The inverse of this function is f(x) = [tex] \frac{x + 9}{7} [/tex].
All inverse functions can be found by switching the x and f(x) values. Then you can solve for the new f(x). The result is the inverse function. Below is the step-by-step process for finding one.
f(x) = 7x - 9 ----> Switch the x and f(x)
x = 7f(x) - 9 -----> Add 9 to both sides
x + 9 = 7f(x) ----> Divide both sides by 7
f(x) = [tex] \frac{x + 9}{7} [/tex]
if x2 = 49 the only possible answer for x is 7
While the equation x² = 49 suggests that x = 7, it also has a negative solution, x = -7. Both solutions can be verified by substitution into the original equation, proving they are correct through resulting identities.
The equation x² = 49 has two solutions in the realm of real numbers, not just x = 7. To find the values of x that satisfy the equation, we take the square root of both sides. Since the square root of a number has both a positive and a negative value, the solutions are x = 7 and x = -7. To verify these solutions, we can substitute them back into the original equation to confirm that they work, demonstrating identities such as 7² = 49 and (-7)² = 49.
Robin randomly selects a number between 1 and 20. What is the probability that the number selected is the square of a natural number?
The probability that the number selected is the square of a natural number will be 0.20.
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
Robin randomly selects a number between 1 and 20.
Then the total number of the events will be
Total events = 20 {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}
The probability that the number selected is the square of a natural number will be
We know that natural numbers 1, 2, 3, 4, 5, and so on.
Then the square of the natural numbers will be
1, 4, 9, 16, 25, ....
Favorable event = 3 {1, 4, 9, 16}
Then the probability will be
P = 4 / 20
P = 1/5
P = 0.20
The probability that the number selected is the square of a natural number will be 0.20.
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given right triangle XYZ what is the value of tan 60°
Answer:
√3
Step-by-step explanation:
got 100%
You were just approved for a $32,000 car loan at an APR of 1.99% for 60 months. As you make payments over time: your payment is , the amount of interest you will pay each month , and the amount of principal you pay each month .
What it Means...
If you borrow $32,000 at 1.99% for 5 years, your monthly payment will be $560.75.
The payments do not change over time. The loan amortizes over the repayment period, meaning the proportion of interest paid vs. principal repaid changes each month. As the loan amortizes, the amount of monthly interest paid decreases while the amount of principal paid increases.
Loan Amount: $32,000Complete the square to form a perfect square trinomial x^2-14x+
Look at the figure. How can you prove ∆ABD and ∆ACD are congruent?
A. ∆ABD ≅ ∆ACD by the SAS Postulate.
B. It is not possible to determine if the triangles are congruent.
C. ∆ABD ≅ ∆ACD by the SSS Postulate.
Answer: The correct option is (B). It is not possible to determine if the triangles are congruent.
Step-by-step explanation: We are given to select the correct option by which we can prove that ∆ABD and ∆ACD are congruent.
As shown in the figure,
In ∆ABD and ∆ACD, we have
∠ADB = ∠ADC = 90°,
AD is the common side.
So, one angle and the adjacent side of one triangle are congruent to the corresponding angle and the adjacent side of the other triangle.
That is, to prove that the two triangles are congruent, we need one of the following two conditions:
(i) BD = CD
or
(ii) ∠BAD = ∠CAD.
Since none of these two are given, so we cannot determine the congruence of the two triangles.
Therefore, it is not possible to determine if the triangles are congruent.
Thus, option (B) is correct.
Suppose that the probabilities of a customer purchasing 0, 1, or 2 books at a book store are 0.2, 0.4, and 0.4, respectively. what is the expected number of books a customer will purchase? the standard deviation of the customer's book purchases is
The expected number of books a customer will purchase is 1.2 books, and the standard deviation of their book purchases is approximately 0.78 books.
To find the expected number of books a customer will purchase,
use the formula for the expected value (also known as the mean) of a random variable:
Expected Value (μ) = Σ (x × P(x))
Where:
μ is the expected value.
x represents the possible values of the random variable (in this case, 0, 1, and 2).
P(x) is the probability associated with each value of x.
Probability of purchasing 0 books (P(0)) = 0.2
Probability of purchasing 1 book (P(1)) = 0.4
Probability of purchasing 2 books (P(2)) = 0.4
Now, calculate the expected value:
μ = (0 × 0.2) + (1 ×0.4) + (2 × 0.4)
μ = 0 + 0.4 + 0.8
μ = 1.2
To find the standard deviation (σ) of the customer's book purchases,
use the formula for the standard deviation of a discrete random variable:
Standard Deviation (σ) = √[Σ((x - μ)² × P(x))]
Where:
σ is the standard deviation.
x represents the possible values of the random variable.
μ is the expected value.
P(x) is the probability associated with each value of x.
