The inverse function of the function f(x) = 12(x+3) is f(x) = -2x - 3
A function's inverse is a function that offers us the actual value for which the desired function produces a specific outcome.
The function given is:
To find the inverse, we must perform the following procedures.
y takes the place of f(x);
y = -(x+3)/2
Change the x and y variables.
x = -(y+3)/2
Calculate y
2x = - (y + 3)
2x = -y - 3
y = -2x - 3
We get the following in inverted notation:
f(x)⁻¹ = -2x - 3
Thus the obtained inverse function is f(X) = -2x - 3
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The equation y=0.29x+209 gives the cost y of renting a car if the care is driven x miles. Based on this equation, for every mile the car is driven the cost of increases by how much?
The car-driven cost increases with an increase in miles. After substituting x = 1,2,3,4.... you will find that it is increasing by 0.29 every time.
What is an equation?Equations are logical assertions in mathematics that have two algebraic expressions on either side of an equals (=) sign. The expression on the left and the expression on the right is shown to be equal in reference to one another.
According to the question,
y = 0.29 x + 209
Where x is the number of miles and y is representing the driving cost of the car.
Substitute x = 1,2,3,4...... in the above equation.
y₁ = 0.29 (1) + 209 = 209.29
y₂ = 0.29 (2) + 209 = 209.58
y₃ = 0.29 (3) + 209 = 209.87
y₄ = 0.29 (4) + 209 = 210.16 and so on.
Now, take the difference,
y₂ - y₁ = 0.29
y₃ - y₂ = 0.29
y₄ - y₃ = 0.29
Hence, it is clear that with an increase in each mile the cost is increasing by 0.29.
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An object is moving at a speed of 3 kilometers every 5 days. Express this speed in yards per hour.
An object is moving at a speed of 27.3 yards per hour.
How to find the speed in yards?3 kilometers must first be converted to yards.
1 m = 1.09 yards.
1 Km = 1093.61
3 km to yards is 3280.84
Currently, we must convert 5 days to hours. There are 24 hours every day, we shall multiply that number by 5 to find the number of hours in 5 days.
5 * 24 = 120 hours
To determine the speed in yards per hour, divide 3280.84 by 120.
3208.4/120
= 27.34 yards per hour
27.34 is 27.3 approximately.
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f(x) =x^2-3x-18 vertex?
Answer:
(3/2, -81/4)Step-by-step explanation:
Rewrite in vertex form and use this form to find the vertex (h, k).
Answer:
[tex]\sf Vertex \left(\dfrac{3}{2}, \dfrac{-81}{4}\right)[/tex]
Step-by-step explanation:
Vertex of quadratic function: Write the equation in vertex form by using the method completing the square.y = x² - 3x - 18
Add 18 to both sides.
y + 18 = x² - 3x
Divide the co-efficient of x by 2 and square the result and then add it to both sides.
Co-efficient of x = 3. Divide 3 by 2and add (3/2)² to both sides
[tex]\sf y + 18 + \left(\dfrac{3}{2}\right)^2= x^2 - 3x + \left(\dfrac{3}{2}\right)^2\\\\\\y + 18+\dfrac{9}{4}=x^2 - 3x + \dfrac{9}{4}\\\\\\[/tex]
[tex]\sf y + \dfrac{18*4}{1*4}+\dfrac{9}{4}=\left(x - \dfrac{3}{2}\right)^2\\\\\\y + \dfrac{72}{4}+\dfrac{9}{4}=\left(x - \dfrac{3}{2}\right)^2\\\\\\y + \dfrac{81}{4}=\left(x-\dfrac{3}{2}\right)^2\\\\ y = \left(x-\dfrac{3}{2}\right)^2 -\dfrac{81}{4}\\\\[/tex]
Vertex form: f(x) = (x - h)² + k
where h and k are the vertex co-ordinates.
[tex]\sf \boxed{\bf Vertex \left(\dfrac{3}{2}, \dfrac{-81}{4}\right)}[/tex]
AX + 6939 + x4(G.CO.C.10)Solve for xFind the measure of angle A:
The sum of the angles of a triangle always equals 180°, then we can formulate the following expression:
(x + 69)° + (39 + x)° + 90° = 180°
By combining like terms in the above equation, we get:
x + x + 69 + 39 + 90 = 180
2x + 198° = 180°
We can solve for x to get:
2x + 198 - 198 = 180 - 198
2x = 180 - 198
2x = -18
x = -18/2
x = -9
Then, x equals -9.
In order to calculate the measure of angle A, we just have to replace the value of x into the equation 39 + x, then we get:
mmm
Then, the measure of angle A equals 30°.
