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3 years ago

-20x+18≥-102 solve this inequality

Mathematics

2 answers:

Veronika [31]3 years ago

8 0

Answer:

-20x >= -120

x < or = 6

14h > 280

h > 20

Step-by-step explanation:

Mark worked more than 20 hours. The second equation

larisa [96]3 years ago

6 0

Answer:

1) x≥6

--------------------------------------

2) h > 20

Mark worked more than 20 hours.

Step-by-step explanation:

1) -20x+18≥-102

-20x≥-102-18

-20x≥-120

Dividing -20 both side

$\frac{-20}{-20}x$ ≥ $\frac{-120}{-20}$

x≥6

--------------------------------------

2) 14h + 25 > 305

14h > 305-25

14h > 280

Dividing 14 both side

$\frac{14}{14}h > \frac{280}{14}$

h > 20

Mark worked more than 20 hours.

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4 years ago

Determine whether angle ABC should be solved by using the Law of Sines or the Law of Cosines. Then solve the triangle.

drek231 [11]

Answer:

Law of Cosines

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Angle B = 51°

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Step-by-step explanation:

Law of sines is used when we are given

a) two angles and one side or

b) two sides and non-included angle

Law of cosines is used when we are given

a) three sides or

b) two sides and included angle

In the given question we are given three sides so, Law of Cosines will be used to solve the triangle.

Law of Cosines is:

$a^2 = b^2 + c^2 -2bccos A\\b^2 = a^2 + c^2 -2accos B\\c^2 = a^2 + b^2 -2abcosC$

We will find the three angles A ,B and C of the triangle using above formula.

a= 10, b=11, c=14

Putting values and finding angle A

$a^2 = b^2 + c^2 -2bccos A\\(10)^2 = (11)^2 + (14)^2 -2(11)(14)cosA\\100 = 121 + 196 -308cosA\\100 = 317 -308 cosA\\100-317 = -308cosA\\-217/-308 = cos A\\0.704 = cos A\\=> A = cos ^{-1}(0.704)\\A= 45$

Now finding angle B

$b^2 = a^2 + c^2 -2ac cos B\\(11)^2 = (10)^2 + (14)^2 - 2(10)(14)cosB\\121 = 100+196 - 280cosB\\121 -296 = -280cosB\\-175/-280 = cosB\\0.625 = cosB\\=> B = cos^{-1} (0.625)\\B = 51$

Now finding angle C

$c^2 = a^2 + b^2 -2abcosC\\(14)^2 =(10)^2 + (11)^2 -2(10)(11)cosC\\196 = 100+121 -220cosC\\196 -221 = -220cosC\\-25/-220 = cos C\\0.11 = cosC\\=> C = cos^{-1}(0.11)\\C= 84$

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3 years ago

Read 2 more answers