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2 years ago

Find the slope and the y-intercept of the line.

Mathematics

1 answer:

Fantom [35]2 years ago

3 0

Answer:

Slope 'm' = $\frac{5}{2}$

And y-intercept = 2

Step-by-step explanation:

Slope-intercept form of a line is given by the equation,

y = mx + b --------(1)

Here, m = slope of the line

b = y-intercept

Given equation is,

5x - 2y = -4

2y = 5x + 4

y = $\frac{5}{2}x+2$

By comparing this equation with equation (1),

Slope 'm' = $\frac{5}{2}$

And y-intercept = 2

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Consider the vector field f(x,y,z)=(2z+3y)i+(3z+3x)j+(3y+2x)kf(x,y,z)=(2z+3y)i+(3z+3x)j+(3y+2x)k.

natima [27]

$\dfrac{\partial f}{\partial x}=2z+3y\implies f(x,y,z)=2xz+3xy+g(y,z)$

$\dfrac{\partial f}{\partial y}=3x+\dfrac{\partial g}{\partial y}=3z+3x$
$\dfrac{\partial g}{\partial y}=3z\implies g(y,z)=3yz+h(z)$
$\implies f(x,y,z)=3xz+3xy+3yz+h(z)$

$\dfrac{\partial f}{\partial z}=3x+3y+\dfrac{\mathrm dh}{\mathrm dz}=3y+2x$
$\dfrac{\mathrm dh}{\mathrm dz}=-x$

But we assume $h$ is a function of $z$ alone, so there is no solution for $h$ and hence no scalar function $f$ such that $\nabla f=\mathbf f$ .

6 0

2 years ago

Saby used a probability simulator to roll a 6-sided number cube and flip a coin 100 times. The results are shown in the tables b

Degger [83]

Short Answers
P(Both) = 0.1792
Givens
The total number of roles = 100
Total number of heads = 56
Number of times rolled a four = 32 [check this for me].

Set up the probabilities.
P(H) = 56/100
P(4) = 32/100
P(H)*P(4) = P(Both)

Substitute and solve
P(Both) = 56/100 * 32/100 = 1792/10000
P(Both) = 112/625 because there are many cancellations. Or you could just express it as 0.1972

8 0

2 years ago

a ladder 13m long is placed on the ground in such a way that it touches the top of a vertical wall 12m high. find the distance o

Sergio039 [100]

Answer:

by applying Pythagoras theorem;

the ladder(13m) acts as hypotenuse

the wall (12m) acts as height

the distance between the the two is the base

therefore

a² + b² = c²

b²= c²- a²

b²= 169 - 144

b² = 25

√b² = √25

b= 5m

the distance is 5m

8 0

2 years ago

Solve for h. 6+h+8=24

lozanna [386]

Answer:

the answer to your question is h = 10

8 0

3 years ago

Read 2 more answers

A model rocket is launched from a roof into a large field. The path of the rocket can be modeled by the equation

Alexxx [7]

Ok

y=-0.04x^2+8.3x+4.3
when the rocket reaches the ground (when height=0, ie when y=0), then the rocket will land, find the x coordinate

set y=0
0=-0.04x^2+8.3x+4.3
use quadratic formula
if you have ax^2+bx+c=0, then
x= $\frac{-b+/- \sqrt{b^{2}-4ac} }{2a}$
a=-0.04
b=8.3
c=4.3
x= $\frac{-8.3+/- \sqrt{8.3^{2}-4(-0.04)(8.3)} }{2(-0.04)}$
x=208.017 or -0.516785
xrepresents horizontal distance
you cannot have a negative horizontal distance unless you fired and theh wind blew it backwards
therefor x=280.017 is the answer
208.02 m

7 0

3 years ago