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When two or more roads or lines cross each other, they come together. You may also remark that two roads or lines cross.
What is the intersect command?They are referred to be intersecting lines when two or more lines in a plane cross each other.The common point shared by all intersecting lines is known as the point of intersection, and it can be found on all of them. Point O in this case represents the intersection of lines P and Q.
A line is something that is made up of indivisible points that stretch in many directions, to put it simply. Let's use the two points A and B as an example. Now, a line connecting points A and B can be drawn.
Line AB is the name of this line, which stretches in both directions. Arrows are used to represent lines to show that they have no ends and go on forever.
solve log(x)=-x+6
log(x)=-x+6 it can be written as
⇒log(x)+x+6=0
⇒log(1/x+6)=0
It will be in the form of lod(1/a+b)
so we can write log(x)+log(1+6/x)
Therefore, if modulus of 6/x <0 then it can be written as
∞ =log(x)-∑xn/n
n-1
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Related Questions
Curt and Melanie are mixing blue and yellow paint to make seafoam green paint. Use the percent equation to find how much blue paint they should use. Give two decimal places.
Answers
1.05 quarts of blue colors paint they mixed to make seafoam green paint.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
From the given figure, total quantity of paint is 1.5 quarts.
70% of blue paint and 30% of yellow paint.
Let the quantity of blue paint be x.
Now, x =70% of 1.5
x =70/100 ×1.5
x =0.7×1.5
x =1.05 quarts
Therefore, 1.05 quarts of blue colors paint they mixed to make seafoam green paint.
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a triangular park has vertices at a(-1,-1), b(4,4) and c(7,-1). a fountain is to be built that is equidistant from all vertices. find the location d of the fountain.
Answers
The fountain should be located at the coordinates (4,2). This is the midpoint of the line segment that connects the vertices a(-1,-1) and c(7,-1). It is also the same distance from b(4,4).
To find the location of the fountain, we first need to find the midpoint of the line segment connecting the vertices a(-1,-1) and c(7,-1). This midpoint is located at the coordinates (4,2). To verify that this is the correct location, we can calculate the distance between the midpoint and each vertex. To do this, we use the distance formula, which is d=√((x2-x1)2+(y2-y1)2). Using the coordinates for the midpoint (4,2) and the coordinates for vertex a(-1,-1), we get d=√((42-(-12))2+((22-(-12))2). This simplifies to d=√((52+52))=√(50)=7.07. We can repeat the same process for the midpoint and vertex b(4,4) and for the midpoint and vertex c(7,-1). In both cases, we find that the distance is 7.07, so the fountain should be built at the coordinates (4,2).
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please help me!!! I do not understand this!
Answers
(Lesson 2.9: Jointly Distributed RVs.) YES or NO? Suppose X and Y have joint p.d.f. f(x, y) = cxy/(1+x² + y² ) for 0 < x < 1, 0 < y < 1, and whatever constant c makes the nasty mess integrate to 1. Are X and Y independent? a. Yes b. No
Answers
Suppose X and Y have joint p.d.f. f(x, y) = cxy/(1+x² + y² ) for 0 < x < 1, 0 < y < 1, and whatever constant c makes the nasty mess integrate to 1 is No as well as x and y are not independent
What is variables?
Any qualities, quantity, or number that can be gauged or tallied qualifies as a variable. A data item is another name for a variable. Examples of variables include age, sex, company income and expenses, country of birth, capital expenditures, class grades, eye color, and vehicle kind.
