Represent a quadratic function
Rewrite the equation in Ax+By=C form. Use integers for A, B, and C. y=-1/6x+3
The equation y = - 1 / 6 x + 3 in standard form is x + 6y = 18.
How to rewrite equation in standard form?The standard form for linear equations in two variables is Ax + By = C.
where
A , B and C are constantx and y are the independent and dependent variables respectivelyTherefore, let's represent the equation y = - 1 / 6 x + 3 in standard form .
y = - 1 / 6 x + 3
multiply the equation by 6 to eliminate the fraction
6y = 6(- 1 / 6 x) + 6(3)
Therefore,
6y = - x + 18
x + 6y = 18
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What is the value of x?
-6x + 6 > 12
Subtract 6 from both sides.
−6x > 12 - 6Subtract 6 from 12 to get 6.
−6x > 6Divide both sides by −6. Since −6 is <0, the inequality direction is changed.
x < 6/-6Divide 6 by −6 to get −1.
x<−1Austin has a granola recipe that requires 5/6 pounds of oats to make one batch of granola. if Austin uses 2 1/2 pounds of oats while making granola, how many batches has he made?
Step 1
Given; Austin has a granola recipe that requires 5/6 pounds of oats to make one batch of granola. if Austin uses 2 1/2 pounds of oats while making granola, how many batches has he made?
Step 2
Using ratio
[tex]\frac{\frac{5}{6}pounds\text{ of oats}}{2\frac{1}{2}pounds\text{ of oats}}=\frac{1\text{ batch of granola}}{x}[/tex][tex]\begin{gathered} \frac{5}{6}x=\frac{5}{2} \\ 10x=30 \\ x=\frac{30}{10} \\ x=3 \end{gathered}[/tex]Answer;
[tex]3\text{ batches}[/tex]Answer:3
Step-by-step explanation:if austin has to make 1 granola with 5/6pounds but he is using only 5/2 pounds to make 1 granola so that he can make 3 granulas with 5/6
Find the equation of the line graphed below. Write the equation in the form y = mx + b and identify m and b m = b =
ANSWER:
m = -3/4
b = -3
[tex]y=-\frac{3}{4}x-3[/tex]STEP-BY-STEP EXPLANATION:
We have that the equation in its slope-intercept form is the following:
[tex]\begin{gathered} y=mx+b \\ \text{where m is the slope and b is y-intercept} \end{gathered}[/tex]We calculate the slope as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]To calculate the slope we use the intercepts that are (-4, 0) and (0, -3), we replace:
[tex]m=\frac{-3-0}{0-(-4)}=\frac{-3}{4}=-\frac{3}{4}[/tex]Now, the value of b would be -3, since the y-intercept is (0,-3), therefore, the equation would be:
[tex]y=-\frac{3}{4}x-3[/tex]y= −2x+8
x-intercept:
Enter as a coordinate: such as
(a,b)
y
-intercept:
Enter as a coordinate: such as
(a,b)
For given equation y = -2x + 8, the x-intercept is (4, 0) and the y-intercept is (0, 8)
In this question, we have been given an equation y = -2x + 8
We need to find the x-intercept and y-intercept. Also, we need to write it as a coordinate (a, b)
To find the x-intercept we need to substitute y = 0 in the above equation.
0 = -2x + 8
2x = 8
x = 4
So, the x-intercept is (4, 0)
To find the y-intercept we need to substitute x = 0 in the above equation.
y = -2(0) + 8
y = 0 + 8
y = 8
So, the y-intercept is (0, 8)
Therefore, for given equation y = -2x + 8, the x-intercept is (4, 0) and the y-intercept is (0, 8)
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Solve the given equation or inequality graphically. State your answers rounded to two decimals. (a) x3 + 5x2 = −x2 + 5x + 3
The solutions of the equation x³ + 5x² = - x² + 5x + 3 when solved graphically is x = - 0.41, 1.09.
Draw a graph for each side, or component, of the equation and check to see where the curves intersect or are equal, to solve an equation graphically. The answers to the equation are the x values of these places.
Consider the equation,
x³ + 5x² = - x² + 5x + 3
Solving Equations Graphically:
The solution(s) of the equation f(x) = g(x) are the values of x where the graphs of f and g intersect.
Therefore,
f(x) = x³ + 5x² and g(x) = - x² + 5x + 3
By graphing the function we find the intersection of the two functions.
