The inverse of the function y = 4ˣ is f⁻¹(x) = ㏑x / ㏑4.
What is termed as the inverse of the function?An inverse function, also known as an anti function, is a function that can be reversed into another function. Simply put, if any function "f" takes x to y, then its inverse will take y to x. The inverse function is signified by f-1 or F-1 if the function is signified by 'f' or 'F'. Here, (-1) should not be confused with exponent or reciprocal.For the given question;
The function is given as;
y=4ˣ
Interchange the variables of the function.
x = 4∧y
Taking log both side.
㏑ x = ㏑(4∧y)
Using the power rule of log function.
㏑ x = y㏑(4)
y = ㏑ x/㏑(4)
Now, replace y with f⁻¹(x).
f⁻¹(x) = ㏑ x/㏑(4)
Thus, the inverse of the function y = 4ˣ is found to be f⁻¹(x) = ㏑x / ㏑4.
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The correct question is-
Evaluate the inverse when y=4ˣ. Show all of your work.
67×73=1×3(mod 5)show works
Answer
Check Explanation
Explanation
a ≡ b (mod n)
This means a and b have the same remainder when they are divided by n
So, to check if this question works out, we divide what is on the left hand side and what is on the right hand side by what is after the mod.
1) 67 × 73 ≡ 1 × 3 (mod 5)
4891 ≡ 3 (mod 5)
So, to check,
(4891/5) = 978 remainder 1
(3/5) = 0 remainder 3
The remainders are different.
So, this equation is wrong and does not work.
This equation is false.
2) 83¹⁴⁴ ≡ 15¹⁴⁴ (mod 17)
Noting that it is the units digit that determines the remainder
3 raised to the power of a multiple of 4 gives 81 raised to the power of a positive integer
5 raised to power of a multiple of 4 gives 625 raised to the power of a positive integer
So, using these numbers,
83¹⁴⁴ ≡ 15¹⁴⁴ (mod 17)
81 ≡ 625 (mod 17)
(81/17) = 4 remainder 13
(625/17) = 36 remainder 13
The remainders are the same.
So, this equation is correct and it works.
This equation is true.
Hope this Helps!!!
Which of the following statements are true about the process and solution till the following problem 86.89-56.389?
The arithmetic says we should subtract find the difference between 86.89 and 56.389.
Notice we have to put a place holder of 0 at the ending of 86.89 to do the subtraction. Then we have to borrow 1 from the hundredth term(9) of 86.890 to make 0 ten . so ten minus 9 should be 1. Then the difference of the hundreth term(8 - 8) is 0. 8 minus 3 is 5. 6 minus 6 is zero and finally 8 minus 5 is 3.
The answers are B and D
Rewrite as a simplified fraction.
\large{0.8\overline{95} = {?}}0.8
95
=?
0.895 with 95 repeating on and on as a simplified fraction can be re-written as 887/990.
How to determine the fractional equivalent of this repeating decimal?By critically observing the given number, we can reasonably and logically deduce that it has three (3) repeating digits. Since this number has three (3) repeating digits, we would have to multiply n by 1000 as follows:
1000n = 0.895
1000n = 895.95 .......equation 1.
10n = 8.95 .......equation 2.
Subtracting equation 2 from equation 1, we have:
1000n - 10n = 895.95 - 8.95
990n = 887
Dividing both sides by 990, we have:
n = 887/990
Simplified fraction, n = 887/990.
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Complete Question:
Write 0.895 with 95 repeating on and on as a simplified fraction.
brainly 100!!! Which of the following functions is graphed below?
The function that is represented on the graph is (a) y = x^2 + 4, x < 2 and y = x + 4, x ≥ 2
How to determine the graphed function?The graph represents the given parameter
From the graph, we have the following function types
Whole graph: Piecewise functionQuadratic function to the leftLinear function to the rightUsing the options as a guide, we have the equations to be
Quadratic function: y = x^2 + 4Linear function: y = x + 4Next, we calculate the domain
The quadratic function stops at x = 2 with an open circle
So, the domain is x < 2
The linear function starts at x = 2 with a closed circle
So, the domain is x ≥ 2
Hence, the graphed function is (a)
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An architect plans to buy 5 stone spheres and 3 stone cylinders. For the same amount, he can buy 2 stone spheres and 7 stone cylinders. If one stone cylinder costs $32.73 how much does
each stone sphere cost?
Answer:
Each stone sphere costs $43.64Step-by-step explanation:
Let the cost of stone sphere is s and stone cylinder is c.
