We want to see for which one of the given functions, the inverse derivate evaluated in x = 20 is equal to 1/5.
The correct option is B: f(x) = x^3 + 5x + 20
What is inverse derivative?
The inverse function rule in calculus is a formula that converts the derivative of the inverse of a bijective and differentiable function, f, into the derivative of f.
Remember that two functions f(x) and g(x) are inverses if:
f( g(x)) = g( f(x))) = x
And for the inverse derivate of a function, we have the rule:
[tex]\frac{d}{dx}[f^{-1} (f(x))]=\frac{1}{{f^'}(x)}[/tex]
So first we need to find for what value of x each function is equal to 20, and then we need to see if the derivate of the function evaluated in that same value of x is equal to 5.
For example, for the first option we have:
A: f(x) = x + 5
We find the x-value such that the function is equal to 20.
f(15) = 15 + 5 = 20
We derivate the function.
f'(x) = 1
We evaluate the function in the x-value we got above.
f'(15) = 1
This is not the correct option, as this is not 5.
Now we need to do that for all the given options.
The only correct option will be the second one:
B: f(x) = x^3 + 5x + 20
First we find the x-value such that this is equal to 20
f(0) = 0^3 + 5*0 + 20 = 20
Then the x-value is x = 0.
Now we find the derivate of f(x).
f'(x) = 3*x^2 + 5
Now we evaluate that in the x-value we got before:
f'(0) = 3*0^2 + 5 = 5
As wanted, this is equal to 5.
Then we have:
[tex]\frac{d}{dx}[f^{-1} (f(0))]=\frac{1}{{f^'}(0)}[/tex]
[tex]\frac{d}{dx} [f^{-1} (20)]=\frac{1}{5}[/tex]
As wanted.
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on the graph, the horizontal red line is the mechanical energy of an object, and the blue line below it is the potential energy as a function of x. at which value of x is:
The kinetic energy will be maximum if the potential energy is minimum.
Given that,
On the graph, an object's mechanical energy is represented by the horizontal red line, and its potential energy as a function of x is shown by the blue line beneath it. at what x value is:
Value of x at which
1) potential energy at the largest
2kinetic energy at the largest
3)The force on the object in the negative direction.
4)The force on the object the largest magnitude.
More above the x-axis, greater the value of potential energy. Therefore, the point at which potential energy is large at x = 4
Mechanical energy is sum of potential energy and kinetic energy
So, kinetic energy will be maximum if the potential energy is minimum.
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For any positive integer x, let x^R be the integer whose binary representation is the reverse of the binary representation of x. (Assume no leading 0s in the binary representation of x.) Define the function R^+: N rightarrow N where R+(x) = x + x^R. a. Let A_2 = { | R^+ (x) = y}. Show A_2 elementof L. b. Let A_3 = { | R^+ (R^+ (x) = y}. Show A_3 elementof L.
Define the function [tex]R^{+}[/tex]: N ⇒ N where R+(x) = x + [tex]x^{R}[/tex]
(a) Let A₂ = {(x,y) | [tex]R^{+}[/tex] (x) = y} language A₂ ∈L.
(b) Let A₃ = {(x,y) | [tex]R^{+}[/tex] ([tex]R^{+}[/tex] (x)) = y} language A₃ ∈L.
Given that,
For any positive integer x, let [tex]x^{R}[/tex] be the integer with the opposite of x's binary representation in terms of representation. (Assume that x's binary form has no leading 0s.) Specify the function [tex]R^{+}[/tex]: N ⇒ N where R+(x) = x + [tex]x^{R}[/tex]
(a) Let A₂ = {(x,y) | [tex]R^{+}[/tex] (x) = y}. Show A₂ ∈L.
(b) Let A₃ = {(x,y) | [tex]R^{+}[/tex] ([tex]R^{+}[/tex] (x)) = y}. Show A₃ ∈L.
We know that,
Consider the Turing machine M, which computes the inverse of x for every positive inter. The result will also be x if the computation is done using both the integer x and its inverse.
This is because the result of adding a binary number 1 to 0 is always 1. The criterion is that the binary representation of x must not contain 0. In this case, a positive integer x is converted into binary representation.
Only x values with a binary representation of 1 will be accepted by the Turing machine. Even the Turing machine will accept inverse-of-x values with binary representations of 0.
Therefore, It is proved that language A₃ ∈L.
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Point A is the incenter of triangle DEF.
