There would be 32 men in the dance recital.
24/3 = 8
8 times 4 = 32
24/32 = 3/4
Answer:
Option B. 1/2
Step-by-step explanation:
The smaller triangle is a dilation of the larger triangle with the center of dilation at (2, -1).
we have to calculate the scale factor of the dilation.
One point of the large triangle is (-4, -1). After dilation it has become (-1, -1) of the smaller one.
If we consider the x coordinates of the point x = -4 has reduced down to -1 therefore scale factor = side of small triangle/side of the large triangle = (2 + 1)/(2 + 4) = 3/6 = 1/2
Therefore Option B. 1/2 is the answer.
9514 1404 393
Answer:
Lanza is correct.
Step-by-step explanation:
The two missing dimensions on the left are 4.5 m on the vertical line, and 5 m on the horizontal line.
These dimensions let us partition the garden a number of ways. One way is ...
- a rectangle 9 m by 4.5 m
- a rectangle 4 m by 3.5 m
The total of the areas of these is ...
(9)(4.5) +4(3.5) = 40.5 +14 = 54.5 . . . . square meters
At £16 per square meter, Lanza's charge will be ...
£16 × 54.5 = £872
Lanza is correct that she will have to charge more than £800.
The given triangle is isosceles, so the two remaining angles in the triangle both have measure <em>xº</em>. The interior angles of any triangle sum to 180º, so that
58º + <em>xº</em> + <em>xº</em> = 180º
58 + 2<em>x</em> = 180
2<em>x</em> = 122
<em>x</em> = 61
Angles <em>y</em> and <em>z</em> are supplementary to angle <em>x</em>, so that
<em>xº</em> + <em>yº</em> = 180º
and
<em>xº</em> + <em>zº</em> = 180º
and consequently, <em>y</em> = <em>z</em>. In particular, we get
<em>y</em> = 180 - 61
<em>y</em> = 119
and so
<em>z</em> = 119
