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PilotLPTM [1.2K]
3 years ago
7

Suppose a triangle has sides a, b, and c, and let (/) be the angle opposite the side of length a. If cos(/) > 0 what must be

true?
A. b^2 + c^2 < a^2
B. a^2 + b^2 = c^2
C. b^2 + c^2 > a^2
D. a^2 + b^2 > c^2
Mathematics
2 answers:
r-ruslan [8.4K]3 years ago
7 0
   Using the cosine rule

 a² =  b² +  c² -2 bc cos (/)

 Simplifying the equation in terms of cos (/),

 cos (/)= (b² + c² - a²)/(2bc) 

 If cos(/) > 0

 (b² + c² - a²)/(2bc) > 0 -----------------(b² + c² - a²) > 0 

the resulting inequality should be

<span>(b² + c² ) > a² 

The answer is the letter </span><span>C. b^2 + c^2 > a^2</span>
Katena32 [7]3 years ago
5 0
<span>cos(/)>0, that implies that a^2+b^2!=c^2. If that were the case, cos(/) would be 0. cos(/)>0 implies that the adjacent is greater than the hypotenuse. So, the opposite plus the adjacent is greater than the hypotenuses. So, then, that implies b^2+a^2>c^2. So, A.</span>
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Is x = 0 a valid potential solution to the equation log(x + 2) + log(x + 5) = 1? (You don't need to solve this equation, just de
Xelga [282]

Answer:

Yes, since log(2) and log(5) both exist as valid values for the logarithm.

didnt check if ur equation is correct though

8 0
2 years ago
Printing a newsletter costs $1.50 per copy plus $450 in printer's fees. The copies are sold for $3 each.How many copies of the n
alekssr [168]

Answer:

300 Copies

Step-by-step explanation:

Break even Units = Fixed Costs / (Price - Variable Cost)

Fixed Costs = $450

Variable Cost = 1.5

Price = 3

Break Even Units = 450 / (3 - 1.5)

Break Even Units = 450 / 1.5

Break Even Units = 300

300 Copies must be sold to break even.

I hope this helps!

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8 0
3 years ago
In ΔABC, ∠B measures 35° and the values of a and b are 19 and 11, respectively. Find the remaining measurements of the triangle,
Anna35 [415]

Answer:

a)  ∠A = 82.2° , ∠C = 62.8° , c =   17.01

Step-by-step explanation:

<u><em>Explanation</em></u>:-

<u><em>Step(i)</em></u>:-

Given data ∠B measures 35° and the values of a and b are 19 and 11

∠B = 35° and sides a = 19 and b = 11

<em>By using sine rule </em>

<em></em>\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{Sin C}  = 2 R<em></em>

now we will use

\frac{a}{sin A} = \frac{b}{sin B}

\frac{19}{sin A} = \frac{11}{sin 35}

cross multiplication , we get

\frac{19 X sin 35}{11} = sinA

<em>sin A = 0.990</em>

<em>A = sin⁻¹( 0.990) = 82.2°</em>

<em> ∠A = 82.2°</em>

<u><em>Step(ii):-</em></u>

we know that ∠A +∠B +∠C = 180°

                         ∠C = 180° - ∠A -∠B

                          ∠C = 180° -82.2°-35°

                          ∠C = 62.8°

<u><em>Step(iii)</em></u>:-

<em>we will use formula</em>

<em></em>\frac{b}{sin B} = \frac{c}{Sin C}<em></em>

<em></em>\frac{11}{sin 35} = \frac{c}{Sin 62.8}<em></em>

\frac{11 X sin (62.8)}{sin 35} = C

<em>c =   17.01</em>

<u><em>Final answer</em></u>:-

<em> ∠A = 82.2° , ∠C = 62.8° , c =   17.01</em>

                         

4 0
3 years ago
The population of a city is 451,400. The population is expected to decrease at a rate of 3.2% each year.
blondinia [14]

Answer:

Find out the what function equation represents the population of the city after t years .

To prove

The population of a city is 451,400. The population is expected to decrease at a rate of 3.2% each year.

This can be represented by exponential decreasing function.

f(t) = a (1 - r)^{t}

Where a is the initial value.

r is the rate in decimal form

t is the time.

Here

a = 451,400

3.2 % is written in the decimal form.

= \frac{3.2}{100}

= 0.032

Put in the formula

f(t) = 451400 (1 - 0.032)^{t}

f(t) = 451400 (0.968)^{t}

Therefore the decrease in the population of the city after t years is represented by

f(t) = 451400 (0.968)^{t}



5 0
3 years ago
Read 2 more answers
Find the value of x.
Genrish500 [490]

Answer:

11

Step-by-step explanation:

All angles on a triangle equal 180. 80+60=140.

Now to solve for x, we set it to equal 40 for 180-140.

40=3x+7. 40-7=33

33=3x 33/3=11

x=11

8 0
2 years ago
Read 2 more answers
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