Which must be true? Select three options
A.Point A is the center of the circle that passes through points D, E, and F.
B.Point A is the center of the circle that passes through points X, Y, and Z.
C.ZA≅YA
D.EA≅FA
E.AX≅AY
The three options that describe the in-center of the given triangle are;
B. Point A is the center of the circle that passes through points X, Y, and Z.
C. ZA ≅ YA
E. AX ≅ AY
What is the in center of the triangle?The incenter of a triangle is defined as the point of intersection point of all the three interior angle bisectors of the given triangle. This means that, it can also be said to be the point where all the internal angle bisectors of the triangle cross each other.
Now, we are told that Point A is the incenter of triangle DEF. From the definition above, we can deduce that;
An inscribed circle can be drawn with center A passing through points X, Y and Z.
Similarly, since it passes through X, Y and Z, then it means that ZA≅YA, AX≅AY.
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PLEASE HELP!!
(Solving System of Equations from Context)
Jordan is working two summer jobs, making $13 per hour lifeguarding and $10 per hour walking dogs. Last week Jordan earned a total of $177 and worked 3 more hours lifeguarding than hours walking dogs. Determine the number of hours Jordan worked lifeguarding last week and the number of hours he worked walking dogs last week.
Answer:
Jordan worked 18 hours lifeguarding and 15 hours walking dogs.
Step-by-step explanation:
To solve this problem, we can set up a system of two equations to represent the given information. Let "L" represent the number of hours Jordan worked lifeguarding and "W" represent the number of hours he worked walking dogs.
The first equation will represent the total amount of money Jordan earned:
13L + 10W = 177
The second equation will represent the difference in hours between the two jobs:
L - W = 3
We can solve this system of equations using either substitution or elimination.
Using substitution, we can solve for one variable in terms of the other and substitute that expression into the other equation to solve for the other variable.
Solving the second equation for L, we get:
L = W + 3
Substituting this expression for L into the first equation, we get:
(W + 3) + 10W = 177
Combining like terms, we get:
11W + 3 = 177
Subtracting 3 from both sides, we get:
11W = 174
Dividing both sides by 11, we get:
W = 15.818181818181818
Since the number of hours worked must be a whole number, we can round down to 15 hours. Substituting this value back into the equation L = W + 3, we get:
L = 15 + 3 = 18
Therefore, Jordan worked 18 hours lifeguarding and 15 hours walking dogs.
Identify or mark the missing side or angle that would make triangle ABC congruent to triangle PDF by SAS.
Answer:
Mark the sides BC and DF as congruent---------------------------------------------------
We are given a side and an adjacent angle and need to identify the missing side or angle for proof by SAS.
SAS is side-angle-side and requires two sides and the included angle to be congruent on both triangles.
The missing bit is the other side of the marked angle B and D:
sides BC or DF.what is the volume of the rectangular pyramid shown? a square pyramid. the square base has side lengths 15 yards and the height is 12 yards.
The volume of the rectangular pyramid is 900 cubic yards.
The standard formula of the volume of the rectangular pyramid is written as
V = 1/3s²h
where s refers the base edge and h refers the height.
Here we have given that the square base has side lengths 15 yards and the height is 12 yards.
Now, we have to find the volume of the rectangular pyramid
As we know the the value of base edge is 15 yard and the height is 12 yards.
Now, we have to apply the values on the formula then we get,
=> V = 1/3 x 15² x 12
It can be simplified as,
=> V = 4 x 225
When we do the appropriate arithmetic operation, then we get,
=> V = 900 cubic yard.
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Which of the following represents a one to one function?A.Students to thier height B.Students to their weight C.Students to their LRN D.Students to their age
(Option C. Students to their LRN) In this case, each student has a unique LRN, meaning that it can be used in a one-to-one function where each student is mapped to their LRN.
Which of the following represents a one-to-one function?Option C. Students to their LRNA one-to-one function is a type of function where each element in the domain has one and only one image in the range. In this case, each student can be mapped to their LRN (Learning Reference Number) in a one-to-one function. This means that for every student, there is a unique LRN, and for every LRN, there is a unique student. This type of function is useful for keeping track of individual student information, as each student has a unique LRN associated with them.
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Write an equation of a circle whose
center is (-1,3) and passes through the
point (7,-2).
