Step-by-step explanation:
Since the two lines running left to right are parallel, and cut into the right side of the triangle, the angles
and
are equal.
With this information, we can solve for
:
![2x + 7 = 3x - 7](https://tex.z-dn.net/?f=2x%20%2B%207%20%3D%203x%20-%207)
![2x - 3x = -7 - 7](https://tex.z-dn.net/?f=2x%20-%203x%20%3D%20-7%20-%207)
![-x = -14](https://tex.z-dn.net/?f=-x%20%3D%20-14)
![x = 14](https://tex.z-dn.net/?f=x%20%3D%2014)
Now that we know
, we can determine what the actual value of these angles are:
![2x + 7](https://tex.z-dn.net/?f=2x%20%2B%207)
![2(14) + 7](https://tex.z-dn.net/?f=2%2814%29%20%2B%207)
![28 + 7](https://tex.z-dn.net/?f=28%20%2B%207)
![35](https://tex.z-dn.net/?f=35)
or
![3x - 7](https://tex.z-dn.net/?f=3x%20-%207)
![3(14) - 7](https://tex.z-dn.net/?f=3%2814%29%20-%207)
![42 - 7](https://tex.z-dn.net/?f=42%20-%207)
![35](https://tex.z-dn.net/?f=35)
Now, we see that the top line of the two parallel lines cuts the right side of the triangle into two angles,
and
. Since it's cutting a straight line into two angles, we know that the same of these angles must be
°. We already solved for the top angle and found that it is
°, so that means the bottom angle is
°. With this, we can solve for
:
![12y + 1 = 145](https://tex.z-dn.net/?f=12y%20%2B%201%20%3D%20145)
![12y = 144](https://tex.z-dn.net/?f=12y%20%3D%20144)
![y = 12](https://tex.z-dn.net/?f=y%20%3D%2012)
Therefore, the answer is ![x = 14, y = 12](https://tex.z-dn.net/?f=x%20%3D%2014%2C%20y%20%3D%2012)
Answer: The length of radius of a circular pool is 7 meters
Step-by-step explanation:
Given that the circumference of a circular pool cover is about 88 meters
To find the length of radius
As we know circumference of a circle is given by
where C is circumference , and r is radius of the circle
Now as according to question we have
![88= 2\pi r\\\\\Rightarrow 88= 2\times \dfrac{22}{7} r\\\\\Rightarrow r= \dfrac{88\times 7}{2\times 44} = 7 m](https://tex.z-dn.net/?f=88%3D%202%5Cpi%20r%5C%5C%5C%5C%5CRightarrow%2088%3D%202%5Ctimes%20%5Cdfrac%7B22%7D%7B7%7D%20r%5C%5C%5C%5C%5CRightarrow%20r%3D%20%5Cdfrac%7B88%5Ctimes%207%7D%7B2%5Ctimes%2044%7D%20%3D%207%20m)
Hence,the length of radius of a circular pool is 7 meters
The value of “k” that will give two real roots is 25/48
Given the equation (1 – 3k) x^2 + 3x – 4, for the equation to have two real roots, this means that b^2 - 4ac > 0
From the given expression
a = 1 - 3k
b = 3
c = -4
Substitute into the equation b^2 - 4ac = 0
3^2 - 4(1 - 3k)(-4) = 0
9 + 16 (1-3k) = 0
9 + 16 - 48k =0
25 = 48k
k = 25/48
Hence the value of “k” that will give two real roots is 25/48
Learn more here: brainly.com/question/564715
Answer:
3/7 of a cucumber.
Step-by-step explanation:
That would be 3/7 of a cucumber to each of the siblings.
20 + 12x = 56
12x = 56 - 20
12x = 36
x = 36/12
x = 3
Bethany's monthly gym fee is $ 20
Bethany also pays $ 3 for a towel fee each visit