course Mth 158
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13. ½ ? 0= ½ > 0
16. –3 ? –5/2 = -3> -5/2
19. ½ ? 0.5 = ½ =0.5
22.1/4 ? 0.25 = ¼ = 0.25
Write each statement as an inequality.
25. x is less than 2. x<2
28. x is greater than or equal to 2. x > 2
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Graph the numbers x on the real number line.
31. x> -1 you have –1 on a number line with the right side of the number line darker than the left
Use the given real number line to complete each distance.
34. d(C, A) C=0 A=-3 0+3=3 37. d(A,E) A=-3 E=3 3-(-3)=6
Evaluate each expression if x=-2 and y=3
40. 3x+y 3(-2)+3 = -6+3= -3 42. –2x+xy -2(-2)+(-2)(3)= 4-6= -2
46. 2x-3 over y 2(-2)-3 over 3 = -4-3 over 3 = -7 over 3
Find the value of each expression if x=3 and y = -2
49. absolute value of x + absolute value of y = absolute value of 3 + absolute value of –2 =’s 3+2=5
52. absolute value of y over y= absolute value of –2 over –2 =’s 2 over –2 =’s –1
55. ll4xl – l5yll = ll4(3)l – l 5(-2)ll = 12-10= 2
Determine which of the values given below if any, must be excluded from the domain of the variable in each expression. a)x=3 b)x=1 c)x=0 d)x=-1
58. x^2+1 over x .. C
61. x^2 over x^2+1 None
64. –9x^2-x+1 over x^3 +x C
Deterine the domain of the variable x in each expression
67. x over x+4 Domain = {x/x not equal –4}
Use the formula C= 5/9(F-32) for converting degrees Fahrenheit into degrees Celsius to find the Celsius measure of each Fahrenheit temperature
70. F= 212 degrees 5/9(212-32) 5/9(180) = 100
Simplify each expression
73. (-4)^2 = (-4)*(-4)= 16 79.(3^-2)^-1 = 3^(-2)*(-1)= 3^2=9 82. square root of 36= 6
Simplify each expression. Express the answer so that all exponents are posititve. Whenever an exponent is 0 or negative, we assume that the base is not 0.
85. (8x^3)^2= 8^2* x^6= 64*x^6 88. (x^-1 y )^3 = x^-3 y^3
90. x^-2 y over xy^2 = x^-2 over x * y over y^2 = x^-2-1*y^1-2 = x^-3 y-1= 1 over x^3y
93. (3x^-1 over 4y^-1)^-2 = (3y^1 over 4x^1)-^2 = 1 over (3y^1 over 4x^1)^2 = 1 over 3^2 y^1*2 / 4^2 x^1*2 = 1 over 9y^2 / 16x^2 = 16x^2 over 9y^2
Find the value of each expression if x=2 and y=-1
96. –3x^-1 y = -3*2^-1 * -1 = 6*-1= -6
99. (xy)^2 = (2^2*-1^2) = 4*1=4
102. ( square root of x)^2 = square root of 2 * square root of 2= square root of 4= 2
105. x^y = 2^-1 = ½
108. Find the value of the expression 4x^3+3x^2-x+2 if x=1. What is the value of x=2?
4*1^3+3*1^2-1+2 = 4+3-1+2= 7-1+2= 6+2=8
If x=2 .. 4*2^3+3*2^2-2+2 = 4*8+3*4-2+2= 32+12-2+2= 44-2+2= 42+2=44
Use a calculator to evaluate each expression. Round your answer to three decimal places.
111. (8.2)^6 = 304006.671424= 304.006.671
114. (2.2)^-5 = -0.019403791346 = -0.019
117. (-8.11)^-4 = 0.000
Write each number as a decimal.
120. 32.14 = 3.214*10^1
122. 0.00421 = 4.21*10^-3
125. 0.000423 = 4.23*10^-4
Write each number as a decimal.
128. 9.7*10^3 = 0.0097 131. 1.1*10^8 = 110000000 134.6.453*10^-1= .6453
Express each statement as an equation involving the indicated variables.
137. Circumference of a circle: The circumference Cof a circle is the product of pie an its diameter d. C=pie*d
140. The perimeter P of an equilateral triangle is 3 times the length x of one side.
P=3*x
143. The volume V of a cube is the cube o the length x of a side.
V= x^3
146. At the beginning of the month, Mike had a balance of $210 in is checking account. During the next month, he deposited $80, wrote a check for $210, made another deposit of $25m wrote two checks for $60 and $32, and was assessed a monthly service charge of $5. What was his balance at the end of the month.
$8
150. Normal human body temp. is 98.6 degrees F. A temp. x that differs from normal by at least 1.5 degrees F is considered unhealthy. A formula that describes this is x-98.6 greater than equal to 1.5
The formula would be | x - 98.6 | >= 1.5.
a) Show that a temp. of 97 degrees F is unhealthy.
101.2 greater than or equal to 1.5
| 97 - 98.6 | = | -1.6 | = 1.6, which is >= 1.5
b) Show that a temp. of 100 degrees F is not unhealthy
100-98.6 less than or equal to 1.5
153. The wavelength of visible light is about 5 * 10^-7 meter. Express this wavelength as a decimal. 0.0000005 meter
156. The smallest motor ever made is less than 0.05 cm wide. Express this width using scientific notation.
5*10^-2
158. How long does it take a beam of light to reach Earth from the Sun, when the Sun is 93,000,000 miles from Earth? Express your answer in seconds, using scientific notation.
9.3*10^7
Divide 93,000,000 miles by 186,000 miles / second.
161. is there a positive real number closest to 0? No
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Overall your work looks great, but see my notes toward the end. Again I couldn't check every detail of every problem, but I checked enough to convince myself that you know what you're doing.
You really need to take it easy on yourself and use the Query. It's a whole lot less work.