Solve the quadratic equation by completing the square. x^2+8x+9=0First choose the appropriate form and fill in the blanks with correct numbers. Then solve the equation. If there is more than one solution, separate with commas.
The quadratic equation given in the question is
[tex]x^2+8x+9=0[/tex]Step 1: Keep x terms on the left and move the constant to the right side by subtracting 9 on both sides
[tex]\begin{gathered} x^2+8x+9=0 \\ x^2+8x+9-9=0-9 \\ x^2+8x=-9 \end{gathered}[/tex]Step 2: Take half of the coefficient of the x term and square it
The coefficient of the x term is 8
[tex]\begin{gathered} (8\times\frac{1}{2})^2 \\ =(\frac{8}{2})^2 \\ =4^2 \\ =16 \end{gathered}[/tex]Step 3: Add 16 to both sides in the equation in step 1
[tex]\begin{gathered} x^2+8x=-9 \\ x^2+8x+16=-9+16 \\ x^2+8x+16=7 \\ \end{gathered}[/tex]Step 4: Re-write the perfect squares on the left
[tex]\begin{gathered} x^2+8x+16=7 \\ (x+4)^2=7 \\ \text{Which will give us } \\ (x+4)^2-7=0 \\ (x+4)^2=7 \end{gathered}[/tex]Hence,
We will have (x+4)²=7
To solve for the value of x, we will equate to zeros and make x the subject of the formula
[tex](x+4)^2=7[/tex]Step 5: Add 7 to both sides
[tex]\begin{gathered} (x+4)^2-7+=0+7 \\ (x+4)^2=7 \end{gathered}[/tex]Step 6: Square root both sides
[tex]\begin{gathered} (x+4)^2=7 \\ \sqrt[]{(x+4)}^2=\sqrt[]{7} \\ (x+4)=\pm\sqrt[]{7} \\ \end{gathered}[/tex]Step 7: Isolate the x on the left side and solve for x by subtracting 4 from both sides
[tex]\begin{gathered} (x+4)=\pm\sqrt[]{7} \\ x+4-4=\pm\sqrt[]{7}-4 \\ x=\pm\sqrt[]{7}-4 \\ \text{therefore,} \\ x=-4+\sqrt[]{7} \\ x=-4-\sqrt[]{7} \end{gathered}[/tex]Therefore,
The value of x is
x = -4+√7 , -4-√7
a large industrial firm purchases several new word processors at the end of each year, the exact num- ber depending on the frequency of repairs in the previ- ous year. suppose that the number of word processors, x, purchased each year has the following probability distribution:
This firm expects to spend on the new word processor expense of $1855 from the given probability distribution.
What is a probability distribution?
A random variable can have any number of alternative values and likelihoods within a particular range, and a probability distribution would be a statistical function that captures all of these possibilities. This range will be constrained by the minimum and maximum distinct combinations, but the location of the possible value on the probability distribution will rely on a number of other variables. These elements include the mean (median), and standard deviation, of the distribution.Given that the number of word processors, x, purchased each year has the probability distribution.
E(X)=1* (3/10)+2*(2/5)+3*(1/5)=1.7
E(X^2)=1^2(3/10)+2^2(2/5)+3^2(1/5)=3.7
Expense=E(1200x-50x^2)=E(1200x)+E(-50x^2)=1200E(x)-50E(x^2)
So
Expense=1200*1.7-50*3.7=1855
This firm expects to spend on the new word processor expense of $1855 from the given probability distribution.
Complete question: A large industrial firm purchases several new word processors at the end of each year. The exact number of word processors purchased depends on the frequency of the number of repairs in the previous year. Suppose that the number of word processors x that are purchased each year has the following probability distribution:
x 0 1 2 3
f(x) 1/10 3/10 2/5 1/5
The cost of the desired model is $1200 per processor and a discount of 50 X2 dollars is credited towards any purchase. There is also a fixed cost of $600 regardless of the number of processors purchased. How much can this firm expect to spend on new word processors?
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i need help with this
Answer: 8.2 x 10^2
Step-by-step explanation:
1.Відомо, що 3< x < 8; −2 < у < 6. Оцініть значення виразу:
A) 2x+y;
Б) x-y.
Відповідь B, вибачте, якщо я помиляюся
question: 1/3x+4=x-2
please help
Answer: x=9
Step-by-step explanation:
I need help with this question
10x i think is the correct answer
Twice a number increased by 6 is at least 35.
