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2 years ago

What is the domain of the function f(x) = (-5/6)(3/5)superscript x

Mathematics

1 answer:

Georgia [21]2 years ago

5 0

Answer:

$-\infty < x < \infty$

Step-by-step explanation:

Given

$f(x) = (-\frac{5}{6}) \cdot (\frac{3}{5})^x$

Required

The domain

There are no undefined points such as denominator of x or square roots.

Hence, the domain is:

$-\infty < x < \infty$

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Rectangle poster is 3 times as long as wide perimeter is 24 in

Alexxandr [17]

w= width

l = 3w

P = 2(l+w)

substitute

24 = 2(3w+w)

24 = 2(4w)

24 =8w

3 =w

The width is 3 inches

the length is 9 inches

3 0

3 years ago

A triangle has a base of x 1/2 m and a height of x 3/4 m. If the area of te triangle is 16m to the power of 2, what are the base

Olenka [21]

Answer:

The base of triangle is $\frac{8}{\sqrt{3}} \ m$ and the height of triangle is $\frac{12}{\sqrt{3}} \ m.$

Step-by-step explanation:

Given:

A triangle has a base of x 1/2 m and a height of x 3/4 m. If the area of the triangle is 16m to the power of 2.

Now, to find the base and height of the triangle.

The base of triangle = $x\times\frac{1}{2} =\frac{x}{2} \ m.$

The height of triangle = $x\times \frac{3}{4} =\frac{3x}{4}\ m.$

The area of triangle = $16\ m^2.$

Now, we put the formula of area to solve:

$Area=\frac{1}{2} \times base\times height$

$16=\frac{1}{2} \times \frac{x}{2} \times \frac{3x}{4}$

$16=\frac{3x^2}{16}$

Multiplying both sides by 16 we get:

$256=3x^2$

Dividing both sides by 3 we get:

$\frac{256}{3} =x^2$

Using square root on both sides we get:

$\frac{16}{\sqrt{3}}=x$

$x=\frac{16}{\sqrt{3}}$

Now, by substituting the value of $x$ to get the base and height:

$Base=\frac{x}{2}\\\\Base=\frac{\frac{16}{\sqrt{3}}}{2} \\\\Base=\frac{8}{\sqrt{3}} \ m.$

So, the base of triangle = $\frac{8}{\sqrt{3}} \ m.$

$Height=x\times\frac{3}{4} \\\\Height=\frac{16}{\sqrt{3}}\times \frac{3}{4} \\\\Height=\frac{12}{\sqrt{3}} \ m.$

Thus, the height of triangle = $\frac{12}{\sqrt{3}} \ m.$

Therefore, the base of triangle is $\frac{8}{\sqrt{3}} \ m$ and the height of triangle is $\frac{12}{\sqrt{3}} \ m.$

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3 years ago

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jek_recluse [69]

Answer:

$10,091

Step-by-step explanation:

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