What is 5 1/2 x 2 1/3 ?

Learning Task 3

ASHA 777 [7]

Answer:

1. The sides are: 38.5, 39.5, 40.5 and 41.5

2. Presently, Inzo is 15 years old and Miz is 10 years old

3. $Distance = 3682km$

4. Possible pairs are: (12, 14), (16, 18) and (20, 24)

5. $L < 38m$

Step-by-step explanation:

The question has lots of missing details. See the comment section for complete question

Solving (a):

Given

Shape: Quadrilateral

Sides: Consecutive

$Perimeter = 160$

Let one of the sides be x. The other sides will be x + 1, x + 2 and x + 3.

So, the perimeter is:

$Perimeter = x + x + 1 + x + 2 + x + 3$

This gives:

$160 = x + x + 1 + x + 2 + x + 3$

Collect Like Terms

$160 -1-2-3= x+x+x+x$

$154= 4x$

Divide both sides by 4

$38.5 = x$

$x =38.5$

So, the sides are: 38.5, 39.5, 40.5 and 41.5

Solving (b):

Given

Presently: $Inzo = 10 + Miz$

Five years ago: $Miz - 5= \frac{1}{3} * (Inzo-5)$ --- (Missing from the question)

Required: Determine their present ages

Substitute $10 + Miz$ for Inzo in the second equation

$Miz - 5 = \frac{1}{3} * (10 + Miz - 5)$

$Miz - 5 = \frac{1}{3} * (Miz + 5)$

Multiply both sides by 3

$3Miz - 15 = Miz + 5$

Collect Like Terms

$3Miz -Miz = 15 + 5$

$2Miz= 20$

Divide both sides by 2

$Miz = 10$

Substitute 10 for Miz in $Inzo = 10 + Miz$

$Inzo = 10 + 5$

$Inzo = 15$

So presently, Inzo is 15 years old and Miz is 10 years old

Solving (3):

Given

Express Train:

$Speed = 100kph$

$Time = t$

Local Train:

$Speed = 45kph$

$Time = t + 45$

Required: Determine the distance between A and B

Distance is calculated as:

$Distance = Speed * Time$

For the express train:

$Distance = 100 * t$

For the local train

$Distance = 45 * (45 + t)$

Distance between both stations are equal; So,

$100 * t = 45 * (45 + t)$

$100 t = 2025 + 45t$

Collect Like Terms

$100 t -45t= 2025$

$55t= 2025$

Divide by 55

$t = 36.82$

Substitute 36.82 for t in $Distance = 100 * t$

$Distance = 100 * 36.82$

$Distance = 3682km$

Solving (4):

Let the even numbers be: n and n + 2.

Sum greater than 24: $n + n + 2 > 24$

Sum less than 60: $n + n + 2 < 60$

So, we have:

$n + n + 2 > 24$

$2n + 2 > 24$

Collect Like Terms

$2n > 24-2$

$2n > 22$

$n > 11$

$n + n + 2 < 60$

$2n + 2< 60$

Collect Like Terms

$2n < 60-2$

$2n < 58$

Divide by 2

$n$

So, we have:

$n > 11$ and $n < 29$

So, possible pairs are: (12, 14), (16, 18) and (20, 24)

Solving (5):

Given

$Perimeter < 152m$

Required: Find the possible lengths

Let the length be L.

Perimeter is calculated as:

$Perimeter =4 * L$

$Perimeter =4 L$

So, we have:

$4L < 152m$

Divide through by 4

$L < 38m$

Hence, length is less than 38m (e.g. 37m)

5 0

3 years ago

ABCEDEFGH is a regular octagon. The minimum degree of rotation by which this octagon can map onto itself is . It will take incre

Mrrafil [7]

Answer:

45 or multiples of 45 around the centre of octagon

Step-by-step explanation:

Given that ABCDEFGH is a regular octagon. i.e. it has 8 sides.

Since regular ocagon, all interior angles would be equal.

Sum of all interior angles of octagon = 2(8)-4 right angles

= 12 right angles

Hence each angle = 12(90)/8 = 135 degrees

Thus the octagon when rotated will take the same shape if vertices interchange also due to the property that all sides and angles are equal

Since each angle is 135 imagine an octagon with one vertex at origin O, and adjacent vertex B on x axis. OB has to be coincident with BC the next side or the previous side to get it mapped onto itself

The centre will be at the middle with each side subtending an angle of 45 degrees.

Hence if rotation is done around the centre with 45 degrees we will get octagon mapped onto itself.

45, 90, 135 thus multiples of 45

8 0

3 years ago

What is the constant of proportionality for y=-5x ?

Firlakuza [10]

a constant of proportionality is a number you have to multiply x by to get y.

y=kx is the equation that expresses the proportionality of x and y

the constant of proportionality is k, so k=-5

5 0

3 years ago

One gallon is equal to about 3.785 liters. What is this amount rounded to the nearest tenth? To the nearest hundredth? Show your

Leokris [45]

Answer:

3.8 ; 3.79 ; 3

Step-by-step explanation:

Given that:

1 gallon is equal to about 3.785 litres

3.785 to the nearest tenth :

Tenth digit = 7 ; round up 8 to 1 and add to 7

Hence,

3.785 = 3.8 (nearest tenth)

3.785 to the nearest hundredth :

Hundredth digit = 8 ; round up next digit 5 to 1 and add to 8

3.785 = 3.79 ( nearest hundredth)

What is the greatest number of whole liters of water you could pour into a one-gallon container without it overflowing?

The greatest Number of whole liters of water that could be poured into a 1 gallon container without it overflowing is 3 liters because, rounding up 3.785 to the nearest integer of 4 means we will exceed the maximum litres by about 0.215 gallons and hence, cause the container to overflow.

3 0

3 years ago

What is 97.6% as a decimal?

VARVARA [1.3K]

Your percentage of 97.6% as a decimal is 0.976

7 0

3 years ago