The difference of two numbers is 57. the larger number is three less than six times the smaller number. find the numbers.

Emelio wants to solve this equation. x 5 = 35 Help him follow the steps to finish solving for x. 1. Multiplication property of e

antiseptic1488 [7]

Answer: 175

Step-by-step explanation

3 0

2 years ago

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(No links please) There were 2 red marbles, 3 blue marbles and 5 gold marbles in a bag.

Rashid [163]

Answer:

5/9

Step-by-step explanation:

You started with 10 marbles total. You removed one marble and did not replace it, so you now have 9 marbles. The marble that you removed was NOT a gold marble, so you still have 5 gold marbles.

This means that out of the 9 marbles that you have left, 5 of them are gold.

This means you have a 5/9 chance of drawing a gold marble next.

4 0

2 years ago

Pyramid A has a triangular base where each side measures 4 units and a volume of 36 cubic units. Pyramid B has the same height,

omeli [17]

Answer:

The volume of pyramid B is 81 cubic units

Step-by-step explanation:

Given

Pyramid A

$s = 4$ -- base sides

$V = 36$ -- Volume

Pyramid B

$s = 6$ --- base sides

Required

Determine the volume of pyramid B [Missing from the question]

From the question, we understand that both pyramids are equilateral triangular pyramids.

The volume is calculated as:

$V = \frac{1}{3} * B * h$

Where B represents the area of the base equilateral triangle, and it is calculated as:

$B = \frac{1}{2} * s^2 * sin(60)$

Where s represents the side lengths

First, we calculate the height of pyramid A

For Pyramid A, the base area is:

$B = \frac{1}{2} * s^2 * sin(60)$

$B = \frac{1}{2} * 4^2 * \frac{\sqrt 3}{2}$

$B = \frac{1}{2} * 16 * \frac{\sqrt 3}{2}$

$B = 4\sqrt 3$

The height is calculated from:

$V = \frac{1}{3} * B * h$

This gives:

$36 = \frac{1}{3} * 4\sqrt 3 * h$

Make h the subject

$h = \frac{3 * 36}{4\sqrt 3}$

$h = \frac{3 * 9}{\sqrt 3}$

$h = \frac{27}{\sqrt 3}$

To calculate the volume of pyramid B, we make use of:

$V = \frac{1}{3} * B * h$

Since the heights of both pyramids are the same, we can make use of:

$h = \frac{27}{\sqrt 3}$

The base area B, is then calculated as:

$B = \frac{1}{2} * s^2 * sin(60)$

Where

$s = 6$

So:

$B = \frac{1}{2} * 6^2 * sin(60)$

$B = \frac{1}{2} * 36 * \frac{\sqrt 3}{2}$

$B = 9\sqrt 3$

So:

$V = \frac{1}{3} * B * h$

Where

$B = 9\sqrt 3$ and $h = \frac{27}{\sqrt 3}$

$V = \frac{1}{3} * 9\sqrt 3 * \frac{27}{\sqrt 3}$

$V = \frac{1}{3} * 9 * 27$

$V = 81$

6 0

3 years ago

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A scuba diver starts at 85 3/4 meters below the surface of the water and descends until he reaches 103 1/5

RSB [31]

Answer:

From his starting point of 85 3/4, he descended 17 9/20 meters

Step-by-step explanation:

We want to know how much farther he went down from his starting point.

103 1/5 - 85 3/4

S

tart off by making the denominators of both the numbers the same.

103 1/5 - 85 3/4

103 4/20 - 85 15/20

Make them into improper fractions

2064/20 - 1715/20 = 349/20

Make 349/20 into a mixed fraction

17 9/20

5 0

2 years ago

A ball is thrown from first base to second base and then from second base to home plate. How many feet has the ball been thrown?

RSB [31]

Answer:

B. 90 + 90 √2

Step-by-step explanation:

From first base to the second base, it will travel 90 feet.

From the second base to the home plate, it will travel a longer distance. How much? Well, if you look at the layout of the field, you'll see that if you draw a line from second base to the home plate, you'll form two rectangular triangles, one with the 1st base, another one with the 3rd base.

The line from the 2nd base to home plate is the hypotenuse, which we can easily find by:

h²=90² + 90²

h = √(2 * 90²)

h = 90 √2

So, from second base to home plate, the ball has traveled 90 √2

Overall: 90 + 90 √2

8 0

3 years ago