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Mathematics

1 answer:

marta [7]3 years ago

5 0

Hi there!

$\large\boxed{\text{ UVY} = 65^o, \text{ VYZ }= 65^o}$

We can begin by finding ∠VUY so we can solve for ∠UVY.

∠VUY is supplementary to ∠TUY, so:

180 = 144 + ∠VUY

∠VUY = 36°

In a triangle, angles sum up to 180°, so:

180 = 36° + 79° + m∠UVY

m∠UVY = 65°

Solve for m∠VYZ by comparing the angle to m∠UVY because the angles are alternating interior angles. Thus:

m∠UVY = m∠VYZ = 65°.

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James invested $300 in a bank account that earns simple interest. He earns $24 at the end of 12 months. James invests $500 at th

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Answer: $40

Step-by-step explanation:

The key formula to use for this problem is the simple interest formula, which is $I=prt$ ; where I is the interest earned, p is the principal (initial) amount, r is the interest rate, and t is the amount of time that passes.

Since we know that both investments have the same interest rate, we can use the information from the first part of the problem to solve for the interest rate. Using algebra, we can rearrange the simple interest formula to solve for the interest rate: $r=I/pt$ . We know that our interest earned is $24 and our principal amount is $300. To make things easier, we'll also convert months to years, which is easy to do since we know that 12 months = 1 year. This gives us our value for the amount of time that passes. Now, all we have to do is plug in our values into the rearranged equation above.

We should now have: $r=\frac{24}{300*1}=0.08$

Now, to find the interest earned from the $500 investment, we just need to plug in our values from the second part of the problem, along with our calculated interest rate of 0.08, into the original formula of $I=prt$

This should result in $I=500*0.08*1=40$