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emmainna [20.7K]
3 years ago
10

Solve (x - 3)^2+7=97, where X is a real number. Round your answer to the nearest hundredth.​

Mathematics
1 answer:
Eddi Din [679]3 years ago
6 0

Answer:

x ≈ - 6.49, x ≈ 12.49

Step-by-step explanation:

Given

(x - 3)² + 7 = 97 ( subtract 7 from both sides )

(x - 3)² = 90 ( take the square root of both sides )

x - 3 = ± \sqrt{90} ( add 3 to both sides )

x = 3 ± \sqrt{90}

Then

x = 3 - \sqrt{90} ≈ - 6.49 ( to the nearest hundredth )

x = 3 + \sqrt{90} ≈ 12.49 ( to the nearest hundredth )

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Step-by-step explanation:

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Answer:

The arithmetic mean is 10.9

Step-by-step explanation:

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Steve Rogers invested $2400 in an account tht pays 4% compounded continuously and how has $3500. How long did it take Steve's mo
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Step-by-step explanation:

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2 years ago
Please walk me through how to do this so I can di the other questions​
Naddik [55]

Answer:

Axis is a vertical line at x = 2

Vertex is (2, -1)

y-intercept is (0, 3)

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Step-by-step explanation:

To draw the graph of the quadratic equation you must find at least 5 points lie on the graph by choose values of x and find their values of y

Let us do that

Use x = -1, 0, 1, 2, 3, 4, 5

∵ y = x² - 4x + 3

∵ x = -1

∴ y = (-1)² - 4(-1) + 3 = 1 + 4 + 3 = 8

→ Plot point (-1, 8)

∵ x = 0

∴ y = (0)² - 4(0) + 3 = 0 + 0 + 3 = 3

→ Plot point (0, 3)

∵ x = 1

∴ y = (1)² - 4(1) + 3 = 1 - 4 + 3 = 0

→ Plot point (1, 0)

∵ x = 2

∴ y = (2)² - 4(2) + 3 = 4 - 8 + 3 = -1

→ Plot point (2, -1)

∵ x = 3

∴ y = (3)² - 4(3) + 3 = 9 - 12 + 3 = 0

→ Plot point (3, 0)

∵ x = 4

∴ y = (4)² - 4(4) + 3 = 16 - 16 + 3 = 3

→ Plot point (4, 3)

∵ x = 5

∴ y = (5)² - 4(5) + 3 = 25 - 20 + 3 = 8

→ Plot point (5, 8)

→ Join all the points to form the parabola

From the graph

∵ The axis of symmetry is the vertical line passes through the vertex point

∵ x-coordinate of the vertex point is 2

∴ Axis is a vertical line at x = 2

∵ The coordinates of the vertex point of the parabola are (2, -1)

∴ Vertex is (2, -1)

∵ The parabola intersects the y-axis at point (0, 3)

∴ y-intercept is (0, 3)

∵ x² - 4x + 3 = 0

∵ The solutions of the equation are the values of x at y = 0

→ That means the intersection points of the parabola and the x-axis

∵ The parabola intersects the x-axis at points (1, 0) and (3, 0)

∴ Solutions are x = 1 and x = 3

3 0
3 years ago
Consider the image of EFGH for the translation (x, y) → (x – 3, y + 1). What is the ordered pair of F′?
omeli [17]

Answer:

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Step-by-step explanation:

The rule for the translation is given as

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The coordinates of F are (2,2).

We substitute these coordinates into the translation rule to find the coordinates of F'.

F(2,2)\rightarrow F'(2-3,2+1)

F(2,2)\rightarrow F'(-1,3)

3 0
3 years ago
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