Answer:
let inverse f(x) be m:
[tex]m = \frac{1}{2x + 1} \\ 2x + 1 = \frac{1}{m} \\ 2x = \frac{1 - m}{m} \\ x = \frac{1 - m}{2m} [/tex]
substitute x in place of m:
[tex]{ \bf{ {f}^{ - 1}(x) = \frac{1 - x}{2x } }}[/tex]
find the x-intercepts y=2x^2 + 5x + 2/x^2-4x+3
Answer:
[tex]{ \tt{y = \frac{2 {x}^{2} + 5x + 2}{ {x}^{2} - 4x + 3 } }} \\ x - intercept : y = 0 \\ { \tt{ \frac{2 {x}^{2} + 5x + 2 }{ {x}^{2} - 4x + 3 } = 0 }} \\ \\ { \tt{2 {x}^{2} + 5x + 2 = 0}} \\ x = \frac{1}{2} \: \: and \: \: x = - 2[/tex]
X is less than or equal to 2 Write in interval notation.
What is the value of x if x/ 3 + 1 = -2 ?
Perpendicular lines
What is the segment
Use the value of phi = 1.618 to predict the 23rd number in the Fibonacci sequence. The 22nd number in the sequence is 17,711.
- 10,946
- 17,711
- 22,897
- 28,656
Given:
[tex]\phi=1.618[/tex]
22nd number in Fibonacci sequence = 17,711
To find:
The 23rd number in the Fibonacci sequence.
Solution:
The nth term of a Fibonacci sequence is:
[tex]f_n=\dfrac{\phi^n-(1-\phi)^n}{\sqrt{5}}[/tex]
Substituting [tex]\phi=1.618, n=21[/tex], we get
[tex]f_{21}=\dfrac{(1.618)^{21}-(1-1.618)^{21}}{\sqrt{5}}[/tex]
[tex]f_{21}=\dfrac{(1.618)^{21}-(1-1.618)^{21}}{\sqrt{5}}[/tex]
[tex]f_{21}=10941.1724024[/tex]
[tex]f_{21}\approx 10941[/tex]
Now,
[tex]f_{23}=f_{21}+f_{22}[/tex]
[tex]f_{23}=10941+17711[/tex]
[tex]f_{23}=28652[/tex]
It is about 28,656. Therefore, the correct option is D.
math help plz
how to solve literal equations, how to understand and step by step with an example provided please
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Explanation:
Your question covers a good bit of the material in an algebra course. The short answer is, "the same way you solve a numerical equation." The point of algebra is that literals can stand for numbers, and so be manipulated the same way numbers are.
Expressions are evaluated according to the Order of Operations. For equations involving a single variable, the equation specifies what operations are being performed on that variable. To find the vale of the variable (solve for that literal), you need to "undo" the operations that are performed on it. As with many problems that have layers, you work down through the layers from the outside in. Generally, that means working through the list of operations "backwards," undoing the last one first.
Simple example
y = mx + b . . . . . . solve for x
In this equation, the operations performed on x are ...
multiplication by maddition of b to the productIn accordance with the above, the first thing we do is "undo" the addition of b. (Note that this could be a number or literal--or even a complicated expression--and the process would be exactly the same.) To "undo" addition, we add the opposite.
y -b = mx +b -b ⇒ y -b = mx
Next, we "undo" the multiplication by m. That is, we divide by m, or multiply by the reciprocal of m. Either is the same as the other.
(y -b)(1/m) = (mx)(1/m) ⇒ (y -b)/m = x
Now, we have solved this literal equation for x.
_____
Throughout this process you must adhere strictly to the properties of equality. That is, anything you do to one side of the equation must also be done to the other side.
