5) What is the distance between the points (3,-5) and (5,6)?

1. Vanessa and Renita are having a friendly competition at work. Their job is to unpack boxes. Vanessa has unpacked 3 fewer than

Nadya [2.5K]

The number of boxes renita and Vanessa has unpacked each is 6 and 9 boxes respectively.

<h3>Equation</h3>

Number of boxes renita has unpacked = x
Number of boxes Vanessa has unpacked = 2x - 3
Total boxes both unpacked = 15

x + (2x - 3) = 15

x + 2x - 3 = 15

3x = 15 + 3

3x = 18

x = 18/3

x = 6

Therefore,

Number of boxes renita has unpacked = x

= 6 boxes

Number of boxes Vanessa has unpacked = 2x - 3

= 2(6) - 3

= 12 - 3

= 9 boxes

Learn more about equation:

brainly.com/question/2972832

#SPJ1

7 0

1 year ago

Factor completely 2x2 − 50.

Ede4ka [16]

Answer:

(B) 2(x+5)(x−5)

Explanation:

Factor 2x²−50

2(x+5)(x−5)

3 0

3 years ago

Read 2 more answers

If their food and beverages costs$25.30 and there is an 8% meals tax, how much is the bill

Mashutka [201]

Hey there Unrazed90,

Answer :

100% = $25.30
1% = $25.30 / 100
= $0.253
8% = $0.253 x 8
= $2.024
Total = $25.30 + $2.024
= $27.324
= $27

Hope this helps :D

<em>~Natasha ♥</em>

8 0

3 years ago

Find the absolute extrema for f(x,y)=4-x^2-y^4+1/2y^2 over the closed disk D:x^2+y^2 is less than or equal to 1

algol [13]

Find the critical points of $f(x,y)$ :

$\dfrac{\partial f}{\partial x}=-2x=0\implies x=0$

$\dfrac{\partial f}{\partial y}=y-4y^3=y(1-4y^2)=0\implies y=0\text{ or }y=\pm\dfrac12$

All three points lie within $D$ , and $f$ takes on values of

$\begin{cases}f(0,0)=4\\f\left(0,-\frac12\right)=\frac{65}{16}\\f\left(0,\frac12\right)=\frac{65}{16}\end{cases}$

Now check for extrema on the boundary of $D$ . Convert to polar coordinates:

$f(x,y)=f(\cos t,\sin t)=g(t)=4-\cos^2-\sin^4t+\dfrac12\sin^2t=3+\dfrac32\sin^2t-\sin^4t$

Find the critical points of $g(t)$ :

$\dfrac{\mathrm dg}{\mathrm dt}=3\sin t\cos t-4\sin^3t\cos t=\sin t\cos t(3-4\sin^2t)=0$

$\implies\sin t=0\text{ or }\cos t=0\text{ or }\sin t=\pm\dfrac{\sqrt3}2$

$\implies t=n\pi\text{ or }t=\dfrac{(2n+1)\pi}2\text{ or }\pm\dfrac\pi3+2n\pi$

where $n$ is any integer. There are some redundant critical points, so we'll just consider $0\le t< 2\pi$ , which gives

$t=0\text{ or }t=\dfrac\pi3\text{ or }t=\dfrac\pi2\text{ or }t=\pi\text{ or }t=\dfrac{3\pi}2\text{ or }t=\dfrac{5\pi}3$

which gives values of

$\begin{cases}g(0)=3\\g\left(\frac\pi3\right)=\frac{57}{16}\\g\left(\frac\pi2\right)=\frac72\\g(\pi)=3\\g\left(\frac{3\pi}2\right)=\frac72\\g\left(\frac{5\pi}3\right)=\frac{57}{16}\end{cases}$

So altogether, $f(x,y)$ has an absolute maximum of 65/16 at the points (0, -1/2) and (0, 1/2), and an absolute minimum of 3 at (-1, 0).

5 0

3 years ago

A person selecting a bank will consider how convenient it is, how safe it is, and how secure their return is. True False

stira [4]

This is True! To have a secure bank is what everyone wants because if you don't have a secure bank there are numerous amounts of things that can happen to you money.

5 0

3 years ago

Read 2 more answers