A $48$-inch-by-$80$-inch door has a border of $x$ inches; it has two glass panels totaling $1590$ square...
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We have a $48$-inch-by-$80$-inch wooden door with two rectangular glass windows, not necessarily of the same size. The wooden areas of the door are of uniform width, labeled "$x$" in the picture below. The glass occupies $1590$ square inches. Find the width of the wooden areas.
I'm assuming that you would do $(48-2x)(80-3x)$ which would simplify to $3x^{2}-152x+1920$.
I'm really close on the factoring. I don't know what quadratic formula is yet or how to really use it.
factoring
edited Jan 5 at 18:51
Blue
48.3k870153
asked Jan 5 at 18:21
J. DOEEJ. DOEE
16927
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closed as off-topic by amWhy, Abcd, Cesareo, José Carlos Santos, Jyrki Lahtonen Jan 6 at 22:53
This question appears to be off-topic. The users who voted to close gave this specific reason:
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$begingroup$
We have a $48$-inch-by-$80$-inch wooden door with two rectangular glass windows, not necessarily of the same size. The wooden areas of the door are of uniform width, labeled "$x$" in the picture below. The glass occupies $1590$ square inches. Find the width of the wooden areas.
I'm assuming that you would do $(48-2x)(80-3x)$ which would simplify to $3x^{2}-152x+1920$.
I'm really close on the factoring. I don't know what quadratic formula is yet or how to really use it.
factoring
edited Jan 5 at 18:51
Blue
48.3k870153
asked Jan 5 at 18:21
J. DOEEJ. DOEE
16927
$endgroup$
closed as off-topic by amWhy, Abcd, Cesareo, José Carlos Santos, Jyrki Lahtonen Jan 6 at 22:53
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – amWhy, Abcd, Cesareo, José Carlos Santos, Jyrki Lahtonen
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
We have a $48$-inch-by-$80$-inch wooden door with two rectangular glass windows, not necessarily of the same size. The wooden areas of the door are of uniform width, labeled "$x$" in the picture below. The glass occupies $1590$ square inches. Find the width of the wooden areas.
I'm assuming that you would do $(48-2x)(80-3x)$ which would simplify to $3x^{2}-152x+1920$.
I'm really close on the factoring. I don't know what quadratic formula is yet or how to really use it.
factoring
edited Jan 5 at 18:51
Blue
48.3k870153
asked Jan 5 at 18:21
J. DOEEJ. DOEE
16927
$endgroup$
We have a $48$-inch-by-$80$-inch wooden door with two rectangular glass windows, not necessarily of the same size. The wooden areas of the door are of uniform width, labeled "$x$" in the picture below. The glass occupies $1590$ square inches. Find the width of the wooden areas.
I'm assuming that you would do $(48-2x)(80-3x)$ which would simplify to $3x^{2}-152x+1920$.
I'm really close on the factoring. I don't know what quadratic formula is yet or how to really use it.
factoring
factoring
edited Jan 5 at 18:51
Blue
48.3k870153
asked Jan 5 at 18:21
J. DOEEJ. DOEE
16927
edited Jan 5 at 18:51
Blue
48.3k870153
asked Jan 5 at 18:21
J. DOEEJ. DOEE
16927
edited Jan 5 at 18:51
Blue
48.3k870153
edited Jan 5 at 18:51
Blue
48.3k870153
edited Jan 5 at 18:51
Blue
48.3k870153
48.3k870153
asked Jan 5 at 18:21
J. DOEEJ. DOEE
16927
asked Jan 5 at 18:21
J. DOEEJ. DOEE
16927
asked Jan 5 at 18:21
J. DOEEJ. DOEE
16927
16927
closed as off-topic by amWhy, Abcd, Cesareo, José Carlos Santos, Jyrki Lahtonen Jan 6 at 22:53
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – amWhy, Abcd, Cesareo, José Carlos Santos, Jyrki Lahtonen
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by amWhy, Abcd, Cesareo, José Carlos Santos, Jyrki Lahtonen Jan 6 at 22:53
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – amWhy, Abcd, Cesareo, José Carlos Santos, Jyrki Lahtonen
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
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2 Answers
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The area of the wood can be broken into the two rectangles up the sides, which are $80 times x$ and three rectangles in the middle, which are $(48-2x) times x$. The total are of wood is then $2cdot 80 cdot x + 3 cdot (48-2x) x=-6x^2+304x$ This plus the glass area equals the total door area, so
$$-6x^2+304x+1590=48cdot 80=3840\0=6x^2-304x+2250$$
answered Jan 5 at 18:38
Ross MillikanRoss Millikan
295k23198371
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Initially, you gave a correct expression for the area of the glass: $$(48-2x)(80-3x) tag{1}$$
"Simplifying" to $3x^2-152x+1920$, however, is incorrect. You seem to have taken the expanded form of $(1)$ ...
$$6 x^2 - 304 x + 3840 tag{2}$$
... and divided-through by $2$. But $(2)$ is an expression, representing some number. You cannot "simplify" an expression by dividing it by something. (If I have $30$ apples, you can't "simplify" my inventory by dividing by $2$ to say that I only have $15$ apples.)
