Line j passes through points (-6,1) and (-3,6) .line m is parallel to line j and passes through point (15,-1). what is the equation of line m ?

Answers

Answer 1

Answer: Slope of line j;
m= $(change in x)/(change in y)$
m= $(6-1)/(-3--6)$
m= $(5)/(3)$
Parallel lines have equal gradients;
So,
y=mx+c
y=5/3x+c
Replacing for x and y;
-1=5/3(15)+c
-1=25+c
c=-26
y= $(5)/(3) x-26$

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30% of a number equals 30. what is the number?

Answers

it would be 100! 30% of 100 is 30

100 cuz 30% of 100 is 30;)

Find the distance between the two points. Round to the nearest tenth if necessary.(8, 8), (12, 11)

7
5
25
28

9.
Find the distance between the two points. Round to the nearest tenth if necessary.

(–2, –6), (3, 9)

15.8
250
3.2
20

Answers

The distance formula is expressed as square root of the square of the difference of y's and the square of the difference of x's.
In 1) d = square root of (11-8)^2 + (12-8)^2 d = 5
In 2) d = square root of (9+6)^2 + (3+2)^2 d = 5 square root of 10 d = 15.81

Answer:

option B is correct

Option A is correct.

Step-by-step explanation:

Using distance formula:

$d = √((x_1-x_2)^2+(y_1-y_2)^2)$

Given the points:

(8, 8) and (12, 11)

then;

$d = √((8-12)^2+(8-11)^2) = √((-4)^2+(-3)^2) = √(16+9) =√(25) = 5$

Therefore, the distance between the two points is, 5 units.

Given the points:

(-2, -6) and (3, 9)

then;

$d = √((-2-3)^2+(-6-9)^2) = √((-5)^2+(-15)^2) = √(25+225) =√(250) = 15.8$

Therefore, the distance between the two points is, 15.8 units

Volume of triangles prism 8.9 cm 8cm 14cm

Answers

Answer:

A. 1 1/5

Step-by-step explanation:

48/40 = 1 8/40

1 8/40 Simplify to 1 1/5

How much does 1/2 cup of epsom salts weight?

Answers

I believe the answer is 136.5g

Chuck must save a total of 180 for a new bike. So far he has saved 4/5 of the amount. How much money has chuck saved for the bike

Answers

He has saved $144 out of $180

Inverse laplace of [(1/s^2)-(48/s^5)]

Answers

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I am not familiar with Laplace transforms, so my explanation probably won't help, but given that for two Laplace transform $F(s)$ and $G(s)$ , then $\mathcal{L}^(-1)\{aF(s)+bG(s)\} = a\mathcal{L}^(-1)\{F(s)\}+b\mathcal{L}^(-1)\{G(s)\}$

Given that $(1)/(s^2) = (1!)/(s^2)$ and $-(48)/(s^5) = -2\cdot(4!)/(s^5)$

So you have $\mathcal{L}^(-1)\left\{(1)/(s^2) - 2\cdot(4!)/(s^5)\right\} = \mathcal{L}^(-1)\left\{(1)/(s^2)\right\} - 2\mathcal{L}^(-1)\left\{(4!)/(s^5)\right\}$

From Table of Laplace Transform, you have $\mathcal{L}\{t^n\} = (n!)/(s^(n+1))$ and hence $\mathcal{L}^(-1)\left\{(n!)/(s^(n+1))\right\} = t^n$

So you have $\mathcal{L}^(-1)\left\{(1)/(s^2)\right\} - 2\mathcal{L}^(-1)\left\{(4!)/(s^5)\right\} = \boxed{t-2t^4}$ .

Hope this helps...

Final answer:

To find the inverse Laplace transform of the given expression, use partial fraction decomposition to simplify it into individual fractions and then find their inverse transforms.

Explanation:

To find the inverse Laplace transform of the given expression, we can use partial fraction decomposition. First, we factor the denominator: s2*(s3-48). The next step is to represent the expression as a sum of simpler fractions:

1/s2 - 48/s5 = A/s + B/s2 + C/(s - 2) + D/(s + 2) + E/(s + 4) + F/(s2 - 4)

Next, we solve for A, B, C, D, E, and F by performing algebraic manipulations and equating the corresponding coefficients. Finally, we can look up the inverse Laplace transform of each individual fraction term in tables or by using known formulas.

Learn more about Inverse Laplace Transform here:

brainly.com/question/31322563

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