The reason you study inverses and identity elements is so you understand that addition of an additive inverse produces the additive identity element:
x + (-x) = 0
Similarly, multiplication by the multiplicative inverse (reciprocal) produces the multiplicative identity element.
x · (1/x) = 1
When other operations are involved, such as raising to a power, trig functions, roots, logs, exponentiation, each of these has an associated inverse function that produces an identity:
(x^a)^(1/a) = x^1 = x
arcsin(sin(x)) = x
(√x)^2 = x
10^(log(x)) = x or log(10^x) = x
Some of these inverse functions have restricted domains, so care must be used when solving equations involving them.
When a variable of interest appears on both sides of the equal sign, then you must figure a way to rearrange the equation so the terms with the variable can be combined.
Example:
ax + b = cx +d . . . . . solve for x
ax -cx = d -b . . . . . . subtract (cx+b). (Of course, this is subtracted from both sides of the equation.)
x(a -c) = d -b . . . . . combine x-terms
x = (d -b)/(a -c) . . . . divide by the coefficient of x
Note that we had to divide the entire right-side expression by the x-coefficient, so had to enclose it in parentheses.
More Complicated Example:
A recent Brainly problem asked for the solution to ...
T = 2π√(L/g) . . . . solve for L
Here, L is divided by g, a root taken, and that multiplied by 2π. Undoing these in reverse order, we first divide by 2π, square both sides to undo the root, then multiply by g to undo the division:
[tex]T=2\pi\sqrt{\dfrac{L}{g}}\\\\\dfrac{T}{2\pi}=\sqrt{\dfrac{L}{g}}\\\\\left(\dfrac{T}{2\pi}\right)^2=\dfrac{L}{g}\\\\\boxed{L=g\left(\dfrac{T}{2\pi}\right)^2}[/tex]
The problem posted on Brainly had numbers where some of these variables are. That does not affect the solution method, except that sometimes numerical values can be combined where literal values cannot.
_____
Key Points
The equal sign is sacred, and its truth must be preserved at every step.Literal equations are solved the same way numerical equations are solved.Inverse operations and functions are used to "undo" operations and functions.The Order of Operations can be helpful when considering what to do first.The chance of winning the race of the horse A is 1/15 and that of horse B is 1/6. What is
the probability that the race will be won by A or B.
Answer:
7/30
Step-by-step explanation:
P = 1/15 + 1/6 = (2+5)/30 = 7/30
Mr johnson sells erasers for $3 each. He sold 96 erasers last week and he sold 204 erasers this week.
A. $300 B $600 C $100 D $900
I believe your answer is D.) $900
204 + 96 = 300
300 x 3 = 900
I hope this is correct and helps!
Please help!!!!
I’m using Plato
1 by 4 ^ 256 is equal to 4 and 1 by 4 ^ 64 will be root 4 so here the answer will be 4 into 4 root 4
there option 4 will be correct
The annual demand for a product is 16,400 units. The weekly demand is 315 units with a standard deviation of 90 units. The cost to place an order is $31.00, and the time from ordering to receipt is four weeks. The annual inventory carrying cost is $0.20 per unit.
a. Find the reorder point necessary to provide a 95 percent service probability.
b. Suppose the production manager is asked to reduce the safety stock of this item by 55 percent. If she does so, what will the new service probability be?
Answer:
a) The reorder point necessary to provide a 95 percent service probability is 1557 units.
b) The Z value of 0.74 corresponds to 77% service probability.
Step-by-step explanation:
Average weekly demand (d) = 315 units
The standard deviation of weekly demand (\sigmad) = 90 units
Lead time (L) = 4 weeks
At 95% service level value of Z = 1.65
Reorder point = d x L + safety stock
[tex]= d \times L + (Z \times \sigma d \times \sqrt L)\\\\= 315 x 4 + (1.65 x 90 x \sqrt 4)\\\\= 1260 +(1.65 x 90 x 2)\\\\= 1260 + 297\\\\= 1557 units[/tex]
b) Earlier the safety stock was 297 units(calculated in part a)
Now the safety stock is reduced to 55%.so,55% of 297 = 163.35 units
So the new safety stock = 297 - 163.35 = 133.65
[tex]Safety stock = Z \times \sigma d \times \sqrt L\\133.65 = Z x 90 x 2\\133.65 = 180Z\\ Z = 133.65/180\\Z = 0.74[/tex]
The Z value of 0.74 corresponds to 77% service probability.
