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3 years ago

One number is 8 more than another number, and their sum is 20. Find the numbers.

Mathematics

2 answers:

timofeeve [1]3 years ago

8 0

Answer:

The numbers are 6 and 14

Step-by-step explanation:

Say the unknown numbers are x and y

Say y = 8+x ................... eqn 1

and x + y = 20 ................ eqn 2

Then if you replace y by 8+x, eqn 1 becomes

x + 8 + x = 20

Collect the like terms

x + x = 20 - 8

2x = 12

Divide both sides by 2

x = 12/6

x = 6

Then to get y, substitute 6 for x in eqn 1, and we will have

y = 8 + 6

y = 14

melomori [17]3 years ago

6 0

Answer:

First number=6

Second number=14

Step-by-step explanation:

Let the first number be x

So the second number is x+8

So the sum of the two is

X+x+8=20

2x+8=20

2x=20-8

2x=12

X=12/2

The second number will x+8

So 6+8=14

First number=6

Second number=14

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Three security cameras were mounted at the corners of a triangles parking lot. Camera 1 was 110 ft from camera 2, which was 137

Nata [24]

Answer:

Camera 2nd has to cover the maximum angle, i.e. $78.70^\circ$ .

Step-by-step explanation:

Please have a look at the triangular park represented as a triangle $\triangle ABC$ with sides

a = 110 ft

b = 158 ft

c = 137 ft

1st camera is located at point C, 2nd camera at point B and 3rd camera at point A respectively.

We can use law of cosines here, to find out the angles $\angle A, \angle B, \angle C$

As per Law of cosine:

$cos C = \dfrac{a^{2}+b^2-c^2 }{2ab}\\cos B = \dfrac{a^{2}+c^2-b^2 }{2ac}\\cos A = \dfrac{b^{2}+c^2-a^2 }{2bc}$

Putting the values of a,b and c to find out angles $\angle A, \angle B, \angle C$ .

$cos C = \dfrac{110^{2}+158^2-137^2 }{2\times 110 \times 158}\\\Rightarrow cos C = \dfrac{12100+24964-18769 }{24760}\\\Rightarrow cos C =0.526\\\Rightarrow C = 58.24^\circ$

$cos B = \dfrac{110^{2}+137^2-158^2 }{2\times 110 \times 137}\\\Rightarrow cos B = \dfrac{12100+18769 -24964}{30140}\\\Rightarrow cos B = \dfrac{5905}{30140}\\\Rightarrow cos B =0.196\\\Rightarrow B = 78.70^\circ$

$cos A = \dfrac{158^{2}+137^2-110^2 }{2\times 158 \times 137}\\\Rightarrow cos A = \dfrac{24964+18769-12100}{43292}\\\Rightarrow cos A = \dfrac{31633}{43292}\\\Rightarrow cos A = 0.731\\\Rightarrow A = 43.05^\circ$