Which of these is not random?

Find the equation of the line with slope m=1/2 that contains the point (4,6)

vazorg [7]

Answer:

y = 1/2x + 4

Step-by-step explanation:

Use the formula for the equation of a line.

y = mx + b

Where m is the slope, and b is the y-intercept.

The slope is given.

y = 1/2x + b

The points (x, y) are given.

(4, 6)

Put y as 6 and x as 4, solve for b.

6 = 1/2(4) + b

6 = 2 + b

6 - 2 = b

4 = b

The y-intercept is 4 or (0, 4).

The equation of the line is y = 1/2x + 4.

4 0

2 years ago

Solve for x. Round to the nearest tenth, if necessary.

e-lub [12.9K]

Answer:

$\boxed {\boxed {\sf x \approx 1.9}}$

Step-by-step explanation:

We are asked to find x, a missing side in a triangle.

This is a right triangle because there is a small square in the corner representing a 90 degree or right angle. Therefore, we can use right triangle trigonometry. The three main functions are:

sinθ= opposite/hypotenuse
cosθ= adjacent/hypotenuse
tanθ= opposite/adjacent

Examine the triangle. We will use angle S, measuring 54 degrees, for theta. Side QR, measuring x, is opposite angle S. Side QS, measuring 2.3, is the hypotenuse because it is opposite the right angle. Since we have the opposite and hypotenuse, we will use sine.

$sin \theta = \frac {opposite}{hypotenuse}$

θ= 54
opposite= x
hypotenuse = 2.3

$sin (54)= \frac{ x}{2.3}$

We are solving for x, so we must isolate the variable. It is being divided by 2.3 The inverse operation of division is multiplication, so we multiply both sides by 2.3

$2.3* sin (54)= \frac{x}{2.3}*2.3$

$2.3* sin (54)=x$

$2.3*0.8090169944=x$

$1.860739087 =x$

Round to the nearest tenth. The 6 in the hundredth place to the right tells us to round the 8 up to a 9.

$1.9 \approx x$

x is approximately 1.9

7 0

3 years ago

Find a,b,and c for the answer

Svetach [21]

Alright give me a second ok

3 0

3 years ago

Pls help me, I dont get the question. Polynomials

AnnZ [28]

The given polyn. is not in std. form. To answer this question, we need to perform the indicated operations (mult., addn., subtrn.) first and then arrange the terms of this poly in descending order by powers of x:

P(x) = x(160 - x) - (100x + 500)

When this work has been done, we get P(x) = 160x - x^2 - 100x - 500, or

P(x) = -x^2 + 60x - 500

So, you see, the last term is -500. This means that if x = 0, not only is there no profit, but the company is "in the hole" for $500.

6 0

3 years ago

b) If parametric equations of a flow line are x = x(t), y = y(t), explain why these functions satisfy the differential equations

sineoko [7]

Answer:

The equation of the the flow line that passes through the point (x, y) = (−1, −1) is

In y + In x = 0 or in another form, xy = 1.

Step-by-step explanation:

The pathline equation for a vector field is given by F(x,y) = xî - yj

The velocity vector field for the streamline of the flow is given by

V(x, y) = (dx/dt)î + (dy/dt)j

From the question, it is given that

(dx/dt) = x

(dy/dt) = -y

Hence, the velocity vector field for the streamline of the flow in question is

V(x, y) = xî - yj

which coincides with the pathline vector field of the flow.

The only time the pathline and streamline vector field coincide and have the same equation is when the flow is a steady state flow.

That is, the properties of the fluid flowing isn't changing with time!

Hence, this flow is a steady state flow!

We're told to solve the differential equation.

(dx/dt) = x

(dy/dt) = -y

but

(dy/dx) = (dy/dt) × (dt/dx)

(dy/dx) = -y/x

(dy/y) = -(dx/x)

∫(dy/y) = -∫ (dx/x)

In y = - In x + c

where c is the constant of integration

In y + In x = c

In (xy) = c

Inserting the values of (x, y) given in the question,

In (-1 × -1) = c

In 1 = c

0 = c

c = 0

In y + In x = 0

In (yx) = 0

xy = e⁰ = 1

xy = 1

So, the equation of the the flow line that passes through the point (x, y) = (−1, −1) is

In y + In x = 0 or in another form, xy = 1

Hope this Helps!!!

4 0

3 years ago