Answer:
32.1
Step-by-step explanation:
we get angle f 180-(123+43)=14
then we use sin law
x/sin123=9.6/sin14
yhen cross multiplication we get the answer
Answer: $1548
Step-by-step explanation:
We are told the normal rate of payment is $36 per hour
and with an excess of 40 hours the pay will be 1 and a half the normal rate(1.5)
And John works for 42hours
For first we know John worked for an excess of 2 hours
And calculating his pay for 40hours of the normal rate that week, we multiply $36 by 40 which will give $1440
Then the extra 2 hours, the new pay rate will be $36 multiplied by 1.5 which will give $54 per hour
And for the extra 2 hours, John will get extra $54 multiplied by 2 which will give $108
Adding both $1440 and $108, we will get $1548
Answer:
The correct option is;
Use a scale factor of 2
Step-by-step explanation:
The parameters given are;
A = (1, -6)
B = (5, -6)
C = (6, -2)
D = (0, -2)
A'' = (1.5, 4)
B'' = (3.5, 4)
C'' = (4, 2)
D'' = ( 1, 2)
We note that the length of side AB in polygon ABCD = √((5 -1)² + (-6 - (-6))²) = 4
The length of side A''B'' in polygon A''B''C''D'' = √((3.5 -1.5)² + (4 - 4)²) = 2
Which gives;
AB/A''B'' = 4/2 = 2
Similarly;
The length of side BC in polygon ABCD = √((6 -5)² + (-2 - (-6))²) = √17
The length of side B''C'' in polygon A''B''C''D'' = √((4 -3.5)² + (2 - 4)²) = (√17)/2
Also we have;
The length of side CD in polygon ABCD = √((6 -0)² + (-2 - (-2))²) = 6
The length of side C''D'' in polygon A''B''C''D'' = √((4 -1)² + (2 - 2)²) = 3
For the side DA and D''A'', we have;
The length of side DA in polygon ABCD = √((1 -0)² + (-6 - (-2))²) = √17
The length of side D''A'' in polygon A''B''C''D'' = √((1.5 -1)² + (4 - 2)²) = (√17)/2
Therefore the Polygon A B C D can be obtained from polygon A''B''C''D'' by multiplying each side of polygon A''B''C''D'' by 2
The correct option is therefore;
Use a scale factor of 2.
Answer:
a) Vertex: ![(h,k) = (5,3.5)](https://tex.z-dn.net/?f=%28h%2Ck%29%20%3D%20%285%2C3.5%29)
b) Vertex: ![(h,k) = (-1,-8)](https://tex.z-dn.net/?f=%28h%2Ck%29%20%3D%20%28-1%2C-8%29)
Step-by-step explanation:
First we need to realize that these equations are the equations of parabolas.
the equation of parabola are generally written as:
![y = a(x-h)^2 +k](https://tex.z-dn.net/?f=y%20%3D%20a%28x-h%29%5E2%20%2Bk)
where the vertex is the point
. <u>(note that the sign of 'h' is changed!)</u>
<u>(also note that the value of 'a' doesn't matter for finding vertex point)</u>
given this information we can now easily find out the vertex of both parabolas
a) ![y = 2(x-5)^2 + 3.5](https://tex.z-dn.net/?f=y%20%3D%202%28x-5%29%5E2%20%2B%203.5)
by comparing it with the general equation above, we can see that -5 is in the place of '-h' and +3.5 is in the place of '+k'
we can write
and solve for h.
![h=5](https://tex.z-dn.net/?f=h%3D5)
similarly,
![k=3.5](https://tex.z-dn.net/?f=k%3D3.5)
hence the vertex of this graph is ![(h,k) = (5,3.5)](https://tex.z-dn.net/?f=%28h%2Ck%29%20%3D%20%285%2C3.5%29)
b) ![y=-(x + 1)^2-8](https://tex.z-dn.net/?f=y%3D-%28x%20%2B%201%29%5E2-8)
by comparing it with the general equation above, we can see that +1 is in the place of '-h' and -8 is in the place of '+k'
we can write
and solve for h.
![h = -1](https://tex.z-dn.net/?f=h%20%3D%20-1)
similarly,
![k=-8](https://tex.z-dn.net/?f=k%3D-8)
hence the vertex of this graph is ![(h,k) = (-1,-8)](https://tex.z-dn.net/?f=%28h%2Ck%29%20%3D%20%28-1%2C-8%29)
10x6=60 thats it it really is