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Margaret [11]
2 years ago
12

Solve the following simultaneous equations using an appropriate method.

Mathematics
1 answer:
luda_lava [24]2 years ago
8 0
A) SUBSTITUTION: 4x + 3(-2x +8)=16
4x + -6x + 24 = 16
-2x= -8
x= 4
y= 0

b) ELIMINATION:
12x -8y = -76
-12x -15y = -39
-23y= -115
y=5
x= -3

c) ELIMINATION:
-12x+28y=36
12x-9y=21
19y= 57
X=4
y=3

d) SUBSTITUTION:
-4(23 -3y) +5y=-7
-92+12y+5y =-7
-92 +17y = -7
17y = 85
y=5
x=8
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What is the distance, to the nearest whole number, from K (5, 6) to P (1, 1)?
Elza [17]

Answer:

<h3>The answer is 6 units</h3>

Step-by-step explanation:

The distance between two points can be found by using the formula

d =  \sqrt{ ({x1 - x2})^{2}  +  ({y1 - y2})^{2} }  \\

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

K (5, 6) P (1, 1)

The distance from K to P is

|KP|  =  \sqrt{ ({5 - 1})^{2} +  ({6 - 1})^{2}  }  \\  =  \sqrt{ {4}^{2} +  {5}^{2}  }  \\  =  \sqrt{16 + 25}  \\  =  \sqrt{41}  \\  = 6.403124

We have the final answer as

<h3>6 units to the nearest whole number</h3>

Hope this helps you

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2 years ago
Ben has 400 counters in a bag. He gives 35 of the counters to Sonia 130 of the counters to Phil 75 of the counters to Lance What
aniked [119]

Answer:

2/5

Step-by-step explanation:

subtract 130,35,and 74 from 400 you will have 160/400 left then you find the greatest common and divide! and get 2/5

8 0
2 years ago
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Why is sin(20) = sin(160) = -sin(200) = -sin(340)?
AveGali [126]
Because they're all the same distance from the x axis on a coordinate plane. Also, remember that in quadrant I, all trig values are positive. In Q II, only sine and cosecant are positive. In Q III, only tangent and cotangent are positive. In Q IV, only cosine and secant are positive. Think of it as <u>A</u>ll <u>S</u>tudents <u>T</u>ake <u>C</u>alculus.
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Fruit juice comes in two types of containers. The first is a rectangular prism that is 9 inches tall and has a rectangular base
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The volume of a rectangular prism:

V_p=Bh\\\\B=wl\\\\w=2\ in;\ l=3\ in;\ h=9\ in

substitute

V_p=2\cdot3\cdot9=54\ in^3

The volume of a cylinder:

V_c=\pi r^2h\\\\r=1.5\ in;\ h=8\ in

substitute:

V_c=\pi\cdot(1.5)^2\cdot8=\pi\cdot2.25\cdot8=18\pi\ in^3\approx18\cdot3.14=56.52\ in^3

Answer: C. The cylinder has the greater volume.

3 0
2 years ago
Arrange the entries of matrix A in increasing order of their cofactors values
givi [52]

To find the cofactor of

A=\left[\begin{array}{ccc}7&5&3\\-7&4&-1\\-8&2&1\end{array}\right]

We cross out the Row and columns of the respective entries and find the determinant of the remaining 2\times 2 matrix with the alternating signs.


Ac_{11}=\left|\begin{array}{ccc}4&-1\\2&1\end{array}\right|


Ac_{11}=4\times 1- -1\times 2


Ac_{11}=4+ 2

Ac_{11}=6




Ac_{12}=-\left|\begin{array}{ccc}-7&-1\\-8&1\end{array}\right|


Ac_{12}=-(-7\times 1- -1\times -8)


Ac_{12}=-(-7- 8)

Ac_{12}=15




Ac_{21}=-\left|\begin{array}{ccc}5&3\\2&1\end{array}\right|


Ac_{21}=-(5\times 1- 3\times 2)


Ac_{21}=-(5-6)


Ac_{21}=1







A_c{23}=-\left|\begin{array}{ccc}7&5\\-8&2\end{array}\right|


Ac_{23}=-(7\times 2 -8\times 5)


Ac_{23}=-(14-40)


Ac_{23}=26




A_c{31}=\left|\begin{array}{ccc}5&3\\4&-1\end{array}\right|


Ac_{31}=5\times -1 -4\times 3


Ac_{31}=-5-12


Ac_{31}=-17


A_c{33}=\left|\begin{array}{ccc}7&5\\-7&4\end{array}\right|


Ac_{33}=7\times 4- -7\times 5


Ac_{33}=28+35


Ac_{33}=63


Therefore in increasing order, we have;

Ac_{31}=-17,Ac_{21}=1,Ac_{11}=6,Ac_{23}=26,Ac_{12}=15, Ac_{33}=63



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2 years ago
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