Answer:
a) The polynomial is equivalent to [tex]A = (x-15)^{2}[/tex], and the side length of the playground is [tex]x -15[/tex] feet.
b) The perimeter of the playground, measured in feet, is [tex]p = 4\cdot (x-15)[/tex].
Step-by-step explanation:
a) By Geometry, we know that area of the square is equal to the square of the side length. If [tex]A = x^{2}-30\cdot x +225[/tex] is the area of the square, then must be a perfect square trinomial, that is:
[tex](x-a)^{2} = x^{2}-2\cdot a\cdot x + a^{2}[/tex] (1)
Then, we must observe the following properties:
[tex]-2\cdot a = -30[/tex] (2)
[tex]a = 15[/tex]
[tex]a^{2} = 225[/tex] (3)
[tex]a = 15[/tex]
Therefore, the polynomial is equivalent to [tex]A = (x-15)^{2}[/tex], and the side length of the playground is [tex]x -15[/tex] feet.
b) The perimeter of a square equals four times the side length. That is:
[tex]p = 4\cdot (x-15)[/tex]
The perimeter of the playground, measured in feet, is [tex]p = 4\cdot (x-15)[/tex].
The polynomial that represents the side length is x - 15, and the perimeter of the playground is 4x - 60
The expression of the area is given as:
[tex]A = x^2 - 30x + 225[/tex]
Expand the expression
[tex]A = x^2 - 15x - 15x + 225\\[/tex]
Factorize
[tex]A= (x - 15)^2[/tex]
The area of a square is:
[tex]A = l^2[/tex]
Where l represents the side length.
So, we have:
[tex]l = x - 15[/tex]
The perimeter is then calculated as:
[tex]P = 4l = 4*( x - 15)[/tex]
[tex]P = 4x - 60[/tex]
Hence, the perimeter of the playground is 4x - 60
Read more about polynomials at:
https://brainly.com/question/4142886
What is the area of this quadrilateral?
2 ft
3 ft
8 ft
8 ft
3 ft
2 ft
A. 40 square feet
B. 80 square feet
C. 24 square feet
D. 20 square feet
MathWiz wya boo??.......
Answer:
i dont see angle S
Step-by-step explanation:
Answer:
108
Step-by-step explanation:
3x + 12 + 5x + 8=180
8x + 20= 180
8x= 160
x= 20
Angle S:
5x + 8
5(20) + 8
100 + 8
108
Which image shows a reflection ABC
Answer:
A I think
Step-by-step explanation
Answer:
A
Step-by-step explanation:
I am not sure but I think it's A
If a linear system has no solution, what happens when you try to solve the system by adding or subtracting?
Lori is running in a marathon, which is 26.2 miles long. So far she has run one-tenth of the marathon. How far has Lori run?
Answer:
2.62
Step-by-step explanation:
Please help me......
Answer:
[tex]\frac{3}{8}[/tex]
Step-by-step explanation:
[tex]A=6*\frac{1}{4} ^2\\\\A=6*\frac{1}{16} \\\\A=\frac{6}{16} \\\\A=\frac{3}{8}[/tex]
Answer:
[tex]A = \frac{3}{8}ft^2[/tex]
Step-by-step explanation:
Using the given formula, [tex]A=6s^2[/tex], and the given value for the side length of the cube, [tex]\frac{1}{4}[/tex] foot, substitute the given value into the equation and solve.
[tex]A=6(\frac{1}{4})^2[/tex]
Remember, setting any value to the second power is the same as multiplying the base (the value that is being squared) by itself. Apply this information to the given problem,
[tex]A = 6(\frac{1}{4}*\frac{1}{4})\\\\A = 6(\frac{1}{16})\\\\A = \frac{6}{16}\\\\A = \frac{3}{8}[/tex]
ABC is dilated by a factor of 3 to produce A'B'C'.
Answer:
Im Pretty Sure The Answer is B! :) hope this helps
Step-by-step explanation:
The mass of Jupiter is 1.8987x10/\27 kilograms and is roughly 317.8 times the mass of Earth. The mass of the solar system is about 1.992x10/\30 kilograms. The Sun accounts for about 99.8% of this mass.
a. Find the mass of Earth in kilograms
b. What is the approximate mass of all of the other objects in the solar system, not counting the sun?
c. what percentage of the mass obtained in part b is represented by jupiter?
plsssssssssssssssss help!!!!
Answer:
i dont really get the question
How do you graph (0,4) need help thank you!
Answer:
Just move 4 spaces up
Step-by-step explanation:
Answer:
left 0 up 4
Step-by-step explanation:
What is the volume of the pyramid shown below?
Height = 21 cm
5 cm
5 cm
A 35 cubic centimeters
B 70 cubic centimeters
C 175 cubic centimeters
D 210 cubic centimeters
Volume of a square pyramid = 1/3 x length x width x height
Volume = 1/3 x 5 x 5 x 21 = 175 cubic centimeters.
The answer is C
multiple choice ! pls help
Complete the Area Model by dragging responses to the correct location.
Answer:
Step-by-step explanation:
The solution to the area model equation is x² + 6x + 8.
What is an equation?An equation is an expression that can be used to show the relationship between two or more variables and numbers.
