What's In The Middle Of America And Australia? Write the letter of each answer in the box containing the exercise number.
Answers
Estimate the intercepts of the graph of the function.
1.
V
2.
ty у
y = 2 x + 3
Ty=2x-6
-8
Y
3.
tyy=-(x - 2)2
7
14
E. x-intercept: about 1,
y-intercept: about - 1
T. x-intercept: about 3,
y-intercept: about -6
L. x-intercept: about -6,
y-intercept: about 3
T. x-intercept: about -1,
y-intercept: about 1
E. x-intercept: about 2,
y-intercept: about -4
-4
4
1
= x2 - 4
6.
5.
ya
-2
2x
2 x
y = (x - 1)
Hy = (x + 1)3
H. c-intercepts: about -2 and 2,
y-intercept: about - 4
R. positive: -5 < x < 1, negative:
x < -5 and x > 1, increasing:
x < -2, decreasing: * > -2,
y-→-o as I — to and
V →-o as X -> -
Approximate when the function is positive, negative,
increasing, or decreasing. Then describe the end
behavior of the function.
8.
7.
y = - x + 2 +3 ty
y = -2x + 2
-2
2x
E. negative: for all real numbers,
increasing: x < -2 , decreasing:
X > -2; y → -oo as x → too
and y → -- as x -
-4
-2
10.
9.
y =
- (x3 + 6x2 – 32)
các + 2)2 - 1 AY
ty у
t
R. positive: x < -4 and 4 < x <
negative: x > 2, increasing:
-4 < x < 0, decreasing: < <
and x > 0; y → -- as x →
and y → to as x → -
2
-4
Х
-4
-2
9
T. positive: x < 1, negative: x
decreasing: for all real numb
-> -as y → to and
y → to as x ---
7
4
8
5
6
1
2.
3
10

22 and 22

step-by-step explanation:

10 plus 12 equals 22.

12 plus 10 also equals 22 because regardless of what order they're in, they're gonna equal the same thing.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.