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Alexandra [31]
2 years ago
7

In △ABC,c=71, m∠B=123°, and a=65. Find b. A. 101.5 B. 117.8 C. 123.0 D. 119.6

Mathematics
1 answer:
tia_tia [17]2 years ago
8 0

Answer:

Option D

Step-by-step explanation:

The questions which involve calculating the angles and the sides of a triangle either require the sine rule or the cosine rule. In this question, the two sides that are given are adjacent to each other the given angle is the included angle. This means that the angle B is formed by the intersection of the lines a and c. Therefore, cosine rule will be used to calculate the length of b. The cosine rule is:

b^2 = a^2 + c^2 - 2*a*c*cos(B).

The question specifies that c=71, B=123°, and a=65. Plugging in the values:

b^2 = 65^2 + 71^2 - 2(65)(71)*cos(123°).

Simplifying gives:

b^2 = 14293.0182932.

Taking square root on the both sides gives b = 119.6 (rounded to the one decimal place).

This means that the Option D is the correct choice!!!

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Power
= Work done  /  Time
= 15000 N * 3 m / 50 s
= 45000/50  N-m/s
= 900 W

It may sound like an extremely low value, but 3.0 / 50 s is also a very slow speed.

8 0
2 years ago
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Choose Yes or No to tell if the digit in the ones place is 1/10 the value of the digit in the tens place.
Radda [10]

Answer:

  • 4099 yes
  • 4110 no
  • 5909 no
  • 5011 yes

Step-by-step explanation:

The digits will be related by a factor of 10 if they are the same digit. 4099 and 5011 have the same digit in the tens and ones places. 4110 and 5909 do not.

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2 years ago
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Budget planners in two towns, Alphaville and Betaville, developed models to determine the budget surplus (in dollars) for a year
kramer

Answer:

(a)-3x^2+150x-10000

(b)-\$16,863,760,000

Step-by-step explanation:

Alphaville's Budget Surplus Model is -2x^2+ 500x

Betaville's Budget Surplus Model is x^2- 100x + 10000.

We want to determine the expression that shows how much greater Alphaville’s annual budget surplus is than Betaville’s for a particular amount of tax revenue.

  • To do this, we subtract Betaville's Model from Alphaville's model.

-2x^2+ 500x-(x^2- 100x + 10000)\\

Opening the brackets

-2x^2+ 500x-x^2+100x - 10000\\

Collect like terms and simplify

-2x^2-x^2+100x + 500x- 10000\\=-3x^2+150x-10000

The expression that shows how much greater Alphaville's Budget is:

-3x^2+150x-10000

(b) If the tax revenue that year in each town is $75,000

We want to evaluate the expression derived above when the tax revenue that year in each town is $75,000 i.e.at x=75000

-3x^2+150x-10000\\=-3(75000)^2+150(75000)-10000\\=-\$16,863,760,000

3 0
2 years ago
The Sweet water High School Project Graduation committee is hosting a dinner-and-dance fundraiser at the Sweet water Community C
yan [13]

Answer:

<h2> 105 tickets</h2>

Step-by-step explanation:

To solve this problem we need to model an equation to represent the situation first.

the goal is to archive $7500 in the even, bearing in mind that there is a cost of $375 fee for rent, we need to put this amount into consideration

let the number of tickets be x

so

75x-375>=7500--------1

Equation 1 above is a good model for the equation

we can now solve for x to determine the number of tickets to be sold to archive the aim

75x-375>=7500--------1

75x>=7500+375

75x>=7875

divide both sides by 75 we have

x>=7875/75

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so they must sell a total of 105 tickets and above to meet the target of $7500 with the rent inclusive

4 0
2 years ago
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In 2005, there were 74,250 car accidents. In 20,187 of them, the driver was a
zhuklara [117]

Answer:

27.19% probability that a female driver was involved in an accident

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question:

74,250 car accidents. Of those, in 20,187, the driver was a female.

Based on this, what is the probability that a female driver was involved in an accident?

p = 20187/74250 = 0.2719

27.19% probability that a female driver was involved in an accident

6 0
2 years ago
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