Answer:
x^4 -53x^2 +108x +160
Step-by-step explanation:
If <em>a</em> is a zero, then (<em>x-a</em>) is a factor. For the given zeros, the factors are ...
p(x) = (x +8)(x +1)(x -4)(x -5)
Multiplying these out gives the polynomial in standard form.
= (x^2 +9x +8)(x^2 -9x +20)
We note that these factors have a sum and difference with the same pair of values, x^2 and 9x. We can use the special form for the product of these to simplify our working out.
= (x^2 +9x)(x^2 -9x) +20(x^2 +9x) +8(x^2 -9x) +8(20)
= x^4 -81x^2 +20x^2 +180x +8x^2 -72x +160
p(x) = x^4 -53x^2 +108x +160
_____
The graph shows this polynomial has the required zeros.
Hello - let's do this step by step. Show your work.
You're asking: 9(8−x)=3x.
Now, simplify both sides of the equation.
9(8−x)=3x
(9)(8)+(9)(−x)=3x (To do that, distribute)
72+−9x=3x
−9x+72=3x
Now, subtract 3x from both sides.
−9x+72−3x=3x−3x
Simplify,
−12x+72=0
After, subtract 72 from both sides.
−12x+72−72=0−72
−12x=−72
Last thing, divide both sides by -12.
-12x/12 = -72/-12
Divide.
Therefore, you have <u>x = 6</u> as your final answer.
X= shorter leg
x+6= longer leg
(x+6)+6= hypotenuse
Use the Pythagorean theorem to find the length of each side.
a= one leg
b= other leg
c= hypotenuse.
SHORTER LEG:
a^2 + b^2= c^2
substitute each length above
x^2 + (x+6)^2= [(x+6)+6]^2
square each set of parentheses; add inside right side parentheses before squaring
x^2 + (x+6)(x+6)= (x+12)(x+12)
squaring is multiplying each parentheses by itself one time; use the FOIL method: multiply first, multiply outside, multiply inside, multiply last
x^2 + x^2 + 6x + 6x + 36= x^2 + 12x + 12x + 144
combine like terms
2x^2 + 12x + 36= x^2 + 24x + 144
subtract x^2 from both sides
x^2 + 12x + 36= 24x + 144
subtract 24x from both sides
x^2 - 12x + 36= 144
subtract 144 from both sides
x^2 - 12x - 108= 0
factor
(x + 6)(x - 18)= 0
set each parentheses equal to 0
x + 6= 0
x= -6
x - 18= 0
x= 18 cm shorter leg
***Since a side cannot be a negative number, x= 18. Substitute x=18 to find the other sides.
LONGER LEG:
= x+6
= 18 + 6
= 24 cm longer leg
HYPOTENUSE:
= (x+6)+6
= 18 + 6 + 6
= 30 cm hypotenuse
CHECK:
18^2 + 24^2= 30^2
324 + 576= 900
900= 900
ANSWER:
x= 18 cm shorter leg
x+6= 24 cm longer leg
(x+6)+6= 30 cm hypotenuse
Hope this helps! :)
Answer:
2.88 pounds or 288 ounces
Step-by-step explanation:
you need 12oz
and 24 bags
multiply those
