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2 years ago

Write a recursive formula for the sequence 1, 5, 9, 13

Mathematics

1 answer:

11Alexandr11 [23.1K]2 years ago

5 0

Answer:

$\bold{a(n) \ = \ a(n \ + \ 1) \ + \ 4}$

Explanation:

Sequence: 1, 5, 9, 13

Add(ing) 4 every time

$\bold{a(1) \ = \ 1}$

$\bold{\bold{a(n) \ = \ a(n \ + \ 1) \ + \ 4}}$

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Of the 400 eighth-graders at pascal middle school, 117 take algebra, 109 take advanced computer, and 114 take industrial technol

Hatshy [7]

If 164 of the 400 eighth-graders take none of these courses, then 400-164=236 students take some courses.

Let x students take all three courses, then:

1. 70-x take only both algebra and advanced computer,

2. 34-x take only both algebra and industrial technology,

3. 29-x take only both advanced computer and industrial technology.

Now let's count how many student take only one course:

1. 117-(x+34-x+70-x)=13+x take algebra,

2. 109-(x+29-x+70-x)=10+x take advanced computer,

3. 114-(x+29-x+34-x)=51+x take industrial technology.

Now count all students that take some courses:

51+x+10+x+13+x+29-x+34-x+70-x+x=236,

x=236-51-10-13-29-34-70,

x=29.

Answer: all three courses take 29 students.

6 0

2 years ago

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Each morning darnell does a combination of aerobics and stretching exercises. the exercises burn different amounts of calories p

iogann1982 [59]

Answer:

x=34

Step-by-step explanation:

8 0

2 years ago

If ray NP bisects <MNQ, m<MNQ=(8x+12)°, m<PNQ=78°, and m<RNM=(3y-9)°, find the value of x and y

aksik [14]

Step 1

<u>Find the measure of angle x</u>

we know that

If ray NP bisects <MNQ

then

m<MNQ=m<PNM+m<PNQ ------> equation A

and

m<PNM=m<PNQ -------> equation B

we have that

m<MNQ=(8x+12)°

m<PNQ=78°

substitute in equation A

(8x+12)=78+78-------> 8x+12=156------> 8x=156-12

8x=144------> x=18°

Step 2

<u>Find the measure of angle y</u>

we have

m<PNM=(3y-9)°

m<PNM=78°

3y-9=78------> 3y=87------> y=29°

therefore

<u>the answer is</u>

the measure of x is 18° and the measure of y is 29°

7 0

2 years ago

Find the surface area of the triangular prism. A triangular prism. The base is a right triangle with base 1 foot, height 2 feet

mylen [45]

Answer:

Step-by-step explanation:

The formula for calculating the surface area of a triangular prism is expressed as shown below:

SA= bh + pH

b= base of the triangle

h- height of the triangle

p= perimeter of the triangle

H= height of the prism

Given b = 1foot

h = 2feet

perimeter of the triangle = sum of all its sides = 1ft + 2ft + 2.2ft

p = 5.2ft

H = 3ft

Substituting the values into the formula for finding the surface area:

SA = 1(2)+5.2(3)

SA = 2+15.6

SA = 17.6ft²

The surface area of the triangular prism is 17.6ft²

3 0

2 years ago

It takes 32 hours for a motorboat moving downriver to get from pier A to pier B. The return journey takes 48 hours. How long doe

lina2011 [118]

Answer:

Time taken by the un powered raft to cover this distance is T = 192.12 hr

Step-by-step explanation:

Let speed of boat = u $\frac{km}{hr}$

Speed of current = v $\frac{km}{hr}$

Let distance between A & B = 100 km

Time taken in downstream = 32 hours

$32 = \frac{100}{u +v}$

$u + v = \frac{100}{32}$

u + v = 3.125 ------ (1)

Time taken in upstream = 48 hours

$48 = \frac{100}{u -v}$

$u -v = \frac{100}{48}$

u - v = 2.084 ------- (2)

By solving equation (1) & (2)

u = 2.6045 $\frac{km}{hr}$

v = 0.5205 $\frac{km}{hr}$

Now the time taken by the un powered raft to cover this distance

$T = \frac{100}{v}$

Because un powered raft travel with the speed of the current.

$T = \frac{100}{0.5205}$

T = 192.12 hr

Therefore the time taken by the un powered raft to cover this distance is

T = 192.12 hr

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2 years ago

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