Math Statement

Problem 1

Calculate $31 - 8$ .

See Solution

Problem 2

Calculate $-2^{5} \div 4$ .

See Solution

Problem 3

Calculate $(4+27)-32$ .

See Solution

Problem 4

Solve for $x$ in the equation: $3(x+3)-5=16$ .

See Solution

Problem 5

Evaluate $\frac{n p}{n+p}$ for $n=9$ and $p=15$ .

See Solution

Problem 6

Multiply and simplify $(2x - 5)(3x - 3)$

See Solution

Problem 7

Calculate $8 \div 2(2+2)$ .

See Solution

Problem 8

Calculate $\frac{16^{7}+8^{9}-(-4)^{13}-(-2)^{25}}{2^{7} \cdot(-4)^{4} \cdot 4^{5}+(-16)^{6}}$ .

See Solution

Problem 9

Solve $3x - 5 = 16$ for $x$ and express your answer in set notation.

See Solution

Problem 10

Solve $3x - 5 = 16$ for $x$ and express your answer in set notation.

See Solution

Problem 11

Evaluate the integral $\int \frac{9 x+2}{x^{2}+x-6} d x$ .

See Solution

Problem 12

Решите у в уравнении: $4y + 3 = 6y - 7$ .

See Solution

Problem 13

Calculate the integral $\int_{2}^{3} 3 x^{2} d t$ .

See Solution

Problem 14

Evaluate the integral $\int_{-2}^{2} \frac{1+x^{2}}{1+2^{x}} d x$ .

See Solution

Problem 15

Calculate the integral $\int \tan^{3} x \sec x \, dx$ .

See Solution

Problem 16

What is the result of $9-3 \div \frac{1}{3}+1$ ?

See Solution

Problem 17

Find $y$ if $\log _{y} \frac{1}{9}=3$ .

See Solution

Problem 18

Solve for $y$ in the equation $y^{2}+7 y-60=0$ .

See Solution

Problem 19

פתרו את המשוואה $3 x + 5 = 14$ ומצאו את ערך $x$ . תשובה: $x =$

See Solution

Problem 20

Find the $z$ -score for $x=7$ given that the mean is 4 and the standard deviation is 2.

See Solution

Problem 21

פתרו את המשוואה $3 x + 5 = 14$ ומצאו את $x =$

See Solution

Problem 22

Evaluate $-3 \Delta -1$ for the operation $a \Delta b = \frac{a+b}{\sqrt{ab}}$ where $a, b \neq 0$ .

See Solution

Problem 23

Expand the expression $(x-5)(x+2)$ .

See Solution

Problem 24

Calculate $31 - 8$ .

See Solution

Problem 25

Calculate $\frac{32}{4}$ .

See Solution

Problem 26

Calculate $2^{5} \div 4$ .

See Solution

Problem 27

Calculate $(4+27)-\frac{32}{4}$ .

See Solution

Problem 28

Calculate $-2^{5} \div 4$ .

See Solution

Problem 29

Calculate $-32 \div 4$ .

See Solution

Problem 30

Find the integral of $-\frac{1}{5} \sin u \, du$ .

See Solution

Problem 31

Calculate $\left((1^{4} \times 2^{2})+3^{3}\right)-\frac{2^{5}}{4}$ .

See Solution

Problem 32

Calculate $\frac{16^{7}+8^{9}-(-4)^{13}-(-2)^{25}}{2^{7} \cdot(-4)^{4} \cdot 4^{5}+(-16)^{6}}$ .

See Solution

Problem 33

Calculate the value of $(1^{4} \times 2^{2}+3^{3})-2^{5} \div 4$ and $6 \div 2(1+2)$ .

See Solution

Problem 34

Calculate $31 - \frac{32}{4}$

See Solution

Problem 35

Solve the system of equations: $6x - 7y = -8$ and $-x - 4y = -9$ .

See Solution

Problem 36

Solve the equation $\frac{7x - 8}{5} = \frac{2x + 5}{4}$ .

See Solution

Problem 37

Solve the equation: $\frac{5(x+11)}{3}=\frac{3(1+x)}{2}$ for $x$ .

See Solution

Problem 38

Solve $3x - 5 = 16$ for $x$ and express your answer in set notation.

See Solution

Problem 39

Solve the system of equations: $10x - 14y = -4$ and $-10x - 20y = -30$ .

See Solution

Problem 40

Multiply and simplify $(2x - 5)(3x - 3)$ .

