MATHEMATICS HIGH SCHOOL

The perimeter of a parallelogram is 50inches. If the length of one side is 15

​inches, what is the length of a side adjacent to​ it?

Answers

Answer 1
Answer: Given:
Perimeter of parallelogram = 50 inches
Length of one side is 15 inches

Find the length of the adjacent side.

Parallelograms have 4 sides and its measures of opposite sides are equal.

Perimeter = 2a + 2b
where:
a are opposite sides of equal measure
b are opposite sides of equal measure

50 inches = 2(15 inches) 
50 inches = 30 inches + 2b
50 inches - 30 inches = 2b
20 inches = 2b
20 inches / 2 = b
10 inches = b 

The length of the adjacent side is 10 inches.

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The width (W) of a rectangular garden is 7 feet longer than the length (L). The area of the garden is 30 square feet

Answers

Well you have to remember that area is length times width. So 4.285714286 Or since most gardens are shaped like a square. You would have to 7×7+7×(number above) to get the answer. Hope that helps

2 less than one third of the points that the Panthers scored

Answers

1/2 p-2 = x is the answer to 2 less than one third of the points the panthers scored...
So the score was 10. Divide 10 by 3 to see what exactly one third was which is 3.3. Then subtract 2 from 3.3, which will be 1.3!

A biologist wants to determine the effect of a new fertilizer on tomato plants. What could be a response variable?

Answers

Answer:

Step-by-step explanation:

The response variable is also called as the outcome variable or dependent variable. The changes occurring in the response variable is due to changes in the independent variable.

In the given situation, the response of new fertilizer on the tomato plants is to be checked. Hence, the growth of tomato plants is the response variable. The new fertilizer is the independent variable.

Plant growth could be a response variable! :)

What is true concerning the lines graphed by the system of equations shown below 8x+6=2y 12x-3=3y

Answers

Answer: the lines are parallel to each other

Step-by-step explanation:

First, what we can do is solve both equations for y, putting them in slope-intercept form, y = mx + b:

2y = 8x + 6                            3y = 12x - 3
/ 2      / 2                                / 3       / 3
y = 8x/2 + 6/2                         y = 12x/3 - 3/3
y = 4x + 3                                y = 4x - 1

For both equations, m = 4, or they have the same slope of 4. Lines that have the same slope are parallel to each other.

I hope this helps! :)

How to find the perimeter and the area of a rectangle on a coordinate plane using the distance formula? : A(3,8) B(5,4) C(-4,-1) D(-6,3) Round to the nearest tenth if necessary.

Answers

I used some site to plot the points. 

First, let's recall the formulas for Perimeter and Area of a Rectangle.
Perimeter = 2(l+w)
Area = l×w
Also, the distance formula is
D = \sqrt{( x_(2)-x_(1))^2+{(y_(2)-y_(1))^2}

Now, we need to determine l and w.
So, the length is the distance of AD or BC
and the width is the distance of DC or AB
(I'll just use the sides that I've labelled for ease)

So first to determine the length, we need to calculate the distance of AD
Points are A(3,8) and D(-6,3) 
x_(1) =3, x_(2) =8, y_(1) =6, y_(2) =-3
D_(AD)= \sqrt{( 6-3)^2+{(-3-8)^2}
D_(AD)= √((3)^2+(-11)^2)
D_(AD)= √(9+121)
D_(AD)= √(130) ≈ 11.40
So the length of the rectangle is 11.40 units.

Now, the width!
So first to determine the width, we need to calculate the distance of DC
Points are D(-6,3) and C(-4,-1)
x_(1) =6, x_(2) =-4, y_(1) =-3, y_(2) =-1
D_(DC)= \sqrt{(-4-6)^2+{(-1- -3)^2}
<span>D_(DC)= \sqrt{(-4-6)^2+{(-1+3)^2}
D_(DC)= √((-10)^2+(2)^2)
D_(AD)= √(100+4)
D_(AD)= √(104) ≈ 10.20
So the width of the rectangle is ≈10.20 units.

Let's now solve for Perimeter and Area using
l = 11.40
w = 10.20

Perimeter = 2(l+w)
Perimter = 2(11.40+10.20)
Perimter = 2(21.60)
Perimter = 43.2 units

Area = l×w
Area = (11.40)(10.20)
Area = 116.28 
Area = 116.3 units² (rounding)

In conclusion, given points A(3,8) B(5,4) C(-4,-1) D(-6,3), the Perimeter is 43.2 units and the Area is  ≈116.3 units² using the distance formula. 

A species of plant experiences exponential growth after it is introduced into an area where it has never been. Which statement best describes exponential growth?

Answers

Answer:

C. Within a few years the population increases dramatically

True. As we can see on the functionA = A_o e^(rt) if we increase the time by 10 units for example the final amount is increasing by a factor of e^(10)=22026.47 and that represent a dramatically increase.

Step-by-step explanation:

When we have a exponential growth model the general formula is given by:

A = A_o e^(rt)

Since says "growth" the rate of increase r>0, A_o represent the initial amount and A the amount after the time t.

Assuming the possible options for the answer. We analyze one by one

A. Each individual plant grows much larger than usual

False, for this model we assume that all the individuals in the population modeled have similar characteristics, because if the individuals are different we can't use a deterministic model like this one.

B. The population immediately decreases

False. We are assuming that the model is for a growth rate so then is not possible to have a decrease.

C. Within a few years the population increases dramatically

True. As we can see on the functionA = A_o e^(rt) if we increase the time by 10 units for example the final amount is increasing by a factor of e^(10)=22026.47 and that represent a dramatically increase.

D. The specie's reproductive potential declines

False, we are considering a growth model in which it makes no sense to consider that the potential, population or quantity measured decrease.
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