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amid [387]
3 years ago
13

find the first fourth and tenth terms of the arithmetic sequence described by the given rule a (n)=5+(n-1)(1/2)

Mathematics
1 answer:
gulaghasi [49]3 years ago
5 0
An=a1+d(n-1)
a1=first term
d=common differnce

easy

inptu 4 for n and 10

a4=5+(4-1)1/2
a4=5+3(1/2)
a4=5+3/2
a4=6 and 1/2
4th term is 6 and 1/2


10th term
a10=5+(10-1)1/2
a10=5+(9)1/2
a10=5+9/2
a10=9 and 1/2




4th term is 6 and 1/2
10th term is 9 and 1/2

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Pls show work! questions on pic
Lena [83]

Answer:

a.(10,23)

b.(7,30)

e.(20,20)

Step-by-step explanation:

We are given that

x=Width of garden

y=Length of garden

According to question

x\geq 5

y\geq 20

Perimeter of rectangle=2(x+y)

Where x=Width  of rectangle

y=Length of rectangle

Fencing used =2(x+y)

2(x+y)\leq 80

First we change inequality  into equality

x=5...(1)

y=20...(2)

2(x+y)=80

x+y=40...(3)

Substitute x=0 in equation (3)

y=40

Substitute y=0  in equation (3)

x=40

Substitute x=0 and y=0 in equation (3)

2(x+y)\leq 80

0\leq 80

It is true. Therefore, the  shaded region below the line.

0\geq 5

0\geq 20

These are false equation .Therefore, the shaded region above the line.

Substitute x=5 in equation (3)

5+y=40

y=40-5=35

Substitute y=20 in equation (3)

x+20=40

x=40-20=20

Intersection point of equation (1) and (3) is (5,35) and intersect point of equation (2) and (3) is (20,20).

Now,

a.(10,23)

Substitute in

2(x+y)\leq 80

2(10+23)\leq 80

66\geq 80

10>5 and 23>20

it satisfied all inequality.

Hence, it is a solution.

b.(7,30)

7>5

30>20

2(7+30)=74

it satisfied all inequality.

Hence, it is a solution.

c.(18,25)

18>5

25>20

2(18+25)=86>80

It does not satisfied third inequality

Hence, it is not a solution.

d.(8,35)

8>5

35>20

2(8+35)=86>80

It does not satisfied third inequality

Hence, it is not a solution.

e.(20,20)

2(20+20)=80

20>5

20=20

it satisfied all inequality.

Hence, it is a solution.

4 0
3 years ago
Somebody help me please.I am taking algebra in freshman high school
ad-work [718]
The pattern is the amount you need to add increases by 2 each time. Ex. 1+1=2 2+3=5 3+5=8
8 0
3 years ago
Does the construction demonstrate how to copy an angle correctly using technology?
Ksivusya [100]

Answer:

No, the distance between points A and F was used to create circle H.

Step-by-step explanation:

In the given example the points F and G are the radius of the circle H. The distance from point A to point F is used to draw the circle H. The center point for circle H is point A. The circle is the copied and the angles are used to create another circle.

4 0
3 years ago
A rectangle is to be inscribed in an isosceles right triangle in such a way that one vertex of the rectangle is the intersection
svet-max [94.6K]

Answer:

x  =  2  cm

y  = 2  cm

A(max) =  4 cm²

Step-by-step explanation: See Annex

The right isosceles triangle has two 45° angles and the right angle.

tan 45°  =  1  =  x / 4 - y        or     x  =  4  -  y     y  =  4  -  x

A(r)  =  x* y

Area of the rectangle as a function of x

A(x)  =  x  *  (  4  -  x )       A(x)  =  4*x  -  x²

Tacking derivatives on both sides of the equation:

A´(x)  =  4 - 2*x             A´(x)  =  0            4   -  2*x  =  0

2*x  =  4

x  =  2  cm

And  y  =  4  - 2  =  2  cm

The rectangle of maximum area result to be a square of side 2 cm

A(max)  = 2*2  =  4 cm²

To find out if A(x) has a maximum in the point  x  =  2

We get the second derivative

A´´(x)  =  -2           A´´(x)  <  0   then A(x) has a maximum at  x = 2

5 0
2 years ago
Stumped on a few questions.. Grrrr Will give as many hearts and thanks as possible for right answer!&lt;3 :)
Llana [10]
Th one on the left I wanna say x=16 and the right is x=10
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3 years ago
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