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3 years ago

Between which two ordered pairs does the graph of f(x) = one-halfx2 + x – 9 cross the negative x-axis?

Mathematics

2 answers:

Anit [1.1K]3 years ago

6 0

Answer:

Step-by-step explanation:

we have that

$f(x) = x^2 + x - 9$

Using a graph tool

see the attached figure

The function represent a vertical parabola that open up

the vertex is a minimum-------> is the point (-0.5, -9.3)

The x-intercepts are the points when the y coordinate is equal to zero

The x-intercepts are the points (-3.5, 0) and (2.5, 0)

the function cross the negative x-axis at point

therefore, the answer is

(-4, 0) and (-3, 0)

k0ka [10]3 years ago

3 0

Answer:

(-6,0)(-5,0)

Step-by-step explanation:

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From a piece of tin in the shape of a square 6 inches on a side, the largest possible circle is cut out. What is the ratio of th

wel

Answer:

$\sf \dfrac{1}{4} \pi \quad or \quad \dfrac{7}{9}$

Step-by-step explanation:

The width of a square is its side length.

The width of a circle is its diameter.

Therefore, the largest possible circle that can be cut out from a square is a circle whose diameter is equal in length to the side length of the square.

Formulas

$\sf \textsf{Area of a square}=s^2 \quad \textsf{(where s is the side length)}$

$\sf \textsf{Area of a circle}=\pi r^2 \quad \textsf{(where r is the radius)}$

$\sf \textsf{Radius of a circle}=\dfrac{1}{2}d \quad \textsf{(where d is the diameter)}$

If the diameter is equal to the side length of the square, then:
$\implies \sf r=\dfrac{1}{2}s$

Therefore:

$\begin{aligned}\implies \sf Area\:of\:circle & = \sf \pi \left(\dfrac{s}{2}\right)^2\\& = \sf \pi \left(\dfrac{s^2}{4}\right)\\& = \sf \dfrac{1}{4}\pi s^2 \end{aligned}$

So the ratio of the area of the circle to the original square is:

$\begin{aligned}\textsf{area of circle} & :\textsf{area of square}\\\sf \dfrac{1}{4}\pi s^2 & : \sf s^2\\\sf \dfrac{1}{4}\pi & : 1\end{aligned}$

Given:

side length (s) = 6 in
radius (r) = 6 ÷ 2 = 3 in

$\implies \sf \textsf{Area of square}=6^2=36\:in^2$

$\implies \sf \textsf{Area of circle}=\pi \cdot 3^2=28\:in^2\:\:(nearest\:whole\:number)$

Ratio of circle to square:

$\implies \dfrac{28}{36}=\dfrac{7}{9}$

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2 years ago

Surface area of a box 12 x 6 x 9.5

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9514 1404 393

Answer:

486 square units

Step-by-step explanation:

Use the surface area formula with the given numbers.

SA = 2(LW +H(L +W))

SA = 2(12·6 +9.5(12 +6)) = 2(72 +9.5(18)) = 486

The surface area of the box is 486 square units.

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Vaselesa [24]

Answer:

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