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3 years ago

The difference of the square of a number and 40 is equal to 3 times that number. Find the positive solution.

Mathematics

1 answer:

Wewaii [24]3 years ago

5 0

Answer: The answer is 8.

Step-by-step explanation: The first step is to convert the expression into figures. We shall call the unknown number Y. So if we are told “the square of a number,” that means Y squared, or better still, Y^2. Further we are told “the difference between the square of a number and 40” and that can be written as;

Y^2 - 40.

Next we are told that this expression is equal to 3 times that number (that is 3Y). That can now be written out as follows,

Y^2 - 40 = 3Y

If we move all expressions to one side of the equation, what we would have is,

Y^2 - 3Y -40 = 0

(Remember that when a positive value crosses to the other side of an equation it becomes negative and vice versa)

We now have a quadratic equation

Y^2 -3Y - 40 = 0

By factorizing we now have

(Y -8) (Y + 5) = 0

Therefore Y - 8 = 0 or

Y + 5 = 0

Hence, Y = 8 or Y = -5

Since we are asked to calculate the positive solution, Y = 8

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A standard piece of paper is 0.05 mm thick. Let's imagine taking a piece of paper and folding the paper in half multiple times.

tatyana61 [14]

Answer:

(a) $g(n)=0.05\cdot 2^n$

(b) $g^{-1}(n)=\log_{2}20g(n)$

Step-by-step explanation:

Part A

The paper's thickness = 0.05mm

When the paper is folded, its width doubles (increases by 100%).

The thickness of the paper grows exponentially and can be modeled by the function:

$g(n)=0.05(1+100\%)^n\\\\g(n)=0.05\cdot 2^n$

Part B

$g(n)=0.05\cdot 2^n\\2^n=\dfrac{g(n)}{0.05}\\ 2^n=20g(n)\\$Changing to logarithm form, we have:\\\log_{2}20g(n)=n\\$Therefore:\\g^{-1}(n)=\log_{2}20g(n)$

Part C

If the thickness of the paper, g(n)=384,472,300,000 mm

Then:

$g^{-1}(n)=\log_{2}20g(n)\\g^{-1}(n)=\log_{2}20\times 384,472,300,000\\=\dfrac{\log 20\times 384,472,300,000}{\log 2} \\g^{-1}(n)=42.8 \approx 43\\n=43$

You must fold the paper 43 times to make the folded paper have a thickness that is the same as the distance from the earth to the moon.

3 0

2 years ago

HELP PLEASE

Vikki [24]

Answer:

The answer is 1.35 answer (1). You can graph both equations to give you the answer.

Step-by-step explanation:

Graph the equations and see where they intersect.

5 0

2 years ago

Read 2 more answers

Simplify completely quantity x squared plus 4 x minus 45 all over x squared plus 10 x plus 9 and find the restrictions on the va

dem82 [27]

(x² + 4x - 45)/(x² + 10x + 9)

Numerator = N = x² + 4x - 45 
= x² + 9x - 5x - 45
= (x² + 9x) - (5x + 45)
= x(x + 9) - 5(x + 9)
= (x + 9)(x - 5)

Denominator = D = x² + 10x + 9 
= x² + x + 9x + 9
= (x² + x) + (9x + 9)
= x(x + 1) + 9(x + 1)
= (x + 1)(x + 9)

Hence, the given expr. = N/D 
= {(x + 9)(x - 5)}/{(x + 1)(x + 9)
= (x - 5)/(x + 1)

Restrictions : x ≠ - 1, x = 5 

I hope my answer has come to your help. Thank you for posting your question here in Brainly.

7 0

3 years ago

Read 2 more answers

4x-5=x-1+3x I need help

labwork [276]

Answer:

x = no solutions

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Step-by-step explanation:

Step 1: Define equation

4x - 5 = x - 1 + 3x

Step 2: Solve for x

Combine like terms: 4x - 5 = 4x - 1
Subtract 4x on both sides: -5 ≠ -1

Here we see that -5 does not equal -1.

∴ This equation has no solutions.

8 0

2 years ago

I hope I’m correct but correct me if I’m wrong is this complementary?

Nesterboy [21]

Answer:

Linear Pair

Step-by-step explanation:

The kind of angle formed by a and b when put together is a straight angle.

A straight angle means that a+b=180 degrees.

a and b are supplementary.

They are also a linear pair since they are already put together. Meaning, they share a common vertex and a common side while forming a straight angle together.

They aren't complementary because the angles exceed 90 degrees when added together. Complementary angles should add up to 90 degrees exactly.

They aren't vertical angles because they don't happen across from each other in two intersecting lines. (Note: Vertical angles are also congruent.)

They aren't alternate interior because they don't even happen at two different intersections. So we would definitely not go to to that, alternate exterior, same side interior, same exterior, or corresponding angles. Because all of these require the angles to happen at two different intersections.

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2 years ago