Answer:
Commutative Property of Addition
Step-by-step explanation:
This is because the commutative property of addition and multiplication is
[tex]a+b=b+a\\a*b=b*a[/tex]
and as an example
[tex]5+9=14 \\9+5=14\\10*6=60\\6*10=60[/tex]
need some help with these!!
Find the dimensions of a rectangle (in m) with area 1,000 m2 whose perimeter is as small as possible. (Enter the dimensions as a comma separated list.)
The perimeter of the rectangle is the sum of its dimensions
The dimensions that minimize the perimeter are [tex]\mathbf{10\sqrt{10 },10\sqrt{10 }}[/tex]
The area is given as:
[tex]\mathbf{A = 1000}[/tex]
Let the dimension be x and y.
So, we have:
[tex]\mathbf{A = xy = 1000}[/tex]
Make x the subject
[tex]\mathbf{x = \frac{1000}{y}}[/tex]
The perimeter is calculated as:
[tex]\mathbf{P = 2(x + y)}[/tex]
Substitute [tex]\mathbf{x = \frac{1000}{y}}[/tex]
[tex]\mathbf{P = 2(\frac{1000}{y} + y)}[/tex]
Expand
[tex]\mathbf{P = \frac{2000}{y} + 2y}[/tex]
Differentiate
[tex]\mathbf{P' = -\frac{2000}{y^2} + 2}[/tex]
Set to 0
[tex]\mathbf{ -\frac{2000}{y^2} + 2 = 0}[/tex]
Rewrite as:
[tex]\mathbf{ -\frac{2000}{y^2} = -2}[/tex]
Divide both sides by -1
[tex]\mathbf{\frac{2000}{y^2} = 2}[/tex]
Multiply y^2
[tex]\mathbf{2000 = 2y^2}[/tex]
Divide by 2
[tex]\mathbf{1000 = y^2}[/tex]
Take square roots of both sides
[tex]\mathbf{y = \sqrt{1000 }}[/tex]
[tex]\mathbf{y = 10\sqrt{10 }}[/tex]
Substitute [tex]\mathbf{y = \sqrt{1000 }}[/tex] in [tex]\mathbf{x = \frac{1000}{y}}[/tex]
[tex]\mathbf{x = \frac{1000}{\sqrt{1000}}}[/tex]
[tex]\mathbf{x = \sqrt{1000}}[/tex]
[tex]\mathbf{x = 10\sqrt{10 }}[/tex]
Hence, the dimensions that minimize the perimeter are [tex]\mathbf{10\sqrt{10 },10\sqrt{10 }}[/tex]
Read more about perimeters at:
https://brainly.com/question/6465134
This question has two parts. First, answer Part A. Then, answer Part B.
Part A
Fill in the blank question.
Nick wants to purchase a pair of binoculars that is on sale for $155.75. The sales tax rate in his county is 6.5%.
Calculate the amount of sales tax Nick will pay on the purchase. Round to the nearest cent if necessary.
sales tax: $
Part B
Fill in the blank question.
How much will Nick pay in all for the pair of binoculars after sales tax is included? Round to the nearest cent if necessary.
total cost: $
Answer:
Step-by-step explanation:
A) $155.75(0.065) = 10.12375 = $10.12
B) $155.75 + $10.12 = $165.87
Find the complementary Angle of 24 / 1/5
Which point would not be on the graph of the function y=+5?
Answer:
Any point that does NOT have a positive 5 in the y position
pls help me i will mark you brilliant
2. a) 3 days.
b) 1 hour.
3. a) 20 km
b) 1200 l
Can someone help me with this I have a headache and don't have the time or energy to use my brain
Answer:
Step-by-step explanation:
Jasmine ran 5 miles in 42 minutes
Answer:
5 divided by 42 is 0.11 repeating
Step-by-step explanation:
Determine the smallest integer value of x in the solution of the following inequality
Answer:
-2
Step-by-step explanation:
4x - 7 > -17
(add 7 on both sides)
4x > -10
(divide both sides by 4 to isolate x)
x > - 2.5
An integer can not be a fraction. So the smallest integer value x can be is -2 because -2 is greater than -2.5.
Write an equation for the nth term of the arithmetic sequence 7,2,-3,-8,
Answer:
-5n+12
Step-by-step explanation:
find the difference which is -5
then find the difference from -5 to 7 which is 12
put it in the sequence
-5n+12
Answer:
-5n+12 that would be your equation
PLS HELP REWARDING A LOT!!
Answer:
157°
Step-by-step explanation:
Sum of interior angles of polygon
(n-2)*180 ---- n = total number of sides
7 angles, 7 sides
5*180 = 900
final angle will be
900-162-115-125-138-105-98
=157
Answer:
157
Step-by-step explanation:
it is obvious that it's a heptagon
so (n-2) x180
n=7
(7-2) x 180 =900
900-162-115-125-138-105-98
900-743=157
final unknown=157°
What is the slope of a line passing through the points (2, 5) and (0, −4)?
