Answer:
Step-by-step explanation:
f-1(Exponet) (x)= x/3-2.
Express your answer in numerals. Raj had 400 cookies. He sold 2 5 of them yesterday and 1 10 of them today. How many cookies did Raj have left?
Answer:
35
Step-by-step explanation:
Use the Pythagorean Theory and the following information to determine the length of the third side of a right triangle which has a hypotenuse of 30 and leg “a” equal 18
10 задание пожалуйста
pls say the question more easily
How do I subtract 8 1/2 - 6 7/8
I need help.... Could someone please help me
furthering dendritic untiring s very crushed iridium rushes Rivendell ft Zarathustra
William says that 15years from now his age will be 3 times his age 5 years ago if x represents williams present age complete the following sentences
Answer:
Is the question complete
Part a: Assume that the height of your cylinder is 8
inches. Consider A
as a function of r
, so we can write that as A(r)=2πr2+16πr
. What is the domain of A(r)
? In other words, for which values of r
is A(r)
defined?
Part b: Continue to assume that the height of your cylinder is 8
inches. Write the radius r
as a function of A
. This is the inverse function to A(r)
, i.e., to turn A
as a function of r
into r
as a function of A
.
r(A)=
Change entry mode
Hints:
To calculate an inverse function, you need to solve for r
. Here, you would start with A=2πr2+16πr
. This equation is the same as 2πr2+16πr−A=0
which is a quadratic equation in the variable r
, and you can solve that using the quadratic formula. You will want to keep A
as a variable when you plug the values into the quadratic formula.
If you want to type in 3π+1x+1
in Mobius, in text mode you can type in (3*pi+1)/(x+1). There is more information in the Introduction to Mobius unit.
Part c: If the surface area is 300
square inches, then what is the radius r
? In other words, evaluate r(300)
. Round your answer to 2 decimal places.
Hint: To compute a numeric square root such as 17.3−−−−√
, you could
Use a spreadsheet such as Microsoft Excel or OpenOffice Calc and type in =sqrt(17.3)
Use a browser to connect to the Internet and type in sqrt(17.3) into a search field
Use a calculator
The radius is
Number
inches if the surface area is 300
square inches.
Hence, in answering the stated question, we may say that We know, equation however, that r must be positive, therefore we take the positive square root: \(r(A) = -4 + square root(64 + 2A) /\)
What is equation?A math equation is a method that links two claims and represents equivalence using the equals sign (=). An equation is a mathematical statement that establishes the equivalence of two mathematical expressions in algebra. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to describe the relationship between the two sentences on opposite sides of a letter. In usually, the logo and the programme are the same. For instance, 2x - 4 equals 2.
Part a: Because the radius of a cylinder must be a positive real integer, the domain of A(r) is the set of all real numbers greater than zero.
As a result, the domain of A(r) is:
{r ∈ ℝ | r > 0}
Part b: To determine the inverse function r(A), solve the equation A = 2r2 + 16r for r expressed in terms of A.
To begin, we may simplify the equation by removing 2r:
A = 2πr(r + 8)
Hence, using the quadratic formula, we can find r:
\(r = (-16 \sqrt((16)2 - 4(2 )(-A)) / 2(2 )\\r = (-16 \sqrt(2562) + 8A) / 4 r = -4 \sqrt(64 + 2A) /\)
We know, however, that r must be positive, therefore we take the positive square root:
\(r(A) = -4 + square root(64 + 2A) /\)
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The radius is apprοximately 11.51 inches when the surface area is 300 square inches.
What is equatiοn?A math equatiοn is a methοd that links twο claims and represents equivalence using the equals sign (=). An equatiοn is a mathematical statement that establishes the equivalence οf twο mathematical expressiοns in algebra.
Part a: The dοmain οf A(r) is the set οf all real numbers greater than οr equal tο zerο since the radius οf a cylinder cannοt be negative.
