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3 years ago

Write an equation in slope-intercept form

Mathematics

1 answer:

madam [21]3 years ago

3 0

Answer:

y = -7x +6

Step-by-step explanation:

Point (x1,y1) = (0,6)

point (x2,y2) = (1,-1)

Points (0,6) and (1,-1)

m = y2 - y1 / x2-x1

m = -1-6 / 1-0

m= -7

y - y1 = m (x - x1)

y - 6 = -7(x - 0)

y = -7x + 6

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If Wayne buys a motorcycle for $8000. Each year the motorcycle loses 20% of its value from the previous year. How much is the mo

nexus9112 [7]

20/100 x 8000 = 1600
1600 x 3 = 4800
8000 - 4800 = 3200

The motorcycle is worth $3,200 after three years.

7 0

3 years ago

Read 2 more answers

Find the solution of the differential equation dy/dt = ky, k a constant, that satisfies the given conditions. y(0) = 50, y(5) =

irga5000 [103]

Answer: The required solution is $y=50e^{0.1386t}.$

Step-by-step explanation:

We are given to solve the following differential equation :

$\dfrac{dy}{dt}=ky~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

where k is a constant and the equation satisfies the conditions y(0) = 50, y(5) = 100.

From equation (i), we have

$\dfrac{dy}{y}=kdt.$

Integrating both sides, we get

$\int\dfrac{dy}{y}=\int kdt\\\\\Rightarrow \log y=kt+c~~~~~~[\textup{c is a constant of integration}]\\\\\Rightarrow y=e^{kt+c}\\\\\Rightarrow y=ae^{kt}~~~~[\textup{where }a=e^c\textup{ is another constant}]$

Also, the conditions are

$y(0)=50\\\\\Rightarrow ae^0=50\\\\\Rightarrow a=50$

and

$y(5)=100\\\\\Rightarrow 50e^{5k}=100\\\\\Rightarrow e^{5k}=2\\\\\Rightarrow 5k=\log_e2\\\\\Rightarrow 5k=0.6931\\\\\Rightarrow k=0.1386.$

Thus, the required solution is $y=50e^{0.1386t}.$

8 0

3 years ago

Read 2 more answers

The volume of a pyramid that fits exactly inside a cube is 49 cubic feet. what is the volume of the cube?

8090 [49]

The volume of a pyramid is 1/3 the volume of the cube mentioned in the question since it fits exactly inside it. So multiply 49*3 = 147 cubic feet

6 0

3 years ago

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write the equation in slope intercept form for the line that passes through (-2,2) and is parallel to 2x+4y=16

ratelena [41]

Answer:

<h3>Step 1 - Find the gradient of 2x + 4y = 16</h3>

2x + 4y = 16

4y = 16 - 2x

y = 4 - 1/2x

gradient = -1/2

<h3>Step 2 - Find the Equation</h3>

y - y1 = m(x - x1)

m = gradient, (x1, y1) = (-2,2)

y - 2 = -1/2 (x + 2)

y - 2 = -1/2x - 1

y = -1/2x + 1 → ANSWER

Hope it helps!

7 0

3 years ago

The sum of the reciprocals of two consecutive even integers is 7/24. Write an equation that can be used to find the two integers

sergejj [24]

Assume the first even integer is x.
The next even integer will be 2 digits after this digit. So the next even integer will be x+2.

The reciprocals of these two even integers can be written as $\frac{1}{x}$ and $\frac{1}{x+2}$ respectively.

The sum of their reciprocals is 7/24. So we can set up the equation as:

$\frac{1}{x}+ \frac{1}{x+2}= \frac{7}{24}$

Taking LCM on left hand side:

$\frac{x+2+x}{x(x+2)}= \frac{7}{24} \\ \\ 
 \frac{2x+2}{ x^{2} +2x}= \frac{7}{24}$

Cross Multiplying the denominators:

$24(2x+2)=7({ x^{2} +2x}) \\ \\ 
48x+48=7 x^{2} +14x \\ \\ 
7 x^{2} +14x-48x-48=0 \\ \\ 
7 x^{2} -34x-48=0 \\ \\ 

$

Using the quadratic formula to solve the above equation:
$7 x^{2} -34x-48=0 \\ \\ 
x= \frac{34+- \sqrt{1156+1344} }{14} \\ \\ 
x= \frac{34+- \sqrt{2500} }{14} \\ \\ 
x=\frac{34+-50 }{14} \\ \\ 
x=6 \\ x=- \frac{8}{7} 
$

Since, the value of x can only be an integer, we discard the fractional value and keep x=6

So the first even integer is 6 and the next even integer is 8. The sum of reciprocals of 6 and 8 is 7/24

5 0

3 years ago