Answer:
9/2
Step-by-step explanation:
m=∆y/∆x
m= (5+4)/(2—0)
m=9/2
Aldo earns 51 dollars a week working at the bookstore he makes one dollar more for each book that he sells . the amount , A (in dollars )that Aldo earns a week of he sales b books is given by the following function
A(b)=51+b
Answer:
False.
Step-by-step explanation:
A x b does not equal to A + b. Addition and mutiplication is different.
free 100 xp answer with fav movies pls for 100 free xp , 100 free xp always is given by algebros every day. Please do enjoy this plentiful amount of free xp I care about how you are feeling introduce yourself with telling me about your fav movie and why it is your fav. Enjoy! Please answer
Step-by-step explanation:
My favorite movie would have to be the Pirates of the Caribbean collection. Captain Jack sparrow aka Johnny Depp is is just great at his character.
Answer:
FREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XPFREE XP
Step-by-step explanation:
For questions 3 - 6, find F'(x), the inverse of F(x).
3. F(x) = x-10
4. F (x) = x/6 + 3
5. F(x) = 3x + 7
6. F(x) = 8x
Answer:
3) f'(x) = x + 10
4) f'(x) = 6x - 18
5) [tex]\displaystyle\mathsf{f'(x)=\frac{1}{3}x-\frac{7}{3}}[/tex] or [tex]\displaystyle\mathsf{f'(x)=\frac{x - 7}{3}}[/tex]
6) f'(x) = ⅛x or [tex]\displaystyle\mathsf{f'(x)=\frac{x}{8}}[/tex]
Step-by-step explanation:
3. f(x) = x - 10Step 1: In order to find the inverse function of f(x) = x - 10, start by replacing f(x) with y.
y = x - 10
Step 2: Switch x and y:
x = y - 10
Step 3: Add 10 to both sides to isolate y:
x + 10 = y - 10 + 10
x + 10 = y
Step 4: Replace y with f'(x):
f'(x) = x + 10 ⇒ This is the inverse function of f(x).
4. [tex]\displaystyle\mathsf{f(x)=\:\frac{x}{6}\:+\:3}[/tex]Replace f(x) with y:
[tex]\displaystyle\mathsf{y=\:\frac{x}{6}\:+\:3}[/tex]Switch x and y:
[tex]\displaystyle\mathsf{x=\:\frac{y}{6}\:+\:3}[/tex]Subtract 3 from both sides:
[tex]\displaystyle\mathsf{x-3=\:\frac{y}{6}\:+\:3-3}[/tex][tex]\displaystyle\mathsf{x-3=\:\frac{y}{6}}[/tex]Multiply both sides by 6 to isolate y:
[tex]\displaystyle\mathsf{6(x-3)=\:\frac{y}{6}(6)}[/tex]6x - 18 = y
Replace y with f'(x):
f'(x) = 6x - 18 ⇒ This is the inverse function of f(x).
5. f(x) = 3x + 7Replace f(x) with y:
y = 3x + 7
Switch x and y:
x = 3y + 7
Subtract 7 from both sides:
x - 7 = 3y + 7 - 7
x - 7 = 3y
Multiply both sides by ⅓:
⅓(x - 7) = 3y (⅓)
[tex]\displaystyle\mathsf{\frac{1}{3}x-\frac{7}{3}=y}[/tex]
Replace y with f'(x):
[tex]\displaystyle\mathsf{f'(x)=\frac{1}{3}x-\frac{7}{3}}[/tex] or [tex]\displaystyle\mathsf{f'(x)=\frac{x - 7}{3}}[/tex] ⇒ This is the inverse function of f(x).
6. f(x) = 8x
Replace f(x) with y:
y = 8x
Switch x and y:
x = 8y
Multiply both sides by ⅛:
⅛(x) = ⅛(8y)
⅛x = y or [tex]\displaystyle\mathsf{\frac{x}{8}=y}[/tex]
Replace y with f'(x):
f'(x) = ⅛x or [tex]\displaystyle\mathsf{f'(x)=\frac{x}{8}}[/tex] ⇒ This is the inverse function of f(x).
5/6(-4 1/2)(-2 1/5) what is the answer
$200 is shared between Bill and Ann. Ann’s share is $50 more than Bill’s share. Calculate the size of each of their shares.
First subtract the difference between the two:
200 - 50 = 150
Now divide that by 2:
150/2 = 75
Bills share is $75
Now add the $50 to 75 to get Ann's share:
75 + 50 = $125
Ann's share is $125
Bill's share is $75
5^-x = 6
Help ASAP
STEPS MUST.
We have to Find:
The value of x[tex] \sf \longmapsto5^{ - x }= 6[/tex]
Let's start.
Take Logarithm of both sides[tex] \sf \longmapsto log(5^{-x}) = log(6) [/tex]
Solving Further[tex] \sf \longmapsto - x \: log(5) = log(6)[/tex]
[tex] \sf \longmapsto - x = \dfrac{ log(6) }{ log(5) } [/tex]
Take the minus from (-x) and put in on log(6)[tex] \sf \longmapsto \: x = \dfrac{ -log(6) }{ + log(5)} [/tex]
Done
What is 3/4+1 2/3+1/2=
Answer:
Exact Form:
35/12
Decimal Form:
2.916- (6 goes on)
Mixed Number Form:
2 11/12
The side of an equilateral triangle is 12. Its area is
Select one:
a. 72
b. 48
c. 144
d. 36 square root 3
A≈62.35
..................
