Exponents/Square Roots
Solve all 3 problems:
42 73 95
42 = 16
73 = 343
95 = 59,049
Solve into standard form:
3.2 x 101 =
32
*jump decimal to the right 1 time*
*making number larger with a positive exponent*
Simplify: Combine like terms
2x + 6 - 4x + 10 - 3 + 10x
8x + 13
2x - 4x + 10x = 8x
6 + 10 -3 = 13
Solve this inequality:
2x + 6 < -2
x < 2
2x + 6 < -2
2x < 4
x < 2
A student says that the number is irrational because "it never ends". Is the student correct?
Yes, irrational numbers have non-terminating (repeating) decimals
Solve all 3 problems:
- Square Root of 81
- Square Root of 625
- Square Root of 289
Square Root of 81 = 9
Square Root of 625 = 25
Square Root of 289 = 17
Solve into standard form:
4.63 x 10-3
0.00463
*3 jumps to the left*
*make number smaller with negative exponent*
Solve equation:
2x - 1 = 3x + 2
x = -3
2x - 1 = 3x + 2
2x = 3x + 3
-1x = 3
x = -3
When do you flip your sign when solving inequalities? (which two operations)
flip when multiplying or dividing by a negative number
Which statement is true:
A. 0.12 = 1/8
B. 7 x 10-2 < 7/100
C. 98% = 9.8 x 10-1
D. 3.4 x 104 < 8 x 103
C. 98% = 9.8 x 10-1
98% = 0.98
9.8 x 10-1 = 0.98
Provide the exponent needed:
Squared (means what # exponent):
Cubed (means what # exponent):
Squared: Exponent of 2
Cubed: Exponent of 3
Provide me an example of both a standard form answer and a scientific notation form answer.
Standard form:
- 0.9876
-3,900,876
Scientific notation:
- 3.5 x 103
- 8.765 x 10-5
Simplify:
5(3 - 2x) - 4(x + 1)
-14x + 11
5(3 - 2x) = 15 - 10x
-4(x + 1) = -4x -4
15 - 10x -4x -4 = -14x +11
Which value of p satisfies -8(p + 2) < -56
A. 0
B. 4
C. 5
D. 7
C. 5
-8(p + 2) < -56
-8p -16 < -56
-8p < -40
p > 5
Which of the following shows the numbers listed from least to greatest?
A. 0.43, 5.17 x 10-1, 50%, 5/8
B. 5/8, 5.17 x 10-1, 50%, 0.43
C. 0.43, 50%, 5.17 x 10-1, 5/8
D. 5.17 x 10-1, 5/8, 50%, 0.43
C. 0.43, 50%, 5.17 x 10-1, 5/8
0.43
50% = 0.50
5.17 x 10-1
5/8 = 0.625
0.43, 0.50, 0.517, 0.625
Between which two consecutive whole numbers is
Square Root of 129 located?
11 & 12
What is the range our front # can fall in between for scientific notation?
Ex ____ x 103
*What range can the number I am multiplying by fall in between?*
1.00-9.99
*can not be lower than 1 or higher than 10*
Solve for X:
-4 + 6x = 10x + 20
x = -6
-4 + 6x = 10x + 20
-4 = 4x + 20
-24 = 4x
-6 = x
Which mathematical inequality represents the following statement? Six times a number is greater than 3 less than 4 times the same number.
A. 6x > 3 - 4x
B. 6x < 3 - 4x
C. 6x > 4x - 3
D. 6x < 4x - 3
C. 6x > 4x - 3
*six times a number 6x*
*greater than >*
*3 less than -3*
*4 times the same number 4x*
Sonja went out for dinner. Her bill was $65.80. If Sonja wants to leave a 20% tip, what will be the total cost, no including tax, of the dinner?
A. $78.96
B. $52.64
C. $72.38
D. $13.16
A. $78.96
65.80 x 0.20 = 13.16
65.8 + 13.16 = 78.96
Put these square roots in order from greatest to least:
Square Root of 60
Square Root of 2
Square Root of 345
Square Root of 5
Square Root of 112
Square Root of 345 = 18.57
Square Root of 112 = 10.58
Square Root of 60 = 7.746
Square Root of 5 = 2.236
Square Root of 2 = 1.414
18.57, 10.58, 7.746, 2.236, 1.414
Convert back into scientific notation form:
3,459,089.00
3.459089 x 106
*get my front number in range from 1.00-9.99*
*count my jumps to find exponent*
What value of y makes the equation true?
3(2y + 3) = 9y - 15
A. y = 8
B. y = 6
C. y = -2
D. y = -5
A. y = 8
3(2y + 3) = 6y +9
6y + 9 = 9y - 15
9 = 3y -15
24 = 3y
8 = y
Look at this inequality.
6x - 2(x + 3) > 3x + 4
Select all the steps that are valid when solving this inequality.
A. Combine like terms on one side
B. Combine 6x - 2(x + 3) as 3x
C. The solution to inequality is x > 10
D. Flip the inequality sign while subtracting
E. Apply distributive property to -2(x +3)
A. Combine like terms on one side
C. The solution to inequality is x > 10
E. Apply distributive property to -2(x + 3)
Which of the measurements form a right triangle?
*Think pythagorean theorem* a2 + b2 = c2
A. 10cm, 24cm, 26cm
B. 9cm, 12cm, 18cm
C. 5cm, 7cm, 10cm
D. 17cm, 23cm, 40cm
A. 10cm, 24cm, 26cm
102 = 100 100 + 576 = 676
242 = 576
262 = 676