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)
Given :
![\dfrac{x}{9}=\dfrac{5}{11}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%7D%7B9%7D%3D%5Cdfrac%7B5%7D%7B11%7D)
Multiply by ( 9 x 11 ) i.e. 99 on both sides,
![= > \dfrac{x}{9} \times 99 = \dfrac{5}{11} \times 99 \\ \\ \\ = > x \times 11 = 5 \times 9 \\ \\ = >x = \frac{5 \times 9}{11} \\ \\ \\ = > x = \frac{45}{11}](https://tex.z-dn.net/?f=%20%3D%20%20%3E%20%20%5Cdfrac%7Bx%7D%7B9%7D%20%20%5Ctimes%2099%20%3D%20%20%5Cdfrac%7B5%7D%7B11%7D%20%20%5Ctimes%2099%20%5C%5C%20%20%5C%5C%20%20%5C%5C%20%20%3D%20%20%3E%20x%20%5Ctimes%2011%20%3D%205%20%5Ctimes%209%20%5C%5C%20%20%5C%5C%20%20%3D%20%20%3Ex%20%3D%20%20%5Cfrac%7B5%20%5Ctimes%209%7D%7B11%7D%20%20%5C%5C%20%20%5C%5C%20%20%5C%5C%20%20%3D%20%20%3E%20x%20%3D%20%20%5Cfrac%7B45%7D%7B11%7D%20)
Therefore the numeric value of x is 45 / 11.
Answer:
There is a 1/3 (or 0.33%) probability of rolling a number greater than or equal to 5.
Step-by-step explanation:
First, find what numbers are greater than or equal to 5:
5 and 6
Find what options you can get on a number cube:
1, 2, 3, 4, 5, and 6
Out of the 6 possible outcomes, there are only 2 that will get a number greater than or equal to 5. Write this as a fraction:
2/6
Simplify:
1/3
Answer:
There are no tables given
Answer:
520
Step-by-step explanation:
Number of students riding bus
![=65\% \: of \: 800 \\ = \frac{65}{100} \times 800 \\ = 65 \times 8 \\ = 520 \\](https://tex.z-dn.net/?f=%3D65%5C%25%20%5C%3A%20of%20%5C%3A%20800%20%5C%5C%20%20%3D%20%20%5Cfrac%7B65%7D%7B100%7D%20%20%5Ctimes%20800%20%5C%5C%20%20%3D%2065%20%5Ctimes%208%20%5C%5C%20%20%3D%20520%20%5C%5C%20)