What is 10 times 3 in standard form

What is the result of a dilation of scale factor 3 centered at the origin of the line 2y + 3x=10?? PLEASE HELP PLEASEEEEEEEEE

maks197457 [2]

Given:

The equation of a line is:

$2y+3x=10$

The line is dilated by factor 3.

To find:

The result of dilation.

Solution:

The equation of a line is:

$2y+3x=10$

For $x=0$ ,

$2y+3(0)=10$

$2y+0=10$

$y=\dfrac{10}{2}$

$y=5$

For $x=2$ ,

$2y+3(2)=10$

$2y+6=10$

$2y=10-6$

$2y=4$

Divide both sides by 2.

$y=\dfrac{4}{2}$

$y=2$

The given line passes through the two points A(0,5) and B(2,2).

If the line dilated by factor 3 with origin as center of dilation, then

$(x,y)\to (3x,3y)$

Using this rule, we get

$A(0,5)\to A'(3(0),3(5))$

$A(0,5)\to A'(0,15)$

Similarly,

$B(2,2)\to B'(3(2),3(2))$

$B(2,2)\to B'(6,6)$

The dilated line passes through the points A'(0,15) and B'(6,6). So, the equation of dilated line is:

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

$y-15=\dfrac{6-15}{6-0}(x-0)$

$y-15=\dfrac{-9}{6}(x)$

$y-15=\dfrac{-3}{2}x$

Multiply both sides by 2.

$2(y-15)=-3x$

$2y-30=-3x$

$2y+3x=30$

Therefore, the equation of the line after the dilation is $2y+3x=30$ .

3 0

3 years ago

The temperature of a city changed -24 degrees Celsius over a 6 week period. Write an expression the show the average change in t

Ne4ueva [31]

Answer:

The expression is (-24) / 6 = -4degrees which means that in each week the average change in temperature was -4 degrees Celsius.

Step-by-step explanation:

Change in a quantities can as well be interpreted as rate of change which is used in many everyday problems, such as weather forecast, traveling , in science and so on.When we are talking about rate of change it's is usually in ratio such as Miles per hour or feet per second can be used in calculation involving rates of speed. It is how one quality is changing with respect to time , for instance, rate equals distance divided by time: r = d/t.

In finance rate of change is also applicable we can have Unit price which is a particular rate that compares a price to some unit of measure. Example is $64 per dozen.

Therefore, Given from the question,

The temperature of a city changed -24 degrees Celsius ,

Time =6 weeks period.

Then change is r = d/t.

= (-24) / 6

Change = (-24) / 6 = -4 degrees

This means that each week the average change in temperature was -4 degrees Celsius.

3 0

4 years ago

How is experimental probability used to make predictions?

Oksana_A [137]

Experimental Probability is use to help make predictions by using materials that relate to the that probability so see if it could happen in real life.

EX: What is the probability of flipling a coin and landing on heads?

When u flip the coin you will have 2 possible choices..heads or tails..so be flipping a real coin you can see your chances ~Amiya

8 0

3 years ago

Si en una sustracción se disminuye el minuendo en 5 y se aumenta el sustraendo en 5 ¿que sucede con el resultado?

dimaraw [331]

Hi you look so pretty and gorgeous for me and do you want to be my friend.

3 0

3 years ago

A drawer contains 3 white shirts, 2 blue shirts, and 5 gray shirts. A shirt is randomly

shutvik [7]

Answer:

Probability that first shirt is white and second shirt is gray if first shirt selected is set aside = $\frac{1}{4}$

Step-by-step explanation:

Given that

3 white, 2 blue and 5 gray shirts are there.

To find:

Probability that first shirt is white and second shirt is gray if first shirt selected is set aside = ?

Solution:

Here, total number of shirts = 3+2+5 = 10

First of all, let us learn about the formula of an event E:

$P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}$

$P(First\ White) = \dfrac{\text{Number of white shirts}}{\text {Total number of shirts left}}$

$P(First\ White) = \dfrac{3}{10}$

Now, this shirt is set aside.

So, total number of shirts left are 9 now.

$P(First\ White\ and\ second\ gray) = P(First White) \times P(Second\ Gray)\\\Rightarrow P(First\ White\ and\ second\ gray) = P(First White) \times \dfrac{\text{Number of gray shirts}}{\text{Total number of shirts left}}\\\\\Rightarrow P(First\ White\ and\ second\ gray) = \dfrac{3}{10} \times \dfrac{5}{9}\\\Rightarrow P(First\ White\ and\ second\ gray) = \dfrac{1}{2} \times \dfrac{1}{2}\\\Rightarrow P(First\ White\ and\ second\ gray) = \bold{\dfrac{1}{4} }$

So, the answer is:

Probability that first shirt is white and second shirt is gray if first shirt selected is set aside = $\frac{1}{4}$

4 0

3 years ago