Answer: GCF of 54 and 45: 9.
Step-by-step explanation: The factors of 54 include: 1, 2, 3, 6, 9, 18, 27, and 54. The factors of 45 include: 1, 3, 5, 9, 15, and 45. The largest common factor of 45 and 54 is 9.
Answer:
1.35
Step-by-step explanation:
13.5/100 times 10 = 1.35
Answer:
Step-by-step explanation:
The value of the expression is its distance from zero. The absolute value is the positive value without any minus sign.
![|-7.1|=7.1\\\\|2.7+4.2|=|6.9|=6.9\\\\|4-9|=|-5|=5\\\\|-3.1+8.8|=|5.7|=5.7](https://tex.z-dn.net/?f=%7C-7.1%7C%3D7.1%5C%5C%5C%5C%7C2.7%2B4.2%7C%3D%7C6.9%7C%3D6.9%5C%5C%5C%5C%7C4-9%7C%3D%7C-5%7C%3D5%5C%5C%5C%5C%7C-3.1%2B8.8%7C%3D%7C5.7%7C%3D5.7)
Answer:
a. ![x=4\sqrt{3}](https://tex.z-dn.net/?f=x%3D4%5Csqrt%7B3%7D)
b. ![m\angle B =60\°](https://tex.z-dn.net/?f=m%5Cangle%20B%20%3D60%5C%C2%B0)
Step-by-step explanation:
a. The sides of an Equilateral triangle are all equal.
Then, in this case:
![AB=BC=CA=8](https://tex.z-dn.net/?f=AB%3DBC%3DCA%3D8)
Based on this, you can identify that AD divides the side BC into two equal parts and the triangle into two equal Right triangles. Then:
![CD=BD=\frac{8}{2}=4](https://tex.z-dn.net/?f=CD%3DBD%3D%5Cfrac%7B8%7D%7B2%7D%3D4)
Knowing the length CD, you can find "x" using the Pythagorean Theorem. This is:
![a^2=b^2+c^2](https://tex.z-dn.net/?f=a%5E2%3Db%5E2%2Bc%5E2)
Where "a" is the hypotenuse and "b" and "c" are the legs.
In this case:
![a=8\\b=x\\c=4](https://tex.z-dn.net/?f=a%3D8%5C%5Cb%3Dx%5C%5Cc%3D4)
Substituting values and solving for "x", you get:
![8^2=x^2+4^2\\\\\sqrt{8^2-4^2}=x\\\\x=4\sqrt{3}](https://tex.z-dn.net/?f=8%5E2%3Dx%5E2%2B4%5E2%5C%5C%5C%5C%5Csqrt%7B8%5E2-4%5E2%7D%3Dx%5C%5C%5C%5Cx%3D4%5Csqrt%7B3%7D)
b. By definition, the measure of each interior angle of an Equilateral triangle is 60 degrees. Therefore:
![m\angle B =60\°](https://tex.z-dn.net/?f=m%5Cangle%20B%20%3D60%5C%C2%B0)
X = 71 degrees
And here is a sentence to fill the minimum word rule