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saveliy_v [14]
2 years ago
15

The function f(x) = –x2 – 4x + 5 is shown on the graph. On a coordinate plane, a parabola opens down. It goes through (negative

5, 0), has a vertex at (negative 2, 9), and goes through (1, 0). Which statement about the function is true? The domain of the function is all real numbers less than or equal to −2. The domain of the function is all real numbers less than or equal to 9. The range of the function is all real numbers less than or equal to −2. The range of the function is all real numbers less than or equal to 9.
Mathematics
1 answer:
sertanlavr [38]2 years ago
5 0

The true statement about the function f(x) = -x² - 4x + 5 is that:

  • The range of the function is all real numbers less than or equal to 9.
<h3 /><h3>What is the domain and range for the function of y = f(x)?</h3>

The domain of a function is the set of given values of input for which the function is valid and true.

The range is the dependent variable of a given set of values for which the function is defined.

  • The domain of the function: f(x) = -x² - 4x + 5 are all real number from -∞ to +∞

For a parabola ax² + bx + c  with the vertex \mathbf{(x_v,y_v)}

  • If a < 0, then the range is f(x) ≤ \mathbf{y_v}
  • If a > 0, then the range f(x) ≥  \mathbf{y_v}
  • Here; a = -1,

The vertex for an up-down facing parabola for a function y = ax² + bx + c is:

\mathbf{x_v = -\dfrac{b}{2a}}

Thus,

  • vertex \mathbf{(x_v,y_v)} = (-2, 9)

Range: f(x) ≤ 9

Therefore, we can conclude that the range of the function is all real numbers less than or equal to 9.

Learn more about the domain and range of a function here:

brainly.com/question/26098895

#SPJ1

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dalvyx [7]

Answer:

Slope = 2      y - intercept = ( 0 , -2 )      equation:  y = 2x - 2

Step-by-step explanation:

We can begin solving by first understanding what slope is.

Slope is the rate of change in a line.

The formula for slope is:

(For any two points on a line)

m =  y₁ - y₂  /  x₁ - x₂

**m is the variable for slope

Two points on the line are: ( 6, 10 ) and ( 2, 2 )

Here is where we'll plug in the formula:

m = 10 - 2  /  6 - 2

m = 8  /  4

m = 2

Now that we have our slope, we only have to look at the graph to find the y-intercept.

The y-intercept is the point on the graph crosses the y-axis (this effectively means that the x value will always be 0)

When we look at the graph, we can see that the y-intercept is: ( 0, -2 )

All that's left is to right the equation in slope-intercept form.

The equation is arranged just as it says in the name:

y = mx + b

(m = slope   b = y -intercept)

When we plug in our variables, the equation becomes:

y = 2x - 2

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3 years ago
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I think the answer to your question might be 6
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Brianna's family spent $134 on 2 adult tickets and 3 youth tickets at an amusement park. Max's family spent $146 on 3 adults tic
Firdavs [7]

The price of 1 youth ticket is $ 22

<em><u>Solution:</u></em>

Let "y" be the price of 1 youth ticket

Let "a" be the price of 1 adult ticket

To find: price of 1 youth ticket

<em><u>Brianna's family spent $134 on 2 adult tickets and 3 youth tickets at an amusement park</u></em>

So we can frame a equation as:

2 adult tickets x price of 1 adult ticket + 3 youth tickets x price of 1 youth ticket = 134

2 \times a + 3 \times y = 134

2a + 3y = 134 ---- eqn 1

<em><u>Max's family spent $146 on 3 adults tickets and 2 youth tickets</u></em>

So we can frame a equation as:

3 adult tickets x price of 1 adult ticket + 2 youth tickets x price of 1 youth ticket = 146

3 \times a + 2 \times y = 146

3a + 2y = 146 ----- eqn 2

<em><u>Let us solve eqn 1 and eqn 2 to find values of "y"</u></em>

Multiply eqn 1 by 3

6a + 9y = 402 ---- eqn 3

Multiply eqn 2 by 2

6a + 4y = 292 ----- eqn 4

Subtract eqn 4 from eqn 3

6a + 9y = 402

6a + 4y = 292

( - ) -------------------

5y = 110

y = 22

Thus the price of 1 youth ticket is $ 22

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3 years ago
Tony saw 6 birds in a tree. 1/6 of them flew away. How many were left?
Andreyy89

Answer:

5 birds flew away

Step-by-step explanation:

1/6x6=1

( 1 bird flew away)

so, 6-1=5

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AlladinOne [14]

Answer:

b = 4 inches, c = ~5.66 inches

Step-by-step explanation:

The triangle is isosceles so b is equal to the adjacent side. Use the Pythagorean theorem to find c.

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