See Solution

Problem 41

Multiply and simplify: $(2x - 5)(3x - 3)$

See Solution

Problem 42

Calculate $\frac{6}{2}(1+2)$ .

See Solution

Problem 43

Find $y$ if $\log_{y} \frac{1}{9} = 3$ .

See Solution

Problem 44

Find the $z$ -score for $x = 7$ given that the mean $\mu = 4$ and standard deviation $\sigma = 2$ .

See Solution

Problem 45

Expand $(x-5)(x+2)$ using the FOIL method.

See Solution

Problem 46

Multiply and simplify: $(2x - 5)(3x - 3)$ .

See Solution

Problem 47

Calculate $1^{4} \times 2^{2} + 3^{3}$ .

See Solution

Problem 48

Find the $z$ -score for $x = 7$ given $\mu = 4$ and $\sigma = 2$ using $z = \frac{x - \mu}{\sigma}$ .

See Solution

Problem 49

Calculate $(1 \times 4) + 27$ .

See Solution

Problem 50

Calculate $1 \times 4 - 7$ .

See Solution

Problem 51

Calculate $1 \times 4 + 27$ .

See Solution

Problem 52

Calculate $\left((1^{4} \times 2^{2})+3^{3}\right)-(2^{5} \div 4)$ .

See Solution

Problem 53

Convert the parabola equation $(x+6)^{2}=12(y-1)$ to standard form.

See Solution

Problem 54

Multiply and simplify $(2x - 5)(3x - 3)$ .

See Solution

Problem 55

Multiply and simplify $(2x-5)(3x-3)$ .

See Solution

Problem 56

Rewrite $y=2 x^{2}-4 x+7$ in focus-directrix form.

See Solution

Problem 57

Find $m \angle 16$ if $m \angle 1=5x+8$ and $m \angle 16=7x-20$ .

See Solution

Problem 58

Multiply and simplify: $(2x-5)(3x-3)$ .

See Solution

Problem 59

Convert the parabola equation $y=-\frac{1}{8}(x-4)^{2}+7$ to standard form.

See Solution

Problem 60

Prove that two lines are parallel if and only if alternate exterior angles are congruent: $\angle 1 \cong \angle 8$ .

See Solution

Problem 61

Convert $y=-\frac{1}{8}(x-4)^{2}+7$ to standard form and choose the correct option from 1-4.

See Solution

Problem 62

Convert $y=x^{2}-4 x-8$ to vertex form. Which is correct? 1) $(x+2)^{2}=y-12$ 2) $(x+2)^{2}=y+12$ 3) $(x-2)^{2}=y-12$ 4) $(x-2)^{2}=y+12$

See Solution

Problem 63

Convert $y=3 x^{2}+12 x-1$ to vertex form and select the correct option from:
1. $y=3(x-4)^{2}+1$
2. $y=3(x+2)^{2}-13$
3. $y=3(x-2)^{2}+13$
4. $y=3(x+4)^{2}-1$

See Solution

Problem 64

Differentiate $x^{e^{x}}$ with respect to $x$ .

See Solution

Problem 65

What is the value of $6 \div 2(1+2)$ ?

See Solution

Problem 66

Convert $y=x^{2}-4 x-8$ to vertex form. Which is correct?
1. $(x+2)^{2}=y+12$
2. $(x+2)^{2}=y-12$
3. $(x-2)^{2}=y+12$
4. $(x-2)^{2}=y-12$

See Solution

Problem 67

Convert $x=\frac{1}{4}(y-2)^{2}+3$ to standard form. Which option is correct?
1. $x=\frac{1}{4} y^{2}-y+4$
2. $y=\frac{1}{4} x^{2}-x+4$
3. $x=-\frac{1}{4} y^{2}-y-4$
4. $y=-\frac{1}{4} x^{2}-x-4$

See Solution

Problem 68

Solve $60 \div 2(3+7)$ .

See Solution

Problem 69

Find $k$ such that $x^{2}+k(x+2)+3(x+1)>0$ for all $x$ . What is the range of $k$ ?

See Solution

Problem 70

Show that the roots of $m x^{2}+2 x+1=m$ are always real for any real constant $m$ .

See Solution

Problem 71

Show that the roots of the equation $m x^{2}+2 x+1=0$ are real for a real constant $m$ .

See Solution

Problem 72

Calculate $(1^{4} \times 2^{2} + 3^{3}) - 2^{5} \div 4$ .

