Answer:
∠QST = 115°
Step-by-step explanation:
Because all angles on a straight line must add to 180 and so should the total angles in a triangle:
∠UST + 23x = 180
And:
∠UST + 12x + 55 = 180
So knowing this, ∠U + ∠T must add up to 23x because 180 - ∠UST is the same for both above equations:
55 + 12x = 23x
Subtract 12x from both sides to isolate the 55 and 23x:
55 + 12x - 12x = 23x - 12x
55 = 11x
Divide both sides by 11:

x = 5
As ∠QST = 23x, we can substitute in the known x:
23x =
23(5) =
23 * 5 = 115
So ∠QST = 115°
Hope this helps!
Answer:
Horizontal asymptote: y = 0
Vertical asymptote: x = 3
Step-by-step explanation:
The vertical asymptote in this graph would be when x = 3 because it would make the denominator 0, which would make the equation undefined.
There will not be any holes in the graph, because there won't be any point undefined in the function except for when x = 3, but that's a vertical asymptote.
Now, for the horizontal asymptote, we see what value y approaches as x approaches plus and minus infinity. Since x is in the denominator, y will approach 0 when it's plus or minus infinity.
Horizontal asymptote: y = 0
Vertical asymptote: x = 3
Answer:
V=3.098 yd³
Step-by-step explanation:
To answer this question we need to work with formula of the Volume of rectangular prism, the patio. Once it is required 1 inch deep. Some relations will be useful.
As 1 yard = 1 feet/3
1 yard = 1 inch/36
1 feet=12 inches
a) 23 feet 9 inches
23 ft 9''=23 +9/12=23.75 ft
b)10 feet 1 inch
10 feet 1" = 10ft + 1/12=10.083 ft
c)4 inches: 4/12 =0.33
V= w.l.h
V=23.75*10.083*0.33=79.025 ft³
Converting from cubic yard to cubic feet:
V≈79.025 : 27 yd³=2.926 yd³
Considering the possible spillage due to uneven base. ( adding 5%of V)
V≈ 2.92+0.05*(2.92)=3.098 yd³
Answer:
The standard form of the expression (5a+2)(a+4) is
.
Step-by-step explanation:
Here, the given expression is (5a+2)(a+4).
Now, (5a+2)(a+4) = 5a(a+4) + 2(a+4)
= 
= 
or, 
Also, Standard Quadratic form is 
Hence, the standard form of (5a+2)(a+4) is
.
Answer:
0.4735
Step-by-step explanation:
10 defective, 62 not defective
P(good) = 62/72 = 31/36
All 5 good:
(31/36)⁵ = 0.4734738145