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IgorC [24]
3 years ago
6

For each sequence, find the first 4 terms of a sequence: a) n²+3 b) 2n²

Mathematics
2 answers:
Vesna [10]3 years ago
8 0

Answer:

a) 4, 7, 12, 19

b) 2, 8, 18, 32

Step-by-step explanation:

Sequence is just number line sir, so to begin with you get n=1, then n=2, then n=3, then n=4, these are the first 4 terms

Rudiy273 years ago
8 0

Answer:

a) 4, 7, 12, 19

b) 2, 8, 18, 32

Step-by-step explanation:

In order to find the first 4 terms, you have to substitute 1 to 4 into n for both expressions :

a) {n}^{2}  + 3

1st \: term \\  {1}^{2}  + 3 = 4

2nd \: term \\  {2}^{2}  + 3 = 7

3rd \: term \\  {3}^{2}  + 3 = 12

4th \: term \\  {4}^{2}  + 3 = 19

b)2 {n}^{2}

1st \: term \\ 2( {1}^{2} ) = 2

2nd \: term \\ 2( {2}^{2} ) = 2(4) = 8

3rd \: term \\ 2( {3}^{2} ) = 2(9) = 18

4th \: term \\ 2( {4}^{2} ) = 2(16) = 32

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Consider the quadratic equations
Debora [2.8K]
Consider the two functions as
<span>y1(x) =3x^2 - 5x, 
y2(x) = 2x^2 - x - c

The higher the value of c, father apart the two equations will be.
They will touch when the difference, i.e. y1(x)-y2(x)=x^2-4*x+c has a discriminant of 0.
This happens when D=((-4)^2-4c)=0, or when c=4.
(a)
So when c=4, the two equations will barely touch, giving a single solution, or coincident roots.
(b) 
when c is greater than 4, the two curves are farther apart, thus there will be no (real) solution.
(c) 
when c<4, then the two curves will cross at more than one location, giving two distinct solutions.

It will be more obvious if you plot the two curves in a graphics calculator using c=3,4, and 5.


</span>
6 0
4 years ago
Read 2 more answers
Really need help quickly
Vlada [557]

Answer:

a

Step-by-step explanation:

4 0
3 years ago
Factor completely x2 − 36. (1 point)
puteri [66]

Answer:

Solution given:

x²-36

x²-6²

(x+6)(x-6)

is your answer

6 0
3 years ago
1. Find the area of the composite figure to the nearest hundredth.
Leto [7]

Answer:

#1: 751.56 mm²

#2: 477 km²

Step-by-step explanation:

First I noted the semicircle on the left, which has a radius of 12.5 mm. The formula for finding the area of a semicircle is 1/2(πr²).

1/2(3.14 * (12.5)²)

<em>12.5 squared is 156.25.</em>

1/2(3.14 * 156.25)

<em>Multiply 3.14 by 156.25 to get 490.625.</em>

1/2(490.625)

<em>Divide 490.625 by 2 to get 245.3125.</em>

245.3125 mm² for the semicircle

Then, I split the rest of into a 12.5 by 25 rectangle and a 31 by 12.5 triangle.

(12.5 * 25) + 1/2(31 * 12.5)

<em>Multiply 12.5 by 25 to get 312.5.</em>

312.5 + 1/2(31 * 12.5)

<em>Multiply 31 by 12.5 to get 387.5.</em>

312.5 + 1/2(387.5)

<em>Multiply 1/2 by 387.5 to get 193.75</em>

312.5 + 193.75

<em>Add 312.5 and 193.75 to get 506.25.</em>

506.25 mm² for the rest of the figure.

Now add the two measures, and you have your answer for #1.

245.3125 + 506.25 = 751.5625 mm², which rounds to 751.56 mm².

The area of the composite figure is 751.56 mm².

Now for #2. First, find the area of the triangle.

1/2(40 * 27)

<em>Multiply 40 by 27 to get 1080.</em>

1/2(1080)

<em>Multiply 1/2 by 1080.</em>

590 km² for the triangle.

Now find the area of the circle.

3.14 * 6²

3.14 * 36

113.04 km² for the circle.

Now subtract the area of the circle from the area of the triangle.

590 - 113.04

476.96 km², which rounds to 477.0 km².

The area of the shaded region is 477 km².

6 0
3 years ago
Read 2 more answers
Can someone help me !! And PLEASE SHOW YOUR WORK
Alona [7]
The formula for the area of a trapezoid is A=1/2(base one+base two)h
All you have to do is find the base one, base two, and height using the given information and then plug it into the equation.
7 0
3 years ago
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