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3 years ago

Need help with math question

Mathematics

1 answer:

lyudmila [28]3 years ago

6 0

Answer:

7 18-inch wreaths

26 22-inch wreaths

Step-by-step explanation:

Let's say the number of 18-inch wreaths is x and the number of 22-inch wreaths is y.

We know that the number of 22-inch wreaths sold was 5 more than 3 times the number of 18-inch wreaths sold. We can write this into the expression as:

y = 5 + 3x

We also know that each 18-inch wreath was $20 and each 22-inch wreath was $25. The total cost was $790, so:

20x + 25y = 790

Now, let's substitute 5 + 3x in for y in the second equation:

20x + 25y = 790

20x + 25(5 + 3x) = 790

20x + 125 + 75x = 790

95x + 125 = 790

95x = 665

x = 7

Plug this value into y = 5 + 3x to find y:

y = 5 + 3x

y = 5 + 3 * 7 = 5 + 21 = 26

So, 7 18-inch wreaths were sold and 26 22-inch wreaths were sold.

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we have been asked to verify that -5, 1/2, and 3/4 are the zeroes of the cubic polynomial $4x^3+20x^2+2x-3$

To verify that whether the given values are zeros or not we will substitute the values in the given Polynomial, if it will returns zero, it mean that value is Zero of the polynomial. But if it return any thing other than zeros it mean that value is not the zero of the polynomial.

Let $f(x)=4x^3+20x^2+2x-3\\\\\text{when x=-5}\\\\f(-5)=4(-5)^3+20(-5)^2+2(-5)-3=-13\\\\\text{when x=}\frac{1}{2}\\$

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$\text{when x=}\frac{3}{4}\\\\$

$f( \frac{3}{4} ) = 4 ( \frac{3}{4} )^3+20(\frac{3}{4})^2+2(\frac{3}{4})-3=\frac{183}{16}\\$

Hence -5, 1/2, and 3/4 are not the zeroes of the given Polynomial.

Since sum of roots $=\frac{-b}{a}= \frac{-20}{4}=-5\\$

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Hence we do not find any relation between the coefficients and zeros.

Anyway if the given values doesn't represents the zeros then those given values will not have any relation with the coefficients of the p[polynomial.

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