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4 years ago

Given: < 1 and < 2 are right angles. Prove: < 1 = < 2

1 answer:

5 0

Statement.
(1). ∠1 is right angle & ∠2 is right angle

(2). ∠1 = ∠2

Reason
(1). Given

(2). Euclid’s Fourth Postulate states that all right angles are equal to one another.

Warning
This is assuming, that we only include Euclidean geometers.
This is because Euclidean geometry only recognise angles between straight lines.

So we have Non-Euclidean geometry for things that are not straight but this raises a question what is a straight line?

A general definition is (A curve is "straight' if tangent vectors stay tangent when parallel-transported along that curve)

Want more info

http://www.physics.ucc.ie/apeer/PY4112/Curvature.pdf

(Elementary Geometry from an Advance Standpoint, by Edwin Moise).

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Given that f(x)=x^2-4x -3 and g(x)=x+3/4 solve for f(g(x)) when x=9

SSSSS [86.1K]

Answer:

f(g(9)) = 945/16

Step-by-step explanation:

To find f(g(x)), you have to substitute g(x) wherever there is an x in f(x).

g(x) = x + 3/4

f(x) = x² - 4x - 3

f(g(x)) = (x + 3/4)² - 4(x + 3/4) - 3

f(g(x)) = x² + 3/2x + 9/16 - 4x + 3 - 3

f(g(x)) = x² - 5/2x + 9/16 + 3 - 3

f(g(x)) = x² - 5/2x + 9/16

Now, put a 9 wherever there is an x in f(g(x)).

f(g(9)) = (9)² - 5/2(9) + 9/16

f(g(9)) = 81 - 5/2(9) + 9/16

f(g(9)) = 81 - 45/2 + 9/16

f(g(9)) = 117/2 + 9/16

f(g(9)) = 945/16

7 0

3 years ago

You fly a hot air balloon 3.5 miles above the ground. What is the measure of BD⌢, the portion of Earth that you can see? Round y

STatiana [176]

Answer:

$\Delta s \approx 334.545\,m$

Step-by-step explanation:

Let assume that Earth is a sphere, the following trigonometric diagram is constructed and presented below. The central angle is given by this inverse trigonometric equation:

$\theta = 2\cdot \cos^{-1} \left(\frac{r}{r+h} \right)$

$\theta = 2\cdot \cos^{-1}\left(\frac{4000\,mi}{4000\,mi+3.5\,mi} \right)$

$\theta = 4.792^{\circ}$

The distance of the portion of Earth that can be seen is:

$\Delta s = \frac{4.792^{\circ}}{360^{\circ}}\cdot (2\pi)\cdot (4000\,mi)$

$\Delta s \approx 334.545\,m$

7 0

3 years ago

A total of 430 tickets were sold for the school play . They were either adult tickets or student tickets . There were 70 fewer s

Maurinko [17]

So first we assume that half is adult and have is student.

So
215 adult 215 student

Now since it said they were 70 less student tickets than adult tickets we subtract 70.
215 - 70 = 145

Now we add the 70 we subtracted from student tickets to the adult tickets.
215 + 70 = 285

So there were
285 adult tickets sold and 145 student tickets sold

I hope this helped. Have a great day!

6 0

3 years ago

What is the value of x???

svetoff [14.1K]

I do believe it would be x=30

3 0

3 years ago

You prepare 10 scoops of dog food for 5 dogs, and prepare 16 scoops of dog food for 8 dogs. What

Svetllana [295]

Answer:

<em>12 scoops of dog food are needed for 6 dogs,</em>

Step-by-step explanation:

<u>Proportions</u>

The number of scoops of dog foods and the number of dogs are proportional variables.

We are given that 10 scoops of dog foods are used for 5 dogs. This gives a proportion of 10/5=2 scoops per dog.

We also know that 16 scoops are used for 8 dogs. The proportion is also 16/8=2 scoops per dog.

Thus, the constant of proportionality is 2.

For 6 dogs, you need to prepare 2*6 = 12 scoops of dog food.

12 scoops of dog food are needed for 6 dogs,

3 0

3 years ago