 2xy^{3} - 2x^{4} }{y^{5}} \\\\\frac{d^{2} y}{dx^{2}} = - \frac{-2x (y^{3} + x^{3})}{y^{5}} \\\\\frac{d^{2} y}{dx^{2}} = - \frac{-2x (1)}{y^{5}} \\\\\frac{d^{2} y}{dx^{2}} = - \frac{-2x}{y^{5}}$

3 0

2 years ago

Henri has $24,000 invested in stocks and bonds. The amount in stocks is $6,000 more than three times the amount in bonds. How mu

kotykmax [81]

Answer:

The amount of investment in bonds is US$ 4,500 and the amount of investment in stocks is US$ 19,500

Step-by-step explanation:

Total investment in stocks and bonds = US$ 24,000

Amount of investment in bonds = x

Amount of investment in stocks = 3x + 6,000 (amount in stocks is $6,000 more than three times the amount in bonds)

For finding the value of x (amount of investment in bonds), we use this equation:

x + 3x + 6,000 = 24,000

x + 3x = 24,000 - 6,000

4x = 18,000

x = 4,500 (dividing by 4)

The amount of investment in bonds is US$ 4,500

Now let's find the amount of investment in stocks:

3x + 6,000 = 3 (4,500) + 6,000 = 13,500 + 6,000 = 19,500

The amount of investment in stocks is US$ 19,500

5 0

3 years ago

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Simplify the following functions so that your answers do not include trig functions. In each case, assume x∈(−1,1). cos(2sin−1x−

Roman55 [17]

Answer:

cos(2sin−1x)=1−2x2

Step-by-step explanation:

et sin−1x=θ , so that, x=sinθ,|x|≤1,θ∈[−π2,π2].

3 0

2 years ago