Let (2x-12) degrees represent the measure of an acute angle. What are the possible values of x?
Answers
Right angle is an angle that measure 90 degrees
Obtuse angle is an angle that measure more than 90 degrees.
In the given situation, we need to find the value of x of an acute angle with the given situation
=> (2x-12)
=> 0 < (2x -12) < 90
=> 12 < 2x < 102
=> 6 < x < 51
Let’s check our answer
=> 2 (51- 6)
=> 102 – 12
=> 90
Thus, the value of x = 51 degrees
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Using the coordinates of two points (84, 80) and (74, 65), determine the slope of the line of best fit.a. The slope of the line is 1.5. b. The slope of the line is 15. c. The slope of the line is -10. d. The slope of the line is -15
Answers
just about everything there is to know about the line.
y = mx + b
In that form, 'm' is the slope of the line, and 'b' is the y-intercept.
2x+y=82x+y=8
If we double each side of the second equation, 2x+y=82x+y=8, we have 4x+2y=164x+2y=16. Explain why the same pair that is the solution to the system is also a solution to this new equation.
If needed, you can support your explanation with hanger diagrams (upload a picture), or by inventing a situation that the equations represent.
If we add the two equations in the original system, we have 6x+7y=326x+7y=32. Explain why the same (x, y) pair is also a solution to this equation.
Again, you can support your explanation with diagrams or a situation, if needed.
Answers
Final answer:
The equations are a system of linear equations. Modifying them through multiplication or addition while keeping both sides balanced doesn't change the solution. Any pair (x,y) satisfying one equation will satisfy the others.
Explanation:
In mathematics, these equations are a system of linear equations. This is essentially a set of two or more equations, with a common set of variables. The same pair (x, y) are the solutions for all equations, as the second equation is a simplified, scalar multiple of the first.
So, for the first original equation (4x + 6y = 24), and the modified one (4x + 2y=16) which is the second equation of the system doubled, we can see that the multiplier is the same for both the 'x' and 'y' on the left side, and the right side of the equation. Therefore, if a pair (x,y) has been found to satisfy the first equation, it will also work for the second, as essentially, the equations are equivalent.
Similarly, adding the original system of equations, we get 6x + 7y = 32. This also has the same solution set, just expressed differently. As long as you're performing the same operation (like doubling, adding etc.) to each side of the equations, the balance remains constant, retaining the same solution.
Learn more about System of Linear Equations here:
#SPJ12
Answer:
7.9
Step-by-step explanation:
because you don't make sentence
Question 4 options:
18x^4 – 12x^2 = 6x(3x^3 – 2x)
12x^5 + 8x^3 = 2x^3(6x^2 + 4)
20x^3 + 12x^2 = 4x^2(5x + 3)
24x^6 – 18x^5 = 6x^5(4x – 3)
Answers
1)False 18x^4-12x²=6x(3x^3-2x)=6x²(3x²-2)
2) False 12x^5+8x^3=2x^3(6x²+4)=4x^3(3x²+2)
3)True 20x^3+12x²=4x²(5x+3)
4)True 24x^6-18x^5=6x^5(4x-3)
4)
2) y= -1/2x+3
3) y= -1/2x-3
4) y= -2x-3
Please explain why the answer is what it is.
Answers
y = mx + c
we know y, m and x, find c
-6 =
-6 = -3 + c
-6 + 3 = -3 + 3 + c
-3 = c
y =
Answer is the third one.
Answers
Answer: Yes.
Step-by-step explanation:
First, we will solve the given equation for y.
Given:
-6 + 4y < 6
Add 6 to both sides of the equation:
4y < 12
Divide both sides of the equation by 4:
y < 3
Then, we will confirm if the given coordinate point is within this range. We find that this is a solution.
y < 3
-3 < 3 ✓
a. x = 8, y = 17
b. x = 6, y = 8
c. x = 8, y = 10
d. x = 8, y = 6
Answers
3x - 14 = x + 2
3x - x = 2 + 14
2x = 16
2x / 2 = 16/2
x = 8
To check: 3x - 14 = x + 2 ; 3(8) - 14 = 8 + 2 ; 24 - 14 = 10 ; 10 = 10
4y - 7 = y + 11
4y - y = 11 + 7
3y = 18
3y / 3 = 18 / 3
y = 6
To check: 4y - 7 = y + 11 ; 4(6) - 7 = 6 + 11 ; 24 - 7 = 17 ; 17 = 17