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4 years ago

The fourth term of an arithmetic

Mathematics

1 answer:

yulyashka [42]4 years ago

5 0

Answer:

Step-by-step explanation:

Given AP where:

a₄ = 2a₂ - 1
a₆ = 7

To find

a₁ = ?

Since

a₄ = a₁ + 3d
a₂ = a₁ + d
a₆ = a₁ + 5d

Initial equations will change as:

a₁ + 3d = 2(a₁ + d) - 1 ⇒ a₁ + 3d = 2a₁ + 2d - 1 ⇒ a₁ = d + 1
a₁ + 5d = 7 ⇒ a₁ = 7 - 5d

Comparing the above:

d + 1 = 7 - 5d
6d = 6
d = 1

Then:

a₁ = d + 1 = 1 + 1 = 2
a₁ = 2

The first term is 2

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The length of a rectangle is represented by 2x + 4, and its width is represented by 3x + 1. the perimeter of the rectangle is 25

defon

Formula to find perimeter
2(l + w) = perimeter

Input the algebra to the formula, and you'll find x
2(2x + 4 + 3x + 1) = 25
2(5x + 5) = 25
10x + 10 = 25
10x = 15
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3 years ago

Drag the similar figure into the table.

Wittaler [7]

There wasn't no pictures nor choices so I'm afraid that I had to look it up... The first link was from Brainly and "Tetianaalnasraween05" was asking the same question.

Original Figure: 6 and 3

'Similar' Figure(s):

1.) 4 and 2

2.) 10 and 4

3.) 6 and 6

Ratio of sides are 3/2 and 6/4, 6/4 could be simplified as 3/2, so as my guess, it is, 4 and 2

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4 0

3 years ago

The credit purchase of a new oven for $5,900 was posted to Kitchen Equipment as a $5,900 debit and to Accounts Payable as a $5,9

JulsSmile [24]

Answer: $10,800

Step-by-step explanation:

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6 0

3 years ago

When the sum of a number and 3 is subtracted from 10 the result is 5 solve om algebraic equation?

german

Answer:

y = 2

Step-by-step explanation:

Algebraic Equation is an equation where alphabets are used to represent numbers.

Solving the above question,

Let the number = y

Therefore,

Sum of the number = y + 3

If it's subtracted from 10 it becomes

10 - ( y + 3 )

The result : 10 - y - 3 = 5

- y = 5 - 10 + 3

- y = -2

Therefore,

y = 2

5 0

2 years ago

Find the point P on the line yequals=66x that is closest to the point (74 comma 0 )(74,0). What is the least distance between P

tekilochka [14]

Answer:

The point P that is closest to the point (74, 0) is P(7.4, 22.2), and the least distance between P and (74, 0) is 70.2

Step-by-step explanation:

Given

y = 66x

And a point A(74, 0)

We are required to find the point on the line that is closest to A, and then find the distance between these points.

Let the point be P(s, t)

Because it's coordinate satisfies the given equation

y = 3x

Let t = 3s, then we have

p(s, t) = P(s, 3s)

Next, we find the distance between P and A

Let the distance be

D = √[(x1 - y1)² + (x2 - y2)²]

Here x1 = 74, x2 = 0, y1 = s, y2 = 3s.

D = √[(74 - s)² + (0 - 3s)²]

= √(s² - 148s + 5476 + 9s²)

= √(10s² - 148s + 5479)

To maximize the distance, we find the derivative of D with respect to s, and set it to 0.

That is dD/ds = 0

dD/ds =

(20s - 148)/2√(10s² - 148s 5479) = 0

=> 20s - 148 = 0

20s = 148

s = 148/20

s = 7.4

Since t = 3s, we have

t = 22.2

So, the point is P(7.4, 22.2)

Finally, we find the distance D.

D = √[(74 - s)² + (0 - 3s)²]

D = √[(74 - 7.4)² + (0 - 3×7.4)²]

D = √(4435.56 + 492.84)

= √4928.4

D = 70.2

Therefore, the distance is 70.2

4 0

3 years ago