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.
Let f(x) = -6x + 3 and g(x) = 5x + 4. Find f • g and state its domain.
Answer:
30x + 21 is your best answer
Which pair of transformations moves quadrilateral 1 to quadrilateral 2?
a:Reflect over the line y = -3, then rotate it 90 degrees counterclockwise about the origin
b:Reflect it over the x-axis, then rotate it 180 degrees about the origin
c:Rotate it 90 degrees counterclockwise about the point (-3, -3) then translate it 8 units to the right
d:Translate it 8 units to the right, then reflect it over the line y=-3
Answer:
Answer choices:
a. Reflection takes it to Q2, further rotation takes it back to Q3
Incorrectb. Reflection takes it to Q2, rotation takes to Q4 with right shape.
Correctc. Rotation takes is to Q4, translation keeps in same Q but with wrong shape
Incorrectd. Translation takes it to Q4, reflection keeps it in same Q but with wrong shape
IncorrectBecause the shape is present in Q3
So reflection over x axis takes it to Q2
Then 180° rotation about origin takes it to Q4
Hence Option B is correct
Rearrange the formulae to make x the subject:
ay/x - dx= wx
Thanks in advance
Answer:
[tex] \frac{ay}{x} - dx = wx [/tex]
multiply x through out:
[tex]ay - {dx}^{2} = w {x}^{2} \\ {wx}^{2} + {dx}^{2} = ay[/tex]
factorise out x²:
[tex] {x}^{2} (w + d) = ay \\ {x}^{2} = \frac{ay}{w + d} [/tex]
take square root on both sides:
[tex] \sqrt{ {x}^{2} } = \sqrt{ \frac{ay}{w + d} } \\ \\ x = \sqrt{ \frac{ay}{w + d} } [/tex]
Step-by-step explanation:
the biggest obstacle is usually a division by x.
so, let's get rid of it by multiplying both sides of the equation by x
ay - dx² = wx²
then
ay = wx² + dx² = (w+d)x²
y = (w+d)x²/a = x² × (w+d)/a
if LN=9x-39, LM=47, and MN=3x+10 find MN
Answer:
11
Step-by-step explanation:
ML+LN=MN solve for x
(47)+(9x-39)=(3x+10) = 1/3
x = 1/3
plug into MN
3(1/3)+10=11
A system of equations is shown below. Which statement about the ordered pair (-7,-3) is true?
3x + 3y = - 30
2x + y = -17
a) It is not a solution to either equation.
b) It is one of many solutions to the system.
c) It is the only solution to the system.
d) It is a solution to the first but not the second equation.
HELPP MEEEEEEEEEEE PLSSSSSSSSSSSSSSS
Answer:
hmm looks like you are over thinking it its just 20-8
Step-by-step explanation:
least common multiple of 2 and 3?i forgot how to do this completly over the summer lol
Answer:
6
Step-by-step explanation:
Multiples of 2: 2, 4, 6, 8, 10
Multiples of 3: 3, 6, 9, 12, 15
Brainliest, please!
Some math help please?
Answer:
∠ LMP = 77° , ∠ NMP = 103°
Step-by-step explanation:
The 2 angles on the straight line sum to 180° , that is
∠ LMP + ∠ NMP = 180 , substitute values
- 16x + 13 - 20x + 23 = 180 , that is
- 36x + 36 = 180 ( subtract 36 from both sides )
- 36x = 144 ( divide both sides by - 36 )
x = - 4
Then
∠ LMP = - 16x + 13 = - 16(- 4) + 13 = 64 + 13 = 77°
∠ NMP = - 20x + 23 = - 20(- 4) + 23 = 80 + 23 = 103°
The salary of A is 25% above that of B. How Much percent is B's salary below that of A?
Answer: 20% lower then A's salary.
Step-by-step explanation:
PLEASE HELP I WILL GIVE BRAINLIEST TO THE CORRECT ANSWER
himari is solving the equation 4 ( x - 3 ) = 16. Her first step is 4x - 12 = 16
which step could be the next step? select all that apply.
