Henry ate 3/8 of a sandwich. Keith ate 4/8 of the same sandwich. How much more of the sandwich did Keith eat than Henry?

jenyasd209 [6]

9514 1404 393

Answer:

(a) none of the above

Step-by-step explanation:

The largest exponent in the function shown is 2. That makes it a 2nd-degree function, also called a quadratic function. The graph of such a function is a parabola -- a U-shaped curve.

The coefficient of the highest-degree term is the "leading coefficient." In this case, that is the coefficient of the x² term, which is 1. When the leading coefficient of an even-degree function is positive, the U curve has its open end at the top of the graph. We say it "opens upward." (When the leading coefficient is negative, the curve opens downward.)

This means the bottom of the U is the minimum value the function has. For a quadratic in the form ax²+bx+c, the horizontal location of the minimum on the graph is at x=-b/(2a). This extreme point on the curve is called the "vertex."

This function has a=1, b=1, and c=3. The minimum of the function is where ...

x = -b/(2·a) = -1/(2·1) = -1/2

This value is not listed among the answer choices, so the correct choice for this function is ...

none of the above

__

The attached graph of the function confirms that the minimum is located at x=-1/2

_____

Additional comment

When you're studying quadratic functions, there are few formulas that you might want to keep handy. The formula for the location of the vertex is one of them.

8 0

2 years ago

Find the area of the trapezoid to the nearest tenth.

erica [24]

Answer:

2.2 metres squared

Step-by-step explanation:

We need to find the area of this trapezoid.

The area of a trapezoid is denoted by:

$A=\frac{(b_1+b_2)h}{2}$ , where $b_1$ and $b_2$ are the parallel bases and h is the height

Here, we already know the lengths of the two bases; they are 0.9 metres and 2.3 metres. However, we need to find the length of the height.

Notice that one of the angles is marked 45 degrees. Let's draw a perpendicular line from top endpoint of the segment labelled 0.9 to the side labelled 2.3. We now have a 45-45-90 triangle with hypotenuse 2.0 metres. As one of such a triangle's properties, we can divide 2.0 by √2 to get the length of both legs:

2.0 ÷ √2 = √2 ≈ 1.414 ≈ 1.4

Thus, the height is h = 1.4 metres. Now plug all these values we know into the equation to find the area:

$A=\frac{(b_1+b_2)h}{2}$

$A=\frac{(0.9+2.3)*1.4}{2}=2.2$

The answer is thus 2.2 metres squared.

~ an aesthetics lover

8 0

3 years ago

The air Temperature is -12C at sunrise and rises 4 degrees c every hour for several hours the air temperature after x hours is r

Stolb23 [73]

Let f(x) = y.

y = 4x - 12

Let x = 0

y = 4(0) - 12

y = - 12

This leads to the point (0, -12).

Let y = 0.

0 = 4x - 12

1 2 = 4x

12/4 = x

3 = x

This leads to the point (3, 0).

We now graph both points and then connect each point with a straight line.

4 0

2 years ago

Complete factorization

Lostsunrise [7]

Answer:

A. 2x + 1

Step-by-step explanation:

6x³ - 15x² - 9x

3x (2x² - 5x - 3)

3x (2x² + x - 6x - 3)

3x (x (2x + 1) - 6x - 3)

3x (x (2x + 1) - 3 (2x + 1))

= 3x (2x + 1) (x - 3)

one of the factor of the complete factorization is A. 2x + 1

5 0

2 years ago

Read 2 more answers

Please give answer of 6 number

Irina18 [472]

Answer:

$7,500$

Step-by-step explanation:

Let's solve this problem step-by-step. The library had 1,500 books in 2011. The ratio of books in 2011 and in 2012 is 1:2. Therefore, let the number of books in 2012 be $x$ .

We have the following proportion:

$\frac{1}{1,500}=\frac{2}{x},\\x=2\cdot 1,500=3,000$

Therefore, there were 3,000 books in 2012. The ratio of books in 2012 and in 2013 is 2:5. Let the number of books in 2013 be $y$ .

We have:

$\frac{2}{3,000}=\frac{5}{y},\\2y=5\cdot 3,000,\\2y=15,000\\y=\boxed{7,500}$

Therefore, there were 7,500 books in 2013.

8 0

3 years ago

Read 2 more answers