Dοmain οf A(r): r ≥ 0
Part b: Tο find the inverse functiοn r(A), we start with the equatiοn fοr A(r), set it equal tο A, and sοlve fοr r using the quadratic fοrmula:
\(2 \pi r^2 + 16 \pi r - A = 0\)
\(r = [-16 \pi \± \sqrt{((16 \pi)^2 - 4(2 \pi)(-A))}] / 2(2 \pi)\)
\(r = [-16\pi \± \sqrt{(256\pi^2 + 8 \pi A)}] / 4\pi\)
Simplifying this expressiοn, we get:
\(r = (-4 \± \sqrt{(64 + 2A)}) / 2\)
\(r(A) = -2 \± \sqrt{(32 + 0.5A)\)
Since the radius οf a cylinder cannοt be negative, we take the pοsitive square rοοt:
\(r(A) = -2 + \sqrt{(32 + 0.5A)\)
Part c: Tο find the radius when the surface area is 300 square inches, we plug in A = 300 intο the expressiοn fοr r(A) and simplify:
\(r(300) = -2 + \sqrt{(32 + 0.5(300))\)
r(300) = -2 + sqrt(182)
r(300) ≈ 11.51
Therefοre, the radius is apprοximately 11.51 inches when the surface area is 300 square inches.
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Arrange the terms of the polynomial in descending powers of p. w^(5)p^(5)+w^(6)p-wp^(6)+29
The given polynomial is:
w^(5)p^(5) + w^(6)p - wp^(6) + 29
To arrange the terms in descending powers of p, we need to write the polynomial in the form:
ap^m + bp^n + cq^r + ...
where m > n > r > ..., and a, b, c, ... are constants.
In this case, we can rearrange the terms as follows:
wp^(6) - w^(5)p^(5) + w^(6)p + 29
So, the polynomial in descending powers of p is:
wp^(6) - w^(5)p^(5) + w^(6)p + 29
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From least to greatest, What are the x–coordinates of the three points where the graphs of the equations intersect? If approximate, enter values to the hundredths.
,
,
The x-coordinates where the graphs of the equations intersect are x = -1 and x = 3
How to determine the x-coordinates where the graphs of the equations intersect?From the question, we have the following parameters that can be used in our computation:
y = 2x
y = x² - 3
The x-coordinates where the graphs of the equations intersect is when both equations are equal
So, we have
x² - 3 = 2x
Rewrite the equation as
x² - 2x - 3 = 0
When the equation is factored, we have
(x + 1)(x - 3) = 0
So, we have
x = -1 and x = 3
Hence, the x-coordinates are x = -1 and x = 3
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Question
From least to greatest, What are the x–coordinates of the three points where the graphs of the equations intersect? If approximate, enter values to the hundredths.
y = 2x
y = x² - 3
Maggie's brother is 5 years younger than twice her age. The sum of their ages is 22.
How old is Maggie?
