Core Connections Course 1 Student 1st Edition Chapter 4 Variables and Ratios
Core Connections Course 1 Student 1st Edition Chapter 4 Exercise 4.2 Solutions Page 185 Problem 1 Answer
The given original picture of the mascot is as below :
It is required to fills the large grid using original picture of the mascot Fill the large grid given from the teacher using the original mascot.
The enlargement grid has been filled as below :
Hence, the filled grid using original picture of the mascot is as below :
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Core Connections Course Chapter 4 Page 186 Problem 2 Answer
The assigned part of the mascot is foot.
Also, the original and enlarged mascot are as below :
It is required to assigned part on the original mascot in centimeters and the corresponding part of the enlarged mascot.
Hence, length of foot of original mascot is 2 centimeters and length of foot of enlarged mascot is 4 centimeters.
Core Connections Course Chapter 4 Page 186 Problem 3 Answer
The table, original and enlarged mascot are as below :
It is required to measure different parts of the original and enlarged mascot and complete the given table.
Measure the length of different parts of mascot and fill the measurement in the table.
Data collected from different groups measuring different parts of mascot is as below :
For original mascot,
Length of the foot=2cm
Length of the ear=1.5cm
Length of the tail=4cm
Length of the eye=2cm
Length of the nose=2.5cm
For enlarged mascot,
Length of the foot=4cm
Length of the ear=3cm
Length of the tail=8cm
Length of the eye=4cm
Length of the nose=5cm
Use the measured values in step 1 to complete the table as below :
Hence, the given table is completed as below :
Page 186 Problem 4 Answer
We have completed table from part-b as below :
It is required to examine the data collected and describe the relationship between parts of the original mascot picture and the enlarged model of the mascot.
Solution : Notice the completed table, all the parts in enlarged mascot became double than the parts in the original mascot.
Thus, each part of the original mascot has increased by same ratio to form the enlarged mascot.
Hence, all the parts in enlarged mascot became double than the parts in the original mascot i.e. each part of the original mascot has increased by same ratio to form the enlarged mascot.
Core Connections Course Chapter 4 Page 186 Problem 5 Answer
The original and enlarged mascot are as below :
It is required to tell if any part of the enlarged picture that seems to be the wrong size.
Solution : Notice the original and enlarged mascot, no any part of the enlarged picture that seems to be the wrong size. If it happens then parts nearby this wrong sized part will be also in wrong size and eventually shape of the whole enlarged mascot will be changed.
Hence, no any part of the enlarged picture that seems to be the wrong size. If it happens then parts nearby this wrong sized part will be also in wrong size and eventually shape of the whole enlarged mascot will be changed.
Chapter 4 Exercise 4.2 Variables And Ratios Solutions Core Connections Course 1 Page 186 Problem 6 Answer
It is given that the nose got two times bigger and the eyes got five times bigger.
It is required to explain why is it necessary that all parts of the original picture grow in the same way.
Solution : All parts of the original picture should grow in the same way so that the ratio between the length and width of the picture stays the same.
If the nose got two times bigger, it should have gotten two times bigger in both length and width. It is necessary to preserve the ratio so the shape of the objects stays the same.
Hence, it is important that all parts of the original picture grow in the same way so that the ratio between the length and width of the picture stays the same.
It is necessary to preserve the ratio so the shape of the objects stays the same.
Core Connections Course Chapter 4 Page 188 Problem 7 Answer
The given initial dimension of square is 5×5.It is required to draw a design inside 5×5square and then enlarge the image to 15×15.
Draw 5×5 square on graph paper and draw a design inside it. Now, draw the same image enlarged such that dimension of the square is 15×15.
A square having 5 units on each side is drawn below. A figure of yellow square of side 3 units is drawn inside it.
Another square of side 15 units is drawn on the right, to inscribe the same figure inside new square we had to increase the side of yellow square 3 times because side of square is increased 3 time.
New picture inside the square is 9 unit wide and 9 unit long.
Hence, following the given steps we have picture as shown below :
Also, new picture inside the square is 9 unit wide and 9 unit long.
Core Connections Course 1 Chapter 4 Exercise 4.2 Step-By-Step solutions Page 188 Problem 8 Answer
Total amount is given $43.00.It is required to divide $43.00 evenly.
To distribute the earned $43.00 evenly among the 4 friends divide the total amount $43 by 4.
Dividing the total amount $43.00 by 4 we have, $43/4=$10.75
Therefore each friend will receive$10.75.
Hence, dividing the earnings$43.00 evenly each friend earns $10.75.
Core Connections Course Chapter 4 Page 188 Problem 9 Answer
The given generic rectangle is as below :
It is required to complete the given generic rectangle.
