The difference quotient of the function f(x) = 4x² + 3x - 5 is [f(x + h) - f(x)]/h = 8x + 4h + 3
How to evaluate the difference quotient?The function is given as
f(x) = 4x² + 3x - 5
Start by calculating the function f(x + h)
So, we have the following
f(x + h) = 4(x + h)² + 3(x + h) - 5
Expand
f(x + h) = 4(x² + 2xh + h²) + 3(x + h) - 5
Open the brackets
f(x + h) = 4x² + 8xh + 4h² + 3x + 3h - 5
The difference quotient is then calculated as
[f(x + h) - f(x)]/h
This gives
[f(x + h) - f(x)]/h = (4x² + 8xh + 4h² + 3x + 3h - 5 - 4x² - 3x + 5)/h
Evaluate the like terms
[f(x + h) - f(x)]/h = (8xh + 4h² + 3h)/h
Evaluate the quotients
[f(x + h) - f(x)]/h = 8x + 4h + 3
Hence, the value of [f(x + h) - f(x)]/h is 8x + 4h + 3
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Complete question
If f(x) = 4x² + 3x - 5, then [f(x + h) - f(x)]/h is equal to which of the following?
help meeeeeee pleaseee !!!!
The equation of the line that passes through the points ( -3,18 ) and ( 2,-7 ) is f(x) = -5x + 3.
What is the equation of line passing through the given points?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the data in the question;
Point 1( -3,18 )
x₁ = -3y₁ = 18Point 2( 2, -7 )
x₂ = 2y₂ = -7First, we find the slope of the line.
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
m = ( -7 - 18 ) / ( 2 - (-3) )
m = ( -25 ) / ( 2 + 3 )
m = ( -25 ) / ( 5 )
m = -5
Next, next we find the y-intercept
y = mx + b
18 = (-5)(-3) + b
18 = 15 + b
b = 18 - 15
b = 3
Now that the values of slope m and y-intercept b is known, plug these into y = mx + b to determine the equation of the line.
y = mx + b
y = (-5)x + 3
y = -5x + 3
Therefore, the equation of the line is y = -5x + 3
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Shiloh has 47 books. She wants to put them all on bookshelves. How many bookshelves will Shiloh need if each shelf holds 5 books?
A.
47
÷
5
=
7
R
2
Shiloh will need 8 shelves.
B.
47
÷
9
=
5
R
2
Shiloh will need 9 shelves.
C.
47
÷
5
=
7
R
2
Shiloh will need 7 shelves.
D.
47
÷
5
=
9
R
2
Shiloh will need 10 shelves.
The number of bookshelves needed if each bookshelves contain 5 books is 10.
How to find the number of shelves will hold the books?She has 47 books. . She wants to put them all on bookshelves.
Therefore, the number of bookshelves she will need if each shelf holds 5 books can be calculated as follows:
The total number of books she has in her possession is 47 books.
All the books must have a place in the bookshelves.
Each bookshelves can only contain 5 books.
Hence,
let
x = number of bookshelves
Therefore, the equation to find the number of bookshelves is as follows:
5x = 47
divide both sides by 5
x = 47 / 5
x = 9.4
Therefore, Shiloh will require 10 book shelves.
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12. What is the equation in point-slope form of the
line that passes through the points (2, -3) and (-5, 8)?
⇒First step is to find the gradient
[tex]m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} } \\m=\frac{8-(-3)}{-5-2} \\m=\frac{8+3}{-7} \\m=-\frac{11}{7}[/tex]
In the general equation y=mx+c let us find the value of c by plugging in the known values
I will use the point (-5,8) Note you can use any .You will get the same value of c.
[tex]8=-\frac{11}{7} (-5)+c\\8=\frac{55}{7} +c\\c=8-\frac{55}{7} \\c=\frac{1}{7}[/tex]
The equation now is:
[tex]y=-\frac{11}{7} x+\frac{1}{7}[/tex]
What is 1/3 divided by 2/3
Answer:
1/2
Step-by-step explanation:
Do divide fractions, multiply the first number by the reciprocal (the numbers flipped) of the second number.
