Answer:
1 x 1+0 x 1/10+5 x 1/100+9 x 1/1000
Step-by-step explanation:
- f:R → R
f(x + 7) = 3x - 6
g(2x + 1) = x2-1
= (f-1og)(5) = ?
Answer:
[tex]f^{-1}\,\circ \,g(5) = 10[/tex]
Step-by-step explanation:
Let [tex]f(x+7) = 3\cdot x -6[/tex] and [tex]g(2\cdot x +1) = x^{2}-1[/tex], we proceed to derive [tex]f(x)[/tex] and [tex]g(x)[/tex] by algebraic means:
(i) [tex]f(x+7) = 3\cdot x -6[/tex]
1) [tex]f(x+7) = 3\cdot x -6[/tex] Given
2) [tex]f(x+7) = 3\cdot (x+0) - 6[/tex] Modulative property
3) [tex]f(x+7) = 3\cdot [(x+7) +(-7)]-6[/tex] Existence of additive inverse/Associative property
4) [tex]f(x+7) = 3\cdot (x+7) +3\cdot (-7)-6[/tex] Distributive property
5) [tex]f(x+7) = 3\cdot (x+7) -21-6[/tex] [tex]a\cdot (-b) = -a\cdot b[/tex]
6) [tex]f(x+7) = 3\cdot (x+7) -27[/tex] Definition of subtraction
7) [tex]f(x) = 3\cdot x - 27[/tex] Composition of functions/Result
(ii) [tex]g(2\cdot x + 1) = x^{2}-1[/tex]
1) [tex]g(2\cdot x + 1) = x^{2}-1[/tex] Given
2) [tex]g(2\cdot x + 1) = (x\cdot 1)^{2}-1[/tex] Modulative property
3) [tex]g(2\cdot x +1) = [(2\cdot x)\cdot 2^{-1}]^{2}-1[/tex] Existence of additive inverse/Commutative and associative properties
4) [tex]g(2\cdot x +1) = (2\cdot x)^{2}\cdot 2^{-2}-1[/tex] [tex]a^{c}\cdot b^{c}[/tex]/[tex](a^{b})^{c} = a^{b\cdot c}[/tex]
5) [tex]g(2\cdot x + 1) = \frac{(2\cdot x)^{2}}{4}-1[/tex] Definitions of division and power
6) [tex]g(2\cdot x + 1) = \frac{(2\cdot x + 0)^{2}}{4} -1[/tex] Modulative property
7) [tex]g(2\cdot x +1) = \frac{[(2\cdot x + 1)+(-1)]^{2}}{4} -1[/tex] Existence of additive inverse/Associative property
8) [tex]g(2\cdot x + 1) = \frac{(2\cdot x + 1)^{2}+2\cdot (2\cdot x + 1)\cdot (-1)+(-1)^{2}}{4} -1[/tex] Perfect square trinomial
9) [tex]g(2\cdot x + 1) = \frac{(2\cdot x + 1)^{2}}{4}+\frac{[2\cdot (-1)]\cdot (2\cdot x + 1)}{4} +\frac{(-1)^{2}}{4}-1[/tex] Addition of homogeneous fractions.
