Answer:6x+126in^2
Step-by-step explanation:
a =15 long
b=x. Wide
A=ax
A=15x represenrs picture area
Add on each side of picture 3 in
a1=15+6=21 in
b1=x+6
Calculate area
A1=a1b1
A1=21(x+6)
Area of frame = A1-A
Area of frame=21(x+6)-15x=21x-15x+126=6x+126in^2
1/10 of 32 million is 3.2 million.
Because
1/10 x 32,000,000 = 3,200,000
Answer:
1, 2, 3, 4, 6, 8, 9, 11, 13, 16, 18 and 23 cents cant be made with 5-cents and 7-cent postage.
Step-by-step explanation:
You can make any multiple of 5 with those stamps. Also, you can make any number x with stamps proven that that number is big enough. If you start with a number that is a multiple of 5, then you can increase that number by 2 each time you replace a 5 with a 7 (in each example, we are starting in a postage of value 5j made by 5-cent stamps):
- If x = 5j + 1, for an integer j, (j ≥ 4), then you can replace 4 five cent stamps with 3 7 cent stamps, to obtain x.
- If x = 5j + 2, you can replace 1 five cent stamp with one seven cent stamp to obtain x (j≥1)
- If x = 5j+3, you can replace 5 five cent stamps with 4 seven cent stamps to obtain x (j ≥5).
- If z = 5j+4, you can replace 2 five-cent stamps with 2 seven-cent stamos to obtain x (j≥2)
Note therefore, that if j is at least 5, then we can obtain a postage with value x. This means that any postage of value at least 25 can be made witg five-cent of seven-cent stamps. Lets see for smaller values
- 1, 2, 3 and 4 cent postage are impossible to make
- 5 cent package is possible, so is 7
- 6,7, 8 and 9 are impossible to make (any package with at least 2 stamp has a value at least 10)
- 10 is possible (5+5)
- 11 is not possible (5+5 = 10, 5+7 = 12)
- 12 is possible (5+7)
- 13 is impossible (5+7 = 12, but 7+7 = 14. Also any combination of 3 stamps has a value at least 15)
- 14 is possible (7+7)
- 15 is possible (5+5+5)
- 16 is not possible (5+5+5 = 15, 5+5+7 = 17)
- 17 = 5+5+7 is possible
- 18 is not possible (5+7+7 = 19, and any postage with 4 stamps has a value of 20 or higher)
- 19 = 5+7+7 is possible
- 20 = 5+5+5+5 is possible
- 21 = 7+7+7 is possible
- 22 = 5+5+5+7 is possible
- 23 is not possible (you cant reach 23 with 3 stamps, and you will get a value at least 25 with 5. If you use 4 stamps, you can obtain only even values)
- 24 = 5+5+7+7 is possible
So we conclude that the amounts of postage that are impossible to make are: 1, 2, 3, 4, 6, 8, 9, 11, 13, 16, 18 and 23 cents.
<span><span>
Step 1: Distribute each term of the first polynomial to every term of the
second polynomial. In this case, we need to distribute the 4x and the
–5.
</span>
<span>
<span>Step 2: Combine like terms.</span></span></span>
2 × 3 = 6
6 squared = 36
36 + 3 = 39
Hope this helps!