Answer:
T = 59
U = 27
V = 94
Step-by-step explanation:
(5x +4) + (8x + 6) + (2x+5) = 180
15x + 15 = 180
15x = 165
x = 11
Answer:
Second option: On a coordinate plane, rectangle A'B'C'D' prime has points
(See the graph attached)
Step-by-step explanation:
For this exercise it is importnat to know that a Dilation is defined as a transformation in which the Image (The figure obtained after the transformation) has the same shape as the Pre-Image (which is the original figure before the transformation), but they have different sizes.
In this case, you know that the vertices of the rectangle ABCD ( The Pre-Image) are the following:

Therefore, to find the vertices of the rectangle A'B'C'D' (The Image) that results of dilating the rectangle ABCD by a factor of 4 about the origin, you need to multiply the coordinates of each original vertex by 4. Then, you get:

Finally, knowing those points, you can identify that the graph that shows the result of that Dilation, is the one attached.
Since A and B are the midpoints of ML and NP, we can say that AB is parallel to MN and LP. In order to find ∠PQN, we can work with the triangles PQB and NQB. According to SAS (Side-Angle-Side) principle, these triangles are congruent. BQ is a common side for these triangles and NB=BP and the angle between those sides is 90°, i.e, ∠NBQ=∠PBQ=90°. After finding that these triangles are equal, we can say that ∠BNQ is 45°. From here, we easily find <span>∠PQN. It is 180 - (</span>∠QNP + ∠NPQ) = 180 - 90 = 90°
The answer is: " 40 students " .
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Explanation:
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60% of x = 24 . Find "x" . in which "x" = total number of students;
60 % = 60/100 = 6/10 = 3/5.
(3/5) x = 24 ;
Multiply EACH SIDE of the equation by "5" ; to get rid of the fraction:
5* (3/5)x = 24*5 ;
3x = 120 ;
Divide each side of the equation by "3" ;
to isolate "x" on one side of the equation; and to solve for "x" ;
3x / 3 = 120 / 3 ;
x = 40 .
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The answer is: " 40 students " .
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The way I see it is like this:
He ended with $42.15 -- the last thing that he did before that was buy the umbrella
$42.15 + $23.75 (umbrella) = $65.90
The next thing backwards in order is that he spent "half of his remaining money on a painting", so what he has left is one half what he had before he bought the painting.
$65.90 + $65.90 (cost of the painting) = $131.80
Before that, he spent $25 on dinner and $20 on a cab. So we add those all up:
$131.80 + $25 (dinner) + $20 (cab) = $176.80 (how much money he had at the start of the weekend)
To write it as a single equation:
$42.15 = -$23.75 + (-$25.00 + -$20.00)/2