MATHEMATICS HIGH SCHOOL

The perimeter of a square garden is to be at least 30 feet but not more than 64 feet. Find all possible values for the length of its sides.

Answers

Answer 1
Answer:

Answer:

7.5\leq x\leq 16

Step-by-step explanation:  

Let x be the length of each side of square.

Since the perimeter of the square is 4 times the length of each side, so perimeter of our given circle will be 4x.

We have been given that the perimeter of a square garden is to be at least 30 feet but not more than 64 feet.

This means the perimeter of the garden should we greater than or equal to 30 feet and less than or equal to 64 feet.

We can represent this information in an equation as:

30\leq 4x\leq64

Let us divide our inequality by 4 to solve for x.

(30)/(4)\leq (4x)/(4)\leq(64)/(4)

7.5\leq x\leq 16

We can represent our answer in interval notation as: [7.5,16]

Therefore, the length of the square's side can be any number between 7.5 feet and 16 feet including both 7.5 and 16 as well.
Answer 2
Answer: 4x \in <30.64>/:4 \n x \in <7.5,16>

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The length of a rectangle is five inches less than twice its width. If the rectangle has a perimeter of 80 inches, findthe length and width.

Answers

the length the width the perimeter
50 + 30 = 80

What is the value of x in the solution to the system of equations? 4x - 2y = 5 y = 3x - 1​

Answers

Answer:

\huge\boxed{\sf x = -2}

Step-by-step explanation:

4x - 2y = 5 -------------------------------(1)

y = 3x - 1 ----------------------------------(2)

Put Eq. (2) in (1)

4x - 2(3x-1) = 5

4x - 6x + 1 = 5

-2x + 1 = 5

Subtracting 1 to both sides

-2x = 5 - 1

-2x = 4

Dividing both sides by -2

x = 4 / -2

x = -2

\rule[225]{225}{2}

Hope this helped!

~AnonymousHelper1807

Answer:

X = 7

Step-by-step explanation:

Please mark brainliest.

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. A hot air balloon descends at a rate of 320 feet per minute for 3 minutes. Use integers to calculate and represent the balloons total change in altitude. Math symbols Relations Geometry Groups Trigonometry Statistics Greek Previous Next

Answers

The total change in altitude= 960ft.

Step-by-step explanation:

Rate at which balloon descend = 320 ft per minute

Time = 3 mins

Total height descended = 320 x 3

= 960 ft.

The total change in altitude= 960ft.

Find the vertex, focus, directrix, and focal width of the parabola: -1/40x^2=y

Answers

for
(x-h)^2=4p(y-k)
vertex is (h,k)
distance from vertex to directix=p=distance from vertex to focus
|4p|=focal width

remember, focus is on the side of the parabola where it opens and directix is at the back
when p is negative, it opens down
when p is positive, it opens up

look at equation
-1/40(x-0)^2=(y-0)
times -40 to both sides
(x-0)^2=-40(y-0)
(x-0)^2=4(-10)(y-0)
vertex=(0,0)
p=-10,it's negative so it opens down

focus is 10 units below vertex (y direction)
focus=(0,-10)

diretix is 10 above
directix is y=10

focal width=|4p|=|4(-10)|=|-40|=40




vertex=(0,0)
focus=(0,-10)
directix is y=10
focal width=40 units

Bc reflects about a line such that N is the reflection of B and O is the reflection of C. Point N is shown on the coordinate plane, but point O is not. What will the coordinates of point O be?

Answers

From my research, the coordinate points can be found on image below. Since N is the reflection of B and O is the reflection of C, if we were to draw a line to the right of N and a vertical line below C, the point of intersection of these two lines should give us the location of point O. Doing just that, point O is found at (5,5).

The coordinates of point O of the given Reflection is; 5, 5

How to find the point coordinates?

The coordinates point is missing and so I have attached it.

Now, from the question, we are told that N is the reflection of B and O is the reflection of C. Thus, from the attached image, drawing a line to the right of N and a vertical line below C, the point of intersection of these two lines would give us the location of point O.

Drawing a line to the right of N and a vertical line below C, the point of intersection of these two lines which is point O has coordinates at (5,5).

Read more about Point Coordinates at; brainly.com/question/17206319

#SPJ5

Consider the following set of equations:Equation A: y = 2x + 4
Equation B: y = 3x + 1

Which of the following is a step that can be used to find the solution to the set of equations?
2x + 4 = 3x + 1
2x = 3x + 4
2x + 4 = 3x
2x + 1 = 3x + 4

Answers

the first one 2x+4= 3x+1

Answer:

a

Step-by-step explanation:
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