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3 years ago

Determine the discriminant for the given equation x^2+4x+5=0. Then describe the roots(how many and what type).

1 answer:

3 0

Discriminant = b^2 - 4ac, where a, b and c come from the form of the quadratic equation as ax^2 + bx + c

Discriminant = (4)^2 - 4(1)(5)
= 16 - 20
= -4

-4 < 0, therefor there are no roots

(If the discriminant = 0, then there is one root
If the discriminant > 0, there are two roots, and if it is a perfect square (eg. 4, 9, 16, etc.) then there are two rational roots
If the discriminant < 0, there are no roots)

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What is the factored form of the polynomial?

Ilya [14]

(x-9)(x-3), because -9 and -3 make a sum of -12 and a product of +27

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2 years ago

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Find the first term of the arithmetic sequence in which a38= -5 and the common difference is -2.9

mestny [16]

Answer:

102.3

Step-by-step explanation:

a_38 = -5

difference d= -2.9

We use general formula

$a_n = a_1 + (n-1)d$

WE make the formula for a_38 th term

Plug in 38 for n

$a_{38} = a_1 + (38-1)d$

Now plug in -2.9 for d and -5 for a_38

$-5 = a_1 + (38-1)(-2.9)$

$-5 = a_1 - 107.3$

Now add 107.3 on both sides

102.3 = a_1

option A is correct

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2 years ago

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You are given f(0) = 1 and g(0) = -2 and g(1) = 3. What is g ∘ f ( 0 ) equal to?

Sergeu [11.5K]

Answer:

g∘f (0) = 1

Explanation:

The composition of the functions f and g represented by g ∘ f ( 0 ) means that g is applied to f(0), i.e f(0) is the input to the function g.

Since f(0) = 1, you are going fo find g(1):

$$ g\circ f(x)=g(f(x)) $\\\\$ g\circ f(0)=g(f(0)) $\\\\$ g\circ f(0)=g(1) $=3$

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2 years ago

I will mark as BRAINLIEST and 8 points if correct.

g100num [7]

Answer:

the answer is d

Step-by-step explanation:

6 0

2 years ago

The 5th term in a geometric sequence is 160. The 7th term is 40. What are possible values of the 6th term of the sequence?

omeli [17]

Answer:

C. The 6th term is positive/negative 80

Step-by-step explanation:

Given

Geometric Progression

$T_5 = 160$

$T_7 = 40$

Required

$T_6$

To get the 6th term of the progression, first we need to solve for the first term and the common ratio of the progression;

To solve the common ratio;

Divide the 7th term by the 5th term; This gives

$\frac{T_7}{T_5} = \frac{40}{160}$

Divide the numerator and the denominator of the fraction by 40

$\frac{T_7}{T_5} = \frac{1}{4}$ ----- equation 1

Recall that the formula of a GP is

$T_n = a r^{n-1}$

Where n is the nth term

So,

$T_7 = a r^{6}$

$T_5 = a r^{4}$

Substitute the above expression in equation 1

$\frac{T_7}{T_5} = \frac{1}{4}$ becomes

$\frac{ar^6}{ar^4} = \frac{1}{4}$

$r^2 = \frac{1}{4}$

Square root both sides

$r = \sqrt{\frac{1}{4}}$

r = ± $\frac{1}{2}$

Next, is to solve for the first term;

Using $T_5 = a r^{4}$

By substituting 160 for T5 and ± $\frac{1}{2}$ for r;

We get

$160 = a \frac{1}{2}^{4}$

$160 = a \frac{1}{16}$

Multiply through by 16

$16 * 160 = a \frac{1}{16} * 16$

$16 * 160 = a$

$2560 = a$

Now, we can easily solve for the 6th term

Recall that the formula of a GP is

$T_n = a r^{n-1}$

Here, n = 6;

$T_6 = a r^{6-1}$

$T_6 = a r^5$

$T_6 = 2560 r^5$

r = ± $\frac{1}{2}$

So,

$T_6 = 2560( \frac{1}{2}^5)$ or $T_6 = 2560( \frac{-1}{2}^5)$

$T_6 = 2560( \frac{1}{32})$ or $T_6 = 2560( \frac{-1}{32})$

$T_6 = 80$ or $T_6 = -80$

$T_6 =$ ±80

Hence, the 6th term is positive/negative 80

8 0

2 years ago