Answer:
a. 3
Step-by-step explanation:
We solve this question gathering the information given in the question.
June serves 8 guests slices of both pies.
This is soon going to be used
June serves a total of 10 slices of apple pie
This includes the 8 guests which got served both pieces. So 10 - 8 = 2 guests were served only apple pie.
11 slices of blueberry pie.
By the same logic as above, 11 - 8 = 3 guests were served only blueberry pie.
So
8 + 2 + 3 = 13 guests were served at least one pie.
16 - 13 = 3 guests had no pie at all.
Answer:
Slope of the line segment PQ is 1/2.
Step-by-step explanation:
We are given with a line connecting two points P and Q.
The coordinates of P are (4,4) and the coordinates of Q are (-2,1).
Slope of line joining two points
and ![(x_{2},y_{2})](https://tex.z-dn.net/?f=%28x_%7B2%7D%2Cy_%7B2%7D%29)
is given by the formula ![\frac{y_{2}-y_{1}}{x_{2}-x_{1}}](https://tex.z-dn.net/?f=%5Cfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_%7B1%7D%7D)
Hence the slope of the line PQ is ![\frac{1-4}{-2-4}=\frac{-3}{-6}= \frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1-4%7D%7B-2-4%7D%3D%5Cfrac%7B-3%7D%7B-6%7D%3D%20%5Cfrac%7B1%7D%7B2%7D)
Therefore correct option is 'C' that is 1/2.
There is a math trick my teacher taught me called SOH CAH TOA.
That is an acronym for Sin, Opposite over Hypotenuse. Cosine, Adjacent over Hypotenuse, Tan, Opposite over Adjacent.
Sin: To find Sin, you divide the opposite side of the missing angle by the Hypotenuse.
Repeat the process for the other two.
Answer:
The ratio of any two corresponding lengths in two similar geometric figures.
Step-by-step explanation:
You can see immediately that the length of each of the sides in triangle DEF is equal to the length of the corresponding side in ABC multiplied by “a”.
If you divide the length of DE by the length of AB:
a^2/a =a.
You get a scale factor of “a”
Answer:
- 2((4a +1) +8) cm
- 8a +18 cm
- 8a +18 = 42
Step-by-step explanation:
For the first line, you are copying the dimensions from the figure to the blanks. The dimensions on the figure are (4a +1), and (8), both in centimeters. When you have filled in that line, it will read ...
2((4a +1) +8) cm
__
For the second line, you must collect terms and use the distributive property to eliminate parentheses from the above expression.
2((4a +1) +8) cm = 2(4a +9) cm = 2(4a) +2(9) cm
= 8a +18 cm
__
The third line simply sets this expression equal to the given perimeter, 42:
8a +18 = 42
_____
<em>Additional comment</em>
To solve this equation, you can subtract 18 from both sides:
8a +18 -18 = 42 -18
8a = 24 . . . . . . . . . . . simplify
Then divide both sides by 8.
8a/8 = 24/8
a = 3
Finally, the length of the rectangle is ...
4a +1 = 4(3) +1 = 12 +1 = 13
The rectangle is 13 cm long and 8 cm high. Its perimeter is ...
2(13 +8) = 2(21) = 42 . . . cm