Intermediate Algebra
10th Edition
ISBN: 9781305191495
Author: Jerome E. Kaufmann; Karen L. Schwitters
Publisher: Cengage Learning US
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Chapter 2.7, Problem 13PS
To determine
To solve:
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rections: For problem
rough 3, read
each question carefully and be sure to
show all work.
1. Determine if
9(4a²-4ab+b²) = (6a-3b)² is a
polynomial identity.
2. Is (2x-y) (8x3+ y³) equivalent to
16x4-y4?
3. Find an expression that is equivalent to
(a - b)³.
Directions: For problems 4 and 5,
algebraically prove that the following
equations are polynomial identities. Show
all of your work and explain each step.
4. (2x+5)² = 4x(x+5)+25
5. (4x+6y)(x-2y)=2(2x²-xy-6y²)
Name:
Mussels & bem
A section of a river currently has a population of 20 zebra mussels. The
population of zebra mussels increases 60 % each month. What will be the
population of zebra mussels after 2 years?
9
10
# of
months
# of
mussels
1
2
3
4
5
6
7
8
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Graph your data. Remember to title your graph.
What scale should be used on the y-axis?
What scale should be used on the x-axis?
Exponential Growth Equation
y = a(1+r)*
In a national park, the current population of an endangered species of bear is 80. Each year, the
population decreases by 10%. How can you model the population of bears in the park?
# of years
# of bears
9
10
2
3
4
5
6
7
8
°
1
Graph your data. Remember to title your graph.
What scale should be used on the y-axis?
What scale should be used on the x-axis?
SMOKY
19
OUNTAINS
NATIONAL
Exponential Decay Equation
y = a(1-r)*
PARK
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- Last Chance Mine (LCM) purchased a coal deposit for $2,918,300. It estimated it would extract 18,950 tons of coal from the deposit. LCM mined the coal and sold it, reporting gross receipts of $1.24 million, $13 million, and $11 million for years 1 through 3, respectively. During years 1-3, LCM reported net income (loss) from the coal deposit activity in the amount of ($11,400), $550,000, and $502,500, respectively. In years 1-3, LCM extracted 19,950 tons of coal as follows: (1) Tons of Coal 18,950 Depletion (2) Basis (2)(1) Rate $2,918,300 $154.00 Tons Extracted per Year Year 1 4,500 Year 2 8,850 Year 3 6,600 Note: Leave no answer blank. Enter zero if applicable. Enter your answers in dollars and not in millions of dollars. a. What is LCM's cost depletion for years 1, 2, and 3? Cost Depletion Year 1 Year 2 Year 3arrow_forwardConsider the following equation. log1/9' =6 Find the value of x. Round your answer to the nearest thousandth. x = ✓arrow_forwardExpanding a logarithmic expression: Problem type 3 Use the properties of logarithms to expand the following expression. 4(8+x)² log 5 ) Your answer should not have radicals or exponents. You may assume that all variables are positive. log 4(8 + X 5 -x)²arrow_forward
- Use the properties of logarithms to expand the following expression. log 6(x+5)² 3/24 Your answer should not have radicals or exponents. You may assume that all variables are positive. log 6(x + 3 I 4 5)² log Xarrow_forwardExpanding a logarithmic expression: Problem type 2 Use the properties of logarithms to expand the following expression. 3 yz log 5 x 0/3 An Each logarithm should involve only one variable and should not have any radicals or exponents. You may assume that all variables are positive. log yz 3 厚 5 Explanation Check log ☑ 2025 MG ¿W MIII LLC. All Rights Reserved. Terms of Use | Privacy Centerarrow_forwardExpanding a logarithmic expression: Problem type 2 Use the properties of logarithms to expand the following expression. 3 yz log 5 x 0/3 An Each logarithm should involve only one variable and should not have any radicals or exponents. You may assume that all variables are positive. log yz 3 厚 5 Explanation Check log ☑ 2025 MG ¿W MIII LLC. All Rights Reserved. Terms of Use | Privacy Centerarrow_forward
- What is the domain and range, thank you !!arrow_forwardAssume a bivariate patch p(u, v) over the unit square [0, 1]² that is given as a tensor product patch where u-sections (u fixed to some constant û; v varying across [0, 1]) are quadratic polynomials Pu:û(v) = p(û, v) while v-sections are lines pv:ô (u) = p(u, v). The boundary lines pv:o(u) and pv:1 (u) are specified by their end points p(0,0) 0.8 and p(1,0) 0.2 as well as p(0, 1) 0.3 and p(1, 1) = 0.8. The boundary quadratics pu:o(v) and pu:1 (v) interpolate p(0,0.5) = 0.1 and p(1, 0.5) = 0.9 in addition to the above given four corner-values. = = = Use Pu:û(v) = (1, v, v² ) Mq (Pu:û(0), Pu:û (0.5), Pu:û(1)) with Ma = 1 0 0 -3 4-1 2 4 2 (Pv:ô as well as pu: (u) = (1, u) M₁ (pv:v (0), P: (1)) with M₁ = = (19) 0 to formulate p(u, v) using the "geometric input" G with G = = (P(0,0%) p(0,0) p(0,0.5) p(0,1) ) = ( 0.39 0.8 0.1 0.3 0.2 0.9 0.8 p(1,0) p(1, 0.5) p(1, 1) See the figure below for (left) a selection of iso-lines of p(u, v) and (right) a 3D rendering of p(u, v) as a height surface…arrow_forwardO Functions Composition of two functions: Domain and... Two functions ƒ and g are defined in the figure below. 76 2 8 5 7 8 19 8 9 Domain of f Range of f Domain of g Range of g 3/5 Anthony Find the domain and range of the composition g.f. Write your answers in set notation. (a) Domain of gof: ☐ (b) Range of gof: ☐ Х Explanation Check 0,0,... Español لكا ©2025 McGraw Hill LLC. All Rights Reserved Torms of lico Privacy Contor Accessibility.arrow_forward
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