Algebra Solutions

Determine the interval(s) on which the function is (strictly) increasing.

Answer: No function was provided. Please resubmit the problem with t

Oct 25, 2026

f(x) = 6x^2 + 19x + 8 Star method

Answer: Factored form: $(2x + 1)(3x + 8)$; zeros are $x = -\frac{1}{

Oct 22, 2026

3x^2+x-1/3=0

Answer: $x = \dfrac{-1 + \sqrt{5}}{6} \approx 0.207$ and $x = \dfrac

Oct 20, 2026

2a*sqrt(125a^2*b) - a^2*sqrt(80b) + 4*sqrt(20a^4*b)

Answer: $14a^2\sqrt{5b}$

Oct 16, 2026

x^2 - 2x + 10 = 0

Answer: $x = 1 + 3i$ and $x = 1 - 3i$ (two complex conjugate solutio

Oct 11, 2026

[3 -1 | -1] [1 -5 | 6] --(-3R2+R1)--> ?

Answer: $\begin{bmatrix} 0 & 14 & | & -19 \\ 1 & -5 & | & 6 \end{bma

Oct 10, 2026

a^2 - 8 when a = 4

Answer: $8$

Oct 10, 2026

a^2 - 18, when a = 6

Answer: $18$

Oct 10, 2026

a) Complete the table of values for y = 2x + 3 x | -2 | -1 | 0 | 1 | 2 | 3 y | | 1 | | | 7 | b) Draw the graph of y = 2x + 3 on the grid.

Answer: Completed table: x = -2 → y = -1, x = -1 → y = 1, x = 0 → y

Oct 9, 2026

x^2 + 5x + 6 = 0

Answer: $x = -2$ and $x = -3$

Oct 9, 2026

For the unity-feedback system shown, with forward path containing: - An integrator: 1/s - A plant: 3/(s+4) - An inner feedback loop with gain 2 - An outer feedback path with gain 6s (i) Obtain the open loop transfer function G(s) for the system and hence determine the system type. (ii) Determine the position error constant K_p, velocity error constant K_v, and acceleration error constant K_a for the system. (iii) Calculate the steady-state error that may be expected for a unit ramp input.

Answer: (i) Equivalent open-loop TF: $G_{eq}(s) = \frac{3}{s^2+28s-3

Oct 8, 2026

(X^2+3)-(y+6) =

Answer: $x^2 - y - 3$

Oct 8, 2026

Rectangle PQRS with PQ = (2x + 8) m and SR = 18 m. PR = 32 m, SQ = _____, x = _____

Answer: $x = 5$, and $SQ = 32$ m

Oct 7, 2026

4 + 3*sqrt(x-4) = x

Answer: $x = 4$ and $x = 13$ (both solutions are valid)

Oct 7, 2026

Use the graph of f to determine each of the following. (a) the domain of f (b) the range of f (c) the zeros of f (d) f(0) (e) the intervals on which f is increasing (f) the intervals on which f is decreasing (g) the values for which f(x) <= 0 (h) any relative maxima or minima (i) the value(s) of x for which f(x) = 2 (j) Is f(4) positive or negative?

Answer: (a) Domain: $[-5, 5]$ (b) Range: $[-4, 4]$ (c) Zeros: $x = -

Oct 6, 2026

Write the equation in slope-intercept form. y–4= 7 8 (x–8)

Answer: $y = \frac{7}{8}x - 3$

Oct 5, 2026

x - y = 3

Answer: Infinitely many solutions: every pair $(x, y)$ where $x = y

Oct 5, 2026

An amount of money invested for 1 year in a savings account will earn $400. That same amount of money invested in a mini-mall development will earn $2,400 interest in a year, because the interest paid is 10% more than that paid by the savings account. Find the rate of interest paid by each investment (as percents).

Answer: Savings account rate: $2\%$; Mini-mall rate: $12\%$

Oct 5, 2026

3 ( 2 x − 5 ) + 4 = 2 ( x + 7 )

Answer: $x = \frac{25}{4} = 6.25$

Oct 3, 2026

3(2x - 5) + 4 = 2(x + 7) + 3x

Answer: $x = 25$

Oct 3, 2026

2x+5=13

Answer: $x = 4$

Oct 2, 2026

2x+5=14

Answer: $x = 4.5$

Oct 2, 2026

Estimate the equation of the line of best fit using two points on the line: (6, 15) and (9, 21). y = 3x + 3 y = 2x + 3 y = 2x - 3 y = x + 3

Answer: $y = 2x + 3$

Oct 1, 2026

Graph a line that is perpendicular to the given line. Determine the slope of the given line and the one you graphed in simplest form. The given line is a vertical line (x = -3) with an undefined slope. The perpendicular line would be a horizontal line with a slope of 0. Original Slope: undefined Perpendicular Slope: 0

