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2 years ago

The polynomial x^3-kx^2+kx+2 has a factor of (x-2). What is the value of k?

1 answer:

5 0

$\text{Let}~ f(x) = x^3-kx^2 +kx +2.\\\\\text{If}~ x-2~ \text{is a factor of}~ f(x)~ \text{then,}\\ \\f(2) =0\\\\\implies 2^3-k\cdot 2^2 +2k+2 =0\\\\\implies -4k+2k+8+2=0\\\\\implies 10-2k=0\\\\\implies 2k =10\\\\\implies k= \dfrac{10}2 = 5\\\\\\\text{Hence, the value of k is 5.}$

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Audrey has 32 dimes and quarters in her piggy bank with a total value of $6.50. how many of the coins are dimes and how many are

fgiga [73]

D + q = 32....d = 32 - q
0.10d + 0.25q = 6.50

0.10(32 - q) + 0.25q = 6.50
3.20 - 0.10q + 0.25q = 6.50
-0.10q + 0.25q = 6.50 - 3.20
0.15q = 3.30
q = 3.30 / 0.15
q = 22 <=== 22 quarters

d + q = 32
d + 22= 32
d = 32 - 22
d = 10 <=== 10 dimes

7 0

3 years ago

Name the algebraic property demonstrated in the example below.

svp [43]

Commutative property of multiplication

5 0

3 years ago

Which number is an integer? Negative three-fourths 0 2. 3 Pi.

elena55 [62]

The number that is an integer is 0.

An integer is a number that does not have fractions or decimals. Examples of integers are 50, - 1. A fraction is a number that is made up of numerators and denominators. An example is 3/4. A decimal is made up of tenths, hundredths and thousandths. An example is 2.3.

Negative three-fourths is not an integer because it is a fraction. 2.3 and pi is not an integer because it is a decimal.

A similar question was answered here: brainly.com/question/15984496

5 0

2 years ago

The Henley's took out a loan for $195,000 to purchase a home. At a 4.3% interest rate

ella [17]

Interest paid after 30 years is $494,546.99.

Solution:

Principal (P) = $195,000

Interest rate (r) = 4.3%

Time (t) = 30 years

n = number of times interest calculated per year

n = 1

Compound interest formula:

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

where A is the final amount

$$A=195000\left(1+\frac{4.3\%}{1}\right)^{1\times 30}$

$$A=195000\left(1+\frac{4.3}{100}\right)^{30}$

$$A=195000\left(\frac{100+4.3}{100}\right)^{30}$

$$A=195000\left(\frac{104.3}{100}\right)^{30}$

A = 689546.99

Interest = Amount - Principal

= 689546.99 - 195000

= 494546.99

Interest paid after 30 years is $494,546.99.

6 0

3 years ago

4,284 passengers traveling by the intercity bus every day, the intercity bus operates 6 hours every day, find the number of pass

Lemur [1.5K]

Answer:

714

Step-by-step explanation:

So lets go over what we know.

The bus only goes for 6 hours each day.

So lets just think of a full day as 6 hours.

Each day(6 hours), 4284 passangers ride the bus.

To find passangers per hour, we must divide the total passangers by the total hours.

This is 4284(total passangers) divided by 6(total hours):

4284/6

714

So each hour, there are 714 passangers.

Hope this helps!

7 0

3 years ago