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tia_tia [17]
2 years ago
14

Find all of the roots of the equation.

Mathematics
1 answer:
kakasveta [241]2 years ago
5 0

I think it's letter C.

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for the polynomial P(x)=4x^2-5x+6 and c =1, find p(c) by (a. direct substitution and (b. the remainder theorem
nata0808 [166]
p(x)=4x^2-5x+6

c=1\implies p(c)=4(1)^2-5(1)+6=5

By the remainder theorem, the remainder upon dividing a polynomial p(x) by a linear binomial x-c is equal to p(c). Via synthetic division, we get

1   |  4   -5   6
.    |        4  -1
- - - - - - - - - - -
.    |  4   -1   5

which translates to

\dfrac{4x^2-5x+6}{x-1}=4x-1+\dfrac5{x-1}

or

4x^2-5x+6=(4x-1)(x-1)+5

Indeed, when x=1, the first term on the right hand side vanished and we're left with 5.
8 0
3 years ago
Macy's is having a Fall sale where everything is 30% off. Angela has a coupon for an additional 10%
givi [52]

Answer:

$113.40

Step-by-step explanation:

The dress is $180 subtracted by 30% ($54) and is now $126

$126 - 10% which is $12.60 and is now $113.40

5 0
3 years ago
sing traditional methods, it takes 108108 hours to receive a basic driving license. A new license training method using Computer
solniwko [45]

Answer:

z_{stat} = -1.50            

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 108

Sample mean, \bar{x} = 107

Sample size, n = 110

Alpha, α = 0.02

Population standard deviation, σ = 7

Formula:

z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }

Putting all the values, we have

z_{stat} = \displaystyle\frac{107 - 108}{\frac{7}{\sqrt{110}} } = -1.50

The test statistic is -1.50

8 0
3 years ago
Aimee and Ben are purchasing a condominium and are financing $160,000. The mortgage is a 20 year 3/1 ARM with a cap structure of
yarga [219]

Answer:

$1169.45

Step-by-step explanation:

Using the formula:

P = L \Big( \dfrac{c(1+c)^n}{(1+c^n) -1} \Big)

where;

Loan amount L = 160000

number of months (n) = 20 × 12 = 240

Lets assume that the interest rate per month c = 6.25% since it is not given.

i.e. (6.25/( 100*12) ) = 5.208 × 10⁻³

∴

P = 160000 * \dfrac{5.208 *10^{-3} (1+5.208 *10^{-3})^{240}}{(1+5.208 *10^{-3})^{240}-1}

P = $1169.45

6 0
3 years ago
Given the following sets. A = {0, 1, 2, 3} B = {a, b, c, d} C = {0, a, 2, b} Find A C.
strojnjashka [21]
AC = {0,2}

this is because it is what they have in common
8 0
3 years ago
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