Hence, the graphs intersect each other at ( - 0.411, 0.776) and ( 1.092, 7.268).
Therefor,e the solution of the equation x³ + 5x² = - x² + 5x + 3 is x = - 0.41 and x = 1.09.
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Find the nth term of this quadratic sequence
2,8, 18, 32, 50,
Answer:
72
Step-by-step explanation:
8 = 2×2^2
18 = 2×3^2
32 = 2×4^2
50 = 2×5^2
72 = 2×6^2
i need help the problem is
solve for y
2x+y=3
Answer:
y = 3 - 2x
Step-by-step explanation:
Subtract 2x from both sides of the equation.
Answer:
y = x or 1x
Step-by-step explanation:
x as a variable can also be expressed as 1x.
so we can say that 2x + 1x
because x & y are two different type of variables. you think of y as a question mark ( ? ).
Now the new equation is
y = ?
so 1x + ? = 3
because x is the same thing as a 1x you can say that 2x + 1x = 3
If you randomly select a card from a well-shuffled standard deck of 52 cards, what is the probability that the card you select is a diamond or 7?
the probability that the card you select is a diamond or 7 is 4/13
WHAT IS PROBABILITY ?Mathematical representations of the likelihood of an event occurring or of a proposition being true are dealt with in the area of probability. A number between 0 and 1 represents the likelihood of an event, with 0 roughly denoting impossibility and 1 representing certainty.
CALCULATIONLets take diamond first total diamonds are 13 and total cards are 52 So prob is 13/52 which is 1/4
Lets take 7s
total 10s in the deck is 4 (one in each suite) (one in each suite)
Prob of 7s is 4/52 which is 1/13
Final answer =1/13+1/4=17/52 Total prob is addition of above two as it is "or."
Because the prob of the 7th diamond has been inserted twice, edit it as follows: 17/52-1/52=16/52=4/13
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L is a point of a tangency . Segment PL have a common point at P . Find the length of KN
In a paragraph of no less than 125 words, explain why you appreciate/love your chosen piece of music.
I adore BTS (the Korean boy band) because they encourage self-love. Their songs are artistically and romantically rich. They're well-known throughout the world and at the moment's top boy band in the US.
What is music about?In this sense, understanding the worth and excellence of various musical genres is referred to as appreciation. The word "appreciation" has philosophical roots; in that discipline, it is defined in relation to music as "a type of formal counterpart of emotional experience."
Someone's mood can be improved by listening to their music, which can also thrill or calm the listener. Importantly, music also enables us to experience almost all of the emotions we go through in life. There are countless options. Dopamine release in the mesolimbic reward system can be triggered by listening to extremely pleasurable music.
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O GRAPHS AND FUNCTIONSDomain and range from the graph of a continuous function
According to the graph we have:
Domain are the values of x. We can see that the graph extends horizontally from -5 to 3, but -5 and 3 are not included. Then, the domain is
[tex](-5,3)[/tex]Range are the values of y. Therefore, we see that the graph extends vertically from 4 to -3, so the range is:
[tex](-3,4)[/tex]Answer:
a. domain = (-5, 3)
b. range = (-3, 4)
Scott is a software salesman. His base salary is $2500, and he makes an additional $80 for every copy of English is Fun he sells.Let P represent his total pay (in dollars), and let N represent the number of copies of English is Fun he sells. Write an equation relating P to N. Then use this equation to find his total pay if he sells 28 copies of English is Fun.
SOLUTION
Given the question in the question tab, the following are the solution steps to get the equation
Step 1: Represent the statement using mathematical notation
Base salary is $2500 (Base salary is constant since it does not change)
P represent his total pay (in dollars)
N represent the number of copies of English is Fun he sells
price made per copy of the product is $80
The equation relating P to N will be written as:
[tex]P=2500+80N[/tex]Part B: Using this equation in step 1 above to find his total pay if he sells 28 copies of English is Fun
[tex]\begin{gathered} P=2500+80N \\ N=28 \\ P=2500+80(28) \\ P=2500+2240 \\ P=\text{\$}4740 \end{gathered}[/tex]Hence, his total pay if he sells 28 copies of English is Fun is $4740
7. On February 12th, a fire occurred at a local dry cleaning plant and the inpatient service days for the localhospital (120 beds) was reported to be 130. What is the bed occupancy rate for February 12th? Round toone decimal place.
