Help pls fam whats 10x58

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

2 years ago

You have $60 and your sister has $120. You are saving $7 per week and your sister is saving $5 per week. How long will it be bef

Akimi4 [234]

Answer:

27 weeks

Step-by-step explanation:

6 0

3 years ago

The end points of line segment PQ are P(1, 3), and Q(7, 7). What is the midpoint of line segement PQ?

dangina [55]

Answer:

D) (4, 5)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Coordinates (x, y)
Midpoint Formula: $\displaystyle (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Step-by-step explanation:

Step 1: Define

Point P(1, 3)

Point Q(7, 7)

Step 2: Identify

P(1, 3) → x₁ = 1, y₁ = 3

Q(7, 7) → x₂ = 7, y₂ = 7

Step 3: Find Midpoint

Simply plug in your coordinates into the midpoint formula to find midpoint

Substitute in points [Midpoint Formula]: $\displaystyle (\frac{1+7}{2},\frac{3+7}{2})$
[Midpoint] Add: $\displaystyle (\frac{8}{2},\frac{10}{2})$
[Midpoint] Divide: $\displaystyle (4,5)$

8 0

3 years ago

A group of researchers wants to develop an experiment to determine whether a new drug effectively treats hypothyroidism. The res

Rashid [163]

Some possible ethical issues to this type of testing that they are subjected to unpleasant and hazardous procedures, as well as stress and injury.

<h3>What is experiment?</h3>

Any well-defined method that yields an observable outcome that cannot be precisely predicted in advance is referred to as a experiment. To avoid any ambiguity or surprise, a experiment must be properly defined.

A) Because human experimentation is immoral, animal research has been employed as a research approach.

However, using animals is unethical because they are subjected to unpleasant and hazardous procedures, as well as stress and injury. The use of non-animal methods to substitute animal methods as much as possible will provide both ethical and technical benefits. Researchers should make the use of non-animal methods for a top priority experiments.

B) Even though the purpose of an experiment is to ensure success in rabbits, this is incorrect in people because action is what will operate properly.

The absence of thyroid-stimulating hormone in rabbit serum is a mistaken notion. As a result, it is preferable to test the drug further, and it was a success. As a result, there will be no dysfunctionality for humans.

Thus, some possible ethical issues to this type of testing that they are subjected to unpleasant and hazardous procedures, as well as stress and injury.

Learn more about the experiment here:

brainly.com/question/14298568

#SPJ1

8 0

1 year ago

A: 7,500 miles

kvasek [131]

Answer:

the minimal number is 3

Step-by-step explanation:

6 0

3 years ago