The joint p.d.f of X and Y is f(x, y)
f(x,y) = cxy/ 1+[tex]x^{2}[/tex]+[tex]y^{2}[/tex] for 0 < x < 1 and 0 < y < 1
marginal p.d.f of x = f(x):
f(x) = {1y_of(x,y)dy
= {1y=0 /cxy/ 1+x+[tex]y^{2}[/tex] dy
Cx/2 ( {1y=0 /2y/1+ [tex]x^{2}[/tex] + [tex]y^{2}[/tex] dy)
Take substitute 1+[tex]x^{2}[/tex]+ [tex]y^{2}[/tex] = t⇒2y dy=dt
Lower limit: y = 0⇒t=1+[tex]x^{2}[/tex]
Upper limit: y=1➡t=1+[tex]x^{2}[/tex]+1
F(x) = cx/2
f 1y= 0 2y
=0 1+2+[tex]y^{2}[/tex]dy)
=Cx/2({1+[tex]x^{2}[/tex]+1dt/t
=1+[tex]x^{2}[/tex]t)
=cx/2(In(t) - ln(1+[tex]x^{2}[/tex])/1[tex]x^{2}[/tex])
=cx/2 (In (1+[tex]x^{2}[/tex]+1))-In(1+[tex]x^{2}[/tex]))
=cx/2 (In (1+[tex]x^{2}[/tex]+1/1+[tex]x^{2}[/tex]))
=Cx (In(1+1/1+[tex]x^{2}[/tex]))
marginal p.d.f of y = f(y):
f(y) = {1x
=0(x,y)dx
= F1x
=0/cxy/ 1+[tex]x^{1}[/tex][tex]y^{2}[/tex]=dx
= cy/2({1x)
=0/2x/1+[tex]y^{2}[/tex]+[tex]x^{2}[/tex]dx}
Take substitute 1 + [tex]y^{2}[/tex] + [tex]x^{2}[/tex] = t 2x dx = dt
Lower limit: x = 0
t = 1 + [tex]y^{2}[/tex]
Upper limit: x =1
=t + [tex]y^{2}[/tex] + 1
F(y)=cy/2({1x=0 2x/1+[tex]y^{2}[/tex]+[tex]x^{2}[/tex]/dx)
=cy({1+[tex]y^{2}[/tex]+1dt/t
=1[tex]y^{2}[/tex]t/)
=Cy/2((In(t))1+[tex]y^{2}[/tex]+1/1+[tex]y^{2}[/tex])
=cy(In(1+[tex]y^{2}[/tex]+1) – In( 1+[tex]y^{2}[/tex]))
=cy(In(1+[tex]y^{2}[/tex]+1/1+[tex]y^{2}[/tex]))
=cy/2(In(1+1/1+y2))
Now we have to check for independence.
F(x,y)= cxy/1+[tex]x^{2}[/tex]+[tex]x^{2}[/tex] for0<x<1 and 0<y<1
F(x) = cx/2( In(1+1/1+[tex]x^{2}[/tex])) for 0<x<1
F(y)=cy/2(In(1+1/1+[tex]y^{2}[/tex])) for < y <1
=f(x)*f(y)
=c2xy/4 ( In ( 1+1/1+[tex]x^{2}[/tex] ) *In( 1+1/1+[tex]y^{2}[/tex])) #f(x,y)
F(x,y) #f(x)* f(y) for all x and y
=x and y are not independent.
no is correct answer.
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In UITH, Dr Steve has worked more night shift than Dr. Greg who has worked five night shifts. Dr. Okon has worked fifteen night shifts more than Dr Steve an Dr Greg combined. Dr Uche has worked eight night shifts less than Dr Steve. How many night shifts has Dr Steve worked?
Answers
The equation to show the number of hours that Steven worked will be S = O - G - 15
How to calculate the equationAn equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
In this case, Dr Steve has worked more night shift than Dr. Greg who has worked five night shifts. Dr. Okon has worked fifteen night shifts more than Dr Steve an Dr Greg combined. Dr Uche has worked eight night shifts less than Dr Steve.
The expression can be illustrated as:
G = 5
O = G + S + 15
The equation for Steven will be:
S = O - G - 15
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Geometry Dilation
Please help!!!!
Answers
Answer:
C' (-2, -2)
D' (-2, 2)
E' (2, 0)
F' (0, -2)
Step-by-step explanation:
A dilation of factor k about the origin is a transformation that enlarges a figure by a factor of k, while keeping the origin fixed.
It means that each point (x, y) on the pre-image is transformed to a new point (kx, ky) in the dilated figure.
Therefore, the rule for a dilation of 2 about the origin is:
(x, y) → (2x, 2y)From inspection of the given diagram, the vertices of the pre-image are:
C = (-1, -1)D = (-1, 1)E = (1, 0)F = (0, -1)Applying the dilation rule (x, y) → (2x, 2y):
C' = (2 · -1, 2 · -1) = (-2, -2)D' = (2 · -1, 2 · 1) = (-2, 2)E' = (2 · 1, 2 · 0) = (2, 0)F' = (2 · 0, 2 · -1) = (0, -2)Helpp me with this pleass
Answers
Answer:
see below
Step-by-step explanation:
z+66+z+69+43z=180
so 45z=180-66-69 = 45
so z=1
so angle U= 43 its opposite side length ST is the smallest
same logic for the other 2.