What is the standard form equation of the quadratic function shown in this graph?
Answer:
A is the equation in standard form
Step-by-step explanation:
HELP PLSSSS I will GIVE BRAINLYEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Round 1001 to the nearest thousand.
1000 is the correct answer !
Wade has a test score of 77% on his first test and 65% on his second test. What must he score on a third test to have an average of 80% overall?
93%
98%
89%
None of these choices are correct.
Answer: 98%
Step-by-step explanation:
The third test score = x[tex]\frac{77+65+x}{3} =80\\\frac{142+x}{3} =80\\142+x=80*3\\x=240-142=98[/tex]
8. Discount: An auto dealer paid $8730 for a
large order of special parts. This was not the
original price. The amount paid reflects a 3%
discount off the original price because the
dealer paid cash. What was the original price
of the parts?
Answer: 5,987
Step-by-step explanation:
Which rule describes the transformation shown?
1. (x,y) → (-y, x+7)
2. (x,y) → (x+7,-y)
3. (x,y) → (-x, y+7)
4. (x,y) → (y+7, -x)
Answer:
2. (x,y) → (x+7,-y)
Step-by-step explanation:
Point A:
The original coordinate of point A was (-6,-6).
The coordinate after the transformation is A'(1,6), which eliminates option 3.
Point B:
The original coordinate of point B was (-2,4).
After the transformation, we have B'(5,-4), which eliminates option 1 and option 4. This means that the correct answer is:
2. (x,y) → (x+7,-y)
When f(x) = 4 , what is the value of ?
A. 0
B. 2
C. 3
D. 4
Find the point P along the directed line segment from point A(–9, 5) to point B(11, –2) that divides the segment in the ratio 4 to 1.
Answer:
[tex]P = (7, -\frac{3}{5})[/tex]
Step-by-step explanation:
Given
[tex]A = (-9,5)[/tex]
[tex]B = (11,-2)[/tex]
[tex]m : n = 4 : 1[/tex]
Required
Point P
This is calculated as:
[tex]P = (\frac{m * x_2 + n * x_1}{m + n}, \frac{m * y_2 + n * y_1}{m + n})[/tex]
So, we have:
[tex]P = (\frac{4 * 11 + 1 * -9}{4 + 1}, \frac{4 * -2 + 1 * 5}{4+1})[/tex]
[tex]P = (\frac{35}{5}, \frac{-3}{5})[/tex]
[tex]P = (7, -\frac{3}{5})[/tex]
Keiko, Chang, and Abdul sent a total of 109 text messages over their cell phones during the weekend. Keiko sent 7 fewer messages than Chang. Abdul sent 4
times as many messages as Keiko. How many messages did they each send?
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Answer:
Keiko: 17Chang: 24Abdul: 68Step-by-step explanation:
Let c represent the number of messages sent by Chang. Then Keiko sent (c-7) messages, and Abdul sent 4(c-7) messages. The total number sent was ...
c + (c -7) +4(c -7) = 109
6c -35 = 109 . . . . . . . . . . simplify
6c = 144 . . . . . . . . . . . add 35
c = 24 . . . . . . . . . . . divide by 6
c-7 = 17
4(c-7) = 68
Keiko sent 17, Chang sent 24, and Abdul sent 68 text messages.
which ordered pairs are in the solution set of the system of linear inequalities?
y > -1/3x+2
-
y <2x+3
A. (2,2), (3,1) (4,2)
B. (2,2) (3,-1) (4,1)
C. (2,2) (1,-2) (0,2)
D. (2,2) (1,2) (2,0)
==========================================================
Explanation:
The graph of [tex]y \ge -\frac{1}{3}x+2[/tex] has the boundary y = (-1/3)x+2 which is a solid line. This line goes through (0,2) and (3,1). We shade above the boundary because of the "greater than" sign.
