Given that the area of a triangle ABC is 4.5 m², a=4, b=3, find two possible measures for angle C. Round your answer to the nearest tenth

Answers

Answer 1

Answer:

[tex]C = 48.6[/tex]

Step-by-step explanation:

Given

[tex]Area= 4.5m^2[/tex]

[tex]a =4[/tex]

[tex]b = 3[/tex]

Required

Find angle C

The area of the triangle will be calculated using:

[tex]Area = \frac{1}{2}ab \sin C[/tex]

So, we have:

[tex]4.5= \frac{1}{2} * 4 * 3 * \sin C[/tex]

[tex]4.5= 6 * \sin C[/tex]

Divide both sides by 6

[tex]0.75= \sin C[/tex]

Take arc sin of both sides

[tex]\sin^{-1}(0.75)= C[/tex]

[tex]48.6 = C[/tex]

[tex]C = 48.6[/tex]


Related Questions

what is the cost to drive from san francisco to los angeles (405 mi) if the cost of gasoline is $2.34/gal and the automobile gets 8.5 mi/L

Answers

Answer:

The cost is $ 29.5.

Step-by-step explanation:

distance = 405 miles

Cost = $ 2.34 /gal

Average = 8.5 miles per litre

So, the amount of gasoline to travel for 405miles

= 405/8.5 = 47.65 liter

1 gal = 3.785 liters

So,

47.65 liter = 47.65 / 3.785 = 12.6 gal

So, the cots is

= $ 2.34 x 12.6 = $29.5

Helpppppp ,would this just be -1.2?

Answers

Answer:   1.2

Explanation:

The result of any absolute value function is never negative. It represents distance on a number line.

The distance from -1.2 to 0 on the number line is exactly 1.2 units.

So that's why |-1.2| = 1.2

In short, we erase the negative sign.

4b^2+300=0 this is a quadratic equation that I am trying to solve including any solutions with imaginary numbers I will include a picture ​

Answers

Answer:

b= 5i square root of 3

b = -5i square root of 3

Step-by-step explanation:

4b^2+300=0

4b^2 = -300

b^2 = -75

b = square root of -75

b = -75^1/2

^1/2 means square root

b = 25^1/2 * 3^1/2 * i

b= 5i square root of 3

b = -5i square root of 3

Consider a relation on the set of all states in the United States given by: two states are related if they have a border in common. Is it an equivalence relation

Answers

Answer:

Yes it is an equivalence relation

Explanation:

An equivalence relation is a binary relation between two values that are symmetric, transitive and reflexive. In other words, when we say a value x is equal(using "=") to a value y, there is an equivalence relation between them.

Example, given set {x, y, z} where ~ means equivalence:

x ~ y if y ~ z means symmetric

since x ~ y and y ~ z, then x ~ z means transitive

x ~ x means reflexive

Equivalence relations share a common attribute or attributes(example, a satisfying condition)

The above condition that two states are related from the set of all US states if they have a border in common satisfies the condition of equivalence listed hence it is an equivalence relation.

Please explain :)

Expand 5x(x+2)

Thanks :)

Answers

Answer:

[tex] {5 x }^{2} +10x[/tex]

Step-by-step explanation:

[tex]5x(x+2)[/tex]

[tex]5x \times x+5x \times 2[/tex]

[tex]5(x \times x)+5x \times 2[/tex]

[tex]5 {x}^{2} +5x \times 2[/tex]

[tex]5 {x}^{2} + 10x[/tex]

Hope it is helpful....

Translate the following into an algebraic expression: If it would take Mark m hours to clean the house alone and with his brother Sam they can clean the house together in t hours. How many hours would it have taken Sam if he was working alone

Answers

t=m or it could be m-t

14. A professor records the number of class days (x) each student misses over the course of a semester and uses a frequency distribution to display the data. What is the probability a student missed exactly 1 day

Answers

Question is incomplete, however here's an explanation to solve questions such as this

Answer and explanation:

Probability= number of favorable outcomes/total number of outcomes

The frequency distribution recorded by the professor would show number of times(frequency) each student missed a class day.

