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3 years ago

What is the point-slope form of a line that has a slope of 3 and passes through the point (–1, 4)?

Mathematics

1 answer:

DaniilM [7]3 years ago

4 0

Answer:

y-4=3(x+1)

Step-by-step explanation:

The formula is y-y₁=m(x-x₁).

So implement the first y which was 4. Then implement the slope for m(because m represents slope). That will be 3. Lastly take your x1 which is -1, and subtract it from x but if you have to negatives it becomes positive or adding.

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The bar graph below shows the student's favorite ice cream flavors. a) Use the graph's lines as a ruler to draw the intervals on

PtichkaEL [24]

Butter pecan: 25
Vanilla: 35
Chocolate: 50

The dotted line between 20 and 30 (butter pecan) will be nothing more than anything including 5. In this case, it is 25 counting up to 30.
The solid lines directly leading to a number will be that number, for instance, chocolate is 50.

3 0

2 years ago

Solve these linear equations in the form y=yn+yp with yn=y(0)e^at.

WINSTONCH [101]

Answer:

a) $y(t) = y_{0}e^{4t} + 2$ . It does not have a steady state

b) $y(t) = y_{0}e^{-4t} + 2$ . It has a steady state.

Step-by-step explanation:

a) $y' -4y = -8$

The first step is finding $y_{n}(t)$ . So:

$y' - 4y = 0$

We have to find the eigenvalues of this differential equation, which are the roots of this equation:

$r - 4 = 0$

$r = 4$

So:

$y_{n}(t) = y_{0}e^{4t}$

Since this differential equation has a positive eigenvalue, it does not have a steady state.

Now as for the particular solution.

Since the differential equation is equaled to a constant, the particular solution is going to have the following format:

$y_{p}(t) = C$

$(y_{p})' -4(y_{p}) = -8$

$(C)' - 4C = -8$

C is a constant, so (C)' = 0.

$-4C = -8$

$4C = 8$

$C = 2$

The solution in the form is

$y(t) = y_{n}(t) + y_{p}(t)$

$y(t) = y_{0}e^{4t} + 2$

b) $y' +4y = 8$

The first step is finding $y_{n}(t)$ . So:

$y' + 4y = 0$

We have to find the eigenvalues of this differential equation, which are the roots of this equation:

$r + 4 =$

$r = -4$

So:

$y_{n}(t) = y_{0}e^{-4t}$

Since this differential equation does not have a positive eigenvalue, it has a steady state.

Now as for the particular solution.

Since the differential equation is equaled to a constant, the particular solution is going to have the following format:

$y_{p}(t) = C$

$(y_{p})' +4(y_{p}) = 8$

$(C)' + 4C = 8$

C is a constant, so (C)' = 0.

$4C = 8$

$C = 2$

The solution in the form is

$y(t) = y_{n}(t) + y_{p}(t)$

$y(t) = y_{0}e^{-4t} + 2$

6 0

3 years ago

Mr. Ortiz pays a state tax of 10.4% on certain purchases. Which expression is the same as the total cost of p, a purchase of $14

Nata [24]

Answer:

idk

Step-by-step explanation:

IDK

4 0

3 years ago

Pete can buy daffodil bulbs in packages of 3 for $6.39 or in packages of 2 for $4.40. How much money does he save by buying 30 b

tatyana61 [14]

Answer:

The correct answer is Pete saves $2.10 by buying bulbs in packages of 3 for $6.39 each.

Step-by-step explanation:

Pete can buy daffodil bulbs in packages of 3 for $6.39 or in packages of 2 for $4.40.

He needs to buy 30 bulbs at a better price.

Money spent by buying bulbs in packs of 3 = 10 × 6.39 = $63.90.

Money spent by buying bulbs in packs of 2 = 15 × 4.40 = $66.

Money saved if bought in packs of 3 = 66 - 63.90 = $ 2.10.

Thus Pete should buy 30 daffodil bulbs in packages of 3 and save $2.10.

7 0

3 years ago

Which statement is true about the line that passes through the points (11,-5) and (0,-5)

o-na [289]

Answer:

The line has a slope of 0. The equation would be y=-5.

Step-by-step explanation:

There are true statements.

7 0

2 years ago

Read 2 more answers