Answer:
7 and 1
Step-by-step explanation:
Let the numbers be a and b.
<u>A positive number is 7 times another number:</u>
<u>If 3 is added to both the numbers then one of the new number becomes 5 by 2 times the other new number:</u>
<u>To solve this we substitute </u><u>a</u><u> with </u><u>7b</u><u> in the second equation:</u>
- 7b + 3 = 5/2 × (b +3) ⇒ multiplying both sides by 2
- 14b + 6 = 5b + 15 ⇒ collecting like terms
- 14b - 5b = 15 - 6
- 9b = 9
- b = 1 ⇒ solved for b
<u>Then, finding a:</u>
- a= 7b
- a=7*1
- a= 7 ⇒ solved for a
<u>So the numbers are</u> 7 and 1
Answer:

Step-by-step explanation:
Alrighty let's do this.
We know that formula for the Area of a triangle is:

They give us the area as
, so let's include it in the equation.

Now we reach a stage where we have 2 unknown variables! That means we can't solve it in its current state. So the idea you should have in cases like these where you have 2 or more unknown variables is, "Can I represent this one variable in terms of another variable?" In this case you can do exactly that. You can represent height in terms of length of the base. We are told the height of the triangle is 4 meters less than the base. That is telling us that 
So replace
in the equation with
.
You will now get:

Now we can work towards solving. Let's get simplifying.

bring everything to one side so we can make a quadratic and factor:

We get that
.
Since we need the height of the triangle we'll need to call back on what h is. We found earlier that
, so to find h, we just sub in our b value into that.

We find that 
Answer:
OPTION A: 2x + 3y = 5
Step-by-step explanation:
The product of slopes of two perpendicular lines is -1.
We rewrite the given equation as follows:
2y = 3x + 2
⇒ y = 
The general equation of the line is: y = mx + c, where 'm' is the slope of the line.
Here, m =
.
Therefore, the slope of the line perpendicular to the line given =
because
.
To determine the equation of the line passing through the given point and a slope we use the Slope - One - point formula which is:
y - y₁ = m(x - x₁)
The point is: (x₁, y₁) = (-2, 3)
Therefore, the equation is:
y - 3 =
(x + 2) $
⇒ 3y - 9 = -2(x + 2)
⇒ 3y - 9 = -2x - 4
⇒ 2x + 3y = 5 is the required equation.