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3 years ago

Two system of equations 2y =14-2x and y=-x + 7 is graphed. What is the solution to the system of equations

Mathematics

2 answers:

Molodets [167]3 years ago

7 0

Answer:

Infinitely many solutions

Step-by-step explanation:

<u>Given equations</u>

2y =14-2x and
y= -x + 7

<u>Rewriting the first equation</u>

2y = 14 - 2x
2y = -2x + 14
y = -x + 7

As we see it is same as the second equation. So same two lines, overlapping when graphed and the system has infinitely many solutions

Trava [24]3 years ago

6 0

<h2>Answer:</h2>

To solve this system, we will use the graphing method.

Based on the graph shown below, we can conclude that this system has infinite solutions, because they are the same line.

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How to solve the rational equation? (Please include steps not just the answer)

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1/3 + 1/2 = 1/x

2 and 1/5

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Kim is creating a mosaic in her garden. She finds the tile below and wants to know the missing side length ‘x’. Calculate the mi

GrogVix [38]

Answer:

x = 7.99 cm

Step-by-step explanation:

By applying cosine rule in the given triangle,

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3 years ago

In each problem 7 through 14, verify that each given function is a solution of the differential equation. Y" - y = 0; y1(t) = et

Lilit [14]

Answer:

Since L.H.S = R.H.S = 0, for both $y_{1} (t) = e^{t}$ and $y_{2} (t) = cosh(t)$ , y₁ and y₂ both satisfy the equation y" - y = 0 and are thus solutions to the differential equation.

Step-by-step explanation:

To check whether the given functions are solutions the given differential equation, we differentiate the functions and then insert it into the given equation.

So y" - y = 0 and

$y_{1} (t) = e^{t}\\y_{1}' (t) = e^{t}\\ y_{1}" (t) = e^{t}$

Substituting these values of y and y" into the left hand side of the equation, we have

y" - y

$y_{1}" (t) - y_{1} (t) = e^{t} - e^{t} = 0$

Since L.H.S = R.H.S

So $y_{1} (t) = e^{t}$ is a solution of the differential equation.

When

$y_{2} (t) = cosh(t)\\ y_{2}'(t) = sinh(t) \\y_{2}"(t) = cosh(t)$

Substituting y and y" into the left hand side of the equation, we have

y" - y

$y_{2}"(t) - y_{2} (t) = cosh(t) - cosh(t) = 0$

Since L.H.S = R.H.S

So, $y_{2} (t) = cosh(t)$ is a solution of the differential equation.

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4 years ago

1/2(1/4x - 3/5)=1/4 (2/5+3/4 x)

Sliva [168]

Answer:

Are you asking for a fraction?

Step-by-step explanation:

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3 years ago

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You have 6 pints of glaze. It takes 7/8 of a pint to glaze a bowl and 9/16 of a pint to glaze a plate.

son4ous [18]

Answer:

a. How many bowls could you glaze?

6 bowls

How many plates could you glaze?

10 plates

b. You want to glaze 5 bowls, and then use the rest for plates.

How many plates can you glaze?

2 plates

How much glaze will be left over?

8/9 of glaze would be left

c. How many of each object could you glaze so that there is no glaze left over? Explain how you found your answer.

4 4/23 bowls and 4 4/23 plates

Step-by-step explanation:

We are told in the question

Number of pints of glaze = 6 pints

Number of pints to glaze a bowl= 7/8 of pint

Number of pints to glaze a plate = 9/16 of a pint

How many bowls could you glaze?

7/8 pint = 1 bowl

6 pints = x

Cross Multiply

x = 6 pints/ 7/8

= 6 × 8/7

= 48/7

= 6.8571428571 bowls

We can only glaze whole numbers of a bowl, hence, we can only glaze 6 bowls

How many plates could you glaze?

9/16 pint = 1 bowl

6 pints = y

y = 6 pints/ 9/16

= 6 × 16/9

= 10.666666667 plates

We can only glaze whole number of a plate, hence, we can only glaze 10 plates

b. You want to glaze 5 bowls, and then use the rest for plates.

1 bowl = 7/8 pints

5 bowls = z

Cross Multiply

z = 5 × 7/8pints

= 4 3/8 pints of glaze would be used for bowls

How many plates can you glaze?

The rest is for plates, hence:

The amount of glaze left for plates is calculated as:

6 pints - 4 3/8

1 5/8 pints of glaze would be left over to glaze plates.

So therefore,

9/16 pints = 1 plate

1 5/8 pints =

= 2 8/9

Hence we can only glaze 2 plates

How much glaze will be left over?

2 8/9 pints - 2 pints

= 8/9 pints of glaze.

c. How many of each object could you glaze so that there is no glaze left over?

We have 6 pints of glaze

Number of pints to glaze a bowl= 7/8 of pint

Number of pints to glaze a plate = 9/16 of a pint

Let the number of each objects be represented by x

7/8 × x + 9/16 × x = 6 pints

= 4 4/23 bowls and 4 4/23 plates

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3 years ago