So, 1/3 * 3/2
1/3 * 3/2 = 3/6
3/6 = 1/2
hi. I was hoping you can solve this for me. I would be so grateful.
We have
1. The timing shown in the morning is from 8:15 to 12:15, this is the number of hours worked in the morning is 4 hours.
The pay is $13.50 per hour
Therefore, the pay earned in the morning is:
[tex]\begin{gathered} pay=N\text{. hours }\times pay\text{ per hour } \\ \text{pay = 4}\times13.50 \\ \text{pay}=54 \end{gathered}[/tex]then, the pay earned in the morning is $54
2. The timing shown in the afternoon is from 13:00 to 17:30, this is the number of hours worked in the afternoon is 4 hours and 30 minutes. Therefore, the pay in the afternoon is:
[tex]pay\text{ =4.5}\times13.50=60.75[/tex]then, the pay earned in the afternoon is $60.75
The pay per 1 day is:
pay in the morning + pay in the afternoon
[tex]total\text{ pay = 54+60.75=114.75}[/tex]Answer: pay for a day is $114.75
Felix is making a pattern with tiles shaped like parallelograms. He needs 5 black tiles
and 5 white tiles. The tiles cost $0.50 per cm².
What is the total area of the tiles Felix needs
to buy?
Answer: 80
Step-by-step explanation:
You do 2 times= 8 and multiply 8 to the 5 white and black tiles which equals 40+40=80.
The total area for the parallelogram shaped tiles Felix needs to buy is 80cm² at the price of $40.
Area of parallelogramIn calculating for the area of parallelogram, the base is multiplied by the height, as the same way for calculating the area of a rectangle.
Given that, the base of one parallelogram shaped tile is 4cm with height as 2cm.
Area of one parallelogram shaped tile = 4cm × 2cm
Area of one parallelogram shaped tile = 8cm²
Total area for the 5black and 5white tiles = 10 × 8cm²
Total area for the 5black and 5white tiles = 80cm²
Therefore, Felix needs to buy a total of 80cm² of 10 parallelogram shaped tiles.
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please helpppppp
For the three-part question that follows, provide your answer to each part in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of your response as Part A, Part B, and Part C.
Greg bought a regular-sized box of his favorite cereal. A regular-sized box contains 12 servings.
Part A: If Greg eats 1 1/2 servings for breakfast every day, how many breakfasts can Greg eat from 1 box? Show all work.
Part B: The regular-sized box of cereal costs $4.29. How much does 1 breakfast from a regular-sized box of cereal cost Greg? Round to the nearest hundredth. Show all work.
Part C: If Greg purchased the family-sized box of cereal that contains 18 servings, how many more breakfasts could Greg eat from 1 box? Show all work.
a. Greg can eat 8 breakfasts from 1 box.
b. The cost of 1 breakfast from a regular-sized box is $34.32.
c. Greg will enjoy 4 breakfast more.
How to calculate the fraction?a. A regular-sized box contains 12 servings. If Greg eats 1 1/2 servings for breakfast every day, the number of breakfasts that Greg can eat from 1 box will be:
= 12 ÷ 1 1/2
= 12 ÷ 1.5
= 8
b. Since the regular-sized box of cereal costs $4.29. The cost of 1 breakfast from a regular-sized box of cereal cost Greg will be:
= 8 × $4.29
= $34.32
c. If Greg purchased the family-sized box of cereal that contains 18 servings, the number of breakfasts will be:
= 18 ÷ 1.5
= 12 breakfast
The difference will be:
= 12 - 8
= 4 breakfast more.
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One way to determine whether a number is prime or composite is by creating a factor table.
Complete the factor table and the sentences below about the number 18.
