What do you think of when you hear "decimal notation

The product of 4 and a number f decreased by 2 is 15

Debora [2.8K]

Answer: The number is: "2 " .

__________________________________________

Step-by-step explanation:

__________________________________________

Write the expression; which is an equation, as follows:

__________________________________________

" 4x − 12 = 2(-x) " ; in which "x" represents "the number for which we shall solve" .

___________________________________________

Note:

If the "number" = "x" ; the "opposite of the number" = " -x " ;

___________________________________________

Rewrite as: " 4x − 12 = -2x " ;

_____________________________________________

→ Add "12" ; & add "2x" ; to EACH SIDE of the equation:

4x − 12 + 12 + 2x = -2x + 12 + 2x ;

to get: 6x = 12 ;

____________________________________________________

Now, divide each side of the equation by "6" ;

to isolate "x" on one side of the equation; & to solve for "x" ;

____________________________________________________

6x / 6 = 12 / 6 ;

to get: x = 2 .

____________________________________________________

Answer: The number is: "2 " .

____________________________________________________

Let us check our answer, by plugging in "2" for "x" in our original equation:

_____________________________________________________

→ " 4x − 12 = 2(-x) " ;

Let us plug in "2" for "x" ; to see if the equation holds true; that is; if both side of the equation are equal; when "x = 2" ;

→ " 4(2) − 12 = ? 2(-2) ??

→ 8 − 12 = ? -4 ? ;

→ -4 = ? -4 ?? Yes!

__________________________________________________

7 0

3 years ago

Read 2 more answers

How to solve 2x(x+3)=2x^2+15

Travka [436]

Answer: x = 5/2 = 2.5

Step-by-step explanation:

Given expression

2x (x + 3) = 2x² + 15

Expand parentheses and apply the distributive property

2x · x + 2x · 3 = 2x² + 15

2x² + 6x = 2x² + 15

Subtract 2x² on both sides

2x² + 6x - 2x² = 2x² + 15 - 2x²

6x = 15

Divide 6 on both sides

6x / 6 = 15 / 6

x = 15/6

$\boxed{x=\frac{5}{2} }$

Hope this helps!! :)

Please let me know if you have any questions

5 0

3 years ago

Read 2 more answers

What's the volume to this prism?

DIA [1.3K]

Answer:

36 cubic inch

Step-by-step explanation:

The formula for the volume of a rectangular prism is:

$V=whl$

----------------------------------------------------------------------------------------------------------------

So:

6 × 3 × 2 = 36

----------------------------------------------------------------------------------------------------------------

Have a good day :)

8 0

3 years ago

I WILL MARKED BRAINLIEST IF YOU COULD ANSWER THIS!

tester [92]

Answer:

s = -2400t + 17400

Step-by-step explanation:

Let's say t is the x value on a coordinate plane, and s is the y. Then, we have the points (0, 17400) and (6, 3000). The slope of these is 14400/-6 or -2400.

Now we just have the equation y = -2400x + b, and from the point (0, 17400) we can find that b is 17400. So, we have y = -2400x + 17400. Convert these back into t and s and you get your answer, s = -2400t + 17400.

6 0

3 years ago

Suppose X, Y, and Z are random variables with the joint density function f(x, y, z) = Ce−(0.5x + 0.2y + 0.1z) if x ≥ 0, y ≥ 0, z

kompoz [17]

a.

$f_{X,Y,Z}(x,y,z)=\begin{cases}Ce^{-(0.5x+0.2y+0.1z)}&\text{for }x\ge0,y\ge0,z\ge0\\0&\text{otherwise}\end{cases}$

is a proper joint density function if, over its support, $f$ is non-negative and the integral of $f$ is 1. The first condition is easily met as long as $C\ge0$ . To meet the second condition, we require

$\displaystyle\int_0^\infty\int_0^\infty\int_0^\infty f_{X,Y,Z}(x,y,z)\,\mathrm dx\,\mathrm dy\,\mathrm dz=100C=1\implies \boxed{C=0.01}$

b. Find the marginal joint density of $X$ and $Y$ by integrating the joint density with respect to $z$ :

$f_{X,Y}(x,y)=\displaystyle\int_0^\infty f_{X,Y,Z}(x,y,z)\,\mathrm dz=0.01e^{-(0.5x+0.2y)}\int_0^\infty e^{-0.1z}\,\mathrm dz$

$\implies f_{X,Y}(x,y)=\begin{cases}0.1e^{-(0.5x+0.2y)}&\text{for }x\ge0,y\ge0\\0&\text{otherwise}\end{cases}$

Then

$\displaystyle P(X\le1.375,Y\le1.5)=\int_0^{1.5}\int_0^{1.375}f_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy$

$\approx\boxed{0.12886}$

c. This probability can be found by simply integrating the joint density:

$\displaystyle P(X\le1.375,Y\le1.5,Z\le1)=\int_0^1\int_0^{1.5}\int_0^{1.375}f_{X,Y,Z}(x,y,z)\,\mathrm dx\,\mathrm dy\,\mathrm dz$

$\approx\boxed{0.012262}$

7 0

3 years ago