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3 years ago

4 - 4y = -2 - 9x - 4y = -3

Mathematics

1 answer:

arsen [322]3 years ago

7 0

Answer:

x = -1/3 , y = 3/2

Step-by-step explanation:

Solve the following system:

{4 - 4 y = -2

-9 x - 4 y = -3

Express the system in standard form:

{0 - 4 y = -6

-9 x - 4 y = -3

Express the system in matrix form:

(0 | -4

-9 | -4)(x

y) = (-6

-3)

Write the system in augmented matrix form and use Gaussian elimination:

(0 | -4 | -6

-9 | -4 | -3)

Swap row 1 with row 2:

(-9 | -4 | -3

0 | -4 | -6)

Multiply row 1 by -1:

(9 | 4 | 3

0 | -4 | -6)

Divide row 2 by -2:

(9 | 4 | 3

0 | 2 | 3)

Divide row 2 by 2:

(9 | 4 | 3

0 | 1 | 3/2)

Subtract 4 × (row 2) from row 1:

(9 | 0 | -3

0 | 1 | 3/2)

Divide row 1 by 9:

(1 | 0 | -1/3

0 | 1 | 3/2)

Collect results:

Answer: {x = -1/3 , y = 3/2

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Malia is placing a barrier around the edge of a circular path with a diameter of 13 meters. The barriers are in lengths of 2.5 m

Bezzdna [24]

Answer:

B. 17

Step-by-step explanation:

We have been given that Maria is placing a barrier around the edge of a circular path with a diameter of 13 meters.

Since we know that circumference of a circle equals $2\pi r$ , where,

r= Radius of the circle.

Since we have been given the diameter of the circular path, so let us divide our given diameter by 2 to find radius of our circular path.

$\text{Radius of circular path}=\frac{13}{2}=6.5$

Let us find the circumference of our circular path.

$\text{Circumference of circular path}=2*3.14*6.5$

$\text{Circumference of circular path}=40.82$

Since circumference of circular path is 40.82 meters, so to find the number of pieces of barrier we will divide circumference of circular path by length of each barrier.

$\text{Number of barriers used}=\frac{40.82}{2.5}$

$\text{Number of barriers used}=16.328$

As the barrier will be used as a whole piece, therefore, Malia needs 17 pieces of barrier and option B is the correct choice.

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3 years ago

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Which is a good comparison of the estimated sum and the actual sum of 7 7\8 + 2 11\12

sasho [114]

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3 years ago

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Estimate the product by rounding 9x54

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3 years ago

Which ratio is smaller 3/5 or 7/10

Oksanka [162]

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3 years ago

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vivado [14]

Answer:

The number of times members and non-members will have to rent a boat in order to pay the same amount=20

Step-by-step explanation:

We can have two expressions to show the total cost paid by a member and non-member;

Total cost by member=Cost per summer season+cost per number of times they rent a boat×number of times they rent a boat

where;

Cost per summer season=$105

Cost per number of times they rent a boat=$9.50

Number of times they rent a boat=n

Replacing;

Total cost by a member=105+(9.5×n)=9.5 n+105......equation 1

Total cost by a non-member=Cost per number of times they rent a boat×number of times they rent a boat

where;

Cost per number of times they rent a boat=$14.75

Number of times they rent a boat=n

Replacing;

Total cost by a non-member=(14.75×n)=14.75 n......equation 2

To calculate the number of times they would have to rent a boat in order to pay the same amount, we equate equation 1 to equation 2

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n=105/5.25

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