asinus

Hello dp1806!

\(Let\ f(x) = \begin{cases} 3x + 5 &\text{if }x<-3\ then\ {\color{blue}f(x)\in \{\mathbb{R}<-4\}} \\ 7-4x&\text{if }x\ge -3\ then\ \color{blue}f(x)\in \{\mathbb{R}\le19\} \end{cases} \\ Find\ f(5) \)

           \(f(5)=3x+5=20\\ f(5)=7-4x=-13\)

  !

Hello guest!
You have come to the right place with us.
Please ask us your questions, we look forward to hearing from you!

Sie sind bei uns an der richtigen Stelle.
Bitte stellen Sie uns Ihre Fragen, wir freuen uns darauf!

LG

  !

The midpoint of AB is M(7,-7). If the coordinates of A are (8,-6), whatare the coordinates of B?

Hello Guest!

\(m=\frac{y_A-y_M}{x_A-x_M}=\frac{-6+7}{8-7}=1\)

\(m=1\)

\({\color{blue}y=m(x-x_M)+y_M}=1(x-7)-7\)  (Point-direction equation)

\(x_A-x_M=8-7=1\)

\(x_A-x_M=1\)

\(x_B=x_M-(x_A-x_M)=7-1=6\)

\(x_B=6\)

\(f(6)=6-14=-8\)

\(y_B=-8\)

The coordinates of B are (6, -8)

  !

Find the equation of a line in slope intercept form that is parallel to the line y = -2x - 3 that goesthrough the point (2, 1).

Hello Guest!

Point-directional shape  \(y=m(x-x_1)+y_1\)

\(m=-2\)

\(y=-2(x-2)+1\)

The equation is            \(y=-2x+5\)

  !

Help out if you can!

Hello Guest!

\(r=\sqrt{\frac{25\pi}{\pi}}\\ r=5\)

\(D=2r\cdot \sqrt{2}\)

\(A=\frac{D^2\pi}{4}=\frac{(2r\cdot \sqrt{2})^2\pi}{4}\)

\(A=50\pi\)   [C]

  !

What is the solution to (x - 5)(2x + 1)(x - 7) > 0? Please show all steps!

Hello Guest!

\(f(x)=(x - 5)(2x + 1)(x - 7) > 0\)

\(\large \{\) \(if\ (x - 5)(2x + 1)(x - 7) = 0\)  \(then \)  \(x\in\{-0.5;\ 5;\ 7\}\)  \(\large \}\)

 \(if\ f(x)>0\)  \(then \)   \(x\in\mathbb{R}\)  |-0.5 < x < 5 and x > 7

  !

Find the area of this shape.

Hello Guest!

\(A=16cm\times 7cm+\frac{1}{2}\times (16-8)cm\times (13-7)cm\)

\(A=136\ cm^2\)

  !

Katie has a collection of nickels, dimes and quarters with a total value of $3.95. There are 4 more dimes than nickels and 3 more quarters than nickels, how many of each coin does she have?

Hello Katie!

\(5n+10d+25q=395\\ d=n+4\\ n+3=q\\ \)

\(5n+10(n+4)+25(n+3)=395\\ 5n+10n+40+25n+75=395\\ 40n=280\)

\(n=7\\ q=10\\ d=11\)

\(Hi \ Katie,\ you\ have\ seven\ nickels, ten\ quarters\ and\ eleven\ dimes.\)

  !

Three notebooks, 2 binders and 1 pack of pencils costs $6. Twonotebooks, 1 binder and 2 packs of pencils costs $6.92. One notebook, 3 binders and 3 packs of pencils costs $10.84. How much does one binder cost?

Hello Guest!

3n+2b+p=6

2n+b+2p=6.92

n+3b+3p=10.84

\(3n+2b+p=6\\ 2n+b+2p=6.92\\ n+3b+3p=10.84 \)

\(n=(6-2b-p)/3\\ n=(6.92-b-2p)/2\\ n=10.84-3b-3p\)

\((6-2b-p)/3=(6.92-b-2p)/2\\ 10.84-3b-3p=(6.92-b-2p)/2\)

\(2-\frac{2}{3}b-\frac{1}{3}p=3.46-\frac{1}{2}b-p\\ \frac{2}{3}p=3.46-2+\frac{1}{6}b\\ p=\frac{4.38+\frac{1}{2}b}{2}\\ \color{blue}p=2.19+\frac{1}{4}b \)

\(10.84-3b-3p=(6.92-b-2p)/2\\ 10.84-3b-3p=3.46-\frac{1}{2}b-p\\ 7.38-\frac{5}{2}b=2p \)

\(p=3.69-\frac{5}{4}b\)

\(3.69-\frac{5}{4}b=2.19+\frac{1}{4}b\\ 3.69-2.19=\frac{6}{4}b\)

\(b=1\)

A binder costs 1 $.

n = 0,5200000000000005      at Brünner
b = 0,9999999999999997
p = 2,44
  !

Ues the diagrams to solve for x and y.

 please try to explain too please​

Hello Guest!

I. x + y = 16

II. x = 8 + y

Substitute x in equation I.

8 + y + y = 16

8 + 2y = 16     |-8 on both sides

2y = 16 - 8

2y = 8             | : 2   on both sides        

y = 4      

Substitute y in equation I      

x + 4 = 16       | -4 on both sides      

x = 16 - 4

x = 12       

  !