Ace Algebra 1 with our Extensive Collection of Math Problems

Express the exponential equation
$6^{3} = 216$

Oxinailelpels3t14 2022-04-05

f(x), g(x), 2 quadratic polynomials:
$| f (x) | \geq | g (x) | \forall x \in R$ . Find the number of distinct roots of equation $h (x) h^{″} (x) + {(h^{'} (x))}^{2} = 0$ if $h (x) = f (x) g (x)$

Aleah Choi 2022-04-05

Double root in Trigonometric equation?
Consider the function $f (x) = \sin^{2} x + \sin x$ in the domain $[0, 2 π]$ , find the subset of the domain where $f \geq 0$ .

Javion Kerr 2022-04-05

Drawing two perpendicular tangent line from the origin to $y = x^{2} - 2 x + a$ .
We drew two perpendicular tangent line from the origin (the point (0,0) ) to the curve $y = x^{2} - 2 x + a$ , what is the value of a?
1) $\frac{5}{4}$
2) $\frac{- 5}{4}$
3) $\frac{3}{4}$
4) $\frac{- 3}{4}$

Lorelei Stanton 2022-04-05

E.g. to find the extremum of $f (x) = x - x^{2}$ we can notice that $f (x) = 6 x - x^{2} = x (6 - x) = (6 - x) x$ . This operation maps every value x to $6 - x$ through the axis of symmetry and vice-versa (e.g. 0 is mapped to 6 and 6 mapped to 0). This operation preserves symmetry for $x = 3$ the axis of symmetry and hence the extremum of the function.
What about the function $f (x) = 6 x + x^{2} = x (6 + x) = (6 + x) x$ ? We know that the minimum of this function is at $x = - 3$ but $6 + (- 3) = 3$ . Also this operation maps e.g 4 to 10, but 10 to 16! Hence, this approach fails with this example (symmetry is not preserved).
Why is that so? Why is this approach not working for all the quadratic functions?

r1fa8dy5 2022-04-05

Does $\sqrt{1 + \sqrt{2}}$ belong to $Q (\sqrt{2})$ ?

Leon Robinson 2022-04-05

Find all the real roots of
$x^{2} + \frac{x^{2}}{{(x + 1)}^{2}} = 3$

Harold Hoover 2022-04-04

Find all the values of a for which both the root of the equation $(a - 2) x^{2} - 2 a x + a = 0$ lies in the interval $(- 2, 1)$ ,

Janiyah Hays 2022-04-04

Find all integer values of m such that the equation $\sqrt{9 - x} = \sqrt{3 m - x^{2} + 9 x} - \sqrt{x}$ has exactly four distinct real roots.

Lorelei Stanton 2022-04-04

Factoring the quadratic equation $3 x^{2} - 23 x + 14 = 0$

afasiask7xg 2022-04-04

Factor a quadratic when the leading coefficient is not equal to 1 and you can't factor by grouping?
If one has a quadratic, for example $5 x^{2} - 10 x - 2$ , which has real roots which via the quadratic equation are $\frac{5 \pm \sqrt{35}}{5}$ , can you find its factored form. As I understand it $5 x^{2} - 10 x - 2 \neq (x - root1) (x - root2)$ ? How can you turn this type of quadratic into a factored form?

Yasmine Larson 2022-04-04

What is $4 \sqrt{3}$ minus $4 \sqrt{3}$ ?

Alissa Hutchinson 2022-04-04

What is $\sqrt{5}$ minus $\sqrt{5}$ ?

revistasbibxjm87 2022-04-04

Solve for b and c:
${\begin{cases} 6 b + 3 c = - 5 \\ 4 b + 3 c = 7 \end{cases}$

bedblogi38am 2022-04-04

Solve for d and f: ${\begin{cases} 5 d + 6 f = 2 \\ 5 d + 3 f = 3 \end{cases}$

Landon Mckinney 2022-04-04

Solve for f and g: ${\begin{cases} 3 f + 5 g = - 5 \\ 6 f + 5 g = 7 \end{cases}$

When you are a high school student or someone already enrolled in college, even those simple research projects will include Algebra 1 equations, which means that getting some help cannot be avoided. Thankfully, you can access Algebra 1 problems and answers free of charge, which will let you see what Algebra 1 practice problems can be used for certain questions. Just remember to check calculations twice as these can easily get complex. The majority of Algebra 1 answers will be familiar to most students dealing with financial concepts as it is not related to advanced Math problems in most scenarios.

Algebra I