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3 years ago

What makes the statement true? 8^-2=?

2 answers:

6 0

I think the correct answer would be 1/64. A negative exponent just means that the base is on the wrong side of the fraction line, so you need to flip the base to the other side. It is calculated as follows:

8^-2 = 1/8^2 = 1/64

Hope this answers the question. Have a nice day.

loris [4]3 years ago

4 0

Answer:

$\frac{1}{64}$ makes the statement true.

Step-by-step explanation:

Given expression,

$8^{-2}$

By using the property of exponent, i.e. $a^m=\frac{1}{a^{-m}}$

$\implies 8^{-2}=\frac{1}{8^{2}}$

$=\frac{1}{64}$

Hence, the true statement would be,

$8^{-2}=\frac{1}{64}$

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Which statements about the line that passes through (−2, 0) and (2, −4) are true? Select all that apply.

Gennadij [26K]

The statement about the line that passes through (-2, 0) and (2, -4) that are true are:

Option B:The line intersects the y-axis at (0, −2).

Option C: The equation of the line is y = −x − 2.

Option D: The line intersects the x-axis at (−2, 0).

Solution:

Given, two points are (-2, 0) and (2, -4)

We have to select the options that states true about line that passes through given two points.

Now, let us find the line equation that passes through given two points using point slope form.

$\mathrm{y}-\mathrm{y}_{1}=\mathrm{m}\left(\mathrm{x}-\mathrm{x}_{1}\right) \text { where } \mathrm{m} \text { is slope and }\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right) \text { is a point on the line. }$

Now slope "m" is given as:

$\mathrm{m}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{0-(-4)}{-2-2}=\frac{4}{-4}=-1$

Then, line equation = y – 0 = -1(x – (-2))

y = -1(x + 2)

y = -x – 2 --- equation 1

Now let us check options.

Option a) slope of line is 1

We know that slope of our line is -1 so this option is wrong.

Option b) line intersects y – axis at (0, -2)

When line meets y – axis x becomes 0 ⇒ 0 + y + 2 = 0 ⇒ y = -2 so point is (0, -2).

This option is right.

Option c) equation of line is y = -x – 2

The given equation is x + y + 2 = 0 ⇒ y = -x – 2 . so this option is correct.

Option d) line intersects at (-2, 0)

When line meets x – axis y becomes 0 ⇒ x + 0 + 2 = 0 ⇒ x = -2. So point is (-2, 0).

This option is right.

Hence, options b, c, d are correct.

8 0

4 years ago

Find the general solution for differential equation (D4 - 5D3 + 5D2 + 5D - 6)y = 0

slava [35]

Given differential equation, (D4 - 5D3 + 5D2 + 5D - 6)y = 0

=> For general solution of equation,

Solve D4 - 5D3 + 5D2 + 5D - 6 = 0

=> D4 - 5D3 + 6D2 - D2 + 5D - 6 = 0

=> D2 (D2 - 5D + 6) - (D2 - 5D + 6) = 0

=> (D2 - 5D + 6)(D2 - 1) = 0 ................................(1)

Now

D2 - 1 = (D - 1)(D + 1) and

Factors of D2 - 5D + 6

D2 - 5D + 6 = D2 - 2D - 3D + 6

= D(D - 2) - 3(D - 2)

= (D - 3)(D - 2)

Therefore, equation (1) implies

(D2 - 5D + 6)(D2 - 1) = (D - 3)(D - 2)(D - 1)(D + 1) = 0

=> D = 3, 2, 1, -1 or D = -1, 1,, 2, 3

=> General solution of differential equation is,

=> y = C1 e-x + C2 ex + C3 e2x + C4 e3x .

Hope it helps

8 0

4 years ago

A right rectangular prism is packed with cubes of side length fraction 1 over 8 inch. If the prism is packed with 16 cubes along

frez [133]

Answer:

A. fraction 1 and 1 over 2 cubic inches

Step-by-step explanation:

Unit cube side = 1/8 in

Volume of prism:

V= lwh =
16*(1/8)*8*(1/8)*6*(1/8) =
2*1*3/4 =
3/2 = 1 1/2 cubic inches

Correct option is A

6 0

3 years ago

You can drive 420 miles on 20 gallons in 6 hours. How far can you drive on 1 gallon?

Svetllana [295]

Answer:

21 miles

Step-by-step explanation:

20 gallons = 420 miles

Divide by 20

1 gallon = 21 miles

7 0

3 years ago

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What is angle D equal??

olganol [36]

63% Please Give me Brainlyest

7 0

3 years ago