Answer:
1/6
Step-by-step explanation:
2/12 simplified is 1/6
Answer:
Domain: (−∞,∞),{x|x∈R}
Range: (−∞,∞),{y|y∈R}
Step-by-step explanation:
Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.
Domain: (−∞,∞),{x|x∈R}
Range: (−∞,∞),{y|y∈R}
Hmm
(a+b)^2=(a+b)(a+b)=a^2+2ab+b^2
basically
for
ax^2+bx+c
it is a perfect trinomial when
b=2(√a)(√c)
remember to take both positive and negative roots into consideration
because
(a+b)^2=a^2+2ab+b^2 and
(a-b)^2=a^2-2ab+b^2
see each
first one
-70=2(9)(4)
-70=72
false
second
-90=2(8)(5)
-90=80
false
third
-72=(9)(4)
-72=72
false
but, the last one could be negative
(9x-4)^2 is factor
that is the answer
the answer is 81x^2-72x+16
Answer:
C. ![(x-3)(x+6)](https://tex.z-dn.net/?f=%28x-3%29%28x%2B6%29)
Step-by-step explanation:
I think the equation meant
?
Anyways, to factor these kinds of quadratic, keep into consideration:
![ax^2+bx+c=(x+w)(x+v)](https://tex.z-dn.net/?f=ax%5E2%2Bbx%2Bc%3D%28x%2Bw%29%28x%2Bv%29)
ONLY if:
![w+v=b\\wv=c](https://tex.z-dn.net/?f=w%2Bv%3Db%5C%5Cwv%3Dc)
Start off by finding factors of c, which in this case, -18:
±(1, 2, 3, 6, 9, 18)
If one of the numbers is negative then the other number must be positive.
Find which two factors will sum up to b, which in this case, is 3.
![1+(-18)\neq 3\\2+(-9)\neq 3\\3+(-6)\neq 3\\6+(-3)=3\\9+(-2)\neq 3\\18+(-1)\neq 3\\](https://tex.z-dn.net/?f=1%2B%28-18%29%5Cneq%203%5C%5C2%2B%28-9%29%5Cneq%203%5C%5C3%2B%28-6%29%5Cneq%203%5C%5C6%2B%28-3%29%3D3%5C%5C9%2B%28-2%29%5Cneq%203%5C%5C18%2B%28-1%29%5Cneq%203%5C%5C)
The only two factors that work are 6 and -3.
Replace them into the factored form:
![(x+w)(x+v)\\(x+6)(x-3)\\(x-3)(x+6)](https://tex.z-dn.net/?f=%28x%2Bw%29%28x%2Bv%29%5C%5C%28x%2B6%29%28x-3%29%5C%5C%28x-3%29%28x%2B6%29)
Answer:
The answer is below
Step-by-step explanation:
a) The graph is attached
b) The table shows a linear relationship between x and y.
A linear equation is in the form y = mx + b, where y is a dependent variable, x is an independent variable, m is the rate of change (slope) and b is the value of y when x = 0.
x represent the distance on map in mm and y represent the actual distance in mile. The table (x, y) has the points (10, 25) and (20, 50). The equation is given by:
![y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-25=\frac{50-25}{20-10} (x-10)\\\\y-25=2.5(x-10)\\\\y-25=2.5x-25\\\\y=2.5x](https://tex.z-dn.net/?f=y-y_1%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%20%28x-x_1%29%5C%5C%5C%5Cy-25%3D%5Cfrac%7B50-25%7D%7B20-10%7D%20%28x-10%29%5C%5C%5C%5Cy-25%3D2.5%28x-10%29%5C%5C%5C%5Cy-25%3D2.5x-25%5C%5C%5C%5Cy%3D2.5x)
The slope m = 2.5. This means that for every 1 mm on the map, the actual distance increases by 2.5 miles.
c) y = 2.5x
put x = 48 mm
y = 2.5(48)
y = 120 miles
The actual distance between Toledo and Columbus is 120 miles
d) y = 2.5x
Put y = 225 miles
225 = 2.5x
x = 225/2.5
x = 90 mm
The distance on map between Cincinnati and Cleveland is about 90 mm.