Determine whether b can be written as a linear combination of a1 and a2 and a3

RUDIKE [14]

$2 \frac{1}{2}x- \frac{3}{4}(2x+5)= \frac{3}{8}$
$2 \frac{1}{2}x- \frac{6}{4}x- \frac{15}{4}= \frac{3}{8}$
$( 2\frac{1}{2}- \frac{6}{4})x= \frac{3}{8}+ \frac{15}{4}$
$( \frac{5}{2}- \frac{6}{4})x= \frac{3}{8}+ \frac{15}{4}$
$( \frac{10}{4}- \frac{6}{4})x= \frac{3}{8}+ \frac{30}{8}$
$\frac{4}{4}x= \frac{33}{8}$
$x= \frac{33}{8}=4 \frac{1}{8}$

Correct answer: C

6 0

4 years ago

A man walking on a railroad bridge is 2/5 of the way along the bridge when he notices a train at a distance approaching at the c

makkiz [27]

Answer:

The Man needs to run at 9 mph

Step-by-step explanation:

Let M stand for the man's speed in mph. When the man

runs toward point A, the relative speed of the train with respect

to the man is the train's speed plus the man's speed (45 + M).

When he runs toward point B, the relative speed of the train is the

train's speed minus the man's speed (45 - M).

When he runs toward the train the distance he covers is 2 units.

When he runs in the direction of the train the distance he covers

is 3 units. We can now write that the ratio of the relative speed

of the train when he is running toward point A to the relative speed

of the train when he is running toward point B, is equal to the

inverse ratio of the two distance units or

(45 + M) 3

----------- = ---

(45 - M) 2

90+2 M=135-3 M

⇒5 M = 45

⇒ M = 9 mph

The Man needs to run at 9 mph

3 0

3 years ago

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A dog weighs two pounds less than three times the weight of a cat. The dog also weights twenty-two more pounds than the cat. Wri

8090 [49]

Answer:

Weight of dog: 34 pounds,

Weight of cat: 12 pounds.

Step-by-step explanation:

Let d represent weight of dog and c represent weight of cat.

We have been given that a dog weighs two pounds less than three times the weight of a cat.

3 times weight of cat: $3c$

We can represent the given information in an equation as:

$d=3c-2...(1)$

We are also told that the dog also weights twenty-two more pounds than the cat. We can represent the given information in an equation as:

$d=c+22...(2)$

Equate both equations:

$3c-2=c+22$

$3c-c-2=c-c+22$

$2c-2=22$

$2c-2+2=22+2$

$2c=24$

$\frac{2c}{2}=\frac{24}{2}$

$c=12$

Therefore, the weight of cat is 12 pounds.

Substitute $c=12$ in equation (2)

$d=c+22$

$d=12+22$

$d=34$

Therefore, the weight of dog is 34 pounds.

4 0

4 years ago

Help in this Question

Vadim26 [7]

1 gallon = 16 cups. so 16x3.5=56. so 56 cups

7 0

3 years ago

Read 2 more answers

Is it unusual for the sampling mean to be exactly the same as the population mean?

8090 [49]

Answer:

NO

Step-by-step explanation:

This is because the sample should ideally be representative of the whole population. If the right sampling methods are used, the sample should well exhibit the properties of the whole population. The sample mean should be as precise as possible to the population mean , hence it is not unusual for the sampling to mean to be exactly the same as the population mean

4 0

4 years ago