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Answer:
a) The equation in intercept form by factoring is (x+6)(x+4)
b) From the given graph x- intercepts are (-4,0) and (-6,0) and zeros (roots) of the function are -6 and -4.
c) The solutions of is
that is x= -6 and x = -4.
Step-by-step explanation:
The given quadratic equation is
Put the function f(x) = 0 , then
a) The equation in intercept form by factoring is ,
Consider the given function,
taking 2 common, we get,
The above is a quadratic equation of the form
Solving quadratic equation using middle term splitting method,
Thus, The equation in intercept form by factoring is (x+6)(x+4).
b) From the given graph x- intercepts are (-4,0) and (-6,0) .
Zeroes / roots of a function are those points where the value of the function is zero.
Put f(x) = 0 as solved above
that is
or
or
Thus, zeros (roots) of the function are -6 and -4.
For checking put x = -6 and -4 in the function we get f(x) =0 .
c) The solutions of is
that is x= -6 and x = -4 as shown above.
Let's approach this problem by slowly eliminating choices.
First consider the keyword "at most" and "no more than". This means that the inequality should be less than or equal to the constant value stated. This will automatically eliminate two choices with the greater than symbol favoring the variables - choices A and D.
Next we associate the right constants to the right coefficients of variables. The two kinds of weight the truck transports are 30 and 65 lbs, and we know that this should not exceed 3,800 lbs. This is therefore our first inequality. The other inequality is for the volume. The combinations of the two volumes 4 and 9 cubic feet should not exceed 400 cubic feet when transported.
If you try to construct the inequality and miss it among the choices, don't worry! Let's try doing some simplifications first and see if it matches either B or C.
After simplification you can get
from dividing the equation by 5 and 
for leaving it as it is.
Looking carefully, we can see that this is equivalent to option B.
ANSWER: B.
First consider the keyword "at most" and "no more than". This means that the inequality should be less than or equal to the constant value stated. This will automatically eliminate two choices with the greater than symbol favoring the variables - choices A and D.
Next we associate the right constants to the right coefficients of variables. The two kinds of weight the truck transports are 30 and 65 lbs, and we know that this should not exceed 3,800 lbs. This is therefore our first inequality. The other inequality is for the volume. The combinations of the two volumes 4 and 9 cubic feet should not exceed 400 cubic feet when transported.
If you try to construct the inequality and miss it among the choices, don't worry! Let's try doing some simplifications first and see if it matches either B or C.
After simplification you can get
Looking carefully, we can see that this is equivalent to option B.
ANSWER: B.