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mihalych1998 [28]
3 years ago
15

Use the discriminant to describe the roots of each equation. Then select the best description. x2 - 5x + 7 = 0

Mathematics
1 answer:
miv72 [106K]3 years ago
5 0
The general form of a quadratic (second degree) equation is 

a x^{2} +bx+c=0, where

D= b^{2}-4ac is called the Discriminant.


The Discriminant determines how many roots the equation will have as follows:

i)  if D>0, the equation has 2 roots.
ii) if D=0, the equation has 1 double root.
iii) if D<0, the equation has no roots.


In our equation, x^{2} -5x+7=0, a=1, b=-5, c=7

so the discriminant is D=(-5)^2-4*1*7=25-28<0


Thus the equation has no roots.


Remark: the equation has no roots in the Real numbers, but it has 2 roots in a larger set of numbers to be discussed in the future, the Complex numbers.
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20=7x+4-5x what is x
defon
Combine like terms
20=2x+4

Subtract 4 from both sides
16=2x

Divide both sides by 2
8=x

Final answer: x=8
7 0
3 years ago
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If x=(10-3i) and y=(3-10i), then xy=? and x/y=?
Solnce55 [7]

Answer:

xy=-109i

\frac{x}{y}=\frac{60}{109}+\frac{91}{109}i

Step-by-step explanation:

xy=(10-3i)(3-10i)

To compute x times y must use foil on the right hand side.

First:  10(3)=30

Outer: 10(-10i)=-100i

Inner: -3i(3)=-9i

Last: -3i(-10i)=30i^2=-30

------------------------------------Add like terms:

-109i

----------------

\frac{x}{y}

\frac{10-3i}{3-10i}

Multiply top and bottom by bottom's conjugate:

\frac{(10-3i)(3+10i)}{(3-10i)(3+10i)}

Foil the top and just do first and last of Foil for the bottom since the bottom contains multiplying conjugates:

\frac{30+100i-9i-30i^2}{9-100i^2}

Replace i^2 with -1:

\frac{30+91i+30}{9+100}

\frac{60+91i}{109}

\frac{60}{109}+\frac{91}{109}i

7 0
3 years ago
A yard is 3 times as long as it is wide. 176 feet of fencing is needed to enclose the yard. Find the dimensions of the yard
svet-max [94.6K]
The perimeter of a rectangle is twice the sum of its side lengths.

P=2(L+W), we are told that L=3W and P=176 so

2(3W+W)=176

2(4W)=176

8W=176

W=22 ft, since L=3W

L=66 ft

So the yard is 22 feet wide and 66 feet long.


5 0
3 years ago
Read 2 more answers
LA DISTANCIA ENTRE LA TIERRA YLA LUNA ES DE 384 392 KM. LOS AUSTRONAUTAS DE LA APOLO XL SALIERON EL 16 DE JULIO DE 1969 DESDE EL
KengaRu [80]

Complete question :

la distancia entre la tierra y la luna es de 384 392 km. Los astronautas de la Apolo XL salieron el 16 de julio de 1969 desde el Centro Espacial Kennedy y al alcanzaron la orbita el 19 de julio de 1969. Suponiendo que cada dia recorrieron la misma cantidad de kilometros cuantos kilometros recorrieron por dia

Responder:

128130,66 kilometros

Explicación paso a paso:

Dado que:

Distancia entre la tierra y la luna = 384,392 km

Tiempo empleado = (19 de julio - 16 de julio) mismo año = 3 días

Velocidad = distancia / tiempo

El tiempo empleado es (3 * 24) = 72 horas

Por lo tanto,

velocidad = 384,392 / 72

= 5338,7777 kilómetros por hora

Dado que se supone que la distancia recorrida diariamente es la misma m:

El número de kilómetros recorridos por día:

5338,7777 kilómetros por hora * 24

= 128130,66 kilometros

4 0
2 years ago
If you skip 2 hundreds from 419, what number will you land on?
defon
I think what's your trying to say is 419-200? If so it's 219
7 0
3 years ago
Read 2 more answers
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