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3 years ago

Write the equation of the line, in slope-intercept form, that passes through the point (-2, -1) and has slope 5.

Mathematics

1 answer:

Mrrafil [7]3 years ago

7 0

Y=Mx+b so it would be -1=5(-2)+b then solve for B

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Solve the following 3 × 3 system. Enter the coordinates of the solution below.

defon

9514 1404 393

Answer:

(x, y, z) = (-1, 0, -3)

Step-by-step explanation:

We notice that the coefficients of z are such that elimination of the z term from the equations is made easy.

Adding equations 1 and 2:

(2x -3y -2z) +(x +3y +2z) = (4) +(-7)

3x = -3

x = -1

Adding equations 2 and 3:

(x +3y +2z) +(-4x -4y -2z) = (-7) +(10)

-3x -y = 3

Substituting for x, we get ...

(-3)(-1) -y = 3

0 = y . . . . . . . . . . . add y-3 to both sides

Then z can be found from any equation. Substituting for x and y in the second equation gives ...

-1 +2z = -7

2z = -6 . . . . . add 1

z = -3 . . . . . .divide by 2

The solution is (x, y, z) = (-1, 0, -3).

3 0

3 years ago

Scientists want to know the total trout population in a part of Lake Michigan. They tagged and released 200 trouts back into the

blondinia [14]

The estimate would be 1200.

We will set up a proportion for this. 10 out of 60 of the sample were tagged, so that is the first ratio. The 200 that were tagged would be in the numerator of the second ratio (10 was the portion tagged, and 200 is the portion tagged, so they both go on top). We do not know the total number so we use a variable:

10/60 = x/200

Cross multiply:

10*x = 60*200
10x = 12000

Divide both sides by 10:
10x/10 = 12000/10
x = 1200

6 0

3 years ago

This extreme value problem has a solution with both a maximum value and a minimum value. use lagrange multipliers to find the ex

noname [10]

$L(x,y,z,\lambda)=10x+10y+2z+\lambda(5x^2+5y^2+2z^2-42)$

$L_x=10+10\lambda x=0\implies1+\lambda x=0$

$L_y=10+10\lambda y=0\implies1+\lambda y=0$

$L_z=2+4\lambda z=0\implies1+2\lambda z=0$

$L_\lambda=5x^2+5y^2+2z^2-42=0$

$\begin{cases}L_x=0\\L_y=0\\L_z=0\end{cases}\implies1+\lambda x=1+\lambda y=1+2\lambda z=0\implies x=y=2z$

$5x^2+5y^2+2z^2=5(2z)^2+5(2z)^2+2z^2=42z^2=42\implies z^2=1$

$z^2=1\implies z=\pm1\implies x=y=\pm2$

There are two critical points, at which we have

$f\left(2,2,1\right)=42\text{ (a maximum value)}$

$f\left(-2,-2,-1\right)=-42\text{ (a minimum value)}$

3 0

3 years ago

WILL MARK BRAINIEST IF CORRECT.

bonufazy [111]

Answer:

1, 2, 5 and 6 are the answers.

Step-by-step explanation:

2 is correct because the arrow shows that the number line continues till infinity. 5 is correct because any fraction is possible as no restriction of integer value is placed. Any number less than 7 is not included. There are some confusions with 1 as it's not a solid color, So, I assume -7 is not included.

3 0

3 years ago

What does changing the h variable do to the graph of a quadratic function

deff fn [24]

Changing the h value will move the graph horizontally left or right.

5 0

3 years ago