Answer: 32
Step-by-step explanation: this is arithmetic sequence
general formula = a+(n-1)d
nth term = 5+(n-1)3
=5+3n-3
=2+3n
10th term = 2+3(10)
=32
Girls:boys=5:4
So girls=5x
Boys=4x
total students=36
5x+4x=36
9x=36
x=4
So girls are=5x=5×4=20
Boys are=4x=4×4=16
Answer:
- ∠ABE = 60°
- ∠DBE = 40°
- ∠FBA = 47°
- y = 2
Step-by-step explanation:
The various markings tell you that ...
GH = GI
5x -10 = 3x
2x = 10
x = 5
and
∠ABD ≅ ∠DBC
10y° = (8y+4)°
2y = 4
y = 2
The markings on GH and GI tell you that ΔGBI ≅ ΔGBH, so ...
∠CBE ≅ ∠DBC ≅ ∠ABD = 10y° = 20°
__
A) m∠ABE = 60° . . . matches choice D
__
B) m∠DBE = 40° . . . matches choice C
__
C) m∠FBA = 7(5) +6(2) = 35 +12 = 47 . . . matches choice C
__
D) The value of y is 2. . . . matches choice A
STP is a right, isosceles triangle.
The diagonals of a square cut the square itself in two equal right isosceles triangles. So, both diagonals cut the square in four right isosceles triangles.
STP is a right triangle because the two diagonal are perpendicular to each other, and it is isosceles because ST and TP are both half a diagonal, because the two diagonals intersect in their midpoint.
So, the angles of STP are 90, 45 and 45 degrees.
As for the lengths, SP is a side of the square, so let's call its length
. The diagonals of a square are
units long, and so 
Answer:
Step-by-step explanation:
First we need to find their rate of speed.
r = d / t
For ant,
Convert millimeters to inches.
1 inch = 25.4 mm
18 mm = 0.7 inch
r = 0.7 / 5
r = 0.14 inches per second
For beetle,
r = 8 / 3
r = 2.7 inches per second
From the rates, you can tell that the beetle crosses the Garden first.
To know how long it takes for the ant to cross is by dividing the length by the rate.
1 yard = 36 inches
13 yards = 468 inches
468 ÷ 0.14 = 668.5 ≈ 669 seconds
In terms of minutes:
11 minutes and 15 seconds
The ant would cross the garden in 11 minutes and 15 seconds (or 669 seconds <em>up to you</em>).