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Dovator [93]
3 years ago
5

Define variables and write each phrase as an algebraic expression for ten more than Ruben

Mathematics
2 answers:
statuscvo [17]3 years ago
6 0
Variables are those unknowns which could have more than one value, and Algebraic expression is an expression that contains numbers, variables(EX, x and y) and Operations (EX,-, +).

maxonik [38]3 years ago
3 0
This is awfully general.  Ruben has or does something.  Whatever.  Let's call that Whatever "r."  Then the expression in question is  "r+10."
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The difference between the roots of the equation 3x2+bx+10=0 is equal to 4 1 3 . find<br> b.
inna [77]
Given that the difference between the roots of the equation 3x^2+bx+10=0 is 4 \frac{1}{3} = \frac{13}{3}.

Recall that the sum of roots of a quadratic equation is given by - \frac{b}{a}.

Let the two roots of the equation be \alpha and \alpha + \frac{13}{3}, then 

\alpha + \alpha + \frac{13}{3} =2 \alpha + \frac{13}{3} =- \frac{b}{a} =- \frac{b}{3}  \\  \\ i.e.\ \ 2 \alpha + \frac{13}{3}=- \frac{b}{3} . . . (1)

Also recall that the product of the two roots of a quadratic equation is given by \frac{c}{a}, thus:

\alpha \left( \alpha + \frac{13}{3} \right)= \alpha ^2+ \frac{13}{3} \alpha = \frac{c}{a} = \frac{10}{3}  \\  \\ i.e.\ \ \alpha ^2+ \frac{13}{3} \alpha=\frac{10}{3} . . . (2)

From (1), we have:

2 \alpha =- \frac{b}{3} - \frac{13}{3}  \\  \\ \Rightarrow \alpha =- \frac{b}{6} - \frac{13}{6}

Substituting for alpha into (2), gives:

\left(- \frac{b}{6} - \frac{13}{6}\right)^2+ \frac{13}{3} \left(- \frac{b}{6} - \frac{13}{6}\right)= \frac{10}{3}  \\  \\ \Rightarrow \frac{b^2}{36} + \frac{13b}{18} + \frac{169}{36} - \frac{13b}{18} - \frac{169}{18} = \frac{10}{3}  \\  \\ \Rightarrow \frac{b^2}{36} - \frac{289}{36} =0 \\  \\ \Rightarrow \frac{b^2}{36} = \frac{289}{36}  \\  \\ \Rightarrow b^2=289 \\  \\ \Rightarrow b=\pm\sqrt{289}=\pm17
5 0
3 years ago
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Zinaida [17]

Answer:

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Step-by-step explanation:

6 0
2 years ago
Here are some points, have a good day!
Mnenie [13.5K]

Answer:

.....

Step-by-step explanation:

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6 0
2 years ago
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Which sequence of transformations could be used to map triangle MNO onto M”N”O”?
Bumek [7]

Answer:

Option D

Step-by-step explanation:

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3 0
2 years ago
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If you help ill give you some of my banana milk...
snow_tiger [21]

Given:

The function is:

f(x)=4x^2-25x-21

To find:

The domain of the given function.

Solution:

Domain is the set of input values.

We have,

f(x)=4x^2-25x-21

It is a quadratic polynomial.

We know that a quadratic polynomial is defined for all real values of x. So, the given function is defined for all real values of x and the domain of the given function is:

Domain = Set of all real number

Domain = (-∞,∞)

Therefore, the correct option is B.

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