See Solution

Problem 73

Find the derivative of $x^{2}$ with respect to $x$ .

See Solution

Problem 74

Calculate $31 - 32 \div 4$ .

See Solution

Problem 75

Solve the system of equations: $5x - 14y = -23$ and $-6x + 7y = 8$ .

See Solution

Problem 76

Calculate $(4+27)-32 \div 4$ .

See Solution

Problem 77

Multiply and simplify $(2 x-5)(3 x-3)$ .

See Solution

Problem 78

Determine if the series converges or diverges: $\sum_{n=1}^{\infty}\left[\left(\frac{6}{7}\right)^{n}-\frac{3}{2^{n}}\right]$ . If it converges, find the sum.

See Solution

Problem 79

Find the sum of the series $\sum_{n=1}^{\infty} \frac{1}{n(n+2)}$ .

See Solution

Problem 80

Find the limit of the sequence $a_{n}=\sqrt{n^{2}+3 n}-n$ . Options: A) 3 B) 2 C) $1 / 2$ D) $3 / 2$ E) 0 F) 1 G) $\infty$ H) does not exist.

See Solution

Problem 81

1. Prove $n^{7}-n$ is divisible by 42 for all positive integers $n$ . Show primes ≠ 2, 5 divide numbers like 1, 11, etc.
2. Prove if $p>3$ is prime, then $p^{2} \equiv 1(\bmod 24)$ .
3. Find the number of trailing zeros in $1000!$ .
4. If $p$ and $p^{2}+2$ are primes, prove $p^{3}+2$ is prime.
5. Prove $\operatorname{gcd}(2^{a}-1,2^{b}-1)=2^{\operatorname{gcd}(a, b)}-1$ for positive integers $a, b$ .

See Solution

Problem 82

Solve the equation $-3 h^{2} / 2 - 24 h - 45 / 2 = 0$ .

See Solution

Problem 83

Determine if these series are absolutely convergent, conditionally convergent, or divergent:
(I) $\sum_{n=1}^{\infty}\left(\frac{\pi}{2}\right)^{n}$
(II) $\sum_{n=1}^{\infty} \frac{(-1)^{n-1} e}{\sqrt{n}}$
(III) $\sum_{n=1}^{\infty} \frac{1}{\sqrt{n}(\sqrt{n}+1)^{3}}$

See Solution

Problem 84

Prove that $n^{7}-n$ is divisible by 42 for all positive integers $n$ and that primes other than 2 or 5 divide infinitely many of $1, 11, 111, 1111,$ etc.

See Solution

Problem 85

Prove that for any positive integer $n$ , $n^{7}-n$ is divisible by 42. Also, show $p^{2} \equiv 1(\bmod 24)$ for primes $p>3$ .

See Solution

Problem 86

Prove that $n^{7}-n$ is divisible by 42 for all positive integers $n$ and $p>3$ prime, $p^{2} \equiv 1(\bmod 24)$ .

See Solution

Problem 87

Find $a$ and $b$ if the line $y=x+h$ is tangent to $y=\frac{k}{1-x}$ and $k=\frac{(h+a)^{2}}{b}$ .

See Solution

Problem 88

Any two parallel lines lie in the same plane. True or False?

See Solution

Problem 89

A ball's position is given by $x(t)=0.000015 t^5 - 0.004 t^3 + 0.4 t$ . Find its velocity at $t=10.0$ s.

See Solution

Problem 90

Is it true or false that 'If two rays are parallel, then the lines containing them must be coplanar'?

See Solution

Problem 91

Find values of $k$ so that $2 x^{2}+k^{2}+2-2(k+2) x > 0$ for all $x$ .

See Solution

Problem 92

A ball's position is given by $x(t)=0.000015 t^5 - 0.004 t^3 + 0.4 t$ . Find its velocity at $t=10.0$ s.

See Solution

Problem 93

Find the integral of $x^{2}$ with respect to $x$ .

See Solution

Problem 94

Rewrite $y=-x^{2}-6 x+1$ as $y=a-(x+b)^{2}$ . Find the max value of $y$ and its $x$ value. Sketch the curve.

See Solution

Problem 95

Prove $x^{2}-x+2 \geq \frac{7}{4}$ for all values of $x$ .

See Solution

Problem 96

Find $x$ such that $1+x^{2} \geq-\frac{7 x-x^{2}}{3}$ and determine the minimum of $y=1+x^{2}+\frac{7 x-x^{2}}{3}$ .