In this case, you already calculated μ as 1.2, and you have the probabilities P(0), P(1), and P(2).
Now, calculate the standard deviation:
σ = √[((0 - 1.2)² × 0.2) + ((1 - 1.2)² × 0.4) + ((2 - 1.2)² × 0.4)]
σ = √[(1.44 ×0.2) + (0.16 × 0.4) + (0.64 × 0.4)]
σ = √[0.288 + 0.064 + 0.256]
σ = √0.608
σ ≈ 0.78
Therefore, the expected number and the standard deviation of books a customer will purchase is 1.2 books and approximately 0.78 books respectively.
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For which k will the graph of f(x)=x^2−kx+k^2 cross the x-axis twice?
J is 25 more than 3 help???
2x - y + 3z = -9
x + 3y - z = 10
3x + y - z = 8
find the ordered triple
PLEASE HELPS NEED THIS DONE BEFORE 3 O CLOCK
1)Jerome noticed the following house numbers on his street:
305, 318, 331, 344
The house numbers follow a pattern. Which expression can be used to determine the nthnth house number on his street?
A) 292 +13n
B) 292n
C) 292n + 13
D) 13(n + 292)
2) A polynomial expression is shown below.
(mx+8)(2x−4)
The expression is simplified to:
−6x2+28x−32-6x2+28x-32
What is the value of m?
A) 3
B) 4
C) -3
D) -4
3) What is the domain of the function shown below? (PICTURE AT BOTTOM)
A) 2
B) −8 ≤ x <3and 4 ≤ x <8
C) −8 ≤ x < 8
D) −7 ≤ x ≤ 7
Answer:
Jerome noticed the following house numbers on his street:
Answer 292 +13n
A polynomial expression is shown below. What is the value of m?
Answer -3
What is the domain of the function shown below
Answer −8 ≤ x <3and 4 ≤ x <8
Find the inverse of this 3x3 matrix. [1 5 2]
[ 1 1 7]
[0 -3 7]
Answer:
A
Step-by-step explanation:
⎡−25 26 −33⎤
⎥ 4 −4 5 ⎥
⎥ 3 −3 4 ⎦
how many rootes are in f(x)=(x^2-3x+1)^2
2
5
6
9
226Ra has a half-life of 1599 years. How much is left after 1000 years if the initial amount was 10 g?
How many triangles are with two sides each 6 inches long and one angle measure of 90°.
The description relates to an isosceles right triangle.
An isosceles right triangle can be described as the triangle that has two sides that are both equal while it also has an angle that will be 90° which is the right angle.
In this case, the two equal sides are given as 6 inches while it also has an angle of 90°. Therefore, it's an isosceles right triangle.
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The cylinder shown has a volume of π in3. Find the volume of a cone with the same base and height as the cylinder.
Answer:
Step-by-step explanation:
Alright, lets get started.
Suppose the height of cylinder is h and radius of base is r.
The volume of cylinder will be : [tex]\pi r^2h[/tex]
The cone is of same height means h and same base means radius will be r.
The formula of volume of cone is : [tex]\frac{1}{3} \pi r^2h[/tex]
It means the volume of cone is one third of the volume of cylinder.
The volume of cylinder is given as π.
So, the volume of cone will be : [tex]\frac{\pi }{3}[/tex] : Answer
Hope it will help :)
tickets for a football match are sold at $30 for adults and $15 for children a company bought 28 tickets if x of these tickets were for adults, write in terms of x a. the number of tickets for children b. the amount spent on tickets for adults c. the amount spent on tickets ...
The number of tickets for children is represented by '28-x' and the amount spent on tickets for adults is '$30x'. The amount spent on tickets for children is '$15*(28-x)'.
Explanation:We will use the concept of algebraic expressions to solve this question. If we represent the number of adult tickets as x, we know that the total number of tickets is 28. Hence, the number of children tickets can be represented as 28-x. The cost of a ticket for adults is $30, so the amount spent on adult tickets can be represented as $30x. Similarly, as the cost of a ticket for children is $15, the amount spent on children tickets can be represented as $15*(28-x).
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The number of ticket for children is (28 - x), the amount spent on tickets for adults would be $30x, and the total amount spent on tickets would be $30x + $15(28 - x).
Explanation:If a company bought 28 tickets and x of these tickets were for adults, then:
a. The number of tickets for children would be 28 - x. This is because from the total number of tickets purchased, we subtract the number of adult tickets to find the number of children's tickets.
b. The amount spent on tickets for adults would be $30x. This is because each adult ticket costs $30 and there are x number of adults.
c. To find out the total amount spent by the company, we will multiply the number of adult tickets by the price of an adult ticket ($30x) and add this to the product of the number of children tickets (28 - x) and the price of a child's ticket ($15). Therefore, the total spent would be $30x + $15(28 - x).
