Let the unknown number be "x"
We will write an algebraic equation from the word problem given. Then we will solve for "x".
Given,
Sum of number (x) and 4 times the reciprocal is 13/3
We can convert it into an algebraic equation:
[tex]x+(4\times\frac{1}{x})=\frac{13}{3}[/tex]Now, let's solve for the unknow, x,
[tex]\begin{gathered} x+(4\times\frac{1}{x})=\frac{13}{3} \\ x+\frac{4}{x}=\frac{13}{3} \\ \frac{x^2+4}{x}=\frac{13}{3} \\ 3(x^2+4)=13\times x \\ 3x^2+12=13x \\ 3x^2-13x+12=0 \\ (x-3)(x-\frac{4}{3})=0 \\ x=3 \\ x=\frac{4}{3} \end{gathered}[/tex]The numbers are
[tex]\begin{gathered} 3 \\ \text{and} \\ \frac{4}{3} \end{gathered}[/tex]Ebony is building a shelf to hold two boxes shown. What is the least width she should make the shelf?
Answer:
There exists the same question from other source that shows the two boxes.
Box 1 has a length of 4/5 feet
Box 2 has a length of 3/4 feet
Because Ebony is trying to find the total amount of space needed to hold the boxes, use addition.
Here, is the solution:
= 4 / 5 + 3 / 4
= (16 + 15) / 20
= 31 / 20
So, Ebony can make a shelf at least 31/20 feet wide or 1 11/20 feet.
solve for x: 2/3x-1=5
The given equation is
[tex]\frac{2}{3}x-1=5[/tex]First, we have to sum 1 on each side
[tex]\begin{gathered} \frac{2}{3}x-1+1=5+1 \\ \frac{2}{3}x=6 \end{gathered}[/tex]Now, we multiply the equation by 3/2
[tex]\begin{gathered} \frac{2}{3}x\cdot\frac{3}{2}=6\cdot\frac{3}{2} \\ x=\frac{18}{2} \\ x=9 \end{gathered}[/tex]Therefore, the solution is 9.Which of the following best defines the term ""algorithm""?
A combination of zeroes and ones that represents an instruction to the computer
The rules for writing instructions in a specific programming language
A set of step-by-step instructions to solve a problem or perform a task
A way to write programming code in short English phrases to describe the program components
The basic definition of algorithm is A set of step-by-step instructions to solve a problem or perform a task.
Option c is the right answer.
-3x^4+27x^2+1200=0Find all the zeros of the equation y problem is the calculation after the info in the picture
Transform the variable x² into u
[tex]-3x^4+27x^2+1200=0\Longrightarrow-3u^2+27u+1200=0[/tex]Use the quadratic formula to solve for solutions in u, with a = -3, b = 27, c = 1200.
[tex]\begin{gathered} u=\frac{ -b \pm\sqrt{b^2 - 4ac}}{ 2a } \\ u=\frac{ -27 \pm\sqrt{27^2 - 4(-3)(1200)}}{ 2(-3) } \\ u=\frac{-27\pm\sqrt[]{729-(-14400)}}{-6} \\ u=\frac{ -27 \pm\sqrt{15129}}{ -6 } \\ u=\frac{ -27 \pm123\, }{ -6 } \\ \\ u_1=\frac{-27+123}{-6}=\frac{96}{-6}=-16 \\ u_2=\frac{-27-123}{-6}=\frac{-150}{-6}=25 \\ \\ \text{Which means that if we factor} \\ -3u^2+27u+1200=0 \\ \text{Then it is} \\ (u+16)(u-25)=0 \end{gathered}[/tex]Revert u back into x²
[tex]\begin{gathered} (u+16)(u-25)=0\Longrightarrow(x^2+16)(x^2-25)=0 \\ \\ \text{Recall the special factor} \\ (a^2-b^2)=(a+b)(a-b)\text{ and apply it to }(x^2-25) \\ \\ (x^2+16)(x^2-25)=0 \\ (x^2+16)(x+5)(x-5)=0 \end{gathered}[/tex]Equate to zero all the factors, and solve for x
[tex]\begin{gathered} x^2+16=0 \\ x^2=-16 \\ \sqrt[]{x^2}=-16 \\ x_1=\pm\sqrt[]{-16} \\ \\ x+5=0 \\ x_2=-5 \\ \\ x-5=0 \\ x_3=5 \end{gathered}[/tex]The real zeroes to the given equation is x = -5, and x = 5.