Answer:
9 years old
Step-by-step explanation:
Let maggie's age be m,
and let maggie's brother's age be b
b = 2m - 5,
m + b = 22
Substitute "2m - 5" for b in the second equation (substitution)
m + (2m - 5) = 22 -> Remove parenthesis
m + 2m - 5 = 22 -> Combine like terms
3m = 22 + 5 = 27 -> Divide either side by 3
m = 27/3 = 9
Solution: Maggie is 9 years old
in an arithmetic sequence the sixth term is half the fourth term and the third term is 15
The Required sequence of the arithmetic progression will be,
= 21, 18, 15, 12, 9, 6
According to the question,
The term that is given is the third term of the sequence = 15
Let the fourth term of the sequence be = x
Let the sixth term of the sequence be = \(\frac{x}{2}\)
So let's make a structure of the sequence=
_, _, 15, x, _, \(\frac{x}{2}\)
Let us consider d as the difference between two terms,
d = x - 15
x = 15 + d -------- equation 1
According to the arithmetic progression if we add the difference of x and 15 into x it will give us the fifth term
let the fifth term be y
x + d = y ------- equation 2
And similarly adding the difference d to y will give the sixth term that is \(\frac{x}{2}\)
y + d = \(\frac{x}{2}\) ------- equation 3
substituting the value of y from equation 2 to equation 3
x + d + d = \(\frac{x}{2}\)
x + 2d = \(\frac{x}{2}\)
2d = - x + \(\frac{x}{2}\)
d = - \(\frac{x}{4}\)
Now substituting the value of d into equation 1,
x + 15 + (- \(\frac{x}{4}\) )
x + \(\frac{x}{4}\) = 15
\(\frac{5x}{4}\) = 15
x = \(\frac{15 *4}{5}\)
x= \(\frac{60}{5}\)
x = 12
Now we know that the third term of the series x = 12
Similarly the sixth term = \(\frac{x}{2}\)
= \(\frac{12}{2}\)
= 6
So as we can see that the total difference between each term is = 3
Therefore, the required sequence = 21, 18, 15, 12, 9, 6
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Whenever Deven and Laura owe each other money, they "pay" each other using stickers. They've agreed that a Harry Potter sticker is worth 49 dollars and a Twilight sticker is worth 35 dollars. They can even use stickers as "change" if one person overpays the other. For example, if Deven owes Laura 189 dollars, he can give her 6 Harry Potter stickers ($6 \cdot 49 = 294$ dollars), and she can return 3 Twilight stickers ($3 \cdot 35 = 105$ dollars). This trade is like a transfer of $294-105=189$ dollars. What is the smallest positive debt, in dollars, that can be paid off using sticker trading?
The smallest positive debt that can be paid off using sticker trading is $7$ dollars.
To find the smallest positive debt that can be paid off using sticker trading, we need to consider the values of the stickers (in dollars) and find the smallest positive amount that can be reached through a combination of these values.
Given that a Harry Potter sticker is worth $49 and a Twilight sticker is worth $35, we can approach this problem using the concept of the greatest common divisor (GCD) of these two values.
The GCD of $49$ and $35$ is $7$. This means that any multiple of the GCD can be represented using these sticker values.
In other words, any positive multiple of $7$ dollars can be paid off using sticker trading.
Therefore, the smallest positive debt that can be paid off using sticker trading is $7$ dollars.
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On the first math exam, 16 students received an A grade. On the second math exam,
12 students received an A. grade. What percentage decrease is that?
Answer: that four of them are stupid
Step-by-step explanation:
Answer:
25% :D
Step-by-step explanation:
Is (49,13),(61,36),(10,27),(76,52),(23,52) a function
Answer:
No
Step-by-step explanation:
To determine whether the given set of ordered pairs {(49,13),(61,36),(10,27),(76,52),(23,52)} represents a function, check if each x-value is associated with a unique y-value.
Check the x-values in the set: 49, 61, 10, 76, and 23. There are no repeated x-values. Still need to check if each x-value has a unique corresponding y-value.
Check the y-values: 13, 36, 27, 52, and 52. There is one repeated y-value, 52, for the pairs (76, 52) and (23, 52).
Conclusion: the y-value 52 is associated with 2 different x-values, therefore the given set of ordered pairs does not represent a function.
What is the range of the data below? 6.5, 7.6, 9.1, 2.4, 8.8
100 students are interviewed to see which of biology, chemistry or physics they prefer. 55 of the students are girls. 25 of the girls like biology best. 27 of the boys prefer physics. 23 out of the 29 who prefer chemistry are girls. What percentage of the students prefer biology?
Using percentages we know that 62% or 62 students out of 100 students prefer biology.
What are percentages?In mathematics, a value or ratio that can be expressed as a fraction of 100 is known as a percentage.
When determining a percentage of a number, we should first divide it by 100 before multiplying the result by 100.
Thus, the proportion refers to a component per 100.
The word percent denotes a percentage of 100. It is represented by the symbol "%."
So, according to the given situation:
34 females enjoy biology
Do boys enjoy biology?
It is 34%≤
Then,
27% favor chemistry
10% favor physics.
