Answer:
The value of x that minimizes the total area of the two squares is x = 5.
Step-by-step explanation:
A wire 10 centimeters long is cut into two pieces, with one piece measuring x centimeters and the other (10 - x) centimeters.
Each piece is bend into the shape of a square, and we want to find the value of x that minimizes the total area of the two squares.
If x is bend into a square with four equivalent sides, then each side measure:
[tex]\displaystyle A = \frac{x}{4}[/tex]
Likewise, each side of the second square will measure:
[tex]\displaystyle A = \frac{10-x}{4}[/tex]
The area of a square is its side squared. Hence, the area of both squares will be given by:
[tex]\displaystyle T = \left( \frac{x}{4}\right) ^2 + \left(\frac{10-x}{4}\right)^2[/tex]
Simplify:
[tex]\displaystyle \begin{aligned} T &= \frac{x^2}{16} + \frac{x^2 - 20x + 100}{16} \\ \\ &=\frac{2x^2-20x+100}{16}\\ \\ &= \frac{1}{8}x^2-\frac{5}{4}x+\frac{25}{4} \end{aligned}[/tex]
Since this is a quadratic with a positive leading coefficient, the minimum value will occur at the vertex point.
Recall that the x-coordinate of the vertex is given by:
[tex]\displaystyle x = -\frac{b}{2a}[/tex]
In this case, a = 1/8 and b = - 5/4. Hence:
[tex]\displaystyle x = -\frac{\left(-\dfrac{5}{4}\right)}{2\left(\dfrac{1}{8}\right)} = 5[/tex]
In conclusion, the value of x that minimizes the total area of the two squares is x = 5.
Lauren bought snacks for her team's practice. She bought a bag of popcorn for $2.37 and a 6-pack of juice bottles. The total cost before tax was $15.45. How much was each bottle of juice?
Answer:
$2.18
$15.45-$2.37=$13.08
$13.08/6
$2.18
Name the algebraic property demonstrated in the example below:
3 ⋅ (x ⋅ y) = (3 ⋅ x) ⋅ y
Answer:
It's Associative Property of Multiplication.
Thank You
What is the y-intercept of the function f(x) = 2 • 3x?
A.
(0, 2)
B.
(0, 3)
C.
(0, 6)
D.
(2, 0)
Answer:
(0,2)
Step-by-step explanation:
Hi there!
[tex]f(x) = 2*3^x[/tex]
The y-intercept of any function occurs when x=0.
To find the y-intercept, solve for f(0):
[tex]f(0) = 2*3^0\\f(0) = 2*1\\f(0) = 2[/tex]
Therefore, the y-intercept is 2 and occurs at (0,2).
I hope this helps!
Which expression is equivalent to –9+(-9)
O 9+ (-9)
-9 - 9
Submit Answer
O-9- (-9)
O9- (-9)
Write an equation for the situation then solve for x.
35) A stray dog ate 21 of your muffins. That was 3/4 of all of them! With how many did you
start?
Answer:
28
.75 * x = 21
x = 21/.75
x=28
Step-by-step explanation:
Answer:
28 muffins
Step-by-step explanation:
Let x = the number of muffins
x*3/4 = 21
Multiply each side by 4/3
4/3 * 3/4x = 4/3 *21
x = 28
You started with 28 muffins
f(a)=(a+2)^2
g(a)=5a+4
g(f(-2))
Evaluate g(f(-2)) = ???
Answer:
-2gf
Step-by-step explanation:
Sofia is driving to Texas. She travels at 70 kilometers per hour for 2 hours, and 63 kilometers per hours for 5 hours. Over 7 hours time period what was sofia's average speed ?
Answer:
65 kph
Step-by-step explanation:
There were a total of 7 hours. So two hours were at 70 and the other 5 hours at 63: the equation would be: (70+70+63+63+63+63+63)/7=65
In algebra (grade 7) :-
what does + and - make?
what does + and + make?
what does - and + make?
what does - and - make?
Noemy had homework three days of the school week. What is the ratio of days with homework to days without homework?
Answer:
3 : 2
Step-by-step explanation:
Number of days having homework during school week = 3
Number of days not having homework during school week = 5 - 3 = 2
Homework days : Without home work days = 3 : 2
Evaluate this expression. − 4/5 − (− 2/5 ) + 4/7
A) − 22/35
B) − 3/5
C) 6/35
D) 2
Answer:
c) 6/35
Step-by-step explanation:
− 4/5 − (− 2/5 ) + 4/7
= − 4/5 + 2/5 + 4/7
= 6/35
Answer:
The choose C. 6/35
Step-by-step explanation:
[tex] - \frac{4}{5} + \frac{2}{5} + \frac{4}{7} \\ \frac{ - 28 + 14 + 20}{35} = \frac{6}{35} [/tex]
Please help me I’ll give a brainliest! Even if you are only able to do one of them it help because I don’t understand how to do it!!!
