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3 years ago

What is the LCM and GCF for 32 and 45

2 answers:

6 0

The greatest common factor (GCF) of 32 and 45 is: 1
Factors of 32: 1, 2, 4, 8, 16, 32
Factors of 45: 1, 3, 5, 9, 15
The only common factor between them is 1, also making it the greatest common factor.

The least common multiple (LCM) of 32 and 45 is: 1440
32 × 45 = 1440 / 45 × 45 = 1440

GCF = 1
LCM = 1440

jeyben [28]3 years ago

5 0

LCM: 1440
GCF: 1
should be it

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use the matrix tool to solve the system of equations enter the answer as an ordered pair. 8x+5y=9 -x+y=7

Dimas [21]

Answer:

x = -44/13

y = -65/13

Step-by-step explanation:

Using matrix form means using the crammers rule

The matrix form of the expression is written as;

$\left[\begin{array}{ccc}8&5\\-1&1\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}9\\7\\\end{array}\right]$

AX = B

taking the determinant of A;

|A| = 8(1) - 5(-1)

|A| = 8 + 5

|A| = 13

After replacing the first row with the column matrix;

$A_x =\left[\begin{array}{ccc}9&5\\7&-1\\\end{array}\right]$

|Ax| = 9(-1)-5(7)

||Ax| = -9 - 35

|Ax| = -44

x = |Ax|/|A|

x = -44/13

similarly for y

$A_x =\left[\begin{array}{ccc}8&9\\-1&7\\\end{array}\right]$

|Ay| = 8(7)+9

|Ay| = 56+9

|Ay| = 65

y = |Ay|/|A|

y = -65/13

6 0

3 years ago

Please answer soon.

Eva8 [605]

<u>Answer-</u>

Set of constraints to model the problem are,

$12x+9y\geq 510\\y \leq 2x\\y \geq 25$

<u>Solution-</u>

Let us assume,

x = the number of lawns weeded by Gwen,

y = the number of dogs walked by Fabio.

Gwen charges $12 each time she weeds a yard and Fabio charges $9 each time he walks a dog,

$\text{Earnings of Gwen} = 12x\\\text{Earnings of Fabio} = 9y\\\text{Total earnings of Gwen and Fabio} = 12x+9y$

They need at least $510 to purchase the new gaming station, means they need $510 or more than $510.

An equation for this situation will be,

$12x+9y\geq 510$

The number of dog walked by Fabio has scheduled is no more than twice the number of yards Gwen has scheduled to weed, means y must be less than or equal to 2x.

An equation for this situation will be,

$y \leq 2x$