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3 years ago

Show that the statement is true. If DF has endpoints D(-1,8) and E(3,-2), then the midpoint M of DE lies

Mathematics

1 answer:

Sergio [31]3 years ago

5 0

please help me with my homework

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Ayudemen porfavor . Determine 4 ala potencia x + 4 ala potencia -x, si se sabe que 2ala potencia x + 2 ala potencia -x =3

Afina-wow [57]

Answer:

Es igual a 7.

Step-by-step explanation:

Ok, sabemos que:

$2^x + 2^{-x} = 3$

Queremos calcular:

$4^x + 4^{-x}$

Tambien sabemos que 4 = 2*2

Entonces:

$4^x + 4^{-x} = (2*2)^x + (2*2)^{-x}$

y sabemos que 2*2 = 2^2

Entonces:

$4^x + 4^{-x} = (2*2)^x + (2*2)^{-x} = (2^2)^x + (2^2)^{-x}$

y ahora podemos usar la relación:

$(a^n)^m = (a^m)^n = a^{m*n}$

entonces:

$(2^2)^x + (2^2)^{-x} = (2^x)^2 + (2^{-x})^2$

Ahora podemos completar cuadrados sumando y restando el termino:

$2*(2^x)*(2^{-x})$

Asi tendremos:

$(2^x)^2 + (2^{-x})^2 = (2^x)^2 + (2^{-x})^2 + 2*(2^x)*(2^{-x}) - 2*(2^x)*(2^{-x}) = (2^x + 2^{-x})^2 - 2*(2^x)*(2^{-x})$

Entonces de momento tenemos que:

$4^x + 4^{-x} = (2^x + 2^{-x})^2 - 2*(2^x)*(2^{-x})$

Sabemos que el termino que esta dentro del parentesis es igual a 3.

Y tambien podemos usar la propiedad:

$a^n*a^m = a^{n + m}$

en el termino de la derecha.

Asi tendremos:

$(2^x + 2^{-x})^2 - 2*(2^x)*(2^{-x}) = (3)^2 - 2*2^{x + (-x)} = 9 - 2 = 7$

7 0

3 years ago

Which of the following is a linear function?

Tamiku [17]

Answer:

Step-by-step explanation:

$\text{The equation of a linear function:}\\\\f(x)=mx+b\\\\m-slope\\b-y-intercept\\----------------------------\\\\A.\ f(x)=\dfrac{2}{x}+7\qquad\bold{NOT}\ /\text{x is in denominator}/\\\\B.\ f(x)=\sqrt{2+7x}\qquad\bold{NOT}\ /\text{x is under square roots}/\\\\C.\ f(x)=2-7x\qquad\bold{YES}\ /m=-7,\ b=2/\\\\D.\ f(x)=2+x+x^2\qquad\bold{NOT}\ /\text{x is in the second power}/$

3 0

3 years ago

Enter the number in sdentific notation. 86,257 = Hint: Move the decimal left 4 places.

marin [14]

Answer:

8.6257*10^4

Step-by-step explanation:

move the decimal left 4 places

multiply 10^however many decimal places you moved

boom

6 0

3 years ago

Reflect the point (8,-7) across the x-axis

skelet666 [1.2K]

Answer:

Hrubecct u n

Step-by-step explanation:

Jdbheikng

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2 years ago

Read 2 more answers

A jogging track has a length of 1144 yards yd. How long is this in miles mi? First fill in the blank on the left side of the equ

nikdorinn [45]

Answer:

length=0.65 mi

length in yr= 0.65x1760=1144

3 0

2 years ago