1. 4x - 12 + 12 = 16 + 12
2. 4x - 12 - (-12) = 16 - (-12)
3. 1/4 x ( 4x - 12 ) = 16 x (1/4)
4. 4x/4 - 12 = 16/4
5. 4 x ( 4x - 12 ) = 16 x 4
Answer:
1. could be the next step.
3. could be the next step.
Step-by-step explanation:
The dot plot below shows the numbers of years of experience of the teachers at City High School.
++
0 2 4 6 8 10 12 14 16 18 20
Years of Experience
Determine where a gap is present in the data set.
between 14 and 18 years
between 5 and 7 years
oooo
between 2 and 4 years
between 11 and 19 years
Submit
Reset
Answer: Between 14 and 18 years
Step-by-step explanation:
There are no dots in that area.
3-7 + 2 2/6 * 4/5 =
what’s the answer?
3 - 7 + 2 2/6 * 4/5
-4 + 14/6 * 4/5
-4 + 7/3 * 4/5
-4 + 28/15
-32/15
PLEASE ANSWER QUICK!
What does the 1/2 indicate in this equation?
y=1/2x+1
the y-intercept
the x-intercept
the slope
I don't know.
Compare to slope intercept form I e y=mx+b where m is slope and b is y intercept
here
m=1/2b=1Option C
my family uses 3 cartons of milk a day . how many cartons did we use in january
Answer:
93 cartons
Step-by-step explanation:
January-31
no of cartons-3 × 31=93
solve the equation
4(2^m+1)-16^m=0
[tex]\\ \rm\longmapsto 4(2^m+1)-16^m=0[/tex]
[tex]\\ \rm\longmapsto 8^m+4-16^m[/tex]
take 4common[tex]\\ \rm\longmapsto 4(2^m+1-4^m)=0[/tex]
[tex]\\ \rm\longmapsto 2^m-4^m+1=0[/tex]
[tex]\\ \rm\longmapsto 2^m=4^m[/tex]
[tex]\\ \rm\longmapsto 2^m=2^{2^m}[/tex]
[tex]\\ \rm\longmapsto 2^m=m[/tex]
[tex]\\ \rm\longmapsto m=\dfrac{1}{2}[/tex]
What is the length of a rectangle with width 12in. and area 66in.²?
Answer:
5.5 inches
Step-by-step explanation:
Because Length * Width = Area, Length * 12 = 66.
If we solve for Length by dividing both sides by 12, we end up with Length = 5.5 inches
14 +3n = 8n - 3(n - 4)
Answer:
n=1
Step-by-step explanation:
Start by distributing the -3 to (n-4)
14+3n=8n-3n+12
Then combine like terms on the right
14+3n=5n+12
Subtract 12 from both sides
2+3n=5n
Subtract 3n from both sides
2=2n
Divide both sides by 2
1=n
Pleaseee help ill mark brainliest please include explanation too
Answer:
TO place the triangle ABC on EDF flip the triangle so the you get the mirror image of the triangle and then place it on top of the triangle EDF
hope this helps!
Julio, Amari, and Henry take turns unloading a trailer holding 240 cases of soda. First, Julio unloads 15 of all the cases. Next, Amari unloads 117 of the remaining cases.
How many cases of soda are still left on the trailer for Henry to unload?
Answer:
answer: 55
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
240 - 15 = 225
225 - 117 = 8
Determine whether each function is one-to-one, onto, both, or neither.
===================================================
Explanation:
We see that the function passes the horizontal line test. It is impossible to draw a single horizontal line and have that horizontal line cross the curve at multiple points. It's similar to the vertical line test.
Since the curve passes the horizontal line test, that makes it one-to-one. Any y value is paired with a unique x value, and vice versa.
The function is also onto because we can generate any y value output we want. The curve extends forever upward and downward. The range is the set of all real numbers.
Therefore, the function is both one-to-one and onto.