10) [tex]g(x) = \frac{x^{2}}{4}-\frac{2\cdot x}{4} + \frac{1}{4}-1[/tex] Composition of functions/[tex]a\cdot (-b) = -a\cdot b[/tex]
11) [tex]g(x) = \frac{x^{2}}{4}-\frac{x}{2}-\frac{3}{4}[/tex] Definitions of division and subtraction/Result
Now we find the inverse of [tex]f(x)[/tex]:
1) [tex]f = 3\cdot x - 27[/tex] Given
2) [tex]f + 27 = (3\cdot x - 27)+27[/tex] Compatibility with addition
3) [tex]f+ 27 = 3\cdot x +[27+(-27)][/tex] Definition of substraction/Commutative and associative properties
4) [tex]f+27 = 3\cdot x[/tex] Existence of additive inverse/Modulative property
5) [tex](f+27) \cdot 3^{-1} = (3\cdot 3^{-1})\cdot x[/tex] Compatibility with multiplication/Commutative and associative properties
6) [tex](f+27)\cdot 3^{-1} = x[/tex] Existence of multiplicative inverse/Modulative property
7) [tex]f^{-1} (x) = \frac{x+27}{3}[/tex] Symmetrical property/Notation/Result
Finally, we proceed to calculate [tex]f^{-1}\,\circ \, g (5)[/tex]:
1) [tex]f^{-1} (x) = \frac{x+27}{3}[/tex], [tex]g(x) = \frac{x^{2}}{4}-\frac{x}{2}-\frac{3}{4}[/tex] Given
2) [tex]f^{-1}\,\circ\, g(x) = \frac{\frac{x^{2}}{4}-\frac{x}{2}-\frac{3}{4}+27}{3}[/tex] Composition of functions
3) [tex]f^{-1}\,\circ \,g(5) = 10[/tex] Result
Which statement is true? Question 8 options: A) – |–13| = 13 B) |–13| = 13 C) |13| = – 13 D) – |13| = 13
Answer:
Statement B is true because after -ve 13 come out it becomes +ve
Answer:
Option B is correct
Step-by-step explanation:
Identify the slope and y-intercept of the graph
below, then write the equation
(4,4) (0,-1)
There is a graph I have to label
A 12 foot tall building casts a 9 foot long shadow. How long of a shadow will a 5 foot tall woman have?
6.66 feet
6.66 feet
3.75 feet
3.75 feet
2 feet
2 feet
Answer:
22feet11111111111111dddddd
Answer:
Step-by-step explanation:
It is 3.75
Need help 15 points
Answer:
correct answer is d....
Answer:
d (22)^40 +(-7)^40 its very easy
Write 6.7% and 0.056% as a simplified fraction ( please )
Answer:
67/1000 and the other one is 7/12500
16. Complete the following equation
using <, >, or =
3.20_3.02
O A.>
B.<
OC. =
Answer:
the correct answer would be A
Answer:
the answer is A
Step-by-step explanation:
3.20_3.02
.20 is bigger than .02 so 3.20 is greater than 3.02
What is the slope of this line?
Answer:
Slope = ½
Step-by-step explanation:
Find the slope using two points on the line, (-4, 0) and (0, 2):
[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 0}{0 - (-4)} = \frac{2}{4} = \frac{1}{2} [/tex]
Slope (m) = ½
5/32 × 64y/100 please help :,)
Answer: y /10
Step-by-step explanation: step 1 = simplify y/100
step 2 = (5/32 x 64) x y/100
step 3 = simplify 5/32
step 4 = (5/32 x 64) x y/100
step 5 = The answer is y/10
Ratio 2:3 if Moses ran 8 laps and how many did Louis run
Answer:
8:12
Step-by-step explanation:
8/2=4
4 times 3 = 12
Suppose that the grades of Business Mathematics and Statistic module is modeled well
by a normal probability distribution with mean (212) and standard deviation (122). Let
X be the random variable representing this distribution. Find two symmetric values "a"
and "b" such that Probability [ a
Answer:
a = -2.57 and b = 2.57
Step-by-step explanation:
Explanation:
Given mean of the Population = 212
Standard deviation of the Population = 122
Let X be the random variable of the Normal distribution
[tex]Z = \frac{x-mean}{S.D}[/tex]
Given P( a ≤ z ≤b) = 0.99
put a=-b
P( -b ≤ z ≤b) = 0.99
⇒ |A( b) - A( -b)| =0.99
⇒ | A( b) + A( b)| =0.99
⇒ 2 |A (b)| = 0.99
⇒ | A(b)| = 0.495
From normal table find value in areas
b = 2.57 ( see in normal table)
Given a =-b
a = - 2.57
The midpoint of AB is M (-1, -5). If the coordinates of A are (3, -8), what are the coordinates of B?