See Solution

Problem 97

Find the length of line segment $AB$ where $A$ and $B$ are intersections of $2x + 3y = 6$ and $x^2 - 2y^2 - xy = 0$ .

See Solution

Problem 98

Find all solutions for the function $f(x)=2 x^{3}-6 x^{2}+9 x-27$ .

See Solution

Problem 99

Find the integral $\int \sin (3 x) d x$ . Choose from: (a) $3 \cos (3 x)+C$ , (b) $\frac{1}{3} \cos (3 x)+C$ , (c) $-3 \cos (3 x)+C$ , (d) $-\frac{1}{3} \cos (3 x)+C$ .

See Solution

Problem 100

Calculate the integral $\int_{1}^{5} \frac{x-1}{x} dx$ and choose the correct answer: (a) $5-\ln 5$ , (b) $4-\ln 5$ , (c) $2-\ln 5$ , (d) $1-\ln 5$ .

See Solution

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Math Statement

Problem 1

Calculate 31−8 31 - 8 31−8.

Problem 2

Calculate −25÷4 -2^{5} \div 4 −25÷4.

Problem 3

Calculate (4+27)−32 (4+27)-32 (4+27)−32.

Problem 4

Solve for x x x in the equation: 3(x+3)−5=16 3(x+3)-5=16 3(x+3)−5=16.

Problem 5

Evaluate npn+p \frac{n p}{n+p} n+pnp​ for n=9 n=9 n=9 and p=15 p=15 p=15.

Problem 6

Multiply and simplify (2x−5)(3x−3) (2x - 5)(3x - 3) (2x−5)(3x−3)

Problem 7

Calculate 8÷2(2+2) 8 \div 2(2+2) 8÷2(2+2).

Problem 8

Calculate 167+89−(−4)13−(−2)2527⋅(−4)4⋅45+(−16)6 \frac{16^{7}+8^{9}-(-4)^{13}-(-2)^{25}}{2^{7} \cdot(-4)^{4} \cdot 4^{5}+(-16)^{6}} 27⋅(−4)4⋅45+(−16)6167+89−(−4)13−(−2)25​.

Problem 9

Solve 3x−5=16 3x - 5 = 16 3x−5=16 for x x x and express your answer in set notation.

Problem 10

Solve 3x−5=16 3x - 5 = 16 3x−5=16 for x x x and express your answer in set notation.

Problem 11

Evaluate the integral ∫9x+2x2+x−6dx \int \frac{9 x+2}{x^{2}+x-6} d x ∫x2+x−69x+2​dx.

Problem 12

Решите у в уравнении: 4y+3=6y−74y + 3 = 6y - 74y+3=6y−7.

Problem 13

Calculate the integral ∫233x2dt \int_{2}^{3} 3 x^{2} d t ∫23​3x2dt.

Problem 14

Evaluate the integral ∫−221+x21+2xdx \int_{-2}^{2} \frac{1+x^{2}}{1+2^{x}} d x ∫−22​1+2x1+x2​dx.

Problem 15

Calculate the integral ∫tan⁡3xsec⁡x dx \int \tan^{3} x \sec x \, dx ∫tan3xsecxdx.

Problem 16

What is the result of 9−3÷13+1 9-3 \div \frac{1}{3}+1 9−3÷31​+1?

Problem 17

Find y y y if log⁡y19=3 \log _{y} \frac{1}{9}=3 logy​91​=3.

Problem 18

Solve for y y y in the equation y2+7y−60=0 y^{2}+7 y-60=0 y2+7y−60=0.

Problem 19

פתרו את המשוואה 3x+5=14 3 x + 5 = 14 3x+5=14 ומצאו את ערך x x x. תשובה: x= x = x=

Problem 20

Find the z z z-score for x=7 x=7 x=7 given that the mean is 4 and the standard deviation is 2.

Problem 21

פתרו את המשוואה 3x+5=14 3 x + 5 = 14 3x+5=14 ומצאו את x= x = x=

Problem 22

Evaluate −3Δ−1 -3 \Delta -1 −3Δ−1 for the operation aΔb=a+bab a \Delta b = \frac{a+b}{\sqrt{ab}} aΔb=ab​a+b​ where a,b≠0 a, b \neq 0 a,b=0.

Problem 23

Expand the expression (x−5)(x+2)(x-5)(x+2)(x−5)(x+2).

Problem 24

Calculate 31−8 31 - 8 31−8.

