Answer:
The answer is Congruent: (x,y)-(x+5,y), (x,y)-(x,-y),(x,y)-(-x,-y) Not Congruent: (x,y)-(5x,5y)-(x,y)-(0.5x,0.5y). Or the answer for congruent is answer choice 1, 4 and 5. Not Congruent is answer choice 2 and 3.
Step-by-step explanation:
The remainder theorem says that dividing a polynomial <em>f(x)</em> by a 1st-degree polynomial <em>g(x)</em> = <em>x</em> - <em>c</em> leaves a remainder of exactly <em>f(c)</em>.
(a) With <em>f(x)</em> = <em>px</em> ³ + 4<em>x</em> - 10 and <em>d(x)</em> = <em>x</em> + 3, we have a remainder of 5, so
<em>f</em> (-3) = <em>p</em> (-3)³ + 4(-3) - 10 = 5
Solve for <em>p</em> :
-27<em>p</em> - 12 - 10 = 5
-27<em>p</em> = 27
<em>p</em> = -1
(b) With <em>f(x)</em> = <em>x</em> + 3<em>x</em> ² - <em>px</em> + 4 and <em>d(x)</em> = <em>x</em> - 2, we have remainder 8, so
<em>f</em> (2) = 2 + 3(2)² - 2<em>p</em> + 4 = 8
-2<em>p</em> = -10
<em>p</em> = 5
(you should make sure that <em>f(x)</em> was written correctly, it's a bit odd that there are two <em>x</em> terms)
(c) <em>f(x)</em> = 2<em>x</em> ³ - 4<em>x</em> ² + 6<em>x</em> - <em>p</em>, <em>d(x)</em> = <em>x</em> - 2, <em>R</em> = <em>f</em> (2) = 18
<em>f</em> (2) = 2(2)³ - 4(2)² + 6(2) - <em>p</em> = 18
12 - <em>p</em> = 18
<em>p</em> = -6
The others are done in the same fashion. You would find
(d) <em>p</em> = 14
(e) <em>p</em> = -4359
(f) <em>p</em> = 10
(g) <em>p</em> = -13/2 … … assuming you meant <em>f(x)</em> = <em>x</em> ⁴ + <em>x</em> ³ + <em>px</em> ² + <em>x</em> + 20
Answer:
12x-9
Step-by-step explanation:
7x+3(2x-3)-x
7x-6x-9-x
13x-9-x
12x-9
3.5(c-8)+c = 12.5
⇒ 3.5c- 3.5*8+ c= 12.5 (distributive property)
⇒ (3.5c+ c) -28= 12.5
⇒ 4.5c= 12.5+ 28
⇒ 4.5c= 40.5
⇒ c= 40.5/ 4.5
⇒ c= 9
The correct answer is 9~
