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2 years ago

Complete the sentence. the roots of the equation x^2 - 8x - 48 = 0 are -4 and blank

Mathematics

2 answers:

prisoha [69]2 years ago

8 0

Answer:

12 is the answer.

Step-by-step explanation:

The best way to get the roots of the equation is to factorize the equation but when the factors are not possible then we should apply the quadratic equations formula to get the value of x.

Now we will try to factorize

x² - 8x -48 = 0

Now we multiply coefficient of highest degree term and constant term

48×1 = 48 which may be factored in 12×4. 8×6, 24×2.

Now we will choose 12×4 out of three because the 12-4 = 8 which is the coefficient of x.

Now its simple.

x²-12x + 4x -48 = 0

x(x -12) + 4(x-12) = 0

(x +4)(x-12) = 0

Therefore roots are x + 4 = 0

x = -4

and x - 12 = 0

x = 12

So the answer is 12.

Likurg_2 [28]2 years ago

3 0

Answer:

12 is the answer.

Step-by-step explanation:

We have given an equation.

x²-8x-48 = 0

We have given one root of equation. We have to find the other root of equation.

We use method of factoring to solve this.

Splitting the middle term, we have

x²-12x+4x-48 = 0

Making groups, we have

x(x-12)+4(x-12) = 0

Taking (x-12) common, we have

(x-12)(x+4) = 0

Applying Zero-Product Property, we have

x-12 = 0 or x+4 = 0

x = 12 or x = -4.

Hence, the roots of the given equation are -4 and 12.

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Answer:

The total amount accrued, principal plus interest, from compound interest on an original principal of $ 300.00 at a rate of 6% per year compounded 2 times per year over 0.5 years is $ 309.00.

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Step-by-step explanation:

a) How much will you have at the middle of the first year?

Using the formula

$A\:=\:P\left(1+\frac{r}{n}\right)^{nt}$

where

Principle = P

Annual rate = r

Compound = n

Time = (t in years)

A = Total amount

Given:

Principle P = $300

Annual rate r = 6% = 0.06 per year

Compound n = Semi-Annually = 2

Time (t in years) = 0.5 years

To determine:

Total amount = A = ?

Using the formula

$A\:=\:P\left(1+\frac{r}{n}\right)^{nt}$

substituting the values

$A=300\left(1+\frac{0.06}{2}\right)^{\left(2\right)\left(0.5\right)}$

$A=300\cdot \frac{2.06}{2}$

$A=\frac{618}{2}$

$A=309$ $

Therefore, the total amount accrued, principal plus interest, from compound interest on an original principal of $ 300.00 at a rate of 6% per year compounded 2 times per year over 0.5 years is $ 309.00.

Part b) How much at the end of one year?

Using the formula

$A\:=\:P\left(1+\frac{r}{n}\right)^{nt}$

where

Principle = P

Annual rate = r

Compound = n

Time = (t in years)

A = Total amount

Given:

Principle P = $300

Annual rate r = 6% = 0.06 per year

Compound n = Semi-Annually = 2

Time (t in years) = 1 years

To determine:

Total amount = A = ?

so using the formula

$A\:=\:P\left(1+\frac{r}{n}\right)^{nt}$

so substituting the values

$A\:=\:300\left(1+\frac{0.06}{2}\right)^{\left(2\right)\left(1\right)}$

$A=300\cdot \frac{2.06^2}{2^2}$

$A=318.27$ $

Therefore, the total amount accrued, principal plus interest, from compound interest on an original principal of $ 300.00 at a rate of 6% per year compounded 2 times per year over 1 year is $ 318.27.

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2 years ago

Complete the sentence. the roots of the equation x^2 - 8x - 48 = 0 are -4 and *blank*

Complete the sentence. the roots of the equation x^2 - 8x - 48 = 0 are -4 and blank