What is 2mm to kilometers?

The product of the first three terms of a geometric progression is 3375, and their sum is 65. Find the first term of this progre

artcher [175]

Answer:

5 or 45

Step-by-step explanation:

If the first term is "a" and the common ratio is "r", then the first three terms are ...

a, ar, ar²

Their product will be ...

a × ar × ar² = (ar)³ = 3375

ar = ∛3375 = 15

Their sum will be ...

a + ar + ar² = 65 = 15/r + 15 + 15r

Subtracting 15 and multiplying by r/5, we have the quadratic in r:

10r = 3 + 3r²

3r² -10r +3 = 0 . . . . in standard form

(3r -1)(r -3) = 0 . . . . factored

r = 1/3 . . or . . 3 . . . . values of r that make the factors zero

The first term is 15/r = 45 or 5

_____

The first three terms could be 5, 15, 45; or they could be 45, 15, 5.

5 0

3 years ago

I need help 2(x + 1) = 2x + 2.

Ksju [112]

$2(x + 1) = 2x + 2\\
2x+2=2x+2\\
0=0\\
x\in\mathbb{R}$

7 0

3 years ago

1. If the product of the integers a,b, and c is 1, then what is the difference between the largest and the smallest possible val

DochEvi [55]

Problem 1

The largest value would be 1 and the smallest would be -1.

To get a product of 1, either all are 1 or two of the variables are -1 and the other one is 1.

Largest value = (1)^2 * (1)^3 * (1)^4 =1

Smallest value = (- 1)^2 * (- 1)^3 * (1)^4 = -1

The difference is:

largest value – smallest value = 1 – (-1) = 2

Therefore the answer is letter D.

Problem 2

% loss = (final price – initial price) * 100%/ initial price

where, final price per dozen = ( $2.50 / piece) (12 piece / dozen) = $30

Therefore,

% loss = ($30 - $33) * 100 / $33

% loss = - 300/ 33 = 9 1/11

Therefore the answer is letter C.

7 0

3 years ago

Isabel is thinking of an even number between 234 and 250 . The sum of the digits is double the digit in the ones place. What is

Dvinal [7]

Since the required number is between 234 and 250, then the first digit of the number is 2 and the second digit can either be 3 or 4.

Let the second and the third digits be x and y respectively, then

2 + x + y = 2y

Consider when the second digit is 3, then

2 + 3 + y = 2y
5 = y

Thus, the number is 235.

Similarly, consider when the second digit is 4, then

2 + 4 + y = 2y
6 = y

Thus, the number is 246.

Since the required number is an even number, therefore, Isabel's number is 246.

4 0

3 years ago

The diagonals of a rhombus bisect each other of measures 8cm and 6cm .Find its perimeter. please help !!!!!!!!!!!!!!!!!!!!!!!!

Delvig [45]

Answer:

20 cm

Step-by-step explanation:

8/2 = 4

6/2 = 3

3 and 4 are the sides of the triangle (four triangles in rhombus)

$a^{2} + b^{2} = c^{2} \\4^{2} + 3^{2} = c^{2}$

c = 5

5 x 4 = 20

Hope that helped!!! k

8 0

3 years ago