Please help me on my assignment The select is options x and y
SOLUTION
The domain of f is all the x-values, of the points on the graph, while the range is the corresponding y-values.
The domain of this function is all real numbers, hence the domain f is the interval
[tex](-\infty,\infty)[/tex]The range of f is from negative infinity to 7. Hence the range of f is interval
[tex](-\infty,7\rbrack[/tex]Beth has 2 jobs and at her first job she earns $12.25 and worked 36 hours. At her second job, she earns $9.00 per hour and worked 12 hours. How much did she earn for both jobs?
Beth earns $21.25 for both the jobs by working 36 hours at one job and 12 hours at another job
What is Addition?Addition: Addition is a way of combining things and counting them together as one large group. Addition in math is a process of combining two or more numbers. Addends are the numbers added, and the result or the final answer we get after the process is called the sum
Given that, Beth has 2 jobs and at her first job she earns $12.25 and worked 36 hours. At her second job, she earns $9.00 per hour and worked 12 hours
Her earnings for both the jobs is addition of her salary gives the answer
on adding $12.25+$9.00 = $21.25
She earns $21.25 for both the jobs by working 36 hours at one job and 12 hours at another job
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A.) State the random Variable: select from one of the following - X= the number of heads observed - X=tossing a coin - X= number of coins tossed - X= the number of heads observed when you flip a coin three times - X= the probability that you observe heads B.) construct a probability distribution table for the number of heads obtained over three tosses. Enter the X values from smallest to largest C.) determine the shape of the probability distribution of x - left skewed -symmetric -right skewed - uniform D.) find the MEAN number of heads for this distribution E.) find the standard deviation for the number of heads for this distribution F.) find the probability of obtaining two or less heads over three tosses of a coin
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
A.) State the random variable:
X= the number of heads observed when you flip a coin three times
Step 3:
B.) construct a probability distribution table for the number of heads obtained over three tosses. Enter the X values from smallest to largest:
X P(X)
0 1/8
1 3/8
2 3/8
3 1/8
Step 4:
C.) Determine the shape of the probability distribution of x
- symmetric
Step 5:
D.) find the MEAN number of heads for this distribution
[tex]\begin{gathered} Mean\text{= ( 0 X }\frac{1}{8})\text{ + ( 1 x }\frac{3}{8})\text{ + ( 2 x }\frac{3}{8})\text{ + (3 x }\frac{1}{8}) \\ \text{Mean = 0+ }\frac{3}{8}+\frac{6}{8}+\frac{3}{8} \\ \text{Mean = }\frac{12}{8} \\ \text{Mean = 1. 5} \end{gathered}[/tex]Step 6:
E.) find the standard deviation for the number of heads for this distribution:
[tex]S\tan dard\text{ Deviation = }\sqrt[]{(x\text{ -}\mu)^2\text{ P ( X = x )}}[/tex][tex]\begin{gathered} \sin ce\text{ }\mu\text{ = 1. 5, then we have that:} \\ \sqrt[]{\lbrack(0-1.5)^2X\text{ }\frac{1}{8}\rbrack+\lbrack(1\text{ - }1.5)^2\text{X }\frac{3}{8}\rbrack+\lbrack(2-1.5)^2}X\frac{3}{8}\rbrack+\lbrack(3-1.5)^2\text{ X }\frac{1}{8} \end{gathered}[/tex][tex]\begin{gathered} \sqrt[]{(2.\text{ 25 X }\frac{1}{8})\text{ + ( 0.25 X }\frac{3}{8})\text{ + ( 0. 25 X }\frac{3}{8})\text{ + (2.25 X }\frac{1}{8})} \\ =\text{ }\sqrt[]{0.28125+\text{ 0.09375 + 0.09375 + 0.28125}} \\ =\sqrt[]{0.75} \\ =0.866\text{ ( 3 decimal places)} \end{gathered}[/tex]
Step 7:
F.) find the probability of obtaining two or less heads over three tosses of a coin
[tex]P\text{ ( obtaining two or less heads) = }\frac{3}{8}+\text{ }\frac{3}{8}+\frac{1}{8}\text{ = }\frac{7}{8}[/tex]Eric picks 5/8 basket of strawberries. Kiki picks 1/5 basket of strawberries. Which answer is the most accurate estimate for how many more baskets of strawberries Eric picks than Kiki? 0 baskets 1/2 basket 3/4 basket 1 basket
The number exists described mathematically as a quotient, where the numerator and denominator exist split. Both are integers in a simple fraction. The baskets of strawberries Eric picks than Kiki exists 17 / 40.
