Answer:
C.
Step-by-step explanation:
Your fractions are missing there fraction bars:
3/4 (20y − 8) + 5 = 1/2 y + 1/4 (20y + 8)
15y − 6 + 5 = 1/2 y + 5y + 2
15y − 1 = 11/2 y + 2
A. 11/2y and 2 aren't like terms because one contains the variable y and the other contains no variable
B. The distribute property can't be used there because you don't have 15(y-1) you have 15y-1
C. Subtracting 11/2y sounds like a good step because there is a y term on the opposing side.
15y-1=11/2y+2
Subtracing 11/2y on both sides
9.5y-1=2
That looks pretty good because then you would add 1 on both sides giving:
9.5y =3
Last step would get the y by itself which is dividing both sides by 9.5 giving you 6/19.
D. You could actually do this but it doesn't help you get x by itself. The equation would look like this: 15/2 y-1/2=11/4 y+1
Answer:
C. Subtract 11/2y from each side of the equation.
Step-by-step explanation:
In the formula for average rate of change, what does the triangle in front of the x and y stand for?
Answer:
It a delta notation that change in y over change in x
Answer:
C
Step-by-step explanation:
Edge 2021
Classify ABC by its angles if mA=x, mB=2x and mC=3x
Answer:
All 3 angles of any triangle have a sum = 180. Therefore, x + 2x + 3x = 180 6x = 180 x = 180/6 = 30. So It is a 30-60-90 special right triangle!!
Step-by-step explanation:
A bag contains 5 blue marbles , 2 black marbles and 3 red marbles .a marble is randomly drawn from the bag the probability of not drawing a black marble is . The probability of drawing a red marble is
Answer: not a black marble: 4/5
Red marble: 3/10
Step-by-step explanation: Count the number of marbles.
5+2+3=10
The total number of marbles that aren’t black are 8 out of 10. The fraction is 8/10. It can be simplified to 4/5.
The number of red marbles is 3 out of 10. As a fraction, it’s 3/10.
Identifying Slope and y-Intercept of a Line
Identify the slope and y-intercept of each linear function's equation
y = 1 - 3x
slope = 3 y-intercept at -1
y = 3x - 1
slope = -1 y-intercept at 3
X-3 = y
slope = -3; z-intercept at 1
--> + 3 = y
slope = 1:y-intercept at -3
Previous Activity
Step-by-step explanation:
The slope-intercept form of an equation of a line:
y = mx + b
m - slope
b - y-intercept
y = 1 - 3x = -3x + 1
slope = -3
y-intercept at 1
y = 3x - 1
slope = 3
y-intercept at -1
x - 3 = y → y = 1x - 3
slope = 1
y-intercept at -3
x + 3 = y → y = 1x + 3
slope = 1
y-intercept at 3
How to graph a continuous function
Answer:
There are several ways to graph a continuous function. I advise you to graph several points that belongs to the function and then join the points.
If the function is linear, two points will be enough to build the graph. If we have functions of higher degree, is better to plot some points, observe the pattern and then join the points.
If the function is extremly difficult to graph by hand, the help of a graphing calculator may be needed.
To graph a continuous function, identify the independent and dependent variables, ensure the values on axes are evenly spaced, plot values as coordinates, and draw a smooth curve connecting the points without lifting the pen. The area under the graph is significant in calculus for representing continuous change, and for continuous probability distributions, it defines the probability as the area under the curve.
To graph a continuous function, first identify your independent and dependent variables. The independent variable is typically placed on the X-axis, while the dependent variable goes on the Y-axis. Ensure the scales for both axes are evenly spaced to accurately represent the continuous values. After setting up the axes, plot the pairs of values that the function defines as x and y coordinates. For a continuous function, you should be able to draw the curve connecting these points without lifting your pen off the paper.
In the context of calculus, the area under the graph represents the aggregation of continuous change over an interval, which differs from discrete sums used for step changes. This is critical when working with functions to determine areas, volumes, or growth over an interval. As such, if you are graphing a function like f(x) = x², you would plot points for x values from the interval and then draw a smooth curve through those points to represent the function continuously.
