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gogolik [260]
3 years ago
13

For what value of x does 84^3x=512^2x+12

Mathematics
1 answer:
stealth61 [152]3 years ago
7 0

2.193 X 10^-5

this is the answer

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Mary wants to fill in a cylinder vase. At the flower store they told her that the vase should be filled for the flowers to last
frutty [35]
For the problem, we are asked t o calculate the volume of the cylindrical vase and it will represent the amount of water that Mary should pour. For a cylinder, the volume is calculated as follows:

V = πr²l
V = π(3)²(8)
<span>V = 226.19 in³ water needed</span>
8 0
3 years ago
Kristen lives directly east of the park. The football field is directly south of the park. The library sits on the line formed b
klemol [59]

Imagine right triangle PHF, where P - park, H - home and F - football field, then PH, PF are legs and HF is hypotenuse . Denote point L to be library. You know that point L lies on the segment FH and FL=8, LH=2. Also you know that PL is an altitude to the hypotenuse.

Use the property of altitude drawn from the vertex of right angle to the hypotenuse (the length of the altitude is geometrical mean between legs' projections onto hypotenuse):

PL=\sqrt{HL\cdot LF},\\  PL=\sqrt{2\cdot 8}=\sqrt{16} =4 mi.

This means that the distance between park and libriry is 4 miles.

Consider right triangle PLF ( angle L is right angle and PF - hypotenuse). By the Pythagorean theorem,

PF^2=PL^2+LF^2,\\ PF^2=4^2+8^2,\\ PF^2=16+64=80,\\ PF=\sqrt{80} =4\sqrt{5} mi. The distance between park and football field is 4\sqrt{5} miles.

Answer: the distance between park and libriry is 4 miles and the distance between park and football field is 4\sqrt{5} miles.

6 0
3 years ago
One number is 7 more than another number. the sum of the numbers is 63. what are the numbers?
worty [1.4K]
Let the smaller number be x
x+x+7=63
2x+7=63
2x=56
x=28

28+7=35

The two numbers are 28 and 35
6 0
3 years ago
Hey guys if i can get some pointers on how to do this that would be great ive been stuck on this problem for over an hour my not
leva [86]

Answer:

  • a) 3
  • b) 6
  • c) 9
  • d) the outputs are 3 times as far apart as the inputs

Step-by-step explanation:

(a) "x" in considered to be the input to the function f(x). The variable(s) in parentheses as part of the function name are the inputs. The function value itself is the output.

That is, for an input (x-value) of 0, the output (f(0)) is 5. For an input of 1, the output (f(1)) is 8. These input values (0 and 1) are 1 unit apart: 1 - 0 = 1. The corresponding output values are 3 units apart: 8 - 5 = 3.

(b) Inputs -1 and 1 are 2 units apart (1-(-1)=2). The corresponding output values, 2 and 8, are 6 units apart. (8-2=6)

(c) Inputs 0 and 3 are 3 units apart. The corresponding output values, 5 and 14, are 9 units apart.

(d) The ratio of output differences to input differences can be seen to be ...

... 3/1 = 6/2 = 9/3 = 3

Output differences are 3 times input differences.

_____

<em>Comment on the problem</em>

These ratios are constant everywhere, so the function is considered to be "linear." The ratio is the "slope" of the line you see when the function is graphed.

5 0
4 years ago
For (x + 4)(x + 9) to equal 0, either (x + 4) or (x + 9) must equal
Ilia_Sergeevich [38]
If (x+4)(x+9) then either x+4 = 0 or x+9 = 0

This is by the zero product property
4 0
3 years ago
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