According to question we have equation:
5s + 3c = 2s + 7cSolve it for s:
5s - 2s = 7c - 3c3s = 4cSubstitute the value of c:
3s = 4*32.733s = 130.92s = 130.92/3s = 43.64Can someone help me with my practice? I am having trouble with this question.
We are to solve an inequality and give the answer in graph form.
The inequality is:
[tex]6-5+n\ge\text{ 18}[/tex]Let's solve for n in order to be able to answer the question.
we start by trying to isolate n on one side of the inequality symbol. So first combine 6-5 = 1 and re-write the inequality:
[tex]1+n\ge18[/tex][tex]\begin{gathered} n\ge18-1=17 \\ n\ge17 \end{gathered}[/tex]Now, subtract 1 from both sides, and you get the final answer:
n must be larger than or equal to 17. WHich agrees with the first answer option provided by the problem.
need this asap 50 points for it
Answer:
the subtraction property of equality
Step-by-step explanation:
trust
Answer:
Subtraction
Step-by-step explanation:
O EQUATIONS AND INEQUALITIESSolving a word problem using a quadratic equation with rationa...
Answer:
[tex]\begin{gathered} length\text{ = 8 m} \\ width\text{ = 5.5 m} \end{gathered}[/tex]Explanation:
Here, we want to get the dimensions of the rectangle
Let us represent the length by l and the width by w
From the question:
The length of the rectangle is 3 m less than double the width
Mathematically:
[tex]l\text{ = 2w-3}[/tex]The product of the two represents the area
[tex]\begin{gathered} A\text{ = l }\times\text{ w} \\ lw\text{ = 44} \end{gathered}[/tex]Now, let us substitute the first equation with the second:
[tex]\begin{gathered} w(2w-3)\text{ = 44} \\ 2w^2-3w\text{ = 44} \\ 2w^2-3w-44\text{ = 0} \end{gathered}[/tex]Solving the quadratic equation, we have:
[tex]\begin{gathered} 2w^2-11w+8w-44\text{ = 0} \\ 2w^2+8w-11w-44\text{ = 0} \\ 2w(w\text{ + 4\rparen -11\lparen w+4\rparen = 0} \\ (2w-11)(w+4)\text{ = 0} \\ 2w=\text{ 11} \\ w\text{ = }\frac{11}{2} \\ \\ w\text{ = 5.5} \end{gathered}[/tex]Recall:
[tex]\begin{gathered} lw\text{ = 44} \\ 5.5l\text{ = 44} \\ l\text{ = }\frac{44}{5.5}\text{ = 8 } \end{gathered}[/tex]
Mrs. Smith runs a dessert parlor. Her top-selling items are mixed berry smoothies and milkshakes. She sells mixed berry smoothies for $5 each and milksh
for $3 each. Mrs. Smith wants to sell at least 60 mixed berry smoothies and milkshakes in all and wants to earn at least $210. Each mixed berry smoothie ta
7 minutes to make, and each milkshake takes 3 minutes to make.
O
New folder
How many mixed berry smoothies and milkshakes should Mrs. Smith make to minimize the time she spends making the desserts, also selling at least the
minimum total number and earning at least the minimum amount of money?
Answer:
Step-by-step explanation:
0 mixed berry smoothies and 70 milkshakes
Please solve for y. There should be no actual numbers besides for 9.
Answer:
y= x/(n-9)
Step-by-step explanation:
Move 9 to the right side to get n-9
Take y over to get x=y(n-9)
Then shift n-9 over to other side to get y= x/(n-9)
Solve for x to the nearest tenth.
Answer:
x = 11,2 inchs
Step-by-step explanation:
I infer that the units are in inches.
8-3 = 5
Then:
By the Pythagorean Teorem:
x² = 10² + 5²
x² = 100 + 25
x² = 125
√x² = √125
x = 11.18
to the nearest tenth:
x = 11.2 inches
Which of the following properly describe
"slope"? Select all that apply.
0
A)
ratio of the change in y-values
(rise) for a segment of the graph to
the corresponding change in x-
values (run)
OB) x₂-x₂
y₂-M1
C) ₂-₁
x₂-x₂
D) run/rise
☐ E) rise/run
Use the Rational Zeros Theorem to list all possible zeros of the function below.
f(x) = 11x³ 2x² + x + 10.
-
[Enter all possible zeros predicted by the Rational Zero Theorem individually and separated by commas
(1,-1,-1/2,1/2,etc.) Note: You do not need to factor the polynomial.]
The all possible zeros predicted by the Rational Zero Theorem individually and separated by commas are ±1/1, ±1/11, ±2, ±2/11, ±5, ±5/11, ±10, ±10/11.