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Treys online music club charges a monthly rate of $20 plus $0.80 per song download. Debs online music club charges a monthly rate of $21 plus $0.60 per song download. For what number of songs will the monthly charge be the same for both clubs? How much will it cost?
Answer:
For 5 songs the monthly charge be the same for both clubs.
It will cost $ 24.
Step-by-step explanation:
Let, for x songs, the monthly charges are same for both clubs,
Given,
For Treys online music club,
Monthly rate = $ 20,
Additional Charges for a song = $ 0.80,
⇒ Additional Charges for x song = $ 0.80x,
Thus, the total monthly charges for x songs = Monthly rate + Additional Charges for x song
= 20 + 0.80x
Now, for Debs online music club,
Monthly rate = $ 21,
Additional Charges for a song = $ 0.60,
⇒ Additional Charges for x song = $ 0.60x,
Thus, the total monthly charges for x songs = Monthly rate + Additional Charges for x song
= 21 + 0.60x
Hence, we can write,
[tex]20 + 0.80x = 21 + 0.60x[/tex]
[tex]0.80x - 0.60x = 21 - 20[/tex]
[tex]0.20x = 1[/tex]
[tex]\implies x = \frac{1}{0.20}=5[/tex]
Hence, for 5 songs the monthly charge be the same for both clubs.
Also, the cost for 5 songs = 20 + 0.80 × 5 = 20 + 4 = $ 24
PLZZZZZZ HELPPPP
Solve the system of equations using the substitution method.
{2x+8y=4x=−3y+5 Enter your answers in the boxes.
The method of substitution is a three step method to solve the equations. In this method , one equation for one of the variables is solved and in the first step.
The outcome is then substituted to the second equation in the second step for solving the equation.The value is re-substituted to the original equation to find the outcome in the third step.
On solving the equations by substitution method we get x=14 and y=-3
Calculation:Given equations:
[tex]\rm 2x+8y = 4[/tex] (1)
[tex]\rm x=-3y+5[/tex] (2)
On substituting [tex]x=-3y+5[/tex] in equation 1:
[tex]\begin{aligned}\rm 2(-3y+5)+8y&=4\\\\-6y+10+8y&=4\\\\2y+10&=4\\\\2y&=4-10\\\\ 2y &= -6\\\\y&=\dfrac{-6}{2}\\\\y&=-3\end[/tex]
Substituting [tex]\rm y=-3[/tex] in equation 2:
[tex]\rm x&=-3y+5\\\\x&=-3(-3)+5\\\\x=9+5\\\\x=14[/tex]
Therefore the values of x and y for the given equations is 14 and -3 respectively.
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I WILL GIVE U BRAINLY!!!
Which substance has been changed most over time from its original plant material?
A.
peat
B.
anthracite coal
C.
bituminous coal
D.
lignite
Quadrilateral ABCD is inscribed in a circle. What is the measure of angle A? Enter your answer in the box. m∠A= ° A quadrilateral inscribed in a circle. The vertices of the quadrilateral lie on the edge of the circle and are labeled as A, B, C, D. The interior angle A is labeled as left parenthesis 3 x plus 6 right parenthesis degrees. The angle C is labeled as left parenthesis x plus 2 right parenthesis degrees.
The measure of angle A in a cyclic quadrilateral ABCD, where the measure of angle A is (3x + 6) degrees and the measure of angle C is (x + 2) degrees, is determined to be 135 degrees.
Explanation:Given that quadrilateral ABCD is inscribed in a circle, it follows from the properties of cyclic quadrilaterals that the sum of the opposite angles of such a quadrilateral is always 180 degrees. Therefore, if the measure of angle A is represented by the expression (3x + 6) degrees and the measure of angle C is represented by the expression (x + 2) degrees, then we can set up an equation that (3x + 6) + (x + 2) = 180. Solving this equation gives x = 43. Using x = 43, substitute it into 3x + 6 to get the value of angle A, which is equal to 135 degrees.
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The formula for the volume of a cube is V(s) = s3 where s is the side length of the cube. In which quadrant(s) is the graph of the function V(s)?
Answer:
The answer is A: Quadrant 1
Step-by-step explanation:
On Edge :)
Write the explicit formula for the geometric sequence.
64, 32, 16, 8, ...
A) an = 8 · 4n-1
B) an = 8 · 2n-1
C) an = 32 · 0.5n-1
D) an = 64 · 0.5n-1
Answer:
D) [tex]a_{n}[/tex][tex]=64[/tex]×[tex]0.5^{n-1}[/tex]
Step-by-step explanation:
The answer is D because it is the only answer that has an=64 and a decimal, 64 is your first term and the sequence is getting smaller
AND OR
Answer:
D) [tex]a_{n}[/tex][tex]=64[/tex]×[tex]0.5^{n-1}[/tex]
Step-by-step explanation:
Explicit Formula: an = a1 · dn-1
a1 = 64, d = 0.5
an = 64 · 0.5n-1
Find the points on the curve y = 2x3 + 3x2 − 12x + 9 where the tangent line is horizontal.
the points on the curve [tex]y = 2x^3 + 3x^2 - 12x + 9 are (-2,29) \; and \; (1,2)[/tex]where the tangent line is horizontal.
