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natka813 [3]
3 years ago
7

The length of a rectangular garden is 5 meters shorter than twice it width, the area of its region is 150 square meters. Find th

e dimensions of the garden?
What is the formula?​
Mathematics
1 answer:
grin007 [14]3 years ago
7 0

Step-by-step explanation:

length = x - 5

width = 2x

2x(x-5) = 150 m^2

2x^2 - 10x = 150 m^2

2x^2 - 10x - 150 = 0

(x=11.51 or x = -6.513)

if you wanna check,

2(11.51) × (11.51-5) = 150

23.02 × 6.51 = 150

149.8602 = 150

I'm not sure if its correct though^^

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The length of the hypotenuse of a right angled triangle exceeds the length of the base by 2cm and exceeds twice the length of th
insens350 [35]

Answer: a = 8;  b = 15;  c = 17

Step-by-step explanation:

c = b + 2  and c = 2a + 1

b = c − 2 and a =  \frac{c-1}{2}

​

c² = b² + a²  

c^{2} = (c-2)^{2} + \frac{c-1}{2}\\

c^{2}= \frac{4 (c-2)^{2}+(c - 1)^{2}  }{4}

4c^{2}={4 (c^{2} + 4 -4c)+c ^{2}  + 1-2c

4c^{2}={4 c^{2} + 16 -16c)+c ^{2}  + 1-2c

c^{2}-18c+17=0

c(c -17)-1(c-17)=0

​(c -1)(c-17)=0

c = 1 or c = 17

If c = 1 then b = 1 - 2 = -1, that's not possible

So x = 17

b = 17 - 2 = 15

a = \frac{17-1}{2}  = 8

Length sides of the triangle are 17 cm, 15 cm and 8 cm.

I saw some of this on a site but I want to make sure its correct so we're gonna apply the pythagorean theory and see if its correct.

a^{2} + b^{2} = c^{2} \\8^{2} + 15^{2} = 17^{2} \\64 + 225 = 289\\289 = 289\\

This shows that this is correct.

Hope this helped! Again, some of this was from a site, not from me.

3 0
3 years ago
–3.4 + (–8 + 2) = [ ? + (–8)] + 2<br><br> whats the missing number
Ilia_Sergeevich [38]
I suppose what makes this question annoying is that there is the question mark so what i'll do first is substitute the question mark with x. also, there are annoying parenthesis so we'll first eliminate the ones we don't need. now we just have to solve for x. -3.4 + (-8 + 2) = (x + (-8)) + 2 adding a negative number is subtracting that number so x + (-8) = x - 8 -3.4 + 2 - 8 = x - 8 + 2 -3.4 -6 = x - 6 x = -3.4 make sure you are aware that the negative sign belongs to the number after it so -2 + 4 is not -(2+4) = -6 but rather 4 - 2 = 2. let me know if you have any questions!
7 0
3 years ago
Who drove the fastest? Select the correct answer. A Hector drove 205 miles in 5 hours. B Harlin drove 357 miles in 6 hours. C Ke
nikklg [1K]

Answer:

soooo it D

Step-by-step explanation:

you have to divide

A. h 205 divide by 5 =41 m

B. h 357 divide by 6= 59.5

C. k 419 divide by 7 = 59.8..............

D. s 508 divide by 8= 63.5

8 0
3 years ago
Dubnium-262 has a half-life of 34 s. How long will it take for 500.0 grams to
dmitriy555 [2]

Answer:

the time taken for the radioactive element to decay to 1 g is 304.8 s.

Step-by-step explanation:

Given;

half-life of the given Dubnium = 34 s

initial mass of the given Dubnium, m₀ = 500 grams

final mass of the element, mf = 1 g

The time taken for the radioactive element to decay to its final mass is calculated as follows;

1 = 500 (0.5)^{\frac{t}{34}} \\\\\frac{1}{500} =  (0.5)^{\frac{t}{34}}\\\\log(\frac{1}{500}) = log [(0.5)^{\frac{t}{34}}]\\\\log(\frac{1}{500})  = \frac{t}{34} log(0.5)\\\\-2.699 = \frac{t}{34} (-0.301)\\\\t = \frac{2.699 \times 34}{0.301} \\\\t = 304.8 \ s

Therefore, the time taken for the radioactive element to decay to 1 g is 304.8 s.

4 0
2 years ago
Can someone please help me find the answers to these two questions please?
Sliva [168]

Answer:

Question 13: x = 47°

Question 14: x = 67°

Step-by-step explanation:

Question 13:

add up all the known factors meaning 16, 27 and 90°, then subtract 180 from what you got from adding known factors

Question 14:

out out of all numbers meaning 19, 4 and 90°, then subtract 180 from what you got from adding all known factors

5 0
3 years ago
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