Express 24 minutes as a fraction of 2'/2 hours.
Step-by-step explanation:
1hr = 60
½ hr = 30
60 + 30 = 90
A man walks 50km a day he gets R1 for every 1000 steps. How much money will he have at the end of his 50km walk if 1,6Km is = to 2000 steps.
we have 1,6Km is = to 2000 steps => 1 km = 1250 steps
=> 50km = 1250 x 50 = 62500 steps
so he'll have: 62500/1000 = 62,5 R1
ok done. Thank to me :>
Please help me with these questions. I’m genuinely confused.
Answer:
16. 1 4/5
17. 2 2/3
18. 4/11
19. 4 1/2
20. 4/7
21. 1/2
22. 1 2/5
23. 2 1/2
24. 4 2/3
Step-by-step explanation:
1. subtract whole numbers first
2. subtract fractions next (simplify if you can)
3. subtract fractions and whole numbers
Explain the meaning of 5?
a. 1 + 2 + 3 + 4 + 5
b. 5-4-3-2-1-0
c. 0 x 1 x 2 x 3 x 4 x 5
d. 5 ∙ 4 ∙ 3 ∙ 2 ∙ 1
if u get this right u get branist
5(2)^2-2(7) = 6
6(7+2)/2 = 27
Therefor the correct answer is the < symbol.
I hope this helps! :)
Analyze the solution set of the following system by following the given steps. 2x + y = 5 3y = 9 − 6x Write each equation in slope-intercept form. y = -2 x + 5 y = -2 x + 3 What do the equations have in common? How are they different?
Step-by-step explanation:
Given the following systems of linear equations, 2x + y = 5, and 3y = 9 − 6x
Write each equation in slope-intercept form.The slope-intercept form is: y = mx + b, where m = slope, and b = y-intercept.
2x + y = 5Subtract 2x from both sides:
2x - 2x + y = - 2x + 5
y = -2x + 5 ⇒ This is the slope-intercept form, where the slope, m = -2, and the y-intercept, b = 5.
3y = 9 − 6xDivide both sides by 3 to isolate y:
3y = − 6x + 3
[tex]\frac{3y}{3} = \frac{-6x + 9}{3}[/tex]
y = -2x + 3 ⇒ This is the slope-intercept form, where the slope, m = -2, and the y-intercept, b = 3.
What do the equations have in common?y = -2x + 5
y = -2x + 3
These equations have the same slope, m = -2.
How are they different?They have different y-intercepts.
y = -2x + 5 ⇒ The y-intercept is (0, 5), where b = 5.
y = -2x + 3 ⇒ The y-intercept is (0, 3), where b = 3.
The equations have the same slope but different y-intercepts, meaning they are parallel lines that run parallel to each other and are spaced vertically apart by a difference of 2 units.
Step 1: Write each equation in slope-intercept form.
Given system of equations:
1. 2x + y = 5
2. 3y = 9 - 6x
Slope-intercept form of an equation is y = mx + b, where m is the slope and b is the y-intercept.
Let's rewrite the equations in slope-intercept form:
1. 2x + y = 5
Subtract 2x from both sides: y = -2x + 5
2. 3y = 9 - 6x
Divide both sides by 3: y = -2x + 3
Step 2: The equations have the same slope (-2) but different y-intercepts 5 and 3.
The common slope (-2) indicates that the lines represented by these equations have the same steepness or inclination.
The difference in y-intercepts means that the lines are parallel and run parallel to each other.
Learn more about Slope here:
https://brainly.com/question/3605446
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Please help me with these questions. I’m genuinely confused.
Answer:
16: 5
17: 6 4/9
Step-by-step explanation:
I only will give u the answer for a few questions
I 13.12.21 Mather asianmen I choose the best answert the next two numbers in the pattern 1, 4, 9, 16 are. (A) 26,36 (B) 25, 36 (C) 24,35 (D) 36,48
Answer:
(B) 25, 36
Step-by-step explanation:
1 = 1²
4 = 2²
9 = 3²
16 = 4²
25 = 5²
35 = 6²
i need help on this math problem
Answer:
[tex]\sqrt{81}[/tex] = 9
[tex]\sqrt{169}[/tex] = 13
Step-by-step explanation:
Decide where the first digit of the quotient should be placed without performing division The first digit of the quotient for 2,370 = 24 should be in the Choose... ones tens hundreds thousands
Answer:
tens place
Step-by-step explanation:
24 can't be into the thousands place or the hundreds place. hope this helps
Answer
hundredths place
Step-by-step explanation:
When performing long division, the first digit of the quotient appears over the least significant digit of the first portion of the dividend that is greater than or equal to the divisor.
Here, when performing long division we compare ...
64 vs 1 . . . no quotient digit
64 vs 15 . . . no quotient digit
64 vs 159 . . . the first quotient digit appears with the same place value as the 9 in 1.59. That is, the first quotient digit will be 0.02, 2 in the hundredths place.