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DanielleElmas [232]
3 years ago
7

Use the definition of exponential notation to demonstrate why 2^3*4^3=2^9

Mathematics
2 answers:
Mashcka [7]3 years ago
8 0
2^3*4^3=2^9 

8*4^3=2^9 

8*64=2^9

 
 

8*64=512 

512=512 

<span>Infinitely Many Solutions</span>
deff fn [24]3 years ago
6 0
Exponential notation allows the representation of numbers in shorter form.
(2 x 2 x 2)(4x4x4) = 2x2x2x2x2x2x2x2x2
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The length of an equilateral triangle is increased by 5 cm. The perimeter of the new triangle is 72 cm. What is the side length
Igoryamba

Answer:

19cm

Step-by-step explanation:

An equilateral triangle is a triangle where the length of the 3 sides are the same.

the perimeter is the sum of the 3 sides

for example, if the length of the side of the an equilateral triangle is 5, the perimeter is 5 x 3 = 15

let x = unknown length of side

length after increase = x + 5

(x + 5) x 3 = 72

divide both sides of the equation by 3

x + 5 = 24

subtract 5 from both sides of the equation

x = 24 - 5 = 19cm

6 0
3 years ago
Sophia is dilating a figure. One of her pre-image points with coordinates (-3, 5) has an image with coordinates (-9, 15). If one
Galina-37 [17]
The dilation factor Sophia is using appears to be
  (image coordinate)/(original coordinate) = -9/-3 = 15/5 = 3

Then the problem tells us
  (pre-image point)×3 = (3, 1)
so we conclude
  (pre-image point) = (3, 1)/3 = (1, 1/3)
8 0
3 years ago
Read 2 more answers
The average (arithmetic mean) of y numbers is x. If 30 is added to the set of numbers, then the average will be x − 5. What is t
Alenkasestr [34]

Answer:

y = \frac{1}{5}(x^{2}-35x)

Step-by-step explanation:

Let the total numbers are n.

If the average of y numbers is x then we can form an equation

\frac{y}{n}=x

⇒ \frac{n}{y}=\frac{1}{x}

⇒ n = \frac{y}{x} --------(1)

Now 30 is added to the set of numbers then average becomes (x - 5)

\frac{y+30}{n+1}=(x-5)

⇒ \frac{(n+1)}{(y+30)}=\frac{1}{(x-5)}

⇒ (n + 1) = \frac{y+30}{x-5}

⇒ n = \frac{y+30}{x-5} - 1 ----- (2)

Now we equate the values of n from equation 1 and 2

\frac{y}{x} = \frac{y+30}{x-5} - 1

y(x - 5) = x(y + 30) - x(x - 5)  [ By cross multiplication ]

xy - 5y = xy + 30x - x² + 5x

xy - xy - 5y = 35x - x²

-5y = 35x - x²

x² - 35x = 5y

y = \frac{1}{5}(x^{2}-35x)

6 0
3 years ago
Read 2 more answers
Brainliest first &amp; correct!
Ilia_Sergeevich [38]

Answer:  Choice A

y = -3(x+2)^2 + 10

=================================================

Work Shown:

y = -3x^2-12x-2 is in the form y = ax^2+bx+c with

a = -3

b = -12

c = -2

The x coordinate of the vertex is

h = -b/(2a)

h = -(-12)/(2*(-3))

h = 12/(-6)

h = -2

We'll plug this into the original equation to find the corresponding y coordinate of the vertex.

y = -3x^2-12x-2

y = -3(-2)^2-12(-2)-2

y = 10

So k = 10 is the y coordinate of the vertex.

Overall, the vertex is (h,k) = (-2,10)

Meaning that we go from this general vertex form

y = a(x-h)^2 + k

to this

y = -3(x - (-2))^2 + 10

y = -3(x+2)^2 + 10

8 0
3 years ago
What is the volume of this figure? Round your answer to the nearest tenth
andrey2020 [161]

Answer:

6430.72 centimeter cubic

5 0
2 years ago
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