-3x · 5x? 3 B) -15x3 х A) 15 C)

L = 20 and W = 15
Explanation:
Let's review what is known about the rectangle in question - the area is 300 cm squared and the ratio of the Length to the Width (which I'll shorten to L and W) is 4:3.
Let's start with the ratio. We know that they are related to each other - 4 of a basic unit of length for L and 3 of that same basic unit of length for W. So we can say that
L =
4
x
and W =
3
x
We also know from the formula for the area of a rectangle that LW = Area of the rectangle. Substituting in the terms with the x's in them gives us
(
4
x
)
(
3
x
)
=
300
so let's solve for x:
12
x
2
=
300
x
2
=
300
12
=
25
x
=
√
25
=
5
(ignoring the negative root since that makes no sense in this application)
Substituting x back into our equations for L and W, we get
L =
4
(
5
)
=
20
and W =
3
(
5
)
=
15
Checking our work - there is a ratio of L:W of 4:3. And LW =
20
⋅
15
=
300
Hope this is what you meant

5 0

4 years ago

Janelle drew KL in isosceles trapezoid FGHJ to create similar trapezoids FKLJ and KGHL. Based on the given information, what are

Tems11 [23]

Answer:

w = 36 centimeters

y = 24 centimeters

Step-by-step explanation:

The exact question is as follows :

Given - Janelle drew KL in isosceles trapezoid FGHJ to create similar trapezoids FKLJ and KGHL.

To find - Based on the given information, what are the values of y and w in centimeters?

Solution -

We can see that from the diagram,

Trapezoid FKLJ is 3 times bigger than Trapezoid KGHL

So,

The side KL = 3 times side GH

⇒12 = 3×4

⇒12 = 12 centimeters

So,

side FJ = 3 times side KL

⇒w = 3×12

⇒w = 36 centimeters

Now,

The side KF = 3 times side KG

⇒KF = 3×8

⇒KF = 24

Now,

We know,

In isosceles trapezoid two opposite sides (the bases) are parallel, and the two other sides (the legs) are of equal length

So,

Side LJ = side KF

⇒y = 24 centimeters

∴ we get

w = 36 centimeters

y = 24 centimeters

5 0

3 years ago

The population of a city is modeled by P(t)=0.5t2 - 9.65t + 100,where P(t) is the population in thousands and t=0 corresponds to

ira [324]

Answer:

Step-by-step explanation:

This equation is a positive parabola, opening upwards. Parabolas of this type have a vertex that is a minimum value. In order to find the year where the population was the lowest, we have to complete the square to find the vertex. The rule for completing the square is to first set the parabola equal to 0, then next move the constant over to the other side of the equals sign. The leading coefficient on the x-squared term HAS to be a positive 1. Ours is a .5, so will factor it out. Doing those few steps looks like this:

$.5(t^2-19.3t)=-100$

Next we take half the linear term, square it, and add it to both sides. Don't forget the .5 sitting out front there as a multiplier. Our linear term is 19.3. Taking half of that gives us 9.65, and 9.65 squared is 93.1225

$.5(t^2-19.3t+93.1225)=-100+46.56125$

In this process, we have created a perfect square binomial on the left. Stating that binomial and doing the addition on the right looks like this:

$.5(t-9.65)^2=-106.8775$

Now finally we will divide both sides by .5 then move over the constant again to get the final vertex form of this quadratic:

$(t-9.65)^2+106.8775=y$

From this we can see that the vertex is (9.65, 106.8775) which translates to the year 2009 and 107,000 approximately.

In our situation, that means that the population was at its lowest, 107,000 in the year 2009.

For part b. we will replace the y in the original quadratic with a 200,000 and then factor to find the t values. Setting the quadratic equal to 0 allows us to factor to find t:

$0=.5t^2-9.65t-199900$

If you plug this into the quadratic formula you will get t values of

642.02 and -622.72

The two things in math that will never EVER be negative are distances/measurements and time, so we can safely disregard the negative value of t. Since the year 2000 is our t = 0 value, then we will add 642 years to the year 2000 to get that

In the year 2642, the population in this town will reach 200,000 (as long as it grows according to the model).

7 0

4 years ago

-3x · 5x? 3 B) -15x3 х A) 15 C) –8x4 D) 2x2