What is the difference between 7986 and 20500

Use the four functions below for this question:

Darina [25.2K]

f (x ) = 2 x + 5
For g (x) we will solve the system:
- 1 =-2 m + b
+
-9 = 2 m + b
----------------------
-10 = 2 b, b = -5
-9 = 2 m - 5
2 m = -4
m = -2
g ( x ) = - 2 x - 5
For h (X):
m = (-1-5 ) / ( 3-0 ) = -6/3 = -2
5 = 0 + b, b = 5
h ( x) = - 2 x + 5.
Now we have 4 linear functions:
1 ) f ( x ) = 2 x + 5
The slope is m = 2, y - intercept: y = 5 , zero: x = -2.5 and the function increases ( m > 0 ).
2 ) g(x) = - 2 x - 5
The slope is m = - 2, y-intercept: y =-5 , zero: x = -2.5 and the function decreases ( m < 0 ).
3 ) h ( x ) = - 2 x + 5
The slope is m = - 2, y - intercept . y = 5, zero: x = 2.5 and the function decreases.
4 ) j (x) = 2 x + 5
The slope is m = 2, y -intercept: y = 5, zero: x = -2.5 and the function decreases.
The functions f( x ) and j ( x ) are parallel and also g( x ) and h ( x ). They have the same slope.
The functions f ( x ) and j (x ) are increasing and h ( x ) and h ( x ) are decreasing.

6 0

4 years ago

#2 <br> #3 <br> Need help for my discrete math class

miss Akunina [59]

For (2), start with the base case. When n = 2, we have

(n + 1)! = (2 + 1)! = 3! = 6

2ⁿ = 2² = 4

6 > 4, so the case of n = 2 is true.

Now assume the inequality holds for n = k, so that

(k + 1)! > 2ᵏ

Under this hypothesis, we want to show the inequality holds for n = k + 1. By definition of factorial, we have

((k + 1) + 1)! = (k + 2)! = (k + 2) (k + 1)!

Then by our hypothesis,

(k + 2) (k + 1)! > (k + 2) 2ᵏ = k•2ᵏ + 2ᵏ⁺¹

and k•2ᵏ ≥ 2•2² = 8, so

k•2ᵏ + 2ᵏ⁺¹ ≥ 8 + 2ᵏ⁺¹ > 2ᵏ⁺¹

which proves the claim.

Unfortunately, I can't help you with (3). Sorry!

3 0

3 years ago

Pls help I’ll brainlest due ASAP

Sholpan [36]

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3 0

3 years ago

Read 2 more answers

Which is true regarding the triangular frame? It is an acute triangle. About 0.8 foot needs to be removed from the 20-foot board

Ivanshal [37]

Question:

Arielle is building the wooden framework for the roof of a house. she needs the angle created by the vertical and horizontal boards of the frame to be a right angle. the height of the vertical board is 12 feet. the length of the horizontal board is 15 feet. the support beam that will connect the ends of the two boards measures 20 feet. which is true regarding the triangular frame? it is an acute triangle. about 0.8 foot needs to be removed from the 20-foot board to create a right triangle. it is an obtuse triangle. about 0.8 foot needs to be removed from the 20-foot board to create a right triangle. it is an acute triangle. about 7 feet need to be removed from the 20-foot board to create a right triangle. it is an obtuse triangle. about 7 feet need to be removed from the 20-foot board to create a right triangle.

Answer:

It is an obtuse triangle.About 0.8 foot needs to be removed from the 20 foot board to create a right triangle.

Explanation:

Let us use pythagorean theorem to check whether it is a right triangle.

The vertical board is 12 feet and the horizontal board is 15 feet.

By pythagoean theorem,

$\begin{aligned}c^{2} &=12^{2}+15^{2} \\&=144+225 \\c &=\sqrt{369} \\c &=19.2\end{aligned}$