When considering continuous probability distributions, the graph will depict a curve known as the probability density function (pdf). Probability is calculated as the area under the curve, emphasizing the importance of a continuous, unbroken line in representing these types of distributions.
Jenny and Dan have $330 altogether. Jenny has $60 more than Dan. How much should Jenny take from Dan so that she has twice as much as Dan?
Answer:
$135
Step-by-step explanation:
Givens:
1) Jenny + Dan = $330
2) Jenny = $60 + Dan
Substitute Jenny's value into equation 1
(Dan = D)
$60 + D + D = $330
2D = $270
D = $135
Hope this helps :)
how to find perimeter of ceiling
Answer:
add up the lengths of all the sides of the ceiling,is there a diagram that comes with this or something?
Step-by-step explanation:
Answer: multiply
Step-by-step explanation: you must multiply length x width
The cat’s weight changed -8 oz. while she was sick. Which of the following shows a greater change in weight? A. Loss of 9 oz B. Loss of 6 oz. C. Gain of 5 oz. D. Gain of 3 oz.
Answer:
The correct answer option is A. Loss of 9 oz.
Step-by-step explanation:
We are given that a cat's weight change -8 oz. while she was sick. It means that the cat lost 8 ounces of weight.
We are to determine whether which of the given answer options show a greater change in weight.
The correct answer for this is: loss of 9 oz which is a greater loss than 8 oz.
Lisa's dog is 11 pounds heavier than Marcia's dog. Let m represent the weight of Marcia's dog. Write a variable expression to represent the weight of Lisa's dog.
Answer:
The required variable expression is [tex]L= M + 11[/tex]
Step-by-step explanation:
Consider the provided information.
Let m represent the weight of Marcia's dog.
Let L represent the weight of Lisa's dog.
Lisa's dog is 11 pounds heavier than Marcia's dog.
That means if we add 11 pounds in Marcia's dog weight, the weight of Marcia's dog will be equal to Lisa's dog.
This can be written as:
[tex]L= M + 11[/tex]
Where m represent the weight of Marcia's dog and L represent the weight of Lisa's dog.
Hence, the required variable expression is [tex]L= M + 11[/tex]
solve 8x + 3y = 13 3x + 2y = 11 by using elimination. SHOW ALL WORK!! PLEASE HELP!!! THANK YOU SO MUCH!! :)))))
Answer:Y=7
Step-by-step explanation:
-8x-3y = -13 (eq 1)
-3x-2y = -11 (eq 2)
First, multiply equation 1 by 2.
-16x-6y = -26
Second, multiply equation 2 by 3.
-9x-6y = -33
Subtract the system of equations:
-16x-6y = -26
-9x-6y = -33
-7x = 7
x = -1
Substitute this value into one of the original equations to solve for y
-3x-2y = -11
-3(-1)-2y = -11
3-2y = -11
-2y = -14
y = 7
Really hope this helps :)
Hey There!
We have been given:
[tex]8x + 3y = 13 \\ 3x + 2y = 11[/tex]
Find the lcm of 3 and 2 to eliminate one equation:
3 * 2 = 6
2 * 3 = 6
Multiply each equation to get to 6:
[tex]2(8x + 3y = 13)\\ 16x + 6y = 26[/tex]
[tex]3(3x + 2y = 11)\\ 9x+6y=33[/tex]
Eliminate:
[tex]16x + 6y = 26\\ -(9x+6y=33)\\ -9x - 6y=-33[/tex]
Simplify:
[tex]16x + 6y = 26\\ -9x - 6y=-33 \\ 7x = -7[/tex]
Solve for x by dividing 7 in both sides:
[tex]7x = -7\\ x = -1[/tex]
Solve for y by substituting x in any equation with -1:
[tex]8(-1) + 3y = 13[/tex]
Simplify:
[tex]-8 + 3y = 13[/tex]
Add 8 in both sides:
[tex]3y = 21[/tex]
Solve for y by dividing 3 in both sides:
[tex]y = 7[/tex]
The value of x is -1 and the value of y is 7
Our answers:
x = -1
y = 7
Find the perimeter of a parallelogram if two of its adjacent sides are 25 inches and 30 inches.
