Can someone please help me with b, d, and 9-13? I already drew a number line, thanks in advance! :)
1 answer:
B)
d)
9) I'm not really sure how to answer it, but I guess like 2.1, 2.2, 2.5, etc.,
10)
so {5, 6, 7, 8} is the answer
11) for some reason it won't let me insert a picture but put place
above 2, and then place
above 3, and then place
in between 2 and 3, but place it a little closer to three since
12) place
between 2 and three, but closer to two since
and also
and for number 13) the square root of 144 is 12, and the square root of 169 is 13, so any numbers between 12 and 13 will work.
I hope this helped and if not, message me and ill try to explain!
d)
9) I'm not really sure how to answer it, but I guess like 2.1, 2.2, 2.5, etc.,
10)
so {5, 6, 7, 8} is the answer
11) for some reason it won't let me insert a picture but put place
above 2, and then place
above 3, and then place
in between 2 and 3, but place it a little closer to three since
12) place
between 2 and three, but closer to two since
and also
and for number 13) the square root of 144 is 12, and the square root of 169 is 13, so any numbers between 12 and 13 will work.
I hope this helped and if not, message me and ill try to explain!
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The given statement is:
41 fewer than the quantity t times 307 is equal to n.
The equation is given by:
9514 1404 393
Explanation:
1) 2x^2 -5x -3 = 0 . . . . standard form equation
To convert this to factored form, you can look for factors of the product (2)(-3) that have a sum of -5. It can help to start by listing the ways that -6 can be factored. Since we want the sum of factors to be negative, we want to have larger negative factors.
-6 = (1)(-6) = (2)(-3)
The sums of these factor pairs are -5 (what we want) and -1 (not relevant). We can call these factors p=1 and q=-6.
If a = 2 is the leading coefficient of our standard form quadratic, we want to use these factors in the form ...
(ax +p)(ax +q)/a . . . . . factored form of the quadratic
(2x +1)(2x +(-6))/2 . . . .fill in the values we know
(2x +1)(x -3) . . . . . . . factor 2 from the second binomial
So, the factored form of the quadratic equation is ...
(2x +1)(x -3) = 0 . . . . factored form equation
__
2) f(x) = x^2 +7x +10 . . . . standard form quadratic function
Using the thinking process described above, we are looking for factors of 10 that have a sum of 7. We know those are 2 and 5. So, the factored form of the function is ...
f(x) = (x +2)(x +5) . . . . . . factored form quadratic function
The leading coefficient is 1, so we have no further work to do.
<u>Roots, x-intercepts, zeros</u>
The graph attached below shows this function crosses the x-axis when x=-2 and x = -5. These values of x are variously called "roots", "x-intercepts", and "zeros" of the function. They are values for which the factors and the function are zero. (x+2=0 when x=-2, for example)
<u>Solutions</u>
Often, we are interested in solving the equation ...
f(x) = 0
For that equation, the <em>solutions</em> <u>are</u> the <em>zeros</em> or <em>x-intercepts</em> or <em>roots</em>. The graph attached also shows solutions for ...
f(x) = 4
Those solutions are x = -6 and x = -1. The function value is not zero for these values of x, so the <em>roots</em>, <em>x-intercepts</em>, or <em>zeros</em> <u>are not</u> <em>solutions</em> to this equation.
