Question 1. 5x+2y=-7
15x+6y=21
No solution, One solution, or infinite solution?

Question 2.
Y=2x+1
2x-4=1
No solution, one solution, or infinite solution?

Question 3.
6x+4y=10
3x+2y=5
No solution, one solution, or infinite solution?

Q1: no solution

Q2: one solution

Q3: infinite solutions

Step-by-step explanation:

Question 1

No solution

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Explanation:

Multiply both sides of the first equation by 3. Doing so leads to

3*(5x+2y) = 3*(-7)

15x+6y = -21

The second equation is 15x+6y = 21

Let's say we let z = 15x+6y

This means the system

becomes

but we can't have z be equal to more than one value at a time. We have a contradiction and therefore there are no solutions.

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Question 2

One solution

The solution is (x,y) = (5/6)

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Explanation:

Apply substitution

2x - 4y = 1

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

2x - 8x - 4 = 1

-6x - 4 = 1

6x = 1+4

6x = 5

x = 5/6

Then use this to find y

y = 2x+1

y = 2(5/6)+1

y = 5/3 + 1

y = 5/3 + 3/3

y = 8/3

The one solution is (x,y) = (5/6)

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Question 3

Infinitely many solutions

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Explanation:

Multiply both sides of the second equation by 2

3x+2y = 5 becomes 2*(3x+2y) = 2*5 which turns into 6x+4y = 10

This is exactly identical to the first equation of the original system given.

So both equations represent the same thing. We have infinitely many intersection points, and infinitely many solutions.

All of these solutions are on the line 3x+2y = 5

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°

the correct answer is b. negative exponential growth.

step-by-step explanation:

you can tell it's an exponential function because it decreases rapidly then levels out and never touches the x-axis.

it is negative because the y-axis decreases as the x-axis increases.

therefore it is a negative exponential growth graph.

hope i !