Answer: (x + 1)^2 + (y - 3)^2 = 65
Step-by-step explanation:
Answer: (x+1)²+(y-3)²=89
Step-by-step explanation:
An equation of a circle: (x-a)²+(y-b)=R²
The center of a circle is (-1,3), hence a=-1 b=3
(x-(-1))²+(y-3)=R²
(x+1)²+(y-3)²=R² (1)
Substitute the coordinate (7,-2) belonging to the circle into equation (1):
(7+1)²+(-2-3)²=R²
8²+(-5)²=R²
64+25=R²
89=R²
Thus, R²=89
Hence,
(x+1)²+(y-3)²=89
Find the area of this triangle. 30ft and 8ft.
Answer: 120 square feet
Step-by-step explanation:
Area formula of triangle:
(height of triangle x length) divided by 2
[tex]\frac{30*8}{2} =\frac{240}{2} =120[/tex]
Answer:
120 ft²
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4 cm}\underline{Area of a triangle}\\\\$A=\dfrac{1}{2}bh$\\\\where:\\ \phantom{ww}$\bullet$ $b$ is the base. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]
From inspection of the given triangle:
b = 30 fth = 8 ftSubstitute the given base and height into the formula to find the area of the triangle:
[tex]\implies A=\dfrac{1}{2} \cdot 30 \cdot 8[/tex]
[tex]\implies A=15 \cdot 8[/tex]
[tex]\implies A=120\; \sf ft^2[/tex]
Therefore, the area of the given triangle is 120 ft².
What is the GCF of 4 and 8 and 12?; What is the greatest factor of 8?; What is the greatest common factor of 4xy2 and 20x2y4?; How do you find the GCF?; What is the GCF of greatest?; What is the greatest common factor of 12a and 9a2?
The greatest common factor of 4, 8 and 12 is 4
The first number = 4
The second number = 8
The third number = 12
The GCF is stands for greatest common factor.
To find the greatest common factor use the prime factorization method
Prime factorization
Factorize the number 4 = 2 × 2
Factorize the number 8 = 2 × 2 × 2
Factorize the number 12 = 2 × 2 × 3
Here we have to take the common terms from the prime factorization
The greatest common factor = 2 × 2
Multiply the number
= 4
Therefore, the greatest common factor is 4
I have solved the question in general, as the given question is incomplete
The complete question is:
What is the GCF of 4 and 8 and 12?
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Evaluate 2xx ÷ 3yy for x = 1 2 and y = 3 5 -show the steps
The value of 2xx ÷ 3yy is 288/1225
What is simplification?In mathematics, simply or simplification is reducing the expression/fraction/problem to a simpler form. It makes the problem easy with calculations and solving.
Given that, an expression 2xx ÷ 3yy, where x = 12 and y = 35
2x12x12/3x35x35 = 288/1225
Hence, The value of 2xx ÷ 3yy is 288/1225
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In a recent year, companies spent a total of $87.5 billion on newspaper, television, and radio ads. The total amount spent on television and
radio ads was only $2.9 billion more than the amount spent on newspaper ads alone. The amount spent on newspaper ads was $5.4 billion
more than what was spent on television ads. How much was spent on each form of advertising? (Hint: Let the variables represent numbers of
billions of dollars.)
How much was spent on newspaper ads? $
How much was spent on television ads? $
How much was spent on radio ads? $ billion
billion
billion
Answer:
newspaper ads: $42.3 billiontelevision ads: $36.9 billionradio ads: $8.3 billionStep-by-step explanation:
You want the amount spent on ads in each medium given the total and relations between amounts spent for newspaper, television, and radio ads.
SetupLet n, t, r represent the amounts spent on ads in newspapers, television, and radio, respectively. The given relations tell you ....
n +t +r = 87.5
-n +t +r = 2.9
n -t = 5.4
SolutionThe augmented coefficient matrix can be reduced to row-echelon form using a suitable calculator or spreadsheet. This tells you the amounts spent in each medium. The attachment shows this.
newspaper ads: $42.3 billiontelevision ads: $36.9 billionradio ads: $8.3 billion__
Additional comment
The value of n can be found by subtracting the second equation from the first. That can be used in the third equation to find t, and both of those values can be used in either of the first two equations to find r.
Find the point in the first quadrant where the line y = 4 x intersects a circle of radius 5 centered at the origin.
The graph of the point of intersection is given below.
The point of intersection.
(5/√17, 20/√17) and (-5/√17, 20/√17)
What is a circle?A circle is a two-dimensional figure with a radius and circumference of
2πr.
