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mote1985 [20]
1 year ago
15

What expressions are equivalent to the one below. check all that apply. 8^x

Mathematics
1 answer:
tangare [24]1 year ago
7 0

The (32/4)^x is equal to the 8^x.

We have given that,

A. (32/4)^x

B. 32^x/4

C. 8*8^x+1

D. x^4

E. 32^x/4^x

F. 8*8^x-1

We have to determine the expression equivalent to the 8^x.

<h3>What is the expression?</h3>

An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Therefore the expression equivalent to the 8^x is A.

That is,

=\frac{32}{4}^x\\ =8^x

Therefore the (32/4)^x is equal to the 8^x.

To learn more about the expression visit:

brainly.com/question/723406

#SPJ1

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Find all real solutions of the equation by completing the square. (Enter your answers as a comma-separated list.) x2 − 4x − 8 =
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Answer:

After completing the square the expression is (x-2)^2 -12 =0 and real solution are x = 5.46 and x = -1.46

Step-by-step explanation:

We need to complete the square:

x^2 − 4x − 8 = 0

x^2 -2(x)(2)+(2)^2 -8 -4 =0

(x^2 -4x +4) - 12 = 0

(x-2)^2 -12 =0

Now, finding the value of x

(x-2)^2 -12 =0

(x-2)^2 = 12

taking square root on both sides

\sqrt{(x-2)^2}= \sqrt{12} \\(x-2) = \pm\sqrt{12} \\x = \pm\sqrt{12} +2\\x = \sqrt{12}+2 \,\,and\,\,x=-\sqrt{12}+2\\x= 3.46+2 \,\,and\,\,x=-3.46+2\\x =5.46\,\,and\,\,x=-1.46

So, After completing the square the expression is (x-2)^2 -12 =0 and real solution are x = 5.46 and x = -1.46

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Just need help on #7 thru 8(a), b and c
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7

a. The slope of the line passing through the points R(3, 5) and H(-1,2) is -3/4

b. The distance between two points (x₁, y₁) and (x₂,y₂) is 5 units

c.  The midpoint of the R(3, 5) and H(-1,2) is  (2, 4)

8.

a. The transformation rule is  (x,y) → (x + 1, y - 1)

b.

  • The x-coordinate is shifted 1 unit to the left and
  • The y - coordinate is shifted 1 unit downwards.

c. The image of B' the pre-image of B(5, 6) is (6, 5)

<h3 /><h3>7 a. How to find the slope of the line?</h3>

The slope of a line passing through the points (x₁, y₁) and (x₂,y₂) is m = (y₂ - y₁)/(x₂ - x₁)

Given that

  • (x₁, y₁) = (3, 5) and
  • (x₂,y₂) = (-1, 2)

So, m = (y₂ - y₁)/(x₂ - x₁)

m = (2 - 5)/(-1 - 3)

m = -3/-4

m = -3/4

So, the slope of the line passing through the points R(3, 5) and H(-1,2) is -3/4

<h3>b. The distance between the points</h3>

The distance between two points (x₁, y₁) and (x₂,y₂) is d = √[(y₂ - y₁)² + (x₂ - x₁)²]

Given that

  • (x₁, y₁) = (3, 5) and
  • (x₂,y₂) = (-1, 2)

d = √[(y₂ - y₁)² + (x₂ - x₁)²]

d = √[(2 - 5)² + (-1 - 3)²]

d = √[(-3)² + (-4)²]

d = √[9 + 16]

d = √25

d = 5 units

So, the distance between two points (x₁, y₁) and (x₂,y₂) is 5 units

<h3>7 c How to find the midpoint of the R(3, 5) and H(-1,2) </h3>

The midpoint of the the points (x₁, y₁) and (x₂,y₂) is (x, y)  = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Given that

  • (x₁, y₁) = (3, 5) and
  • (x₂,y₂) = (-1, 2)

So, the midpoint (x, y)  = [(x₁ + x₂)/2, (y₁ + y₂)/2]

(x, y)  = [(3 + (-1))/2, (5 + 3)/2]

(x, y)  = [(3 - 1)/2, (5 + 3)/2]

(x, y)  = [4/2, 8/2]

(x, y)  = (2, 4)

So, the midpoint of the R(3, 5) and H(-1,2) is  (2, 4)

<h3>8. a The rule for the transformation of point A(1, 4) to point B(2, 3)</h3>

Given that point A(1, 4) and point B(2, 3) we see that point B(1 + 1, 4 - 1).

Let pont A be (x,y).

So, point B = (x + 1, y - 1)

So, the transformation rule is  (x,y) → (x + 1, y - 1)

<h3>b. Describe the transformation</h3>

Since the transformation rule is   (x,y) → (x + 1, y - 1), we see that

  • the x-coordinate is shifted 1 unit to the left and
  • the y - coordinate is shifted 1 unit downwards.
<h3>c. The image of B' the pre-image of B(5, 6)</h3>

Since the transformation rule is  (x,y) → (x + 1, y - 1) and point B is (5, 6), thus the image of B' is

(x,y) → (x + 1, y - 1)

(5,6) → (5 + 1, 6 - 1)

(5,6) → (6, 5)

So, the image of B' the pre-image of B(5, 6) is (6, 5)

Learn more about slope of a line here:

brainly.com/question/1617757

#SPJ1

3 0
1 year ago
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