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2 years ago

Which expression is equivalent to 3 cube root (343x^9 y^12 z^6) ? 7x3y4z2 7x3y6z2 49x3y6z2 49x3y4z2

2 answers:

7 0

Cube root of 343 = 7

of x^9 it is x^3 ( because x^9 = x^3 * x^3 * x^3)

of y^12 it is y^4

of z^6 it is z^2

So the correct choice is A

3241004551 [841]2 years ago

3 0

Answer:

A. $7x^3*y^4*z^2$

Step-by-step explanation:

We have been given an expression $\sqrt[3]{343x^9y^{12}z^6}$ . We are asked to find the equivalent expression to our given expression.

Using exponent property $(a^b)^c=a^{b\cdot c}$ we can rewrite the terms of our given expression as:

$\sqrt[3]{7^3*(x^3)^3*(y^4)^{3}*(z^2)^3}$

Using property $\sqrt[n]{a^n}=a$ we will get,

$7x^3*y^4*z^2$

Therefore, the simplified form of our given expression would be $7x^3*y^4*z^2$ and option A is the correct choice.

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josh is 6 years older than 4 times Kim's age. The sum of their ages is less than 31. what is the oldest Kim could be? show all y

Mice21 [21]

Answer:

4 years old.

Step-by-step explanation:

Lets say that Josh's age is j and Kim's age is k. As Josh is 6 years older than 4 times Kim's age, we can write this as an equation:

j = 4k + 6

This is, John's age is equal to four times Kim's plus 6 years.

We then know that, when summed their ages is less than 31, so:

k + j < 31

Replace John's age by our first equation:

k + 4k + 6 < 31

5k + 6 < 31

Subtract 6 in both sides:

5k + 6 - 6 < 31 - 6

5k < 25

Dividing both sides by 5:

5k/5 < 25/5

k < 5

So, Kim's age MUST be less than 5.

If we talk about discrete values, this is 1, 2, 3, 4, 5, 6...., we will say than the oldest Kim could be is 4. If Kim is 5 years old, the sum of ages is 31 and we need it ti be LESS than 31. (we are not considering fractional numbers as 4.5 years old).

So, Kim can be, at maximum, 4 years old.

7 0

2 years ago

To aid in sea navigation, Little Gull Island Lighthouse shines a light from a height of 91 feet above sea level with an unknown

algol13

Answer:

$\approx 6^\circ$

Step-by-step explanation:

Given that:

Little Gull Island Lighthouse shines a light from a height of 91 feet above the sea level.

The angle of depression is unknown.

Distance of the point at sea surface from the base of lighthouse is 865 ft.

This situation can be modeled or can be represented as the figure attached in the answer area.

The situation can be represented by a right angled $\triangle ABC$ in which we are given the base and the height of the triangle.

And we have to find the value of $\angle BAD \ or \ \angle C$ (Because they are the internal vertically opposite angles).

Using tangent ratio:

$tan\theta = \dfrac{Perpendicular}{Base}$

$tanC = \dfrac{AC}{BC}\\\Rightarrow tanC = \dfrac{91}{865}\\\Rightarrow tanC = 0.105\\\Rightarrow \angle C \approx 6^\circ$

Therefore, the angle of depression is: $\approx 6^\circ$

7 0

2 years ago

Which oh the following are among the five basic postulates of Euclidean geometry

igomit [66]

1. A straight line segment can be drawn joining any two points.

2. Any straight line segment can be extended indefinitely in a straight line.

3. Given any straight line segment, a circle can be drawn having the segment as radius and one endpoint as center.

4. All right angles are congruent.

5. If two lines are drawn which intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough. This postulate is equivalent to what is known as the parallel postulate.

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2 years ago

A newly introduced fitness program is gaining popularity among the members of a fitness club. The number of members, s(1), who j

ahrayia [7]

Answer:

Option A will be the answer.

Step-by-step explanation:

The number of members, s(t), who joined the program t months after it was introduced is modeled by the function below

$s(t) = 10(2)^{x} + 10$

The function is an exponential function and y-intercept of the function is at (0,20) point.

Now, from the graph given in the options, the first graph matches the criteria.

Hence, option A will be the answer. (Answer)

6 0

2 years ago

Given that a rectangle with length $3x$ inches and width $x + 5$ inches has the property that its area and perimeter have equal

scoray [572]

Answer:

First, we need to know how to calculate the area and the permiter of a rectangle.

To calculate the area, we multiply base by height and to calculate the perimeter, we sum all sides.

Knowing this, we can say that the area is 3x * (x+5) and the perimiter is 3x + 3x + x + 5 + x + 5, as we know both are the same, we write it as an equation:

$3x * (x+5) = 3x + 3x + x + 5 + x + 5$