What is meant by fractions?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
Based on the given conditions, formulate: 5/8 - 1/5
Find common denominator and write the numerators above common denominator: (5 × 5) / (8 × 5) - 8 / (8 × 5)
Calculate the product or quotient: 25 / 40) - (8 / 40)
Write the numerators over the common denominator: (25 - 8) / 40
Calculate the sum or difference: 17 / 40
get the result: 42.5% or 0.425
Therefore, the correct answer is 42.5% or 0.425.
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In the similaritytransformation of AABCto ADFE, AABC was dilated bya scale factor of [? ], reflectedacross the [ ], and movedthrough the translation [ ].
Given
To find:
The scale factor for the dilation of ΔABC to ΔDEF.
Explanation:
It is given that
Write down all the numbers that are between 30 and 60 and have a difference of 4 between their digits.
Answer:
The whole numbers that are between 30 and 60 and have a difference of 4 are 31, 35, 39, 43, 47, 51, 55 and 59
Step-by-step explanation:
Hope this helps!!!
If f(x) = 3x² + 5x-4, then
f(x+h)-f(x)
h
(3x+3h)²+(5x+5h)-4-(3x²+5x-4)
h
3(x+h)2 +5x-4-3x²-5x+4
h
is equal to which of the following?
3(x+h)² +5(x+h)-4-3x²+5x-4
h
3(x2+2xh+h²)+5(x+h)-4-(3x2 +5x-4)
h
function f(x) =[tex]3x^{2} +5x -4[/tex] then ,
= [tex]\frac{F(x + h)- F(x)}{h}[/tex]
= [tex]\frac{3(x+h)^{2}+5(x+h)-4 -3x^{2} - 5x +4}{h}[/tex]
What are functions ?The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given that : f(x) =[tex]3x^{2} +5x -4[/tex]then ,= [tex]\frac{F(x + h)- F(x)}{h}[/tex]
= [tex]\frac{F(x + h)- F(x)}{h}[/tex]
= [tex]\frac{F(x + h)- F(x)}{h}[/tex]
= [tex]\frac{3(x^{2} +2xh +h^{2} )+5(x+h)-4 -(3x^{2} +5x -4)}{h}[/tex]
= [tex]\frac{3(x+h)^{2}+5(x+h)-4 -3x^{2} - 5x +4}{h}[/tex]
hence option d is correct
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Find (if possible) conditions on a and b such that the following system has no solution, onesolution and infinitely many solutions.2 – 2y = 1ac + by = 5.
We are given the following system of equations
[tex]\begin{gathered} x-2y=1 \\ ax+by=5 \end{gathered}[/tex]Let us find the conditions on a and b such that the following system has no solution, one
solution and infinitely many solutions.
No solution:
A system of equations has no solution when the two equations are parallel.
Recall that two parallel equations have equal slopes.
If the value of a = 1 and the value of b = -2 then the two equations will be parallel and hence they will have no solution.
[tex]\begin{gathered} x-2y=1 \\ x-2y=5 \end{gathered}[/tex]The graph of the above system of equations is shown below
Question: solve ABC below using either the law of sines or law of cosines. Round to the nearest tenth.
