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Thepotemich [5.8K]
2 years ago
9

PLEASE HELP I WILL MARK BRAINLIEST AND GIVE EXTRA POINTS!

Mathematics
1 answer:
olga2289 [7]2 years ago
3 0

Answer:

ohh I don't know these kind of questions so I can't help hehe

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HELP!! Algebra help!! Will give stars thank u so much <333
Anna35 [415]

Answers:

  • Part a)  \bf{\sqrt{x^2+(x^2-3)^2}
  • Part b)  3
  • Part c)   2.24
  • Part d)  1.58

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

Work Shown:

Part (a)

The origin is the point (0,0) which we'll make the first point, so let (x1,y1) = (0,0)

The other point is of the form (x,y) where y = x^2-3. So the point can be stated as (x2,y2) = (x,y). We'll replace y with x^2-3

We apply the distance formula to say...

d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\\\\d = \sqrt{(0-x)^2+(0-y)^2}\\\\d = \sqrt{(0-x)^2+(-y)^2}\\\\d = \sqrt{x^2 + y^2}\\\\d = \sqrt{x^2 + (x^2-3)^2}\\\\

We could expand things out and combine like terms, but that's just extra unneeded work in my opinion.

Saying d = \sqrt{x^2 + (x^2-3)^2} is the same as writing d = sqrt(x^2-(x^2-3)^2)

-------------------------------------------

Part (b)

Plug in x = 0 and you should find the following

d(x) = \sqrt{x^2 + (x^2-3)^2}\\\\d(0) = \sqrt{0^2 + (0^2-3)^2}\\\\d(0) = \sqrt{(-3)^2}\\\\d(0) = \sqrt{9}\\\\d(0) = 3\\\\

This says that the point (x,y) = (0,3) is 3 units away from the origin (0,0).

-------------------------------------------

Part (c)

Repeat for x = 1

d(x) = \sqrt{x^2 + (x^2-3)^2}\\\\d(1) = \sqrt{1^2 + (1^2-3)^2}\\\\d(1) = \sqrt{1 + (1-3)^2}\\\\d(1) = \sqrt{1 + (-2)^2}\\\\d(1) = \sqrt{1 + 4}\\\\d(1) = \sqrt{5}\\\\d(1) \approx 2.23606797749979\\\\d(1) \approx 2.24\\\\

-------------------------------------------

Part (d)

Graph the d(x) function found back in part (a)

Use the minimum function on your graphing calculator to find the lowest point such that x > 0.

See the diagram below. I used GeoGebra to make the graph. Desmos probably has a similar feature (but I'm not entirely sure). If you have a TI83 or TI84, then your calculator has the minimum function feature.

The red point of this diagram is what we're after. That point is approximately (1.58, 1.66)

This means the smallest d can get is d = 1.66 and it happens when x = 1.58 approximately.

6 0
2 years ago
Which expression equals 93102
Karo-lina-s [1.5K]

Answer:

you got this

Step-by-step explanation:

goodluck

4 0
2 years ago
Based on the graph, which inequality is correct for a number that is to the right of -4
Anon25 [30]

2 > -4

2 is greater than -4

3 0
3 years ago
What is the value of x?
Makovka662 [10]

Answer:

A-100

Step-by-step explanation:

Use the Pythagorean therom.

a^2+b^2=c^2

6^2+8^2=c^2

36+64=100.

Hope this helps. Kinda confused me.


4 0
3 years ago
An architect draws a blueprint of a house. He draws the living room on the blueprint as 4.5 in. long by 6 in. wide with a scale
s2008m [1.1K]

Answer:

the answer is 8.5

Step-by-step explanation:

yeet

8 0
3 years ago
Read 2 more answers
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