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3 years ago

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Maribelle uses x yards of material to make a quilt. A customer requests 5 quilts that are 20% larger than the normal pattern. Wr

ite an expression to represent the total yards of material needed for the requested quilts in two different ways?

1 answer:

trasher [3.6K]3 years ago

4 0

Answer:

i. 5(x + 0.2x) yards

ii. 6x yards

Step-by-step explanation:

Since the requested quilts are 20% larger than the normal pattern, then;

20% of x = 0.2 x

Thus,the yards of material to make each of the requested quilts increased by 0.2x yards.

So that;

To make one of the requested quilt, the yards required = x + 0.2x

For 5 requested quilts, the total yards required = 5(x + 0.2x)

Total yards of material for the requested quilts is 5(x + 0.2x).

Also,

5(x + 0.2x) = 5x + 5(0.2x)

= 5x + x

= 6x

Thus, the total yards required is 5(x + 0.2x) or 6x.

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Find an m > 0 such that the the equation x^4−(3m+2)x^2+m^2=0 has four real solutions that form an arithmetic sequence.

Aleonysh [2.5K]

Answer:

The value of m is 6.

Step-by-step explanation:

Here, the given equation,

$x^4-(3m+2)x^2+m^2=0$

$x^4+0x^3-(3m+2)x^2+0x+m^2=0$

Let the roots of the equation are a-3b, a-b, a+b and a + 3b, ( they must be form an AP )

Thus, we can write,

$a-3b+a-b+a+b+a+3b=\frac{\text{coefficient of }x^3}{\text{coefficient of }x^4}$

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$\implies a=0----(1)$

$(-3b)(-b)+(-b)(b)+(b)(3b)+(3b)(-3b)+(-b)(3b)+(-3b)(b)=\frac{\text{coefficient of }x^2}{\text{coefficient of }x^4}}$

$=\frac{-3m-2}{1}$

$3b^2-b^2+3b^2-9b^2-3b^2-3b^2=-3m-2$

$-10b^2=-3m-2$

$\implies b^2=\frac{3m+2}{10}-----(2)$

$(-3b)(-b)(b)(3b)=\frac{\text{Constant term}}{\text{coefficient of}x^4}= m^2$

$9b^4=m^2$

$9(\frac{3m+2}{10})^2=m^2$

$9(\frac{9m^2+4+12m}{100})=m^2$

$81m^2+36+108m=100m^2$

$-19m^2+108m+36=0$

$19m^2-108m-36=0$

$19m^2-114m+6m-36=0$

$19m(m-6)+6(m-6)=0$

$(19m+6)(m-6)=0$

$\implies m=-\frac{6}{19}\text{ or }m=6$

But m > 0,

Hence, the value of m is 6.

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