All categories

3 years ago

How can you tell that a system of linear equations will have infinitely many solutions without computation?

1 answer:

3 0

If you can manipulate the two equations so that they have exactly the same coefficients (e. g., 3x + 4y = 8 and 2x + 4y = 8), then you conclude that the two lines coincide (overlap), and that there are thus infinitely many solutions.

You might be interested in

What multiplied by 3 equals 15 but added by 3 equals 18

Ivenika [448]

Answer:

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

A room with a length of 270 cm and width 150 cm is to be covered with square tiles .What is the largest size of tiles to be used

Damm [24]

Find the greatest common factor of both numbers:

Factors for 150:

150: 1, 2, 5 , 6, 10, 15, 25, 30, 50, 75, 150

Factors for 270:

1, 2, 3, 5, 6 , 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270

The largest number they both have in common is 30, so the largest tile could be 30 cm^2.

5 0

3 years ago

You must calculate the number of sheets of plywood needed for subflooring. Each sheet of plywood measures 4'by 8. The measuremen

snow_lady [41]

Answer:

25 sheets of plywood will be needed

Step-by-step explanation:

Each sheet of plywood measures $4ft*8ft=32ft^{2}$ .

We have to cover the surface of the house, minus the surface of the hole of the stairs.

$Surface _{to cover} = Surface _{house} -Surface _{hole}= (28ft*30ft)-(12ft*4ft)= 840ft^{2}-48ft^{2}=792ft^{2}$

To know how many sheets will be needed, we divide the surface to be covered by the surface of each sheet

$Sheets_{needed} =\frac{Surface _{house}}{Surface _{sheet}} =\frac{792ft^{2}}{32\frac{ft^{2}}{sheet} } = 24,75 sheets$

As we can't buy 0,75 of a sheet, we round it up, i.e. we will need 25 sheets of plywood for subflooring.

8 0

3 years ago

John does 5 pushups on the first day of a 30-day month, and then increases the number of pushups by 2 pushups a day. how many pu

xxMikexx [17]

He has done 70 push ups because by the 15th he has done 35 push ups add 15 more days and u get 70 .

7 0

3 years ago

Read 2 more answers

Everett is rolling a block with the numbers 1, 2, 3, 4, 5, and 6 on it. Finley is drawing one disk from a basket of three disks:

ioda

Option A:

The probability that Everett and Finley end up with an even number and a blue disk is $\frac{1}{6}$ .

Solution:

Given data:

Everett is rolling a block with numbers = {1, 2, 3, 4, 5, 6}

Finley is drawing one disk from basket with colors = {blue, red, yellow}

Total number of numbers = 6

Total number of colors = 3

$$\text { Probability }=\frac{\text {Number of possible outcomes}}{\text {Total number of outcomes}}$

$P\text{(Even number)} =\frac{3}{6}$

$P\text{(Blue disk)} =\frac{1}{3}$

$P\text{(Even number and Blue disk)} =\frac{3}{6}\times\frac{1}{3}$

$$=\frac{3}{18}$

Divide numerator and denominator by the common factor 3.

$$=\frac{3\div3}{18\div3}$

$$=\frac{1}{6}$

Option A is the correct answer.

Hence the probability that Everett and Finley end up with an even number and a blue disk is $\frac{1}{6}$ .

3 0

3 years ago