Find the additive inverse and the multiplicative inverse, if it exists, of the given number. 5 in modulo 8 arithmetic
The additive inverse of 5 modulo 8 is the number a such that
5 + a ≡ 0 (mod 8)
Then
a ≡ -5 ≡ -5 + 8 ≡ 3 (mod 8)
The multiplicative inverse is m such that
5m ≡ 1 (mod 8)
Use the Euclidean algorithm:
8 = 1•5 + 3
5 = 1•3 + 2
3 = 1•2 + 1
Then
1 = 3 - 1•2
1 = 3 - 1•(5 - 1•3) = 2•3 - 1•5
1 = 2•(8 - 1•5) - 1•5 = 2•8 - 3•5
and so
1 ≡ 2•8 - 3•5 ≡ (-3)•5 (mod 8)
which means the inverse of 5 is
-3 ≡ 8 - 3 ≡ 5 (mod 8)
What Value is equivalent to 30-6 x 3
Answer:
5/1
Step-by-step explanation: I could be wrong though
Have a Good Day <3
3. Mr. Morris orders a bottle of lotion that contains (15)liters. He use 2/6 of a liter of
lotion a day. How many days can he use the bottle of lotion until it is empty?
Pls help and show me how to do it
Answer:
45
Step-by-step explanation:
If he uses 2/6 of a liter thats 3 days for 1 liter.
3 x 15 is 45. so 45 days
Which equation is linear? y=x4 y=xy –x3 ОООС f(x) = 3х + 1 y=xУ
Answer:
f(x) = 3х + 1
Step-by-step explanation:
PLEASE HELP WITH THIS QUESTION
Answer:
Heigh <= 63
Width <= 56
Length <= 61
Step-by-step explanation:
Height: x+7
Width: x
Length: x + 5
(x + 7) + (x) + (x + 5) <= 180 cm^3
3x + 12<= 180
3x <= 180-12
x <= 168/3
x <= 56
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).
If the equation of the line is f(x) = 1/3x - 5 , what would be the new equation if there was a reflection over the y- axis, a dilation of -6, and a translation of 4 units up?
pls help I already solved but I'm not sure if I did a step out of order
Answer: Thus, after the transformation, the graph consists of points (x,y) satisfying y=2(x−3)2. This is the equation of the transformed graph.
Step-by-step explanation:
Consider the graph y=x2. Suppose the graph is dilated from the x-axis by a factor of 2, and then translated 3 units to the right. What is the equation of the resulting graph?
Solution
The transformation given is Trans(3,0)∘Dilx-axis,2. Denote by (x′,y′) the image of a point (x,y) under this transformation. A point (x,y) is sent to (x,2y) by the dilation, and then to (x+3,2y) by the translation, so (x′,y′)=(x+3,2y).
The original graph consists of points (x,y) such that y=x2. Then it is transformed so that (x,y)↦(x′,y′)=(x+3,2y). We must find what equation is satisfied by x′ and y′.
Since x′=x+3 and y′=2y, we have x=x′−3 and y=y′/2. Thus y=x2 implies
y′2=(x′−3)2or equivalentlyy′=2(x′−3)2.
What is 0.14 as a fraction
Answer:
7/50
Step-by-step explanation:
Here is an easy way of converting a decimal number to fraction.
Step 1:
Write it down as 0.14/1
Step 2:
Multiply bottom and top by 10 for every number after the decimal, since there is 2 numbers after the decimal you do 10*10 = 100
[tex]\frac{0.14(100)}{1(100)}[/tex] = 14/100
Step 3:
You can simplify 14/100 to 7/50 and thats why 7/50 is the answer
Answer:
[tex]\frac{14}{100}[/tex] or [tex]\frac{7}{50}[/tex]
Step-by-step explanation:
To find 0.14 we have to see what place it's in, since it was in the hundredths place, we put 14 over 100, which is 14/100.
To simplify this fraction we have to find the GCM (Greatest Common Factor), the GCM of 14 and 100 is 2. Then we divide both the bottom and the top by 2 (whatever you do to the bottom, you do to the top), which gives us 7/50.
To conclude, 0.14 as a fraction is 14/100 or 7/50.
Find the y intercept of the line -5x-2y=-14
Answer:
the y intercept is7
Step-by-step explanation:
at y-axis x=0, y=7
HURRY!! (No links please and please include an explanation)
If A is the set of all whole numbers, choose the set B that will make the following
statement false.
B ⊆ A
B = {0, 2, 4, 6)
B = {0}
B = {-1, 0, 1)
B = {1, 2, 3, 4)
Answer:
B= (-1,0,1)
Step-by-step explanation:
because -1 is not a whole number.
Answer:
B = {-1, 0, 1)
Step-by-step explanation:
The answer is B = {-1, 0, 1) because -1 is not a whole number.
Hope this helps :)
C is wrong help me please
Answer:
A
Step-by-step explanation:
x from 0 < x < 2 is wrong because < means goes to but does not equal that value, and [tex]\leq[/tex] means it INCLUDES that value. Because the function includes it (not an open hole), you should choose A.
can someone help me with this please?
Answer:
Okay, Please copy paste the question. I cannot see.