Answer:
The x which is not in the domain of the function is the root of the denominator
6) x+3=0, x=-3 is the x which is not in the domain of the function
7) |2x+5|=0, x=-5/2 is the x which is not in the domain of the function
8) x^2-16=0, x=±4 are the x which are not in the domain of the function
Need help with 6 and 7
Answer:
part 7 = 15cm
Step-by-step explanation:
[tex]x {}^{2} = (12) {}^{2} + (9) {}^{2} \\ x {}^{2} = 144 + 81 \\ x {}^{2} = 225 \\ x = \sqrt{225} = 15[/tex]
Whats the answer and the steps
2(3x-4)
Answer:
-24
Step-by-step explanation:
2(3x-4)
6x-8
What is 10% of a number whose square
is 81
Answer: 0.9
Step-by-step explanation:
Let x be the number
Determine the value of the number
x² = 81
√x² = √81
x = 9
Find the 10% of the number
Final number = rate of percentage × original number
Final number = 10% × 9
Final number = [tex]\boxed{0.9}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
use the following list to find the average or mean, the median, the mode, and the range 10, 15, 5, 8, 6, 6, 2
Answer:
Mean - 7.43
Median - 6
Mode - 8
Range - 13
Step-by-step explanation:
To find the mean/average, add up all the numbers and divide the sum by the # of data points. (ex. you have 7 numbers, so you divide the sum of the numbers by 7.)
The median of a set of data is the middle number of ascending numbers in the data. If there was an even number of data points you would have to add the 2 middle numbers and divide by 2.
The mode is the number that appears most frequently in the data set.
To find the range, just subtract the lowest number in the data set from the greatest number.
Answer:
mean= 7.4, median = 6, mode =6, range = 13
Step-by-step explanation:
mean = 10 + 15 + 5 + 8 + 6 + 6 + 2 ÷ 7
= 52 ÷ 7
= 7.4
median= 2, 5, 6, 6, 8, 10 , 15
6
median is the middle number from ascending order
mode = 6
mode is the number that occurs the most
range = 15 - 2
13
range is the different between the largest and smallest number
Brainliest is appreciated
What fraction is equal to −0.37¯¯¯¯¯?
Answer: -37/100
Step-by-step explanation:
Given
-0.37
Convert to division form (Any division that can get -0.37)
-37 ÷ 100
Convert to fraction
[tex]\boxed{-\frac{37}{100} }[/tex]
Finally, always make sure the final fraction is no longer divisible.
Hope this helps!! :)
Please let me know if you have any questions
3 attempts remaining.
150 moths lived in a lab. Each week, some moths died, and about 1/5 survived . How many moths were still alive after 2 weeks?
Tell me both the numbers for the 2 boxes pls
This is finding the midpoint. Please help
Answer:(4,1) ?
Step-by-step explanation:
(x1 + x2/ 2 , y1+y2/ 2)
(1+7/ 2, 5+(-3)/ 2)
(4,1)
Step-by-step explanation:
[tex]( \frac{1 + 5 }{2} ) \: and( \frac{7 + 3}{2} ) = ( \frac{6}{2} ) + ( \frac{10}{2} ) = [/tex]
(3,5)
Question 13 of 23
If f(x) = 3x - 15, what is f(4)?
A. 3
O B. -8
O C. 12
O D. -3
Answer:
f(4) = 3×4 - 15
f(4) = 12-15 = -3
Answer : D. -3
...........
Answer:
D.-3
Step-by-step explanation:
f(4)=3•4-15
=12-15
=-3
Which variable is dependent temperature or time of day? Which variable is independent?
Answer:
The temperature depends on the time.
The independent variable is the variable the experimenter manipulates or changes.
Hope it helps you.HELPPPPPP MEEEE PLESDEEEE
Answer:
7, 5, 1, 3
Step-by-step explanation:
Hope this Helps!
Please mark me Brainliest
The price of Pepsi stock was $0.65 in 1981 and $27.56 in 2011. What was the average rate of change for the stock per year
from 1981 to 2011 rounded to the nearest hundredth?
A roll of ribbon is 32 cm long. How many pieces 11 cm long can be cut from the roll?
Tìm x
a) (x+3)²+(x-2)²=2x²
This is midpoint please help.
Step-by-step explanation:
[tex]thank \: you[/tex]
Answer:
(1, 13)
Step-by-step explanation:
it is above in the photo.
NEED ASAP DUE IN 1 HOUR
hey please help i’ll give brain
Answer:
[tex]7 \times 6 = 5 \: sixes + 2 \: sixes \\ 7 \times 6 = 30 + 12 \\ = 42 \\ \\ thank \: you[/tex]
Hi ;-)
[tex]7\cdot6=5 \ \text{sixes}+\boxed2 \ \text{sixes}\\\\=\boxed{30}+12\\\\=\boxed{42}[/tex]
A group of 20 people are going to run a race. The top 6 finishers advance to the finals. In how many different ways can they advance?
4^x when x = 2 need asap
Answer:
16
Step-by-step explanation:
Substitute the value of the variable into the equation and simplify.