66+1=67
69+1=70
so ST<US <TU
Each side of a rhombus is 10 cm long and one of its diagonals measures 16cm. Find the length of the other diagonal
Answers
The length of the other diagonal is 22.36 cm.
What is diagonals ?Diagonal is defined as a sloping line or the slant line, that connects to the vertices of a shape.
Let's call the length of the other diagonal "d".
Since a rhombus has perpendicular diagonals that bisect each other
we can use the Pythagorean theorem to find the length of the other diagonal:
d^2 = 10^2 + 10^2 = 100
d = sqrt(100) = 10 * sqrt(10) = 10 * 2.236 = 22.36 cm
Therefore, the length of the other diagonal is 22.36 cm.
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During this same time, the digital print manager tracked the number of visits to the website’s homepage. he found that before launching the new marketing plan, there were 4,800 visits. over the course of the next 5 weeks, the number of site visits increased by a factor of 1.5 each week. write an equation to model the relationship between the number of weeks, x, and the number of site visits, f(x).
Answers
An equation to model the relationship between the number of weeks, x, and the number of site visits, f(x) is 4800 = a(1.5)^x.
He found that before launching the new marketing plan, there were 4,800 visits.
Over the course of the next 5 weeks, the number of site visits increased by a factor of 1.5 each week.
Over the course of the next 5 weeks, initial visitor at x = 0, 4800
Increasing factor = 1.5
Equation of the model is given as:
f(x) = a(b)^x
From the question b = 1.5
Now the equation of model is:
f(x) = a(1.5)^x
At x = 0, f(x) = 4800
Now the equation of the model is:
4800 = a(1.5)^x
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how can we recognize if two real world quantities can be represented with a reciprocal function in a table of values?
Answers
We can graph a reciprocal function using the function’s table of values and transforming the graph of y=1/x
A new function called the reciprocal function is produced when the reciprocal function is found. These functions have intriguing characteristics and distinctive graphs. We also represent these patterns using reciprocal functions when two expressions are inversely proportional. A constant on the numerator and an algebraic expression in the denominator makes up reciprocal functions.
How to find the reciprocal of a function?
By dividing 1 by the provided number, we can find the reciprocal of a given number. Similar reasoning is used to get a function's reciprocal: we divide 1 by the function's expression.
We can graph a reciprocal function using the function’s table of values and transforming the graph of y=1/x
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In the triangle below,
x= [? ]°. Round to the nearest
tenth.
9 cm
90⁰
17 cm
19
Answers
After solving the equation the triangle given in question the 63.8°.
What is triangle?A triangle is a three-sided polygon with three angles. It is one of the basic shapes in geometry and is very versatile as it can be used to create many other shapes and structures. Triangles are generally classified by the length of their sides, which can be equal (an equilateral triangle), longer in one side than the other two sides (an isosceles triangle) or different in length on all three sides (a scalene triangle). They can also be classified by their angles, which can be acute (the angles are all less than 90 degrees), right (one angle is exactly 90 degrees) or obtuse (one angle is greater than 90 degrees).
x = 63.8°
Using the Law of Cosines, we can calculate the value of x:
x² = 17² + 9² - 2(17)(9)cos(90°)
x² = 289 + 81 - 306
x² = 64
x = √64
x = 8
Therefore, x = 63.8° (rounded to the nearest tenth).
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23. Graph the inequality x≤ 8.
Answers
The graph of the inequality is added as an attachment
How to determine the graphFrom the question, we have the following parameters that can be used in our computation:
x≤ 8
The above expression is an inequality that implies that
The value of x does not exceed 8
Next, we plot the graph
See attachment for the graph of the inequality
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The base of a triangular pyramid is an equilateral triangle. Each side of the base measures 12 in. The area of the base is 62.4 in². The slant height of the pyramid is 6 in.
What is the surface area of the pyramid?
Enter your answer in the box.
