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siniylev [52]
3 years ago
7

Amanda has 72 baseball cards this is eight times as many cards as John has how many baseball cards does John have

Mathematics
1 answer:
SVETLANKA909090 [29]3 years ago
3 0
576 because 72×8=576
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A jar of jam contains 55% fruit.How much fruit would I need for ten 454g jars of jam?​
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Marie has a small copy of Rene Magritte's famous painting, The Schoolmaster. Her copy has dimensions 2 inches by 1.5 inches. The
Alex73 [517]
A. Find the dimensions of the original painting.

 

Since the scale is 1 in : 40 cm

2 in ( 40 cm / 1 in) = 80 cm

1.5 in ( 40 cm / 1 in) = 60 cm

80 cm by 60 cm

 

B. Find the area of the original painting.

<span>A =  80 cm x 60 cm = 4800 sq cm</span>

 

C. Since 1 inch is 2.54 cm, find the dimensions of the original painting in inches.

80 cm ( 1 in / 2.54 cm) = 31.5 in

60 cm ( 1 in / 2.54 cm) = 23.6 in

 

D, Find the area of the original painting in square inches.

A = 31.5 in x 23.6 in = 743.4 sq in

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3 years ago
You are given a number. Do you know the number that is 1/5 as big?<br><br> Need answer ASAP ❤️❤️❤️
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Answer:

Step-by-step explanation:

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2 years ago
Find a factorization of x² + 2x³ + 7x² - 6x + 44, given that<br> −2+i√√7 and 1 - i√/3 are roots.
Levart [38]

A factorization of x^4+2x^3+7x^2-6x+44 is (x^2+4x+11)(x^2-2x+4).

<h3>What are the properties of roots of a polynomial?</h3>
  • The maximum number of roots of a polynomial of degree n is n.
  • For a polynomial with real coefficients, the roots can be real or complex.
  • The complex roots of a polynomial with real coefficients always exist in a pair of conjugate numbers i.e., if a+ib is a root, then a-ib is also a root.

If the roots of the polynomial p(x)=ax^4+bx^3+cx^2+dx+e are r_1,r_2,r_3,r_4, then it can be factorized as p(x)=(x-r_1)(x-r_2)(x-r_3)(x-r_4).

Here, we are to find a factorization of p(x)=x^4+2x^3+7x^2-6x+44. Also, given that -2+i\sqrt{7} and 1-i\sqrt{3} are roots of the polynomial.

Since p(x)=x^4+2x^3+7x^2-6x+44 is a polynomial with real coefficients, so each complex root exists in a pair of conjugates.

Hence, -2-i\sqrt{7} and 1+i\sqrt{3} are also roots of the given polynomial.

Thus, all the four roots of the polynomial p(x)=x^4+2x^3+7x^2-6x+44, are: r_1=-2+i\sqrt{7}, r_2=-2-i\sqrt{7}, r_3=1-i\sqrt{3}, r_4=1+i\sqrt{3}.

So, the polynomial p(x)=x^4+2x^3+7x^2-6x+44 can be factorized as follows:

\{x-(-2+i\sqrt{7})\}\{x-(-2-i\sqrt{7})\}\{x-(1-i\sqrt{3})\}\{x-(1+i\sqrt{3})\}\\=(x+2-i\sqrt{7})(x+2+i\sqrt{7})(x-1+i\sqrt{3})(x-1-i\sqrt{3})\\=\{(x+2)^2+7\}\{(x-1)^2+3\}\hspace{1cm} [\because (a+b)(a-b)=a^2-b^2]\\=(x^2+4x+4+7)(x^2-2x+1+3)\\=(x^2+4x+11)(x^2-2x+4)

Therefore, a factorization of x^4+2x^3+7x^2-6x+44 is (x^2+4x+11)(x^2-2x+4).

To know more about factorization, refer: brainly.com/question/25829061

#SPJ9

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1 year ago
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