The graph of y < 2x+3 has a dashed boundary line of y = 2x+3, and we shade below the boundary because of the "less than" sign.
The two regions overlap in the upper right corner where it's shaded in the darkest color. The points (2,2), (3,1) and (4,2) are in this upper right corner region. If we plug the coordinates of each point into each inequality, then we'll get true statements.
For instance, let's try (x,y) = (2,2) into the first inequality
[tex]y \ge -\frac{1}{3}x+2\\\\2 \ge -\frac{1}{3}(2)+2\\\\2 \ge -\frac{2}{3}+2\\\\2 \ge -\frac{2}{3}+\frac{6}{3}\\\\2 \ge \frac{-2+6}{3}\\\\2 \ge \frac{4}{3}\\\\2 \ge 1.33\\\\[/tex]
Which is true since 2 is indeed larger than 1.33, so that confirms (2,2) is in the shaded region for [tex]y \ge -\frac{1}{3}x+2\\\\[/tex]
Let's check the other inequality as well
[tex]y < 2x+3\\\\2 < 2(2)+3\\\\2 < 4+3\\\\2 < 7\\\\[/tex]
That works too. So (2,2) is in BOTH shaded regions at the same time; hence, it's a solution to the system. You should find that (3,1) and (4,2) work for both inequalities also. This will confirm choice A is the answer.
--------------------------------
Extra info (optional section)
A point like (3,-1) does not work for the first inequality as shown below
[tex]y \ge -\frac{1}{3}x+2\\\\-1 \ge -\frac{1}{3}(3)+2\\\\-1 \ge -1+2\\\\-1 \ge 1\\\\[/tex]
Since -1 is neither equal to 1, nor is -1 larger than 1 either. The false statement at the end indicates (3,-1) is not a solution to that inequality.
Based on the graph, the point (3,-1) is not above the blue solid boundary line. All of this means we can rule out choice B.
You should find that (1,-2) is a similar story, so we can rule out choice C. Choice D can be ruled out because (2,0) is not a solution to the first inequality.
PLS HELP please give an explanation if you don’t have one pls still give answer
(a^2 - b^2)=???????????????????????????
[tex](a^2 - b^2) = (a + b)(a - b)[/tex]
A meteorologist preparing a talk about global warming compiled a list of weekly low temperatures (in degrees Fahrenheit) he observed at his southern Florida home last year. The coldest temperature for any week was 36°F, but he inadvertently recorded the Celsius value of 2°. Assuming that he correctly listed all the other temperatures, explain how this error will affect these summary statistics:a) measures of center: mean and median.b) measures of spread: range, $IQR,$ and standard deviation.
Answer:
nr.herkyrsfdlufshfsyfs
Step-by-step explanation:
dsfsyfksutryrysyrslufzmfyzydzufmzmhfzl
hdhfuthfzhkrskyrsgj
the first term of an arithmetic sequence is -5, and the tenth term is 13. find the common difference
Answer:
2
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
Equivalent question: Find the slope of line going through points (1,-5) and (10,13).
Line points up vertically and subtract. Then put 2nd difference on top of first difference.
(1,-5)
(10,13)
---------'subtracting
-9, -18
So the slope of the line gong through point's (1,-5) and (10,13) is -18/-9=2.
The common difference of an arithmetic sequence whose first term is -5 and whose tenth term is 13 is 2.
Mackenzie earns 4% commission as a salesperson. She sold a digital camera that cost $767. How much commission did Mackenzie earn?
Answer:
like about $500 and because of the ca!erlsn
Find the slope of the line that passes through the two points 2,-4 & 4,-1
Answer:
Step-by-step explanation:
I have this saved on my computer in notepad b/c this type of question get asked sooo often :/
point P1 (-4,-2) in the form (x1,y1)
point P2(3,1) in the form (x2,y2)
slope = m
m = (y2-y1) / (x2-x1)
My suggestion is copy that above and save it on your computer for questions like this
now use it
Point 1 , P1 = (2,-4) in the form (x1,y1)
Point 2 , P2 = (4,-1) in the form (x2,y2)
m = [ -1-(-4) ] / [ 4-2]
m = (-1+4) / 2
m = 3 / 2
so now we know the slope is 3/2 :)
A board is 87 cm in length and must be cut so that one piece is 21 cm longer than the other piece. Find the length of each piece. Round your answers to the nearest centimeter, if necessary. * + 21?
