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2 years ago

Find the vertex of f(x)=4x^2+19x+12. Please help, thanks!

Mathematics

1 answer:

pickupchik [31]2 years ago

6 0

Answer:

(-19/8, -9/16)

Step-by-step explanation:

Recall that the vertex of a parabola is situated on the axis of symmetry, which here is

-b -19

x = ------- = --------- = -2 3/8

2a 8

To find the y-coordinate of the vertex, evaluate f(x)=4x^2+19x+12 at -19/8.

Using a calculator, we find that f(-19/8) = -10.5625.

Then the vertex is at (-19/8, -10.5625), or (-19/8, -9/16)

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Determine the answer to (−3) + (−5) and explain the steps using a number line

ASHA 777 [7]

Answer:

-8

Step-by-step explanation:

When adding a negative number on a number line, we move to the left. This is because adding a negative number is the same as subtracting. If we start at -3 and move 5 to the left, we will end at -8.

8 0

2 years ago

Please include Work!!!

Natalka [10]

5.3/8=.6625 yrds^2 should be right

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2 years ago

A solid right pyramid has a square base. The length of the base edge is4 cm and the height of the pyramid is 3 cm period what is

Illusion [34]

Answer:

The volume of this pyramid is 16 cm³.

Step-by-step explanation:

The volume $V$ of a solid pyramid can be given as:

$\displaystyle V = \frac{1}{3} \cdot b \cdot h$ ,

where

$b$ is the area of the base of the pyramid, and
$h$ is the height of the pyramid.

Here's how to solve this problem with calculus without using the previous formula.

Imaging cutting the square-base pyramid in half, horizontally. Each horizontal cross-section will be a square. The lengths of these squares' sides range from 0 cm to 3 cm. This length will be also be proportional to the vertical distance from the vertice of the pyramid.

Refer to the sketch attached. Let the vertical distance from the vertice be $x$ cm.

At the vertice of this pyramid, $x = 0$ and the length of a side of the square is also $0$ .
At the base of this pyramid, $x = 3$ and the length of a side of the square is $4$ cm.

As a result, the length of a side of the square will be

$\displaystyle \frac{x}{3}\times 4 = \frac{4}{3}x$ .

The area of the square will be

$\displaystyle \left(\frac{4}{3}x\right)^{2} = \frac{16}{9}x^{2}$ .

Integrate the area of the horizontal cross-section with respect to $x$

from the top of the pyramid, where $x = 0$ ,
to the base, where $x = 3$ .

$\displaystyle \begin{aligned}\int_{0}^{3}{\frac{16}{9}x^{2}\cdot dx} &= \frac{16}{9}\int_{0}^{3}{x^{2}\cdot dx}\\ &= \frac{16}{9}\cdot \left(\frac{1}{3}\int_{0}^{3}{3x^{2}\cdot dx}\right) & \text{Set up the integrand for power rule}\\ &= \left.\frac{16}{9}\times \frac{1}{3}\cdot x^{3}\right|^{3}_{0}\\ &= \frac{16}{27}\times 3^{3} \\ &= 16\end{aligned}$ .

In other words, the volume of this pyramid is 16 cubic centimeters.

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2 years ago

What times what equals 252

Dovator [93]

There are numerous factors of 252. The factors are 1 times 252, 2 times 126, 3 times 84, 4 times 63, 6 times 42, 7 times 36, 9 times 28, 12 times 21, and 14 times 18. Hope this helped :)!

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3 years ago

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icang [17]

The ansa is 256=(12+x)(12+x)

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2 years ago