We can use the following formula:
[tex]_{\text{ }}Bed_{\text{ }}occupancy_{\text{ }}rate=\frac{\#_{\text{ }}of_{\text{ }}inpatient_{\text{ }}days_{\text{ }}for_{\text{ }}a_{\text{ }}given_{\text{ }}period}{_{\text{ }}avalaible_{\text{ }}beds\times\#_{\text{ }}days_{\text{ }}in_{\text{ }}the_{\text{ }}period}_{}\times100[/tex]So:
[tex]_{\text{ }}Bed_{\text{ }}occupancy_{\text{ }}rate=\frac{130}{120\cdot365}\times100[/tex]Answer:
0.3%
The graph of a linear function is given below.What is the zero of the function ?A. -3B. -3/2C. -2/3D. -2
Using the graph, we can deduce the following:
• x-intercept: x = -2
,• y-intercept: y = -3
Let's determine the zero of the function.
The zero of a function can be said to be the root of the function. It is also called the x-intercept of the function.
The zero of a function is the point the line crosses the x-axis.
From the graph the x-intercept is at x = -2.
Therefore, the zero of the function is:
x = -2
ANSWER:
D. -2
A population grows according to an exponential growth model. The initial population is 212 and the population after one year is 263.
Complete the formula where P is the population and n is the number of years.:
P=212*(___)n
Round your answer to three decimal places.
Answer: P=212*(1.240)n
Step-by-step explanation:
1) Find the % growth
263-212= 51
51/212 = 0.240566037735849
2) Add 1 to the decimal as the population isn't decreasing but increasing.
0.240566037735849 + 1 = 1.240
3) Fill in the equation
P=212*(1.240)n
What is the next step in the construction?
An arc is, in general, any straight curve that connects two points. The term "arc length" refers to an arc's length. Make an arc by setting the compass's needle at A. Please indicate intersections B and C.
What is meant by arc?An arc is, in general, any straight curve that connects two points. The term "arc length" refers to an arc's length. A graph arc is an ordered pair of adjacent vertices in a graph. An arc is specifically any section of a circle's circumference (other than the full curve).
An "arc" in mathematics is a straight line that connects two endpoints. An arc is typically one of a circle's parts. In essence, it is a portion of a circle's circumference. A curve contains an arc.
A circle's circumference forms an arc. An arc length is the length of the arc, whereas an arc measure is the measurement of the angle the arc makes at the center of a circle.
Therefore, the correct answer is option b) Step 2. Put the point of the compass at A and make an arc. Label the intersections B and C
The complete question is:
What is the next step in the construction?
a) Step 1: Select a point on line 1 and label it point A. Draw in PA.
b) Step 2. Put the point of the compass at A and make an arc. Label the intersections B and C
c) Step 3. Without changing the compass setting. put the compass at point P and make an identical arc. Label the intersection D
d) Step 4. Put the compass at point B and use it to measure the distance to C.
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a student has 200 Naira if someone gives her 160 Naira how much will she have if someone gives her x Naira how much would she have
Answer:
360 naira hope it will be helpful
Step-by-step explanation:
Can you show me step by step how to get this answer please?
Answer: first six cannot go into three because three is too small so six is going to go into 31 Six can go into 31 five times because 6×5 = 30 then since you’re subtracting 31 and 30 you would be left with one you would have to bring the 1 from the 12 down and then it would be 11. 11 can go into six once so 6-11 =5 so then you have to bring the two from the 12 down so then that would equal 6-2=4 and your done! It was a little confusing so if it didn’t make sense I’m sorry
hot-air balloon is floating above a straight road. To calculate their height above the ground, the balloonists simultaneously measure the angle of depression to two consecutive mileposts on the road on the same side of the balloon. The angles of depression are found to be 26∘ and 30∘.
How high (in feet) is the ballon?
The height of balloon is 1.99 miles above the ground.
What is angle of depression ?In the event when the line of sight is directed downhill from the horizontal line, an angle is created with it. Angle of depression is the angle produced between the horizontal line and the observer's line of sight when the object being observed is below the level of the observer.
Let's give the balloon's height above the earth and the distance it is from the first milepost horizontally a name.