The next step should be to take your calculated glass area, and equate it with the given glass area:
$$6x^2-304x+3840 = 1590 tag{3}$$
Here, you are allowed to divide-through by $2$ if you like (it helps to make the numbers smaller), provided that you do so to both sides.
$$3x^2-152x+1920 = 795 tag{4}$$
(If I have $30$ apples, then it's perfectly valid to say that half my inventory is half of $30$; that is, half my inventory is $15$. (Note how this situation is different from the one I described after $(2)$.) So, here, it's valid to say that half the calculated area of glass is half the given area of glass.)
From here, we can re-write (subtracting $795$ from both sides) ...
$$3x^2-152x+1125 = 0 tag{5}$$
... and then hope to factor the left-hand side. Can you proceed from here?
answered Jan 5 at 18:40
BlueBlue
48.3k870153
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add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The area of the wood can be broken into the two rectangles up the sides, which are $80 times x$ and three rectangles in the middle, which are $(48-2x) times x$. The total are of wood is then $2cdot 80 cdot x + 3 cdot (48-2x) x=-6x^2+304x$ This plus the glass area equals the total door area, so
$$-6x^2+304x+1590=48cdot 80=3840\0=6x^2-304x+2250$$
answered Jan 5 at 18:38
Ross MillikanRoss Millikan
295k23198371
$endgroup$
add a comment |
$begingroup$
The area of the wood can be broken into the two rectangles up the sides, which are $80 times x$ and three rectangles in the middle, which are $(48-2x) times x$. The total are of wood is then $2cdot 80 cdot x + 3 cdot (48-2x) x=-6x^2+304x$ This plus the glass area equals the total door area, so
$$-6x^2+304x+1590=48cdot 80=3840\0=6x^2-304x+2250$$
answered Jan 5 at 18:38
Ross MillikanRoss Millikan
295k23198371
$endgroup$
add a comment |
$begingroup$
The area of the wood can be broken into the two rectangles up the sides, which are $80 times x$ and three rectangles in the middle, which are $(48-2x) times x$. The total are of wood is then $2cdot 80 cdot x + 3 cdot (48-2x) x=-6x^2+304x$ This plus the glass area equals the total door area, so
$$-6x^2+304x+1590=48cdot 80=3840\0=6x^2-304x+2250$$
answered Jan 5 at 18:38
Ross MillikanRoss Millikan
295k23198371
$endgroup$
The area of the wood can be broken into the two rectangles up the sides, which are $80 times x$ and three rectangles in the middle, which are $(48-2x) times x$. The total are of wood is then $2cdot 80 cdot x + 3 cdot (48-2x) x=-6x^2+304x$ This plus the glass area equals the total door area, so
$$-6x^2+304x+1590=48cdot 80=3840\0=6x^2-304x+2250$$
answered Jan 5 at 18:38
Ross MillikanRoss Millikan
295k23198371
answered Jan 5 at 18:38
Ross MillikanRoss Millikan
295k23198371
answered Jan 5 at 18:38
Ross MillikanRoss Millikan
295k23198371
answered Jan 5 at 18:38
Ross MillikanRoss Millikan
295k23198371
295k23198371
add a comment |
add a comment |
$begingroup$
Initially, you gave a correct expression for the area of the glass: $$(48-2x)(80-3x) tag{1}$$
"Simplifying" to $3x^2-152x+1920$, however, is incorrect. You seem to have taken the expanded form of $(1)$ ...
$$6 x^2 - 304 x + 3840 tag{2}$$
... and divided-through by $2$. But $(2)$ is an expression, representing some number. You cannot "simplify" an expression by dividing it by something. (If I have $30$ apples, you can't "simplify" my inventory by dividing by $2$ to say that I only have $15$ apples.)
The next step should be to take your calculated glass area, and equate it with the given glass area:
$$6x^2-304x+3840 = 1590 tag{3}$$
Here, you are allowed to divide-through by $2$ if you like (it helps to make the numbers smaller), provided that you do so to both sides.
$$3x^2-152x+1920 = 795 tag{4}$$
(If I have $30$ apples, then it's perfectly valid to say that half my inventory is half of $30$; that is, half my inventory is $15$. (Note how this situation is different from the one I described after $(2)$.) So, here, it's valid to say that half the calculated area of glass is half the given area of glass.)
