Answer:
x = 4, x ≠ -1
Step-by-step explanation:
√3x + 4 = x
(√3x + 4)² = x² (Square both sides to get rid of the radical.)
3x + 4 = x²
0 = x² - 3x - 4 (Set everything to 0 by moving everything to one side.)
0 = (x - 4)(x + 1) (Factor.)
x = 4 x = -1
Now we need to check for extraneous solutions:
√3(4) + 4 = 4
√12 + 4 = 4
√16 = 4
4 = 4
√3(-1) + 4 = -1
√-3 +4 = -1
√1 = -1
1 ≠ -1
-1 is an extraneous solution.
Triangle WYZ and triangle TWY are congruent, therefore WZ = TW
WZ = TW
3x - 5 = 2x
3x - 2x = 5
x = 5
The value of x is 5
Because there is no whole number that you can divide into both the numerator and the denominator to get a proper fraction.
12) This one would be (b) because if you were reading it out loud it would be 2 is less than 3x, and 3x is greater than 5.
13) To make this easier for you I would change everything to a decimal.
Peaches: 3.25 pounds
Mangos: 4.35 pounds
Since the peaches are .89 per pound you times
3.25(.89)=2.8925 (which rounds to 2.89)
Since the magpies cost 1.26 per pound you would times
4.375(1.26)=5.5125 (rounds to 5.51)
Then 5.51-2.89=2.62
So the answer is A
14)3x is greater than or equal to nine
In this case x would have to be three or greater. So the answer would be B
15) The answer is B
16)c
— -5=20
2
You first get rid of your constant which in this case is -5, so you add 5 to both sides.
C
— -5=20
2
+5 +5
Then you would get
C
— =25
2
Now you want to try to get the variable alone, so you cancel the twos out, what you do to one side you have to do to the other.
2 C
— =25(2)
2
C=50
The answer is D
<h3>Supplementary Angles:</h3>
Angles which adds up to 180°.
<h3>Given:</h3>
A = 2x + 8
B = 2x + 8
<h3>To Find:</h3>
The measurement of B.
<h3>Solution:</h3>
A + B = 180°
or, 2x + 8 + 2x + 8 = 180°
or, 4x + 16 = 180°
or, 4x = 180 - 16 = 164°
or, x = 164/4 = 41°
<h2>Answer:</h2>
B = 2x + 8 = 2(41) + 8 = 82 + 8 = 90°
<u>B</u><u> </u><u>=</u><u> </u><u>9</u><u>0</u><u>°</u>