We are required to fund the probability that a student would miss class

Probability = number of times the student missed class/ total number of classes missed by all students

Example, if student missed class 20 times in a semester and all students in total missed class 200 times

Probability that the student would miss class=20/200= 1/10

(a) What is the probability that a person who was polled prefers chocolate ice cream to vanilla? Round your answer to four decimal places.

Answers

Answer:

[tex]P(k)=0.2628[/tex]

Step-by-step explanation:

Given

[tex]n = 1693[/tex] --- sample size

[tex]k = 445[/tex] --- those that prefer chocolate ice cream to vanilla

Required

[tex]P(k)[/tex]

This is calculated as:

[tex]P(k)=\frac{k}{n}[/tex] --- probability formula

So, we have:

[tex]P(k)=\frac{445}{1693}[/tex]

[tex]P(k)=0.2628[/tex]

HELP PLEASSSSSS I will give brainlyest!!!!!!!!!!!!!!!!!!

Answers

Answer:

1/2

Step-by-step explanation:

Convert 2/3 to 4/6

Subtract: 4/6 - 1/6

You get 3/6

Simplify: 1/2

Hope this helps!

Answer: The answer is 1/2

I need help with these questions

Answers

Answer:

1) 6m+8n

4) 21x+14y

7) 14c+16d

10) d+3e

Step-by-step explanation:

Given: x + 2 < -5.



Choose the solution set.

{x | x R, x < -3}
{x | x R, x < 3}
{x | x R, x < -7}
{x | x R, x < 7}

Answers

Answer:

C

Step-by-step explanation:

x + 2 < -5

x < - 5 - 2

x < - 7

Answer:

{x| x R, x<-7}

Step-by-step explanation:

=> x+2<-5

=> x<-5-2

=> x<-7

Find the derivative of 4x^3-7x+8 ÷ x​

Answers

Step-by-step explanation:

If a fraction [tex]f(x)[/tex] is defined as

[tex]f(x) = \dfrac{g(x)}{h(x)}[/tex]

then the derivative [tex]f'(x)[/tex] is given by

[tex]f'(x) = \dfrac{g'(x)h(x) - g(x)h'(x)}{h^2(x)}[/tex]

So the derivative can be calculated as follows:

[tex]f'(x) = \dfrac{d}{dx}\left(\dfrac{4x^3 - 7x + 8}{x} \right)[/tex]

[tex]=\dfrac{(12x^2 - 7)x - (4x^3 - 7x + 8)}{x^2}[/tex]

[tex]= \dfrac{12x^3 - 7x - 4x^3 + 7x - 8}{x^2}[/tex]

[tex]= \dfrac{8x^3 - 8}{x^2}[/tex]

I’m confused with this question

Answers

9514 1404 393

Answer:

  (a) max: None; min: -5

  (b) max: 5; min: None

Step-by-step explanation:

a) The upward pointing arrow on the end of the graphed curve tells you that the graph extends upward indefinitely. There is no absolute maximum value.

The solid dot at (-4, -5) is the lowest point on the graph. That tells you the absolute minimum is -5.

__

b) The solid dot at (-4, 5) is the highest point on the graph. That tells you the absolute maximum is 5.

The open dot at (3, -5) is the lowest point on the graph. This means values of the function can be arbitrarily close to -5, but -5 is not one of them. There is no absolute minimum value.

Find the time required for an investment of 5000 dollars to grow to 8600 dollars at an interest rate of 7.5 percent per year, compounded quarterly.

Answers

Answer:

about 7.3 years

Step-by-step explanation:

[tex]8600=5000(1+\frac{.075}{4})^{4*t}\\1.72=(1.01875)^{4t}\\log_{1.01875}1.72=4t\\29.19428479=4t\\t=7.298571198[/tex]

Answer:

The answer is t=7.3

Lunch break: In a recent survey of 643 working Americans ages 25-34, the average weekly amount spent on lunch as $43.21 with standard deviation $2.95. The weekly amounts are approximately bell-shaped. Part: 0 / 30 of 3 Parts Complete Part 1 of 3 Your Answer is incorrect (a) Estimate the percentage of amounts that were less than $40.26. Round the answer to one decimal place. Approximately % of the amounts were less than $40.26.

