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3 years ago

The table shows the value of Susie's bank account during a 5-year period. At what rate has her account value been growing?

Mathematics

2 answers:

Finger [1]3 years ago

8 0

A) $16,000 per year

Talja [164]3 years ago

4 0

The value of Susie's account increases by $4,000 a year.
8,000 + 4,000 = 12,000; 12,000 + 4,000 = 16,000; 16,000+ 4,000 = 20,000; and 20,000 + 4,000 = 24,000.

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A triangle has two sides of length 2 and 18. What is the largest possible whole-number length for the third side?

Snezhnost [94]

Answer:

Step-by-step explanation:

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2 years ago

Find all solutions of the equation in the interval [0, 2pi).

natali 33 [55]

Answer:

Step-by-step explanation:

Begin by squaring both sides to get rid of the radical. Doing that gives you:

$sin^2x=1-cosx$

Now use the Pythagorean identity that says

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$1-cos^2x=1-cosx$ . Now move everything over to one side of the equals sign and set it equal to 0 so you can factor:

$1-cos^2x+cosx-1=0$ and then simplify to

$cosx-cos^2x=0$

Factor out the common cos(x) to get

$cosx(1-cosx)=0$ and there you have your 2 trig equations:

cos(x) = 0 and 1 - cos(x) = 0

The first one is easy enough to solve. Look on the unit circle and see where, one time around, where the cos of an angle is equal to 0. That occurs at

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8 0

3 years ago

Melissa and Emily are playing at the pool.They have three different measuring jars for; liters, cups, and pints. They find that

Deffense [45]

7 cups + 3 litres = 9.8 pints
$7c+3l=9.8p$ ⇒ Equation 1

5 litres - 9 cups = 6 pints
$5l-9c=6p$ ⇒ Equation 2

Relationship between cups and litres
Rearranging equation 1 to make pints the subject
$7c+3l=9.8p$
$p= \frac{7c+3l}{9.8}$ ⇒ substitute this into Equation 2

$5l-9c= \frac{7c+3l}{9.8}$
$49l-88.2c=7c+3l$
$49l-3l=7c+88.2c$
$46l=95.2c$
$l=2.1c$

Hence, 1 litre = 2.1 cups

Relationship between cups and pints
Rearrange equation 1 to make litres the subject
$7c+3l=9.8p$
$3l=9.8p-7c$
$l= \frac{9.8p-7c}{3}$ ⇒ Substituting this into Equation 2

$5( \frac{9.8p-7c}{3})-9c=6p$
$\frac{49p-35c}{3}-9c=6p$
$\frac{49}{3}p- \frac{35}{3}c-9c=6p$
$\frac{49p}{3}-6p= \frac{35}{3}+9c$
$\frac{31}{3}p= \frac{62}{3}c$
$p=2c$

Hence, 1 pint = 2 cups

Relationship between pints and litres
Rearranging equation 1 to make cup the subject

$7c=9.8p-3l$
$c= \frac{9.8p-3l}{7}$ ⇒ subsitute this into equation 2

$5l-9( \frac{9.8p-3l}{7})=6p$
$5l- \frac{63}{5}p+ \frac{27}{7}l=6p$
$5l+ \frac{27}{7}l=6p+ \frac{63}{5}p$
$\frac{62}{7}l= \frac{93}{5}p$
$l=2.1p$

Hence, 1 litre = 2.1 pints

7 0

3 years ago