PART A: A landmark on the first map is a triangle with side lengths of 3 cm, 4 cm, and 5 cm. What are the side lengths of the tr
1 answer:
Complete Question:
Johnny printed two maps of a walking trail near his home. The length of the walking trail on the first map is 8 cm.
(a) Choose a length between 5 cm and 15 cm for the walking trail on the second map: ________cm.
(b) Determine the scale factor from the first map to the second map.
(c) A landmark on the first map is a triangle with side lengths of 3 cm, 4 cm, and 5 cm. What are the side lengths of the triangle landmark on the second map?
(d) Draw one of the triangles from part C. Label the side lengths and vertices accordingly. You may use this drawing tool or draw your triangle on paper:
Answer:
(a) Length = 4cm
(b) Scale factor = 0.5
(c) 3cm, 4cm and 5cm are represented by 1.5cm, 2cm and 2.5cm respectively, on the second scale
(d) See attachment for triangle
Step-by-step explanation:
(a) Choose a length between 5 cm and 15 cm
<em>--- This is solely up to you (you can make use of any length between 5 cm and 15 cm)</em>
(b) The scale factor
The scale factor (k) is calculated as:
(c) What are side lengths of 3 cm, 4 cm, and 5 cm on the second landmark
Using:
The old lengths, in this case are: 3cm, 4cm and 5cm
Make New length the subject
When
When
When
So: 3cm, 4cm and 5cm are represented by 1.5cm, 2cm and 2.5cm respectively, on the second scale
(d) See attachment for triangle
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Completing the square is pretty hard to explain for me but I'll try my best and hopefully you get what I'm saying in these steps.
First make sure your numbers are all on one side leaving zero on the other side:
z² - 12z + 11 = 0
The next step is the tricky part to explain. So look on the first number and the third number in the formula. The first number is 1z². What multiples equal 1? The only multiples would be one times one (1 x 1). So below z² write one over one like this:
z² - 12z + 11 = 0
But remember this is 1 x 1 and not actually division. For the + 11, think of all the multiples that equal positive 11. It can be 1 x 11 or -1 x -11 so put the first option in fraction form first to test. It doesn't matter which is on top or bottom.
So now you should be left with these:
Now you need to cross multiply here. 1 x 11 and 1 x 1. That will give you two positive numbers 1 and 11. In order to get your middle number from step 1 you need to add these two numbers and see if you will get -12. As you can see 11 + 1 doesn't equal -12 so now we need to use our second option -1 x -11. Our paper should now be changed to this:
Cross multiply. 1 x -11 and 1 x -1. You get -11 and -1 as the result. Add both together and you get -12.
Now you just need to rearrange your fractions here. you can replace your 1 over one to z over z since z x z still equals your problem's z²:
Finally solve for z. Separate parentheses to two separate equations like this:
z - 11 = 0 and z - 1 = 0
z = 11 and z = 1
That should be your answer. Sorry if it still doesn't make sense still.
First make sure your numbers are all on one side leaving zero on the other side:
z² - 12z + 11 = 0
The next step is the tricky part to explain. So look on the first number and the third number in the formula. The first number is 1z². What multiples equal 1? The only multiples would be one times one (1 x 1). So below z² write one over one like this:
z² - 12z + 11 = 0
But remember this is 1 x 1 and not actually division. For the + 11, think of all the multiples that equal positive 11. It can be 1 x 11 or -1 x -11 so put the first option in fraction form first to test. It doesn't matter which is on top or bottom.
So now you should be left with these:
Now you need to cross multiply here. 1 x 11 and 1 x 1. That will give you two positive numbers 1 and 11. In order to get your middle number from step 1 you need to add these two numbers and see if you will get -12. As you can see 11 + 1 doesn't equal -12 so now we need to use our second option -1 x -11. Our paper should now be changed to this:
Cross multiply. 1 x -11 and 1 x -1. You get -11 and -1 as the result. Add both together and you get -12.
Now you just need to rearrange your fractions here. you can replace your 1 over one to z over z since z x z still equals your problem's z²:
Finally solve for z. Separate parentheses to two separate equations like this:
z - 11 = 0 and z - 1 = 0
z = 11 and z = 1
That should be your answer. Sorry if it still doesn't make sense still.
Steps:
but since one of the interiors are missing we will do this.
=
the 50 is canceled so we are left with 100-50 which is 50 so the answer is
Inform me if its wrong.