5(3x – 2) + 11 = 106
please show work on computer
solve for x
Answer: 7
Step-by-step explanation:
5(3x – 2)= 15x-10
15x-10+11 = 15x+1
15x + 1 = 106 -1
15x = 105 /15
x = 7
0Is (2, 9) a solution to these simultaneous equations?
y = 3x + 3
y = x + 7
==============================================
Explanation:
The given solution is (2,9) which means x = 2 and y = 9 pair up together.
Replace x with 2 and replace y with 9.
Let's do so for the first equation
y = 3x+3
9 = 3*2+3
9 = 6+3
9 = 9
We get the same thing on both sides, which confirms the first equation.
Now let's check the second equation.
y = x+7
9 = 2+7
9 = 9
This equation is confirmed as well.
Both equations are true when (x,y) = (2,9) which confirms it is indeed the solution to the system.
----------------------------
If you are a visual learner, then I recommend graphing out the equations using a tool like GeoGebra or Desmos.
The two lines intersect at (2,9) which visually confirms it is the solution.
Adele opens an account with $150 and deposits $35 a month. Kent opens an account with $70 and also
deposits $35 a month. Will they have the same amount in their accounts at any point? If so, in how many
months and how much will be in each account?
Answer:
no there will never have the same amount in their accounts at any point
Step-by-step explanation:
the cube root of 64 is 4. how much larger is the cube root of 65.1? estimate using the linear approximation.
The exact difference is 0.022916
Given that the cube root of 64 is 4
We need to find how much larger is the cube root of 65.1 using the linear approximation.
Linear approximations:
They are ways to define a line tangent to a curve. At a particular range near the tangent point, the line can serve as an approximation for the function. However, linear approximations are determined through a combination of differentiation.
Here, when the tangent point is defined at x=a
then the linear approximation of a function is defined as f(x) ≈ f(a)+f′(a)(x−a)
Consider a = 64 f(x) = x^(1/3)
f'(x) = 1/3 x ^(-2/3)
So linear approximation is f(x) = 4 + 1/3 (64)^(-2/3) * (x-64)
x = 65.1
f(65.1) = 4 + 1/3 (64)^(-2/3) * (65.1 - 64)
f(65.1) - 4 = 1/3 1.1 (64)^(-2/3) = 1/3 * 1.1 * 1/16 = 1.1 / 48 = 0.0229
The exact difference is 0.022916
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lütfen acil yapabilir misiniz
Answer:
te mando un feo vida okay
word problems QKB
Mr. Olsen's class went to the science museum to see dinosaur fossils. They saw a young
brontosaurus that was 5 feet tall. They also saw an adult brontosaurus that was 15 feet tall.
How many times as tall as the young brontosaurus was the adult brontosaurus?
this is a math problem that i need help with
Answer:
d = 8 , a₁ = - 6 , a₂ = 2
Step-by-step explanation:
the recursive formula is
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + d
where d is the common difference
compare with
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 8
then common difference d = 8
the initial term is the first term, that is a₁ = - 6
then
a₂ = a₁ + d = - 6 + 8 = 2
Your bank account currently has a balance of $180. you withdraw $20 each week. write an equation that represents how many money (y) will be in your account x weeks. use your equation to find how many weeks until your account has a balance of zero.
The equation which represents money in the account after x weeks is:
20x+y=180
Hence the time after which the account has a balance of zero is 9 weeks.
Given, the bank account has a current balance of $180.
Withdrawal of $20 takes place every week.
we are asked to determine the amount of time (in weeks) needed for the account to have no balance is = ?
let x be the time time (weeks)
and y be the money left in the bank.
the equation will be:
20x + y = $180
Hence if the balance is zero, then how many weeks will it be.
substitute y=0
20x+0=180
20x=180
x=180/20
x=9
Hence it will take 9 weeks until the account has a balance of zero.
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The current I in an electrical conducter varies inversely as the resistance R of the conducter. The current is 1/6 ampere when the resistance is 36288 ohms. What is the current when the resistance is 49392 ohms?
The current when the resistance is 49392 ohms is 0.122 amperes.
If a current passes through two points is directly proportional to voltage and inversely proportional to the resistance.
The ohm's law is V=IR
Here V is the voltage, I is the current and R is the resistance.
Here we need to find the current flow through the conductor. The unit of current in amperes.
The current is I = 1/6 amperes when resistance is R = 36288 ohms.
To find voltage :
I = V/R
1/6 = V/36288
6V = 36288
V = 36288/6
V = 6048
Therefore, the voltage is 6048 volts.
Now, the current when the resistance is R = 49392 ohms:
I = V/R
I = 6048/49392
= 0.122 amperes.
Hence the current is 0/122 amperes.
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What is the remainder when P (x) is divided by (x + 1)?
Answer:
4
Explanation:
From the graph, the roots of the polynomial are -2, 1, and 1.
