Step-by-step explanation:
Let's call L the length and W the width. The length is 10 feet longer than the width, so:
L = W + 10
The area is the length times width, so:
119 = LW
Substituting:
119 = (W + 10) W
119 = W² + 10W
0 = W² + 10W − 119
0 = (W + 17) (W − 7)
W = -17 or 7
Since W must be positive, W = 7.
L = W + 10
L = 17
The length and width are 17 feet and 7 feet, respectively.
Reading the question carefully, "<span>He draws the diameter of the circle through center P using a straight edge. Next he opens his compass to a width equivalent to the radius of the circle." - that implies that Mateo is still in the process of drawing the circle by which the equilateral is inscribed to.
The next steps should be:
*He should draw the upper and lower arcs using the compass opened to a width equivalent to the radius of the sircle.
*Make a vertical diameter using centroid P as basis.
*Draw two right triangles facing the opposite directions using the top most point by which the vertical diameter of the circle touches the top most circumference of the circle.
Doing these steps, Mateo will be able to draw an equilateral triangle inscribed in a circle.
</span>
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.)
Answer:
Slope is 2
Step-by-step explanation:
(-2, -4) and (2, 4)
Slope:
m=(y2-y1)/(x2-x1)
m=(4+4)/(2+2)
m=8/4
m = 2
Answer:
The required inequality is: 
Step-by-step explanation:
Consider the provided information.
Gurnaz has been mowing lawns to save money for a concert. Gurnaz will need to work for at least six hours to save enough money, but he must work fewer than 16 hours this week.
Let the number of hours Gurnaz work is represented by x.
Gurnaz will need to work for at least six hours to save enough money,
That means he can work 6 or more than 6 hours,
He must work fewer than 16 hours this week. That means the value of x should be less than 16.
Thus, the required inequality is:
Now draw the graph of the inequality.
Use a dot or close circle to represents ≤ or ≥ and use a open circle to represent < or >.
The value of x is greater than or equal to 6 also the value of x is less than 16. The required graph is shown below.
