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Elina [12.6K]
3 years ago
9

Write the factorizations of the exponents below and then compute the exponents below

Mathematics
1 answer:
matrenka [14]3 years ago
5 0

Given:

The exponents.

To find:

The factorizations of the exponents and their values.

Solution:

We know that,

a^n=a\times a\times a\times ...\times a(n-times)

Using this rule, we get the factorizations of the given exponents and their values.

2^3=2\times 2\times 2=8

3^2=3\times 3=9

6^2=6\times 6=36

4^3=4\times 4\times 4=64

7^3=7\times 7\times 7=343

8^2=8\times 8=64

3^4=3\times 3\times 3\times 3=81

7^2=7\times 7=49

6^3=6\times 6\times 6=216

9^2=9\times 9=81

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PLEASE HELP DUE TONIGHT
Alika [10]

Answer:

The answer should be 20,000 feet

Step-by-step explanation:

sin 0 =opposite/hypotenuse

sin 30 = AB/AC

sin 30 = 10000/c

c= 10000/sin 30

c=10000/1/2

c=20,000 feet

4 0
3 years ago
the sum of two numbers is zero. when 15 times the smaller numbers is added to 10 times the larger, the result is 1. find the two
EleoNora [17]

We have two numbers say a, b. And a system of equations.

a+b=0\wedge\dfrac{a+b}{15}+10(a+b)=1

It looks a bit intimidating but it's actually very easy.

Instead of term a + b in the second equation we can say it's zero because the first equation describes a + b as being equal to 0.

So,

\dfrac{0}{15}+10\cdot0=1\Longrightarrow 0+0=1

The above equation is not true therefore numbers a and b do not exists in the real number domain.

a,b\notin\mathbb{R}

No solution.

Hope this helps.

7 0
4 years ago
Select the correct answer from the drop-down menu. A vertical pole is supported by two ropes staked to the ground on opposite si
Ainat [17]

Answer:

6.78 m

Step-by-step explanation:

Since the set up forms a triangle with length of ropes two sides of the triangle a = 8 m and b = 7 m respectively, the distance between them which is c = 6 m forms the third side of the triangle.

To find the height of the pole, we need to find the angle between any of the ropes and the ground. So, choosing the 8 m long rope side and using the cosine rule,

b² = a² + c² - 2accosФ where Ф is the angle opposite the 7 m long side which is also the angle between the 8 m long side and the ground.

So, making, Ф subject of the formula, we have

b² - (a² + c²) = 2accosФ

cosФ = [b² - (a² + c²)]/2ac

Ф = cos⁻¹{[b² - (a² + c²)]/2ac}

substituting the values of the variables into the equation, we have

Ф = cos⁻¹{[b² - (a² + c²)]/2ac}

Ф = cos⁻¹{[7² - (8² + 6²)]/2(8)(6)}

Ф = cos⁻¹{[49 - (64 + 36)]/96}

Ф = cos⁻¹{[49 - 100]/96}

Ф = cos⁻¹{-51/96}

Ф = cos⁻¹{-0.53125}

Ф = 122.09°

Since the height of the pole, h is a perpendicular bisector to the base of the triangle, and the 8 m long side form a triangle with it and the ground and the 8 m long side being the hypotenuse side of this triangle, we have that

sinФ = h/a where a = 8 m and Ф = 122.09° = the angle between the 8 m long side and the ground.

h = asinФ

substituting the values of the variables into the equation, we have

h = asinФ

h = (8 m)sin122.09°

h = 8 m × 0.8472

h = 6.78 m

3 0
3 years ago
Using the formula for the area of a triangle, , write an expression for the area of ΔABC. Base your answer on the work you did i
Montano1993 [528]

Answer:

Area = \frac{1}{2} * AC * D

Step-by-step explanation:

From the complete question, we have:

Length D to be perpendicular to side AC

So, the area of the triangle is:

Area = \frac{1}{2} * Base * Height

Since:

Length D is perpendicular to side AC

Then:

Base = AC

Heigjt =D

So:

Area = \frac{1}{2} * AC * D

4 0
3 years ago
Which statement is true about the y-intercept of a quadratic function?
Dafna11 [192]

Answer:

A.

Step-by-step explanation:

A quadratic function may only intercept the y-axis once. This is because the definition of a y-intercept tells us that it is the point where x = 0. If there are multiple points where x = 0, then the expression cannot be a function. As such, a quadratic function can only have one.

Choice B contradicts the previous statement.

Choice C is wrong because the x-intercept is the zero of the function. This is because at a given x-coordinate that touches the x-axis, the y-coordinate will be 'zero'.

Choice D is wrong because the y-intercept is where x = 0.

I hope this helps!

3 0
3 years ago
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