Therefore, the polynomial P(x) is defined below:
[tex]P(x)=(x+2)(x-1)(x-1)[/tex]When P(x) is divided by x+1, the remainder will be the value of x when x+1=0
When x+1=0
[tex]x=-1[/tex]Therefore:
[tex]\begin{gathered} P(-1)=(-1+2)(-1-1)(-1-1) \\ =1\times-2\times-2 \\ =4 \end{gathered}[/tex]The remainder when P (x) is divided by (x + 1) is 4.
Your car has 10 gallons of gas. You use 1 gallon for every 20 miles you travel.
Answer:
You would travel 200 miles before running out of gas.
Step-by-step explanation:
1:20 so 10:200 each time you multiple by 10
During christmas abok store sold 32 books. If the ratio of books to bookmarks sold was 4:1 how many bookmarks did the store sell?
Answer:
8 bookmarks were sold
Step-by-step explanation:
Answer: The answer is 8 not sure how to explain it. Can I get a brainliest plsssssssssssss
there are 500 people if one table seats 8 people how many tables do you need
2y+8x=0
use the slope and y intercept form to graph the equation
Answer:
Step-by-step explanation:
2y+8x=0
Converting to y-intercept form:
2y = -8x
y = -4x
So, the slope is -4 and the y-intercept is at (0,0).
Draw a line representing the rise and a line representing the run of the line. State the slope of the line in simplest form.
The slope of the line is 7 x - 8 y + 56 = 0 0r 8 y = 7x - 56
What does it mean by slope of a line ?
The ratio of the difference between the y- and x-coordinates of the two points that make up the line must be calculated. The slope of the line is the value that is obtained. It displays how the line's y-axis climb compares to its x-axis run.
Given : The two points are A( 0, 7 ) and B ( -8 , 0 )
The formula of the slope of the line is
y₂ - y₁ = m ( x₂ - x₁ )
And m = y₂ - y₁ / x₂ - x₁
m = - 7 / - 8 = 7/8
therefore , y - 0 = 7/8 ( x + 8 )
8 y = 7x + 56
7 x - 8 y + 56 = 0
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Write the slope-intercept form of the equation of the line through the given point (1, 2) with the given slope of -3:
The equation of the line with the point (1, 2) with the slope - 3 will be;
⇒ y = - 3x + 5
What is Equation of line?
The equation of line with slope m and passes through the point
(x₁, y₁) defined as;
⇒ y - y₁ = m (x - x₁).
Given that;
The slope of the line = -3
The point on the line is (1, 2).
Now,
Since, The equation of the line with slope m and passes through the point (x₁, y₁) defined as;
⇒ y - y₁ = m (x - x₁).
Hence, The equation of the line with slope - 3 and passes through the point (1, 2) will be;
⇒ y - y₁ = m (x - x₁).
⇒ y - 2 =-3 (x - 1).
⇒ y - 2 = -3x + 3
⇒ y = - 3x + 3 + 2
⇒ y = - 3x + 5
Therefore, The equation of the line with the point (1, 2) with the slope - 3 will be;
⇒ y = - 3x + 5
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Which of the following criteria always proves triangles congruent? Select all that apply.
Responses
Corresponding congruent Angle-Side-Angle
Corresponding congruent Angle-Side-Angle
Corresponding congruent Side-Angle-Side
Corresponding congruent Side-Angle-Side
Corresponding congruent Side-Side-Angle
Corresponding congruent Side-Side-Angle
3 congruent sides
2 congruent sides
3 congruent angles
The criteria that always proves triangles are congruent are;
Option A; Corresponding congruent Angle-Side-Angle
Option B; Corresponding congruent Side-Angle-SideOption
D: 3 congruent sides
How to illustrate the information?If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.
According to the ASA rule, two triangles are said to be congruent if any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and side included between the angles of the second triangle.
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____ + _____= 16 + +____ - ______=12 = = 26 16
In the first line, we are going to have that if you put 7 then to have the sum rigth the next space have to be 9, following that idea the space down of the 9 have to be also 7 and the first space on the second line have to be 19. So we are going to have 7 + 9 = 16 in the first line and in the second line 19 - 7 = 12, and the other two operations are going to be solve also 7 + 19 = 26 and 9 + 7 = 16.
Then the answer is 7 + 9 = 16 in the first line and in the second line 19 - 7 = 12.
Ahmed spent $ 27 and now has no money left. He had before his purchase.
Answer: $27
Step-by-step explanation:
Your question is unfinished but I'm assuming you want to know how much he had before his purchase.
If he spent $27 and is now broke that means he only had $27 in his wallet before his purchase
