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kondaur [170]
3 years ago
12

What is the slope of the line given by the equation y=-3X? A. 1/3 B. -1/3 C. -3 D. 3

Mathematics
2 answers:
lana66690 [7]3 years ago
6 0
C, hope this helps, -3
vfiekz [6]3 years ago
5 0

Answer:

\boxed{-3}

Step-by-step explanation:

The slope-intercept form of an equation is determined by the constant equation y=mx+b where m is the slope and b is the y-intercept of the line.

Therefore, we can use the equation given and implement it to find your slope.

y=-3x

Our equation does not have a y-intercept, b. Therefore, it can just be inferred as +0.

Because we do have a m, we can then find out what our slope is: \boxed{-3}.

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Factor a number, variable, or expression out of the trinomial 5x^2 - 25x + 10
Harman [31]
Hope you do well , i pray blessings and growth to you .
6 0
2 years ago
For each of the following vector fields F , decide whether it is conservative or not by computing curl F . Type in a potential f
Phantasy [73]

The key idea is that, if a vector field is conservative, then it has curl 0. Equivalently, if the curl is not 0, then the field is not conservative. But if we find that the curl is 0, that on its own doesn't mean the field is conservative.

1.

\mathrm{curl}\vec F=\dfrac{\partial(5x+10y)}{\partial x}-\dfrac{\partial(-6x+5y)}{\partial y}=5-5=0

We want to find f such that \nabla f=\vec F. This means

\dfrac{\partial f}{\partial x}=-6x+5y\implies f(x,y)=-3x^2+5xy+g(y)

\dfrac{\partial f}{\partial y}=5x+10y=5x+\dfrac{\mathrm dg}{\mathrm dy}\implies\dfrac{\mathrm dg}{\mathrm dy}=10y\implies g(y)=5y^2+C

\implies\boxed{f(x,y)=-3x^2+5xy+5y^2+C}

so \vec F is conservative.

2.

\mathrm{curl}\vec F=\left(\dfrac{\partial(-2y)}{\partial z}-\dfrac{\partial(1)}{\partial y}\right)\vec\imath+\left(\dfrac{\partial(-3x)}{\partial z}-\dfrac{\partial(1)}{\partial z}\right)\vec\jmath+\left(\dfrac{\partial(-2y)}{\partial x}-\dfrac{\partial(-3x)}{\partial y}\right)\vec k=\vec0

Then

\dfrac{\partial f}{\partial x}=-3x\implies f(x,y,z)=-\dfrac32x^2+g(y,z)

\dfrac{\partial f}{\partial y}=-2y=\dfrac{\partial g}{\partial y}\implies g(y,z)=-y^2+h(y)

\dfrac{\partial f}{\partial z}=1=\dfrac{\mathrm dh}{\mathrm dz}\implies h(z)=z+C

\implies\boxed{f(x,y,z)=-\dfrac32x^2-y^2+z+C}

so \vec F is conservative.

3.

\mathrm{curl}\vec F=\dfrac{\partial(10y-3x\cos y)}{\partial x}-\dfrac{\partial(-\sin y)}{\partial y}=-3\cos y+\cos y=-2\cos y\neq0

so \vec F is not conservative.

4.

\mathrm{curl}\vec F=\left(\dfrac{\partial(5y^2)}{\partial z}-\dfrac{\partial(5z^2)}{\partial y}\right)\vec\imath+\left(\dfrac{\partial(-3x^2)}{\partial z}-\dfrac{\partial(5z^2)}{\partial x}\right)\vec\jmath+\left(\dfrac{\partial(5y^2)}{\partial x}-\dfrac{\partial(-3x^2)}{\partial y}\right)\vec k=\vec0

Then

\dfrac{\partial f}{\partial x}=-3x^2\implies f(x,y,z)=-x^3+g(y,z)

\dfrac{\partial f}{\partial y}=5y^2=\dfrac{\partial g}{\partial y}\implies g(y,z)=\dfrac53y^3+h(z)

\dfrac{\partial f}{\partial z}=5z^2=\dfrac{\mathrm dh}{\mathrm dz}\implies h(z)=\dfrac53z^3+C

\implies\boxed{f(x,y,z)=-x^3+\dfrac53y^3+\dfrac53z^3+C}

so \vec F is conservative.

4 0
3 years ago
If you change the y-intercept in the equation y = -2x + 5 to y = -2x + 1, how will its graph change? A. It will increase at a fa
FinnZ [79.3K]
The starting value will decrease.
6 0
3 years ago
Estimate the quotient to the tenths place. Then find the quotient. Round to the nearest thousandth 3)1.066 The estimate is The q
riadik2000 [5.3K]

Answer:

Estimate = 0.4

Quotient = 0.355 ---> Approximated to nearest thousandth

Step-by-step explanation:

Question like this is better answered using attachment;

See Attachment

When 1.066 is divided by 3,

The quotient is 0.3553......

When estimating to tenths,

We stop the quotient at 0.35 then round it up.

This gives 0.4

When estimating to nearest thousandth,

We stop the quotient at 0.3553 then round it up;

This gives 0.355

7 0
3 years ago
Is (-2, -6) a solution to this system of equations? 3x + 18y = -14 15x − 7y = 12 yes no
soldi70 [24.7K]

Answer:

No

Step-by-step explanation:

Plug in (-2, -6) to see if it's the solution or not

3(-2) + 18(-6) ?  -14

-6  + ( -108) ? -14

-114 ≠ -14

Answer is NO

6 0
3 years ago
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