P(x) = 11x³ + 2x² + x + 10
The factors of the constant term 10 is ±1, ±2, ±5, ±10 (=p)
The factors of leading coefficient are ±1, ±11 (= q)
The possible rational zeros are p/q : ±1/1, ±1/11, ±2/1, ±2/11, ±5/1, ±5/11, ±10/1, ±10/11.
After simplification the possible roots are ±1/1, ±1/11, ±2, ±2/11, ±5, ±5/11, ±10, ±10/11.
Therefore, ±1/1, ±1/11, ±2, ±2/11, ±5, ±5/11, ±10, ±10/11. are the all possible zeros predicted by the Rational Zero Theorem individually and separated by commas.
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Write 100 minutes in hours and minutes.
Answer:
1 hour and 40 minutes
Step-by-step explanation:
60 minutes in an hour
we have 100 minutes
100 - 60 = 40
in 100 minutes we already have 1 hour
now we have 40 minutes left
can 40 minutes make another 60?
No.
so 100 minutes make
1 hour and 40 minutesThe slope of line ℓ
is greater than 0 and less than 1. Write an inequality for the slope of a line perpendicular to ℓ
.
By properties of perpendicular lines and algebra properties, the slope of the line perpendicular to line ℓ is represented by m' > 1.
How to represent an inequality associated with a line perpendicular to another line
Let m be the slope of a line, in accordance with analytic geometry, the slope of line perpendicular to the first one is equal to m' = - 1 / m. The statement can be summarized by the following inequality:
0 < m < 1
Then, by algebra properties for inequalities we find that that slope for the perpendicular line is:
0 < m · m⁻¹ < m⁻¹
0 < 1 < m⁻¹
1 < m⁻¹
- m⁻¹ > 1
- 1 / m > 1
m' > 1
The slope of the line perpendicular to line ℓ is represented by m' > 1.
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Need an explanation why it’s 46.4
(Please help I need this asap)
Answer:
9 + 7 + 7.2 = 23.2
23.2 x 2 = 46.4
Step-by-step explanation:
if the expected frequencies rule for chi-square had been violated by the data, which categories could be combined together in a meaningful way to increase the expected frequencies?
If the chi-square test's expected frequencies rule is broken, either the row or the column is combined to provide a higher frequency that can be used to run the independence test.
Generally speaking, if more than 20% of the anticipated frequencies have a value of less than 5, Chi-Square should not be used (it does not matter what the observed frequencies are).
Both the chi-square test and Fisher's exact test are inappropriate if the sampled values' independence is broken. This presumption will be broken if the same subject results in more than one observation in the contingency table.
There are distinct assumptions for each non-parametric test as well. The data in the cells should represent frequencies or counts of cases rather than percentages or other data transformations, according to the Chi-presumptions. square's The variables' levels are mutually exclusive.
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a fence is to be built to enclose a rectangular area of 280 square feet. the fence along three sides is to be made of material that costs 6 dollars per foot, and the material for the fourth side costs 13 dollars per foot. find the dimensions of the enclosure that is most economical to construct.
Fencing of any rectangular region is basically represent perimeter of that rectangular region.
For most economical fencing, length L = 21.05 feet and width W = 13.301 feet.
How to estimate the length and width of the rectangular region?Area of rectangular region is 280 square feet.
And length is L and width is W.
Area of rectangular region = L × W=280 square feet
W=280 / L
Since, The fence along three sides is to be made of material that costs 6 dollars per foot, and the material for the fourth side costs 14 dollars per foot.
Therefore, Total cost, C = 6(2L + W) + 13W = 12 L + 19 W
Total cost, C = 12 L+ 5,320 / L
To find most economical cost, differentiate above function and equate to zero.
C' = 12 - 5,320 / L²
simplifying the above equation, we get
⇒ 12 - 5,320 / L² = 0
⇒ L² = 5,320 / 12
L = 21.05 feet
Therefore, L = 21.05 feet
Substituting value of L in area equation.
We get, W = 13.301 feet.
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The table lists recommended amounts of food to order for 19 party guests. Nathan and Sydney are hosting a graduation party for 40 guests. They know there will also be guests stopping by who may have come from other parties. For ordering purposes, they will count each of these "drop-in" guests as half a guest. How much of each food item should Nathan and Sydney order for a graduation party with 15 drop-in guests?table: fried chicken =28 meats =4 1/3 lasangnia = 10 3/4
For the graduation party, Nathan and Sydney should order pieces of 70 fried chicken , 11 pounds of meats and 36 pounds of lasangnia .
In the question ,
it is given that
there are 15 drop in guests , and drop in guests are counted as half a guest .
