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gulaghasi [49]
3 years ago
12

A colony of 1,000 bacteria doubles in size every 14 minutes. What will the population be 42

Mathematics
1 answer:
Virty [35]3 years ago
3 0
It will be 3,000 because 14 x 3 = 42 and 1,000 x 3 = 3,000
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find the area of the trapezium whose parallel sides are 25 cm and 13 cm The Other sides of a Trapezium are 15 cm and 15 CM​
Snezhnost [94]

\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}

  • Given - <u>A </u><u>trapezium</u><u> </u><u>ABCD </u><u>with </u><u>non </u><u>parallel </u><u>sides </u><u>of </u><u>measure </u><u>1</u><u>5</u><u> </u><u>cm </u><u>each </u><u>!</u><u> </u><u>along </u><u>,</u><u> </u><u>the </u><u>parallel </u><u>sides </u><u>are </u><u>of </u><u>measure </u><u>1</u><u>3</u><u> </u><u>cm </u><u>and </u><u>2</u><u>5</u><u> </u><u>cm</u>

  • To find - <u>Area </u><u>of </u><u>trapezium</u>

Refer the figure attached ~

In the given figure ,

AB = 25 cm

BC = AD = 15 cm

CD = 13 cm

<u>Construction</u><u> </u><u>-</u>

draw \: CE \: \parallel \: AD \:  \\ and \: CD \: \perp \: AE

Now , we can clearly see that AECD is a parallelogram !

\therefore AE = CD = 13 cm

Now ,

AB = AE + BE \\\implies \: BE =AB -  AE \\ \implies \: BE = 25 - 13 \\ \implies \: BE = 12 \: cm

Now , In ∆ BCE ,

semi \: perimeter \: (s) =  \frac{15 + 15 + 12}{2}  \\  \\ \implies \: s =  \frac{42}{2}  = 21 \: cm

Now , by Heron's formula

area \: of \: \triangle \: BCE =  \sqrt{s(s - a)(s - b)(s - c)}  \\ \implies \sqrt{21(21 - 15)(21 - 15)(21 - 12)}  \\ \implies \: 21 \times 6 \times 6 \times 9 \\ \implies \: 12 \sqrt{21}  \: cm {}^{2}

Also ,

area \: of \: \triangle \:  =  \frac{1}{2}  \times base \times height \\  \\\implies 18 \sqrt{21} =  \: \frac{1}{\cancel2}  \times \cancel12  \times height \\  \\ \implies \: 18 \sqrt{21}  = 6 \times height \\  \\ \implies \: height =  \frac{\cancel{18} \sqrt{21} }{ \cancel 6}  \\  \\ \implies \: height = 3 \sqrt{21}  \: cm {}^{2}

<u>Since </u><u>we've </u><u>obtained </u><u>the </u><u>height </u><u>now </u><u>,</u><u> </u><u>we </u><u>can </u><u>easily </u><u>find </u><u>out </u><u>the </u><u>area </u><u>of </u><u>trapezium </u><u>!</u>

Area \: of \: trapezium =  \frac{1}{2}  \times(sum \: of \:parallel \: sides) \times height \\  \\ \implies \:  \frac{1}{2}  \times (25 + 13) \times 3 \sqrt{21}  \\  \\ \implies \:  \frac{1}{\cancel2}  \times \cancel{38 }\times 3 \sqrt{21}  \\  \\ \implies \: 19 \times 3 \sqrt{21}  \: cm {}^{2}  \\  \\ \implies \: 57 \sqrt{21}  \: cm {}^{2}

hope helpful :D

6 0
1 year ago
How do you solve this ?
TEA [102]

JK=9x-11\\KL=5x+2\\JL=(9x-11)+(5x+2)=(9x+5x)+(-11+2)=14x-9\\\\JK+KL=JL\\\\\text{substitute}\\\\14x-9=10x+7\ \ \ \ |+9\\\\14x=10x+16\ \ \ \ |-10x\\\\4x=16\ \ \ \ |:4\\\\x=4\\\\JK=9x-11\to JK=9(4)-11=36-11=25

4 0
3 years ago
5300 round to the nearest thousand
AleksAgata [21]
5,000
 is 300 closer to 100 or 1000?
or 
 is 3 closer to 1 or 10?
6 0
2 years ago
Read 2 more answers
How many terms are in the expression shown below?
german

The answer would be B

a2 = 1

ab=2

8b and b2=3

6 0
3 years ago
Read 2 more answers
Stephanie has a homeowners insurance policy for her $355,000 home with an annual premium of $0.42 per $100 of value and a deduct
frosja888 [35]

Answer:

$0.28 per 100 of value (B)

Step-by-step explanation:

Stephanie has a homeowner insurance policy of $355,000

Annual premium = $0.42 per 100

There is a deductible of $500

Stephanie has an annual out of pocket expense of

[($355,000/100) x $0.42] + $500 = $1,991

From the question, Stephanie now wants a new deductible amount of 1000.

Let X be the new annual premium

[(355,000X) / 100] + 1000 = 1991

3550X + 1000 = 1991

3550X = 1991 -1000

3550X = 991

X = 991/3550

X = 0.2791

X = 0.28 ( approximately)

The new annual premium is $0.28 per 100 of value

5 0
3 years ago
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