Problem 25

Calculate 324 \frac{32}{4} 432​.

Problem 26

Calculate 25÷42^{5} \div 425÷4.

Problem 27

Calculate (4+27)−324 (4+27)-\frac{32}{4} (4+27)−432​.

Problem 28

Calculate −25÷4-2^{5} \div 4−25÷4.

Problem 29

Calculate −32÷4-32 \div 4−32÷4.

Problem 30

Find the integral of −15sin⁡u du-\frac{1}{5} \sin u \, du−51​sinudu.

Problem 31

Calculate ((14×22)+33)−254 \left((1^{4} \times 2^{2})+3^{3}\right)-\frac{2^{5}}{4} ((14×22)+33)−425​.

Problem 32

Calculate 167+89−(−4)13−(−2)2527⋅(−4)4⋅45+(−16)6 \frac{16^{7}+8^{9}-(-4)^{13}-(-2)^{25}}{2^{7} \cdot(-4)^{4} \cdot 4^{5}+(-16)^{6}} 27⋅(−4)4⋅45+(−16)6167+89−(−4)13−(−2)25​.

Problem 33

Calculate the value of (14×22+33)−25÷4(1^{4} \times 2^{2}+3^{3})-2^{5} \div 4(14×22+33)−25÷4 and 6÷2(1+2)6 \div 2(1+2)6÷2(1+2).

Problem 34

Calculate 31−324 31 - \frac{32}{4} 31−432​

Problem 35

Solve the system of equations: 6x−7y=−86x - 7y = -86x−7y=−8 and −x−4y=−9-x - 4y = -9−x−4y=−9.

Problem 36

Solve the equation 7x−85=2x+54 \frac{7x - 8}{5} = \frac{2x + 5}{4} 57x−8​=42x+5​.

Problem 37

Solve the equation: 5(x+11)3=3(1+x)2 \frac{5(x+11)}{3}=\frac{3(1+x)}{2} 35(x+11)​=23(1+x)​ for x x x.

Problem 38

Solve 3x−5=16 3x - 5 = 16 3x−5=16 for x x x and express your answer in set notation.

Problem 39

Solve the system of equations: 10x−14y=−410x - 14y = -410x−14y=−4 and −10x−20y=−30-10x - 20y = -30−10x−20y=−30.

Problem 40

Calculate $31 - 8$ .

Calculate $-2^{5} \div 4$ .

Calculate $(4+27)-32$ .

Solve for $x$ in the equation: $3(x+3)-5=16$ .

Evaluate $\frac{n p}{n+p}$ for $n=9$ and $p=15$ .

Multiply and simplify $(2x - 5)(3x - 3)$

Calculate $8 \div 2(2+2)$ .

Calculate $\frac{16^{7}+8^{9}-(-4)^{13}-(-2)^{25}}{2^{7} \cdot(-4)^{4} \cdot 4^{5}+(-16)^{6}}$ .

Solve $3x - 5 = 16$ for $x$ and express your answer in set notation.

Solve $3x - 5 = 16$ for $x$ and express your answer in set notation.

Evaluate the integral $\int \frac{9 x+2}{x^{2}+x-6} d x$ .

Решите у в уравнении: $4y + 3 = 6y - 7$ .

Calculate the integral $\int_{2}^{3} 3 x^{2} d t$ .

Evaluate the integral $\int_{-2}^{2} \frac{1+x^{2}}{1+2^{x}} d x$ .

Calculate the integral $\int \tan^{3} x \sec x \, dx$ .

What is the result of $9-3 \div \frac{1}{3}+1$ ?

Find $y$ if $\log _{y} \frac{1}{9}=3$ .

Solve for $y$ in the equation $y^{2}+7 y-60=0$ .

פתרו את המשוואה $3 x + 5 = 14$ ומצאו את ערך $x$ . תשובה: $x =$

Find the $z$ -score for $x=7$ given that the mean is 4 and the standard deviation is 2.

פתרו את המשוואה $3 x + 5 = 14$ ומצאו את $x =$

Evaluate $-3 \Delta -1$ for the operation $a \Delta b = \frac{a+b}{\sqrt{ab}}$ where $a, b \neq 0$ .

Expand the expression $(x-5)(x+2)$ .

Calculate $31 - 8$ .

Calculate $\frac{32}{4}$ .

Calculate $2^{5} \div 4$ .

Calculate $(4+27)-\frac{32}{4}$ .

Calculate $-2^{5} \div 4$ .