The conclusion from the factor table of 18 is that, 18 is not a prime number i.e. it is composite
How to determine the factor table?From the question, the number is given as
Number = 18
The factors of 18 are represented as
Factors of 18 = 1, 2, 3, 6, 9 and 18
When these factors are picked in pairs, we have the following representations
Factors pairs of 18 = (1, 18), (2, 9), (3, 6)
Next, we represent the factors on a factor table
So, we have
Factors Factor pairs Prime factorization
1, 2, 3, (1, 18) 2 x 3²
6, 9 and (2, 9)
18 (3, 6)
Because the number 18 has factors other than 1 and 18, then the number 18 is a composite number
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need answers asap
I'm also giving brainliest to the right answer
Answer:
y = 3x + 3 :D
Step-by-step explanation:
Equation of line: y = mx + b :)
b: Y intercept
m: Slope
Now lets solve :)
Lets find M first :)
We need 2 points so lets use (0,3) and (1,6) :)
We fist need to subtract :)
6 - 3 = 3
1 - 0 = 1
Now we divide :)
3/1 = 3
Lets put that into our equation :)
y = 3x + b
Now lets find B :)
To find b, we need to see where the line intercepts the y axis! This will be at point (0,3)!
The y intercept will be 3 :)
The final equation will be y = 3x + 3 :)
Have an amazing day!!
Please rate and mark brainliest if helpful!
Graph a line with a slope of2that contains the point (-3,5).5
We will investigate how to graph a straight line on cartesian coordinate plane.
All equations of straight line are expressed in a general slope-intercept form as follows:
[tex]y\text{ = m}\cdot x\text{ + c}[/tex]Where,
[tex]\begin{gathered} m\colon\text{ slope} \\ c\colon\text{ y-intercept} \end{gathered}[/tex]To graph any straight line we need the equation of the straight line or atleast two points that must lie on the line.
We are given the slope ( m ) and one of the points that lie on the line as follows:
[tex]\begin{gathered} m\text{ = -}\frac{2}{5} \\ \\ (\text{ -3 , 5 )} \end{gathered}[/tex]We need one another point that lies on the line to plot the graph of a straight line. To find another point we must completely express the equation of the straight line ( general form given above ).
We see that an equation of a straight line is defined by two parameters i.e ( m and c ). We are given the value of the slope ( m ). We will go ahead and plug it into the general slope-intercept form given above:
[tex]y\text{ = -}\frac{2}{5}\cdot x\text{ + c}[/tex]Now to determine the value of parameter ( c ) we must have atleast one point that lies on the line. We will use the point given to us and plug in the respective coordinates in the equation developed above and solve for ( c ) as follows:
[tex]\begin{gathered} (\text{ x , y ) }\to\text{ ( -3 , 5 )} \\ \\ 5\text{ = -}\frac{2}{5}\cdot(-3)\text{ + c} \\ \\ 5\text{ = }\frac{5c\text{ + 6}}{5} \\ \\ 25\text{ = 6 + 5c} \\ \\ c\text{ = }\frac{19}{5} \end{gathered}[/tex]We will go ahead and update the equation of the straight line as follows:
[tex]y\text{ = -}\frac{2}{5}\cdot x+\frac{19}{5}[/tex]Now to get one more point to graph the plot we will assume any value of the for either variable ( x or y ) and then determine the value of the other variable as follows:
[tex]\begin{gathered} x\text{ = 2} \\ \\ y\text{ = -}\frac{2}{5}\cdot(2)\text{ +}\frac{19}{5} \\ \\ y\text{ = }\frac{-4+19}{5} \\ \\ y\text{ = }\frac{-15}{5} \\ \\ y\text{ = -3} \end{gathered}[/tex]Therefore, we have the two points to plot the graph as follows:
[tex](\text{ -3 , 5 ) \& ( 2 , -3 )}[/tex]We can go ahead and select the above points on the given grid to construct the straight line!
