The triangle has a 45-deg angle.
The base angles are congruent and measure 67.5 deg.
The congruent sides measure 1 ft.
Use law of sines to find the length of the base.
![\dfrac{\sin 67.5^\circ}{1~ft} = \dfrac{\sin 45^\circ}{b}](https://tex.z-dn.net/?f=%20%5Cdfrac%7B%5Csin%2067.5%5E%5Ccirc%7D%7B1~ft%7D%20%3D%20%5Cdfrac%7B%5Csin%2045%5E%5Ccirc%7D%7Bb%7D%20)
![b = \dfrac{\sin 45^\circ}{\sin 67.5^\circ}~ft](https://tex.z-dn.net/?f=%20b%20%3D%20%5Cdfrac%7B%5Csin%2045%5E%5Ccirc%7D%7B%5Csin%2067.5%5E%5Ccirc%7D~ft%20)
![b = 0.765~ft](https://tex.z-dn.net/?f=%20b%20%3D%200.765~ft%20)
Draw a height from the vertex of the 45-deg angle to the base.
Half of the base is 0.765 ft/2 = 0.383 ft
We can find the height of the triangle using the small triangles.
0.383^2 + h^2 = 1^2
h = 0.9239 ft
A = bh/2 = 0.765 * 0.9239/2 ft^2
A = 0.354 ft^2
Answer:
6cm
The dimensions are 6cm x 6cm x 6cm
Step-by-step explanation:
Surface area of a cube = 6a²
where a = edge
but because this cube isn't covered, the sides would by 5 and not 6
5a² = 180cm²
divide both sides by 5
a² = 36cm²
Find the square root of each side
a = 6cm
The dimensions are 6cm x 6cm x 6cm
Use the slope-intercept form to find the slopeand y-intercept.
Slope: 2
Y-Intercept: 9
Answer:
B
Step-by-step explanation:
- y = 7 , that is y = - 7
Is a horizontal line parallel to the x- axis and passing through all points with a y- coordinate of - 7
Answer:
Fifth Day (1024 pounds)
Step-by-step explanation:
For every subsequent day, he collected 4 times the previous day.
This increase is a ratio/product, therefore the sequence is a geometric sequence.
The nth term of a geometric sequence, ![U_n=ar^{n-1}](https://tex.z-dn.net/?f=U_n%3Dar%5E%7Bn-1%7D)
Where:
a=first term
r=common ratio
n=number of terms
Corey collected 4 pounds of newspaper on day 1., a=4
After day one he collected 4 times the amount and for every subsequent day, he collected 4 times the previous day. r=4
We want to determine on which day he will first collect over a 1000 pounds of new paper.
![U_n=1000\\4 X 4^{n-1} =1000\\4^{n-1}=250](https://tex.z-dn.net/?f=U_n%3D1000%5C%5C4%20X%204%5E%7Bn-1%7D%20%3D1000%5C%5C4%5E%7Bn-1%7D%3D250)
In order to apply law of indices, we look for the next term greater than 250 which is an index of 4.
![4^{n-1}>256>250\\4^{n-1}>4^4\\n-1>4\\n>4+1\\n>5](https://tex.z-dn.net/?f=4%5E%7Bn-1%7D%3E256%3E250%5C%5C4%5E%7Bn-1%7D%3E4%5E4%5C%5Cn-1%3E4%5C%5Cn%3E4%2B1%5C%5Cn%3E5)
Therefore on the fifth day, he will collect an amount over 1000 pounds, precisely 1024 pounds.