The diagonal of a square is equal to the side x times square root of 2, xSqrt(2)
z = xSqrt(2), its rate of change is just Sqrt(2)
Answer:
see below
Step-by-step explanation:
The sum of the interior angles is 180
<1 + <2 + <4 = 180
<1 + 31+ <4 = 180
<1 + <4 = 180-31
<1 + <4 = 149
<2 + <3 = 180 because it forms a straight line
31 + <3 = 180
<3 = 180-31
<3 = 149
Setting theses equal (since they are both equal to 149)
<1 + <4 = <3
The exterior angle is equal to the sum of the opposite interior angles
The answer would be 20-(3+2) because first you do what is inside the parentheses 3+2=5 and now you have to subtract 20-5=15. Cody’s change should be $15.
Triangle ABC is equilateral, because AB=BC=AC=a. Then
m∠A=m∠B=m∠C=60°.
Let point D lie on the ray BC to the right from points B and C and let CD=x. Then BD=a+x, AB=a.
Consider triangle ACD. In this triangle, m∠ACD=180°-m∠ACB=180°-60°=120°.
By the cosine theorem,
![AD^2=AC^2+CD^2-2\cdot AC\cdot CD\cdot \cos \angle ACD,\\\\AD^2=a^2+x^2-2\cdot a\cdot x\cdot \cos 120^{\circ},\\\\AD^2=a^2+x^2+ax,\\\\AD=\sqrt{a^2+x^2+ax}.](https://tex.z-dn.net/?f=AD%5E2%3DAC%5E2%2BCD%5E2-2%5Ccdot%20AC%5Ccdot%20CD%5Ccdot%20%5Ccos%20%5Cangle%20ACD%2C%5C%5C%5C%5CAD%5E2%3Da%5E2%2Bx%5E2-2%5Ccdot%20a%5Ccdot%20x%5Ccdot%20%5Ccos%20120%5E%7B%5Ccirc%7D%2C%5C%5C%5C%5CAD%5E2%3Da%5E2%2Bx%5E2%2Bax%2C%5C%5C%5C%5CAD%3D%5Csqrt%7Ba%5E2%2Bx%5E2%2Bax%7D.)
Since
then
![AD^2=(a+x)^2-ax](https://tex.z-dn.net/?f=AD%5E2%3D%28a%2Bx%29%5E2-ax%3C%28a%2Bx%29%5E2%3DBD%5E2%5CRightarrow%20AD%3CBD)
and
![AD^2=a^2+x^2+ax>a^2=AB^2\Rightarrow AD>AB.](https://tex.z-dn.net/?f=AD%5E2%3Da%5E2%2Bx%5E2%2Bax%3Ea%5E2%3DAB%5E2%5CRightarrow%20AD%3EAB.)
Therefore, you get double inequality
or ![BD>AD>AB.](https://tex.z-dn.net/?f=BD%3EAD%3EAB.)
Answer:
Step-by-step explanation:
The following statements are true
- The expression -(-3.5) is equivalent to 3.5. The product of 2 minus sign will give a positive sign i.e -*- = + hence -(-3.5) = (-*-)*35 = +35 = 35.
- The opposite of 0 is itself. There is no negative value of zero hence 0 is still the same as -0 making the opposite of zero to still be be zero. The minus sign in -0 is insignificant due to the insignificance of the zero digit.
- The opposite of -3.5 is located 3.5 units to the right of 0 on the number line. Fora number line, the origin is always located at the centre. The value to the right are along the positive x-axis and are all positive values while the values located towards the left are the negative x-axis. The opposite value of - 3.5 is gotten by negating the value of -3.5 i.e -(-3.5) to give +3.5 and +3.5 is a positive value which is located towards the right of a number line.
This makes the fourth statement to be False