SOLUTION:
First we calculate for a with cosines rule
[tex]\begin{gathered} a^2=b^2+c^2-2bcCosA \\ b=\text{ 29yd, c= 23yd, A= 99}\degree \\ a^2=(29)^2+(23)^2-2(29)(23)Cos(99) \\ a^2=841^{}+529^{}-1334\times(-0.1564) \\ a^2=841^{}+529^{}-1334\times(-0.1564) \\ a^2=841^{}+529^{}+208.68 \\ a^2=1578.686 \\ a=\text{ }\sqrt[]{1578.686} \\ a=\text{ 39.73} \end{gathered}[/tex]Then we calculate angle B with sine rule
[tex]\begin{gathered} \frac{a}{\sin A}=\text{ }\frac{b}{\sin B} \\ A=\text{ 99}\degree,\text{ a= 39.73 yd, b= 29 yd} \\ \frac{39.73}{\sin 99}=\text{ }\frac{29}{\sin B} \\ \text{Cross multiplying} \\ \sin \text{ B= }\frac{29\sin 99}{39.73} \\ \sin \text{ B= }\frac{29\times0.987}{39.73} \\ \sin \text{ B= 0.720} \\ B=\text{ }\sin ^{-1}(0.720) \\ B=\text{ 46.05}\degree \end{gathered}[/tex]Then we find the last angle C
[tex]\begin{gathered} A\text{ + B + C= 180}\degree \\ 99\text{ + 46.05}\degree\text{ + C= 180}\degree \\ C=\text{ 180}\degree-\text{ 99}\degree-\text{ 46.05}\degree \\ C=\text{ 34.95}\degree \end{gathered}[/tex]Final answers:
Side
a= 39.7 yd (nearest tenth)
Angles
B= 46.1 degrees (nearest tenth)
C= 35.0 degrees (nearest tenth)
A farmer is building a fence to enclose a rectangular area against an existing wall, shown in the figure below.
Fenced in Region
Three of the sides will require fencing and the fourth wall already exists.
If the farmer has 184 feet of fencing, what is the largest area the farmer can enclose?
Find the greatest common factor of the following monomials2b^4 32b^6 22b^5
The answer is
[tex]2b^4[/tex]First let's see the divider of the coeficient:
2 is a prime
32 = 2^5 = 2*2*2*2*2
22 = 11*2
The GCD of all is 2
Now, we have b to the 4, 5 and 6. We can write it:
[tex]\begin{gathered} b^6=b^4\cdot b^2 \\ b^5=b^4\cdot b \end{gathered}[/tex]Now we have all to get the answer:
[tex]\begin{gathered} 32b^6=2^4b^2\cdot(2b^4) \\ 22b^5=11b\cdot(2b^4) \end{gathered}[/tex]And the remaining is 2b^4. As you can see, all the monomyals can be divided by 2b^4 and that's the greatest common factor
What is the axis of symmetry, vertex, and y-intercept for f(x)=0.5x^2-2x-2
U
For the axis of symmetry, formula is,
[tex]x=\frac{-b}{2a}[/tex][tex]\begin{gathered} \text{where a=0.5 and b=-2} \\ x=\frac{-(-2)}{2(0.5)}=\frac{2}{1}=2 \end{gathered}[/tex]Hence, the axis of symmetry is 2.
To find the vertex, f(x)=0,
[tex]\begin{gathered} 0=0.5x^2-2x-2 \\ \text{Multiply both sides by 2} \\ 0=x^2-4x-4 \\ 0=(x^2-4x)-4 \\ 0=(x-2)^2-(4-2_{} \\ 0=(x-2)^2-2 \\ \text{Vertex are (2, -2)} \end{gathered}[/tex]Hence, the vertex are (2, -2).
[tex]y-intercept\text{ is -2}[/tex]
Hence, y-intercept is -2.
so I have couple question I need help on I could send an image of the work I need help on
Explanation:
1) (-3.4)^0
Note: anything raised to the power of zero is 1
Hence, (-3.4)^0 = 1
3)
The maximum area istype your answer...ft in length by type your answer...ft in width
The measurements are
1. 4unit by 4 unit
2. 6 unit by 2 unit
3. 5 units by 3 units
4. 1 units by 7 units
To arrange the area from the largest to the smallest we have to compute the area of the measurements.
