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valentina_108 [34]
3 years ago
7

For which value of a does the following system of equations have no solution? -x+6y=7 , -5x+10ay=32

Mathematics
1 answer:
dlinn [17]3 years ago
8 0

Remark

If the lines are parallel, there are no solutions to the system of equations. Start with the equation you know the most about.

x + 6y = 7                Subtract x from both sides

x - x + 6y = 7 - x      Combine

6y =  - x + 7             Switch and divide by 6

y = -x / 6 + 7/6

The general equation for a line is y = mx + b where m is the slope of the line.

m = - 1/6

================

Now look at the second equation

10ay - 5x = 32               Add 5x to both sides

10ay = 5x + 32              Divide by 10a

y = (5/10a)x + 32/(10a)  

===============

Now you must make

5/10a = - 1/6                     Cross Multiply

5* 6 = - 10a * 1

30 = - 10a                        Divide by - 10

a = 30 / - 10

a = - 3

So these two equations will have no solution when a = - 3



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A small-appliance manufacturer finds that the profit P (in dollars) generated by producing x microwave ovens per week is given b
Olegator [25]

Answer:

Number of ovens must be manufactured in a given week to generate a profit of $1610  is 70

Step-by-step explanation:

We are given

A small-appliance manufacturer finds that the profit P (in dollars) generated by producing x microwave ovens per week is given by the formula

P=\frac{1}{10}x(300-x)

provided that 0 ≤ x ≤ 200

We are given

profit is $1610

so, we can set P=1610

and then we can solve for x

1610=\frac{1}{10}x(300-x)

Multiply both sides by 10

1610\cdot \:10=\frac{1}{10}x\left(300-x\right)\cdot \:10

16100=x\left(300-x\right)

16100=300x-x^2

-x^2+300x-16100=0

now, we can factor it

(x-70)(x-230)=0

we can solve for x

and we get

x=70,x=230

Since, x=230 does not lie on 0 ≤ x ≤ 200

So, we will consider only x=70

So,

Number of ovens must be manufactured in a given week to generate a profit of $1610  is 70


7 0
3 years ago
Your sister Samantha is turning 48 in April. She is 3 times older than your brother John, and twice as old as you. How old is yo
attashe74 [19]
Is john 16?
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7 0
2 years ago
What does 12−3/4(d+16)=−5 equal solve for d
Ratling [72]

Answer:

d=20/3 or 6.6 repeating

Step-by-step explanation:

Let's solve your equation step-by-step.

12−

3

4

(d+16)=−5

Step 1: Simplify both sides of the equation.

12−

3

4

(d+16)=−5

12+

−3

4

d+−12=−5(Distribute)

(

−3

4

d)+(12+−12)=−5(Combine Like Terms)

−3

4

d=−5

−3

4

d=−5Step 2: Multiply both sides by 4/(-3).

(

4

−3

)*(

−3

4

d)=(

4

−3

)*(−5)

d=

20

3

Answer:

d=

20

3

3 0
3 years ago
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