Answer:
y= -x
Step-by-step explanation:
<u>slope- intercept form</u>
y= mx +c, where m is the slope and c is the y-intercept.
Given that the slope is -1, m= -1.
Substitute m= -1 into the equation:
y= -x +c
To find the value of c, substitute a pair of coordinates into the equation.
When x= 2, y= -2,
-2= -2 +c
c= -2 +2
c= 0
Thus, the equation of the line is y= -x.
9514 1404 393
Answer:
2 1/2 cups
Step-by-step explanation:
A proportion says the ratio of one thing to another is the same for different amounts. Here, we want cups, so we can use the proportion ...
cups/people = 2/12 = x/15 . . . . . where x is the number we want to find
Multiplying by 15 gives ...
x = 15(2/12) = 5/2 = 2 1/2
You will need 2 1/2 cups of zucchini to feed 15 people with the same recipe.
Let x represent the number of pounds of $10.75/lb coffee used in the mix.
.. 10.75x +3.25(100 -x) = 5.65*100 . . . . . . total cost of coffee blend
.. x(10.75 -3.25) = 100*(5.65 -3.25) . . . . . .separate x-terms from non-x terms
.. x = 240/7.5 = 32
32 pounds of $10.75/lb coffee should be used
68 pounds of $3.25/lb coffee should be used
Answer:
The cubic polynomial is: x³ - x² - 6x.
Step-by-step explanation:
Given the degree and the roots of the polynomial we can find it.
An n - degree polynomial has n roots.
Here, given that the degree of the polynomial is 3 and three roots are given. Also, if (x - a) is a factor of a polynomial then x = a is a root of the polynomial. The converse is also true.
Since, the roots of the polynomial are given to -2, 0, 3 then it should have had the following factors.
(x + 2)(x - 0)(x - 3) = 0
Multiplying them we get:
⇒ 
which is the required cubic polynomial.
Hence, the answer.
Answer:
Suppose we have a polynomial of degree N with a leading coefficient A and roots {x₁, x₂, ..., xₙ}
We can write this polynomial as:
P(x) = A*(x - x₁)*(x - x₂)*...*(x - xₙ)
such that the terms:
(x - x₁), (x - x₂), etc...
are called the factors.
In this case, we know that the roots OF THE FACTORS
are:
(x = - 2)
(x = - (1 + √5))
(x = + 3i)
If the root of the polynomial is x = -2, then the factor should be:
(x + 2)
which is zero when we evaluate x in -2
Then the correct option is the first one.