Answer:
P=110in
Step-by-step explanation:let me know if it's correct i'm not 100% sure
Answer:
110 inches
Step-by-step explanation:
The perimeter is basically the sum of all sides
In this case, it will be
25+25=50 for 2 opposite sides
30+30= 60 for 2 other opposite sides
hence 50+60= 110 inches
Which of the following is the coordinate for the image of point M(3, –7) after a 90° clockwise rotation?
Answer:
(-7,-3)
Step-by-step explanation:
The rule of 90° clockwise rotation is given below:
If a point (x,y) is rotated 90° clockwise, the new point would be (y, -x)
Since the point M is given as (3,-7), the rotated point will be (-7,-3).
Note: you can graph and check also
Answer:
(-7, -3)
Step-by-step explanation:
Factor the expression 18x^2 - 8
Answer:
2(3x-2(3x+2)
Step-by-step explanation:
1) 18x^2-8
2) 2(9x^2-4)
3) 2(3x-2)(3x+2)
Answer:
2(3x-2(3x-2) instead of the + 2
Step-by-step explanation:
Help with number two
Answer:
y = -2x+1
Step-by-step explanation:
We have a point and a slope, so we can use the point slope form of a line
y-y1 = m(x-x1) where m is the slope and (x1,y1) is the point
y-3 = -2(x--1)
y-3=-2(x+1)
Distribute the 2
y-3 = -2x-2
Add 3 to each side
y-3+3 = -2x-2+3
y = -2x+1
This is in slope intercept form
Evaluate the expression and place your answer in the space provided 3^2+(-2+3)•5
Answer:
14
Step-by-step explanation:
Evaluate exponents, followed by brackets, multiplication and addition
Given
3² + (- 2 + 3) × 5
= 9 + 1 × 5 ← exponents and bracket
= 9 + 5 ← multiplication
= 14 ← addition
Answer:
The correct answer is 14.
Step-by-step explanation:
I'll give you an a hint. You'd need to know about the order of operations is parenthesis, exponent, multiply, divide, add, and subtract.
First, do parenthesis.
(-2+3)=1
3²+1*5
Next, exponent.
3²=3*3=9
9+1*5
Then, multiply.
5*1=5
Finally, add.
9+5=14
So, the correct answer is 14.
I hope this helps!
Marvin is buying a watch from his brother
for $130. His brother tells him that he
can pay $30 down and the rest in 10
equal installments.
Answer:
$30 down
and 10 installments of $10 each
Step-by-step explanation:
paying $30 down means the left price to divide into installments is : 130-30 = 100
since he will pay the rest in equal installments, we divide by the number of installments to get how much each one will be :
100/10 = $10
Simplify (-2/3)/(-7/4)
Answer:
8/21
Step-by-step explanation:
(-2/3)/(-7/4)
When dividing, reciprocate the dividend then multiply to the divisor.
Reciprocate
-4/7
Multiply
-2/3 * -4/7
8/21
Answer
8/21
To simplify (-2/3)/(-7/4), we first convert the division operation into multiplication by using the reciprocal of the second fraction. This results in (-2/3)×(-4/7). We, then, multiply the numerators together and the denominators together, leading to the final simplified fraction of 8/21.
Explanation:To simplify this expression, (-2/3)/(-7/4), it is useful to first understand that division is the same as multiplying by the reciprocal. The reciprocal of a fraction is obtained by switching the numerator and the denominator. The reciprocal of (-7/4) is thus (-4/7). Therefore, the expression becomes (-2/3)×(-4/7).
The next step is to multiply the numerators together and the denominators together. So (-2 × -4) / (3 × 7) gives 8/21. The negative signs cancel each other out as a negative time a negative equals a positive.
