Elizabeth is 7 years older than her sister

What are the correct answers and why? Simple and concise explanation please!!!

dezoksy [38]

Answer:

$\large\boxed{-\bigg[(x-3)^2+2x\bigg]+1}\\\\\boxed{-x^2+4x-8}$

Step-by-step explanation:

$(g\ \circ\ f)(x)=g\bigg(f(x)\bigg)$

$f(x)=(x-3)^2+2x\\\\g(x)=-x+1\\\\g\ \circ\ f\to\text{put f(x) instead of x in the function g(x)}:\\\\(g\ \circ\ f)(x)=-\bigg[\underbrace{(x-3)^2+2x}_{x}\bigg]+1$

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$-\bigg[(x-3)^2+2x\bigg]+1=-(x-3)^2-2x+1\\\\\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\=-(x^2-(2)(x)(3)+3^2)-2x+1=-(x^2-6x+9)-2x+1\\\\=-x^2-(-6x)-9-2x+1=-x^2+6x-9-2x+1\\\\\text{combine like terms}\\\\=-x^2+(6x-2x)+(-9+1)=-x^2+4x-8$

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$-x^2+4x-8=-x^2+4x-2^2+2^2-8=-(x^2-4x+2^2)+4-8\\\\=-(\underbrace{x^2-(2)(x)(2)+2^2}_{(a-b)^2=a^2-2ab+b^2})-4=-(x-2)^2-4=-(x+1-3)^2-4$

$In\ (-x+1-3)^2+2x,\ x^2\ will\ be\ positive.\\In\ (-x+1-3)^2+2(-x+1),\ x^2\ will\ be\ positive.$

6 0

3 years ago

Read 2 more answers

The area of a rectangle is 105 square units. Its width measures 7 units. Find the length of its diagonal. Round to the nearest t

mezya [45]

Answer:

16.6

Step-by-step explanation:

The rectangle has an area of 105. It's width is 7.

1: Find the length

$\frac{area}{width}$ =length

$\frac{105}{7}$ = 15

Length=15

2: Pythagorean theorem

$a^{2} +b^2=c^2$

$7^{2}$ + $15^2=c^2$

49+225= $c^2$

275= $c^2$

$\sqrt{275}$ = $\sqrt{c^2\\}$

16.55≈c

Rounded to nearest tenth

16.6

6 0

3 years ago

Dan Perkins goat is attached to the corner of the 14-foot-by-7-foot pump house by a 14-foot length of rope. The goat eats the gr

fenix001 [56]

<span>This pattern consists of three-fourths of a circle of radius 14 feet and one-fourth of a circle of radius 7 feet. What area of grass can Dan Perkins goat eat?</span>

We know that the formula for the area of the pitch circle are:
$\pi*r^2*\alpha$ where alpha is the pinch of circle, r is radius, and pi is mathematics constant approximately equal 3,14

$\pi*14^2*\frac{3}{4}+\pi*7^2*\frac{1}{4}=461,58+38,465=500,045(feet^2)$

5 0

3 years ago

D=.5*a*t^2 - solving for a<img src="https://tex.z-dn.net/?f=d%3D.5%2Aa%2At%5E2" id="TexFormula1" title="d=.5*a*t^2" alt="d=.5*a*

Leviafan [203]

Answer:

$\displaystyle a=\frac{d}{.5*t^2}$

Step-by-step explanation:

<u>Equation Solving</u>

We are given the equation:

$d=.5*a*t^2$

It's required to solve it for a.

Swap sides to have the letter on the left side:

$.5*a*t^2=d$

Divide by $.5*t^2$ :

$\mathbf{\displaystyle a=\frac{d}{.5*t^2}}$

7 0

3 years ago

Find the percent increase. Round to the nearest percent. From 85 books to 143 books The percent increase is

klasskru [66]

We are given :

Initial = 86
Final = 143

Let's find the percent increase with the help of formula:

$\boxed{ \sf \: formula : 100 \times \frac{(final - initial)}{initial} }$

$\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}$

$\tt \% \: increase = 100 \times \frac{(143 - 85)}{85}$

$\tt \% \: increase = 100 \times \frac{58}{85}$

$\tt\% \: increase = 20 \times \frac{58}{17}$

$\tt\% \: increase = \frac{1160}{17}$

$\tt\% \:increase = 6823.53$

3 0

2 years ago