Answer:
r=90
q=45?
t=52
Step-by-step explanation:
The figure/drawing isn't needed to answer this question.
The question tells us ABCD ~ WXYZ, which means trapezoid ABCD is similar to WXYZ.
Point A corresponds to point W, B corresponds with X, C corresponds with Y, and D corresponds with Z (first, second, third, and last letters correspond with each other according to the similarity statement).
Now let's check each answer choice and see which applies to these similar trapezoids:
- Since point B corresponds with point X and the trapezoids are similar, they must be congruent angles. Thus, the first choice is correct.
- Point Y does not correspond with point A. Thus, it is possible the angles are not congruent. The second choice is incorrect.
- Point A corresponds with W and B corresponds with X. Thus, line segment AB will be similar to line segment WX. However, they are not equal. Thus, the third choice is incorrect.
- There's an equal sign in this choice, too, just like the last, and the two segments are corresponding line segments. Thus, the fourth choice is incorrect.
- This looks like the third choice, but with a similarity symbol instead of an equal sign. Now, the statement is true and the fifth choice is correct.
- This looks like the fourth choice but with a similarity instead of an equal sign. Now, the statement is true and the sixth choice is correct.
Let me know if you need any clarifications, thanks!
Answer:
AC = 12
Step-by-step explanation:
From the question, we have that BD is perpendicular to AC
This means that it is at 90 degrees to the base
so we have two similar right triangles
Let us use Pythagoras’ theorem to get the measure of one of the legs (AD and DC)
Let us call the leg x
We have the Pythagoras’ theorem stating that the square of the hypotenuse (the side facing the right angle; 10 here) is equal to the sum of the squares of the two other sides
10^2 = x^2 + 8^2
100 = x^2 + 64
x^2 = 100-64
x^2 = 36
x = √36
x = 6
AD = DC = 6
AC = 2 * AD
AC = 2 * 6
AC = 12
Answer:
zh
Step-by-step explanation:
<h2>
Answer:</h2>
The constraint which represent a thriving population of penguins at the zoo is:
0 < x ≤ 10 and 0 < y ≤ 20.
<h2>
Step-by-step explanation:</h2>
Let x = the number of female penguins and y = the number of male penguins.
Now, it is given that:
The group needs two times more males than females to thrive, and the zoo only has room for 10 female penguins.
This means that:
0 < x ≤ 10
( Because there are no room for more than 10 penguins )
Also,
y= 2x
Since,
x>0
This means that: 2x>0
i.e. y>0
and x ≤ 10
i.e. 2x ≤ 20
i.e. y ≤ 20
Hence, the constraints which represent a thriving population of penguins at the zoo is:
0 < x ≤ 10 and 0 < y ≤ 20.