So therefore (-2/3)/(-7/4) simplifies to 8/21.
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72% of high school students at Wilson High School are attending the homecoming dance. There are 325 students at the school. How many of them ae going to the dance
Answer:
[tex]\large\boxed{234\,\text{students}}[/tex]
Step-by-step explanation:
In this question, we're trying to find how many students are going to the homecoming dance.
To find the answer, we need to use some information that was provided to us from the question.
Important information:
72% of high school students are attending the homecoming danceThere are 325 students at the schoolWith the information above, we can solve the question.
To make this simple, we're going to need to figure out how much of 325 is 72%, due to the fact that we need to find the 72% of students that are going to the dance (out of 325 students).
To do this, we would multiply 325 by 0.72
[tex]325*0.72=234[/tex]
When you multiply, you should get 234.
This means that 234 students from the school are going to the dance.
I hope this helped you out.Good luck on your academics.Have a fantastic day!Approximately 234 out of 325 students at Wilson High School, which constitutes about 72% of the whole body, are attending the homecoming dance.
Explanation:The subject of this question is mathematics, specifically a practical application of percentage calculations. In this scenario, we need to determine the number of students from Wilson High School attending the homecoming dance if 72% of the total student body, which comprises 325 students, is attending.
To solve this, we multiply the total number of students (325) by the percentage of students attending the dance in decimal form (0.72). So, 325 * 0.72 will give us the number of students attending the dance.
After calculating, we find that 234 (rounded to the nearest whole number) students are planning to attend the homecoming dance at Wilson High School.
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What graph represents the compound inequality x<5/4 or x>5/2
For this case we have to:
[tex]x \leq \frac {5} {4}[/tex]: Represents all values less than or equal to[tex]\frac {5} {4}.[/tex]
[tex]x \geq \frac {5} {2}[/tex]: Represents all values greater than or equal to [tex]\frac {5} {2}.[/tex]
As the inequalities include the sign "=", then the borders of the graphs will be closed.
[tex]\frac {5} {4} = 1.25\\\frac {5} {2} = 2.5[/tex]
The word "or" indicates one solution or the other, so the correct option is graph B
ANswer:
Option B
Answer:
SECOND graph.
Step-by-step explanation:
Given compound inequality,
[tex]x \leq \frac{5}{4}\text{ or }x \geq \frac{5}{2}[/tex]
[tex]\because \frac{5}{4}=1.25\text{ or }\frac{5}{2}=2.5[/tex]
[tex]\implies x \leq 1.25\text{ or }x\geq 2.5[/tex]
If x ≥ 1.25
In the number line closed circle on 1.25 and shaded left side from 1.25,
If x ≤ 2.5
In the number line closed circle on 2.5 and shaded right side from 2.5
Hence, SECOND option is correct.
the sum of to numbers is 15 and their quotient is 2.
PLEASE HELP MEEE
Answer:
The two numbers are 5 and 10.
Step-by-step explanation:
We need to solve the following system of equations:
We know that:
A + B = 15
A/B = 2
Solving the system of equations we have:
A/B = 2 ⇒ A = 2B
Then:
2B + B = 15 ⇒ 3B = 15 ⇒ B = 5
Then, we need to find A:
A = 10
Answer:
The two numbers are 5 and 10
Step-by-step explanation:
Let x be one number and y be the other number
Their sum is 15
x+y = 15
The quotient is 2
x/y =2
Rewriting this equation by multiplying by y
x/y * y = 2*y
x = 2y
Substitute this into the first equation
2y+ y = 15
Combine like terms
3y = 15
Divide by 3 on each side
3y/3 =15/3
y=5
Now we can find x
x = 2y
x =2(5)
x=10
Find the mean absolute deviation to the nearest cent. Explain what this value represents.
Answer:
134.38
This value represents 134.38
Step-by-step explanation:
Find the mean.
950+620+545+810+775+1120+905+775=6500
6500/8=812.5
Subtract the mean of numbers.