Answer: Original slope: undefined (vertical line x = −3). Perpendicu

Sep 29, 2026

(4x^2 - 16) / (2x^2 - 3x - 2)

Answer: $\dfrac{4(x+2)}{2x+1}$, where $x \neq 2$ and $x \neq -\dfrac

Sep 28, 2026

7^8 · 7^-9

Answer: $\dfrac{1}{7}$

Sep 28, 2026

(5x^2 - 20) / (5x^2 - 9x - 2)

Answer: $\frac{5(x+2)}{5x+1}$, where $x \neq 2$ and $x \neq -\frac{1

Sep 28, 2026

3*cbrt(-81x^9)

Answer: $-9x^3\sqrt[3]{3}$

Sep 28, 2026

sqrt(7) * sqrt(35)

Answer: $7\sqrt{5}$

Sep 28, 2026

5th_root(64x^10y^5)

Answer: $2x^{2}y\sqrt[5]{2}$

Sep 28, 2026

5th_root(486x^10y^5)

Answer: $3x^{2}y\sqrt[5]{2}$

Sep 28, 2026

(3*sqrt(x-4))^2

Answer: $9x - 36$

Sep 28, 2026

(sqrt(5) - sqrt(2)) / (sqrt(2) + sqrt(5))

Answer: $\dfrac{7 - 2\sqrt{10}}{3}$

Sep 28, 2026

(sqrt(11) - sqrt(2)) / (sqrt(2) + sqrt(11))

Answer: $\frac{13 - 2\sqrt{22}}{9}$

Sep 28, 2026

7 / (49^(1/3))

Answer: $7^{1/3} = \sqrt[3]{7} \approx 1.913$

Sep 28, 2026

sqrt(18xy) / sqrt(3x^2y)

Answer: $\dfrac{\sqrt{6x}}{x}$

Sep 28, 2026

sqrt(9xy) / sqrt(3x^2y)

Answer: $\dfrac{\sqrt{3x}}{x}$

Sep 28, 2026

4th_root(7a^3) * 4th_root(343a^2)

Answer: $7a\sqrt[4]{a}$

Sep 28, 2026

(3√(6a^6)) / (3√(2a^5b))

Answer: $\dfrac{\sqrt[3]{3ab^2}}{b}$

Sep 28, 2026

11^12 × 11^3 = 11^x

Answer: $x = 15$

Sep 24, 2026

17^4 × 17 = 17^[]

Answer: $\square = 5$, so $17^4 \times 17 = 17^5$

Sep 24, 2026

23^9 × 23^7 = 23^[]

Answer: $\square = 16$, so $23^9 \times 23^7 = 23^{16}$

Sep 24, 2026

3^5 × 3^2 = 3^[]

Answer: The missing exponent is $7$, giving $3^5 \times 3^2 = 3^7$.

Sep 24, 2026

y = (x + 2)^2 - 4

Answer: $x = 0$ and $x = -4$

Sep 23, 2026

Find the measures of two complementary angles if the measure of the larger angle is five more than four times the measure of the smaller angle.

Answer: The smaller angle is $17°$ and the larger angle is $73°$.

Sep 23, 2026

Y=(X-1)(x+2)(x-4)

Answer: $x = -2, \quad x = 1, \quad x = 4$

Sep 23, 2026

x^7 * (y^2 * z^-7)^2 / (x^-6 * y^-1 * z^-8)

Answer: $\dfrac{x^{13}\, y^{5}}{z^{6}}$

Sep 22, 2026

-7n + 20

Answer: $-7n + 20$ — already fully simplified. No solution exists be

Sep 21, 2026

n + 8 =

Answer: The problem is incomplete — there is no value on the right s

Sep 21, 2026

dy/dx + y = xy^2

Answer: $y = \dfrac{1}{x + 1 + Ce^{x}}$ (general solution), where $C

Sep 21, 2026

Mark and Brad bought the items shown below. Mark's Bill: 2 bicycles 3 scooters 5 iPad Total: $6450 Brad's Bill: 5 bicycles 6 scooters 8 iPad Total: $12150 Calculate the total cost of one bicycle, one doll and one iPad.

Answer: The problem is underdetermined — with only 2 equations and 3

Sep 18, 2026

-3x + 5 = 23

Answer: $x = -6$

Sep 17, 2026

Find the average rate of change of the function from x_1 to x_2. f(x) = -2x + 15, x_1 = 0, x_2 = 3

Answer: The average rate of change is $-2$.

Sep 4, 2026

Find the average rate of change of f(x) = x^2 - 3x + 7 from x_1 = 1 to x_2 = 5.

Answer: The average rate of change is $3$.

