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3 years ago

Write a quadratic function whose zeros are -3 and -4

Mathematics

1 answer:

andreev551 [17]3 years ago

6 0

Answer:

f(x) = (x -(-3))(x -(-4))

Step-by-step explanation:

The function can be written as the product of binomial terms whose values are zero at the given zeros.

(x -(-3)) is one such term

(x -(-4)) is another such term

The product of these is the desired quadratic function. In the form easiest to write, it is ...

f(x) = (x -(-3))(x -(-4))

This can be "simplified" to ...

f(x) = (x +3)(x +4) . . . . simplifying the signs

f(x) = x^2 +7x +12 . . . . multiplying it out

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the height h(t) of a trianle is increasing at 2.5 cm/min, while it's area A(t) is also increasing at 4.7 cm2/min. at what rate i

nekit [7.7K]

Answer:

The base of the triangle decreases at a rate of 2.262 centimeters per minute.

Step-by-step explanation:

From Geometry we understand that area of triangle is determined by the following expression:

$A = \frac{1}{2}\cdot b\cdot h$ (Eq. 1)

Where:

$A$ - Area of the triangle, measured in square centimeters.

$b$ - Base of the triangle, measured in centimeters.

$h$ - Height of the triangle, measured in centimeters.

By Differential Calculus we deduce an expression for the rate of change of the area in time:

$\frac{dA}{dt} = \frac{1}{2}\cdot \frac{db}{dt}\cdot h + \frac{1}{2}\cdot b \cdot \frac{dh}{dt}$ (Eq. 2)

Where:

$\frac{dA}{dt}$ - Rate of change of area in time, measured in square centimeters per minute.

$\frac{db}{dt}$ - Rate of change of base in time, measured in centimeters per minute.

$\frac{dh}{dt}$ - Rate of change of height in time, measured in centimeters per minute.

Now we clear the rate of change of base in time within (Eq, 2):

$\frac{1}{2}\cdot\frac{db}{dt}\cdot h = \frac{dA}{dt}-\frac{1}{2}\cdot b\cdot \frac{dh}{dt}$

$\frac{db}{dt} = \frac{2}{h}\cdot \frac{dA}{dt} -\frac{b}{h}\cdot \frac{dh}{dt}$ (Eq. 3)

The base of the triangle can be found clearing respective variable within (Eq. 1):

$b = \frac{2\cdot A}{h}$

If we know that $A = 130\,cm^{2}$ , $h = 15\,cm$ , $\frac{dh}{dt} = 2.5\,\frac{cm}{min}$ and $\frac{dA}{dt} = 4.7\,\frac{cm^{2}}{min}$ , the rate of change of the base of the triangle in time is:

$b = \frac{2\cdot (130\,cm^{2})}{15\,cm}$

$b = 17.333\,cm$

$\frac{db}{dt} = \left(\frac{2}{15\,cm}\right)\cdot \left(4.7\,\frac{cm^{2}}{min} \right) -\left(\frac{17.333\,cm}{15\,cm} \right)\cdot \left(2.5\,\frac{cm}{min} \right)$

$\frac{db}{dt} = -2.262\,\frac{cm}{min}$

The base of the triangle decreases at a rate of 2.262 centimeters per minute.

6 0

2 years ago

Will choose brainlist

Gekata [30.6K]

Answer: 0.01429

Step-by-step explanation:

1.429 x $10^{-2}$

Now $10^{-2}$ is just 1/100 or 0.01, because 10^2 is 100

Now we can multiply 1.429 by 0.01 which is 1.429 x 0.01

Or the easy way, we can just place the decimal two places to the left because the power is -2, so 2 places to the left. Moving the decimal to the left makes the number smaller.

So, take 1.492 and move its decimal 2 places to the left

We get 0.01429

4 0

2 years ago

The graph of a linear equation passes through three of these points: (0, 5), (2, 2), (3, 1), and (4, -1).

Serggg [28]

Answer:

The point that the graph does not pass through is (3,1)

Step-by-step explanation:

we have

(0, 5), (2, 2), (3, 1), and (4, -1)

Draw the points, and join them to plot the linear equation and determine which point does not belong to the line.

using a graphing tool

see the attached figure

therefore

The point that the graph does not pass through is (3,1)

3 0

3 years ago

A right triangle is formed by connecting coordinates (5, -2), (2, -3), and (-1, 6). What is the area of the triangle in square u

Marianna [84]

Answer:

the triangle formed from the coords is 3cm by 9cm so try 3 × 9 = 27 then 27 ÷ 2 = 13.5 from the formula a = ½bh?

Step-by-step explanation:

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2 years ago

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mixas84 [53]

.590 because if its 5 and up u round up. does that make sence<span />

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3 years ago