950-812.5=137.5
812.5-620=192.5
812.5-545=267.5
812.5-810=2.5
812.5-775=37.5
1120-812.5=307.5
905-812.5=92.5
812.5-775=37.5
Find the mean.
137.5+192.5+267.5+2.5+37.5+307.5+92.5+37.5=1075
1075/8≈134.38
This means that 134.38 is $134.38
MAD
To find the MAD of the data, you must first find the mean. To do this, simply add all the numbers up and divide by the number of data values.
950+620+545+810+775+1120+905+775=812.5
So the mean is 812.5 ($812.5).
The final step to finding the MAD is to difference between each data value and the mean.
|950-812.5| + |620-812.5| + |545-812.5| + |810-812.5| + |775-812.5| + |1120-812.5| + |905-812.5| + |775-812.5|
137.5 + 192.5 + 265.5 + 2.5 + 37.5 + 307.5 + 92.5 + 37.5/8
1073/8=9.625
So, 134.125 is the answer.
BUT... the question said round to the nearest cents. So, it's 13413 cents.
Complete the square to transform the expression x2 + 4x + 2 into the form a(x − h)2 + k.
Answer:
Step-by-step explanation:
y = (x^2 + 4x) + 2
Take 1/2 of the linear term 4/2 = 2 and square that result. 2^2 = 4.
Put it after 4x
y = (x^2 + 4x + 4) +2 Subtract what you put inside the brackets on the outside.
y = (x^2 + 4x + 4) + 2 - 4 Combine the right.
y = (x^2 + 4x + 4) - 2 Express the brackets as a square.
y = (x + 2)^2 - 2
That's your answer
a = 1
h = 2
k = -2
Answer:
(x + 2)2 − 2
Step-by-step explanation:
Just took the test and got it right
???????? Help me please
Answer:
D. (1, 9)
Step-by-step explanation:
Plug in each ordered pair into both inequalities. If both inequalities are satisfied, then the ordered pair is a solution.
The only ordered pair that works is (1, 9).
verify that sin2x=2cotsin^2x is an identity
Answer:
Vertify is an identity
Sin2x=2cotx(sin^2x)
starting from the right-hand side
2cotx(sin^2x)
=2(cosx/sinx)(sin^2x)
=2(cosx/sinx)(sin^2x)
=2sinxcosx=sin2x
ans:right-hand side=left-hand side
Step-by-step explanation:
Step-by-step explanation:
sin^2x = 2cotx sin^2x
Rewrite right side as fractions:
sin^2x = [tex]\frac{2}{1}[/tex] * [tex]\frac{cosx}{sinx}[/tex] * [tex]\frac{(sinx)(sinx)}{1}[/tex]
Multiply together [tex]\frac{cosx}{sinx}[/tex] and [tex]\frac{(sinx)(sinx)}{1}[/tex] :
sin^2x = [tex]\frac{2}{1}[/tex] * [tex]\frac{(cosx)(sinx)(sinx)}{sinx}[/tex]
Cancel out sinx on top and bottom:
sin^2x = [tex]\frac{2}{1}[/tex] * [tex]\frac{(sinx)(cosx)}{1}[/tex]
Multiply together 2 and (sinx)(cosx):
sin^2x = 2sinxcosx
Substitute sin^2x in for 2sinxcosx:
sin^2x = sin^2x
Jennifer sold 57 pieces of art if she sold twice as many paintings as sculptures how many painting did she sell??
so we know she has sculptures and paintings, if she sold twice as many paintings as sculptures, that means that for every 2 paintings, she sold 1 sculpture, so the paintings and sculptures are on a 2:1 ratio.
we know she sold a total of 57, so we'll need to split 57 in a 2:1 ratio, we'll simply divide the whole amount of 57 by (2+1) and distribute accordingly.
