If three times a number plus four is no more than four times the number minus one, which of the

Mathematics

2 answers:

pychu [463]3 years ago

6 0

The number is at least 5

VikaD [51]3 years ago

6 0

Answer:

Step-by-step explanation:

3z+4≤4z-1

3z-4z≤-1-4

-z≤-5

z≥5

sol.

The number is at least 5

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HALP MEEEEEEEEEEEEEEE

nevsk [136]

Answer:

-1, 9, - 21, 69

Step-by-step explanation:

Given recursive formula:

a₁ = -1
aₙ = - 3aₙ₋₁ + 6 for n ≥ 2

The first 4 terms are:

a₁ = - 1, given
a₂ = - 3*(-1) + 6 = 3 + 6 = 9
a₃ = - 3*(9) + 6 = - 27 + 6 = - 21
a₄ = - 3*(-21) + 6 = 63 + 6 = 69

6 0

3 years ago

Solve 5x^2 - 7x + 2 = 0 by completing the square.

Reika [66]

Answer: The correct option is (c) $\dfrac{49}{100}.$

Step-by-step explanation: We are given to solve the following quadratic equation by the method of completing the square:

$5x^2-7x+2=0~~~~~~~~~~~~~~~~~~~(i)$

Also, we are to find the constant added on both sides to form the perfect square trinomial.

We have from equation (i) that

$5x^2-7x+2=0\\\\\Rightarrow x^2-\dfrac{7}{5}x+\dfrac{2}{5}=0\\\\\\\Rightarrow x^2-2\times x\times \dfrac{7}{10}+\left(\dfrac{7}{10}\right)^2+\dfrac{2}{5}=\left(\dfrac{7}{10}\right)^2\\\\\\\Rightarrow \left(x-\dfrac{7}{10}\right)^2=\dfrac{49}{100}-\dfrac{2}{5}\\\\\\\Rightarrow \left(x-\dfrac{7}{10}\right)^2=\dfrac{49-40}{100}\\\\\\\Rightarrow \left(x-\dfrac{7}{10}\right)^2=\dfrac{9}{100}\\\\\\\Rightarrow x-\dfrac{7}{10}=\pm\dfrac{3}{10}\\\\\\\Rightarrow x=\pm\dfrac{3}{10}+\dfrac{7}{10}.$

So,

$x=\dfrac{3}{10}+\dfrac{7}{10},~~~~~~~~x=-\dfrac{3}{10}+\dfrac{7}{10}\\\\\\\Rightarrow x=\dfrac{10}{10},~~~~~~~~\Rightarrow x=\dfrac{-3+7}{10}\\\\\\\Rightarrow x=1,~-\dfrac{2}{5}.$

Thus, the required solution is $x=1,~-\dfrac{2}{5}.$ and the value of the constant added is $\dfrac{49}{100}.$

Option (c) is correct.

3 0

3 years ago

If x+1 and x-1 are the factors of the polynomial ax^3 + x^2 - 2x +b,find the values of a and b

Nadusha1986 [10]

The polynomial remainder theorem says that dividing a polynomial $p(x)$ by $x-c$ leaves a remainder of $p(c)=0$ if $x-c$ is a factor of $p(x)$ . In this case, check $c=-1$ and $c=1$ .