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1 year ago

what are some advantages of writing the polynomial expression -7x^2+32x+240 in factored form when interpreting this situation

Mathematics

1 answer:

hammer [34]1 year ago

6 0

Step-by-step explanation:

The advantages of writing the polynomial expression

-7 $x^{2}$ + 32x + 240 in factored form when interpreting this

situation

Factorizing the quadratic equation gives

-7 $x^{2}$ + 32x + 240

-7 $x^{2}$ +60x - 28x + 240

x×(-7x + 60) -4 ×(-7x + 60)

(x-4)×(-7x + 60)

The roots of the equation 4,-60/7

Advantages of writing the polynomial expression in factored

we directly know the roots

we can easily draw the graph of the quadratic

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1 year ago

Read 2 more answers

3. After completing a statistical analysis of a survey of 40 students, the principal

Serhud [2]

Answer:

Option A

Step-by-step explanation:

A type I error is committed when a researcher rejects the null hypothesis when it is actually true.

The null hypothesis is: U <= 50%

The alternative is: U > 50%

Thus, the principal could have committed an error by rejecting null hypothesis and concluding that more than 50% of students want earlier lunch, when in actuality 50% or less want earlier lunch.

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1 year ago

Shopping for a freezer, Manuit finally settled on one with a purchase price of $850. The annual cost of operating the freezer is

MatroZZZ [7]

Answer:

In 12 months

Step-by-step explanation:

Let a = year when average the average cost of owning a freezer would be less than $117

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1 year ago

Expand (2x-3y)^4 using Pascal's Triangle. Show work

deff fn [24]

(2x+3y)⁴
1) let 2x = a and 3y = b

(a+b)⁴ = a⁴ + a³b + a²b² + ab³ + b⁴
Now let's find the coefficient of each factor using Pascal Triangle

0 | 1
1 | 1 1
2 | 1 2 1
3 | 1 3 3 1
4 | 1 4 6 4 1

0,1,2,3,4,.. represent the exponents of binomials
Since our binomial has a 4th exponents, the coefficients are respectively:

(1)a⁴ + (4)a³b + (6)a²b² + (4)ab³ + (1)b⁴
Now replace a and b by their real values in (1):

2⁴x⁴ +(4)8x³(3y) + (6)(2²x²)(3²y²) + (4)(2x)(3³y³) + (1)(3⁴)(y⁴)

16x⁴ + 96x³y + 216x²y² + 216xy³ + 81y⁴

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1 year ago

For the binomial expansion of (x + y)^10, the value of k in the term 210x 6y k is a) 6 b) 4 c) 5 d) 7

Sloan [31]

Answer:

a) 6

Step-by-step explanation:

Expanding the polynomial using the formula:

$(x+y)^n=\sum_{k=0}^n \binom{n}{k} x^{n-k} y^k$

Also

$\binom{n}{k}=\frac{n!}{(n-k)!k!}$

I think you mean $210x^6y^4$

We can deduce that this term will be located somewhere in the middle. So I will calculate $k= 5; k=6 \text{ and } k =7$ .

For $k=5$

$\binom{10}{5} (y)^{10-5} (x)^{5}=\frac{10!}{(10-5)! 5!}(y)^{5} (x)^{5}= \frac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5! }{5! \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 } \\ =\frac{30240}{120} =252 x^{5} y^{5}$

Note that we actually don't need to do all this process. There's no necessity to calculate the binomial, just $x^{n-k} y^k$

For $k=6$

$\binom{10}{6} \left(y\right)^{10-6} \left(x\right)^{6}=\frac{10!}{(10-6)! 6!}\left(y\right)^{4} \left(x\right)^{6}=210 x^{6} y^{4}$

5 0

2 years ago

what are some advantages of writing the polynomial expression -7x^2+32x+240 in factored form when interpreting this situation ​

what are some advantages of writing the polynomial expression -7x^2+32x+240 in factored form when interpreting this situation