University:
Jackson College
Course:
MAT-010 | Basic Mathematics
Academic year:

2024
Views:

282

Pages:

4
Author:

Bennett Wheeler

Question 1 Find the additive inverse of − 9 𝑥 + 3 −9x+3. Answer 1 For any expression 𝑎 a, the additive inverse is − 𝑎 −a. This means that to find the additive inverse, you negate each term in the expression. For the expression − 9 𝑥 + 3 −9x+3, the additive inverse is: − ( − 9 𝑥 + 3 ) = 9 𝑥 − 3 −(−9x+3)=9x−3 Question 2 Find the exponential model that best fits the graph's points. Exponent should be rounded to four decimal places. Answer 1 Given points on the exponential model: ( 0 , 1 ) (0,1) and ( 5 , 16 ) (5,16). General equation of an exponential model: 𝑦 = 𝑎 𝑒 𝑏 𝑥 y=ae bx . Evaluate the general equation at 𝑥 = 0 x=0 and 𝑥 = 5 x=5: 𝑦 = 𝑎 𝑒 𝑏 ⋅ 0 = 𝑎 ⇒ 𝑎 = 1 y=ae b⋅0 =a⇒a=1 Thus, we have 𝑦 = 𝑒 𝑏 𝑥 y=e bx . Substitute ( 5 , 16 ) (5,16) into 𝑦 = 𝑒 5 𝑏 = 16 y=e 5b =16: Take the natural logarithm on both sides: 5 𝑏 = ln ⁡ 16 5b=ln16 𝑏 = ln ⁡ 16 5 ≈ 0.5545 b= 5 ln16 ≈0.5545 So the model is: 𝑦 = 𝑒 0.5545 𝑥 y=e 0.5545x Question 3 Original Price Percent of Discount Sale Price $20 20% $16 $95 35% $61.75 ? 75% $55.50 ? 40% $78 Answer 1 For $20 with 20% discount: Discount = 0.20 × 20 = 4 Discount=0.20×20=4 Sale Price = 20 − 4 = 16 20−4=16. For $95 with 35% discount: Discount = 0.35 × 95 = 33.25 Discount=0.35×95=33.25 Sale Price = 95 − 33.25 = 61.75 95−33.25=61.75. For 75% discount, Sale Price $55.50: 𝑥 − 0.75 𝑥 = 55.50 ⇒ 0.25 𝑥 = 55.50 x−0.75x=55.50⇒0.25x=55.50 𝑥 = 55.50 0.25 = 222 x= 0.25 55.50 =222 For 40% discount, Sale Price $78: 𝑥 − 0.4 𝑥 = 78 ⇒ 0.6 𝑥 = 78 x−0.4x=78⇒0.6x=78 𝑥 = 78 0.6 = 130 x= 0.6 78 =130 Question 4 Write each equation in slope-intercept form. Are the equations the same or different? Given: 𝑦 + 1 = 2 𝑥 − 3 and 2 𝑥 − 3 𝑦 − 3 = 𝑦 + 1 y+1=2x−3and2x−3y−3=y+1 Answer 1 First equation: 𝑦 + 1 = 2 𝑥 − 3 ⇒ 𝑦 = 2 𝑥 − 4 y+1=2x−3⇒y=2x−4 Second equation: 2 𝑥 − 3 𝑦 − 3 = 𝑦 + 1 2x−3y−3=y+1 Rearrange to get 𝑦 = 2 𝑥 − 4 y=2x−4. Thus, both equations represent the same line, 𝑦 = 2 𝑥 − 4 y=2x−4. Question 5 How do I interpret this equation 5 + 1 × 10 5+1×10? Is the answer 15 or 60? Answer 1 According to the order of operations (PEMDAS), we perform multiplication before addition: 5 + 1 × 10 = 5 + 10 = 15 5+1×10=5+10=15