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3 years ago

Explain why (5,-2) and (-2,5) do not represent the same point

1 answer:

7 0

Let A(5,-2) and B(-2, 5)

To get A we have to go 5 units horizontally (5 on the right) and - 2 units vertically, (down 2 ) whereas for B(-2,5):

To get B we have to go -2 units horizontally (2 on the LEFT) and 5 units vertically, (UP 5)

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ALGEBRAIC EXPRESSION Jeremy had $103 but he is spending $10 per week

Pie

103 ÷ 10 = x
x = how many weeks until all his money is gone? (besides the $3 at the end)

5 0

4 years ago

Explain the main parts and uses of two kinds of proofs. March the word with the right definition.

slava [35]

Answer:

A. - 3.

B. - 1.

C. - 5.

D. - 4.

E. - 2.

Step-by-step explanation:

A. Definition refers to a statement that exactly defines the object, thing or everything.

B. Postulate or axiom is a statement that is accepted as true in order to initiate an argument.

C. Common notion is the statement that helps to understand the common sense about the subject.

D. Theorem is a statement that shows proof on the basis of previously making statements.

E. Corollary is a statement that act as a small proof that has already been proven.

Hence, the correct matches are:

A. - 3.

B. - 1.

C. - 5.

D. - 4.

E. - 2.

7 0

3 years ago

A student reads 56 pages in 4 hours. How many pages will the student read in 7 hours? Do these

Varvara68 [4.7K]

Answer:

Step-by-step explanation:

the time taken is directly proportional and so we multiply 7 by 56 and the divide the answer by 4 to get 98

3 0

3 years ago

In Exercises 3–10, use the Chain Rule to calculate the partial derivatives. Express the answer in terms of the independent varia

sashaice [31]

I'll use subscript notation for brevity, i.e.

$\dfrac{\partial f}{\partial x}=f_x$

$f(x,y,z)=xy+z^2\implies\begin{cases}f_x=y\\f_y=x\\f_z=2z\end{cases}$

$x(r,s)=s^2\implies\begin{cases}x_r=0\\x_s=2s\end{cases}$

$y(r,s)=2rs\implies\begin{cases}y_r=2s\\y_s=2r\end{cases}$

$z(r,s)=r^2\implies\begin{cases}z_r=2r\\z_s=0\end{cases}$

By the chain rule,

$f_r=f_xx_r+f_yy_r+f_zz_r=2xs+4zr=2s^3+4r^3$

$f_s=f_xx_s+f_yy_s+f_zz_s=2ys+2xr=6rs^2$

$x(r,s,t)=r+s-2t\implies\begin{cases}x_r=1\\x_s=1\\x_t=-2\end{cases}$

$y(r,s,t)=3rt\implies\begin{cases}y_r=3t\\y_s=0\\y_t=3r\end{cases}$

$z(r,s,t)=s^2\implies\begin{cases}z_r=0\\z_s=2s\\z_t=0\end{cases}$

By the chain rule,

$f_r=f_xx_r+f_yy_r+f_zz_r=y+3xt=3rt+3r+3s-6t^2$

$f_s=f_xx_s+f_yy_s+f_zz_s=y+4zs=3rt+4s^3$

$f_t=f_xx_t+f_yy_t+f_zz_t=-2y+3xr=3r+3s-12rt$

8 0

3 years ago

Other than itself, which angle is congruent to CBE?

jekas [21]

Answer:

<GBF

Step-by-step explanation:

<GBF is congruent to <CBE because they are vertical angles.

The vertical angle theorem states this is true.

Vertical angles are formed by a pair of intersecting lines and are the angles directly across from each other.

Since <GBF and <CBE are vertical angles, they are hence congruent.

3 0

3 years ago