The equation of a circle is x² + y² = r²
We have,
The equation of a circle
x² + y² = r²
r = 5
x² + y² = 25 ______(1)
The line.
y = 4x _____(2)
Now,
The line intersects the circle.
The point of intersection.
x² + (4x)² = 25
x² + 16x² = 25
17x² = 25
x = √(25/17)
x = ± 5/√17
x = 5/√17 and x = -5/√17
Now,
At x = 5/√17,
y = 4 x 5/√17
y = 20/√17
At x = -5/√17,
y = 4 x 5/√17
y = 20/√17
Thus,
The point of intersection.
(5/√17, 20/√17) and (-5/√17, 20/√17)
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Which one is not a polynomial? (a) 4x² + 2x-1 (b) x²-1
(c) y² + 5y + 1
So option b. x² -1 is the correct option of the given statement Because option b satisfy the requirement of not a polynomial.
In mathematics, what does a polynomial mean?An expression for a polynomial can be generated using only the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables (also known as indeterminates) and coefficients make up a polynomial.
What makes a polynomial unique?It is possible to identify the polynomials by seeing which formulae only include the operations addition, subtraction, multiplication, and non-negative integer exponents. Expressions that include extra operations are regarded as non-polynomial expressions. Specify the grounds for the expressions' non-polynomial status.
Which regulations apply to polynomials?Any function in an equation that uses only positive integer exponents or non-negative integer powers of a variable is known as a polynomial function. These equations include, for instance, the cubic equation, the quadratic equation, and others. A polynomial with an exponent of 1 is, for instance, 2x+5.
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(9^x-4)(9^3x+2)=9^10
Answer: x=3
Step-by-step explanation:
[tex]\displaystyle\\(9^{x-4})(9^{3x+2})=9^{10}\\\\9^{x-4+3x+2}=9^{10}\\\\9^{4x-2}=9^{10}\\\\4x-2=10\\\\4x-2+2=10+2\\\\4x=12[/tex]
Divide both parts of the equation by 4:
[tex]x=3[/tex]
Please help. I tried and couldn’t solve it
Using the law of cosines, the measure of the angles are
α ≈ 127°
β ≈ 28°
γ ≈ 25°
Law of Cosines: Calculating the angles in a triangleFrom the question, we are to solve the triangle.
To solve the triangle, we will determine the value of the unknown angles.
Using the law of cosines, we can write that
cosα = (b² + c² - a²)/2bc
From the given information,
a = 34
b = 20
c = 18
Thus,
cosα = (20² + 18² - 34²)/2(20)(18)
cosα = -432/720
cosα = -0.6
α = cos⁻¹(-0.6)
α = 126.8699°
α ≈ 127°
Calculating angle β
cosβ = (a² + c² - b²)/2ac
cosβ = (34² + 18² - 20²)/2(34)(18)
cosβ = 1080/1224
β = cos⁻¹(1080/1224)
β = 28.0724°
β ≈ 28°
To determine angle γ
α + β + γ = 180° (Sum of angles in a triangle)
127° + 28° + γ = 180°
155 ° + γ = 180°
γ = 180° - 155°
γ ≈ 25°
Hence,
α ≈ 127°
β ≈ 28°
γ ≈ 25°
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if u and v are connected open subsets of r , then there is a straight line that divides each of u and v in half by area
A space whose constituents are all single point sets is said to be completely isolated. Related to this property, the space X is such that the two distinct open sets of x and y are disjoint. In some cases, they are said to be completely isolated. We use U and x and V and y, X is the becomes a join. Of course, all perfectly isolated spaces are completely isolated, but not vice versa. For example, take two copies of the rational number Q and identify them at all points except zero. The resulting quotient topology space is completely separated and subset. In fact, it is not Hausdorff, and strictly speaking, the condition of complete separation is stronger than the condition of being Hausdorff.
In topology and related mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint, non-empty, open subsets. Connectivity is one of the most important topological properties used to distinguish topological spaces.
A subset of a topological space X is a connected space when viewed as a subspace of X.
Some related but stronger conditions are path connections, single connections, and n connections. Another related term is locally attached. It does not imply or derive connectivity.
At a given point x in the topological space X, X is an arbitrary collection of connected subsets each containing x is the union of The connected component of a point x in X is the uniquely largest connected subset of X containing is the union (the subset of X associated with containing x . The maximally connected subset of the non-empty topological space (containing) are called connected components of the space. The components of any topological space X form a partition of X. , is not empty, and their union is the entire space: each component is a closed subset of the original space. If that number is finite, each component is also an open subset. However, that may not be the case if the number of them is infinite. For example, the connected component of the set of rational numbers is an open singleton.