So , the number of half guests = 15/2 = 7.5
number of guests for the party = 40 guests
So , total number of guests = 40+7.5 = 47.5
From the table , we can see that
19 party guests need 28 pieces of fried chicken .
So , 1 party guests will need 28/19 pieces of fried chicken .
so, 47.5 guests will need [tex]47.5*\frac{28}{19}[/tex] pieces of fried chicken
[tex]47.5*\frac{28}{19}[/tex] = 70
hence , 70 pieces of fried chicken is needed .
From the table , we can see that
19 party guests need [tex]4\frac{1}{3}[/tex] = 13/3 pounds of meats .
so, 1 party guests will need 13/(3*19) pounds of meats .
So, 47.5 guests will need [tex]47.5*\frac{13}{3*19}[/tex] pounds of meats .
[tex]47.5*\frac{13}{3*19}[/tex] = 10.833
≈ 11
hence , 11 pounds of meats is needed .
From the table , we can see that
19 party guests need [tex]10\frac{3}{4}[/tex] = 43/3 pounds of lasangnia .
So , 1 party guests will need 43/(3*19) pounds of lasangnia .
So, 47.5 guests will need [tex]47.5*\frac{43}{3*19}[/tex] pounds of lasangnia .
[tex]47.5*\frac{43}{3*19}[/tex] = 35.8333
≈ 36
hence , 36 pounds of lasangnia is needed .
Therefore , For the graduation party Nathan and Sydney should order 70 pieces of fried chicken , 11 pounds of meats and 36 pounds of lasangnia .
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(7, 8) and (-1, 0)find the distance between the two points?
The distance (d) between two points is computed as follows:
[tex]d\text{ = }\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}^{}[/tex]where (x1, y1) and (x2, y2) are the points of interest. In this case, the points are (7, 8) and (-1, 0). Replacing into the equation:
[tex]d\text{ = }\sqrt{(-1-7)^2+(0-8)^2\text{ }}[/tex][tex]d\text{ = }\sqrt{(-8)^2+(-8)^2}=\sqrt{128}[/tex]Funds are distributed to five families affected by floods in the ratio 5:12:2:15:29. The total amount that the five families received was $630.
a) The first family received _____
b) The difference between the amount of money the first and last family received was _____
c) A sixth family joins. They receive n amount of money and the average amount of money donated to all six families becomes 140. How much money does the sixth family receive?
Step-by-step explanation:
We must first add up the ratios:5+12+2+15+29 = 63, this will be the total ratio the money was shared Then we pick out the ratio for each family accordingly:For the first family, 5 out of the total ratio = 5/63
For the second family, 12 out of the total ratio = 12/63
For the third family, 2 out of the total ratio = 15/63
For the fifth family, 29 out of the total ratio = 29/63
a) The first family = 5/63 of the money, $630
we can therefore say the money they received is
= 5/63 ×630
= $50
b) The last family = fifth family = 29/63 of the money, 630
= 29/63 × 630
= $290
recall that the first family received $50 , the positive difference between the money received by both the first and last family
= $290 - $50
= $240
c) Since another family joins in, the total number of families become 6
the money the received is nwe can't find the average without knowing what the second, third, and fourth family received out of that money
we apply the same stepthe second family = 12/63 ×630
= $120
the third family = 2/63 × 630
= $20
the fourth family = 15/63 × 630
= $150
Average generally is = total sum/ frequency or number of occurrences or peoplein this case, we were told the average became $140
which means that
sum of money received by the families/ the number of families involved in the sharing = $140
( $50+$120+$20+$150+$290+n)/6 = $140($630+n)/6= $140
now the plan would be to make n subject of formula
multiply both sides of the equation by 6, the equation will become$630+n = $840
take $630 to the other side, it becomes -$630
n = $840-$630
n = $210
therefore the newly added family received $210
I honestly hope I explained it properly...thank you
twelve hungry teenagers can devour a very large pizza in $20$ minutes. how many teenagers would it take to finish a very large pizza in $15$ minutes? (assume that all teenagers eat pizza at the same rate.)
It would take 9 Teenagers to finish a very large pizza in $15$ minutes.
From the knowlegde of Propotional method/ subject formular in mathematics;
From the questions:
12 Teens finished a very large pizza in $20$ minutes.
The number of teens to finish a very large pizza in $ 15 minutes would calculate thus,
12 Teens=$20$ minutes.
x Teens=$15$ minutes.
then we cross multiply:
x Teens × $20$ minutes =$15$ minutes × 12 Teens
making x Teens subject of the formula we have;
x Teens=$15$ minutes × 12 Teens/$20$ minutes
x Teens=9 Teens
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1.5x+0.5y=12
a. solve for y
b. find ordered pairs for the function
Answer:
Step-by-step explanation:
y=-3x+24
(0,24)
The length of a rectangle is 3 inches greater than the width. (Hint: draw a pictureand label itA. Write a polynomial that represents the area of the rectangle.B. Find the area of the rectangle when the width is 4 inches..