Assign the blank values outside the rectangle as x,y and z.
Now, make the equation using given generic rectangle for x,y and z and solve it to get the values of x,y and z.
Let’s assume x,y,z as the numbers on side of the rectangle as shown below.
We know that 800 is the product of 40 and x and 500 is the product of 5 and y and 30 is the product of 5 and z.
So, 800=40x
⇒x=800/40
⇒x=20
500=5y
⇒y=500/5
⇒y=100
30=5z
⇒z=30/5
⇒z=6
Now, put the values of x,y,z in generic rectangle as below :
Using the generic rectangle with known values of x,y,z remaining rectangle can be filled as :
Total Product=2000+800+120+500+200+30
Total Product=3650
Total Product=25×146
It represents the product between 25 and 146.
Hence, the given generic rectangle can be completed as below :
Also, it represents the product between 25 and 146.
Core Connections Course Chapter 4 Page 190 Problem 10 Answer
We are given a rectangle that measures 5 units by 3 units We need to enlarge it such that each side becomes 4 times the original side
New sides: 20×12
The sides of the rectangle are 20×12.
Solutions For Core Connections Course 1 Chapter 4 Exercise 4.2 Variables And Ratios Page 190 Problem 11 Answer
We need to make a right triangle with a base of 2 units and a height of 3 units.
Then we need to draw three more triangles so that the lengths of the new sides are 50%, 300% and 500% of the original.
The three triangles are:
The three triangles are drawn.
Core Connections Course Chapter 4 Page 190 Problem 12 Answer
We need to plot the given ordered pairs on the graph.
Then we need to connect the points obtained and tell what shape it makes.
By joining the ordered pairs, rectangle is obtained.
graph:
By plotting the ordered pairs, rectangle is obtained.
Core Connections Course 1 Student 1st Edition Chapter 4 Exercise 4.2 Guide Page 190 Problem 13 Answer
We are given the rectangle with coordinates:(−2,4),(2,4),(−2,−4) and (2,−4)
We need to find the length of each of the sides of the shape we made.
We will do this by using x and y coordinate
The length of two vertical sides can be find out by using y coordinate:
Length: =∣4−(−4)∣=8units
The length of two horizontal sides can be find out by using x coordinate:
Length: ∣2−(−2)∣=4 units
The dimensions of rectangle are : 4×8 square units.
Core Connections Course Chapter 4 Page 190 Problem 14 Answer
We need to make a figure that is enlarged by a factor of 1.5 and still has one corner (or vertex) at (−2,−4).
We also need to find the coordinates of the corners (or vertices) for the new shape.
Also, we need to calculate the lengths of the sides now.
We will do this by using the coordinates of the old and the new rectangle.
The coordinates of the new rectangle are:
(−2,8), (4,8), (4,−4),(−2,−4)
The length of the new rectangle will be 1.5 times than the original rectangle.
length: =8×1.5=12 units width: =4×1.5=6 units
The figure is obtained as:
The dimension of the new figure is: Length =12 units and width =6units
Core Connections Course Chapter 4 Page 190 Problem 15 Answer
We need to make a figure that is reduced by a factor of 3/4 and still has one corner (or vertex) at (−2,−4)
We also need to find the coordinates of the corners (or vertices) for the new shape.
Also, we need to calculate the lengths of the sides now.
We will do this by using the coordinates of the old and the new rectangle.
The coordinates of the new rectangle are:
(−2,2),(1,2),(2,−4) ,(−2,−4)
The length of the new rectangle will be 3/4 times than the original rectangle.
Length: =8×3/4=6units
Width: =4×3/4=3units
Graph:
The length of the new figure is 6units and width of the new figure is 3 units.
Core Connections Course Chapter 4 Page 191 Problem 16 Answer
We first need to copy the diagram at right onto graph paper.
Then, we need to draw a smaller copy with sides that are 2/3 the lengths of the original.
We will do this by calculating the new base, height and length of the figure.
Since, the smaller copy is 2/3 the size of the original, the dimensions are:
New sides:
New base:2/3×9=6units
New height:2/3×6=4units
Top length:2/3×3=2units
Graph:
The smaller copy of 2/3 the size of original is being made.
Core Connections Course Chapter 4 Page 191 Problem 17 Answer
We need to tell if an image is enlarged correctly or not.
19/10/2021 Enlarging figures:
We know that to enlarge a figure, we need to increase all dimensions in same proportion.
Ratio of the limbs of the original figure must be equal to that of the new figure.
The enlarged figure must be similar to the original figure, the two figures should match all the slopes correctly and must be identical in shape and form.
If the enlarged figure is similar to the original figure in all the respects, the we can say that the figure has been enlarged correctly.
The enlarged figure must be similar to the original figure.