The volume of Olivia's rectangular lunchbox is 240 cubic inches. The lunchbox has a height of 3 inches, and its length is 2 inches more than its width. How wide is Olivia's lunchbox?
Answers
Answer 1
Answer:
Volumn = Height*Width*Length
Width*(Width+2)=Volumn/Height=240/3=80
Width^2 +2Width-80=0
(Width-8)(Width+10)=0
Width>0 -> Width+10>0
-> Width-8=0 -> Width=8 inches
Width*(Width+2)=Volumn/Height=240/3=80
Width^2 +2Width-80=0
(Width-8)(Width+10)=0
Width>0 -> Width+10>0
-> Width-8=0 -> Width=8 inches
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fill in the blanks with the equivalent measurement.
Question one
1 yard + 4 inches = blank inches
1 yard - 1 foot = blank feet
46 inches - 10 inches = blank yard(s)
7 feet - 4 feet = blank yard(s)
1 yard + 3 inches = blank inches
Answers
1. 1 yard=3 feet; 3 feet= 36 inches; 36 inches + 4 inches= 40 inches
2. 1 yard=3 feet; 3 feet- 1 foot =2 feet
3. 46 inches- 10 inches=36 inches; 36/3 = 12 yards
4. 7 feet- 4 feet=3 feet; 3 feet =1 yard
5. 1 yard=3 feet; 3 feet =36 inches; 36 inches+3 inches=39 inches
2. 1 yard=3 feet; 3 feet- 1 foot =2 feet
3. 46 inches- 10 inches=36 inches; 36/3 = 12 yards
4. 7 feet- 4 feet=3 feet; 3 feet =1 yard
5. 1 yard=3 feet; 3 feet =36 inches; 36 inches+3 inches=39 inches
1 yard + 4 inches = 36 inches + 4 inches = (40 inches)
1 yard - 1 foot = 3 feet - 1 foot = (2 feet)
46 inches - 10 inches = 36 inches / 12 inches = (3 yards)
7 feet - 4 feet = 3 feet = (1 yard)
1 yard + 3 inches = 36 inches + 3 inches = (39 inches)
1 yard - 1 foot = 3 feet - 1 foot = (2 feet)
46 inches - 10 inches = 36 inches / 12 inches = (3 yards)
7 feet - 4 feet = 3 feet = (1 yard)
1 yard + 3 inches = 36 inches + 3 inches = (39 inches)
Answers
5. start at 0,0 left 1 up one
6. start at 0,0 down 3
7. start at 0,0 right 3 up 2
8. left 3 down 1
9. right 1, down 2
10.right 1, up 3
6. start at 0,0 down 3
7. start at 0,0 right 3 up 2
8. left 3 down 1
9. right 1, down 2
10.right 1, up 3
for a - start on the middle line (at 0) going across (x-axis) and go left one, then go up one.
for b - start on the x-axis (at 0) and stay there (don't go up or down because its a 0) then go down 3 on the y-axis until you reach -3
for c - start on the x-axis (at 0) and go over to the right 3 spaces then go up 2 spaces
for d - start on the x-axis (at 0) and go left 3 times until you reach -3, then go down one space to -1
for e - start one x-axis (at 0) then go over 1 space then go down 2 spaces until you reach -2
for f - start on the x-axis (at 0) then go over 1 then go up 3 spaces
*** also your #4 is wrong, the point supposed to be (2,-2) and #3 is supposed to be (1,3)
for b - start on the x-axis (at 0) and stay there (don't go up or down because its a 0) then go down 3 on the y-axis until you reach -3
for c - start on the x-axis (at 0) and go over to the right 3 spaces then go up 2 spaces
for d - start on the x-axis (at 0) and go left 3 times until you reach -3, then go down one space to -1
for e - start one x-axis (at 0) then go over 1 space then go down 2 spaces until you reach -2
for f - start on the x-axis (at 0) then go over 1 then go up 3 spaces
*** also your #4 is wrong, the point supposed to be (2,-2) and #3 is supposed to be (1,3)
Answers
4.70 is not equivalent.
4.07 4.070 and 4.0700 are equivalent. You can add thousand zeros to 4.07 and its value does not change
4.07 4.070 and 4.0700 are equivalent. You can add thousand zeros to 4.07 and its value does not change
Answers
It equals that because when you multiply a whole number by a decimal then the answer will always be smaller then the whole number.
Well first of all, 225.6 * 0.25 does NOT equal 56. It equal 56.4
Second of all, even if it did equal 56... our number system has been defined so that 225.6 * 0.25 just works out to 56.4... there's not really a reason it does equal 56.4
Second of all, even if it did equal 56... our number system has been defined so that 225.6 * 0.25 just works out to 56.4... there's not really a reason it does equal 56.4
Answers
OK. You asked for it. Here we go.
First, let's gather up the tools we might use ...
some things that we know about triangles:
-- Every triangle: Area = (1/2) x (length of the base) x (the height)
-- Isosceles triangle: It has two sides that are the same length.
-- Right triangle: It has one right angle in it.
The sides that meet at the right angle are called the "legs".
They form a corner there, like this _| .
-------------------------------------------
Now we can start using these tools to hack away at the problem.
Farmer Ted has an isosceles right triangle garden.
The problem asks us to figure out how long the legs are.
Before he changes anything, it looks like this _| and both of
those sides are the same length. Call it 'x' until we figure out
what it really is.
Notice that one of them is the base of the triangle, and the other one
is the height. So the area of this triangle is
(1/2) (x) (x) or (1/2) x² .
-------------------------------
Farmer Ted is never satisfied. Suddenly, one day without warning, he
comes along and makes the garden bigger. He makes one of the legs
7 ft longer, and he makes the other one 5 ft longer.
Now the length of one leg is (x + 7) and the other one is (x + 5) .
They're still the base and height of the triangle, so the area of the
bigger garden is
(1/2) (x + 7) (x + 5).
The problem says that this area is 55 square feet more than the original
area, so look out, here comes the equation :
new area = old area + bigger
(1/2) (x + 7) (x + 5) = (1/2) x² + 55
Locked in the mysterious shadowy crevices of this equation is
everything we need in order to figure out the original length of the legs ...
what we called 'x'.
At this point, we can forget about Farmer Ted, forget about the garden,
and just go back to our laboratory with this equation and solve it to find 'x'.
Let's take it slow and easy, one little step at a time:
(1/2) (x + 7) (x + 5) = (1/2) x² + 55
Multiply each side by 2 : (x + 7) (x + 5) = x² + 110
Expand (FOIL) the left side: x² + 12x + 35 = x² + 110
Subtract x² from each side: 12x + 35 = 110
Subtract 35 from each side: 12x = 75
Divide each side by 12 : x = 6.25 feet
==============================================
OK. That's a very nice number. How do we know whether it's correct ?
Let's check it out, and see if it fits the story:
Original area = (1/2 x base x height) = (0.5 x 6.25 x 6.25) = 19.53125 sq ft
One new leg = (6.25 + 7) = 13.25 ft
Other new leg = (6.25 + 5) = 11.25 ft
New area = (1/2 x base x height) = (0.5 x 13.25 x 11.25) = 74.53125 sq ft
How much bigger is the new area ?
74.53125 - 19.53125 = 55 sq ft yay !
When we start with legs that are 6.25-ft and go through the whole story,
the new area is exactly what the problem says it was. So 6.25-ft is the
correct original length of the legs, before Farmer Ted messed with it.
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