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Alexandra [31]
3 years ago
9

A math class is having a discussion on how to determine if the expressions 4 x minus x + 5 and 8 minus 3 x minus 3 are equivalen

t using substitution. The class has suggested four different methods.
Mathematics
2 answers:
dedylja [7]3 years ago
5 0

Answer:

They are NOT equivalent

Step-by-step explanation:

4x-x+5 and 8-3x-3

<u>simplify</u>

3x+5 and 5x-3

NikAS [45]3 years ago
3 0
4x-x+5 = 8x-3x-3
4x - x = 3x
8x - 3x = 5x
5 = 2x-3
+3
8= 2x
x=4
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Please i need an answer urgently. Sum of 3 terms are 252, first term is 192. Find common ratio
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Answer:

r=\frac{1}{4}\\\\r=-\frac{5}{4}

Step-by-step explanation:

<u>Geometric Sequences</u>

The geometric sequence is given as:

a_1, a_1r, a_1r^2, a_1r^3,..., a_1r^{n-1}

Where n is the number of the term, n≥1, and r is the common ratio.

The sum of n terms of the geometric sequence is given by:

\displaystyle S_n=a_1\frac{r^n-1}{r-1}

We are given: S3=252, a1=192, thus substuting:

\displaystyle 252=192\frac{r^3-1}{r-1}

Dividing by 12:

\displaystyle 21=16\frac{r^3-1}{r-1}

Recall that:

r^3-1=(r-1)(r^2+r+1)

Substituting:

\displaystyle 21=16\frac{(r-1)(r^2+r+1)}{r-1}

Simplifying:

21=16(r^2+r+1)=16r^2+16r+16

Rearranging:

16r^2+16r+16-21=0

16r^2+16r-5=0

Rewriting:

16r^2-4r+20r-5=0

Factoring:

4r(4r-1)+5(4r-1)=0

(4r-1)(4r+5)=0

Solving:

r=\frac{1}{4}\\\\r=-\frac{5}{4}

Both solutions are valid

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Step-by-step explanation:

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