Fracción equivalente de 1/3

Three numbers are in the ratio 3:9:10. If 10 is added to the last number, then the three numbers form an arithmetic progression.

MrRa [10]

Answer:

 The numbers are 6, 18, and 30 

Step-by-step explanation:

If the three numbers are in the ratio of 3:9:10,

let the numbers be 3x, 9x and 10x.

If 10 is added to the last number to form an arithmetic progression

Then, 3x 9x (10x+10) are the progression

The common difference of an arithmetic progression (d) = T₂ - T₁ = T₃ - T₂

T₂-T₁ = T₃ - T₂ .............. Equation 1

Where T₁ = first term of the progression, T₂ = Second term of the progression, T₃ = third term of the progression

Given: T₁ = 3x, T₂ = 9x, T₃ = 10x +10

Substituting these values into equation 1

9x-3x = (10x+10)-9x

Solving the equation above,

3x = 10+x

3x-x = 10

2x = 10

x = 10/2

x = 2.

Therefore the numbers are 6, 18, and 30 

7 0

4 years ago

Use unit rate to find the unknown value 16/32 equals blank over 14

grigory [225]

Answer:

x = 7

Step-by-step explanation:

simplify 16/32

16/32 divided by 8/8=2/4

2/4 divided by 2=1/2

so

1/2 = x/14

to get to 14 from 2 you need to multiply by 7

1/2 times 2/2 = 7/14

so x = 7

5 0

3 years ago

When the sum of \, 528 \, and three times a positive number is subtracted from the square of the number, the result is \, 120. F

aleksandr82 [10.1K]

Let $x$ be the unknown number. So, three times that number means $3x$ , and the square of the number is $x^2$

We have to sum 528 and three times the number, so we have $528+3x$

Then, we have to subtract this number from $x^2$ , so we have

$x^2-(3x+528)$

The result is 120, so the equation is

$x^2 - 3x - 528 = 120 \iff x^2 - 3x - 648 = 0$

This is a quadratic equation, i.e. an equation like $ax^2+bx+c=0$ . These equation can be solved - assuming they have a solution - with the following formula

$x_{1,2} = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

If you plug the values from your equation, you have

$x_{1,2} = \dfrac{3\pm\sqrt{9-4\cdot(-648)}}{2} = \dfrac{3\pm\sqrt{9+2592}}{2} = \dfrac{3\pm\sqrt{2601}}{2} = \dfrac{3\pm51}{2}$

So, the two solutions would be

$x = \dfrac{3+51}{2} = \dfrac{54}{2} = 27$

$x = \dfrac{3-51}{2} = \dfrac{-48}{2} = -24$

But we know that x is positive, so we only accept the solution $x = 27$

6 0

3 years ago

An object’s speed decreases by 6% for each minute that it is slowing down. What is the percent that it’s speed will decrease ove

Zarrin [17]

It says decreasing so you have to turn it into a percent (.06%) and then sub tract that from 1. After that you put that into an equation.

3 0

3 years ago

Pre-Calculus Help? Polar and Parametric Equations?

Paraphin [41]

$\bf x=rcos(\theta )\implies \cfrac{x}{cos(\theta )}=r\\\\
y=rsin(\theta )\implies \cfrac{y}{sin(\theta )}=r
\\\\
-------------------------------\\\\
r=3cos(\theta )\implies \cfrac{x}{cos(\theta )}=3cos(\theta )\implies x=3cos(\theta )cos(\theta )
\\\\\\
\boxed{x=3cos^2(\theta )}
\\\\\\
r=3cos(\theta )\implies \cfrac{y}{sin(\theta )}=3cos(\theta )\implies \boxed{y=3cos(\theta )sin(\theta )}$

7 0

3 years ago