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$a, k$ は実数の定数とする。2次方程式 $x^2 - (k+7)x + ak + 12 = 0$ がすべての実数 $k$ に対して実数解を持つような、$a$ の値の範囲を求めよ。

二次方程式判別式不等式実数解
2025/3/16

The problem asks us to calculate the results of two arithmetic expressions. a) $-10,672 + 9615$ b) $...

Integer ArithmeticAdditionSubtractionSigned Numbers
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The problem asks us to divide 1724 by 28 using a calculator and round the result to the nearest whol...

DivisionRounding
2025/3/16

The problem asks us to find the sum of the following numbers: $45.92$, $390$, $51842$, and $993.7$.

AdditionDecimal Numbers
2025/3/16

The problem asks us to simplify the fraction $\frac{56}{70}$ to its lowest terms.

FractionsSimplificationGreatest Common Divisor (GCD)Prime Factorization
2025/3/16

We need to find the missing numbers to make the three fractions equivalent: $\frac{1}{5} = \frac{3}{...

FractionsEquivalent FractionsProportionsRatio
2025/3/16

The problem asks us to find the value of $t$ in the equation $\frac{7}{8} = \frac{t}{32}$.

Linear EquationsSolving EquationsFractions
2025/3/16

The problem asks to find what fraction of 1 meter is 30 centimeters, and to express the answer in it...

FractionsUnit ConversionSimplificationRatio
2025/3/16

We are asked to solve the equation $4(x-9) = 7(x+7)$ for $x$.

Linear EquationsSolving EquationsVariable Isolation
2025/3/16

Solve the equation $\frac{2x}{3} = \frac{3}{7}$ for $x$.

Linear EquationsSolving EquationsFractions
2025/3/16