Area of rectangle=Length×Breadth
[tex]\\ \sf\longmapsto Area=4y+10[/tex]
Take 2 common[tex]\\ \sf\longmapsto Area=2(2y+5)[/tex]
L=2y+5unitsB=2unitsFor 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).
WHAT IS THE EQUATION IN SLOPE INTERCEPT FORM FOR THE LINE THAT PASSES THROUGH THE POINT (-2,6) AND A SLOPE OF -1/4
It's a line so its equation is in the form : y = mx + b where m is the slope/gradient and b the y-intercept.
Since the slope m here is -1/4, we can write :
y = (-1/4)x + b
And since that line passes through the point x=-2, y=6, we can find the y-intercept by solving this equation of unknown b :
b + (-1/4)*(-2) = 6
b = 6 - (-1/4)*(-2)
b = 6 - (2/4)
b = 6 - 1/2
b = (12-1)/2 = 11/2
Finally, the equation is y = (-1/4)x + 11/2
the bottom the range has the same numbers so I just need the domain and range help plz!!
How to identify domain and range from co-ordinate pairs?
If a pair be (x,y)Domain=x
Range=y
Hence.
In the graph here
[tex]\\ \sf\longmapsto D_f=0\leqslant x\leqslant y[/tex]
[tex]\\ \sf\longmapsto R_f=0\leqslant y\leqslant 14[/tex]
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
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.
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:
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Step-by-step explanation:
5/6(-4 1/2)(-2 1/5) what is the answer
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
If a 32 ft. tall tree casts an 8 ft. shadow , how long of a shadow dc 6 ft. tall man have?
Answer:
1.5ft
Step-by-step explanation:
32/8=4
32/4=8
6/4=1.5
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
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.
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Find the median of the list of data.
12, 18, 21, 25, 30, 43
Answer:
23
Step-by-step explanation:
the median is the "Middle" number of the set.21 and 25 are the middle numbers of the set. so now find the middle of 21 and 25.
21 22 23 24 25
23 is the median of the data set
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.
Robert baked 6 pies to donate to a charity dinner before he ran out of sugar. With each additional cup of sugar he buys, he can bake 1 more pie.
Write an equation that shows how the total number of pies Robert can bake, y, depends on the number of cups of sugar he buys, x.
Y=
Answer:
y=4x+6
Step-by-step explanation:
slope intercept form y=mx+b
The total number of pies Robert can bake, y, depends on the number of cups of sugar he buys, x, according to the following equation:
y = 6 + x
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
According to the following equation, the total number of pies Robert may bake, y, is determined by the number of cups of sugar he purchases, x:
y = 6 + x
This equation can be read as: "The number of pies Robert can bake, y, is equal to the number of pies he baked before he ran out of sugar, which is 6, plus the number of additional cups of sugar he buys, x."
For example, if Robert buys 2 additional cups of sugar, he can bake a total of 6 + 2 = 8 pies.
If he buys 3 additional cups of sugar, he can bake a total of 6 + 3 = 9 pies, and so on.
Learn more about the equations here:
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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:
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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
..................
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.
need some help with these!!
Jasmine ran 5 miles in 42 minutes
Answer:
5 divided by 42 is 0.11 repeating
Step-by-step explanation:
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
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:
Find the complementary Angle of 24 / 1/5
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
7. Veronica brought her turtle out of its aquarium for 15 minutes every
night for 7 days. How many total minutes did she bring her turtle
out of its aquarium? Write another scenario that uses the same numbers.
Help me plz I know the answer, but I need help writing another scenario that uses the same numbers.
Answer:
Brittany took a 15 minute walk every morning for 7 days. How many minutes did she walk for?
Step-by-step explanation:
You might be able to use this.
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
Please can some one help me please
Answer:
a)3
b)33
Step-by-step explanation:
a)10% is the same as 10/100 so 30/100=0.3 x 10= 3
b) 3+30 = 33
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°
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
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