We are given that the length of a rectangle is 3 inches greater than the width.
Let us draw a rectangle and label the width and length.
Part A:
Let the width of the rectangle is x inches.
Then the length of the rectangle is (x + 3) inches.
Now recall that the area of a rectangle is given by
[tex]A=L\cdot W[/tex]Where L is the length and W is the width of the rectangle.
[tex]\begin{gathered} A=(x+3)\cdot x \\ A=x^2+3x \end{gathered}[/tex]Therefore, the above polynomial represents the area of the rectangle.
Part B:
We are given that the width is 4 inches.
Substitute the width (x = 4) into the equation of the area that we found in part A.
[tex]\begin{gathered} A=x^2+3x \\ A=(4)^2+3(4) \\ A=16+12 \\ A=28in^2 \end{gathered}[/tex]Therefore, the area of the rectangle is 28 square inches.
True or False: The set of whole numbers is closed under multiplication.
Explanation:
Take any two whole numbers you want. Multiplying them together always result in some (other) whole number.
Examples:
2*3 = 65*7 = 3511*12 = 132In other words,
(whole number)*(whole number) = whole number
This is why we consider the set closed under multiplication.
Graph line with slope 1/2 passing through the point (-1,3)
Answer:
Step-by-step explanation:
First, graph your first point at (-1,3) Then, take your slope which is 1/2 and use rise over run. So from your point of (-1,3) go up 1 in your y coordinate, and 2 in your x coordinate. So your next point should be at (1,4)
7 ft
9 ft
26 ft
What is the area?
The total area of the figure is 298.17 ft².
What is termed as the area of the figure?The total space occupied by a flat (2-D) surface or the shape of an object is defined as its area.Sketch a square on a paper piece with a pencil. It is a two-dimensional figure. The area of the shape just on paper is referred to as its Area.For the given question;
Let divide the given the figure in three parts;
RectangleTrianglesemi circleThe dimensions of the rectangle is;
Length = 26 - 9 = 15 ft
Breadth = 9 ft
Area = length x breadth
Area = 15 x 9
Area = 135 ft²
The dimension of the triangle is-
Base = 9 ft
Height = 15 - 7 = 8 cm
Area = (1/2) base x height
Area = (1/2) x 9 x 8
Area = 36 ft²
The dimension of semi circle is -
Radius = 9 ft
Area = πr²/2
Area = 3.14 x 9² / 2
Area = 127.17 ft²
Total area = rectangle +triangle + semicircle
Total area = 135 + 36 + 127.17
Total area = 298.17 ft²
Thus, the total area of the figure is 298.17 ft².
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Triangle TAB has a perimeter of 40 cmeters. Could the measures of the sides as shown actually represent the measures of the sides of the triangle? Justify your answer.
EXPLANATION
We can apply the Obtuse Triangle Theorem to check if the the measures of the sides appropiately represents the measures of the triangle:
Perimeter = 40 cm = 4x + 2x + 2 + x + 3
Adding like terms:
40 = 7x + 5
Subtracting 5 to both sides:
40 - 5 = 7x
Adding like terms:
35 = 7x
Dividing both sides by 7:
35/7 = x
Simplifying:
[tex]5=x[/tex]Then, by the obtuse triangle theorem, the following relationship should be fulfilled.
3) A car can travel 442 miles on 26 gallons of gasoline. How much gasoline will it need to go 102 miles?
The car will need 6 gallons of gasoline to travel 102 miles
Explanation:Given that the car travels 442 miles on 26 gallons of gasoline.
Because the more the distance, the more the volume of gasoline used, this is a direct proportion.
So, we have:
[tex]\begin{gathered} V=\frac{102\times26}{442} \\ \\ =6 \end{gathered}[/tex]It will need 6 gallons.
please help me with this question !!
Answer: The perimeter of the triangle is 69 cm.
Step-by-step explanation:
Let us consider the side of the triangle be 3x ,4x and 5x.
According to the question,
The longest side of the triangle be 30 cm.
. 5x=30cm
x=6 cm
So the side of the triangle are 18cm ,24 cm and 30 cm.
The perimeter of the triangle is the sum of sides of the triangle.
so perimeter is =15+24+30=69 cm
