1.085*10^3 scientific notation is a number between 1-10 multiplied by 10 to a certain power.
The answer is 6:45. 11:30-4:45 = 6:45
Answer:
- 13. (a) 120°, 120°, (b) 8.94 cm
- 14. (a) 17.9 cm, (b) 22.4 cm
Step-by-step explanation:
- <em>Refer to the attached sketch (not to scale)</em>
<h3>Question 13</h3>
(a) The center of the circle is also the circumcenter of the triangle PQR.
<u>Since ΔPQR is equilateral, all sides are equal, therefore opposite angles are also congruent:</u>
Sum of the three angles is 360° as cover the full circle.
<u>Each angle measure is:</u>
- ∠POQ = ∠QOR = ∠POR = 360°/3 = 120°
(b) Each side is 16 cm and the radius is 12 cm.
The distance of the midpoint M of PQ from the center O is perpendicular bisector of ΔPOQ.
<u>The segment MO is:</u>
- MO² = PO² - PM² = PO² - (PQ/2)²
- MO² = 12² - (16/2)² = 80
- MO = √80 = 8.94 cm (rounded)
<h3>Question 14</h3>
<u>ΔXYZ is isosceles with:</u>
- XY = XZ = 20 cm
- YZ = 18 cm
(a) The altitude of ΔXYZ is a perpendicular bisector of YZ. h = XM is the altitude
<u>Find h:</u>
- h² = XZ² - ZM² = XZ² - (ZY/2)²
- h² = 20² - (18/2)² = 319
- h = √319
- h = 17.9 cm (rounded)
(b) Note the ∠ZXM is half of the ∠ZOM as both the angles intercept half of the arc ZY and ∠ZOM is a central angle.
<u>Find ∠ZXM:</u>
- sin ∠ZXM = ZM/ZX = 9 / 20
- m∠ZXM = arcsin (9/20) = 26.7° (rounded)
<u>Find ∠ZOM:</u>
- m∠ZOM = 2*m∠ZXM = 2*26.7 = 53.4°
<u>Find the measure of the radius:</u>
- sin ∠ZOM = ZM/r
- sin 53.4° = 9/r
- r = 9 / sin 53.4°
- r = 11.2 cm (rounded)
<u>Find the measure of the diameter:</u>
- d = 2r = 2*11.2 cm = 22.4 cm
Answer: First option.
Step-by-step explanation:
<h3>
The missing picture is attached.</h3><h3>
</h3>
You can use these methods to solve a System of Equations and find the value of the variables:
A. Substitution method.
B. Elimination method.
In this case, given the following System of equations:
![\left \{ {{3 x + 2 y = 17} \atop {x + 4 y = 19}} \right.](https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7B3%20x%20%2B%202%20y%20%3D%2017%7D%20%5Catop%20%7Bx%20%2B%204%20y%20%3D%2019%7D%7D%20%5Cright.)
The most efficient method to solve it is the Substitution Method. The procedure is:
Step 1: Solve for one of the variables from the most convenient equation.
Step 2: Make the substitution into the other equation and solve for the other variable in order to find its value.
Step 3: Substitute the value obtained into the equation from Step 1 and evaluate, in order to find the value of the other variable.
Based on this, you can identify that first step to solve the given System of equations, is solving for "x" from the second equation:
![x + 4 y = 19\\\\x=-4y+19](https://tex.z-dn.net/?f=x%20%2B%204%20y%20%3D%2019%5C%5C%5C%5Cx%3D-4y%2B19)
Answer:
228
Step-by-step explanation:
0.4% = 0.004
0.004 x 57000 = 228