Answer:
Solution given:
y=6/7x+7
Comparing above equation with y=mx+c
we get
m=6/7
a What is the slope of a line parallel to it?
Since for parallel slope are equal ,
slope will be 6/7.
b What is the slope of a line perpendicular to it?
Since for perpendicular line slope is reciprocal to another line but negative so
slope of line is-7/6.
Answer:
![\text{\bf{A.}}\qquad\left[\begin{array}{ccc}-19&9&-7\\15&-7&6\\-2&1&-1\end{array}\right]](https://tex.z-dn.net/?f=%5Ctext%7B%5Cbf%7BA.%7D%7D%5Cqquad%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-19%269%26-7%5C%5C15%26-7%266%5C%5C-2%261%26-1%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
Many scientific and graphing calculators will compute this easily.
The inverse of a square matrix is a square matrix of the same dimensions. That eliminates choices C and D. We can check choices A and B by computing a couple of terms of the product of the given matrix and its "inverse". That product should be the identity matrix, with 1 on the diagonal and 0 elsewhere.
Using matrix A,
(r, c) = (1, 1) = 1(-19) +2(15) +5(-2) = -19 +30 -20 = 1 . . . . correct
(r, c) = (2,3) = 3(-7) +5(6) +9(-1) = -21 +30 =9 = 0 . . . . correct
Using matrix B,
(r, c) = (1, 1) = 1(-19) +2(-2) +5(15) = -19 -4 +75 = 52 . . . . incorrect
Indications are that choice A is appropriate.
Firstly, you have to calculate the 25 percent of the 32 apples which is 32 x 0.25 = 8. So the leftover apples would be 32 - 8 = 24. Since she divided the rest equally among 6 pies, you have to divide 24 by 6, which is 4.
Therefore there are 4 apples in each pie.
<u>Let's consider the facts at hand</u>:
- By Vertical Angle Theorem ⇒ ∠BCE = ∠DCF
- ∠BEC = ∠DFC
- Sides BE = DF
<u>Based on the diagram, triangles BCE and triangles DCF are similar</u>
⇒ based on the Angle-Angle theorem
⇒ since ∠BCE = ∠DCF and ∠BEC = ∠DFC
⇒ the two triangles are similar
Hope that helps!
<em>Definitions of Theorem I used:</em>
- <u><em>Vertical Angle Theorem: </em></u><em>opposite angles of two intersecting lines must be equal</em>
- <u><em>Angle-Angle Theorem:</em></u><em> if two angles of both triangles are equal, then the given triangles must be similar</em>
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