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Question Number 217071 Answers: 1 Comments: 0

Find all two-digit numbers that are equal to four times the sum of their digits. Solve this using at least two different methods and verify your answers.

$$\mathrm{Find}\:\mathrm{all}\:\mathrm{two}-\mathrm{digit}\:\mathrm{numbers}\:\mathrm{that}\:\mathrm{are}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{four}\:\mathrm{times}\:\mathrm{the}\:\mathrm{sum}\: \\ $$$$\mathrm{of}\:\mathrm{their}\:\mathrm{digits}.\:\mathrm{Solve}\:\mathrm{this}\:\mathrm{using}\:\mathrm{at}\:\mathrm{least}\:\mathrm{two}\:\mathrm{different}\:\mathrm{methods}\: \\ $$$$\mathrm{and}\:\mathrm{verify}\:\mathrm{your}\:\mathrm{answers}. \\ $$

Question Number 217064 Answers: 1 Comments: 0

Two numbers differ by 6. The sum of their reciprocals is (2/(15)) . Determine the numbers.

$$\mathrm{Two}\:\mathrm{numbers}\:\mathrm{differ}\:\mathrm{by}\:\mathrm{6}.\:\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{their}\:\mathrm{reciprocals}\:\mathrm{is}\:\frac{\mathrm{2}}{\mathrm{15}}\:. \\ $$$$\mathcal{D}{etermine}\:{the}\:{numbers}. \\ $$

Question Number 217079 Answers: 1 Comments: 0

((6C3×4C1)/(15C4))

$$\frac{\mathrm{6}{C}\mathrm{3}×\mathrm{4}{C}\mathrm{1}}{\mathrm{15}{C}\mathrm{4}} \\ $$$$ \\ $$

Question Number 217050 Answers: 1 Comments: 1

Question Number 217046 Answers: 1 Comments: 0

form the differential equation by eliminating the arbritrary constant y^2 =Ax^2 +Bx+C

$${form}\:{the}\:{differential}\:{equation}\:{by}\: \\ $$$${eliminating}\:{the}\:{arbritrary}\:{constant} \\ $$$${y}^{\mathrm{2}} ={Ax}^{\mathrm{2}} +{Bx}+{C} \\ $$

Question Number 217049 Answers: 0 Comments: 1

Hello here its been a while. I′ve been watching Ajfour sir dancing lately on Youtube. I believe he has gotten to saturation point. Is there anyone here into AI and Machine learning?

$${Hello}\:{here}\:{its}\:{been}\:{a}\:{while}.\:{I}'{ve} \\ $$$${been}\:{watching}\:{Ajfour}\:{sir}\:{dancing} \\ $$$${lately}\:{on}\:{Youtube}.\:{I}\:{believe}\:{he}\:{has} \\ $$$${gotten}\:{to}\:{saturation}\:{point}. \\ $$$${Is}\:{there}\:{anyone}\:{here}\:{into}\:{AI}\:{and} \\ $$$${Machine}\:{learning}? \\ $$$$ \\ $$

Question Number 217040 Answers: 2 Comments: 0

Find all positive integers n such that n divides 2^n + 1.

$$\mathrm{Find}\:\mathrm{all}\:\mathrm{positive}\:\mathrm{integers}\:\:\mathrm{n}\:\:\mathrm{such}\:\mathrm{that} \\ $$$$\:\:\mathrm{n}\:\:\mathrm{divides}\:\:\mathrm{2}^{{n}} \:+\:\mathrm{1}.\:\: \\ $$

Question Number 217058 Answers: 1 Comments: 0

The quadratic equation has two equal roots: x^2 +(k−3)x+k=0 (a) Find the value of k. (b) For this value of k, solve the equation for x (c)If x is the length of a rectangle and its width is x−2, find the area of the rectangle.

$$\mathrm{The}\:\mathrm{quadratic}\:\mathrm{equation}\:\:\mathrm{has}\:\mathrm{two}\:\mathrm{equal}\:\mathrm{roots}: \\ $$$$\:\:\:\:\:{x}^{\mathrm{2}} +\left({k}−\mathrm{3}\right){x}+{k}=\mathrm{0} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:{k}. \\ $$$$\left(\mathrm{b}\right)\:\mathrm{For}\:\mathrm{this}\:\mathrm{value}\:\mathrm{of}\:\:{k},\:\mathrm{solve}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{for}\:{x} \\ $$$$\left(\mathrm{c}\right)\mathrm{If}\:\:{x}\:\mathrm{is}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{a}\:\mathrm{rectangle}\:\mathrm{and}\:\mathrm{its}\:\mathrm{width}\:\mathrm{is}\:{x}−\mathrm{2},\:\:\mathrm{find}\:\mathrm{the}\:\mathrm{area}\: \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{rectangle}. \\ $$

Question Number 217032 Answers: 0 Comments: 0

Question Number 217024 Answers: 1 Comments: 0

Question Number 217030 Answers: 1 Comments: 0

Find all positive integers n such that n + 1 divides n^2 + 1

$$\mathrm{Find}\:\mathrm{all}\:\mathrm{positive}\:\mathrm{integers}\:\:\mathrm{n}\:\:\mathrm{such}\:\mathrm{that}\:\: \\ $$$$\:\mathrm{n}\:+\:\mathrm{1}\:\:\mathrm{divides}\:\:\mathrm{n}^{\mathrm{2}} \:+\:\mathrm{1} \\ $$

Question Number 216998 Answers: 0 Comments: 3

Question Number 216995 Answers: 3 Comments: 0

Find all prime numbers p and q such that p^2 − q^2 = 2024

$$\mathrm{Find}\:\mathrm{all}\:\mathrm{prime}\:\mathrm{numbers}\:\:\mathrm{p}\:\mathrm{and}\:\mathrm{q}\: \\ $$$$\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{p}^{\mathrm{2}} −\:\:\mathrm{q}^{\mathrm{2}} =\:\:\mathrm{2024} \\ $$

Question Number 217015 Answers: 2 Comments: 0

If f(2x + 1) = 3x + 5 Find f(x) = ?

$$\mathrm{If} \\ $$$$\mathrm{f}\left(\mathrm{2x}\:+\:\mathrm{1}\right)\:=\:\mathrm{3x}\:+\:\mathrm{5} \\ $$$$\mathrm{Find} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:=\:? \\ $$

Question Number 216990 Answers: 2 Comments: 0

(1) ∫(sec^2 x∙(√(tan x)))dx=?

$$\left(\mathrm{1}\right)\:\int\left(\mathrm{sec}^{\mathrm{2}} {x}\centerdot\sqrt{\mathrm{tan}\:{x}}\right){dx}=? \\ $$

Question Number 216983 Answers: 1 Comments: 0

Question Number 217075 Answers: 0 Comments: 3

Help me please... $\vv{AB}$ and $\vv{CD}$ are two vectors, and $\vv{AB}$ is not the zero vector. Prove that if the vectors $\vv{AB}$ and $\vv{CD}$ are colinear, then there exists a real number $ k $ such that $ \vv{CD} = k \vv{AB} $. (don't use coordinates !)

$$ \\ $$Help me please... $\vv{AB}$ and $\vv{CD}$ are two vectors, and $\vv{AB}$ is not the zero vector. Prove that if the vectors $\vv{AB}$ and $\vv{CD}$ are colinear, then there exists a real number $ k $ such that $ \vv{CD} = k \vv{AB} $. (don't use coordinates !)

Question Number 216959 Answers: 0 Comments: 0