Answer:
a = 36
Step-by-step explanation:
3 + (11/12)a = 36
Subtract 3 from both sides
(11/12)a = 33
multiply both sides by 12
11a = 396
Divide both sides by 11
a = 36
15 = ½ (7x-6)
distribute ½ into parentheses
15 = ½(7x) - ½(6)
15 = ⁷/₂x - 3
multiply by 2
30 = 7x -6
subtract +6 to both side
30 + 6 = 7x
36 = 7x
devide 7 to both side
36
------ = x
7
Explanation:
The formula i.e.
Fuel Efficiency = 32-0.1*speed
represents that the efficiency on very lower speeds will be affected very minor as the multiple of 0.1 which will be subtracted from 32 will be small value.
Secondly, as per attached full question and graph plot, it is clear that up to 26.5 predicted (mpg), the trend of Residual (mpg) is increasing while after 26.5, it starts to decrease nearly linearly.
It's slop can be find out by two point formula i.e.
slope = m =(y2-y1)/(x2-x1)
=(1-2.5)/(27.5-27)
=(-1.5)/(0.5)
=-3
negative sign shows decreasing trend of second half plot
- What is supplementary angle ?
- When sum of two angles is 180°, then each of those two angles will be considered to be the supplementary angle of each other.Example : 150° and 30° are two angles, and their sum is 180°. So, 150° and 30° are supplementary angles.
____________________
<u>Explanation</u> :-
It's given an angle measures 168° more than the measure of its supplementary angle. We are asked to find measure of each angle!
- Let, one of the supplementary angle be "x" . Then the other angle becomes " (x + 168)° "
Sum of these two angles is equal to 180° . Since they are supplementary angles.
![\bf{\underline{\underline{\sf According\ to\ the\ question:-}}}](https://tex.z-dn.net/?f=%20%5Cbf%7B%5Cunderline%7B%5Cunderline%7B%5Csf%20According%5C%20to%5C%20the%5C%20question%3A-%7D%7D%7D%20)
![\qquad](https://tex.z-dn.net/?f=%5Cqquad)
![\pink{\bf \twoheadrightarrow {x\ +\ x\ +\ 168^\circ\ =\ 180^\circ} }](https://tex.z-dn.net/?f=%20%5Cpink%7B%5Cbf%20%20%5Ctwoheadrightarrow%20%7Bx%5C%20%2B%5C%20x%5C%20%2B%5C%20168%5E%5Ccirc%5C%20%3D%5C%20180%5E%5Ccirc%7D%20%20%7D)
![\qquad](https://tex.z-dn.net/?f=%5Cqquad)
![\sf \twoheadrightarrow 2x + 168^\circ= 180^\circ](https://tex.z-dn.net/?f=%20%5Csf%20%20%5Ctwoheadrightarrow%202x%20%2B%20168%5E%5Ccirc%3D%20180%5E%5Ccirc%20)
![\qquad](https://tex.z-dn.net/?f=%5Cqquad)
![\sf \twoheadrightarrow 2x = 180^\circ - 168^\circ](https://tex.z-dn.net/?f=%20%5Csf%20%20%5Ctwoheadrightarrow%202x%20%3D%20180%5E%5Ccirc%20-%20168%5E%5Ccirc%20)
![\qquad](https://tex.z-dn.net/?f=%5Cqquad)
![\sf \twoheadrightarrow 2x = 12^\circ](https://tex.z-dn.net/?f=%20%5Csf%20%20%5Ctwoheadrightarrow%202x%20%3D%2012%5E%5Ccirc%20)
![\qquad](https://tex.z-dn.net/?f=%5Cqquad)
![\sf \twoheadrightarrow x = \cancel{\dfrac{12^\circ}{2}}](https://tex.z-dn.net/?f=%20%5Csf%20%5Ctwoheadrightarrow%20x%20%3D%20%5Ccancel%7B%5Cdfrac%7B12%5E%5Ccirc%7D%7B2%7D%7D%20)
![\qquad](https://tex.z-dn.net/?f=%5Cqquad)
![\pink{\bf \twoheadrightarrow x = 6^\circ }](https://tex.z-dn.net/?f=%20%5Cpink%7B%5Cbf%20%5Ctwoheadrightarrow%20x%20%3D%206%5E%5Ccirc%20%7D)
Then –
![\qquad](https://tex.z-dn.net/?f=%5Cqquad)
![\bf \longrightarrow x +168^\circ](https://tex.z-dn.net/?f=%20%5Cbf%20%20%5Clongrightarrow%20x%20%2B168%5E%5Ccirc)
![\qquad](https://tex.z-dn.net/?f=%5Cqquad)
![\tt \longrightarrow 6^\circ+ 168^\circ](https://tex.z-dn.net/?f=%20%5Ctt%20%5Clongrightarrow%20%20%206%5E%5Ccirc%2B%20168%5E%5Ccirc%20)
![\qquad](https://tex.z-dn.net/?f=%5Cqquad)
![\tt \longrightarrow 174^\circ](https://tex.z-dn.net/?f=%20%5Ctt%20%5Clongrightarrow%20174%5E%5Ccirc)
- The measures of the two given angles are 6° and 174°.
______________________
Answer:
14 miles.
Step-by-step explanation:
The First street, the Main street, and the Oak street forms a right triangle and the angle between the First street and the Oak street is x such that, tan x = 7/5. {Given}
The distance from the intersection point of the First street and the Main street to Oak street along the First street is 10 miles and we have to calculate the distance (d) of Oak street from the same intersection point along the Main street.
Now, using trigonometry on the above mentioned right triangle
![\tan x = \frac{7}{5} = \frac{d}{10}](https://tex.z-dn.net/?f=%5Ctan%20x%20%3D%20%5Cfrac%7B7%7D%7B5%7D%20%3D%20%5Cfrac%7Bd%7D%7B10%7D)
⇒ d = 14 miles. (Answer)