Let Гₓ be the topological space X and Г'ₓ be the intersection of all Clepen sets containing x (called subcomponents of x).
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Which sequence of transformations will result in an image that is similar to its pre image?
The sequence of transformation that produce similar image is (d) a dilation followed by a rotation
How to determine the sequence of transformationsTransformation involves changing the position and/or size of a figure.
There are four types of transformation, and they are:
DilationRotationReflectionTranslationThe representation of the types of transformation are:
Dilation: k(x, y)Rotation: rotation by anglesReflection: reflection across linesTranslation: (x + h, y + k)A dilation transformation would produce a similar image, while other transformation types would produce a congruent image
Hence, the sequence of transformation is (d)
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Evaluate âˆD(1+z2)dVâˆD(1+z2)dV where DD is the solid region bounded below by the upper portion of the cone z2=3x2+3y2z2=3x2+3y2 and above by the sphere x2+y2+z2=4.
Answer: 1
Step-by-step explanation:
In Norway last year, the lowest temperature was −15°C. In Norway last year, the highest temperature was 42°C greater than the lowest temperature. Work out the highest temperature in Norway last year
Answer:
27°
Step-by-step explanation:
Let h = highest temperature
h = -15 + 42
h = 27°
sume of angles of a triangel greater than 180 degrees when teh triange is so large that it extends to cosmological scales
In hyperbolic geometry, the angle sum of a triangle is always less than 180 degrees.
A lune is a wedge of a sphere with angle θ, represented by L(θ) in the proof.
α, β, and γ are the three angles of the triangle.
4πr²+4area[αβγ]=2L(α)+2L(β)+2L(γ)
2(2πr²+2area[αβγ])=2(L(α)+L(β)+L(γ))
2πr²+2area[αβγ]=L(α)+L(β)+L(γ)
At this point, we need to use a theorem that states that a lune whose corner angle is θ radians has an area of 2θr².
2πr²+2area[αβγ]=2αr²+2βr²+2γr²
2πr²+2area[αβγ]=2r²(α+β+γ)
π+area[αβγ]r²=α+β+γ
At this point, it is clear that the sum of the angles is equal to π plus the area[αβγ]r² (which cannot be zero).
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A circle has a circumference of \blue{12}12start color #6495ed, 12, end color #6495ed. It has an arc of length \dfrac{8}{5} 5 8 start fraction, 8, divided by, 5, end fraction. What is the central angle of the arc, in degrees? ^\circ ∘ degrees
The central angle of the arc in degree is 48° when a circle has a circumference of 12 units and it has an arc of length 8/5 units.
Given that,
A circle has a circumference of 12 units and it has an arc of length 8/5 units.
We have to find what is the central angle of the arc in degree.
We know that,
Circumference =12 units
Arc length =8/5= 1.6 units
If the central angle is "θ" then the length of the arc is given by
Arc length= θ/360°×circumference
Substituting values,
1.6=θ/360°×12
θ=48°
Therefore, The central angle of the arc in degree is 48° when a circle has a circumference of 12 units and it has an arc of length 8/5 units.
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Independent random samples, each containing 80 observations, were selected from two populations. The samples from populations 1 and 2 produced 33 and 28 successes, respectively.
Test H0:(p1−p2) = 0 against Ha:(p1−p2) ≠ 0. Use α = 0.05
The test statistic should be: _______
The P-value is _______
From two populations, independent random samples were drawn, each having 80 observations. The test statistic should be z = 2.18 because samples from populations 1 and 2 yielded 33 and 28 successes, respectively.
P-value is set at 0.030.
State the null and alternate hypotheses in step one.
H0: (p1-p2) = 0
Ha: (p1-p2) ≠ 0
Step 2: Calculate the test statistic
We can calculate the test statistic using the formula:
z = (p1-p2)/√(p(1−p)(1/n1+1/n2))
where,
p = (successes in sample 1 + successes in sample 2)/(n1+n2)
= (33 + 28)/(80 + 80)
= 61/160
= 0.30
n1 = sample size of population 1
= 80
n2 = sample size of population 2
= 80
Therefore,
z = (p1-p2)/√(p(1−p)(1/n1+1/n2))
= (33/80 - 28/80)/√(0.38125(1−0.38125)(1/80+1/80))
=2.18
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for each of the three plots, identify the strength of the relationship (e.g. weak, moderate, or strong) in the data and whether fitting a linear model would be reasonable.