[tex]\bf \cfrac{paintings}{sculptures}\qquad 2:1\qquad \cfrac{2}{1}\qquad \qquad \cfrac{2\cdot \frac{57}{2+1}}{1\cdot \frac{57}{2+1}}\implies \cfrac{2\cdot 19}{1\cdot 19}\implies \cfrac{\boxed{38}}{19}[/tex]
You went shopping for batteries. Your bill was $14.39. How many 9-volt batteries did you purchase at $2.39 each if AA batteries cost $1.61 each and you purchased 3 of them ?
Answer:
u bought 4 9-volt batteries and
the cost of the 3 AA batteries bought is $4.83
To find out how many 9-volt batteries were bought, you first need to subtract the total cost of AA batteries ($4.83) from the total bill ($14.39) to get the total spent on 9-volt batteries. Then, divide this total by the price of each 9-volt battery ($2.39). The result is 4, so you bought 4 9-volt batteries.
Explanation:To answer this question, let's first determine how much the total purchase of the AA batteries was. Since AA batteries cost $1.61 each and you bought 3, the total cost for the AA batteries is 3 * $1.61 = $4.83.
Now we need to figure out how much was spent on 9-volt batteries. Subtract the cost of the AA batteries from the total bill: $14.39 - $4.83 = $9.56. This is the total cost of the 9-volt batteries.
The price of each 9-volt battery is $2.39, so to find out how many batteries were bought we divide the total cost of 9-volt batteries by the price of each battery: $9.56 / $2.39 ≈ 4. Therefore, you bought 4 9-volt batteries.
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solution to m^2- 36=0
Answer:
m=(-6,6)
Step-by-step explanation:
m^2 -36 = 0
Reorder the terms:
-36 + m^2 = 0
Solving for variable 'm'.
Add '36' to each side of the equation.
-36 + 36 + m^2 = 0 + 36
Combine like terms: -36 + 36 = 0
0 + m^2 = 0 + 36
m^2 = 0 + 36
Combine like terms: 0 + 36 = 36
m^2 = 36
Simplifying
m^2 = 36
Take the square root of each side:
√m^2=+/-√36
m=(+/-)6
m = {-6, 6}
You need a 45% alcohol solution. On hand, you have a 350 mL of a 15% alcohol mixture. You also have 70% alcohol mixture. How much of the 70% mixture will you need to add to obtain the desired solution?
You will need
_____ mL of the 70% solution
Answer:
420
Step-by-step explanation:
Amount in the 45% solution + amount in the 70% solution = amount in the 45% solution
0.15 × 350 + 0.70 × V = 0.45 × (350 + V)
52.5 + 0.70V = 157.5 + 0.45V
0.25V = 105
V = 420
You need 420 mL of the 70% solution.
After setting up and solving a weighted average equation, the result reveals that you would need 1050 mL of the 70% alcohol solution to achieve the desired 45% alcohol solution.
Explanation:To solve this problem, we can use the concept of weighted averages. The final volume of alcohol in the 45% solution will be the sum of the alcohol in the 15% solution and the 70% solution. Let's denote the volume of the 70% solution we need to add as X ml. So, the equation will be:
0.15 × 350 + 0.70 × X = 0.45 × (350 + X)
Solving this equation will give us the amount of 70% solution needed. After simplifying, you get:
52.5 + 0.7X = 157.5 + 0.45X
Further simplification gives:
0.7X - 0.45X = 157.5 - 52.5
Therefore, X = 1050 ml. So, you will need 1050 ml of the 70% solution.
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Really don’t understand help. With picture
[tex]\bf \textit{Jim's Gym}\\\\ \begin{array}{cccll} initial~fee&visits&cost\\ \cline{1-3} 300&1&300+3(1)\\ &2&300+3(2)\\ &3&300+3(3)\\ &4&300+3(4)\\ &x&300+3(x) \end{array}\implies y = 300+3x \\\\[-0.35em] ~\dotfill\\\\ \textit{Sally's Salon}\\\\ \begin{array}{cccll} initial~fee&visits&cost\\ \cline{1-3} 250&1&250+5(1)\\ &2&250+5(2)\\ &3&250+5(3)\\ &4&250+5(4)\\ &x&250+5(x) \end{array}\implies y = 250+5x[/tex]
when are the plans equal?