Answers
The surface area of the pyramid is given by the equation A = 170.4 inches²
What is the surface area of the pyramid?The total surface area is the summation of the areas of the base and the three other sides. A = B + ( 1/2 ) ( P x h ), where B is the area of the base of the pyramid, P is the perimeter of the base, and h is the slant height of the pyramid
Surface Area of Pyramid = B + ( 1/2 ) ( P x h )
Given data ,
Let the surface area of the pyramid be represented as A
Now , the equation will be
The slant height of the pyramid h = 6 inches
The side of the equilateral triangle = 12 inches
So , the perimeter of the triangle = 3 x side length
Substituting the values in the equation , we get
The perimeter of the triangle = 36 inches
The area of the base = 62.4 inches²
So , Surface Area of Pyramid = B + ( 1/2 ) ( P x h )
Substituting the values in the equation , we get
Surface Area of Pyramid = 62.4 + ( 1/2 ) ( 36 x 6 )
On simplifying the equation , we get
Surface Area of Pyramid = 62.4 + ( 108 )
Surface Area of Pyramid = 170.4 inches²
Hence , the surface area of pyramid is 170.4 inches²
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Is it
1.A
2.B
3.C
4.D
Answers
Answer:
26 R 1
Step-by-step explanation:
The number e is named after
?
Answers
Find the value of x that makes ACDE~ AFGH.
Answers
Answer:
the value of x that makes ACDE~AFGH is 27
a college charges $10,000 per semester for tuition. if that college has two semesters per year, what is the student's lifetime value for a student getting a four-year degree?
Answers
The student's lifetime value for a four-year degree at this college is $80,000.
The student's lifetime value for a four-year degree can be calculated as follows:
Determine the cost per semester: $10,000 per semester
Determine the number of semesters for a four-year degree: 4 years * 2 semesters/year = 8 semesters
Multiply the cost per semester by the number of semesters to get the total cost of tuition: $10,000 * 8 = $80,000
Therefore, the student's lifetime value for a four-year degree at this college is $80,000.
It is important to note that this calculation only considers the cost of tuition and does not take into account other costs such as room, board, books, and supplies, which can add significantly to the total cost of obtaining a degree.
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In 2009 the average weekly wage of men exceeded that of a woman by $162. The um of their average wage equaled $1476. Write and olve a ytem of equation to determine the average wage of men and of women in 2009
Answers
The average wage of men is $819 and of women is $657 in 2009
What is an equation?An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
Information about the problem:
M = W + 162M + W = 1476M = average wage of menW = average wage of womanTo solve this problem we must establish the equations according to the given data and solve the operations:
M = W + 162 (1)
M + W = 1476 (2)
We have two equations with two unknowns, substituting the value (M) in the second equation, we have:
M + W = 1476
W + 162 + W = 1476
162 + 2W = 1476
2W = 1476 - 162
2W = 1314
W = 1314/2
W = 657
Substituting (W) into one of the equations (M) we have:
M = W + 162
M = 657 + 162
M = 819
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a contractor removed 357 cubic yards of earth from a building site. if the contractor's truck can haul 17 cubic yards per load, how many truckloads were needed?
Answers
If the contractor's truck can haul 17 cubic yards per load, then 21 truckloads are needed.
Earth removed from a building site is 357 cubic yards.
A contractor's truck can haul 17 cubic yards per load.
To find how many truckloads were needed, we needed to divide the earth removed from the building site by the contractor's truck capable of hauling.
That is,
The number of truckloads = earth removed from the building site/contractors' truck capable of hauling.
The number of truckloads = 357 cubic yards/17 cubic yards per load
The number of truckloads = 21 truckloads.
Therefore, the required truckloads are 21.
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at the 2007 math olympics, team canada won $17$ out of a possible $100$ medals. which one of the following is closest to the fraction of medals that they won?$$ \frac{1}{4} \qquad \frac{1}{5} \qquad \frac{1}{6} \qquad \frac{1}{7} \qquad \frac{1}{8} $$
Answers
If at 2007 math Olympics, team Canada won 17 out of a possible 100 medals , then the closest fraction for the medals they won is (c) 1/6 .
To find the closest fraction to the number of medals that Canada won, we need to convert 17/100 to a simplified fraction by dividing by 17 .
So , On dividing both the numerator and denominator by 17.
we get , the closest fraction to 17/100 is 1/6 ,
Therefore, the closest fraction to the number of medals won by Canada is 1/6. Option (c) is the closest answer to the question.
The given question is incomplete , the complete question is
At the 2007 math Olympics, team Canada won 17 out of a possible 100 medals. which one of the following is closest to the fraction of medals that they won ?
(a) 1/4
(b) 1/5
(c) 1/6
(d) 1/7
(e) 1/8
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(x + 1) is a factor of x145 + 3x45 – 4.
True or False
Answers
(x + 1) is not a factor of the polynomial,
x¹⁴⁵ + 3x⁴⁵ - 4.
What is a polynomial?An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
Given:
We have a polynomial,
x¹⁴⁵ + 3x⁴⁵ - 4.
If (x + 1) is a factor.
Then x = -1 is a zero of polynomial.
Now,
(-1)¹⁴⁵ + 3(-1)⁴⁵ - 4
= -8
Therefore, (x + 1) is not a factor.
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Solve for x please!!
Answers
que es una computadora cuantica
Answers
A quantum computer is a type of computer that uses quantum mechanics.
How do quantum computers work ?Quantum computers use quantum mechanics, a branch of physics that deals with the behavior of matter and energy at the subatomic and quantum scale, to perform operations and solve problems.
Unlike classical computers, which use binary digits (bits) to represent and process information, quantum computers use quantum bits, or qubits, which can exist in multiple states at the same time, allowing for exponentially faster processing of complex computations and simulations. Quantum computers have the potential to revolutionize fields such as cryptography, drug discovery, and artificial intelligence.
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evaluate the integral. 3 5 arctan 1 x d
Answers
The arctan integral. 3 5 arctan 1 x d = 5 [ [tex]x[/tex] arctan ( [tex]\frac{1}{x}[/tex] ) dx - ( [tex]-(\frac{1}{2} )[/tex] [1+[tex]x^{2}[/tex]] ; where ([tex]\sqrt{3}[/tex] to 1 )
The basic arctan formula can be given by θ = tan-1(Perpendicular / Base). Here, θ is the angle between the hypotenuse and the base of a right-angled triangle.
The signed area of the region in the plane that is circumscribed by the graph of a specific function between two points on the real line can be used to describe definitive integrals. Areas above the plane's horizontal axis are often positive, whereas those below it are typically negative.
= [tex]\int\limits[/tex] 5 arctan ( [tex]\frac{1}{x}[/tex] ) dx ; where ([tex]\sqrt{3}[/tex] to 1 )
[tex]\int\limits[/tex] 5 arctan ( [tex]\frac{1}{x}[/tex] ) dx = [tex]5\frac{(2\sqrt{3} )ln(2)+2\pi -\sqrt{3} \pi }{4\sqrt{3} }[/tex]
= 5 [tex]\int\limits[/tex] arctan ( [tex]\frac{1}{x}[/tex] ) dx
= 5 [ x arctan ( [tex]\frac{1}{x}[/tex] ) dx - ( [tex]-(\frac{1}{2} )[/tex] [1+[tex]x^{2}[/tex]] ; where ([tex]\sqrt{3}[/tex] to 1 )[tex]x_{123}[/tex]
Therefore,
The arctan integral. 3 5 arctan 1 x d = 5 [ [tex]x[/tex] arctan ( [tex]\frac{1}{x}[/tex] ) dx - ( [tex]-(\frac{1}{2} )[/tex] [1+[tex]x^{2}[/tex]] ; where ([tex]\sqrt{3}[/tex] to 1 )
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if p and q vary inversely and p is 30 when q is 6, determine q when p is equal to 60.
Answers
using inverse relation, If p= 60, then q= 3x because i find the constant value is 180.
What is the p increases inversely as q equation?P is approximately equal to 1/Q since P has an inverse relationship to Q. x=k/3 for P=x and Q=3. P = k/x when Q = x.
The correlation between bond prices and interest rates is a prime illustration of an inverse connection. Bond prices normally fall with an increase in interest rates, whereas bond prices often rise with a decrease in interest rates.
P×1/q
( formula now) P= K/Q here K is a constant
30= k/6
k=30×6
k= 180
when P is equal to 60 then q=
because constant k=60
60= 180/q
q=180/60
q=3 unit .
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Identify the domain and range of the function domain
Answers
The term "domain" refers to a group of potential input values, and the domain of a graph is made up of all the input values visible on the x-axis.
How do you determine domain and range is a function or a relation?All the y values from the ordered pairings are listed to determine the range. Values that are repeated inside the domain or range don't need to be listed more than once. Each x must have a unique y value in order for a relation to be a function.
Simply solving for y = f(x) yields the values of the independent variable x and the domain, which we can use to determine the domain and range. Simply write x as x=g(y) to determine the function's range, and then identify g's domain.
Utilizing graphs is another method for determining the domain and range of functions. The collection of possible input values is referred to as the domain, and the domain of a graph is made up of all the input values displayed on the x-axis. The collection of potential output values that make up the range is represented by the y-axis.
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Find the compound interest on Rs. 24000 compounded semi annually (half yearly) for 1½ years at the rate of 10% per annum.
Answers
The compound interest on Rs. 24000 compounded semi annually is
Rs 3783 .
What is Compound Interest?Compound interest, also known as interest on principal and interest, is the practise of adding interest to the principal amount of a loan or deposit.
Given:
p=24000
r=5%
n=3
As we know,
[tex]A=P (1+\frac{r}{100})^{n}[/tex]
A = 24000 [tex]\\\\(1+\frac{5}{100})^{3}[/tex]
A = 24000 ( 1+ 0.05)³
A = 24000 (1.05)³
A = Rs 27783.
and, we know A = P + I
I=A-P
I=27783-24000
I = Rs 3783
Hence, the interest is Rs 2783.
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a 20 ft ladder leans against building so that the angle between the ground and the ladder is 60 degrees. how far from the building is the base of the ladder?
Answers
Salut/Hello!
Answer: 20 ft
Step-by-step explanation:
We can imagine the ladder, wall and ground as a triangle.
(And because we don't know if our triangle has a 90 degrees angle it means it's an ordinary triangle.)
We know that a triangle that has an angle with 60 degrees means all of its angles have 60 degrees because 180 : 3 angles = 60 degrees which means the triangle is equilateral.
Definition of the equilateral triangle: The triangle that has the 3 side with the exact same length.
From the equilateral triangle we know all sides are equal. If the ladder is 20 ft that means the distance between the building and the base of the ladder (which is actually the base of our triangle) is 20 ft.
I hope it was useful! :]
what percentage smoke something (cigars, cigarettes or both)? b. what percentage smoke neither cigars nor cigarettes? c. what percentage smoke cigars but not cigarettes? d. what is the conditional probability that a randomly selected person smokes cigarettes given that he smokes cigars?
Answers
Percentage is a concept used to express a fraction as a part of 100. It is typically expressed as a fraction with a denominator of 100 and is written as a number followed by the percent sign (%). For example, the fraction 3/20 can be expressed as 15%, which means 15 out of every 100. Percentage is a useful concept when comparing two or more values, as it provides a way to measure the relative size of each value. For example, if one group of people has 25% of the total number of votes, this means that they have more votes than the other groups, whose percentages are lower.
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Complete question:
A total of 28% of Americans smoke cigarettes, 7% smoke cigars and 5% smoke both cigarettes and cigars
a. What percentage smoke something (cigars, cigarettes or both)?b. What percentage smoke neither cigars nor cigarettes?c. What percentage smoke cigars but not cigarettes?d. What is the conditional probability that a randomly selected person smokes cigarettes given that he smokes cigars?The Total number of cherries on a plate, in a cup, and in a bowl is 780. The plate contains 145 cherries. The number of cherries in the bowl is 4 times the total number of cherries on the plate and in the cup. How many cherries are in the cup?
Answers
Using Mathematical Expressions, Let's call the number of cherries in the cup "x". There are 11 cherries in the cup.
A mathematical expression is what?A mathematical expression is made up of a statement, at least two integers or variables, and one or more arithmetic operations. This mathematical operation enables the multiplication, division, addition, or subtraction of numbers. The following is the structure of an expression: Expression: (Number/Variable, Math Operator, Math Operator)
We know that:
Total number of cherries = 780
Number of cherries on the plate = 145
Number of cherries in the bowl = 4 * (Number of cherries in the cup + Number of cherries on the plate)
So we can set up the equation:
x + 145 + 4(x + 145) = 780
Simplifying, we can combine like terms:
x + 145 + 4x + 580 = 780
5x + 725 = 780
Subtracting 725 from both sides:
5x = 55
Finally, we can divide both sides by 5:
x = 11
So there are 11 cherries in the cup.
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