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2 years ago

Simplify the problem

Mathematics

1 answer:

Natasha2012 [34]2 years ago

5 0

$\frac{6}{10x^2} \div \frac{6}{10x^3-60x^2} = \frac{6}{10x^2} \cdot \frac{10x^3-60x^2}{6} =\frac{1}{10x^2} \cdot \frac{10x^2(x-6)}{1} =x-6$

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Today is sunday. Tom starts to read a book with 490 pages today. Sundays he reads 25 pages and on all other days he reads 4 page

mrs_skeptik [129]

Based on the information given, it can be noted that Tom will use 117 days to read the book.

How to solve a equation.

Based on the information given, we are informed that Tom starts to read a book with 490 pages today. Sundays he reads 25 pages and on all other days he reads 4 pages.

Let the number of days be represented by x. Therefore, the equation to solve the question will be:

25 + (4 × x) = 490

25 + 4x = 490

4x = 490 - 25

4x = 465

x = 465/4

x = 116.25

x = 117

Therefore, he'll use 117 days to read the book.

Learn more about equations on:

brainly.com/question/13763238

6 0

2 years ago

A biologist has been observing a tree's height. This type of tree typically grows by 0.22 feet each month. Fifteen months into t

Lyrx [107]

Data:

x: number of months

y: tree's height

Tipical grow: 0.22

Fifteen months into the observation, the tree was 20.5 feet tall: x=15 y=20.5ft (15,20.5)

In this case the slope (m) or rate of change is the tipical grow.

m=0.22

To find the line's slope-intercep equation you use the slope (m) and the given values of x and y (15 , 20.5) in the next formula to find the y-intercept (b):

$\begin{gathered} y=mx+b \\ 20.5=0.22(15)+b \\ 20.5=3.3+b \\ 20.5-3.3=b \\ 17.2=b \end{gathered}$

Use the slope(m) and y-intercept (b) to write the equation:

$\begin{gathered} y=mx+b \\ \\ y=0.22x+17.2 \end{gathered}$ A) This line's slope-intercept equation is: y=0.22x+17.2

B) To find the height of the tree after 29 months you substitute in the equation the x for 29 and evaluate to find the y:

$\begin{gathered} y=0.22(29)+17.2 \\ y=6.38+17.2 \\ \\ y=23.58 \end{gathered}$ Then, after 29 months the tree would be 23.58 feet in height

C) In this case as you have the height and need to find the number of moths you substitute the y for 29.96feet and solve the equation for x, as follow:

$\begin{gathered} 29.96=0.22x+17.2 \\ 29.96-17.2=0.22x \\ 12.76=0.22x \\ \frac{12.76}{0.22}=x \\ \\ 58=x \end{gathered}$ Then, after 58 months the tree would be 29.96feet tall

3 0

1 year ago

a road follows the shape of a parabola f(x)=3x2– 24x + 39. A road that follows the function g(x) = 3x – 15 must cross the stream

Nonamiya [84]

the coordinates where the bridges must be built is $(3,-6)$ and $(6,3)$ .

<u>Step-by-step explanation:</u>

Here we have , a road follows the shape of a parabola f(x)=3x2– 24x + 39. A road that follows the function g(x) = 3x – 15 must cross the stream at point A and then again at point B. Bridges must be built at those points.We need to find Identify the coordinates where the bridges must be built. Let's find out:

Basically we need to find values of x for which f(x) = g(x) :

⇒ $f(x)-g(x)=0$