Thank you for answer Yey can I answer in my subject
What is the y-intercept of the graph of y = 2.5x? a. 2.5 c. 0 b. 1 d. -1
Answer:
answer is C
Step-by-step explanation:
General equation of a line is expressed as shown:
y = mx+c where;
m is the slope or gradient of the line
c is the intercept of the line
Given the equation of the line graph as y =2.5x
Comparing the given equation with the general equation, it is seen that m = 2.5 and c = 0 (since there is no value for the intercept)
Based on the explanation, the y-intercept of the graph is therefore 0
Answer:
B
Step-by-step explanation:
To find the x-intercept, substitute in
0 for y and solve for x
To find the y-intercept, substitute in 0 for x and solve for y
x-intercept(s): None
y-intercept(s): (0,1)
Sam takes a job with a starting salary of $50,000 for the first year. He earns a 4% increase each year. Which expression gives the partial sum, S3, (in thousands)?
A decorative wall in a garden is to be built using bricks that are 5 1/2 inches thick and mortar joints are 1/4 inch thick. What is the height of the wall?
Step-by-step explanation:
SAVE
HOME HACKS & ANSWERSBUILDING & REMODELINGWALLS
How to Calculate How Many Bricks to Build a Wall
By KELVIN O'DONAHUE
Hunker may earn compensation through affiliate links in this story.
...
To estimate the number of bricks needed to build a wall, first measure a single brick.
A wall built from brick not only adds security and strength to your property, it also provides a pleasing geometric backdrop for the landscaping. Because of the bricks' size and weight, homeowners generally arrange to have the amount needed for a large project delivered by the masonry company or lumberyard. Doing so requires that you estimate the number of bricks needed before placing the order.
Step 1
Measure the length and thickness of one of the bricks that will be used in the wall. A standard brick is 2-1/4 inches wide and 7-1/2 to 8 inches long. Add 1/2 inch to both the length and thickness to account for the mortar joint between adjacent bricks. For example, a brick that is 2-1/4 inches by 7-1/2 inches, plus mortar joints, will occupy 2 3/4 inches by 8 inches.
Step 2
Measure the length of the space for the wall and convert the number to inches. Divide the length in inches by the length of a brick plus mortar joint. For example, a wall 36 feet, 8 inches long is 440 inches long (36 X 12 = 432 + 8 = 440). Each course (single layer) of bricks will need 440 / 8 = 55 bricks.
SAVE
HOME HACKS & ANSWERSBUILDING & REMODELINGWALLS
How to Calculate How Many Bricks to Build a Wall
By KELVIN O'DONAHUE
Hunker may earn compensation through affiliate links in this story.
...
To estimate the number of bricks needed to build a wall, first measure a single brick.
A wall built from brick not only adds security and strength to your property, it also provides a pleasing geometric backdrop for the landscaping. Because of the bricks' size and weight, homeowners generally arrange to have the amount needed for a large project delivered by the masonry company or lumberyard. Doing so requires that you estimate the number of bricks needed before placing the orderStep 3
Determine the desired height of the wall in inches, and divide the height by the thickness of a brick and mortar joint. For example, a wall 72 inches tall requires 26.18 courses of 2-3/4-inch-wide bricks; rounded up to 27 courses.
Step 4
Multiply the number of bricks per course (55) by the number of courses (27) to obtain the number of bricks in a single-thickness wall or veneer. For our example, the number is 1,485 bricks. Double that number for a double-thickness wall. Bricklayers generally add 5 percent to the estimate to cover broken or wasted bricks, for about 1,560 bricks in this case