Tutor profile: Joelle E.
You have two similar triangles. Two sides of the first triangle measure 3 cm and 4 cm. The corresponding sides of the second triangle are x and 9 cm. Find the length of side x in the second triangle given the information you know.
Since the triangles are similar, there is some kind of constant relationship or ratio between the corresponding sides of the triangles. So I know that the side that measures 3 cm in the first triangle corresponds to the side x in the second triangle and that the side measuring 4 cm in the first triangle corresponds to the side measuring 9 cm in the second triangle. I can set up a proportion that relates these sides by saying that 3/x=4/9. The numerator of the fractions is from one triangle and the denominator are the numbers from the second triangle according to how they correspond. Then I need to solve for x, and I can do that by cross multiplying. I'd get 4x=27. Then divide both sides by 4 and I'd get that x=27/4=6.75 cm. Remember your units! You could also set up the proportion 3/4=x/9 and cross multiply to get the same answer. You just need to make sure that when you are setting up the proportion you are keeping the corresponding elements consistent. In this case, the first fraction shows the sides of the first triangle, and the second fraction shows the sides of the second triangle in how they correspond.
Subject: Basic Math
Sally is baking cookies. Her recipe calls for 3 and a 1/2 cups of flour. She can only find her 1/2 cup measuring cup. How many times will she need to measure out her 1/2 cup to get the amount she needs for her recipe?
If I divide the 3 cups into halves, then I would have 6 halves then another 1/2 cup to make the total of 3 and a 1/2 cups of flour. That would be 7 measurements the size of 1/2 cup. So Sally would need to use her 1/2 cup 7 times to measure out the full amount for her recipe. You could also think about this as 3.5 divided by .5 so 3.5/.5=7.
Find the solutions to the following quadratic equation: 2x^2-13x-7=0
There are a couple different ways that you could solve this equation, but one way that will always work for any quadratic is the quadratic formula. The standard form of a quadratic equation is ax^2+bx+c=0. The quadratic formula is x= (-b+sqrt(b^2-4ac))/2a and x= (-b - sqrt(b^2-4ac))/2a. In this case, a=2, b= -13, c= -7. Putting these values into the formula for a, b, and c we would get two solutions: 1). x= (-(-13)+sqrt(13^2-4(2)(-7)))/2(2) and 2). x= (-(-13) - sqrt(13^2-4(2)(-7)))/2(2) If you simplify this down, then you'd get x= (13+sqrt(169-(-56))/4 and x= (13-sqrt(169-(-56))/4. Simplify again, x=(13+sqrt(225))/4 and x=(13-sqrt(225))/4 Again: x= (13+15)/4 and x= (13-15)/4 Finally: x=28/4 = 7 and x=2/4=1/2 So you would have the solutions of x=7 and x=1/2 Then check! 2(7^2)-13(7)-7=0. and 2(1/2)^2-13(1/2)-7=0. So it works!
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