We know that the area of a parallelogram is the base * the height of it, so if we divide both sides by the height, then area/height=base. Therefore, we must divide the area by the height. To divide using polynomials, we first set it up similar to a regular long division problem:
______________________
2x+3 | 2x²+13x+15
Next, we take the first component of the numerator (2x² in this case) and divide it by the first component of the denominator (2x) to get x. That will form the start of our answer, and at the bottom, we will subtract our numerator by the denominator (2x+3) multiplied by the start of our answer (x). Therefore, we have
_x_____________________
2x+3 | 2x²+13x+15
-(2x²+3x)
_______________
10x+15
We then repeat the process until we finish, and whatever's left at the top is our answer. If there's something left, that's our remainder.
_x+5_____________________
2x+3 | 2x²+13x+15
-(2x²+3x)
_______________
10x+15
- (10x+15)
_________________
0
Therefore, our base has a length of x+5.
Feel free to ask further questions, and Happy Holidays!
Answer:
28
Step-by-step explanation:
Hi! So what we're gonna want to do here is set up a system of equations. Lets say x = regular baskets and y = deluxe baskets. You would set up the system like this:
28x + 24y = 1,188
28x + 13y = 836
So since the number before the x is the same in both equations, we are going to want to cancel that out.
28x + 24y = 1,188
-1(28x + 13y = 836)
----------------
28x + 24y = 1,188
-28x - 13y = -836
Add the two equations together! There will be no x value :)
11y = 352
y = 32... The deluxe basket is going to cost $32
Put the y value into one of the equations to solve for x.
28x + 13(32) = 836
28x + 416 = 836
28x = 420
x = 15... The regular basket will cost $15
Hope this helps!
9514 1404 393
Answer:
(d) (8, 40)
Step-by-step explanation:
A pentagon has 5 sides. 8 of them will have 8×5 = 40 sides. The ordered pair representing (pentagons, sides) will be ...
(8, 40) . . . . . matches the last choice
1) Convert the following measurements.
<span>a. 2 cubic yards to cubic feet
1 cubic yard-------- > 27 cubic feet
2---------------------- X
x=2*27=54 cubic feet
</span><span>b. 135 cubic feet to cubic yards
</span>1 cubic yard-------- > 27 cubic feet
x----------------------- 135
x=135/27=5 cubic yard
c. 6,912 cubic feet to cubic inches
1 cubic feet--------------- > 1728 cubic inches
6912 cubic feet------------- x
x=11943936 cubic inches
<span>d. 279,936 cubic inches to cubic feet
</span>1 cubic feet--------------- > 1728 cubic inches
x------------------------------ 279,936 cubic inches
x=162 cubic feet
2) <span>Solve the following addition problem. Remember to carry as necessary.
7 cu. yd. 9 cu. ft. 134 cu. in. + 1 cu. yd. 12 cu. ft. 200 cu. in.
</span>7 cu. yd
9 cu. ft-------- > 9/27=0.33333 cu yd
134 cu. in-----> 134*2.1433e-5=0.00287
1 cu. yd
12 cu. ft------- 12/27=0.44444 cu yd
200 cu. in----200*2.1433e-5=0.00429 cu yd
(7+0.33333+0.00287)+(1+0.44444+0.00429)=8.78493 cu yd
3 <span>Solve the following subtraction problem. Remember to borrow as necessary.
9 cu. yd. 113 cu. in. – 4 cu. ft. 129 cu. in.
</span>9 cu yd
113 cu in---------113*2.1433e-5=0.00242 cu yd
4 cu. ft--------4/27=0.14814 cu yd
129 cu. in----------129*2.1433e-5=.00276
(9+0.00242)-(0.14814+.00276)=8.85152 cu yd
4 <span>Solve the following multiplication problem.
11 cu. yd. 17 cu. in. × 135
</span>11 cu yd
17 cu in----------17*2.1433e-5=0.00036 cu yd
(11+0.00036)*135=1485.0486 cu yd
5 <span>What’s the capacity of a 3 cubic foot carton in cubic inches?
3 cu feet---------> 3*1728=5184 cu in
6 </span>The Great Pyramid was built in Egypt more than 4,000 years ago. It was built by King Khufu, or Cheops, who intended to use it as a tomb. The pyramid contains about 2,300,000 blocks of stone, each weighing 2 1⁄2 tons. Can you calculate the approximate total weight of the Great Pyramid, in pounds?
2 1/2=(4+1)/2=5/2=2.5
weight=2,300,000*2.5=5750000 ton-------> *2204.62=12676565000 lb
7 <span>Convert the following liquid measures.
a. 5 gallons to pints ------*8=40 pints
b. 128 tablespoons to fluid ounces -----*0.5=64 fluid onces
c. 93 pints to quarts --------*0.5=46.5 quarts
d. 13 quarts to cups ---*4=52 cups
e. 69 teaspoons to tablespoons---------*0.3333=23 </span>tablespoons<span>
f. 112 cups to gallons--------*0.0625= 7 </span>gallons<span>
g. 18 fluid ounces to teaspoons---------*6=108 </span>teaspoons<span>
h. 3 gallons to fluid ounces-----*128= 384 ounces
</span>
8 A local dairy farmer collects 490 gallons of milk a day from his cows. He keeps 1⁄35 of the milk for his own use, and sells the rest. Each quart of milk sells for 35 cents. In dollars, how much does he earn from selling his milk each day? (There are 100 cents in a dollar.)
(34/35)*490=476 gallons to sell------------> *4=1904 quarts
1904*0.35=666.40 dollars
9 A swimming pool has a capacity of 1,386 cubic feet. One gallon of water will fill 231 cubic inches of space. How many gallons of water will it take to fill the entire pool? (Hint: Convert the capacity of the pool to cubic inches first.)
1,386 cubic feet----------> *1728=2395008 cu in
1 gallons will fill --------------- > 231 cu in of space
x--------------------------------- 2395008 cu in
x= 10368 gallons
10 The instructions on a bottle of laundry detergent tell you to add two capfuls of detergent to each gallon of water. One capful of detergent is equal to about one tablespoon. If your washing machine holds 11 gallons of water, how many tablespoons of detergent will you need to add? How many fluid ounces of detergent?
2 capfuls of detergent-----------> 1 gallon of water----------> 2 tablespoon
11--------------------------- > X
x=11*2=22 tablespoon
22 tablespoon-----------------> *0.5=11 fluid onces
11 <span>Convert the following dry measurements.
a. 11 bushels to quarts -------*37,2367=409.60 quarts
b. 3 pecks to pints---------*18.6184=55.85 pints
c. 97 quarts to bushels ------ *0.02685=2.6044 bushels
d. 1,120 quarts to pecks--------* 0.107421=120.31 pecks
</span>
12 Twelve apple pies can be made from one bushel of apples. How many apple pies can be made from one peck of apples?
1 peck---------> *0.25=0.25 bushel
12 apple pies-------------- > 1 bushel
x---------------------------------0.25 bushel
x=0.25*12=3 apple pies
13 <span>Mr. Osaka sprinkles 1.694 pints of dry, powdered plant food on his garden three times a year. In quarts, what’s the total amount of plant food he uses in one year?
</span>1.694 pints*3=5082 pints in one year--------------> *0.5=2541 quarts<span>
</span>