The calculation would be:
27 + 11 = 38
100 - 38 = 62
Therefore, using percentages we know that 62% or 62 students out of 100 students prefer biology.
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Correct question:
100 students are interviewed to see which of biology, chemistry or physics they prefer.72 of the students are girls. 34 of the girls like biology best. 11 of the boys prefer physics. 24 out of the 27 who prefer chemistry are girls. What percentage of the students prefer biology?
- The line AB has equation 5x – 2y = 7. The point A has coordinates (1, -1) and the point B has coordinates (3,k). (a) (i) Find the value of k. (ii) Find the gradient of AB. (b) Find an equation for the line through A which is perpendicular to AB. (c) The point C has coordinates (-6, -2). Show that AC has length pV2, stating the value of p.
Step-by-step explanation:
For finding k we'll have to plug in the x-value of the coordinate (3,k) into the equation, and solve for the y:
5(3) - 2y = 7
15 - 2y = 7
2y = 8
y = 4 => k =4
2) I assume the gradient is the slope of the line. If so, just isolate the y in the original equation and see what's the coefficient of the x:
-2y = -5x + 7
y = (5/2)x + 7/2 => the gradient is 5/2
3) the condition of perpendicularity is expressed by the following relation:
a * a' = -1
Where a is the slope of the first line and a' of the second line. We need to find a' that will be:
-1/a = -1/(5/2) = -2/5
The perpendicular line will be:
y = (-2/5)x + b
We need to find b, and we know that this line passes through A (1,-1):
-1 = (-2/5)*1 + b
b = -1+(2/5) = -3/5
The equation will be:
y = (-2/5)x - 3/5.
4) I don't know what that symbol means (pV2).
Find the intercepts of the parabola y = x² - 4x - 12. Give exact answers and simplify any fractions.
The intercepts of the parabola are A ( 6 , 0 ) and B ( -2 , 0 ) and the y intercept of the parabola is ( 0 , -12 )
What is a Parabola?A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line
The equation of the parabola is given by
( x - h )² = 4p ( y - k )
y = a ( x - h )² + k
where ( h , k ) is the vertex and ( h , k + p ) is the focus
y is the directrix and y = k – p
The equation of the parabola is also given by the equation
y = ax² + bx + c
where a , b , and c are the three coefficients and the parabola is uniquely identified
Given data ,
Let the equation of the parabola be represented as A
Now , the value of A is
y = x² - 4x - 12 be equation (1)
On simplifying , we get
when y = 0
x² - 4x - 12 = 0
On factorizing the quadratic equation , we get
x² - 6x + 2x - 12 = 0
( x + 2 ) ( x - 6 ) = 0
So , the two values of x are
when ( x + 2 ) = 0
x = -2
And , when ( x - 6 ) = 0
x = 6
So , the x intercepts of the parabola are A ( 6 , 0 ) and B ( -2 , 0 )
The y intercept is when x = 0
So , y = 0 - 0 - 12
y = -12
And , the y intercepts of the parabola are ( 0 , -12 )
Hence , the intercepts of the parabola are solved
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3. What is the next term of the geometric sequence?
-1, -3, -9, -27, -81,
Write an equation of the line that passes through (2, -5) and has a slope of 4
Step-by-step explanation:
(y-(-5))/(x-2) = 4
(y+5)/(x-2) = 4
y+5 = 4x - 8
y = 4x - 13
What are the solutions to logs (x²+8)= 1+logg(x)?
x=-2 and x=-4
x-1 and x=8
x= 1 and x = -8
O x=2 and x=4
Step-by-step explanation:
Log(x²+8)=log 10+ log x
Log(x²+8)=log(10×x)
x²+8=10x
x² - 10x + 8=0
x is approximately to - 1 and - 8✅
The solutions to the given equation are x = -1 and x = 8.
Option A is the correct answer.
What is a solution?Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.
We also find the solution in a system of equations using the substitution or elimination method.
Example:
2x + 4 = 8
The solution is x = 2.
