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Sergeu [11.5K]
3 years ago
13

A group of friends are at a baseball game and are purchasing souvenirs. Dustin purchased 5 t-shirts and 1 baseball cap, spending

a total of $119. His Mandy purchased 1 t-shirt and 1 baseball cap, which cost her a total of $43. Assuming that all of the t-shirts and all of the caps are the same price, what is the price of each?
Shirts are $____apiece and caps are $___apiece.
help thanks
Mathematics
1 answer:
Inessa [10]3 years ago
7 0

Answer:

Shirt-$19

Cap-$24

Step-by-step explanation:

5s+1c=119

1s+1c=43

1c=43-1s

substitute:

5s+(43-1s)=119

5s+43-1s=119

4s=119-43

4s=76

1s=19

substitute:

1c=43-(19)

1c=24

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Step-by-step explanation:

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What is the slope of (2,5) and (5,8)
murzikaleks [220]

Answer:

Slope = 1

Step-by-step explanation:

Slope = change in y/change in x

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        =3/3

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3 years ago
Find an n^th degree polynomial with real coefficients satisfying the given conditions. n = 3; -2 and 2 i are zeros; f(-1) = 15.
Ira Lisetskai [31]
So, n = 3, is a 3rd degree polynomial, roots are -2 and 2i

well 2i is a complex root, or imaginary, and complex root never come all by their lonesome, their sister is always with them, the conjugate, so if 0+2i is there, 0-2i is there too

so, the roots are -2, 2i, -2i

now... \bf \begin{cases}
x=-2\implies x+2=0\implies &(x+2)=0\\
x=2i\implies x-2i=0\implies &(x-2i)=0\\
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\end{cases}
\\\\\\
(x+2)\underline{(x-2i)(x+2i)}=0\\\\
-----------------------------\\\\
\textit{difference of squares}
\\ \quad \\
(a-b)(a+b) = a^2-b^2\qquad \qquad 
a^2-b^2 = (a-b)(a+b)\\\\
-----------------------------\\\\
(x+2)[x^2-(2i)^2]=0\implies (x+2)[x^2-(2^2i^2)]=0
\\\\\\
(x+2)[x^2-(4\cdot -1)]=0\implies (x+2)(x^2+4)=0
\\\\\\
x^3+2x^2+4x+8=0

now, if we check f(-1), we end up with 5, not 15
hmmm

so, how to turn our 5 to 15? well, 3*5, thus

\bf 3(x^3+2x^2+4x+8)=f(x)\implies 3(5)=f(-1)\implies 15=f(-1)

usually, when we get the roots, or zeros, if any common factor that is a constant is about, they get in a division with 0 and get tossed, and aren't part of the roots, thus, we can simply add one, in this case, the common factor of 3, to make the 5 turn to 15
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3 years ago
6000 divided by 30 simplified what is it
Katena32 [7]

Answer:

200

Step-by-step explanation:

6,000 divided by 30 is 200

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Help (>﹏<)
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