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3 years ago

If the expression (3^(d)\sqrt(5))/(3^(2)\sqrt(45)) is equal to 3, what is the value of d

1 answer:

8 0

$3^d\cdot\dfrac{\sqrt5}{3^2\cdot\sqrt{45}}=3\\\\\dfrac{3^d\sqrt5}{3^2\sqrt{9\cdot5}}=3\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\\dfrac{3^d\sqrt5}{3^2\sqrt9\cdot\sqrt5}=3\\\\\dfrac{3^d}{3^2\cdot3}=3\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\\dfrac{3^d}{3^{2+1}}=3\\\\\dfrac{3^d}{3^3}=3\qquad\text{multiply both sides by}\ 3^3\\\\3^d=3\cdot3^3\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\3^d=3^{1+3}\\\\3^d=3^4\iff\boxed{d=4}$

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Triangle ABC has verticals A (3,0),B (9,5)and (7,-8) find the length of AC in simplest radical form

AlladinOne [14]

$length = \sqrt{(0+8)^2 + (3-7)^2} = \sqrt{64 + 16} = \sqrt{80} = 4\sqrt{5}$

Answer: Length = 4√5 units.

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4 years ago

Can someone help me with this question? Whoever helps will get brainliest answer. thank you.

enyata [817]

Answer:

Final answer is $x^2$ .

Step-by-step explanation:

Given expression is $x^{\left(\frac{4}{3}\right)}\cdot x^{\left(\frac{2}{3}\right)}$

Now we need to find about what is product of both factors.

We see that both factors are in exponent form having equal base "x".

So we can apply formula: $x^m\cdot x^n=x^{\left(m+n\right)}$

$x^{\left(\frac{4}{3}\right)}\cdot x^{\left(\frac{2}{3}\right)}$

$=x^{\left(\frac{4}{3}+\frac{2}{3}\right)}$

$=x^{\left(\frac{4+2}{3}\right)}$

$=x^{\left(\frac{6}{3}\right)}$

$=x^2$

Hence final answer is $x^2$ .

5 0

3 years ago

What is the maximum height of of Anna's golf ball? The equation is y=x−0.04x2.

elena-s [515]

Given:

The height of a golf ball is represented by the equation:

$y=x-0.04x^2$

To find:

The maximum height of of Anna's golf ball.

Solution:

We have,

$y=x-0.04x^2$

Differentiate with respect to x.

$y'=1-0.04(2x)$

$y'=1-0.08x$

For critical values, $y'=0$ .

$1-0.08x=0$

$-0.08x=-1$

$x=\dfrac{-1}{-0.08}$

$x=12.5$

Differentiate y' with respect to x.

$y''=(0)-0.08(1)$

$y''=-0.08$

Since double derivative is negative, the function is maximum at $x=12.5$ .

Substitute $x=12.5$ in the given equation to get the maximum height.

$y=(12.5)-0.04(12.5)^2$

$y=12.5-0.04(156.25)$

$y=12.5-6.25$

$y=6.25$

Therefore, the maximum height of of Anna's golf ball is 6.25 units.

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3 years ago

Four less than the product of ten and a number is eleven. is

nikitadnepr [17]

Answer:

If written in algebraic form it is, 10x - 4 = 11

Step-by-step explanation:

Four less ( minus 4 ) than the product of ten and a number ( 10 times x ) is eleven ( equal to 11 ).

Hopefully this helps!

Brainliest please?

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3 years ago

The ratio between the volumes of two cubes is 125 to 216. what is the ratio between their respective surface areas?

MAVERICK [17]

Volume of a cube is length * width * height. Because it's a cube, all of these lengths are the same measurement so rather than doing V = l*w*h, we can do one of the measurements cubed, let's call it x.

So Volume = x³. So if we are given the volume, we can the length by doing the cube root.

∛125 = 5
∛216 = 6

Surface area of a cube = 6x². So now we plug both of these measurements into the formula.

For 5:

SA = 6(5)² = 6(25) = 150

For 6:

SA = 6(6)² = 6(36) = 216

The ratio of their surface areas is 150:216 or if you simplify it by dividing both by the GCF of 6, 25:36

8 0

3 years ago

If the expression (3^(d)*\sqrt(5))/(3^(2)*\sqrt(45)) is equal to 3, what is the value of d

If the expression (3^(d)\sqrt(5))/(3^(2)\sqrt(45)) is equal to 3, what is the value of d