A truck driver averages 60 miles per hour while delivering freight and 45 mph on the return trip.The total driving time is 10 hours. How much longer does the return trip take than the delivery
The return trip takes 0.7 hrs more than the delivery.
Let the time taken while going be x therefore the time taken while returning will be 10 - x.
Given :
The truck driver averages 60 miles per hour while delivering freight
The speed is 45 mph on the return trip.
Therefore according to the question,
60x = 45 ( 10 - x) [ As the distance is same]
=> 4x = 3 ( 10 - x)
=> 4x = 30 - 3x
=> 7x = 30
=> x = 30 / 7
=> x = 4.3
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Find the value of x. A. 9B. 145C. 8D. 154
Answer: C. 8
When we have two chords intersecting inside a circle, the products of the lengths of the segments are equal to one another. This means that for the given circle, we have the following:
10 * 4 = 5 * x
We can solve for x by multiplying 10 by 4, which is 40, and then dividing by 5, to isolate x, which is 8.
Plot all of the points of the reflected figure. You may click a plotted point to delete
To reflect the figure, we have to draw the new vertex at the same distance from the line x = -4, the image below shows this reflection.
Notice that the new figure has the same distance from x = -4 as the pre-image.
The points (8, -9) and (0, -2) fall on a particular line. What is its equation in slope-
intercept form?
) Write your answer using integers, proper fractions, and improper fractions in simplest
form.
Video G
Answer:
y = -7/8x -2
Step-by-step explanation:
You want the slope-intercept equation of the line through the points (8, -9) and (0, -2).
SlopeThe slope of the line through points (x1, y1) and (x2, y2) is given by the formula ...
m = (y2 -y1)/(x2 -x1)
For the given points, the slope of the line is ...
m = (-2 -(-9))/(0 -8) = -7/8
InterceptThe y-intercept of the line is the y-value when x = 0. The point (0, -2) tells you the y-intercept is -2.
EquationThe slope-intercept equation is ...
y = mx +b . . . . . . where m is the slope, and b is the y-intercept
For a slope of -7/8 and a y-intercept of -2, the equation is ...
y = -7/8x -2
Leaming Diagnostic Analytics » Recommendations Language arts Science Social Studies Eighth grade Y.2 Find the slope from two points ZAC Find the slope of the line that passes through (9, 10) and (6, 12). Simplify your answer and write it as a proper fraction, improper fraction, or integer.
To find the slope of the line that passes through (9, 10) and (6, 12)
We will use the formula;
[tex]\text{slope =}\frac{y_2-y_1}{x_2-x_1}[/tex]From the points given;
x₁ = 9 y₁=10
x₂ = 6 y₂=12
Substitute the values into the formula;
[tex]\text{slope =}\frac{12-10}{6\text{ - 9}}[/tex]Evaluate;
[tex]\text{slope =- }\frac{2}{3}[/tex]how many time can 7 go into 65
Answer:
9
Step-by-step explanation:
The answer you divide 65 by 7 which would get you 9.2857142857143. The remainder is 2.
MATHEMATICALLY WE WRITE THE PROBLEM AS
[tex] = \frac{65}{7} \\ [/tex]
SOLVING FURTHER
[tex]65 \div 7 \\ = 9.285714286[/tex]
BUT 7 GOES 9 TIMES IN 65 NOT CONSIDERING THE REMINDER.
HOPE THIS HELPS
An item is regularly priced at $43. Bill bought it on sale for 35% off the regular price. Hownmuch did he pay?
Given the regular price is $43.
S.P= 35% off on regular price i.e.
[tex]\begin{gathered} S\mathrm{}P=\text{ }\frac{65}{100}\times43 \\ S\mathrm{}P=27.95 \end{gathered}[/tex]Hence, after 35% off, the price is $27.95
Luna purchased a computer at the list price of ₱56,000, less 30% and 20%. How much must Luna pay for the computer?