[tex]\begin{gathered} \text{area = lw} \\ \text{area}=\text{ 4}\times4=16units^2 \\ \text{area}=\text{ 6}\times2=12units^2 \\ \text{area}=\text{ 5}\times3=15units^2 \\ \text{area}=\text{ 1}\times7=7units^2 \end{gathered}[/tex]The arrangement from highest to smallest is represented as follows
4units by 4 units
5 units by 3 units
6 units by 2 units
1 unit by 7 units
Find the vertex of the graph f(x)=-x^2+6x+1
Giving the function
[tex]f(x)=x^2+6x+1[/tex]the vertex is giving by
[tex]h=\frac{-b}{2a}[/tex]where
a=1
b=6
c=1
then
[tex]h=\frac{-6}{2*1}[/tex][tex]h=\frac{-6}{2}=-3[/tex]then
[tex]f(-3)=-3^2+6(-3)+1[/tex][tex]f(-3)=9-18+1[/tex][tex]f(-3)=-8[/tex]then the vertex is in the point
(-3,-8)
A rented office space has a monthly income of $3,800. A suitable gross income multiplier derived from market data is 11.1. What would the estimated value be? Round to the nearest $1,000.
The estimated value after round will be $506,000.
What is Rounding number?
To making a number simpler but keeping its value close to what it was, is called Rounding.
Given that;
Monthly income of a rented office = $3,800
A suitable gross income multiplier derived from market data = 11.1.
Now,
We know that;
Gross income multiplier = Sale price ÷ Gross income
Here, Gross income multiplier = 11.1
And, The annual gross income will be,
= Monthly gross income x Number of month in a year
= $3,800 x 12
= $45,600
Thus, Estimated sale price is calculated as;
11.1 = Estimated Sale price ÷ $45,600
Estimated Sale price = 45,600 x 11.1
= $506,160
After round off we get;
Estimated Sale price = $506,000
Thus, The estimated value after round will be $506,000.
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Help me with my school work what is the slope of this line
recall,
slope formullar is:
M = y2 - y1/x2 - x1
so taking two points from the table to represent y1, y2, x1 and x2
let x1 = 3
x2 = 7
y1 = -2
y2 = 6
so,
M = 6 - (-2)/7 - 3
M = 6 + 2/7 - 3
M = 8/4
M = 2
therefore, the slope is 2
Find the side length of the square given the area
The area of square is given 72 sq.ft.
ExplanationTo determine the side of square.
Use the formula for area of square.
[tex]A=side^2[/tex]Substitute the values.
[tex]\begin{gathered} 72=side^2 \\ side=\sqrt{72} \\ side=\sqrt{2\times2\times2\times3\times3} \\ side=6\sqrt{2} \end{gathered}[/tex]AnswerHence the side length of square is
[tex]6\sqrt{2}ft[/tex]Pentagon ZEBRA is similar to pentagon
LIONS. What is the length of RA in feet?
E
22 ft
13 ft
Z
18 ft
R
20 ft
A
10.4 ft
I
14.4 ft
17.6 ft
N 12 ft S
L
16 ft
A plane shape measuring 0.4 feet has five straight sides and five angles.
What is pentagon?The geometric shape known as a pentagon has five sides and five angles. Penta here means five, and pentagon means angle. One of the different kinds of polygons is the pentagon. A regular pentagon's internal angles add up to 540 degrees.
Pentagonal form
The pentagon is a polygon with five sides and five angles, just like other polygons including triangles, quadrilaterals, squares, and rectangle
There are various pentagon shapes depending on the sides, angles, and vertices, such as both a regular and irregular pentagon
Concave and convex pentagon.
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You transform the point (1, -2) by reflecting it over the y-axis. What are the coordinates of the new point?
The coordinates of the image after it is reflected is -1, -2)
How to determine the coordinates of the reflected point?The coordinate of the point is given as
Point = (1, -2)
The transformation rule is given as
Reflection over the y-axis
The mathematical representation of this transformation rule is
(x, y) = (-x, y)
So, we have
Point = (1, -2)
This gives
Image = (-1, -2)
Hence, the coordinates of the reflected point is -1, -2)
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One coin is picked at random. What is the probability of picking a nickel? Round the answer the nearest hundredth of a percent.
lease provide the information about which coins are in the group.
