Find the value of x to the nearest hundredth. $$3\cdot7^{4x-6}=34$$

$$x=\frac{\log\left(\frac{34}{3}\right)+6\log7}{4\log7}$$ $$x\approx.36$$

The polynomial function $$f\left(x\right)\ =\ x^3-3x^2+kx+24$$ has roots at 4, -3, and 2. What is the value of k?

$$4k+40=0$$ $$4k=-40$$ $$k=-10$$

$$f\left(x\right)\ =\ x\ +\ 1$$ $$g\left(x\right)=3x^3+2x^2$$ The functions g(x) is divided by f(x) and rewritten in the form $$q\left(x\right)\ +\ \frac{r\left(x\right)}{b\left(x\right)}.$$ Which expression represents q(x)?

Use synthetic division or long division to find the complete answer: $$3x^2-x+1\ +\frac{1}{x+1}$$ . So, q(x) = $$3x^2-x+1$$

Which expression is equivalent to $$\left(2x^2+3x+70\right)\div\left(x^2+x+10\right)?$$

Use long division to find the answer: $$2\ +\frac{x-13}{x^2+x+10}$$

The area of a rectangle is $$4x^2-16$$ Which binomial factor could represent the width of the rectangle?

Factor the expression: $$\left(2x-4\right)\left(2x-4\right)$$ Factor a 2 out of each: $$4\left(x+2\right)\left(x-2\right)$$ So, the width could be represented by either factor, (x+2) or (x - 2).

Which expression is equivalent to $$2t^3-16\ ?$$

$$2\left(t^3-8\right)=$$ $$2\left(t-2\right)\left(t^2+2t+4\right)$$

$$f\left(x\right)=x^2+2x+4$$ $$g\left(x\right)=x-4$$ What is the product of f(x) And g(x)?

$$\left(x-4\right)\left(x^2+2x+4\right)=$$ $$x^3-2x^2-4x-16$$

What is the inverse of the function $$f\left(x\right)\ =\ 5\cdot2^{3x}$$ ?

$$f^{-1}\left(x\right)=\frac{\left(\log x-\log5\right)}{3\cdot\log2}$$

Mary is purchasing x shirts that cost $15 each before tax. h(x) = 15 x models the cost to purchase x shirts j(x) =0.20(15 x ) models the discount that will be applied to the cost of x shirts. What is the value of k if m(x) = kx represents the cost of x shirts after the discount but before tax?

$$15x-.2\left(15x\right)=$$ $$15x-3x\ =\ $$ $$12x$$

Let x be the number obtained by doubling $$\log_3\left(\frac{5}{6}\right).$$ What is the number equal to 3 x ?

$$2\log_3\frac{5}{6}\ =$$ $$\log_3\left(\frac{5}{6}\right)^2=$$ $$\log_3\left(\frac{25}{36}\right)$$ The answer is $$\frac{25}{36}$$

What is the inverse of $$g\left(x\right)\ =\ \frac{3^x+6}{4}$$ ?

$$x=\frac{3^y+6}{4}$$ $$4x=3^y+6$$ $$4x-6\ =3^y$$ $$\log_3\left(4x-6\right)=y$$

This is the graph of a polynomial function. Which could be the graphed function? A. f(x) = -1(x + 2) 2 (x - 1) B. f(x) = -1(x - 2) 2 (x - 1) C. f(x) = (x + 2) 2 (x - 1) D. f(x) = (x + 2) 2 (x - 1)

Remember: an odd degree function that is positive starts down on the left and ends up on the right an odd degree function that is negative starts up on the left and ends down on the right. An even root bounces, while an odd root crosses. Answer: A. f(x) = -1(x + 2) 2 (x - 1)

Which equation is equivalent to $$25-\left(x+5\right)^2$$ A. -z 2 B. 50 - z 2 C. -z(z + 10) D. -z 2 +10z + 50

$$25\ -\left(z^2+10z+25\right)=$$ $$25-z^2-10z-25\ =\ $$ $$-z^2-10z\ =$$ $$-z\left(z+10\right)$$

Factor the expression: $$x^3-2x^2-3x+6$$

$$\left(x^3-2x^2\right)-\left(3x-6\right)=$$ $$x^2\left(x-2\right)-3\left(x-2\right)=$$ $$\left(x-2\right)\left(x^2-3\right)$$

Mary and Jane work in a factory and assemble chairs Mary can assemble 2 chairs in 30 min. Jane can assemble 8 chairs in 60 min. At this rate, how many minutes will it take Mary and Jane, working together, to assemble 20 chairs?

$$R_M=\frac{2}{30}=\frac{1}{15}\ \ \ \ \ \ \ R_J=\frac{8}{60}=\frac{2}{15}$$ $$R_T=\frac{1}{15}+\frac{2}{15}=\frac{3}{15}=\frac{1}{5}$$ $$\frac{1\ chair}{5\ \min utes}\cdot\frac{20}{20}=\frac{20\ chairs}{100\ \min utes}$$

The equation $$0.75=\left|x-145\right|$$ shows the specifications of a particular widget. What is the smallest length, in cm, that the widget can have to meet specifications?

$$144.25\le x\le145.75$$ The answer: $$144.25$$

The function $$f\left(x\right)=\frac{2x^3-x^2-13x-3}{x-3}$$ can be rewritten as $$q\left(x\right)+\frac{r\left(x\right)}{b\left(x\right)}$$ . What is the value of r(x)?

Use synthetic division to divide and get: $$2x^2+5x+2+\frac{3}{x-3}$$ Answer: $$3$$

What is the value of x in $$3\cdot4^{\left(2x-1\right)}=24$$

$$4^{\left(2x-1\right)}=8$$ $$2^{2\left(2x-1\right)}=2^3$$ $$2\left(2x-1\right)=3$$ $$4x-2=3$$ $$4x=5$$ $$x=\frac{5}{4}$$

Mathematics Expressions and Functions Flashcards

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1.

FLASHCARD QUESTION

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2.

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A linear function passes through (4, 5). What is true about the inverse?

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The inverse is linear and must pass through (5, 4).

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A scientist placed 100 bacteria in a petri dish. The number of bacteria triples every 12 hours. How many bacteria, to the nearest bacterium, will be in the dish after 36 hours?

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The dimensions of a rectangular box are such that the length is 3.25 inches more than twice the width. The height is two-thirds of the width. The volume of the box is 37.5 ft^3. What is the width, to the nearest tenth of a foot, of the box?

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