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3 years ago

b is the midpoint of ac, d is the midpoint of ce, bd=3x, and ae=60. find tye length of ab if ac= 5x+10

Mathematics

1 answer:

Ksivusya [100]3 years ago

8 0

Answer:

AB = 30 units.

Step-by-step explanation:

Given that in a triangle ACE, B and D are mid points of AC and CE respectively.

By triangle theorem for mid points, we have

BD = 1/2 AE

Since AE is given as 60, we get BD =30

But BD also equals 3x (given)

So 3x=30 or x =10

Substitute in AC to get AC = 5x+10 = 5(10)+10 = 60

AB = 1/2 AC = 1/2 (60) = 30 units.

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2 years ago

$7000 is compounded semiannually at a rate of 11% for 21years Find the total amount and round to the nearest cent

photoshop1234 [79]

$\text{Given that }\$7000 \text{ is compounded semiannualy at a rate of }11\% \text{ for 21 years}\\
\\
\text{we know that the amount after t year when compounded is given by}\\
\\
A=P\left ( 1+\frac{r}{n} \right )^{nt}\\
\\
\text{here P is the principal amoount, so }P=7000,\\
\\
\text{r is the interest rate, }r=11\%=0.11\\
\\
\text{n is the number of times in a year, here semiannulay, so }n=2,\\
\\
\text{and t is the time, so }t=21\\
\\
\text{so the amount after 21 years is}$

$A=7000\left ( 1+\frac{0.11}{2} \right )^{2(21)}\\
\\
\Rightarrow A=7000\left ( 1+0.055 \right )^{42}\\
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\Rightarrow A=7000\left ( 1.055 \right )^{42}\\
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3 years ago

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babymother [125]

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