Answer:
coordinates of point B are (-5, -2)
Step-by-step explanation:
Recall that the midpoint of the segment that joins (x1, y1) with (x2, y2) is given by:
( (x1 + x2)/2 , (y1+y2)/2)
Therefore, given the information about the midpoint being (-1, -5) and A being (3, -8) we get:
For the x value (x2) of point B:
-1 = (3 + x2) / 2 then -2 = 3 + x2 and finally solving for x2; x2 = -2 - 3 = -5
For the y value (y2) of point B:
- 5 = (-8 + y2) / 2 then -10 = - 8 + y2 and finally y2 = -10 + 8 = - 2
Then point B has the coordinates: (-5, -2)
What multiplication fact can be found by using the arrays for 2x9 and 5x9
Answer:
The answer is "7x9". When added together or in the verbiage of the question "can be found by using the arrays".
Step-by-step explanation:
Answer:
63
Step-by-step explanation:
Find the percent of decrease from 32 to 8
Answer:
75%
Step-by-step explanation:
Find the percentage of 8 out of 32
8/32 times 100 = 800/32 = 25%
8 is 25% of 32, so the percentage to fall from 32 to 8 is 75%because
100% - 25% = 75%
Please help .......You are guaranteed a minimum salary of $2000 per month PLUS 5.75% 5 points
of total sales. What is your gross pay for a month in which total sales are
$80,000 ?*
1.2000
2.$6600
3.$2460
4.$48,000
5.$4600
Answer:
6600
Step-by-step explanation:
0.0575*80000=4600
4600+minimum salary which is 2000=6600
(can I get brainliest please)
Henry drives at a speed of 80 miles per hour.
How long will it take to drive 400 miles?
Answer:
5hrs
Step-by-step explanation:
...................
which values for x and y satisfy the following equations
y=x-1 and 2x + y=8
Victoria learns 2 songs each week in piano lessons.
Which graph shows the number of songs Victoria will learn if she takes lessons for x weeks?
Answer:
the first one
Step-by-step explanation:
she learns the first 2 songs on the first week so the dot has to be lined up with 1 on the x axis and 2 on the y axis. then from there it goes up by 1 on the x axis and 2 on the y axis.
A recipe calls for 1 part coconut to 4 parts sugar. How much sugar will you need if you use 20 grams of coconut?
Answer:
80
Step-by-step explanation:
1:4 = 20:80
We are multiplying 20 by 1 to get 20 grams of coconuts. Also, we are multiplying 4 by 20 to get 80 grams of sugar. Therefore, you will need 80 grams of sugar if you use 20 grams of coconut. By the way, I suggest you review ratios if you are having difficulties with it.
Someone please look at the picture above and help!!! Please thank you very much
knowing that concentration of solutions of medications can be expressed as percentage, what percentage is a solution that's 20g of medication per 100 ml solution?
Answer:
20%
Step-by-step explanation:
The percentage of the concentration can be calculated by dividing the amount of solute by the total amount of the solution. In this case the solute would be the 20g of medication while the total solution amount is 100ml. Therefore, we divide these two values like so...
20 / 100 = 0.20
This is the percentage in decimal form, we can now multiply it by 100 to get the percentage value (which in this scenario is simply reversing the previous division)
0.20 * 100 = 20%
Add. Write your answer in the simplest form.
5 1/5 + 4 3/5 PLZZZ HURRY
10 1/5
9 2/5
10 4/5
9 4/5
Answer:
9 4/5
Step-by-step explanation:
The table shows the amounts of onions and tomatoes in different-sized batches of a salsa recipe.
Elena notices that if she takes the number in the tomatoes column and divides it by the corresponding number in the onions column, she always gets the same result.
What is the meaning of the number that Elena has calculated?
onions (ounces) tomatoes (ounces)
2 16
4 32
6 48
The meaning of the number that Elena has calculated is; the proportion of tomatoes to onions used in making the salsa recipe
How to calculate the unit proportion rate?The unit rate is defined as a ratio that represents the rate of something per unit. For example we can say that A car is driving at a speed of 50 kilometers per hour. Thus, the unit rate is 50 kilometers per hour.
Now, we are given a table showing the amounts of onions and tomatoes in different-sized batches of a salsa recipe.
For 2 ounces of onions used, 16 tomatoes are used
For 4 ounces of onions used, 32 tomatoes are used
For 6 ounces of onions used, 48 tomatoes are used
Now, we are told that she takes the number in the tomatoes column and divides it by the corresponding number in the onions column. This would represent the ratio of tomatoes to onions that is used in making a salsa recipe.
