MATHEMATICS HIGH SCHOOL

One positive integer is 1 greater than 3 times another positive integer. If the product of the two integers is 154, then what is the sum of the two integers?

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

Let the smaller integer be x.

The other integer is 1 greater than 3 times x, or 3x + 1.

The product is 154.

x(3x + 1) = 154

3x^2 + x - 154 = 0

157 = 2 * 7 * 11

14 * 11 = 154

22 * 7 = 154

(3x + 22)(x - 7) = 0

3x + 22 = 0 or x - 7 = 0

3x = -22 or x = 7

x = -22/3 or x = 7

-22/3 is not a positive integer, so we discard that solution.

The smaller integer is 7.

3x + 1 = 3(7) + 1 = 22

The greater integer is 22.

The sum of the integers is 7 + 22 = 29

Answer 2

Answer:

Answer: 29

Step-by-step explanation:

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A vase in the shape of a cylinder has a radius of 4.3 centimeters and a volume of 1330.2 cubic centimeters, as
shown in the diagram.
What is the height of the vase in centimeters? Round your answer to the nearest tenth.

Answers

Answer:

h = 22.91 cm

Step-by-step explanation:

Given that,

The volume of a vase, A = 1330.2 cm³

Radius of the vase, r = 4.3 cm

We need to find the height of the vase. The formula for the volume of a cylinder is given by :

$V=\pi r^2 h\n\nh=(V)/(\pi r^2)\n\nh=(1330.2 )/(3.14* (4.3)^2)\n\nh=22.91\ cm$

h = 23 cm

So, the height of the vase is equal to 23 cm.

1. describe how graphs of y=|x| and y=|x|-15 are related.2. write an equation for the translation of y=|x|
2 units down.

Answers

1. y=|x|-15 is 15 units down y=|x|

2. y=|x|-2 is the equation for the translation of y=|x| two units dwon.

A jar contains 3 red marbles,7 blue, and 2 green.You take one marble without replacing it, and then another.What is the probability that you draw a green and a blue?

Answers

Answer:9/12

Step-by-step explanation:

Like the other person said, it would be 9/12 because there are 12 total marbles (3 red, 7 blue, 2 green) and the blue marble amount plus the green marble amount would be 9, so it would be a 9/12 chance!

What is 7x to the third power minus 1 as a verbal expression

Answers

This woud be Seven(x) cubed minus 1.

A set of equations is given below: Equation S: y = x + 9
Equation T: y = 2x + 1

Which of the following steps can be used to find the solution to the set of equations?

x = 2x + 1
x + 9 = 2x
x + 1 = 2x + 9
x + 9 = 2x + 1