Step-by-step explanation:
The equilateral triangle with side 12 has altitude
all graphs range from -10 through 10 ;)
Answer:B
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
First, we want to find out what is X.3x = -6 ---> x = -2
X is -2 so we want the graph point to start at -2 and from there go down to -10.© Write
[tex] \sqrt{8} [/tex]
power of 2
Answer:
2³
Step-by-step explanation:
2×2×2=8
so √8 = 2³
Hope this helps you
At the beginning of a basketball season, the Panthers won 30 games out of 100 games. At this rate, how many games will they win in a normal 120-game season?
Answer:40
Step-by-step explanation: 12 divided by 3
f(ə) =
g(x) = (x - 2)2 – 7
We can think of g as a translated (shifted) version of f.
Complete the description of the transformation,
Use nonnegative numbers.
To get the function g, shift f up/down v
by
units and to the
right/left
by
units.
Answer: To get function g, shift f DOWN by 7 units and to the RIGHT by 2 units
Step-by-step explanation: g(x)= (x-2)^2-7 since they’re both negatives it should be the opposite. An example would be g(x)=(x+3)^2+5, f goes UP for positive by 5 units, left by 3 units.
(x+5)(x-5) factoring
Answer: x² - 25
Step-by-step explanation:
what are the reasons to #3 and #5??
options for both #3 and #5
- CPCTC
- Given
- When two lines are parallel and cut by a transversal, the consecutive interior angles are supplementary
- opposite sides of a parallelogram are parallel
- reflexive property
- angles that are supplementary to the same angle are congruent
Answers:
3) When two lines are parallel and cut by a transversal, the consecutive interior angles are supplementary.5) angles that are supplementary to the same angle are congruent.==============================================================
Explanation:
Basically, statements 3 and 4 are nearly identical. They both use the exact same reasoning. For statement 3, the parallel lines are QT and RS, with QR being the transversal. Refer to the same side interior angles theorem. It's also known as the consecutive interior angles theorem.
-------------
For statement 5, consider the idea that if
Q+R = 180
Q+T = 180
then those two equations lead to T = R. Both angles T and R are supplementary to angle Q, so they must be the same angle. So that's why we go with the "angles that are supplementary to the same angle are congruent" option for this part.
Does each function describe exponential growth or decay?
Drag and drop the equations into the boxes to correctly complete the table.
Growth
Decay
y = 250(1 + 0.004)^t
y = 426(0.98)^t
y = 12,000(1/2) ^t
9514 1404 393
Answer:
growthdecaydecayStep-by-step explanation:
An exponential function will describe growth if the base of the (positive) exponent is greater than 1. It will describe decay of the base is less than 1.
y = 250(1 + 0.004)^t . . . . . 1.004 > 1 ⇒ growth
y = 426(0.98)^t . . . . . . . . . 0.98 < 1 ⇒ decay
y = 12,000(1/2) ^t . . . . . . . 1/2 < 1 ⇒ decay
Can someone help me on this
Answer:
39V3 Sq.units of that will help you
what is mixed number
help me pleas
Answer:
A mixed number is a number with both a whole number and a fraction. For example 6 3/4, 2 1/2, 7 8/15. Hope this helped:)
Answer:
A mixed number is a number consisting of a whole number and a proper fraction.
Below are examples of mixed numbers:
[tex]4 \frac{1}{2}[/tex]
[tex]1 \frac{3}{5} [/tex]
Simplify.
81‾‾‾√
18
9
−3
−18
9514 1404 393
Answer:
(b) 9
Step-by-step explanation:
Maybe you want to simplify ...
[tex]\sqrt{81}=\sqrt{9^2} =\boxed{9}[/tex]
Number 8 need asappp!!!!
Step-by-step explanation:
Angle A + Angle B = 180
x-34+x+58=180
2x+24=180
2x+24-24=180-24
2x=156
/2 /2
x=78
To solve for Angle B, fill x as 78
58+78
Angle B is 136
Find the lines of symmetry. Select all that apply. Thank you!
Lines r & t are the lines of symmetry here.
◇ The line r cuts the figure vertically into 2 equal halves.
◇ The line t cuts the figure horizontally into 2 equal halves.
◇ The lines q & s don't cut the figure symmetrically (2 unequal parts are formed), so they are not the lines of symmetry.
See the attachments too.
______
Hope it helps ⚜
help me with math and ill mark brainliest
Your neighbour has two children. You learn that he has a son, Samuel. What is the probability that Samuel's sibling is a brother?
Answer:
1/2
Step-by-step explanation:
there is a 50 50 chance that somebody is male or female
What is a circle define and illustrate The following in figures
Answer:
Circle is a closed geometric figure having an infinite number of sides.
Step-by-step explanation:
A circle ⭕ has infinite number of sides want to know how then try and experiment.
First draw a pentagon of five sides, then a hexagon of six sides and keep on increasing the number of sides and then you will notice the shape being close of a circle.
Predict the next number in this pattern:
2/3, 2/27, 2/243, 2/2187, 2/19683, ...
Answer:
aaaaaaaaaaaaaaaaaaaaaaaaaaaa
Step-by-step explanation:
7/8 * 1/2 =7/16 yes but wouldn't you have to divide it though like divide 16 / 7 = 3 3/7???
Answer:
No.
Step-by-step explanation:
I think you're talking about simplifying/reducing the fraction.
You would not do that in this case because the numbers 7 and 16 have no common factors besides 1.
The answer is already in its lowest/reduced form. You do not divide.
Please let me know if this was not what you were talking about!