From the diagram we have:
(x + 4)(x + 2)
Multiplying both terms of the equation to get:
= x² + 2x + 4x + 8
Further simplification gives:
= x² + 6x + 8
The solution to the equation x² + 6x + 8.
Find out more on equation at: https://brainly.com/question/1214333
7) Which number line shows the solution to inequality –4k + 5 > 21 ? *
Answer:
Can't see C or D however the image below shows the right one
Step-by-step explanation:
it took 4 hours to drive 240 mile. At this rate, how long does it take to drive 90 miles
Answer:
1 hour and 30 minutes
Step-by-step explanation:
4 hours = 240 miles
1 hour = 240 ÷ 4 = 60 miles
90 ÷ 60 = 1.5 hours =
1 hour and 30 minutes
What is the slope-intercept formula for a line with a rise of 3, a run of 1 and a y-Intercept of 5?
Answer:
y=3x+5
Step-by-step explanation:
y=mx+b
intercept is 5, postive and represents b
Slope is 3 and represents m
homework please help its over due
Step-by-step explanation:
TRIANGLE 1
c = 2√5
= 2 × √5
= √4 × √5
= √20
a = 2
b = ?
b² = c² - a²
= √20² - 2²
= 20² - 4
= 400 - 4
= 396
b = √396
= √36 × √11
= 6 × √11
= 6 √11
TRIAGLE 2
a = 12
b = 6√11
= √396
c = ?
c² = a² + b²
= 12² + √396
= 144 + √396²
= 144 + 396
c = √540
= √36 × √15
= 6 × √15
= 6 √15
Sorry if i wrong. Im beginner in USA server
Which of the following is equivalent to 8x2+20x+
For which interval is the function [tex]f(x)=x\sqrt{4-x^2}[/tex] continuous?
Factor the following trinomial
x2 + 8x – 9
Answer with step-by-step solution:
x^2+8x-9
x^2+9x-x-9
x(x+9)-(x+9)
(x+9)(x-1)
7 Hershey bars costs $6.23. Find the cost for 5 Hershey bars. *
Cory makes a map of his favorite park, using a coordinate system with units of yards. The old oak tree is at position (3, 7) and the granite boulder is at position (-2, 6). How far apart are the old oak tree and the granite boulder? Round to the nearest tenth if necessary
Answer: 5.09 units
Step-by-step explanation:
Given
Coordinates of Old oak tree are (3,7)
Coordinates of granite boulder are (-2,6)
Distance between them is given by distance formula i.e.
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Distance between them is
[tex]\Rightarrow d=\sqrt{(-2-3)^2+(6-7)^2}\\\Rightarrow d=\sqrt{(-5)^2+(-1)^2}\\\Rightarrow d=\sqrt{25+1}=\sqrt{26}\approx 5.09\ \text{units}[/tex]
Your dinner bill was $33.00. If you leave a 20 % tip, how much will the tip be?
Answer:
Your tip would be $6.60
Step-by-step explanation:
Answer:
$39.60 i think :))
Step-by-step explanation:
I HOPE THIS HELPS YOU OUT WITH YOUR QUESTION! PLZ LET ME KNOW IF IT DID! IT MAKES ME FEEL GOOD THAT SOMEONE APPRECIATES IT! ANYWAY, IF YOU HAVE A FEW MINUTES PLZ GOT TO MY PROFILE AND THANK MY ANSWERS (THE MORE THE MERRIER)
Samuel read 8 books in 10 months. What was his rate of reading in books per month?
Answer:
Answer 1.25
Step-by-step explanation:
Tolal moths he take to read 8 book = 10
Therefore, Total month he will take to read 1 book =10/8=1.25
Which of the following is a solution for the equation x over 6 = 7?
Jenny earned 92 of a possible 120 points on a test. She lost 4 points for each incorrect answer. Write an equation to find out how many incorrect answers Jenny had?
Answer:
4x = 120 - 92
Step-by-step explanation:
4x = 18
x = 4.5 incorrect (partial credit was given)
Answer:
7 incorrect answers
Step-by-step explanation:
120-92= 28=7
4. 4
Tell me what's better 38 packs of water for $14.60 or 63 packs of water for 24.90
Answer:
I think 63 packs
Step-by-step explanation:
But not sure so tell me if I'm right
Help need answer please
Answer:
59.5
Step-by-step explanation:
1st tree to shadow ratio: 17:10
Plug the numbers in to get x:35
17:10=x:35
17/10=x/35
Multiply both sides by 35
595/10=x
59.5=x
PLEASE HELP ME FIND CE!!
Answer:
the answer is 14
Step-by-step explanation:
i am sorry if im wrong
Can someone explain how to do this?
9514 1404 393
Answer:
9 and 10
Step-by-step explanation:
Make use of your knowledge of multiplication tables.
9² = 81
(√89)² = 89
10² = 100
√89 lies between 9 and 10
30 children each sold 20 item for the fund vaised. each child each earned $100 for the school. How much money did the school collect.
please show working
Answer:
$3,000
Step-by-step explanation:
30 children each earned $100
so
[tex]30 *100 = 3000[/tex]
so the school collected $3,000