Since you haven't provided the data to answer the problem, I have my notes here that might guide you solve the problem on your own:
Now, consider a triangle that’s graphed in the coordinate plane. You can always use the distance formula, find the lengths of the three sides, and then apply Heron’s formula. But there’s an even better choice, based on the determinant of a matrix.
Here’s a formula to use, based on the counterclockwise entry of the coordinates of the vertices of the triangle
(x1<span>, </span>y1), (x2<span>, </span>y2), (x3<span>, </span>y3<span>) or (2, 1), (8, 9), (1, 8): </span>A<span> = </span>x1y2<span> + </span>x2y3<span> + </span>x3y1<span> – </span>x1y3<span> – </span>x2y1<span> – </span>x3y2<span>.</span>
6 | 1 1 -40 -4
. | 6 42 12
- - - - - - - - - - - - - -
. | 1 7 2 8
6 | 3 -9 -56 8
. | 18 54 -12
- - - - - - - - - - - - - - -
. | 3 9 -2 -4
The line
<span>The sum of twice x and 3 times y is less than 6
is the same as
2x + 3y < 6
which can be transformed into
y < -2x/3 + 2
and
</span><span>y must be greater than 1 less than twice the x
is
y > 2x - 1
The solution is represented by the first figure.</span>
Answer:
D. 1356.5 cm³
Step-by-step explanation:
The volume of a cone can be represented by:
V = (π)(r²)(h/3)
Substitute the known values:
π = 3.14
r = 12
h = 9
V = (3.14)(12²)(9/3)
Square 12.
V = (3.14)(144)(9/3)
Divide 9 by 3.
V = (3.14)(144)(3)
Multiply 3.14 and 144.
V = (452.16)(3)
Multiply 452.16 and 3.
V = 1356.48
Round to the nearest tenth.
V = 1356.5.
9514 1404 393
Answer:
replace recipe quantities:
1/4 ⇒ 5/8; 1/2 ⇒ 1 1/4; 1 ⇒ 2 1/2; 1 1/2 ⇒ 3 3/4; 2 ⇒ 5
Step-by-step explanation:
The given recipe serves 4, so must be multiplied by 10/4 = 5/2 to make it make 10 servings.
The numbers in the recipe (ignoring units or ingredients) are ...
1/4, 1/2, 1, 1 1/2, 2
Each of these numbers needs to be multiplied by 5/2 to get the number for the larger recipe.
1/4 × 5/2 = 5/8
1/2 × 5/2 = 5/4 = 1 1/4
1 × 5/2 = 5/2 = 2 1/2
(1 1/2) × 5/2 = 3/2 × 5/2 = 15/4 = 3 3/4
2 × 5/2 = 5
Then, to make the larger recipe, rewrite it with the quantities replaced as follows:
old value ⇒ new value
1/4 ⇒ 5/8
1/2 ⇒ 1 1/4
1 ⇒ 2 1/2
1 1/2 ⇒ 3 3/4
2 ⇒ 5
__
For example, 1 1/2 lbs of fresh tomatoes ⇒ 3 3/4 lbs of fresh tomatoes
_____
<em>Additional comment</em>
If you actually want to create the recipe, you may find it convenient to use a spreadsheet to list quantities, units, and ingredient names. Then you can add a column for the quantities for a different number of servings, and let the spreadsheet figure the new amounts. (A spreadsheet will compute quantities in decimal, so you will need to be familiar with the conversions to fractions--or use metric quantities.)