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BartSMP [9]
2 years ago
8

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

Mathematics
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

#SPJ1

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7 0
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


5 0
3 years ago
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