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3 years ago

Use the function f(x) = 2x2 − 3x − 5 to answer the questions.

Mathematics

1 answer:

Dovator [93]3 years ago

5 0

Answer:

see below

Step-by-step explanation:

A: 2x² - 3x - 5

(2x - 5)(x + 1)

B: Set the factored equation equal to zero and solve for x.

(2x - 5)(x + 1) = 0

2x - 5 = 0

2x = 5

x = 5/2

x + 1 = 0

x = -1

The x-intercepts are 5/2 and -1

C) To find the end behavior, you need to look at the term in the unfactored equation with the highest exponential number. For this equation, that is 2x². Since the exponent is positive, both ends of the graph will point in the same direction. Because the leading coefficent is positive, the graph will point upwards. The end behavior of the graph is that as the x-values approach both ∞ and -∞, the function approaches ∞.

D) Since we know that the x-intercepts are 5/2 and -1, you can plot these points. You also know that the graph will be in an upward U shape. Plug in a couple x-values and plot them to make the graphing of the equation more accurate.

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3 years ago

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Help 80 points A concrete planter is formed from a square-based pyramid that was inverted and placed

Rufina [12.5K]

Answer:

The slant height of the pyramid refers to the height of a face of the pyramid.

Notice that each slant height forms a right triangle like the image attached shows, where the hypothenuse is the slant height. Additionally, the bottom leg is 1 yard, because is half of the base side, and the other leg is 2 yard. Using Pythagorean's Theorem, we have

$h^{2} =1^{2} +2^{2} \\h=\sqrt{1+4}=\sqrt{5}$

Therefore, the slant height is the square root of 5 yard.

The surface area of the composite figure is the sum of the surface area of both volumes.

<h3>Surface area of the cube.</h3>

$S_{cube}=5(2yd)^{2} =20 yd^{2}$

Notice that we only included 5 faces of the cube, that is because the sixth is the base of the pyramid, so if we include it here, we would have the wrong total surface area.

<h3>Surface area of the pyramid.</h3>

$S_{pyramid}=\frac{1}{2}pl$

Where $p$ is the perimeter of the base and $l$ is the slant height.

$S_{pyramid}=\frac{1}{2}(8yd)(\sqrt{5}yd )=4\sqrt{5}yd ^{2}$

Therefore, the surface od the composite figure is

$S_{total}=20yd^{2} +4\sqrt{5} yd^{2} \approx 29.94 yd^{2}$

To find the cubic yards of concrete, we need to subtract the volume of the figures, because the concrete would be inside the space between the cube and the pyramid.

$V_{concrete}=V_{cube} -V_{pyramid}=l^{3}- \frac{1}{3}l^{2}h$

Where $l=2yd$ and $h=2yd$

$V_{concrete}=2^{3}-\frac{1}{3}(2)^{2} (2)=8-\frac{8}{3} \approx 5.33 yd^{3}$

Therefore, it would be needed 5.33 cubic yards of concrete to make the planter.

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