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3 years ago

What are the solutions of the equation 4x2 + 3x = 24 – x?

Mathematics

2 answers:

goldenfox [79]3 years ago

6 0

Answer:

x=2 or x=-3

Step-by-step

hope this helps

DENIUS [597]3 years ago

3 0

Answer:

x = -3 or x = 2

Step-by-step explanation:

Re-arrange the terms into the standard quadratic equation form:

4x2 + 3x = 24 – x => 4x^2 + 4x - 24 = 0

Note that we can divide all four terms by 4, obtaining:

x^2 + x - 6 = 0 = (x + 3)(x - 2)

Then x = -3 or x = 2 are the desired solutions.

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The reacttimes data set has 50 observations of human reaction times to a physical stimulus. The reaction times are named times a

scoundrel [369]

Solution: The formula for mean is:

$Mean=\frac{\sum x}{n}$

Where:

$\sum x$ is the sum of given observations

$n$ is the number of observations

$\sum x=87.12$

$n=50$

$\therefore Mean =\frac{87.12}{50}= 1.74$ rounded to two decimal places

To find the median, we need to first arrange the data in ascending order but we are already given the data in ascending order.

Therefore, the median is:

$Median=\left(\frac{n+1}{2} \right)^{th} item$

$=\left(\frac{51}{2} \right)^{th} item$

$=25.5^{th} item$

$=1.52+0.5(1.54-1.52)$

$=1.52+0.01$

$=1.53$

Therefore, the median = 1.53

4 0

3 years ago

Find the generating function for the sequence 1,1,1,2,3,4,5,6,....

marin [14]

Answer:

$P(x)=\dfrac{1}{1-x}+\dfrac{x^3}{(1-x)^2} \quad \text{for} \mid x \mid < 1$ [/tex]

Step-by-step explanation:

The generating function of a sequence is the power series whose coefficients are the elements of the sequence. For the sequence

$1,1,1,2,3,4,5,6,...$

the generating function would be

$P(x)=1+x+x^2+2x^3+3x^4+4x^5+5x^6+...\\$

we can multiply P(x) by x to get

$xP(x)=x+x^2+x^3+2x^4+3x^5+4x^6+...$

Note that

$P(x)-xP(x)=1+(2x^3-x^3)+(3x^4-2x^4)+(4x^5-3x^5)+(5x^6-4x^6)+...\\ \\=1+x^3+x^4+x^5+x^6+...=1+x^3(1+x+x^2+x^3+x^4+...)$

which for $\mid x \mid < 1$ can be rewritten as

$(1-x)P(x)=1+\dfrac{x^3}{(1-x)} \quad \Rightarrow \\\\P(x)=\dfrac{1}{(1-x)}+\dfrac{x^3}{(1-x)^2}$

8 0

3 years ago

Someone help me please

galben [10]

Answer:

∛27 = 3

Step-by-step explanation:

A radical is simply a fractional exponent: $a^{(\frac{m}{n})} = \sqrt[n]{a^{m} }$

Hence, ∛27 = $27^{(\frac{1}{3})}$

Since 27 = 3³, then:

You could rewrite ∛27 as ∛(3)³.

$\sqrt[3]{3^{(3)} } = 3^{[(3)*(\frac{1}{3})]}$

Multiplying the fractional exponents (3 × 1/3) will result in 1 (because 3 is the <u><em>multiplicative inverse</em></u> of 1/3). The multiplicative inverse of a number is defined as a number which when multiplied by the original number gives the product as 1.

Therefore, ∛27 = 3.

3 0

3 years ago

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The formula for centripetal acceleration, a, is given below, where v is the velocity of the object and r is the object's distanc

julsineya [31]

Answer:

Step-by-step explanation:

For this case we have the following equation:

a = v ^ 2 / r

From here, we must clear the value of speed.

We have then:

v ^ 2 = a * r

v = root (a * r)

Answer:

the formula for the velocity is:

v = root (a * r)

3 0

3 years ago

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What is an expression for vector x involving vector r, vector s, and vector t?

navik [9.2K]

X = -3r + s - t ....

3 0

4 years ago