Answers

Answer:

107%

Step-by-step explanation:

Round up all possible algorithms

Marty's barber shop has one barber. Customers arrive at a rate of 2.2 per hour and haircuts are given at a rate of 5 customers per hour. Assume a Poisson arrival rate and an Exponential service time distribution.

Required:
a. What is the probability that one customer is receiving a haircut and one customer is waiting?
b. What is the probability that one customer is receiving a haircut and two customers are waiting?
c. What is the probability that more than two customers are waiting?

Answers

Answer:

Step-by-step explanation:

Arrival rate = ∧ = 2.2 customers per hour  

Service rate = u = 5 customers per hour  

1. Probability that one customer is receiving a haircut and one customer is waiting  

P(2 customers)=(∧/u)^2 * (1-∧/u)=(2.2/5)^2 * (1-2.2/5)=0.1936*0.56= 0.108416

 

2. Probability that one customer is receiving a haircut and two customers are waiting  

P(3 customers)= (∧/u)^3 * (1-∧/u)=(2.2/5)^3 * (1-2.2/5)= 0.085184  

* 0.56= 0.04770304

 

3. Probability that more than two customers are waiting  

P(more than 3 customers)=1- P(less than 3 customers) =  

1- [P(0)+P(1)+P(2)+P(3)]=  

= 1- [(1-2.2/5) +2.2/5*(1- 2.2/5) + 0.108416+0.04770304]=1-0.9625=0.0375

A fair dice is rolled. Work out the probability of getting a number less than 5. Give your answer in its simplest form.​

Answers

Step-by-step explanation:

4/6

=2/3

That's what I could show you

(2x+3)(5x-8)
10x7€ 16x+158–24
10x2-x-24

Answers

Answer:

16X+134

Step-by-step explanation:

Two different businesses model their profits over 15 years, where x is the year, f(x) is the profits of a garden shop, and g(x) is the profits of a construction materials business. Use the data to determine which function is exponential, and use the table to justify your answer.

1. f(x) is exponential; an exponential function increases more slowly than a linear function.
2. f(x) is exponential; f(x) increased more overall than g(x).
3. g(x) is exponential; g(x) has a higher starting value and higher ending value.
4. g(x) is exponential; an exponential function increases faster than a linear function.

Answers

Hi there!

[tex]\large\boxed{\text{Choice 4}}[/tex]

We can look at each function, f(x) and g(x), to determine which is exponential.

Use slope formula: m = y2-y1/x2-x1

f(x) starts off with a slope at about $1800/year, but becomes about $1100/year.

g(x) starts off with a slope of about $1500/year, but becomes about $1874/year.

Thus, g(x) is exponential, because g(x)'s slope is increasing across the interval.

Convert 45 minutes to seconds. There are seconds in 45 minutes (Simplify your answer.) how many seconds are in 45 minutes

Answers

answer:2700sec

Step-by-step explanation:

if 60 sec=min

therefore;60×45

Solve the inequality and write the solution set using both set-builder notation and interval notation. -3a-15≤-2a+6

Answers

Answer:

[tex]\{a[/tex][tex]R\ -21 \le a \le \infty \}[/tex] --- set builder

[tex][-21,\infty)[/tex] --- interval notation

Step-by-step explanation:

Given

[tex]-3a - 15 \le -2a + 6[/tex]

Required

Solve

Collect like terms

[tex]-3a + 2a \le 15 + 6[/tex]

[tex]-a \le 21[/tex]

Divide by -1

[tex]a \ge - 21[/tex]

Rewrite as:

[tex]-21 \le a[/tex]

Using set builder

[tex]\{a[/tex][tex]R\ -21 \le a \le \infty \}[/tex]

Using interval notation, we have:

[tex][-21,\infty)[/tex]

For the expression x-5, what would the value be if x=18?

Answers

Answer:

13

Step-by-step explanation:

Answer:

if x is 18 replace 18 where x is in the question so, it will be 18-5 = 13

2x + 2x + 5x + 5x= please answer quick it's very hard and I like the game to answer please and thank you.

