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2 years ago

Which of the following pairs of numbers contains like fractions?

Mathematics

1 answer:

Romashka [77]2 years ago

3 0

The correct answer is D. Because, by simplyfing all fractions your are left with you have the correct answer.

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On a coordinate plane, a line goes through (negative 3, 2) and (0, 1). A point is at (3, 4). What is the equation of the line th

Novay_Z [31]

Answer:

$y=3x-5$

Step-by-step explanation:

step 1

Find the slope of the given line

we have

(-3,2) and (0,1)

The slope m is

$m=(1-2)/(0+3)=-1/3$

step 2

Find the slope of the line perpendicular to the given line

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of its slopes is -1)

The slope is

$m=3$

step 3

Find the equation of the line in point slope form

we have

$m=3$

$point(3,4)$

$y-4=3(x-3)$ ----> equation in point slope form

Convert to slope intercept form

$y=3x-9+4$

$y=3x-5$

6 0

3 years ago

Read 2 more answers

Find the minimum and maximum of f(x,y,z)=x^2+y^2+z^2 subject to two constraints, x+2y+z=4 and x-y=8.

Alika [10]

The Lagrangian for this function and the given constraints is

$L(x,y,z,\lambda_1,\lambda_2)=x^2+y^2+z^2+\lambda_1(x+2y+z-4)+\lambda_2(x-y-8)$

which has partial derivatives (set equal to 0) satisfying

$\begin{cases}L_x=2x+\lambda_1+\lambda_2=0\\L_y=2y+2\lambda_1-\lambda_2=0\\L_z=2z+\lambda_1=0\\L_{\lambda_1}=x+2y+z-4=0\\L_{\lambda_2}=x-y-8=0\end{cases}$

This is a fairly standard linear system. Solving yields Lagrange multipliers of $\lambda_1=-\dfrac{32}{11}$ and $\lambda_2=-\dfrac{104}{11}$ , and at the same time we find only one critical point at $(x,y,z)=\left(\dfrac{68}{11},-\dfrac{20}{11},\dfrac{16}{11}\right)$ .

Check the Hessian for $f(x,y,z)$ , given by

$\mathbf H(x,y,z)=\begin{bmatrix}f_{xx}&f_{xy}&f_{xz}\\f_{yx}&f_{yy}&f_{yz}\\f_{zx}&f_{zy}&f_{zz}\end{bmatrix}=\begin{bmatrix}=\begin{bmatrix}2&0&0\\0&2&0\\0&0&2\end{bmatrix}$

$\mathbf H$ is positive definite, since $\mathbf v^\top\mathbf{Hv}>0$ for any vector $\mathbf v=\begin{bmatrix}x&y&z\end{bmatrix}^\top$ , which means $f(x,y,z)=x^2+y^2+z^2$ attains a minimum value of $\dfrac{480}{11}$ at $\left(\dfrac{68}{11},-\dfrac{20}{11},\dfrac{16}{11}\right)$ . There is no maximum over the given constraints.

7 0

3 years ago

In a class of students, the following data table summarizes how many students have a

Illusion [34]

Answer:

160/32= 5

5*5= 25 mm

Step-by-step explanation:

5 mm is how many millimeters represents the kilometers.

I hope this helps!

6 0

2 years ago

Which statement is true about f(x) = –6|x + 5| – 2?

snow_lady [41]

Answer:

Step-by-step explanation:

"The graph of f(x) is a horizontal compression of the graph of the parent function" is true; the graph will appear to be narrower than that of y = |x|. I would prefer to state "the graph of f(x) exhibits vertical stretching of the original (parent) function graph."

4 0

3 years ago

Read 2 more answers

Sifa has $156 in the bank. He needs to have at least $400 for spending money on his trip. Write and solve an inequality to find

gregori [183]

Sifa needs to earn $244

Solution
400-156=244

Therefore, He needs to earn $244 more before his trip.

6 0

2 years ago