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Setler [38]
3 years ago
11

What is the answer??

Mathematics
1 answer:
kykrilka [37]3 years ago
5 0

Answer:

Step-by-step explanation:

Let AC = x

AB - AC = 4 cm

AB = 4 +x  ----------------(I)

Pythagorean theorem

AB² + AC² =BC²

(4 + x)² + x² = 9²

Use the identity (a + b)² = a² + 2ab + b² where a = 4 & b = x

4² +2*4*x  +x² + x²= 81

16 + 8x + 2x² = 81

2x² + 8x + 16 - 81 = 0

2x² + 8x - 65= 0

a = 2 ; b = 8 ; c = -65

D = b² - 4ac

   = 8² - 4*2*(-65)

  = 64 +  520

D = 584

√D = √584 = 24.16

x=\frac{-b+\sqrt{D}}{2a} \ or \ x =\frac{-b-\sqrt{D}}{2a}\\\\x= \frac{-8+24.16}{2*2} \ or \ x = \frac{-8-24.6}{2*2}   {Ignore this as it is negative.}

x = 16.16/4

x = 4.04

AC = 4.04 Cm

AB = 4 + 4.04 = 8.04 cm

Area of triangle ABC = \frac{1}{2}* base * height

                                   =\frac{1}{2}*4.04 *8.04\\\\= 2.02 * 8.04

                                   = 16.24 sq.cm

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8 0
2 years ago
The GCD(a, b) = 9, the LCM(a, b)=378. Find the least possible value of a+b.
denis-greek [22]
\mathrm{gcd}(a,b)=9\implies9\mid a\text{ and }9\mid b\implies9\mid a+b

which means there is some integer k for which a+b=9k.


Because 9\mid a and 9\mid b, there are integers n_1,n_2 such that a=9n_1 and b=9n_2, and


\mathrm{lcm}(a,b)=\mathrm{lcm}(9n_1,9n_2)=9\mathrm{lcm}(n_1,n_2)=378\implies\mathrm{lcm}(n_1,n_2)=42

We have 42=2\cdot3\cdot7, which means there are four possible choices of n_1,n_2:

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3, 14
6, 7

which is to say there are also four corresponding choices for a,b:

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27, 126
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So the least possible value of a+b is 117.
6 0
3 years ago
the measure of the supplement of an angle is 30 more than twice the measure of the angle. find the measure of the angles
Ierofanga [76]
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Angle = 37.5 degrees
Supplement angle = 105 degrees

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7 0
3 years ago
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balu736 [363]

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Step-by-step explanation:

3 0
3 years ago
The time t required to do a job varies inversely as the number of people working. It takes 5 hr for 3 cooks to prepare the food
miskamm [114]

Answer: It will take 1.875 hours

Step-by-step explanation:

Given that time t required to do a job varies inversely as the number of people working.

we have it expressed as

t∝1/N

where t is time  required to do a job

N is the number of people working.

Introducing our constant of proportionality, we have tht

t=k1/N

t=k/N

Now since it takes 5 hr for 3 cooks to prepare the food , K becomes

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Given that there are 8 cooks, time required to prepare dinner will be

t=k/N

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t=1.875 hours

7 0
3 years ago
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