How many coins of each denomination.
We are told that there are:
7 quarters
11 dimes
8 nickels
15 cents
in a bag, and are asked to find the probability of picking a nickel at random
So first we add the number of coins in the bag:
7+ 11 + 8 + 15 = 41 coins total
the number of nickels is : 8
therefore the number of sucesses divided the total number of coins is:
8 / 41 this is the actual probability when we give it in percent form:
8 / 41 = 0.195121 which is the decimal form that corresponds to 19.5121 percent.
But since we are asked to round it to the nearest hundredth of a oercent, we type: 19.51 %
Identify the domain of the function shown in the graph.
A. X≥ 0
B. x < 0
C. 0
-8-84-2
D. x is all numbers.
10-
8
8.
4+
2+
y
-2-
4.
-8-
-10+
2
4 6 8 10 12
Answer:
A. [tex] x \geq 0[/tex]
Step-by-step explanation:
The domain of a function is the set of [tex]x[/tex]-values.
What is the volume of the cone?5 cm21 cmA 70π cm³B 105 cm³C 175 cm³D 525 cm³
The formula to find the volume of a cone is:
[tex]\begin{gathered} V=\frac{1}{3}\pi r^2h \\ \text{ Where} \\ r\text{ is the radius of the base} \\ h\text{ is the height} \end{gathered}[/tex]So, we have:
[tex]\begin{gathered} r=5cm \\ h=21cm \end{gathered}[/tex][tex]\begin{gathered} V=\frac{1}{3}\pi r^{2}h \\ V=\frac{1}{3}\pi(5cm)^{2}(21cm) \\ V=\frac{1}{3}\pi(525cm^3) \\ V=\frac{525\pi}{3}cm^3 \\ V=175\pi cm^3 \end{gathered}[/tex]Answer
C 175π
help me please !!!
thank youuu
The collection of all conceivable independent values that a function or relation may take is known as its domain.
A. The domain of the relation is a real number.
B. The domain of the relation is {2 ≤ r ≤ 7}.
How do you find the domain of a relation?The collection of all conceivable independent values that a function or relation may take is known as its domain. It is the compilation of every potential input. The collection of all potential dependent values that a function or relation can generate from its domain values is known as its range.
The range is the set of all "y" values in an ordered pair, while the domain is the set of all "x" values. Keep in mind that ordered pairs exists represented by the following symbols: (x, y). List all the x values from the relation to determine the domain when examining a set of ordered pairs.
A. The domain of the relation is a real number.
B. The domain of the relation is {2 ≤ r ≤ 7}.
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The domain of a function or relation is the set of all possible independent values that it can have.
A. The relation's domain is a real number.
B. The relation's domain is 2 r 7 in size.
How can you determine the scope of a relation?The domain of a function or relation is the set of all possible independent values that it can have. Every potential input has been compiled into it. The term "range" refers to the entire set of potential dependent values that a function or relation can produce given the values in its domain.
Do not forget that ordered pairs exist and are denoted by the following symbols: (x, y). To identify the domain, compile a list of all the relation's x values.
A. The relation's domain is a real number.
B. The relation's domain is 2≤ r≤ 7 in size.
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-m/3=-4 what is m????
The Demand equation for an item currently being marketed is given by D(q) = -0.15 q2 + 56,
where D(g) is in $ that can be charged per unit, and q is in thousands of units that can be sold at
that price. (For example, q=20 means 20,000 units can be sold.) 15,000 units are to be sold, at
what price should each be set? (Be careful with units when you do your calculations!)
The appropriate price = $
- 4 is price should each be set in price demand equation.
What is the price demand equation?
The formula P(x) = -ax + b is frequently used to express price-demand (p). But occasionally you have to construct P(x) using pricing data. • The point slope equation shown below can be used to compute P(x): 200 units are sold at a price of $14.
D(q) = -0.15 q² + 56
to find the price , when 20,000 units are to be sold , replace q = 20 in D(q)
D(20) = - 0.15 × (20)² + 56
= - 0.15 × 400 + 56
= - 60 + 56
= - 4
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