Sep 4, 2026

PROBLEM 3: Determine whether each equation is a function of x or not. a) y = (x^2 - 4) / (x + 2) b) y = sqrt(2x + 5) c) x = y^2 - 4y + 1 d) x^2 + 4y^2 - 6x + 8y - 11 = 0 e) y^3 - 2y = x^2 + 1

Answer: a) y = (x²-4)/(x+2) — IS a function of x (one output per inp

Aug 29, 2026

sqrt(1/5) + sqrt(4/5) + sqrt(5/4)

Answer: $\dfrac{11\sqrt{5}}{10}$

Jul 7, 2026

x^2 + 3 = 4

Answer: $x = 1$ and $x = -1$

Jun 13, 2026

The population of a town decreases by 4% every year. If its population today is 300,000, what will its population be in two years?

Answer: The population after two years will be $276{,}480$.

Jun 9, 2026

x^2+6x-5 solve for x

Answer: $x = -3 + \sqrt{14}\approx 0.742$ and $x = -3 - \sqrt{14} \a

Jun 9, 2026

se f(x)= 1/x. calcule (f(x+h)-f(x))/x

Answer: $\dfrac{-h}{x^2(x+h)}$

May 22, 2026

3(2x - 5) + 4 = 2(x + 7)

Answer: $x = \frac{25}{4} = 6.25$

May 15, 2026

2x + 5 = 13

Answer: $x = 4$

May 3, 2026

A school district is ordering new Chromebooks for students. Each Chromebook costs $285. The district also has to pay a one-time shipping fee of $1,200. If the district has a budget of $30,000, what is the maximum number of Chromebooks they can purchase without going over budget?

Answer: The district can purchase a maximum of **101 Chromebooks** f

Apr 29, 2026

x + 1 < 15

Answer: $x < 14$, or in interval notation $(-\infty, 14)$

Apr 24, 2026

x + (x + 1) + (x + 2) = 42

Answer: $x = 13$ (the three consecutive integers are 13, 14, and 15)

Apr 24, 2026

4x+14=2(x+14)

Answer: $x = 7$

Apr 24, 2026

x^2 - 4x + 4 = 0

Answer: $x = 2$ (a double root — one unique solution)

Apr 19, 2026

sqrt(x) = x - 2

Answer: $x = 4$ (x = 1 is extraneous and rejected)

Apr 19, 2026

(x + 2) / (x - 1) = 3

Answer: $x = \dfrac{5}{2}$

Apr 19, 2026

3(x + 1) = 3x + 3

Answer: All real numbers (infinitely many solutions). Every value of

Apr 19, 2026

2x + 3 = 2x + 5

Answer: No solution — the equation is a contradiction with no value

Apr 19, 2026

x^2 - 9 = 0

Answer: $x = 3$ and $x = -3$

Apr 19, 2026

2x + 5 = 11

Answer: $x = 3$

Apr 19, 2026

x^2 + x - 12 = 0

Answer: $x = -4$ and $x = 3$

Apr 19, 2026

2x^2 - 7x + 3 = 0

Answer: $x = 3$ and $x = \frac{1}{2}$

Apr 19, 2026

x^2 - 5x + 6 = 0

Answer: $x = 2$ and $x = 3$

Apr 19, 2026

x / (x - 1) = 2

Answer: $x = 2$

Apr 18, 2026

(3x - 1)/2 + 4 = (x + 5)/3

Answer: x = -1

Apr 18, 2026

(x^2 - 4) / (x - 2) = x + 2

Answer: The equation is true for all x ≠ 2 (an identity)

Apr 18, 2026

(x^2 - 9)/(x + 3) + 2 = x

Answer: No solution

Apr 18, 2026

(2x^2 - 5x - 3) / (x - 3) = 4

Answer: x = 3 is excluded (undefined); no valid solution exists

Apr 18, 2026

(x^2 - 9)/(x - 3) = 5

Answer: x = 8, but note x ≠ 3

Apr 17, 2026

x^2 + 5x + 6)/(x + 2) = 4

Answer: x = 2

Apr 17, 2026

(3x^2 - 12)/(x + 2) * (x^2 + 5x + 6)/(3(x - 2)^2) + 10/(x - 2)

Answer: $(x^2 + x + 8) / (x - 2)$, where $x eq -2, -3, 2$

Apr 14, 2026

Factor: x² - 9x + 20

Answer: (x - 4)(x - 5)

Apr 12, 2026

(x2−9)/(x2−x−6)

Answer: (x + 3)/(x + 2), where x ≠ 3 and x ≠ −2

Apr 11, 2026

(3x^2 - 12)/(x + 2) · (x^2 + 5x + 6)/(3(x - 2)^2) ÷ 10/(x - 2)

Answer: $$\frac{x + 3}{10(x - 2)}$$

Apr 11, 2026

Solve for x: 2x + 5 = 13

Answer: x = 4

Apr 11, 2026