All categories

3 years ago

What is the correct factorization of: x? - 11x + 18

Mathematics

1 answer:

Dominik [7]3 years ago

8 0

9514 1404 393

Answer:

x² -11x +18 = (x -9)(x -2)

Step-by-step explanation:

The x-coefficient is the sum of the constants in the binomial factors; the constant term is their product. It usually works well to look for factors of the constant that have the right sum. Here, both must be negative.

18 = (-1)(-18) = (-2)(-9) = (-3)(-6)

The factors -2 and -9 have a sum of -11, so those are the binomial constants of interest. The factorization is ...

x² -11x +18 = (x -9)(x -2)

You might be interested in

During the exponential phase, E. coli bacteria in a culture increase in number at a rate proportional to the current population.

NikAS [45]

Answer:

197.2 million

Step-by-step explanation:

The appropriate exponential equation for the population is ...

p(t) = 172.0e^(0.019t)

Then we can compute for t=7.2:

p(7.2) = 172.0e^(0.019·7.2) ≈ 172.0·1.146599 ≈ 197.2

7.2 minutes from now, the population will be about 197.2 million.

___

For continuous growth (or continuous compounding), the exponential formula is ...

f(t) = (value at t=0)×e^(rt)

where r is the growth rate in one unit of time, and t is the number of time periods.

8 0

3 years ago

A boat that sold for $12,500 had a sales tax of $562.50. How much is the tax on a boat that sells for $9,550?

Degger [83]

Answer:

$429.75

Step-by-step explanation:

First, find the tax rate on the sale of the boat: Let r represent that rate. Then,

$12,500r = $562.50. Solving for r, we get r = $562.50 / $12,500 = 0.045

The tax rate is 0.045, or 4.5%.

Applying this tax rate to a boat selling for $9,550:

0.045($9,550) = $429.75. This is the amount of tax on the 2nd boat.

7 0

3 years ago

Raphael dives a standard-sized dump truck. The dimensions of the bed of the truck are length 25 feet,width 8 feet , and height 6

astra-53 [7]

25×8×6
1200 square feet

4 0

3 years ago

Read 2 more answers

Ms. Nina has 10 lbs of 25% sugar syrup. How much water does she need to add to make 10% sugar syrup?

ryzh [129]

She has 10lbs of 25% syrup... so, in the 10lbs, 25% of that is syrup, the rest, namely the 75% remaining is water or other substances.

let's say she adds "x" lbs of water, to get "y" lbs for the 10% mixture.

how much is 25% of 10lbs? well, (25/100) * 10, or 2.5.

the water has no sugar syrup in it, so is just pure water, so the amoun of syrup in it is 0%, how much is 0% of "x" lbs? well, (0/100) * x, or 0.00x, which is just 0.

how much is 10% of "y" lbs? well (10/100) * y, or 0.10y.

whatever "x" and "y" are, we know that 10 + x = y.

we also know that the syrup amount in that is also 2.5 + 0.00x = 0.10y, thus

$\bf \begin{array}{lccclll}
&\stackrel{lbs}{syrup}&\stackrel{concentration~\%}{syrup}&\stackrel{concentration}{amount}\\
&------&------&------\\
\textit{25\% syrup}&10&0.25&2.5\\
\textit{pur water}&x&0.00&0.00x\\
------&------&------&------\\
\textit{10\% mixture}&y&0.10&0.10y
\end{array}
\\\\\\
\begin{cases}
10+x=\boxed{y}\\
2.5+0.00x=0.10y\\
----------\\
2.5 = 0.10\left( \boxed{10+x} \right)
\end{cases}
\\\\\\
2.5=1 + 0.10x\implies 1.5=0.10x
\\\\\\
\cfrac{1.5}{0.10}=x\implies 15=x$

8 0

3 years ago

Read 2 more answers

What is the value of side b?<br> A 20<br> B 15<br> C 10<br> D 5

Pavel [41]

I am not able to see the picture

3 0

2 years ago

Read 2 more answers