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astra-53 [7]
3 years ago
11

4. What are the values of x and y? HELP PLEASE

Mathematics
1 answer:
Sergeeva-Olga [200]3 years ago
8 0
The bottom answer is correct. I had some trouble with this so I had to find x and y in separate parts.

TO FIND X
notice that the top triangle and bottom triangles are similar, meaning if you multiple all three sides of one by a specific number, it becomes the same size as the bottom triangle.

17 x n = 8, therefore n=8/17
8 x n = X, therefore X=64/17

For some reason, this does not give a correct value for Y, so I had to use trig 

TO FIND Y 

Notice that the angle DAB is the same as DBC (lets call this angle Ø)

Using trig rule, we know that the cos of an angle is equal to the adjacent side divided by the hypotenuses.

We can now form some equations:

cosØ = 15/17 (from the top triangle)
cosØ = 8/Y      (from bottom triangle)
Now we know that Y=(8x17)/15 = 136/15

X=64/15  Y=136/15
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Solve with cramer's rule x+2y+3z=11, 2x+y+2z=10, 3x+2y+z=9
nalin [4]

Answer:

x = 2 , y = 0 , z = 3

Step-by-step explanation:

Cramer's rule is a rule through which we can find the solution of linear equation.

we have the three linear equations as

x+2y+3z=11

2x+y+2z=10

3x+2y+z=9

AX=B  

A: coefficient matrix

X= unknown vectors(x,y,z)

D = values of the linear equation (11 , 10 , 9)

now we find the determinant of the given linear equation

determinant of the matrix will be

A = \left[\begin{array}{ccc}1&2&3\\2&1&2\\3&2&1\end{array}\right]  = 1(1-4) - 2(2-6) + 3(4 - 3)

                    = 1(-3) - 2(-4) + 3(1)

                    = -3+8+3 = 8

also D\neq 0

so the determinant is Non zero we can apply Cramer's rule

we will be replacing the first column of the coefficient matrix A with the values of D

by replacing the first column we will get the value of the variable 'x'

Dx =  \left[\begin{array}{ccc}11&2&3\\10&1&2\\9&2&1\end{array}\right]   = 11(1-4) -2(10-18) + 3(20-9) = -33+16+33 = 16

x = \frac{Dx}{D}  = \frac{16}{8} = 2

similarly

Dy = \left[\begin{array}{ccc}1&11&3\\2&10&2\\3&9&1\end{array}\right] = 1(10-18) -11(2-6) + 3(18 -30) = -8 +44 -36 = 0

y = \frac{Dy}{D} = 0

Dz= \left[\begin{array}{ccc}1&2&11\\2&1&10\\3&2&9\end{array}\right] = 1(9 - 20) -2(18 - 30) + 11(4 -3) = -11 +24 +11 = 24

z = \frac{Dz}{D} = \frac{24}{8} = 3

so we have the solution as

x = 2 , y = 0 , z = 3

Therefore the solution for the given linear equations is (2,0,3).

3 0
3 years ago
What is the slope of the line through (-1, -7) and (3,9)?
Radda [10]

Answer:

<u>9+7</u>

3+1

=4

Step-by-step explanation:

5 0
2 years ago
What are all the solutions of x2 + 3x – 4 = 0?<br> -4<br> -2<br> -1<br> 0<br> 1<br> 2<br> 4
Alex17521 [72]

Answer: 1, -4

Step-by-step explanation:

Move all the terms to the left side and set equal to zero. Then set each factor equal to zero. X= 1,-4

7 0
2 years ago
What is the slope of the line whose function f satisfies f(−2)=1  and  f(5)=−10f(−2)=1  and  f(5)=−10?
Radda [10]
M = (f(5) -f(-2))/(5 -(-2)) = (-10 -1)/7
m = -11/7

The slope of the line is -11/7.

4 0
3 years ago
Help Me Please?????????????
vampirchik [111]

Answer

Step-by-step explanation:

8^-5/8^-2

=8^5-(-2)

=8^5+2

=8^7

=2097152

Note in division if the base the base are same then u can subtract their exponent but in multiplication bases are same u should add their exponent.

6 0
3 years ago
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