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Alex_Xolod [135]
2 years ago
5

72

Mathematics
1 answer:
Zigmanuir [339]2 years ago
8 0

Answer:

Ai. Arithmetic sequence

Aii. Tn = 5 + 7n

Bi. Geometric

Bii. Tn = 8 × 2ⁿ¯¹

Step-by-step explanation:

To successfully answer the questions given above, note the following:

1. If the sequence is Arithmetic, then:

2nd – 1st = 3rd – 2nd = common difference (d)

2. If the sequence is geometric, then,

2nd / 1st = 3rd / 2nd = common ratio (r)

3. A sequence can not be arithmetic geometric at the same time.

4. The nth term of arithmetic sequence is:

Tn = a + (n – 1)d

5. The nth term of geometric sequence is:

Tn = arⁿ¯¹

A. Sequence => 12, 19, 26

i. Determination of the type of sequence.

We'll begin by calculating the common difference

1st term = 12

2nd term = 19

3rd term = 26

Common difference (d) = 2nd – 1st

d = 19 – 12 = 7

OR

d = 3rd – 2nd

d = 26 – 19 = 7

Since a common difference exist in the sequence, the sequence is arithmetic sequence.

ii. Determination of the nth term.

Common difference (d) = 7

1st term (a) = 12

nth term (Tn) =?

Tn = a + (n – 1)d

Tn = 12 + (n – 1)7

Tn = 12 + 7n – 7

Tn = 5 + 7n

B. Sequence => 8, 16, 32

Bi. Determination of the type of sequence.

Let us begin by calculating the common ratio.

1st term = 8

2nd term = 16

3rd term = 32

Common ratio (r) = 2nd / 1st

r = 16 / 8

r = 2

OR

r = 3rd / 2nd

r = 32 / 16

r = 2

Since a common ratio exist in the sequence, the sequence is geometric.

Bii. Determination of the nth term.

Common ratio(r) = 2

1st term (a) = 8

nth term =?

Tn = arⁿ¯¹

Tn = 8 × 2ⁿ¯¹

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grigory [225]

Answer:

1) Point (1,0) -----> see the attached figure N 1

2) The value of x is 4

3) I quadrant

4) (1,1)

5)  y>-5x+3

Step-by-step explanation:

Part 1)

we know that

If the point satisfy the inequality

then

the point must be included in the shaded area

The point (1,0) is included in the shaded area

Part 2)

we have

x-2y\geq 4

see the attached figure N 2

we know that

The value for x on the boundary line and the x axis is equal to the x-intercept of the line x-2y= 4

For y=0

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x-2(0)= 4  

x=4

The solution is x=4

Part 3)

we have

x\geq 0 -----> inequality A

The solution of the inequality A is in the first and fourth quadrant

y\geq 0 -----> inequality B

The solution of the inequality B is in the first and second quadrant

so

the solution of the inequality A and the inequality B is the first quadrant

Part 4) Which ordered pair is a solution of the inequality?

we have

y\geq 4x-5

we know that

If a ordered pair is a solution  of the inequality

then

the ordered pair must be satisfy the inequality

we're going to verify all the cases

<u>case A)</u> point (3,4)

Substitute the value of x and y in the inequality

x=3,y=4

4\geq 4(3)-5

4\geq 7 ------> is not true

therefore

the point (3,4) is not a solution of the inequality

<u>case B)</u> point (2,1)

Substitute the value of x and y in the inequality

x=2,y=1

1\geq 4(2)-5

1\geq 3 ------> is not true

therefore

the point  (2,1) is not a solution of the inequality

<u>case C)</u> point (3,0)

Substitute the value of x and y in the inequality

x=3,y=0

0\geq 4(3)-5

0\geq 7 ------> is not true

therefore

the point  (3,0) is not a solution of the inequality

<u>case D)</u> point (1,1)

Substitute the value of x and y in the inequality

x=1,y=1

1\geq 4(1)-5

1\geq -1 ------> is true

therefore

the point  (1,1) is  a solution of the inequality

Part 5) Write an inequality to match the graph

we know that

The equation of the line has a negative slope

The y-intercept is the point (3,0)

The x-intercept is a positive number

The solution is the shaded area above the dashed line

so

the equation of the line is y=-5x+3

The inequality is  y>-5x+3

3 0
3 years ago
Read 2 more answers
How many 1/8 teaspoons are equal to 4 3/4 teaspoons?
Vinvika [58]

1. Convert fraction into same decimal.

To find this answer, we want to first convert the fraction so that the denominators are the same:

3/4 = ?/8

Divide the original denominator by the needed-to-be denominator.

8 / 4 = 2

Do reversal calculations

4 x 2 = 8

So, now that we know to multiply the original denominator by 2 to get the new denominator, multiple the numeriator by the same.

3           6

_  x 2 = _

4           8

So now, the new equation is:

How many 1/8 teaspoons are equal to 4 6/8 teaspoons.

(The reason why you must convert is because then you can simply say that the fraction is 6 1/8's, which means you just have to worry about the whole numbers.

2. Convert the whole numbers into a fraction to make it easier.

In order to convert whole numbers into fractions, first find the denominator your using. Which in this case, it is 8.

?/8

Now remember, for it to be a whole number, the numeriator and denominator MUST be the same.

8/8 = 1

Now remember, there are four 1's. Multiply the numeriator by 4, but keep the denominator the same or else the equation is ruined.

32/8 = 4

3. Add all your information together.

DO NOT forget to add the information you collected during the equation, or else you will get a wrong answer. Add the equation's final answer to the whole numbers final answer.

32 / 8 + 6 / 8 = ?

32 / 8 + 6 / 8 = 38 / 8

Well now, remember something. It is asking us, how many 1/8's were in the equation 4 3/4. We have transformed 4 3/4 into a whole equation, 38/8.

Now, all you need to do is look at the numeriator.

What number do you see?

You see 38.

The denominator is the correct denominator that you need. So, the number of the numeriator is the answer to the equation.

So, how many 1/8 are in 38/8?

38!

5 0
3 years ago
Solve for y when x = 5.<br> y = 3x + 4
pantera1 [17]

Answer:

19

Step-by-step explanation:

Plug in

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5 0
2 years ago
5 biscuits cost 40p altogether how much do 3 biscuits cost
STALIN [3.7K]
If 5 biscuits cost 40p

1 biscuit would cost (40p divided by 5) 8p

8p multiplied by 3 (to get 3 biscuits) would cost 24p

3 biscuits cost 24p
7 0
3 years ago
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Fgh is first translated using the rule x,y &gt;x+3,y-1this is followed by a 90 degrees counter clockwise rotation centered at th
maw [93]

Answer:

Rule:

h = (1 - y,x + 3)

Step-by-step explanation:

<em>I will answer generally, since the coordinates of f, g and h are not given</em>

Given

Point: x, y

Translation Rule

1 : x + 3, y - 1

2: 90 degree counterclockwise

Required

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h = (1 - y,x + 3)

If the initial point of h is (2,3),

The new point is:

h = (1 - 3, 2 + 3)

h = (- 2, 5)

5 0
2 years ago
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