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VARVARA [1.3K]
3 years ago
13

40 POINTS! Please HELP!!!Use the function f(x) to answer the questions:

Mathematics
2 answers:
Hitman42 [59]3 years ago
7 0
<h2>Answer:</h2>

<h2>Step-by-step explanation:</h2>

Eq.  5x^2 + 2x - 3

Part A:

1. Set the output value f(x)  (also known as "y" on a coordinate plane) = 0

2. 5x^2 + 2x - 3 = 0

3. Factor using "ac" method. (5 x 3 = 15, what factors of 15 when added/subtracted = 2?)

  • 5x^2 + 5x - 3x - 3 = 0
  • 5x(x + 1) - 3(x + 1) = 0
  • (5x - 3)(x + 1) = 0

4. Use zero property.

  • 5x - 3 = 0
  • 5x = 3
  • x = 3/5

         OR

  • x + 1 = 0
  • x = - 1

5. These are the x-intercepts: (3/5, 0) and (- 1, 0)

Part B:

Vertex Formula: x = -b/2a

In a quadratic equation the base equation (standard form) is ax^2 + bx + c, where a is a non-zero constant, and b and c are real numbers.

(eq. 5x^2 + 2x - 3)

-2/2(5) = -2/10 = - 1/5 --> x-coordinate

plug (- 1/5) in for x to get - 16/5 as the y-coordinate.

VERTEX: (-1/5, - 16/5) ; minimum because "a" value is positive

Hatshy [7]3 years ago
3 0

Answer:

Part A: (-1, 0), (0.6, 0)

Part B: Minimum, (-0.2, -3.2)

Part 2: We would find the 3 points: the 2 zeros and the vertex and we would be able to graph.

Step-by-step explanation:

Easiest and fastest way to answer these questions is to graph the equation in a graphing calc.

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5 0
2 years ago
Construct the exponential function that contains the points (0,2) and (3,54)
erma4kov [3.2K]

The exponential function that passes through (0,2) and (3,54) is a growth function

The exponetial function is y = 2 * 3^x

<h3>How to construct the exponential function?</h3>

The points are given as:

(x,y) = (0,2) and (3,54)

An exponential function is represented as:

y = ab^x

Substitute the points in the equation

2 = ab^0 and 54 = ab^3

Solve 2 = ab^0

a = 2

Substitute 2 for a in 54 = ab^3

54 = 2b^3

Divide by 2

27 = b^3

Take the cube roots of both sides

b = 3

So, we have:

y = ab^x

This becomes

y = 2 * 3^x

Hence, the exponetial function is y = 2 * 3^x

Read more about exponential functions at:

brainly.com/question/24077767

8 0
2 years ago
Alex makes $61,992 per year and pays about 25% of his gross monthly income in federal and state taxes. He wants to find an apart
ivanzaharov [21]

Answer:

Rent each month = $1421

Amount left after rent and taxes monthly = $2453

Step-by-step explanation:

Gross salary; $61,992 per year

His gross pay per month will be;

61992/12 = $5166

Now, the standard recommended rule in budgeting for house rent is to use between 25% to 30% of your monthly pay for rent.

Now, let's adopt an average of 27.5%

Thus;

Amount he can afford for rent each month = 27.5% × 5166 = $1420.65 ≈ $1421

We are told he pays 25% of his gross monthly income in federal and state taxes.

Thus, amount spent on taxes each month = 25% × 5166 = $1291.5 ≈ $1292

Thus, amount he will gave left after rent and taxes = 5166 - (1421 + 1292) = $2453

4 0
3 years ago
Can the sides of a triangle have lengths 1, 7, and 11? Explain
Airida [17]

No

Given 3 sides of a triangle, the sum of any 2 sides must be greater than the third side.

Consider the 3 given sides 1, 7 and 11

7 + 11 = 18 > 1

1 + 11 = 12 > 7

1 + 7 < 11 ⇒ not valid

Hence these sides do not form a triangle


6 0
3 years ago
Two shapes that represent the cross-sections
777dan777 [17]

Answer:

it's the square and the rectangle

3 0
2 years ago
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