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3 years ago

Please Help! Geometry!

Mathematics

1 answer:

Alona [7]3 years ago

6 0

<h2>Answer: The perimeter of angle ABC = 61.911 Step-by-step explanation: Since we are given two angles and the length of one side, we apply the SINE RULE Sine Rule = sinA / a = sinB / b = sinC / c where A, B, C are the angles of the triangle AND a, b and c are the length of the sides of the triangle. BUT FIRST, lets get the value for the missing angle CAB Sum of angles of a triangle = 180° angle CAB = 180° - (40° + 49° ) angle CAB = 180° - 89 CAB = 91° To get the PERIMETER of ΔABC, we must get the length of all the three sides of the triangle using THE SINE RULE sin49° / 19.5 = sin 40° / AB = sin91° / CB 0.755/19.5 = 0.643 / AB Cross multiplying AB * 0.755 = 0.643 * 19.5 AB = 12.539 / 0.755 AB = 16.608 LETS SOLVE FOR CB sin49° / 19.5 = sin91° / CB CB * sin49° = 19.5 * sin91° CB * 0.755 = 19.5 * 0.999 CB = 19.481 / 0.755 CB = 25.803 Therefore, AC = 19.5 AB = 16.608 CB = 25.803 The perimeter of ΔABC equals to the sum of AC, AB, CB = 19.5 + 16.608 + 25.803 = 61.911.</h2>

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Which of the following are valid (necessarily true) sentences? a. (∃x x = x) ⇒ (∀ y ∃z y = z). b. ∀ x P(x) ∨ ¬P(x). c. ∀ x Smart

Phantasy [73]

Answer:

b; ∀x P(x) ∨ ¬P(x)

Step-by-step explanation:

Suppose that we have a proposition p

Such that p can be true or false.

We can define the negation of p as:

¬p

Such that, if p is false, then ¬p is true

if p is true, then ¬p is false.

Also remember that a proposition like:

p ∨ q

is true when, at least one, p or q, is true.

Then if we write:

p ∨ ¬p

Always one of these will be true (and the other false)

Then the statement is true.

And if the statement depends on some variable, then we will have that:

p(x) ∨ ¬p(x)

is true for all the allowed values of x.

from this, we can conclude that the statement that is always true is:

b; ∀x P(x) ∨ ¬P(x)

Where here we have:

For all the values of x, P(x) ∨ ¬P(x)

7 0

3 years ago

A quadrilateral has angles measuring 105°,80°and 45°.What is the measure of the fouth angle?

valentina_108 [34]

The measurement of fourth angle is: 130°

Further explanation:

Let A, B, C and D be the four angles.

m∠A=105°

m∠B=80°

m∠C=45°

We know that the sum of interior angles of a quadrilateral is 360°

So,

m∠A+m∠B+m∠C+m∠D=360°

105°+80°+45°+m∠D=360°

230°+m∠D=360°

m∠D=360°-230°

m∠D=130°

The measurement of fourth angle is: 130°

Keywords: Quadrilateral, Interior angles

Learn more about quadrilateral at:

#LearnwithBrainly

3 0

3 years ago

What is the value of the expression when n=3 -2n(5+n-8-3n)

igor_vitrenko [27]

-2(3)(5+3-8-3(3))
=-6(5+3-8-9)
=-30-18+48+54
=54

4 0

3 years ago

Read 2 more answers

After 4 new students joined a class, the class had 32 students. Which equation can be used to find n, the number in the class be

Vadim26 [7]

Answer:

n+4=32

Step-by-step explanation:

The initial number n gets additional 4 students making the new total number of students to be 32. Therefore, this situation can be represented as

n+4=32

To get the actual number of students before the additio, we make n the subject of formula hence

n=32-4

n=28

Therefore, the initial number was 28 and the equation is n+4=32

Since no choices were provided, the equation that can be modified is n+4=32

8 0

3 years ago

A 10-pound block of ice melts at a rate of 3% per hour. Find the weight of the block of ice after 1 day.

mylen [45]

Answer:

The weight of the block of ice after 1 day is of 4.81 pounds.

Step-by-step explanation:

Equation for exponential decay:

The equation that models an amount after t hours, subject to exponential decay, is given by:

$A(t) = A(0)(1 - r)^t$

In which A(0) is the initial amount and r is the decay rate, as a decimal.

A 10-pound block of ice melts at a rate of 3% per hour.

This means that $A(0) = 10, r = 0.03$

$A(t) = A(0)(1 - r)^t$

$A(t) = 10(1 - 0.03)^t$

$A(t) = 10(0.97)^t$

Find the weight of the block of ice after 1 day.

One day has 24 hours, so this is A(24).

$A(24) = 10(0.97)^{24} = 4.81$

The weight of the block of ice after 1 day is of 4.81 pounds.

6 0

3 years ago