Describe the solutions of the system using an ordered triple in terms of x. 4x-4y-z=14, -4x+4y+3z=-10, 3x-3y+7z=26.

Which is the equation of a line with a slope of -2 and passes through the point of (3,-4)

lisabon 2012 [21]

Answer:

2x + y = 2

Step-by-step explanation:

y = -2x + b

-4 = -2(3) + b

-4 = -6 + b

2 = b

y = -2x + 2

2x + y = 2

5 0

3 years ago

What comes after 7 1/4 on a number line

djverab [1.8K]

If you’re looking for the next whole number, the answer would be 8 if you’re looking for the next number in this phrase the answer would be 7 2/4

5 0

3 years ago

Read 2 more answers

The coordinates of the vertices for rectangle ABCD are A (2,4), B (6,10), C (9,8) and D (5,2). What

sweet [91]

Answer:

D. $\sqrt{65}$

Step-by-step explanation:

The computation of the length of a diagonal (AC or BD) of the rectangle is shown below:

As we know that

The Diagonal length of AC is

$= (x_2 - x_1)^2 + (y_2 - y_1)^2\\\\= (9 -2)^2 + (8 - 4)^2\\\\= (7)^2 + (4)^2$

$= \sqrt{49 + 16}\\\\= \sqrt{65}$

Therefore correct option is D.

3 0

2 years ago

A group of three undergraduate and five graduate students are available to fill certain student government posts. If four studen

creativ13 [48]

Answer:

$Pr = 0.4286$

Step-by-step explanation:

Given

Let

$U \to\\$ Undergraduates

$G \to$ Graduates

So, we have:

$U = 3; G =5$ -- Total students

$r = 4$ --- students to select

Required

$P(U =2)$

From the question, we understand that 2 undergraduates are to be selected; This means that 2 graduates are to be selected.

First, we calculate the total possible selection (using combination)

$^nC_r = \frac{n!}{(n-r)!r!}$

So, we have:

$Total = ^{U + G}C_r$

$Total = ^{3 + 5}C_4$

$Total = ^8C_4$

$Total = \frac{8!}{(8-4)!4!}$

$Total = \frac{8!}{4!4!}$

Using a calculator, we have:

$Total = 70$

The number of ways of selecting 2 from 3 undergraduates is:

$U = ^3C_2$

$U = \frac{3!}{(3-2)!2!}$

$U = \frac{3!}{1!2!}$

$U = 3$

The number of ways of selecting 2 from 5 graduates is:

$G = ^5C_2$

$G = \frac{5!}{(5-2)!2!}$

$G = \frac{5!}{3!2!}$

$G =10$

So, the probability is:

$Pr = \frac{G * U}{Total}$

$Pr = \frac{10*3}{70}$

$Pr = \frac{30}{70}$

$Pr = 0.4286$

5 0

2 years ago

Find the volume of the wedge-shaped region contained in the cylinder x2 + y2 = 49, bounded above by the plane z = x and below by

fiasKO [112]

$\displaystyle\iiint_R\mathrm dV=\int_{y=-7}^{y=7}\int_{x=-\sqrt{49-y^2}}^{x=0}\int_{z=x}^{z=0}\mathrm dz\,\mathrm dx\,\mathrm dy$

Converting to cylindrical coordinates, the integral is equivalent to

$\displaystyle\iiint_R\mathrm dV=\int_{\theta=\pi/2}^{\theta=3\pi/2}\int_{r=0}^{r=7}\int_{z=r\cos\theta}^{z=0}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta$
$=\displaystyle\int_{\theta=\pi/2}^{\theta=3\pi/2}\int_{r=0}^{r=7}-r^2\cos\theta\,\mathrm dr\,\mathrm d\theta$
$=-\displaystyle\left(\int_{\theta=\pi/2}^{3\pi/2}\cos\theta\,\mathrm d\theta\right)\left(\int_{r=0}^{r=7}r^2\,\mathrm dr\right)$
$=\dfrac{2\times7^3}3=\dfrac{686}3$

4 0

3 years ago