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____ [38]
2 years ago
13

Use an equation to find the value of k

Mathematics
1 answer:
JulijaS [17]2 years ago
7 0

Answer:  k=143

Step-by-step explanation:

Let's start with the standard form of a linear equation:  y = mx + b, where m ios the slope and b is trhe y-intercept (the value of y when x=0).  We know the slope, so:

y = -15x + b

We can find the y-intercept, b, by using the one given point (6,-7) in the equation and solve for b:

y = -15x + b

-7 = -15(6) + b

-7 = -90+b

b = 83

The equation is y = -15x + 83

Use the x value of (-4,k) to find y, which will be k.

y = -15x + 83

y = -15(-4) + 83

y = 60 + 93

y = 143

k is 143

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17) Solve the system as matrix equations using inverses. 17) A company produces three models of MP3 players, models A, B, and C.
Vinvika [58]

Answer:

Model A=30, Model B: 20, Model C: 45

Step-by-step explanation:

Let x be the amount of type A mp3 produced, and the amount of model B mp3's produced and z the amount of model C mp3 produced.

Since in total there are 303 hours for electronics work, then:

3.2x+5.4y+2.2z=303

Since in total there are 393 hours for assembly, then:

2.8x+2.4y+5.8z=393

Since in total there are 416 hours for quality assurance, then:

4.4x+3.4y+4.8z=416

Then, the linear system associated to the problem is

3.2x+5.4y+2.2z=303\\2.8x+2.4y+5.8z=393\\4.4x+3.4y+4.8z=416

with coefficient matrix A=\left[\begin{array}{ccc}3.2&5.4&2.2\\2.8&2.4&5.8\\4.4&3.4&4.8\end{array}\right] and vector of constant terms b=\left[\begin{array}{ccc}303\\393\\416\end{array}\right]

Since the determinant of A is equal to 36.704 then A is invertible.

Then for solve the system Ax=b, is enough find the inverse of A and operate

Ax=b\\A^{-1}Ax=A^{-1}b\\x=A^{-1}b

Using Octave we obtain that

A^{-1}=\left[\begin{array}{ccc}-0.22&-0.50 &0.71\\0.33&0.15&-0.34\\-0.028& 0.35&-0.20\end{array}\right]

Then

x=A^{-1}b=\left[\begin{array}{ccc}30\\20\\45\end{array}\right]

This means that 30 mp3's of model A, 20 of model B and 45 of model C must be produced

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3 years ago
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7 0
3 years ago
Fran bought 4 shirts that were each $13 each. She also bought a pair of socks for 4.29. What was the total amount Fran pair for
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8 0
3 years ago
38 4/7% as a fraction
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