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Vesna [10]
3 years ago
6

Are 5/3 and 1 2/3 equivalent?

Mathematics
2 answers:
Semmy [17]3 years ago
7 0

Answer:

Yes.

Step-by-step explanation:

3/3 is equal to 1. If you add 3/3 to 2/3, you get 5/3, which means that yes, they are equivalent.

crimeas [40]3 years ago
4 0

Answer:

Yes, they are equivalent.

Step-by-step explanation:

3/3 is equivalent to 1, and 2/3+3/3 is 5/3 (Add the numerators)

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6. Minimum value determined by the formula function f (x) = 2x ²-8x + p was 20. Value f (2) is.
Sergeeva-Olga [200]
6)\ \ \ f(x)=2x^2-8x+p\\the\ minimum\ value =20\ \ \ \Leftrightarrow\ \ \ y_{\ of\ vertex}=20\ \ \ \Leftrightarrow\ \ \ - \frac{\Delta}{2a} =20\\\\\Delta=(-8)^2-4\cdot2\cdot p=64-8p\ \ \Leftrightarrow\ \ - \frac{64-8p}{2\cdot2} =20\ \ \Leftrightarrow\ \ -16+2p=20\\\\2p=36\ \ \ \Leftrightarrow\ \ \ p=18\ \ \ \Rightarrow\ \ \ \ f(x)=2x^2-8x+18\\\\f(2)=2\cdot2^2-8\cdot2+18=2\cdot4-16+18=8+2=10

7)\ the\ shape\ factor\ of\ the\ quadratic\ equation\ 4x^2-13x = -3\\ is\ a=4\ \ \ (\ a>0\ \ \ \rightarrow\ \ \ the\ shape\ is\ \cup\ )\\\\8)\ \ \ the\ turning\ point=(-15;3)\ \ \ \Rightarrow\ \ \ f(x)=a(x+15)^2+3\\\\ the\ graph\ passes\ through\ the\ point\ (-12.0) \ \Rightarrow\ \ 0=a(-12+15)^2+3\\\\\Rightarrow\ \ \ a\cdot3^2=-3\ \ \ \Rightarrow\ \ \ a=- \frac{3}{9} =- \frac{1}{3} \ \ \ \Rightarrow\ \ \ f(x)=- \frac{1}{3}(x+15)^2+3

\Rightarrow\ \ \ f(x)=- \frac{1}{3}(x^2+30x+225)+3=- \frac{1}{3}x^2-10x-72\\\\9)\ \ \ 4x^2+px+25=0\\\\\Delta=p^2-4\cdot4\cdot25=p^2-400\\\\two\ solutions\ \ \Leftrightarrow\ \ \Delta>0\ \ \Leftrightarrow\ \ p^2-40>0\ \ \Leftrightarrow\ \ (p-20)(p+20)>0\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \Leftrightarrow\ \ \ p\in(-\infty;\ -20)\ \cap\ (20;\ +\infty)\\-------------------------------

the\ Vieta's\  formulas\  to\ the\ quadratic\ equation\ ax^2+bx+c=0\\\\x_1+x_2=- \frac{b}{a} \ \ \ and\ \ \ x_1\cdot x_2= \frac{c}{a} \\------------------------------\\\\x_1+x_2=- \frac{p}{4} \ \ \ and\ \ \ x_1\cdot x_2= \frac{25}{4} \\\\x_1^2+x_2^2=x_1^2+2\cdot x_1\cdot x_2 +x_2^2-2\cdot x_1\cdot x_2 =(x_1+x_2)^2-2\cdot x_1\cdot x_2 \\\\x_1^2+x_2^2=(x_1+x_2)^2-2\cdot x_1\cdot x_2 \ \ \ \Leftrightarrow\ \ \ 12.5=(- \frac{p}{4} )^2-2\cdot \frac{25}{4} \\\\

12.5= \frac{p^2}{16} +12.5 \ \ \ \Leftrightarrow\ \ \  \frac{p^2}{16}=0 \ \ \ \Leftrightarrow\ \ \  p^2=0 \ \ \ \Leftrightarrow\ \ \  p=0\\\\\\10)\ \ \ x^2-4x+3=0\ \ \ and\ \ \ x^2+4x-21=0\\\\  x^2-4x+3=x^2+4x-21\ \ \Leftrightarrow\ \ -4x-4x=-21-3\\\\\ \ \Leftrightarrow\ \ -8x=-24\ \ \Leftrightarrow\ \ x=3
6 0
3 years ago
a local pizzeria offers 11 topping for their pizzas and you can choose any 5 of them for one fixed price how many different type
yuradex [85]

Step-by-step Answer:

Customer is allowed to choose any five, where order does not count.

This means that there are 11 toppings to choose from for the first one, 10 for the second, 9 for the third, 8 for the fourth, and 7 for the last for a total of 11*10*9*8*7 = 11!/6! choices.

Since order does not count, we have over-counted by 5!, so the final answer should be 11!/(6!*5!) choices.

Mathematically, this number is represented by

C(11,5) = 11!/(6!5!) = 462, and is read

"Combination of 5 choices out of 11", or simply "11 choose 5".

5 0
3 years ago
Use the distributive property to remove the parentheses.<br> -3(-4v- 2u+1)
densk [106]

Answer:

12v6u-3

Step-by-step explanation:

-3 times -4 is positive 12

-3 times -2 is positive 6

-3 times positive 1 is negative 3

7 0
3 years ago
I need help y’all, PLS HELP ME!
kondaur [170]
What is the question?
5 0
3 years ago
Read 2 more answers
Evaluate 2+3y when y=8
zalisa [80]
Plug 8 into the equation for y and you get 2+24 or 26.
6 0
3 years ago
Read 2 more answers
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