Calculate $-32 \div 4$ .

Find the integral of $-\frac{1}{5} \sin u \, du$ .

Calculate $\left((1^{4} \times 2^{2})+3^{3}\right)-\frac{2^{5}}{4}$ .

Calculate $\frac{16^{7}+8^{9}-(-4)^{13}-(-2)^{25}}{2^{7} \cdot(-4)^{4} \cdot 4^{5}+(-16)^{6}}$ .

Calculate the value of $(1^{4} \times 2^{2}+3^{3})-2^{5} \div 4$ and $6 \div 2(1+2)$ .

Calculate $31 - \frac{32}{4}$

Solve the system of equations: $6x - 7y = -8$ and $-x - 4y = -9$ .

Solve the equation $\frac{7x - 8}{5} = \frac{2x + 5}{4}$ .

Solve the equation: $\frac{5(x+11)}{3}=\frac{3(1+x)}{2}$ for $x$ .

Solve $3x - 5 = 16$ for $x$ and express your answer in set notation.

Solve the system of equations: $10x - 14y = -4$ and $-10x - 20y = -30$ .

Multiply and simplify $(2x - 5)(3x - 3)$ .

Multiply and simplify: $(2x - 5)(3x - 3)$

Calculate $\frac{6}{2}(1+2)$ .

Find $y$ if $\log_{y} \frac{1}{9} = 3$ .

Find the $z$ -score for $x = 7$ given that the mean $\mu = 4$ and standard deviation $\sigma = 2$ .

Expand $(x-5)(x+2)$ using the FOIL method.

Multiply and simplify: $(2x - 5)(3x - 3)$ .

Calculate $1^{4} \times 2^{2} + 3^{3}$ .

Find the $z$ -score for $x = 7$ given $\mu = 4$ and $\sigma = 2$ using $z = \frac{x - \mu}{\sigma}$ .

Calculate $(1 \times 4) + 27$ .

Calculate $1 \times 4 - 7$ .

Calculate $1 \times 4 + 27$ .

Calculate $\left((1^{4} \times 2^{2})+3^{3}\right)-(2^{5} \div 4)$ .

Convert the parabola equation $(x+6)^{2}=12(y-1)$ to standard form.

Multiply and simplify $(2x - 5)(3x - 3)$ .

Multiply and simplify $(2x-5)(3x-3)$ .

Rewrite $y=2 x^{2}-4 x+7$ in focus-directrix form.

Find $m \angle 16$ if $m \angle 1=5x+8$ and $m \angle 16=7x-20$ .

Multiply and simplify: $(2x-5)(3x-3)$ .

Convert the parabola equation $y=-\frac{1}{8}(x-4)^{2}+7$ to standard form.

Prove that two lines are parallel if and only if alternate exterior angles are congruent: $\angle 1 \cong \angle 8$ .

Convert $y=-\frac{1}{8}(x-4)^{2}+7$ to standard form and choose the correct option from 1-4.

Convert $y=x^{2}-4 x-8$ to vertex form. Which is correct? 1) $(x+2)^{2}=y-12$ 2) $(x+2)^{2}=y+12$ 3) $(x-2)^{2}=y-12$ 4) $(x-2)^{2}=y+12$

Convert $y=3 x^{2}+12 x-1$ to vertex form and select the correct option from:
1. $y=3(x-4)^{2}+1$
2. $y=3(x+2)^{2}-13$
3. $y=3(x-2)^{2}+13$
4. $y=3(x+4)^{2}-1$

Differentiate $x^{e^{x}}$ with respect to $x$ .

What is the value of $6 \div 2(1+2)$ ?

Convert $y=x^{2}-4 x-8$ to vertex form. Which is correct?
1. $(x+2)^{2}=y+12$
2. $(x+2)^{2}=y-12$
3. $(x-2)^{2}=y+12$
4. $(x-2)^{2}=y-12$

Solve $60 \div 2(3+7)$ .

Find $k$ such that $x^{2}+k(x+2)+3(x+1)>0$ for all $x$ . What is the range of $k$ ?

Show that the roots of $m x^{2}+2 x+1=m$ are always real for any real constant $m$ .

Show that the roots of the equation $m x^{2}+2 x+1=0$ are real for a real constant $m$ .

Calculate $(1^{4} \times 2^{2} + 3^{3}) - 2^{5} \div 4$ .

Find the derivative of $x^{2}$ with respect to $x$ .

Calculate $31 - 32 \div 4$ .