Answer:
<em>The second figure ( rectangle ) has a longer length of it's diagonal comparative to the first figure ( square )</em>
Step-by-step explanation:
We can't confirm the length of these diagonals based on the appearance of the figure, so let us apply Pythagorean Theorem;
This diagonal divides each figure ( square + rectangle ) into two congruent, right angle triangles ⇒ from which we may apply Pythagorean Theorem, where the diagonal acts as the hypotenuse;
5^2 + 5^2 = x^2 ⇒ x is the length of the diagonal,
25 + 25 = x^2,
x^2 = 50,
x = √50
Now the same procedure can be applied to this other quadrilateral;
3^2 + 7^2 = x^2 ⇒ x is the length of the diagonal,
9 + 49 = x^2,
x^2 = 58,
x = √58
<em>Therefore the second figure ( rectangle ) has a longer length of it's diagonal comparative to the first figure ( square )</em>
Let n = the unknown number.
Six times a number = 6 * n = 6n
20 more than number = n + 20
Greater than = >
Put it all together:
6n > n + 20
Subtract n from both sides to get constants on one side and variables on the other:
6n - n > 20
5n > 20
Divide both sides by 5 to isolate variable N
n > 4
or (4, ∞)
Answer:
14. x = 16; y = 23
15. x = 9; y = 13
Step-by-step explanation:
14. (4x + 4) = (7x - 44) (alternate exterior angles are congruent)
4x + 4 = 7x - 44
Collect like terms
4x - 7x = -4 - 44
-3x = -48
Divide both sides by -3
x = -48/-3
x = 16
39° + (8y - 43)° = 180° (consecutive exterior angles are supplementary)
39 + 8y - 43 = 180
Add like terms
-4 + 8y = 180
Add 4 to both sides
8y = 180 + 4
8y = 184
Divide both sides by 8
y = 184/8
y = 23
15. (15x - 26)° = (12x + 1)° (alternate exterior angles are congruent)
15x - 26 = 12x + 1
Collect like terms
15x - 12x = 26 + 1
3x = 27
Divide both sides by 3
x = 27/3
x = 9
28° + (12x + 1)° + (4y - 9)° = 180° (sum of interior angles of ∆)
Plug in the value of x
28 + 12(9) + 1 + 4y - 9 = 180
28 + 108 + 1 + 4y - 9 = 180
Add like terms
128 + 4y = 180
Subtract 128 from each side of the equation
4y = 180 - 128
4y = 52
Divide both sides by 4
y = 52/4
y = 13
Answer:
I think its 3752 but i might be wrong not sure
Step-by-step explanation:
or its 15008