Read more about unit rate at; https://brainly.com/question/4895463
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The school collected $595 from cheesecake sales at the bake -sale fundraiser. Sixty-eight percent of the money came from cheesecake sales. How much money did the school make overall?
Answer: The answer is 999.6 Us dollars
Step-by-step explanation:
38) It is recommended that there be at least 13.8 square feet of ground space in a
garden for every newly planted shrub. A garden is 32.2' by 18'. Find the
maximum number of shrubs the garden
can accommodate.
a) 3 shrubs
b) 13 shrubs
c) 42 shrubs
d) 193 shrubs
Answer:
c) 42 shrubs
Step-by-step explanation:
Calculation to Find the maximum number of shrubs the garden can accommodate
First step is to calculate the Area of Garden
Area of Garden = (32.2 ft)*(18 ft)
Area of Garden= 579.6ft²
Now let calculate the maximum number of shrubs the garden can accommodate using this formula
Maximum number shrubs=(579.6 ft²)/(13.8 ft² per shrub)
Maximum number shrubs = 42 shrubs
Therefore the maximum number of shrubs the garden can accommodate will be 42 shrubs
Help
Pleaseeee xxxxx
Answer:
90 for both
Step-by-step explanation:
90 this is because all right angle equal 90 degrees and, triangles all equal 180 in total so if u add all the angle together it equal 180. I hope this helps.
Answer:
a = 3.46 , c = 9.9
Step-by-step explanation:
These are the following identities:
[tex]sinx=\frac{perpendicular}{hypotenuse} \\\\cosx=\frac{base}{hypotenuse}\\\\tanx=\frac{perpendicular}{base}\\[/tex]
Easier way to learn this is
Some people have curly brown hair till painted black
Sinx = per/hyp cosx = base/hyp tanx = per/base
So if use the angle 60° we can see that the opposite side(perpendicular) to the angle is 6 and the base side is a so we need the identity which uses the opposite side(perpendicular side) and the base side and not the hypotenuse so that is tan x so,
[tex]tan\ 60=\frac{6}{a} \\\\1.732=\frac{6}{a}\\\\1.732a=6\\a=\frac{6}{1.732}\\\\a=3.46\\[/tex]
So a = 3.46
Now to calculate c:
If we take the angle 45° and see the opposite side(perpendicular side) is 7 and the hypotenuse is c so need the identity which uses the opposite side(perpendicular side) and the hypotenuse and not the base, which is sin x so,
[tex]sin 45=\frac{7}{c}\\\\0.707=\frac{7}{c}\\\\0.707c=7\\\\c=\frac{7}{0.707}\\\\c =9.9\\[/tex]
so c = 9.9
if you have a rate of 75 miles per 3 hours how many miles are in 1 hour
A ladder that has a length of 13 m leans against a wall with the base of the ladder 5 m away from the bottom of the wall. Use this information to find how high above the ground the ladder meets the wall
Answer:
did you find the answer ??
The required height of the wall where the ladder meets the wall is 12 m.
Given that,
A ladder that has a length of 13 m leans against a wall with the base of the ladder 5 m away from the bottom of the wall. Use this information to find how high above the ground the ladder meets the wall is to be determined.
In a right-angled triangle, its side, such as hypotenuse, perpendicular and base is Pythagorean triplets.
Here,
Let the height be h,
Applying Pythagoras' theorem,
h = √[13²-5²]
h = √169-25
h = √144
h = 12
Thus, the required height of the wall where the ladder meets the wall is 12 m.
Learn more about Pythagorean triplets here:
brainly.com/question/22160915
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two numbers have a sum of 15 and a product of 26 what are they
complete the steps to solve for x
4/5x -1.4x = 11
Note: Your equation is a little unclear. But, I am assuming the equation
4/5x -1/4x = 11
The solution would anyways clear your concept.
Answer:
The value of x = 20
Step-by-step explanation:
Given the expression
4/5x -1/4x = 11
Multiply by LCM = 20
4/5x × 20 - 1/4x × 20 = 11 × 20
16x - 5x = 220
11x = 220
Divide both sides by 11
11x/11 = 220/11
x = 20
Thus, the value of x = 20