There are two disccount applied to this computer, the first one is 30%. To calculate its value, we need to multiply the original price by the fraction that represents 30%
[tex]\text{discount}1=56000\cdot\frac{30}{100}=16800[/tex]The first discount was 16,800. To determine the price after this, we need to subtract the listed price by the discount 1, this is done below:
[tex]\text{price}2=56000-16800=39200[/tex]Then we need to calculate the second discount, which was equal to 20%.
[tex]\begin{gathered} \text{discount}2=39200\cdot\frac{20}{100}=7840 \\ \end{gathered}[/tex]The final price is the subtraction between the price 2 and the discount 2, we have:
[tex]\text{ final price}=39200-7840=31360[/tex]The final price is 31,360.
f(x) = integrate t ^ 4 dt from 3 to x
We have the function f(t) defined as:
[tex]f(x)=\int_3^xt^4dt[/tex]We have to find f'(x).
We can solve this integral as:
[tex]f(x)=\frac{t^5}{5}|^x_3=\frac{x^5}{5}-\frac{3^5}{5}[/tex]If we derive this expression for f(x) we obtain:
[tex]f^{\prime}(x)=\frac{d}{dx}(\frac{x^5}{5}-\frac{3^5}{5})=\frac{5}{5}x^4+0=x^4[/tex]NOTE: This expression could have been derived from the function inside the integral.
We can now find f'(3) as:
[tex]f^{\prime}(3)=3^4=81[/tex]Answer:
f'(x) = x^4
f'(3) = 81
I can’t figure out how to solve this
Step by step process needed! Thank you!
Simplify Radicals
After simplification the answer is 31.418 or 31.42
Define Radicals
The √ symbol that is used to denote square root or nth roots. Radical Expression - A radical expression is an expression containing a square root.
The given expression is,
2√6(√2 + 5)
First, open the brackets
2√6 * √2 + 5 * 2√6
we know, √6 = √3 * 2 = √3 * √2
so, 2√3 * √2 * √2 + 10√6
We didn't open the both √6 values it's because we want to remove root from √2 so as we know √2 * √2 = 2
2√3 * 2 + 10 * √6
=> 4√3 + 10 * √6
Now, put the values of √3 = 1.732 and √6 = 2.449
=> 4 * 1.732 + 10 * 2.449
=> 6.928 + 24.49
=> 31.418 or 31.42
Therefore, the answer is 31.418 or 31.42
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A lab assistant needs to create a 500 mL mixture that is 5% hydrochloric acid. The assistance has solutions of 3.5% and 6% in supply at the lab. Using the variables x and y to represent the number of milliliters of the 3.5% solution and the number of milliliters of the 6% solution respectively, determine a system of equations that describes the situation. Enter the equations below separated by a comma.How many milliliters of the 3.5% solution should be used? How many milliliters of the 6% solution should be used?
Let
x -----> the number of milliliters of the 3.5% solution
y ----> the number of milliliters of the 6% solution
we have that
3.5%=3.5/100=0.035
6%=6/100=0.06
5%=5/100=0.05
so
0.035x+0.06y=0.05(500) -------> equation A
and
x+y=500 -----> x=500-y ------> equation B
solve the system of equations
substitute equation B in equation A
0.035(500-y)+0.06y=0.05(500)
solve for y
17.5-0.035y+0.06y=25
0.025y=25-17.5
0.025y=7.5
y=300
Find out the value of x
x=500-300=200
therefore
the number of milliliters of the 3.5% solution is 200 mlthe number of milliliters of the 6% solution is 300 mlWrite an algebraic expression as indicated. The algebraic expression for the mountain Roberto‘s other account is
We have here that Roberto has a total of $3300 in two savings account.
Then, if y represents the amount in one account, we have that the sum of both accounts is up to $3300.