Answers

Answer:

14x I answered your question thank you for the points appreciate it

Answer:

2x+2x+5x+5x=14x

Ans: 14x

What are the lengths of the other two sides of the triangle? O AC = 5 and BC = 5 O AC=5 and BC =515 O AC = 5/5 and BC = 5 O AC = 5 and BC =53

Answers

*see attachment for missing diagram

Answer:

AC = 5 and BC = 5√3

Step-by-step explanation:

Given:

m<A = 60°

m<B = 30°

AB = 10

Required:

AC and BC

Solution:

Recall, SOH CAH TOA

✔️Find AC:

Reference angle (θ) = 30°

Hypotenuse = 10

Opposite = AC

Apply SOH:

Sin θ = Opp/Hyp

Substitute

Sin 30° = AC/10

10*Sin 30° = AC

10*½ = AC (sin 30° = ½)

5 = AC

AC = 5

✔️Find BC:

Reference angle (θ) = 60°

Hypotenuse = 10

Opposite = BC

Apply SOH:

Sin θ = Opp/Hyp

Substitute

Sin 60° = BC/10

10*Sin 60° = BC

10*√3/2 = BC (sin 60° = √3/2)

5*√3 = BC

BC = 5√3

The data on the box plot describes the weight of several students in sixth grade. Which of the following statements are true about the data set? Select all that apply.



One-fourth of the students weigh between 90 and 101 pounds.
One-half of the students weigh between 75 and 90 pounds.
The median weight of the sixth graders is 85 pounds.
One-fourth of the students weigh less than 75 pounds.
One-fourth of the students weigh more than 75 pounds.
The total range of weight is 40 pounds.

Answers

Answer:

Step-by-step explanation:

B

If it takes Ohenhen 10km to pass to Emma and it takes Emma 8km to pass to Omusi and considering Ohenhen & Omusi are at perpendicular ends from Emma. What's the distance between Ohenhen and Omusi?​

Answers

Answer:

12.81 km

Step-by-step explanation:

Pythagoras formula for right-angled triangles.

this scenario just says that Emma is the corner point of that triangle with an angle of 90 degrees.

the distance between Ohenhen and Omusi is the baseline (Hypotenuse c) of that triangle. and the distances to Emma are the sides a and b.

so the formula is

c² = a² + b² = 10² + 8² = 100 + 64 = 164

[tex]c = \sqrt{164} [/tex]

c ≈ 12.81 km (rounded to the nearest hundredth).

Indicate the method you would use to prove the two 's . If no method applies, enter "none".

Answers

Answer:

AAS

Step-by-step explanation:

It will be angle angle side because you are given a side and two angles, and when you put them in the correct order, you will get AAS, or SAA (not the correct way to say it)

You want to put a 5 inch thick layer of topsoil for a new 23 ft by 27 ft garden. The dirt store sells by the cubic yard. How many cubic yards will you need to order?

Answers

Answer:

9.5833333333 yd³

9 7/12 yd³

Step-by-step explanation:

23 * 27 * 5/12 = 258.75 ft³

1 yd³ = 3ft * 3ft * 3ft

1 yd³ = 27 ft³

258.75 ft³ * 1 yd³/27 ft³ = 9.5833333333 yd³

9.5833333333 yd³

9 7/12 yd³

Which of the following represents the ratio of the hypotenuse to the given
side?

Answers

Answer:

D. √2 : 1

Step-by-step explanation:

The hypotenuse = 4√2 (longest side of a right triangle)

The given side = 4

Ratio of the hypotenuse to the given side = 4√2 : 4

Simplify by dividing both numbers by 4

√2 : 1

Enunciate demerits of classical probability.

Answers

Answer:

Some demerits of classical probability are provided throughout the following portion.

Step-by-step explanation:

This could only be utilized if somehow the occurrences are fairly probable as well as predictable. Such supposition is established far in advance of the investigation or testing.This only applies whereas if an overall number of occurrences seems to be limited, one such term has quite a restricted scope, such as coins tossing, picking card numbers, etc.
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