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2 years ago

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When solving the linear equation, ax + b = 0 where a≠ 0, what is the answer of the equation x = -b/a referred as?

1 answer:

Oksi-84 [34.3K]2 years ago

7 0

In a system of equations ax + b = 0, a≠ 0, the equation x = -b/a is referred as a non-trivial solution.

<h3>What is a system of equations?</h3>

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

The system Ax + b = 0 has the following solutions:

The zeros, which is the trivial solution.

x = -b/a, which is the non-trivial solution.

More can be learned about a system of equations at brainly.com/question/24342899

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kati45 [8]

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3 years ago

Find S12 for geometric series: (-7.5) + 15 + (-30) + ...

kolezko [41]

Answer:

S12 for geometric series: (-7.5) + 15 + (-30) + ... would be: 10237.5

Step-by-step explanation:

Given the sequence to find the sum up-to 12 terms

$(-7.5) + 15 + (-30) + ...$

As we know that

A geometric sequence has a constant ratio 'r' and is defined by

$a_n=a_1\cdot r^{n-1}$

$\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{a_{n+1}}{a_n}$

$\frac{15}{\left(-7.5\right)}=-2,\:\quad \frac{\left(-30\right)}{15}=-2$

$\mathrm{The\:ratio\:of\:all\:the\:adjacent\:terms\:is\:the\:same\:and\:equal\:to}$

$r=-2$

$\mathrm{The\:first\:element\:of\:the\:sequence\:is}$

$a_1=\left(-7.5\right)$

$a_n=a_1\cdot r^{n-1}$

$\mathrm{Therefore,\:the\:}n\mathrm{th\:term\:is\:computed\:by}\:$

$a_n=\left(-7.5\right)\left(-2\right)^{n-1}$

$a_n=-\left(-2\right)^{n-1}\cdot \:7.5$

$\mathrm{Geometric\:sequence\:sum\:formula:}$

$a_1\frac{1-r^n}{1-r}$

$\mathrm{Plug\:in\:the\:values:}$

$n=12,\:\spacea_1=\left(-7.5\right),\:\spacer=-2$

$=\left(-7.5\right)\frac{1-\left(-2\right)^{12}}{1-\left(-2\right)}$

$=-7.5\cdot \frac{1-\left(-2\right)^{12}}{1+2}$

$\mathrm{Multiply\:fractions}:\quad \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}$

$=-\frac{-30712.5}{1+2}$ ∵ $\left(1-\left(-2\right)^{12}\right)\cdot \:7.5=-30712.5$

$=-\frac{-30712.5}{3}$

$=\frac{30712.5}{3}$

$=10237.5$

Thus, S12 for geometric series: (-7.5) + 15 + (-30) + ... would be: 10237.5

5 0

3 years ago

Question - Find each f(c) using synthetic substitution. f(x) =5x 5 + 10x 4 + 3x 3 + 8x 2 – 6x – 3; c = 3

SpyIntel [72]

Answer:

2157

Step-by-step explanation:

The given function is

$f(x)=5x^5+10x^4+3x^3+8x^2-6x-3$

We want to find f(c) when c=3.

This means the remainder when f(x) is divided by x-3

We perform the synthetic division:

5 10 3 8 -6 -3

<u>3| 15 75 234 726 2160</u>

5 25 78 242 720 2157

Therefore the remainder is 2157

You are right

7 0

3 years ago

If R1 and R2 are the roots of x^2+4x-5=0

professor190 [17]

Factor to find the roots.
(x+5)(x-1)=0

Proof:
5-1=4
5*-1=-5

Then apply the Zero Product Property.
(x+5)=0
x=-5

(x-1)=0
x=1

Roots: x=-5, x=1

3 0

3 years ago

1- Caleb's family room has the dimensions shown. He needs to find the area of the room so that he knows how much carpet to buy.

Rina8888 [55]

Answer: $20\frac{11}{32}\ sq\ yd$

Step-by-step explanation:

Given: The width of the room = $3\frac{7}{8}\ yd=\frac{31}{8}\ yd$

The length of the room = $1\frac{5}{4}\ yd=\frac{21}{4}\ yd$

The area of the rectangular room= $length \times width$

⇒The area of the rectangular room= $\frac{21}{4}\times\frac{31}{8}\ sq\ yd$

⇒The area of the rectangular room= $\frac{651}{32}\ sq\ yd$

⇒The area of the rectangular room= $20\frac{11}{32}\ sq\ yd$

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3 years ago

Read 2 more answers