We can suppose that the other account is x. Then, we have:
[tex]x+y=\$3300[/tex]If we subtract y from both sides of the equation, we have:
[tex]x+y-y=\$3300-y\Rightarrow x=\$3300-y[/tex]Therefore, the algebraic expression for the amount in Roberto's other account is (since x is not mentioned, we have):
[tex]\$3300-y[/tex]In summary, the amount in Roberto's other account is $3300 - y.
does the ordered pair (-1, -9) satisfy the equation y=7-2x
Answer:
No
Step-by-step explanation:
In order to solve this, we plug in the values for x and y. Remember that x = -1 and y = -9
-9 = 7 - 2(-1)
-9 = 7 + 2
-9 ≠ 9
Write the equation of the line that passes through the points(3,0) and(8,3)Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
Answer:
5/3
Step-by-step explanation:
rise over run
(8-3)/(3-0)
In a photograph, a skyscraper measures 5.8 in, tall. The scale of the photo to the actual skyscraper is 1:245. How tall is the actual skyscraper to the nearest foot?○ 118 ft ○ 183 ft○ 237 ft○204 ft
SOLUTION
In a photograph, a skyscraper measures 5.8 in, tall
The scale of the photo to the actual skyscraper is 1 : 245
That is 1 : 245 = 1 / 245 = 5. 8 / x
Cross- multiply we have:
1 X x = 5 . 8 X 245
x = 1421 inches in feet = 118.4167 feet
the table below shows the percentage of votes each sport received in a recent survey of student's favorite sports. will send image
Basketball 12 votes; Soccer 24 votes; Football 24 votes
Here, we want to select the options that could represent the percentage
From what we have, soccer and football are same value and basketball is half of these
So the option where we have the given outline is the correct answer
Looking at the options, the only place we have the outline is;
Basketball 12 votes; Soccer 24 votes; Football 24 votes
Solve: - 4x + 1 ≤ 21 and 5x + 2 < 22A. x ≥ -5 and x < 4B. x > -5 and x ≤ 4C. x ≥ -5 or x < 4D. x > -5 or x ≤ 4
ANSWER
A. x ≥ -5 and x < 4
EXPLANATION
We have the two inequalities:
- 4x + 1 ≤ 21 and 5x + 2 < 22
Let us solve them separately:
FIRST ONE
-4x + 1 ≤ 21
Collect like terms:
-4x ≤ 21 - 1
-4x ≤ 20
Divide through by -4, the sign changes:
[tex]\begin{gathered} x\ge\text{ }\frac{20}{-4} \\ x\text{ }\ge\text{ -5} \end{gathered}[/tex]SECOND ONE
5x + 2 < 22
Collect like terms:
5x < 22 - 2
5x < 20
Divide through by 5:
x < 20 / 5
x < 4
The answer is Option A.
H(x)=(x+5)^9 can be be expressed into the form f(g(x)) where f(x)=x^9, and g(x) is defined below
G(x)=?
The value of g(x) will be expressed as g(x) = (x + 5)
A function may be defined as an expression in which for one value of input variable x there is only one value of output variable y. The input variable is called as independent variable and output variable is called dependent variable. Composite functions are the functions which are written as combination of two functions. A function f(x) may be defined as composite function of another function g(x) when it can be written as either f(g(x)) or g(f(x)). We know that f(x) = x⁹ and the composite function H(x) = f(g(x)) = (x + 5)⁹. So, from this we can say that the function g(x) will be given as (x + 50 as we put (x + 5) as x in the function H(x).
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Use the number line to find the coordinate of the midpoint of
¯¯¯¯¯¯
L
P
.
The mid-point of LP is 1.5.
Here we have to find the mid-point of the line LP
L is on -2 on the line and P is on 5.
To find the mid-point we have a formula:
mid-point = (b - a)/2
where a and b are two points between which we have to find the mid-point.
So, mid-point of LP = 5 - (-2) / 2
= 7/ 2
= 3.5
Now we have to find the value so we will subtract -2 with 3.5.
So the mid-point is 3.5 - 2= 1.5.
Therefore the mid-point of the line LP is 1.5.
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