We can state the following if the angle of this milepost's depression is 24 degrees:
Tan(24)=[tex]\frac{h}{b}[/tex]
b = [tex]\frac{h}{tan(24)}[/tex]
We can state the following for the following milepost as there will be (b+1)miles horizontal distance of and a 20 degree depression at that location.
tan(20)=[tex]\frac{h}{b+1}[/tex]
b +1 = [tex]\frac{h}{tan(20)}[/tex]
Therefore, substituting equation 1
[tex]\frac{h}{tan(24)}[/tex] = [tex]\frac{h}{tan(20)} -1[/tex]
1 = [tex]\frac{h}{tan(20)}[/tex] - [tex]\frac{h}{tan(24)}[/tex]
1 = h× ( [tex]\frac{h}{tan(20)}[/tex] - [tex]\frac{h}{tan(24)}[/tex] )
h = 1.99 miles
Consequently, the height of balloon is 1.99 miles above the ground.
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Doris borrowed 7 dollars from Nikki. Doris then paid back 2 dollars. How much does Doris
still owe Nikki?
Answer:
He still owes Nikki $5.
Step-by-step explanation:
7 - 2 = 5
Answer:
5
Step-by-step explanation:
7-2=5
The surface area of the rectangular prism is given by formula S=2(ab+bh+ah). Find the value of h when a=6, b=5 and s=214
The value for the height of the rectangular prism is found as; h = 7.
What is defined as the rectangular prism?A rectangular prism is a three dimensional solid shape with six faces that have rectangles as their bases. Right rectangular prisms as well as non-right (oblique) rectangle prisms are the two types of rectangular prisms. The right rectangle prism does have two parallel end faces and 4 lateral faces, each of which is an rectangle; this same faces are perpendicular to the bases of the prism.The formula for the surface area of rectangular prism is;
S = 2(ab+bh+ah)
Where,
a=6, b=5 and s=214
Substitute the values in the formula.
214 = 2(6×5 + 5h + 6h)
Simplifying;
30 + 11h = 107
11h = 107 - 30
11h = 77
h = 7
Thus, the value for the height of the prism is found as; h = 7.
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Can you check work please?
When rotating a point 180 degrees counterclockwise about the origin our point A(x,y) becomes A'(-x,-y). So all we do is make both x and y negative.
[tex]\begin{gathered} K(-4,-3)\rightarrow K^{\prime}(4,3) \\ L(-3,-1)\rightarrow L^{\prime}(3,1) \\ M(0,-3)\rightarrow M^{\prime}(0,3) \end{gathered}[/tex]
Which of the following is a true statement about a tangent and a radius?
A. A tangent and a radius of a hexagon are always equal lengths.
B. A tangent and a radius of a circle meet to form a 90 angle.
C. A tangent and a radius in a cylinder form two legs of a right triangle with the cylinders altitude serving as the hypotenuse.
D. A tangent and a radius intersect at the foci of an ellipse.
A tangent and a radius of a circle meet to form a 90 angle is a true statement about a tangent and a radius.
The straight line that "just touches" the curve at a particular location is known as the tangent line (or simply tangent) to a plane curve in geometry. A circle or sphere's radius is any line segment that connects the object's center to its perimeter in classical geometry; in more contemporary use, it also refers to the length of such line segments.
A tangent is a line that very slightly touches the circumference of a circle. The angle between a radius and a tangent is always exactly 90 degrees if the radius and circumference are drawn at the same location.
Hence the correct option is B
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A candy company has fixed costs (costs that it must pay regardless of how much candy they
make) of $500 per day, and it costs them an additional $3 to manufacture each box of candy.
They can sell their candy for $3 a box. If we jet x represent the boxes of candy sold, the number of
boxes they need to sell to break even can be found by solving the equation 3x + 500 = 3x. How
many boxes of candy to they need to sell to break even?
You can never achieve break even by selling any number of boxes of candy if it costs them an additional $3 to manufacture each box of candy.
What is Break even point?In economics, business, and particularly cost accounting, the break-even point is the point at which total cost and total income are equal, or "even."
Although these opportunity costs have been paid and then capital has received the risk-adjusted, projected return, there is no net loss or gain, and one has "broken even."
Fixed cost (in manufacturing) = $500
Manufacturing cost of each candy = $3
and selling price of candy = $3
let x be a box of candy sold,
hence for no of box to be sold for a break even,
3x + 500 = 3x
but if you see above equation, that has no solution
Hence by providing each candy at $3 with $500 fixed cost and selling cost again at $3 you cannot achieve a break-even point.
hence there is no solution, and you will never be able to achieve break even.
