Answer:
A) For the poster: length = 9 inches and width = 3 inches
B) For the banner: length = 10 inches and width = 2 inches
Step-by-step explanation:
A) The perimeter was given as 24 inches, so that;
P = 2 (l+w)
But, l = 3w, where w is the width. So that;
P = 2 (3w + w)
24 = 2 (4w)
24 = 8w
⇒ w = 3 inches
But, l = 3w = 3 × 3 = 9 inches
Therefore for the poster, length is 9 inches and width is 3 inches.
B) With the same value of perimeter, 24 inches:
p = 2 (l+w)
But, l = 5w, where w is the width. So that:
p = 2( 5w + w)
24 = 2 (6w)
24 = 12w
⇒ w = 2 inches
But, l = 5w = 5 × 2 = 10 inches
Therefore, for the banner, length is 10 inches and width is 2 inches.
"A poster is 3 times as long as it is wide"
This means that the length is three times larger than the width of the poster (which is in the shape of a rectangle).
"A banner is 5 times as long as it is wide"
This is exactly the same as the one for the poster, except the length of the banner is FIVE times larger than the width, instead of three.
"Both the banner and the poster have perimeter of 24 inches"
Both the banner and poster are rectangles. The formula for perimeter for rectangles is P = 2L + 2W (L = length, W = width).Perimeter of the Poster = 2L + 2WPerimeter of the Banner = 2L + 2WFor the poster, it was mentioned that the length is 3x larger than the width, so that must mean L = 3 * W = 3W. So therefore:Perimeter of the Poster = 2(3W) + 2W = 6W + 2W = 8W.For the banner, it was mentioned that the length is 5x larger than the width, so that must mean L = 5 * W = 5W. So therefore:Perimeter of the Banner = 2(5W) + 2W = 10W + 2W = 12W.So we found our perimeters, which are 8W for the poster and 12W for the banner. But the question also states that BOTH perimeters are 24 inches. So we must set 8W equal to 24 and 12W equal to 24.8W = 24W = 3 inches (For the poster)12W = 24W = 2 inches (For the banner)So we found our widths of both the poster AND the banner. Now we just need to find the lengths. But remember how I stated earlier that the length for the poster is 3W (L = 3W)? And for the banner, it's L = 5W? We can use that to find the lengths since we already know values for the widths.For the poster:L = 3W = 3(3) = 9 inchesFor the banner:L = 5W = 5(2) = 10 inchesSo the poster has a length of 9 inches and width of 3 inches, and the banner has a length of 10 inches and a width of 2 inchesThe graph for the inequality is attached with the answer.
We have a linear inequality -
y < 3x + 1
We have to plot the graph of this linear inequality.
An inequality in mathematics compares two values or expressions, showing if one is less than, greater than, or simply not equal to another value.
According to the question, we have -
y < 3x + 1
Now, in order to plot the graph for this inequality, let -
y = 3x + 1
Plot the line for the above equation. Remember to plot the graph in the form of dashed line since the inequality is strict inequality.
Consider the point (0, 0) -
Solve the inequality for the point (0, 0), we get -
0 < 3 x 0 + 1
0 < 1
Which is true.
Hence, shade the complete area on that side of line where the point
(0, 0) lies.
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Answer:
Step-by-step explanation:
A 143 divided by 11 equals 13.
To calculate 143 divided by 11 using long division, follow these steps:
To know more about divided:
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Answer:
2/3
Step-by-step explanation:
According to the question,10/27÷5/9
So we will have to be careful when solving this kind of question
So let's solve
10/27÷5/9
To solve we will have to convert the division to multiplication and during this process the 5/9 will actually change to 9/5
10/27×9/5
If you calculate it well,you will get
2/3
Which means that the final answer is 2/3 since it cannot be solved further
So 10/27÷5/9 gives 2/3
Answer:
2/3 or 0.6
Step-by-step explanation: