Explanation:
In a function, each x-value has one y-value.
___
That is the definition of a relation that is a function.
Final answer:
Each x-value in a function has exactly one corresponding y-value. Functions map elements of the domain to unique elements in the range, which can be represented graphically and must pass the vertical line test. The derivative in calculus, such as dy/dx, reflects the rate of change between these variables.
Explanation:
In a function, each x-value has one corresponding y-value. This is a foundational concept in mathematics that defines a relationship whereby each input (or x-value) in the function produces exactly one output (or y-value). Essentially, a function maps each element of the domain to exactly one element in the range.
An example of a function is y = f(x), which could represent a linear function like y = 3x + 2. In this case, for every x-value, there is a specific y-value determined by the function's formula. So if x were 1, then y = 3(1) + 2 = 5. The graphical representation of a function, such as its curve or line on a coordinate plane, must pass the vertical line test. That means if you draw a vertical line through any point on the graph, it should intersect the graph at no more than one point, confirming that each x-value has only one y-value.
Understanding functions is pivotal in different areas of mathematics, including calculus where the derivative of a function represents the rate of change of the y-value with respect to the x-value. In the case of the linear function y = 6+3x, the derivative dy/dx is constant at 3, implying that for every unit increase in x, y will increase by 3 units.
The front and back covers of a textbook are each 0.3 cm thick. Between the covers are 240 sheets of paper each 0.008 cm thick. How much is a stack of 10 books
2.52 × 10 = 25.2
2.52 = 240 × 0.008
The total thickness of a stack of 10 textbooks, where each book has 240 sheets of 0.008 cm thickness and two covers of 0.3 cm thick, is 25.2 cm.
Explanation:The question requires us to find the total thickness of a stack of 10 textbooks. Each book has 240 sheets and two covers. The thickness of each sheet is 0.008 cm and each cover is 0.3 cm thick.
First, we calculate the thickness of one book. The thickness of sheets in one book is 240 multiplied by 0.008 cm (sheet thickness), which equals 1.92 cm. The thickness of the covers of one book is 2 multiplied by 0.3 cm (cover thickness), which equals 0.6 cm. Hence the total thickness of one book is 1.92 cm (sheets) plus 0.6 cm (covers), which equals 2.52 cm.
Therefore, the thickness of a stack of 10 books would be 10 multiplied by 2.52 cm (single book thickness), which equals 25.2 cm
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what is the equation of the line that passes through (0,3) and (-5,3)
Answer:
y=+3
Step-by-step explanation:
the equation of a line is y=mx+c
where m is the slope and c is the y-intercept.
First, let's find what m is, the slope of the line...
The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.
For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:
So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (0,3), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=0 and y1=3.
Also, let's call the second point you gave, (-5,3), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=-5 and y2=3.
Now, just plug the numbers into the formula for m above, like this:
m=[tex]\frac{3-3}{-5-0}[/tex]
or
m=[tex]\frac{0}{-5}[/tex]
or
m=0
So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+c like this:
y=0x+c
Now, what about c, the y-intercept?
To find c, think about what your (x,y) points mean:
(0,3). When x of the line is 0, y of the line must be 3.
(-5,3). When x of the line is -5, y of the line must be 3.
Because you said the line passes through each one of these two points, right?
Now, look at our line's equation so far: y=0x+c. c is what we want, the 0 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (0,3) and (-5,3).
So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for c for the particular line that passes through the two points you gave!.
You can use either (x,y) point you want..the answer will be the same:
(0,3). y=mx+c or 3=0x 0+c, or solving for c: c=3-(0)(0). c=3.
(-5,3). y=mx+c or 3=0x -5+c, or solving for c: =3-(0)(-5). c=3.
See! In both cases we got the same value for c. And this completes our problem.
The equation of the line that passes through the points
(0,3) and (-5,3)
is
y=+3
Hope this helps :)
y = 3
First find the gradient of the line:
(Y²-Y¹)/(X²-X¹)
(3-3)/(-5-0)
0/-5 = 0
Your gradient is 0
Now find the y intercept. This is whrre where the line crosses the y axis, when X = 0
(0,3)
Your y intercept is 3.
Now put It into the formula y = mx + c
m = 0
c = 3
y = 0x + 3
y = 0 + 3
y = 3
HELP ME ASAP!!! I NEED SOMEBODY TO EXPLAIN THIS TO ME!
Will mark BRAINLIEST
Answer:
(-√10)/10
Step-by-step explanation:
The trig identity that relates the sine and the tangent is ...
sin(x) = ±tan(x)/√(1 + tan(x)²)
For your given value of tan(x), this evaluates to ...
sin(x) = ±(1/3)/(√(1 + (1/3)²) = ±1/√10 = (±√10)/10
The given value of the tangent function is positive, so the sine and cosine functions have the same sign (both are negative in this case).
So, your sine function is ...
sin(x) = (-√10)/10
_____
You can derive the above relationship using SOH CAH TOA.
Tan = Opposite/Adjacent
You are given the value of the tangent function as 1/3, so it is convenient to assign Opposite = 1 and Adjacent = 3. Then Hypotenuse is found using the Pythagorean theorem as ...
Hypotenuse = √(Opposite² + Adjacent²) = √(1² + 3²) = √10
Now, the sine is ...
Sin = Opposite/Hypotenuse = 1/√10
Rationalizing the denominator, this is ...
Sin = (√10)/10
__
Now, you need to take into account the quadrant of the angle. Tangent is positive and Cosine is negative in the 3rd quadrant, where the Sine is also negative. Then your sine value is ...
sin(x) = (-√10)/10
what is the value of expression 1/12÷36
Here is a step by step tutorial!
The solution of expression 1/12÷36 is 1/432
What is the value of expression 1/12÷36From the question, we have the following parameters that can be used in our computation:
1/12÷36
Express the expression properly
So, we have
1/12 ÷ 36
NExt, we rewrite it as quotient
so, we have the following representation
1/12 ÷ 36 = 1/12 * 1/36
So, we have
1/12 ÷ 36 = 1/432
Hence, the solution is 1/432
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Please help me with this! Very much appreciate
Answer:
The answers for your two problems, can be found below in the attached images.
Problem 1
Graph
The graph was plotted using a calculator. We can see that the graph opens up.
f(x) = x^2 + 4x +3
Vertex
The vertex is the minimum point of the equation
In this case Vertex (V) = (-2,-1)
Axis of symmetry
The x axis corresponding to the vertex component
x = -2
y intercept
Interception with the y-axis
From the first attached image, we can see that they y intercept occurs
at x = 0, y = 3
(0,3)
Problem 2
Graph.
The graph was plotted using a calculator. We can see that the graph opens up.
f(x) = 2x^2 + 3x +1
Vertex
The vertex is the minimum point of the equation
In this case Vertex (V) = (-0.75,-0.125)
Axis of symmetry
The x axis corresponding to the vertex component
x = -0.75
y intercept
Interception with the y-axis
From the second attached image, we can see that they y intercept occurs
at x = 0, y = 1
(0,1)
Which equation represents a circle that contains the point (–5, –3) and has a center at (–2, 1)? Distance formula: (x – 1)2 + (y + 2)2 = 25 (x + 2)2 + (y – 1)2 = 5 (x + 2)2 + (y – 1)2 = 25 (x – 1)2 + (y + 2)2 = 5
Answer:
[tex](x+2)^2+(y-1)^2=25[/tex]
Step-by-step explanation:
The equation of a circle with center at (h,k) and radius r, is given by
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Since the given circle contains the point (-5,-3) and it is centered at (-2,1), we can determine the radius of the circle using the distance formula;
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
This implies that;
[tex]r=\sqrt{(-2--5)^2+(1--3)^2}[/tex]
[tex]r=\sqrt{(-3)^2+(4)^2}[/tex]
[tex]r=\sqrt{9+16}[/tex]
[tex]r=\sqrt{25}[/tex]
[tex]r=5[/tex]
We now substitute (h,k)=(-2,1) and r=5 into the formula to obtain;
[tex](x+2)^2+(y-1)^2=5^2[/tex]
[tex](x+2)^2+(y-1)^2=25[/tex]
HELP BRAINIEST AND LOTS OF POINTS The set {1,2,3,…42} is split into two sets A and B. How many ways are there to do this so that A and B have the same sum of elements? NEED NOW
Answer:
zero
Step-by-step explanation:
In order for sets A and B to have the same sum of elements, that sum of elements must be the same for each set, and half the sum of elements of the original set.
The sum of elements of the set {1, 2, 3, ..., 42} is an odd number (903), so there cannot be two sets with the same sum that have that total.
Multiply (4x - 5)(4x + 5).
A) 8x2 - 10
B) 16x2 - 25
C) 8x2 - 40x - 10
D) 16x2 - 40x - 25
Max has a box of 200 colored blocks. The box has an equal number of green and blue blocks and an equal number of red and yellow blocks. If Max arranged all of the green blocks in stacks of 12 and all of the blue blocks in stacks of 7, how many red blocks are in the box?
how many triangles can be constructed with sides length of 7 cm x 10 cm + 18 cm
Answer:
zero
Step-by-step explanation:
Assuming your intended side lengths are {7 cm, 10 cm, 18 cm}, the sum of the short sides is not long enough to connect to the ends of the long side. No triangle can be formed.
Which operation should be performed last in this problem: 3^2 + 7 × 4? Why?
Answer:
3^2+7*4~ Addition should be last
Step-by-step explanation:
Parenthesis ----- Addition is second to last in order of operations
Exponents
Multiplication
Division
Addition
Subtraction
Given the problem 3² + 7 × 4, the last operation that should be performed is addition due to the rules dictated by the order of operations (PEMDAS).
Explanation:In the given problem, 3² + 7 × 4, the operation that should be performed last is addition. This is due to the rule of the order of operations, often remembered by the acronym PEMDAS which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). Therefore, in this expression, you first perform the exponentiation (3²), then multiplication (7x4), and add the results last.
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What are the steps you would take to divide two fractions?
Answer:
Step-by-step explanation:
you have to change it into a x and keep change flip and
1/5 / 3/7
1/5 * 7/3 then x
To divide two fractions, you should flip the second fraction to get its reciprocal, then multiply the first fraction with this reciprocal. For instance, in dividing 3/5 by 4/7, you flip 4/7 to get 7/4, then multiply 3/5 by 7/4 to obtain 21/20.
Explanation:To divide two fractions, you will need to follow a few simple steps. Firstly, you need to flip or find the reciprocal of the second fraction (the one that you are dividing by). Secondly, you will multiply the first fraction (the one being divided) by the reciprocal of the second fraction. This process can also be remembered as 'copy, flip, multiply'.
For example, if we have to divide 3/5 by 4/7, first we flip 4/7 to get 7/4. Then we multiply 3/5 by 7/4. The result is 21/20.
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2 hour 40 min after a raft left pier A and traveled downstream, a motorboat left pier B and traveled upstream toward the raft. The two met 27 km away from B. Find the speed of the raft if the speed of the motorboat in still water is 12 km/hour and the distance from A to B is 44 km.
Answer:
3 km/h
Step-by-step explanation:
Let c represent the speed of the current in km/h, and t the time in hours after the raft leaves point A. 2 hours 40 minutes is 8/3 hours.
Distance = Speed × Time
The watercraft meet at a point 27 km upstream from B, so we have two equations involving these variables:
27 = 44 - ct
27 = (12-c)(t -8/3)
Equating these two versions of "27", we have ...
44 -ct = 12t -32 -ct +(8/3)c
76 = 12t + 8/3·c . . . . . add 32+ct
9t +2c = 57 . . . . multiply by 3/4
t = (57 -2c)/9 . . . .solve for t
Now, we can substitute this into the first of the above equations, after rearranging it to ...
ct = 17
c(57 -2c)/9 = 17
2c^2 -57c +153 = 0 . . . . multiply by 9, subtract the left side
c = (57-√((-57)^2 -4(2)(153)))/(2·2) = (57 -√2025)/4 = 12/4 . . . . quadratic formula
c = 3
The speed of the current is 3 km/h.
An orange punch recipe uses 2/3 cup carbonated water for every 4 cups orange juice. Mandy pours 5 cups of orange juice into a bowl.how many cups of carbonated water does Mandy need?
Answer:
(5/6) cup carbonated water
Step-by-step explanation:
We can easily solve this problem by applying a rule of three.
4 cups of orange juice ------------------------ 2/3 cup carbonated water
5 cups of orange juice ------------------------ x
x = (5/4)*2/3 cup carbonated water
x = (10/12) cup carbonated water
x = (5/6) cup carbonated water
x = 0.8333 cup carbonated water
Click an item in the list or group of pictures at the bottom of the problem and holding the button drag drag it into the correct position in the answer box release your moist button when the item is in place if you change your mind drag the item to the trash can click the trash can to clear all your answers A (5,8), B (-3,4) AB =
Answer:
where are the pictures
Step-by-step explanation:
PLEASE HELP QUICKLY;; WILL GIVE 40 POINTS!
Factor the polynomial by factoring out the GCF:
[tex]-6ax^{7}[/tex]+[tex]12a^{6}[/tex]−[tex]3a^{5}[/tex]
um, i tried solving this with a [tex]-3ax^{5}[/tex] GCF but i got it incorrect. help will greatly be appreciated.
Since only the first term has ax for coefficients the GCF cant be -3ax^5.
The GCF would be -3a
Factor -3a out of all the terms:
-3a(2x^7)-3a(-4a^5)-3a(a^4)
Now factor -3a out of the equation for the final answer:
-3a(2x^7-4a^5+a^4)
what two numbers are located 3/8 of a unit from 1/2 on a number line
Answer:
1/8, 7/8
Step-by-step explanation:
1/2 is 4/8.
3/8 less than 4/8 is 1/8.
3/8 more than 4/8 is 7/8.
Find two consecutive numbers if the square root of the smaller number is 3 less than the bigger number.
Answer:
The numbers are 4 and 5
Step-by-step explanation:
Let
x------> the smaller number
x+1----> the bigger number
we know that
[tex]\sqrt{x}=(x+1)-3[/tex] ----> equation that represent the situation
solve for x
[tex]\sqrt{x}=(x-2)[/tex]
squared both sides
[tex]x=(x-2)^{2}\\x=x^{2}-4x+4\\x^{2}-5x+4=0[/tex]
using a graphing calculator to solve the quadratic equation
see the attached figure
the solution is
[tex]x=4[/tex]
[tex]x+1=5[/tex]
The consecutive numbers are 4 and 5 in which the square root of the smaller number is 3 less than the bigger number
EquationAn equation is an expression that shows the relationship between two or more variables and numbers.
Let x represent the smaller number and y the larger number, hence:
y = x + 1 (1)
Also:
[tex]\sqrt{x} =y-3[/tex] (2)
From equation 1 and 2:
x = 4, and y = 5
The consecutive numbers are 4 and 5
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4. Find the value of x. Round to the nearest tenth. The diagram is not drawn to scale. 37 and 35 sorry i cant put an image please hepl me with this ASAP i have little time to turn this in
thank you
35 round to the nearest 10 equal 40
37 round =40
if a scatter plot has no association then a.) it has no ordered pairs B.) its ordered pairs hsve no predictable pattern C.) it has ordered pairs that have a positive pattern D.) it has ordered pairs with a negative pattern
Answer:
If a scatter plot has no association then it's ordered pairs have no predictable pattern.
Step-by-step explanation:
5x+8-7x=-4x+1 How many solutions does this have? A)no solutions B)exactly one solution C)infinitely many solutions
The equation 5x+8-7x=-4x+1 has exactly one solution
Option B is correct
The given equation is:
5x + 8 - 7x = -4x + 1
Simplify both sides of the equation
5x - 7x + 8 = -4x + 1
-2x + 8 = -4x + 1
Collect like terms
-2x + 4x = 1 - 8
2x = -7
Divide both sides by 2
[tex]\frac{2x}{2} =\frac{-7}{2} \\\\x=-3.5[/tex]
As seen above, the equation has exactly one solution
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Final answer:
The equation 5x+8-7x=-4x+1 simplifies to 2x = -7, which means that there is exactly one solution for x, which is x = -7/2. The correct option is: B)exactly one solution
Explanation:
To determine how many solutions the equation 5x+8-7x=-4x+1 has, let's first simplify and solve for x:
Combine like terms on the left side: (5x - 7x) + 8 = -2x + 8.
Bring the term involving x from the right side to the left: -2x + 8 + 4x = 1.
Combine like terms involving x: (4x - 2x) + 8 = 1, which simplifies to 2x + 8 = 1.
Subtract 8 from both sides: 2x = 1 - 8, which simplifies to 2x = -7.
Divide by 2 to solve for x: x = -7/2.
Since we have found a single value for x, the equation has exactly one solution.
Can someone please help me on this problem? I don’t really understand it.
Answer:
Step-by-step explanation:
A temperture in degrees Fahrenheit is shown in expanded notation (9x10)+(4x.01) how is the temperature in degrees Fahrenheit written in numeral
Answer:
90.04 °F
Step-by-step explanation:
Evaluate the expression.
(9×10) + (4×.01) = 90 + .04 = 90.04
(40pts) Help please
bacteria are the most common example of exponential growth The table below shows the number of E-coli bacteria that would be present after each hour of the first six hours.
Answer:
a) each hour the number is multiplied by 16. Such a geometric sequence is described by an exponential growth function.
b) n = 16^t . . . . . n is number of bacteria; t is hours
c) about 7.923×10^28
d) the rule would be multiplied by 100/16=6.25, so becomes n=6.25·16^t
Step-by-step explanation:
a) We presume the table represents exponential growth because it was formulated with that purpose in mind. ("Why?" is always a tricky question.) It represents exponential growth because each table entry is 16 times the one before. A constant multiplier like that is characteristic of exponential growth.
___
b) In part (a) we noted the common ratio is 16. Since the first term (for t=1) is also 16, we can write the equation as ...
n = 16^t
where n is the number of bacteria and t is time in hours
___
c) Evaluating the formula for t=24, we get ...
n = 16^24 ≈ 7.923×10^28
n = 79,228,162,514,264,337,593,543,950,336
This is the estimate of the number present after 24 hours based on the formula.
___
d) If the starting number is different, the rule is multiplied by a factor that gives the appropriate starting value. The above answer assumes your "starting value" is 100 after 1 hour. If the starting value at 0 hours is 100, then the rule of part (b) gets multiplied by 100, not 6.25
n = 100·16^t . . . . . starting with 100 at t=0
n = 6.25·16^t . . . . starting with 100 at t=1
_____
Comment on exponential bacteria growth
The number of bacteria estimated in part (c) have an approximate volume of 102 cubic kilometers, roughly the volume of Lake Nicaragua.
Determine whether the relation is a function. {(-7, -7), (-7, -8), (-1, 4), (6, 5), (10, -1)}
Answer:
The relation is not a function
Step-by-step explanation:
∵ {(-7 , -7) , (-7 , -8) , (-1 , 4) , (6 , 5) , (10 , -1)}
* The relation is a function if every x-coordinate has only
one image of y-coordinate, that means x-coordinate
can not appear more than one time in the order pairs of relation.
* Ex: {(2 , -3 , (2 , 1)} ⇒ not function because 2 has
two values of y -3 and -1
means 2 appears twice in the relation so it's not a function
∵ -7 appears twice in the relation (-7 has 2 values of y -7 and -8)
∴ The relation is not a function
Answer:
It is not a function.
Step-by-step explanation:
We have given the relation.
{(-7, -7), (-7, -8), (-1, 4), (6, 5), (10, -1)}
We have to find whether It is a function or not.
A function is a relation that assigns each input a single output.
This relation is not a function.
Because one input -7 has two outputs -7 and -8.
It is not a function.
Write a possible exponential function in y = a · bx form that represents each situation described below. Homework Help ✎
Has a y‑intercept of (0, 2) and passes through the point (3, 128).
Passes through the points (0, 4) and (2, 1).
Answer:
[tex]y=2\cdot4^x\\y=4\cdot\left(\frac{1}{2}\right)^x[/tex]
Step-by-step explanation:
We're given both the y-intercept and a point on the graphs of both functions, so our work her is largely just substituting x and y values in the general form of the equation for an exponential function.
For the first one, we can start by using the point (0, 2) to solve for a:
[tex]y=a\cdot b^x\\2=a\cdot b^0\\2=a[/tex]
Next, we can use that a-value and the second point to solve for b:
[tex]y=2\cdot b^x\\128=2\cdot b^3\\64=b^3\\4=b[/tex]
This gives us the equation [tex]y=2\cdot4^x[/tex] for the first function.
We can repeat the same process for the second function. Solving for a:
[tex]y=a\cdot b^x\\4=a\cdot b^0\\4=a[/tex]
And then for b, using the point (2, 1):
[tex]1=4\cdot b^2\\\frac{1}{4}=b^2\\\frac{1}{2}=b[/tex]
This gives us the general equation [tex]y=4\cdot\left(\frac{1}{2}\right)^x[/tex]
To write an exponential function in y = a · bx form that represents the given situations, substitute the given points into the equation to find the values of a and b.
Explanation:To write an exponential function in the form y = a · bx that represents the given situations:
For y-intercept of (0,2) and passing through (3,128):Let's substitute the values into the equation to find the values of a and b.At (0,2), we have 2 = a · b0, so a = 2.At (3,128), we have 128 = 2 · b3, solve for b to find it is approximately 8.Therefore, the exponential function is y = 2 · 8x.For passing through (0,4) and (2,1):Let's substitute the values into the equation to find the values of a and b.At (0,4), we have 4 = a · b0, so a = 4.At (2,1), we have 1 = 4 · b2, solve for b to find it is approximately 0.5.Therefore, the exponential function is y = 4 · (0.5)x.Learn more about Exponential functions here:https://brainly.com/question/15352175
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A student is asked to factor, if possible, the given expression. The student's response demonstrates which common misconception? Simplify: a2 + b2 Student's response: (a + b)(a − b)
Answer:
The student assumed he was asked to factor
(a^2 - b^2)
Which is equal to
= (a+b)*(a-b) (His response)
But, he was asked to simplify
(a^2 + b^2)
Which has imaginary roots, and can be factored as:
(b +ai)(b-ai)
Select all that apply. To write a percent as a decimal, _____. move the decimal point two places to the left multiply by 100 move the decimal point two places to the right divide by 100
To write a percent as a decimal- move the decimal point two places to the left and divide by 100.
Explanation:
Lets take an example.
We have to convert 25% into decimals.
So, we will divide 25 by 100 , [tex]\frac{25}{100} =0.25[/tex]
Here, we can see that we have moved the decimal to two places on the left side.
Answer:
Move the decimal point two places to the left
Divide by 100
Step-by-step explanation:
To write a percent as a decimal, there are two possible options, and they are the same thing.
The first one is moving the decimal point two places to the left. For example, 25% =0.25.
The second one is dividing by 100. 25% = 25/100 = 0.25.
So the answers are:
Move the decimal point two places to the left
Divide by 100
A flagpole casts a shadow that is 15 feet and a 5 feet teenager casts a shadow that is 6 feet. How tall is the flagpole? Use a drawing to help solve the problem. Show work!
5/6=f/15
15•5=6•f
75=6•f
75/6=f
12.5=f
The flag pole is 12.5 ft tall
¶
. |
__& ____|
Answer:
The flagpole is 12.5 ft tall.
Step-by-step explanation:
The ratio of object height to shadow length is ...
(teen height) : (teen shadow) = (5 ft) : (6 ft) = 5 : 6
so the height of an object is 5/6 the length of its shadow. Then the height of the flagpole is ...
(5/6) · (15 ft) = 12.5 ft
_____
A suitable scale drawing can show you the answer.
Please help me..... I really will appreciate anyone who does help.
Try to show work/explain.
a) If (5x−2)^2=ax^2−bx+c, what is the value of a+c^2?
b)If (3x+5)2=ax2+bx+c, what is the value of a+b+c?
For both problems, expand the left hand side and match up the coefficients.
a. [tex](5x-2)^2=25x^2-20x+4=ax^2-bx+c[/tex]
[tex]\implies a=25,b=20,c=4[/tex]
[tex]\implies a+c^2=25+4^2=41[/tex]
b. [tex](3x+5)^2=9x^2+30x+25=ax^2+bx+c[/tex]
[tex]\implies a=9,b=30,c=25[/tex]
[tex]\implies a+b+c=9+30+25=59[/tex]