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2 years ago

Write an equation for each line

Mathematics

1 answer:

Scilla [17]2 years ago

5 0

Answer:

Step-by-step explanation:

m has a slope of -2 and a y intercept of 4

y = -2x + 4

n has a slope of 1 and a y intercept of -1

y = 1x - 1

y = x - 1

Ah!... the invisible questions in a sideways posted image.

t has a slope of zero and a y intercept of 3

y = 0x + 3

y = 3

p has infinite slope and no y intercept.

x = -5

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What is the total interest earned in two years on an account containing $500 at 3.5% interest, compounded annually?

Andrei [34K]

Answer: $35.6125

Step-by-step explanation:

3.5% = 0.035

Let's find the deposit amount with interest at the end of the first year:

500 + 500 · 0.035 = 517.5

Let's find the amount of the deposit with interest at the end of the second year:

517.5 + 517.5 · 0.035 = 535.6125

Find the total interest earned over two years:

535.6125 - 500 = 35.6125

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3 years ago

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3 years ago

The coordinate plane shows the floor plan for a swimming pool. What is the area of the pool’s border?"

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5 0

3 years ago

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Find the inverse Laplace transform f(t) of the function F(s). Write uc for the Heaviside function that turns on at c, not uc(t).

zzz [600]

Answer:

F(t) $=\frac{-1}{2}e^{7(t-7)}+\frac{1}{2}e^{-7(t-7)}$

Step-by-step explanation:

We have given $F(S)=\frac{7e^{-7s}}{s^2-49}$

Now $F(S)=e^{-7s}G(s)$

Here $G(S)=\frac{7}{S^2-49}$

Now first find the Laplace inverse of G(S)

Using partial fraction

$\frac{7}{(s+7)(s-7)}=\frac{A}{(S+7)}+\frac{B}{S-7}$

$7=A(S-7)+B(S+7)$

On comparing the coefficient

$A=\frac{1}{2}$ and $B=\frac{-1}{2}$

On putting the value of A and B

$G(S)=\frac{-1}{2(S+7)}+\frac{1}{2(S+7)}$

Taking inverse Laplace

$G(t)=\frac{-1}{2}e^{7t}+\frac{1}{2}e^{-7t}$

Now in G(s) there is onether term $e^{-7s}$

So F(t) $=\frac{-1}{2}e^{7(t-7)}+\frac{1}{2}e^{-7(t-7)}$

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3 years ago

Solve for x.

denis-greek [22]

Answer:

$\frac{3\±\sqrt{3}}{3}$

Step-by-step explanation:

Whe have the function $3x^2-6x+2=0$

To solve this equation we must factor.

To factor, we need to find the points where the function is equal to zero. So we use the quadratic formula

$\frac{-b\±\sqrt{b^2-4ac}}{2a}$

Where:

a = 3

b = -6

c = 2

Then

$\frac{-(-6) + \sqrt{(-6)^2-4(3)(2)}}{2(3)} = \frac{3+\sqrt{3}}{3}\\\\and\\\\\frac{-(-6) - \sqrt{(-6)^2-4(3)(2)}}{2(3)}= \frac{3-\sqrt{3}}{3}$

finally the correct answer is $\frac{3\±\sqrt{3}}{3}$

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3 years ago

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