<h3>
Answer: 40</h3>
=======================================================
Explanation:
The inscribed angle 20 degrees doubles to 2*20 = 40 which is the measure of the central angle, and the arc in which the inscribed angle subtends (or cuts off). This is due to the aptly named inscribed angle theorem.
------------
A slightly longer alternative path would be to do this:
The triangle with interior angles 20 and c is isosceles. Note how the missing angle up top is one of the congruent base angles, so the missing angle is 20 degrees. That means angle c is...
20+20+c = 180
40+c = 180
c = 180-40
c = 140
Then angle b is supplementary to this
b+c = 180
b+140 = 180
b = 180-140
b = 40
This path leads to the same answer. It's slightly longer, but it's a path you can take if you aren't familiar with the inscribed angle theorem.
In fact, this line of thinking is effectively how the inscribed angle theorem is proved as shown in the diagram below.
Answer:
The true statements are:
the first statement: Systems A and C have the same solution
the fourth statement: System C simplifies to 2x - 3y = 4 and 4x - y = 18
the fifth statement: Systems A and B have different soltuoins.
Explanation:
1) The first statement: systems A and C have the same solutiotn: TRUE
The fourth statement proves that that the two systems are equivalent which means that both have the same solution.
2) The second statement: All three systems have different solutions: FALSE
The fourth statement proves that the systems A and C have same solution, so this second statement is false.
3) The third statement: Systems B and C have the same solution: FALSE
<span>You can solve the two systems and will find the solutions are different
Solution of system B.
3x - 4y = 5
y = 5x + 3
replace y = 5x + 3 in the first equation => 3x - 4(5x + 3) = 5
=> 3x - 20x - 12 = 5
=> - 17x = 5 + 12
=> -17x = 17
=> x = - 17 / 17
=> x = - 1
y = 5x + 3 = 5(-1) + 3 = - 5 + 3 = - 2
=> solution x = -1 and y = -2
Solution of system C.
2x - 3y = 4
12x - 3y = 54
subtract
</span>
4) fourth statement: System C simplifies to <span>2x - 3y = 4 and 4x - y = 18 by dividing the second equation by three: TRUE
Look:
Second equation of system C = 12x - 3y = 54
Divide by 3:
12x - 3y 54
----------- = -----
3 3
Distributive property:
12x 3y
------ - ----- = 18
3 3
4x - y = 18, which is the same second equation of system A, so the system C simplifies to the same system A, which is 2x - 3y = 4 and 4x - y = 18.
5) The fifth statement: systems A and B have different solutions: TRUE
</span><span>You can solve the two systems and will find the solutions are different
Solution of system A:
2x - 3y = 4
12x - 3y = 54 since it is equivalent to 4x - y = 18
-------------------
12x - 2x = 54 - 4 subtracting the first equation from the secon
10x = 50 adding like terms
x = 5 dividing by 10
From 2x - 3y = 4 => 3y = 2x - 4 = 2(5) - 4 = 10 - 4 = 6
=> y = 6 / 3 = 2
=> x = 5, y = 2
Solution of system B.
3x - 4y = 5
y = 5x + 3
replace y = 5x + 3 in the first equation => 3x - 4(5x + 3) = 5
=> 3x - 20x - 12 = 5
=> - 17x = 5 + 12
=> -17x = 17
=> x = - 17 / 17
=> x = - 1
Which is enough to prove that the two systems have different solutions.</span>
Answer:
1/4 is left
Step-by-step explanation:
Answer:
f(x)=x-5 is a linear function
Step-by-step explanation:
so there are no restrictions to what x can be. The domain is all real numbers. In interval notation, we show that is can be anything from negative infinity through infinity like this: This says that the lower limit of the domain is negative infinity and the upper limit is positive infinity.
.312
Frequency is 24
To find relative frequency (of Pop music) you would take 24 and divide it by the total students you were surveyed.
24/77 = .3116 rounded to hundredths becomes .312
If they are looking for percentage, you take the .312 and multiply by 100 to get 31.12%
