MATHEMATICS MIDDLE SCHOOL

Which expression is equivalent to 16^3?
6^7
2^11
2^12
2^64

Answers

Answer 1

Answer:

Answer:

2¹²

Step-by-step explanation:

= 16³

We'll divide 16 into the product of its prime factors

= ( 2×2×2×2)³

There are four 2s so it becomes 2⁴

= (2⁴)³

= 2⁴ˣ³

= 2¹²

Answer 2

Answer:

Answer:

2^12

Step-by-step explanation:

16^3 = (2^4)^3 = 2^(4x3) = 2^12

Hope this helps!

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9. A person stands at the window of a building so that his eyes are 12.6 m above the level ground. Anobject is on the ground 58.5 m away from the building on a line directly beneath the person. Compute

the angle of depression of the person's line of sight to the object on the ground.

Answers

The angle of depression of the person's line of sight to the object on the ground is 12.15°.

The information forms a right angle triangle. The person eyes above the ground is the opposite side of the triangle. The object distance from the building in line of the sight is the adjacent side of the right angle triangle.

Therefore,

using trigonometric ratio,

tan Ф = opposite /adjacent

tan Ф = 12.6 / 58.5

tan Ф = 0.21538461538

Ф = tan⁻¹ 0.21538461538

Ф = 12.1549416972

Ф = 12.15°

angle of depression ≈ 12.15°

Answer:

$\theta = 12.16^0.$

Step-by-step explanation:

Given,

Height = 12.6 m

Object distance from the person = 58.5 m

Angle of depression

$tan \theta = (P)/(B)$

$tan \theta = (12.6)/(58.5)$

$tan \theta = 0.2154$

$\theta = 12.16^0$

Hence, angle of depression is equal to $\theta = 12.16^0.$

Every time Jason buys 2 red marbles he buys 1 blue marble. If y = the number of red marbles Jason buys, and x = the number of blue marbles Jason buys, which graph represents this direct variation? A)
B)
C)
D)

Answers

If y is the red marbles and x is the blue marbles, then for every x value you would be able to multiply by 2 to get the y value... it is the equivalent of looking at is as the slope rise/run or 2/1

D is the graph that shows this relationship. Look at the x value and multiply by 2 for the y value.

Answer= Grid D
Because when the line crosses on 2 (y-axis) it only goes right (x-axis)1 time. Also when it crosses on 4 (y-axis) it goes 2 steps to the right (x-axis). I hope it helped.

Isaiah put a 100 gram weight on a pan balance. how many 10 gram weights does he need to balance the scale

Answers

Isaiah need 10 weight to balance the scale.

What is Division method?

Division method is used to distributing a group of things into equal parts.

Given that;

Isaiah put a 100 gram weight on a pan balance.

Now,

Number of 10 gram weight to balance the scale = 100 ÷ 10

= 10

Thus, Isaiah need 10 weight to balance the scale.

Learn more about the division visit:

brainly.com/question/4344214

#SPJ2

Answer=10 10gram weights
10*10grams=100grams
therefore the weight would be even on both sides

11. What is the height of the cylinder? The figure is not drawn to scale. (1 point)V = 282.7 in
Please help ASAP

Answers

Answer:

The height of the cylinder is 3.6 inch.

Step-by-step explanation:

In the attached figure,

Volume of the cylinder is 282.7 square inches

Radius of the cylinder is 5 inches.

It is required to find the height of the cylinder.

The volume of the cylinder is given by the below formula as :

$V=\pi r^2 h$

h is height of cylinder

$h=(V)/(\pi r^2)\n\nh=(282.7)/(3.14* (5)^2)\n\nh=3.6\ \text{inch}$

So, the height of the cylinder is 3.6 inch.

The approximate height of the cylinder is 3.6 inches

How to determine the height?

The given parameters are:

Radius, r = 5 in

Volume, V = 282.7 cubic in

The volume is calculated using:

V = πr²h

So, we have:

3.14 * 5² * h = 282.7

Evaluate

78.5 * h = 282.7

Divide both sides by 78.5

h = 3.6

Hence, the approximate height of the cylinder is 3.6 inches

Answers

Answer:

These transformations do not change the size of the image.

Step-by-step explanation:

By going over the different properties of translations, reflections and rotations, we can determine what exactly is common about each of these.

- Translations: the shifting of a function on the coordinate plane without any change in congruence, shape or size.

In algebra, translations are seen most often in quadratic and linear functions, and always by adding or subtracting a number the function's $x$ and/or $y$ values.
ex.) In the parent function of standard-form quadratic equations, $f(x)=ax^2+bx+c$ , the value $c$ would be considered a value that determines the function's vertical translation. It is a value that would move the equation up or down if changed.

- Reflection: the flipping of a function without any change of its overall shape or size.

In algebra, a reflection is usually seen in vertical reflections across the $x$ -axis.
ex.) The $a$ in standard-form quadratic equations is an example of a reflection across the $x$ -axis. If it's sign is changed (if it is changed from negative to positive and vise-versa), then the equation would be flipped across the $x$ -axis.

- Rotation: the change of a function's rotation without any change in its size, shape or location.

Rotations, are most often seen in linear equations with a line's slope.
ex.) In the standard form linear function, $f(x)=mx+b$ , $m$ or the line's slope changes the rotation of the function.