From here, we can re-write (subtracting $795$ from both sides) ...
$$3x^2-152x+1125 = 0 tag{5}$$
... and then hope to factor the left-hand side. Can you proceed from here?
answered Jan 5 at 18:40
BlueBlue
48.3k870153
$endgroup$
add a comment |
$begingroup$
Initially, you gave a correct expression for the area of the glass: $$(48-2x)(80-3x) tag{1}$$
"Simplifying" to $3x^2-152x+1920$, however, is incorrect. You seem to have taken the expanded form of $(1)$ ...
$$6 x^2 - 304 x + 3840 tag{2}$$
... and divided-through by $2$. But $(2)$ is an expression, representing some number. You cannot "simplify" an expression by dividing it by something. (If I have $30$ apples, you can't "simplify" my inventory by dividing by $2$ to say that I only have $15$ apples.)
The next step should be to take your calculated glass area, and equate it with the given glass area:
$$6x^2-304x+3840 = 1590 tag{3}$$
Here, you are allowed to divide-through by $2$ if you like (it helps to make the numbers smaller), provided that you do so to both sides.
$$3x^2-152x+1920 = 795 tag{4}$$
(If I have $30$ apples, then it's perfectly valid to say that half my inventory is half of $30$; that is, half my inventory is $15$. (Note how this situation is different from the one I described after $(2)$.) So, here, it's valid to say that half the calculated area of glass is half the given area of glass.)
From here, we can re-write (subtracting $795$ from both sides) ...
$$3x^2-152x+1125 = 0 tag{5}$$
... and then hope to factor the left-hand side. Can you proceed from here?
answered Jan 5 at 18:40
BlueBlue
48.3k870153
$endgroup$
add a comment |
$begingroup$
Initially, you gave a correct expression for the area of the glass: $$(48-2x)(80-3x) tag{1}$$
"Simplifying" to $3x^2-152x+1920$, however, is incorrect. You seem to have taken the expanded form of $(1)$ ...
$$6 x^2 - 304 x + 3840 tag{2}$$
... and divided-through by $2$. But $(2)$ is an expression, representing some number. You cannot "simplify" an expression by dividing it by something. (If I have $30$ apples, you can't "simplify" my inventory by dividing by $2$ to say that I only have $15$ apples.)
The next step should be to take your calculated glass area, and equate it with the given glass area:
$$6x^2-304x+3840 = 1590 tag{3}$$
Here, you are allowed to divide-through by $2$ if you like (it helps to make the numbers smaller), provided that you do so to both sides.
$$3x^2-152x+1920 = 795 tag{4}$$
(If I have $30$ apples, then it's perfectly valid to say that half my inventory is half of $30$; that is, half my inventory is $15$. (Note how this situation is different from the one I described after $(2)$.) So, here, it's valid to say that half the calculated area of glass is half the given area of glass.)
From here, we can re-write (subtracting $795$ from both sides) ...
$$3x^2-152x+1125 = 0 tag{5}$$
... and then hope to factor the left-hand side. Can you proceed from here?
answered Jan 5 at 18:40
BlueBlue
48.3k870153
$endgroup$
Initially, you gave a correct expression for the area of the glass: $$(48-2x)(80-3x) tag{1}$$
"Simplifying" to $3x^2-152x+1920$, however, is incorrect. You seem to have taken the expanded form of $(1)$ ...
$$6 x^2 - 304 x + 3840 tag{2}$$
... and divided-through by $2$. But $(2)$ is an expression, representing some number. You cannot "simplify" an expression by dividing it by something. (If I have $30$ apples, you can't "simplify" my inventory by dividing by $2$ to say that I only have $15$ apples.)
The next step should be to take your calculated glass area, and equate it with the given glass area:
$$6x^2-304x+3840 = 1590 tag{3}$$
Here, you are allowed to divide-through by $2$ if you like (it helps to make the numbers smaller), provided that you do so to both sides.
$$3x^2-152x+1920 = 795 tag{4}$$
(If I have $30$ apples, then it's perfectly valid to say that half my inventory is half of $30$; that is, half my inventory is $15$. (Note how this situation is different from the one I described after $(2)$.) So, here, it's valid to say that half the calculated area of glass is half the given area of glass.)
From here, we can re-write (subtracting $795$ from both sides) ...
$$3x^2-152x+1125 = 0 tag{5}$$
... and then hope to factor the left-hand side. Can you proceed from here?
answered Jan 5 at 18:40
BlueBlue
48.3k870153
edited Jan 5 at 19:00
answered Jan 5 at 18:40
BlueBlue
48.3k870153
answered Jan 5 at 18:40
BlueBlue
48.3k870153
answered Jan 5 at 18:40
BlueBlue
48.3k870153
48.3k870153
add a comment |
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