We have,
Using logarithmic properties, we can simplify the given equation:
logs(x² + 8) = 1 + log g(x)
logs(x² + 8) - log g(x) = 1
log[(x² + 8)/g(x)] = 1
(x² + 8)/g(x) = 10
x² + 8 = 10g(x)
Now we can solve for x by substituting the given answer options and solving for g(x):
For x = -2 and x = -4:
x = -2:
(-2)² + 8 = 12, which is not equal to 10 g(x) for any value of g(x).
So x = -2 is not a solution.
x = -4:
(-4)² + 8 = 24, which is also not equal to 10g(x) for any value of g(x).
So x = -4 is not a solution.
For x = -1 and x = 8:
x = -1:
(-1)² + 8 = 9, which is equal to 10g(x) when g(x) = 0.9.
So x = -1 is a solution.
x = 8:
(8)² + 8 = 72, which is equal to 10g(x) when g(x) = 7.2.
So x = 8 is a solution.
For x = 1 and x = -8:
x = 1:
(1)² + 8 = 9, which is equal to 10g(x) when g(x) = 0.9.
So x = 1 is a solution.
x = -8:
(-8)² + 8 = 56, which is not equal to 10g(x) for any value of g(x).
So x = -8 is not a solution.
Therefore,
The solutions to the given equation are x = -1 and x = 8.
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Suppose that $6000 is placed in a savings account at an annual rate of 4%, compounded quarterly. Assuming that no withdrawals are made, how long will it take for the account to grow to $8670?
The time taken for the money to grow to $8670 at compound interest is approximately 9.24 years.
Given the amount of money that is the principal = $6000
Rate = 4% compounded quarterly.
Time = t
Amount = $8670
Now we know that the amount is calculated by the formula:
A = P(1+r/4)ⁿ
8670 = 6000(1+0.01)ⁿ
Hence
log 1.445 = n log 1.01
or, n = 36.99
Number of years = 36.99 / 4 = 9.24 years.
The interest that is added to a loan or deposit is referred to as compound interest. Compound interest is computed for a sum utilizing both the principal and interest already paid. The main distinction between compound interest and simple interest is this.
If we look at our bank statements, interest is usually credited to our account once a year. While the principle remains constant, the interest changes annually.
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Find the missing angle measure just put the number.
Answer:
the answer is x=18 bc 90-72= 18 and the othet one is x=55 bc 180-125=55
What’s the answer (no link I give brainly)
Answer:
The answer is C i'm pretty sure
Hope this helps :)
a train is moving at a speed of 50 kilometers per hour. how long will it take to cover a distance of 550 kilometers?
Answer:
11 hours
Step-by-step explanation:
tell whether the ordered pair is a solution of the equation !! please help i will mark you brainliest!
Answer:
yes both questions the answer are equal
Step-by-step explanation:
(3,5) where 3 is the x coordinate and 5 is the y coordinate
putting it into y=5x-10
5=5(3)-10
5=5
(4,5) where 4 is the x coordinate and 5 is the y coordinate
putting it into y=2x-3
5=2(4)-3
5= 5
whats the answer. please tell me cause these ads are out of control
Answer:
Step-by-step explanation:
if your on computer jus press refresh when your by the answer, it will show u for a split sec
Can you please help me with this standard deviation related problem?
So:
\(\begin{gathered} P(\frac{X1-\mu}{\sigma}\leq Z\leq\frac{X2-\mu}{\sigma}) \\ P(\frac{14.1-13}{1.1}\leq Z\leq\frac{15.2-13}{1.1}) \\ P(1\leq Z\leq2)=0.1359 \end{gathered}\)Therefore:
\(0.1352\times3000\approx408\)Answer:
408 phones
-6 is a solution for
True
False
Answer:
Yes
Step-by-step explanation:
-6 is a solution
Any point that is on the blue line is a solution
There are 3,785 milliliters in 1 gallon, and there are 4 quarts in 1 gallon.
How many milliliters are in 3 gallons?
Paying 20 points