These following answers are correct
We are given residual plots
In given(a) plot there is weak relationship between scatter points
we see curved relationship in this residual plot therefore model is unreasonable .
Note - This model is reasonable when this plot should look approximately normal and scatterplot of residuals should show random
scatter. In these plots we see weak relationship and line as model is unreasonable
2)We are given residual plot.
Given 2nd (c) plot there is strong relationship between scatter points we see positive straigh line relationship in this plot therefore model is resonable.
Also these model look approximately normal land scatterplot of residuals show random scatter.
In these plot we see strong relationship and linear model is reasonable
Therefore, these statements are correct.
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Which of the following statements is TRUE? O a. If f(a) and g(x) are differentiable functions defined on the closed interval [a, b], and f(x) attains its global maximum at x = c and g(x) attains its global maximum at x = d, then the function f(x) · g(x) attains its global maximum on [a, b] at x = cºd. O b. All of the statements are false. a O c. Every local maximum is a global maximum d. The global maximum value of a differentiable function f(x) on a closed interval (a, b) must occur at a critical value or an endpoint e. The critical points of f'(2) are same as the critical points of f(x)
ANSWER
c
It is c because i did the work and i know.
Jeff Ryan bought 200 shares of BUI for $19.50. Eight weeks later he sold the stock for $20.75. Assuming a 3% commission, his bottom line was a gain of:
Multiple Choice
$250.00
$374.50
$8.50
$257.50
His bottom line was a gain from selling and 3% commission is $257.50.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
The cost price of 200 shares of BUI is (19.50×200) = $3900.
The selling price of 200 shares of BUI is (20.75×200) = $4150.
The net gain is (4150 - 3900) = $250 and with 3% commission it is,
= (103/100)×250.
= $257.50.
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I need this please help me
Answer: m∠A = 72°, m∠C = 56°
Step-by-step explanation: All triangles interior angles add up to 180, This is an isosceles triangle which by rule mean that angles m∠A and m∠B and the same value of 72°. Now it becomes an equation to find m∠C, of
72 + 72 + x = 180.
144 + x = 180
x = 56
Find the solutions of the equation in the interval [−2, 2]. Use a graphing utility to verify your results. (Enter your answers as a comma-separated list.)
The value of x for the given trigonometric function is (15/18)π.
What is a trigonometric function?The fundamental 6 functions of trigonometry have a range of numbers as their result and a domain input value that is the angle of a right triangle.
The trigonometric function is very good and useful in real-life problems related to the right angle.
As per the given,
secx = (-2√3)/3
1/cosx = -2/√3
cosx = -√3/2
x = 150° = (15/18)π
Thus, x goes into the second quadrant as shown below.
Hence"The value of x for the given trigonometric function is (15/18)π".
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Use the equations for the total cost C and total revenue R to find the number x of units a company must sell to break even. (Round to the nearest whole unit.)
C = 2.5
x
+ 14,000, R = 6.23x
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The number of units to sell to break even is 3753.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
C = 2.5x + 14,000
R = 6.23x
Where,
C is the total cost.
R is the total revenue.
Now,
The number of x units a company must sell to break even.
2.5x + 14,000 = 6.23x
14000 = 6.23x - 2.5x
14000 = 3.73x
x = 14000 / 3.73
x = 3753
Thus,
The number of units to sell to break even is 3753.
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an escalator has a slope of 3/4 after traveling forward 128 feet, the escalator is 96 feet above the floor. Write this word problem in point slope form
The point slope form of the slope of escalator and distance is y-24 = 3/4(x-32).
The general point slope form is given by the equation -
y - y1 = m (x - x1)
Now we are given the slope as 3/4. So, keeping the values of y1 and x1 in the equation. Let us assume the points as (32, 24). As per the points, 32 is x1 and 24 is y1.
y - 24 = 3/4(x - 32)
y - 24 = 3x/4 - 3/4×32
Performing division on Right Hand Side of the equation
y - 24 = 3x/4 - 3×8
y - 24 = 3x/4 - 24
Rewriting the equation
y - 3x/4 = - 24 + 24
Solving the equation on Right Hand Side of the equation
y - 3x/4 = 0
y = 3x/4
Thus, the equation is y - 24 = 3/4(x - 32).
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