Hi there!
<u><em>FACTS</em></u><em> :</em>
<em>To see if multiple ratios are proportional, you can write them as fractions, reduce them, and compare them. If the reduced fractions are all the same, then you have proportionnal ratios. You can also write them as fractions and divide the numerator (top number) by its denominator (bottom number), and compare the decimal numbers the same way you would compare the fractions (I personnaly find this method easier because you don't need to simplify the fractions).</em>
<u>STEPS TO ANSWER:</u>
x = 1 ; y = 90 → 
1 ÷ 90 = <u>0.01111111...</u>
x = 2 ; y = 150 → 
2 ÷ 150 = <u>0.0133333...</u>
x = 3 ; y = 210 → 
3 ÷ 210 = <u>0.01428571</u>
x = 4 ; y = 270 → 
4 ÷ 270 = <u>0.0148148...</u>
x = 5 ; y = 330 → 
5 ÷ 330 = <u>0.01515152</u>
<em>** You didn't really need to calculate them all because even the first two decimal numbers weren't equivalent, but I wanted to show you the whole process so I calculated them all.</em>
⇒ If you compare all the decimals you got, you can easily see that they are not the same, which means that the ratios between the values of "x" and the values of "y" are not proportional. Therefore, George's reasoning wasn't good.
There you go! I really hope this helped, if there's anything just let me know! :)
Answer:
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Step-by-step explanation:
An isosceles triangle is a type of triangle where 2 sides are equal.
Picture out 2 triangles with the same base length.
On the first triangle, its legs are twice the length of the legs of the second triangle.
To put it into variables, let:
B = the same base length of the two triangles
A = the length of one leg the smaller triangle
2A = the length of one leg of the bigger triangle
Given: Perimeter of smaller triangle = 23cm
Perimeter of bigger triangle = 43cm
Recall the formula for solving the perimeter of a triangle:
Perimeter = A + B + C
where, A, B, and C are the legs of the triangle
Since the triangle involved is an isosceles triangle, therefore, we can say that
Perimeter = 2A + B , 2 legs are equal ( A=C )
Substituting the given perimeter value to the formula.
23cm = 2A + B ⇒ equation 1 (smaller triangle)
43cm = 2(2A) + B ⇒ equation 2 (bigger triangle)
Simplifying equation 2.
43cm = 4A + B
(rearranging) B = 43cm - 4A ⇒ equation 3
Substituting equation 3 to equation 1:
(equation 1) 23cm = 2A + B
23cm = 2A + (43cm - 4A)
23cm = -2A + 43cm
2A = 43cm - 23cm
2A = 20cm ⇒ length of the leg of the bigger triangle
A = 10cm ⇒ length of the leg of the smaller triangle
To solve for the base length, just substitute the value of A to equation 3
(equation 3) B = 43cm - 4A
B = 43cm - 4(10cm)
B = 3 cm
Final Answer:
• For the smaller triangle, the length of the sides are 10cm, 10cm, and 3cm
• For the bigger triangle, the length of the sides are 20cm, 20cm, and 3cm
Answer: f(x)=125g+50
Explanation: He is charging $125 for each gold piece so you would multiply “g” and 125.
You would add 50 as a one time fee so you add 50.
