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Tcecarenko [31]
3 years ago
13

F(x) = x − 3 and g(x) = 2x + 8 Which ordered pair is a solution for the system?

Mathematics
2 answers:
Phoenix [80]3 years ago
8 0

I put it into Desmos and got (-11, -14)

kondor19780726 [428]3 years ago
6 0

f(x)=g(x)\to x-3=2x+8\qquad\text{add 3 to both sides}\\\\x=2x+11\qquad\text{subtract 2x from both sides}\\\\-x=11\to\boxed{x=-11}\\\\\text{Put the value of x to the equation of f(x):}\\\\f(-11)=-11-3=-14\\\\Answer:\ \boxed{x=-11\ and\ y=-14\to(-11,\ -14)}

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ella [17]

Answer:

1. The vertex of the graph of the function is (-4, 7)

2. The vertex represents a minimum value

3. The equation represented by the new graph is g(x) = (x + 4)² + 1

Step-by-step explanation:

The given quadratic function is given in vertex  form, y = a·(x - h)² + k, as follows;

g(x) = (x + 4)² + 7

1. By comparing the given quadratic function and the vertex form of a quadratic equation, we have;

a = 1, h = -4, and k = 7

The vertex of the graph of the function, (h, k) = (-4, 7)

2. Given that a = 1 > 0, the graph of the quadratic function opens upwards and the vertex represents a minimum value

3. Shifting the graph 6 units down from where it is now will give;

The vertex = (h, k - 6) = (-4, 7 - 6) = (-4, 1)

h = -b/(2·a), k = (-b²/(4·a) + c = -a·h² + c

c = k + a·h²

Therefore, initial value of the constant term, c = -1×(-4)² + 7 = 23

After the shifting the graph 6 units down, c = 23 - 6 = 17

∴ k = 1 = -a·(-4)² + 17

∴ -16/16 = -1 = -a

a = 1

Therefore, the equation represented by the new graph is g(x) = (x + 4)² + 1.

5 0
3 years ago
-3x-6y=11. 2x+y = 4 solving linear systems using multiplication and addition show your work
sladkih [1.3K]
<span>Example<span>Problem<span><span>Use elimination to solve the system.</span>   x –<span> y = </span>−6x <span>+ y = 8</span></span> </span><span> Add the equations.</span><span> <span><span>2x = 2</span>x = 1</span><span>Solve for x.</span></span><span> <span>x<span> + y = 8</span><span>1 + y = 8</span>y = 8 – 1y = 7</span><span>Substitute x = 1 into one of the original equations and solve for y.</span></span><span> <span>x<span> – y = −6</span>1 – 7 = −6−6 = −6 TRUE</span><span>x<span> + y = 8</span>1 + 7 = 88 = 8TRUE</span><span>Be sure to check your answer in both equations!</span></span><span>AnswerThe solution is (1, 7). </span></span>
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aleksandrvk [35]

The product of a number y and 12 or 12 times a number y. These are both equivalent expressions to 12y

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Which of the following is a solution to the equation −25x = 10?
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Answer: x=-0.4

Step-by-step explanation:

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