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find the midpoint between. (-1,2) and (-7,-4).
The midpoint of two coordinates can be obtained using the formula:
[tex]\frac{x_1+x_2}{2},\text{ }\frac{y_1+y_2}{2}[/tex]x1 = -1
y1= 2
x2= -7
y2= -4
[tex]\begin{gathered} \frac{-7\text{ +(-1)}}{2},\frac{2+(-4)}{2} \\ \\ \frac{-7-1}{2},\frac{2-4}{2} \\ \frac{-8}{2},\frac{-2}{2} \end{gathered}[/tex][tex]\begin{gathered} \text{midpoint} \\ (-4,-1) \end{gathered}[/tex]Solve the linear programming problems: (find the constraints, objective function, feasible region, and the minimumand maximum values)12. A small business produces oak chairs and walnut chairs. The business can make at most 20 chairs per week.Materials cost $100 per oak chair and $150 per walnut chair. The business has a budget of $2400 per week formaterials. Each oak chair sells for $400 and each walnut chair sells for $500. What are the number of oak and walnutchairs that the small business should produce in order to maximize / minimize sales?
The firm should produce 12 oak chairs and 8 walnut chairs to maximize its profit to $8,800.
What are linear equations?Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is fairly simple (x and y). The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.So,
Production of oak chairs: xProduction of walnut chairs: y(Refer to the graph attached below)
Then,
x + y ≤ 20100x + 150y ≤ 2400x ≥ 0y ≥ 0I = 400x + 500ySo, oak chair produced:
(0, 16) ⇒ $8000(20, 0) ⇒ $8000(12, 8) ⇒ $8800Therefore, the firm should produce 12 oak chairs and 8 walnut chairs to maximize its profit to $8,800.
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The correct question is given below:
Solve the linear programming problem: A small business produces oak chairs and walnut chairs. The business can make at most 20 chairs per week. Materials cost $100 per oak chair and $150 per walnut chair. The business has a budget of $2400 per week for materials. Each oak chair sells for $400 and each walnut chair sells for $500. How many each types of chairs should the business make each week to maximize income?
An election ballot asks voters to select six city commissioners from a group of twenty two candidates. In how many ways can this be done?
In this case, we have 6 places to fill from a pool of 22 candidates. There is no difference in the places: they are all commissioners, so if candidate A is selected, the order does not matter, but there is only one candidate, so there is no repetition.
Then, this is a combination (as the order does not matter) with no repetition of 22 elements in 6 places.
We can calculate this as:
[tex]\begin{gathered} C(n,r)=\frac{n!}{r!(n-r)!} \\ C(22,6)=\frac{22!}{6!(22-6)!}=\frac{22!}{6!\cdot14!}=\frac{22\cdot21\cdot20\cdot19\cdot18\cdot17\cdot16\cdot15}{6\cdot5\cdot4\cdot3\cdot2\cdot1}=17907120 \end{gathered}[/tex]Answer: there are 17,907,120 ways this can be done.
determine the inverse of the given function
f(x)= 2x-9/4
To find the inverse of a function:
Replace f(x) with ySwitch around x and yIsolate yReplace y with f⁻¹(x)Solving the Question[tex]f(x)= 2x-\dfrac{9}{4}[/tex]
⇒ Replace f(x) with y:
[tex]y= 2x-\dfrac{9}{4}[/tex]
⇒ Switch around y and x:
[tex]x= 2y-\dfrac{9}{4}[/tex]
⇒ Isolate y:
[tex]x+\dfrac{9}{4}= 2y\\\\\dfrac{1}{2}(x+\dfrac{9}{4})= 2y(\dfrac{1}{2})\\\\\dfrac{1}{2}x+(\dfrac{1}{2}*\dfrac{9}{4})= y\\\\\dfrac{1}{2}x+\dfrac{9}{8}= y\\\\y=\dfrac{1}{2}x+\dfrac{9}{8}[/tex]
⇒ Replace y with f⁻¹(x):
[tex]f^{-1}(x)=\dfrac{1}{2}x+\dfrac{9}{8}[/tex]
Answer[tex]f^{-1}(x)=\dfrac{1}{2}x+\dfrac{9}{8}[/tex]