---------------------
Extra info:
The term "injective" is the same as "one-to-one" The term "surjective" is the same as "onto"The term "bijective" is a combination of injective and surjective at the same timefind a rational number halfway in between the two numbers. 1/3 and 3/10
Answer:
39/60 is a rational number halfway b/w the given numbers.
Step-by-step explanation:
Add both of these numbers and then divide the result by 2.
(1/3+3/10)/2
=((30+9)/30)/2
=(39/30)*1/2
=39/60
Solve each proportion
Step-by-step explanation:
[tex]thank \: you[/tex]
2. χΣ -4
Please help
Step-by-step explanation:
1)x is less than 7
2)x is greater than and equal to -4
Does 9, 10 and 15 equal a right triangle
Answer:
By virtue of The pythagorean theorem,in a right triangle squares of the similar two sides equal the square of The largest side.Only 9,12 and 15 fit this rule.
Step-by-step explanation:
Hope it help you If you have any questions can ask in the comments
Solve - 3 [ ( x + 2 ) ( x - 1 ) - x ^ { 2 } + 1 ] + 3 ( x - 1 ) (and could you please explain it to me?? I really don't get it. Thanks!)
Answer:
Step-by-step explanation:
[tex](x+2)(x-1)= x^2+2x-x-2= x^2 +x -2\\\\( x + 2 ) ( x - 1 ) - x ^ { 2 } + 1 =x^2+x-2-x^2+1=x-1\\\\- 3 [ ( x + 2 ) ( x - 1 ) - x ^ { 2 } + 1 ] =-3(x-1)=-3x+3\\\\- 3 [ ( x + 2 ) ( x - 1 ) - x ^ { 2 } + 1 ] + 3 ( x - 1 ) =-3x+3+3x-3=6x\\[/tex]
help its urgent please
Hi,
Answer is $0.19
Step-by-step explanation:-
We know that:-
15 dimes = $1.50
20 nickels = $1.00
8 quarters = $2.00
half dollar = $0.50
19 pennies = $0.19
Total = $5.19
Since Billy spended $5, so,
$5.19 - $5 = $0.19
Hope it helps you...
if two planes intersect, then their intersection is a point true or false
I believe that it is true
Step-by-step explanation:
sorry if im wrong
Answer:
False.
Step-by-step explanation:
resolve into factors:- 49m² + 154m + 121
Answer:
4m^2 +154m +12149m^2 +( 77+77)m +121
49m^2 + 77m +77m +121
7m (7m +11) +11 (7m +11)
(7m+11) (7m+11)
hope it was helpful
Answer:
[tex](7m + 11 {)}^{2} [/tex]
Step-by-step explanation:
[tex]49 {m}^{2} + 154m + 121[/tex]
➡️ [tex] {7}^{2} {m}^{2} + 2 \times 7m \times 11 + {11}^{2} [/tex]
➡️ [tex](7 m{)}^{2} + 2 \times 7m \times 11 + {11}^{2} [/tex]
➡️ [tex] = (7m + 11 {)}^{2} [/tex] ✅
Write a rule for the geometric sequence with the given description. The first term is -3, and 5 is the previous term.
Answer:
The rule is (-3)(5)^(n-1).
Step-by-step explanation:
OK so the common ratio is 5 and first term = -3.
nth term = ar^(n-1)
= (-3)(5)^(n-1).
A dressmaker needs to cut 12-inch pieces of ribbon from rolls of ribbon that are 6 feet in length. How many 12-inch pieces can the dressmaker cut from 10 of these rolls of ribbon?
Before you try that problem, answer the question below.
How many inches of ribbon does the dressmaker have, in total?
Answer:
he can cut 60 strips or ribbon
Step-by-step explanation:
The dressmaker has 720 inches of ribbon
from each roll of ribbon, he can make 6 12-inch pieces or ribbon
she has 10 rolls
so 6(strips per roll) x 10(amount of rolls) = 60 strips :)