Given :
The equation of the curve is [tex]y=2x^3\:+\:3x^2\:-\:12x\:+\:9[/tex]
Given tangent line is horizontal . Tangent line is horizontal when slope =0
Slope is nothing but the derivative.
So we find out x values where derivative =0
Lets take derivative for the given curve y
[tex]y=2x^3+3x^2-12x+9\\y'=2(3x^2)+3(2x)-12\\y'=6x^2+6x-12[/tex]
Now we set the derivative =0 and solve for
[tex]6x^2+6x-12=0\\Divide\; whole \; equation \; by \; 6\\x^2+x-2=0\\(x+2)(x-1)=0\\x+2=0, x=-2\\\\x-1=0, x=1[/tex]
So , the slope =0 when x=1 and x=-2
Now we find out the points . Use the original function
[tex]y=2x^3\:+\:3x^2\:-\:12x\:+\:9\\x=-2\\2\left(-2\right)^3+3\left(-2\right)^2-12\left(-2\right)+9=29\\(-2,29)\\\\x=1\\2\left(1\right)^3+3\left(1\right)^2-12\left(1\right)+9=2\\(1,2)[/tex]
the points on the curve [tex]y = 2x^3 + 3x^2 - 12x + 9 are (-2,29) \; and \; (1,2)[/tex]where the tangent line is horizontal.
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Milli plans to rent a room for her birthday party for $40. The catering charge is $12 per person but there is no charge for Milli's meal since she is the guest of honor. If Milli has $100 to spend on her birthday party, what is the maximum number of friends Milli can invite?
Please try this, I forget absolutely everything about rhombuses. Thanks for all the help, shouldn't be too hard
What is the volume of the figure below if a = 3.9 units, b = 5.7 units, and c = 3 units?
A. 157.95 cubic units
B. 351.351 cubic units
C. 124.605 cubic units
D. 113.49 cubic units
Final answer:
The volume of the parallelepiped with sides of lengths a = 3.9 units, b = 5.7 units, and c = 3 units is given by the formula V = a × b × c. After performing the calculation, the volume comes out to be 66.87 cubic units.
Explanation:
To find the volume of the parallelepiped with edges of lengths a, b, and c, you can multiply the length of each edge together. The volume (V) of a parallelepiped (a three-dimensional figure formed by six parallelograms) is given by the product of the lengths of its three dimensions. In this case, the formula to calculate the volume is V = a × b × c.
By plugging in the values provided:
a = 3.9 units
b = 5.7 units
c = 3 units
We get:
V = 3.9 units × 5.7 units × 3 units
Doing the multiplication:
V = 66.87 cubic units
Therefore, the volume of the figure is 66.87 cubic units.
Determine if the functions are even, odd or neither. f(x) = -5x4 - 2 and g(x) = x3 + 2x
Evaluate the integral. (use c for the constant of integration.) 7 ln(x)/ x sqrt(5 + (ln(x))^2) dx
The expression for the integral [tex]\int\frac{7ln(x)}{x\sqrt{5+(ln(x))^2} } dx[/tex] after the evaluation is [tex]\text{I}=7\sqrt{5+(ln(x))^2} +C[/tex].
Given an integral expression:
[tex]\text{I}=\int\frac{7ln(x)}{x\sqrt{5+(ln(x))^2} } dx[/tex]
This can be written as:
[tex]\text{I}=7\int\frac{ln(x)}{x\sqrt{5+(ln(x))^2} } dx[/tex]
It is required to find the integral value.
Let u = 5 + (ln (x))²
Differentiate.
[tex]du=2ln(x)*\frac{1}{x} dx[/tex]
Or [tex]\frac{du}{2} =\frac{lnx}{x} dx[/tex]
Substitute the values.
[tex]\text{I}=7\int\frac{1}{\sqrt{u} } \frac{du}{2}[/tex]
[tex]\text{I}=\frac{7}{2} \int\frac{1}{\sqrt{u} }du[/tex]
[tex]\text{I}=\frac{7}{2} (2\sqrt{u} )+C[/tex]
Substitute back the value of u.
[tex]\text{I}=7\sqrt{5+(ln(x))^2} +C[/tex]
Hence the value of the integral is [tex]\text{I}=7\sqrt{5+(ln(x))^2} +C[/tex].
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How much would $500 invested at 7% interest compounded annually be worth after 5 years?