A rectangle has vertices (-1, 1), (-4, 1), (-1, 3), and (-4, 3). If the

A polynomial function has a zero at 4 (multiplicity 3) and 0 (multiplicity 1). Write a function in standard form that can repres

VLD [36.1K]

Answer:

(x^4) - 64x

Step-by-step explanation:

zeros at 4 and 0 are the roots so can be factor as x*(x-4) and the multiplicity tels to what power you have to raise those factors

$x^{1} *(x-4)^{3}$ becuase multiplicity of 1 for root at 0, and multiplicity of 3 at root 4

now to write this in standard form

$x*(x-4)^{3} = \\x*(x-4)(x^{2} +4x+16)= \\(x^{2} -4x)(x^{2} +4x+16) = \\x^{4} +4x^{3} +16x^{2} -4x^{3} -16x^{2} -64x = \\x^{4} -64x$

8 0

3 years ago

how much water must be added to a 6-liter solution that contains 7% extract of baneberry to get a solution that contains 5% extr

SpyIntel [72]

Answer:

the water to be added is 0.2 L

Step-by-step explanation:

The computation of the water to be added is given below:

The banberry amount is

= 7% of 6 Liters

= 0. 42L

Now

Let us assume the amount of water added be x L

So, the total solution is

= 6+ x L

Now percentage of banberry is

= 0.42 × 100 ÷ (6+x)

5 = 0.42 × 100 ÷ (9 + x)

9 + x = 9.2

x = 0.2 L

hence, the water to be added is 0.2 L

6 0

3 years ago

What is the rule of 72 used to determine? A. the approximate time it takes an investment to triple in value B. the approximate t

ValentinkaMS [17]

Answer:

Step-by-step explanation:

This can be derived using the formula to calculate future value of an amount which is given as:

FV=PV(1+i)^{n}

Where

FV is the future value

PV is the present value

i is the compound interest rate

n is the time period

To calculate how much time it takes to triple an amount, let's substitute $1 in place of PV and $3 in place of FV in the above equation.

3=(1+i)^{n}

Taking natural log on both sides, we get

log_{e} 3= n log_{e}(1+i)

n={\log_{e}3}/{log_{e}(1+i)}....................(1)

Using some log magic, this formula can also be written as

n=log_{(1+i)}3................(2)

Both equations (1) and (2) work fine.

(b)

In order to derive a rule 72 style formula start from equation (1) above. In that formula, we can say that for small values of interest rate,

log_{e}(1+i) ~ i ( This is a property of log)

Substituting this is equation (1), we get

n=log_{e}3/{i}

n={1.098}/{i}

Since, we want to use i as an integer and not as a percentage (so, 3% will be used as 3 and not 0.03), we multiply the RHS by 100

n={109.8}/{i}

and then to make it cleaner, we round off 109.8 to 110.

n={110}/{i}

Now, many times, people round this 109.8 off to 114. This is to make the calculations a little bit easier as 114 is number that has a lot of factors. So, if the numerator is rounded off to 114, the formula becomes

n={114}/{i}

6 0

3 years ago

Read 2 more answers

Please help me

jeyben [28]

Use Pythagorean theorem
a^2 + b^2 = c^2
Other words, lengths of the shortest sides squared are equal to the longest squared

a^2 + 9^2 = 15^2
a^2 + 81 = 225
a^2 = 144
a = squareroot of 144
a = 12

Solution: a = 12

8 0

3 years ago

Jamie needs to build a fence around his garden, as illustrated by polygon ABCDEF on the coordinate grid below. If each unit repr

NNADVOKAT [17]

Answer:

C. 26 yards

Step-by-step explanation:

Jamie's fence total length = perimeter of the polygon

Perimeter of the polygon = AB + BC + CD + DE + EF + FA

AB, FA and DE can be worked accordingly as shown below:

AB = |-5 - 0| = 5 units

FA = |5 - 2| = 3 units