[tex]\bf \stackrel{Jim's}{300+3x}~~=~~\stackrel{Sally's}{250+5x}\implies 50+3x=5x \\\\\\ 50=2x\implies \cfrac{50}{2}=x\implies 25=x[/tex]
So, we can start off by just listing the facts.
The Initial fee for Jim's Gym has an initial fee of $300, and Sally's Salon has an initial fee of $250. Every visit to Jim's Gym costs $3, and Sally's Salon costs $5.
The question is using the variable x, in which x represents the number of visits that person has made.
So the equation for Jim's Gym is 300 + 3x (since, like we've established earlier, it costs $3 per visit.
The equation for Sally's Salon is 250 + 5x (since it costs $5 per visit)
Since we're trying to equalize costs, make the entire equation
300 + 3x = 250 + 5x
Subtract both sides by 250
50 + 3x = 5x
Subtract both sides by 3x
50 = 2x
Divide both sides by 2
x = 25
Option D is the answer.
Given the function f(x)=1+5x^2, calculate the following values:
f(a)=
f(a+h)=
f(a+h)−f(a)/h=
Answer:
[tex]f(a)=1+5a^2[/tex]
[tex]f(a+h)=1+5a^2+10ah+5h^2[/tex]
[tex]\frac{f(a+h)-f(a)}{h}=10a+5h[/tex]
Step-by-step explanation:
We are given [tex]f(x)=1+5x^2[/tex].
Find [tex]f(a)[/tex]. All this means is replace [tex]x[/tex] in [tex]f(x)=1+5x^2[/tex] with [tex]a[/tex].
[tex]f(x)=1+5x^2[/tex]
[tex]f(a)=1+5a^2[/tex]
Find [tex]f(a+h)[/tex]. All this means is replace [tex](a+h)[/tex] in [tex]f(x)=1+5x^2[/tex] with [tex](a+h)[/tex].
[tex]f(x)=1+5x^2[/tex]
[tex]f(a+h)=1+5(a+h)^2[/tex]
[tex]f(a+h)=1+5(a+h)(a+h)[/tex]
[tex]f(a+h)=1+5(a^2+2ah+h^2)[/tex]
[tex]f(a+h)=1+5a^2+10ah+5h^2[/tex]
Find [tex]\frac{f(a+h)-f(a)}{h}[/tex]. So we got to put some parts together; the parts above:
[tex]\frac{f(a+h)-f(a)}{h}[/tex]
[tex]\frac{(1+5a^2+10ah+5h^2)-(1+5a^2)}{h}[/tex]
Now in the first ( ) I see 1+5a^2 and in the second ( ) I see 1+5a^2, so this means you have (1+5a^2)-(1+5a^2) which equals 0.
[tex]\frac{10ah+5h^2}{h}[/tex]
Now assuming h is not 0. we can divide top and bottom by h.
[tex]\frac{10a+5h}{1}[/tex]
[tex]10a+5h[/tex]
To calculate the values for the quadratic function f(x) = 1 + 5x^2, substitute the necessary values for x. The difference quotient involves a simplification process of the terms after substitution.
The problem is to evaluate the function f(x) = 1 + 5x^2 at a given value a and at a + h, and then to find the difference quotient which is part of the process to find the derivative of the function. First, we calculate f(a), then f(a + h), and lastly the difference quotient f(a + h) - f(a) / h.
To get f(a), we substitute x with a in the function, so we get:
f(a) = 1 + 5a^2
For f(a + h), we substitute x with (a + h):
f(a + h) = 1 + 5(a + h)^2
Now to find the difference quotient (f(a + h) - f(a)) / h:
(f(a + h) - f(a)) / h = (1 + 5(a + h)^2 - (1 + 5a^2)) / h
We can simplify this further by expanding and combining like terms, eventually canceling out the h in the denominator. However, without further expansion and simplification, the expression is already accurate.