m∠X + m∠Y < 90° is true.
<h3>How to solve it?</h3>
XYZ is a triangle.
We have to find the option that is true about △XYZ.
By angle sum property of a triangle,
The sum of all the interior angles of a triangle is always equal to 180°.
So, ∠X + ∠Y + ∠Z = 180°
Given, m∠Z > m∠X + m∠Y.
This implies that ∠Z is greater than the sum of the angles ∠X and ∠Y.
so, ∠X + ∠Y must be less than 90°.
Hence, we can say that ∠X + ∠Y < 90°
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<u>A</u><u>n</u><u>s</u><u>w</u><u>e</u><u>r</u><u>:</u>
The breadth of rectangular carpet is 1.8 m.
<u>S</u><u>t</u><u>e</u><u>p</u><u>-</u><u>b</u><u>y</u><u>-</u><u>s</u><u>t</u><u>e</u><u>p</u><u> </u><u>e</u><u>x</u><u>p</u><u>l</u><u>a</u><u>n</u><u>a</u><u>t</u><u>i</u><u>o</u><u>n</u><u>:</u>
We have,
- The area of rectangular carpet that is 23.4 m²
- The length of carpet is 13 m.
We know that,
= Area of rectangle = Length × Breadth
= 23.4 = 13 × Breadth
= 23.4/13 = Breadth
= 234/130 = Breadth
= 1.8 m = Breadth
<h2>__________________________</h2>
<span>Answers:
______________________________________________________
</span><span>[B]: The 8 in the tenths place is 10 times the value of the 8 in the hundredths place.
</span>______________________________________________________
<span>[C]: The 8 in the hundredths place is 10 times the value of the 8 in the tenths place.
______________________________________________________</span>
1. First, let us define the width of the rectangle as w and the length as l.
2. Now, given that the length of the rectangle is 6 in. more than the width, we can write this out as:
l = w + 6
3. The formula for the perimeter of a rectangle is P = 2w + 2l. We know that the perimeter of the rectangle in the problem is 24 in. so we can rewrite this as:
24 = 2w + 2l
4. Given that we know that l = w + 6, we can substitute this into the formula for the perimeter above so that we will have only one variable to solve for. Thus:
24 = 2w + 2l
if l = w + 6, then: 24 = 2w + 2(w + 6)
24 = 2w + 2w + 12 (Expand 2(w + 6) )
24 = 4w + 12
12 = 4w (Subtract 12 from each side)
w = 12/4 (Divide each side by 4)
w = 3 in.
5. Now that we know that the width is 3 in., we can substitute this into our formula for length that we found in 2. :
l = w + 6
l = 3 + 6
l = 9 in.
6. Therefor the rectangle has a width of 3 in. and a length of 9 in.