For the function f(x)=6x^2-2x+1, evaluate and fully simplify each of the following:
(Look at picture)
Answers
Answer to the 1st part: [tex]6x^2+12xh+6h^2-2x-2h+1[/tex]
Answer to the 2nd part: [tex]12x+6h-2[/tex]
==============================================
Work Shown:
Replace every x with (x+h). Expand and simplify
[tex]f(x) = 6x^2-2x+1\\\\f(x+h) = 6(x+h)^2-2(x+h)+1\\\\f(x+h) = 6(x^2+2xh+h^2)-2(x+h)+1\\\\f(x+h) = 6x^2+12xh+6h^2-2x-2h+1\\\\[/tex]
----------------------------
Subtract off f(x), then divide everything over h. Simplify.
[tex]f(x+h) = 6x^2+12xh+6h^2-2x-2h+1\\\\f(x+h)-f(x) = 6x^2+12xh+6h^2-2x-2h+1-(6x^2-2x+1)\\\\f(x+h)-f(x) = 6x^2+12xh+6h^2-2x-2h+1-6x^2+2x-1\\\\f(x+h)-f(x) = 12xh+6h^2-2h\\\\\frac{f(x+h)-f(x)}{h} = \frac{12xh+6h^2-2h}{h}\\\\\frac{f(x+h)-f(x)}{h} = \frac{h(12x+6h-2)}{h}\\\\\frac{f(x+h)-f(x)}{h} = 12x+6h-2\\\\[/tex]
The value of Function, [tex]f (x + h) = 6x^2 + 6 h^2 + 12 x h - 2x -2h + 1[/tex]
And, The value of [tex]\frac{f (x + h)- f(x)}{h} = 12 x + 6h -2[/tex].
Here, the function is given as,
[tex]f (x) = 6x^{2} -2x + 1[/tex]
What is function?
A function from a set X to a set Y assigns to each element of X exactly one element of Y.
Now,
Replace every x with (x + h) and expand it,
[tex]f (x) = 6x^{2} -2x + 1\\f (x+h) = 6(x+h)^{2} -2(x+h) + 1\\f (x+h) = 6 (x^{2} +h^{2} + 2xh) - 2x -2h +1\\f (x+h) = 6x^{2} +6h^{2} +12xh -2x-2h+1\\[/tex]
And,
[tex]f (x+h) - f(x) = ( 6x^{2} +6h^{2} +12xh -2x-2h+1) - (6x^{2} -2x+1)\\\frac{f (x+h) -f (x)}{h} =\frac{ ( 6x^{2} +6h^{2} +12xh -2x-2h+1) - (6x^{2} -2x+1)\\}{h} \\\frac{f (x+h) -f (x)}{h} =\frac{ 6x^{2} +6h^{2} +12xh -2x-2h+1 -6x^{2} +2x-1\\}{h} \\\\\frac{f (x+h) -f (x)}{h} =\frac{12xh +6h^{2}-2h }{h} \\\frac{f (x+h) -f (x)}{h} = 12x + 6h -2[/tex]
Hence,
The value of function [tex]f (x + h) = 6x^2 + 6 h^2 + 12 x h - 2x -2h + 1[/tex]
And, The value of [tex]\frac{f (x + h)- f(x)}{h} = 12 x + 6h -2[/tex].
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Related Questions
Plz help ASAP WILL MARK BRAINLIEST
Answers
Answer:
[tex]c = 3a - 2[/tex]
BRAINLIEST PLEASE ... :-)is -|-4| = |-(-4)| the same?
Answers
Answer:
no the first one is -4 and the other one is positive 4
Answer:Yes
Step-by-step explanation:
Just take away the (4)
If m∠ATB = 20°, m∠BTD = 72°, and m∠CTD = 38°, what is m∠ATC?
Answers
Answer:
54 degrees
Step-by-step explanation:
What is the domain of f?
Answers
Answer:
[tex]\huge \boxed{\mathrm{A}}[/tex]
Step-by-step explanation:
The domain of a function is all possible values for the value of x.
The denominator in a rational function cannot equal to 0.
[tex]x+2\neq 0[/tex]
Subtracting 2 from both sides.
[tex]x\neq -2[/tex]
The domain of the function is all real numbers except -2.
A hot-air balloon, headed due east at an average speed of 15 miles per hour at a constant altitude of 100 feet, passes over an intersection (see the figure). Find an expression for its distance d (measured in feet) from the intersection 1 seconds later.
Answers
Answer:
The distance is [tex]sqrt{10000+484t^2}[/tex]
Step-by-step explanation:
Given that,
Altitude = 100 feet
Average speed = 15 miles/ hour
We need to calculate the speed in feet/sec
Using formula for speed
[tex]v=15 miles/hour[/tex]
[tex]v=15\times 1.46667\ ft/sec[/tex]
[tex]v=22\ ft/sec[/tex]
We need to calculate the distance in t sec
Using formula of speed
[tex]v =\dfrac{d}{t}[/tex]
Put the value into the formula
[tex]22=\dfrac{d}{t}[/tex]
[tex]d=22t[/tex]
According to figure,
We need to calculate the distance
Using pythagorean theorem
[tex]AC=\sqrt{(AB)^2+(BC)^2}[/tex]
Put the value into the formula
[tex]d=\sqrt{100^2+(22t)^2[/tex]
[tex]d=\sqrt{10000+484t^2}[/tex]
Hence, The distance is [tex]sqrt{10000+484t^2}[/tex]
How many significant digits are there in the product of 0.005 and 25.725?
Answers
Answer:
there are 0 significant digits
Step-by-step explanation:
0.0005 has 1 significant digit which is 5
25.725 has 5 significant digits
Suponha que um trabalhador ganhe 20, 00 por dia , quando trabalha até 18 h . Após isso , ganha 5 , 00 a mais por hora trabalhada. Num determinado mês, trabalhou 25 dias mais 20 h noturnas , Sabendo que a décima parte dessa quantia foi gasta com transporte e a metade do restante com aluguel , quanto lhe sobrará nesse mês ?
Answers
Responda:
270, 00
Explicação passo a passo:
Dado o seguinte:
Pagamento diário até as 18h00
Pagamento por hora trabalhada = 5,00
Em um determinado mês:
Trabalhou 25 dias: (25 * 20) = 500,00
20 horas à noite: (20 * 5) = 100,00
Ganho total = 500 + 100 = 600,00
Despesas:
Transporte = 1/10
= (1/10) × 600 = 60,00
Quantidade restante = (600 - 60) = 540,00
Renda:
1/2 de 540 = 270,00
Valor total restante após a dedução das despesas:
600 - (270 + 60)
600 - 330 = 270,00
If a base is negative, how will you know whether the answer is positive or negative before evaluating it?
Answers
Answer:
Explained below.
Step-by-step explanation:
Assuming that the question is related to exponents.
Consider the expression: [tex]a^{b}[/tex]
Here,
a = base
b = exponent
Consider that the value of base is a negative term.
Then an even exponent will give a positive result.
And an odd exponent will give a negative result.
Consider the following values of b and suppose that a = -x.
For b = 4,
[tex]a^{b}=(-x)^{4}=(-x)\times (-x)\times (-x)\times (-x)=x[/tex]
For b = 3,
[tex]a^{b}=(-x)^{3}=(-x)\times (-x)\times (-x) = -x[/tex]
Answer:
Sample Response: When evaluating a power with a negative base, the solution is positive or negative depending on whether the exponent is odd or even. If odd, the value will be negative. If even, the value will be positive.
Step-by-step explanation:
in a lottery there are 10 prizes and 25 blanks what is the probability of getting prizes
Answers
Answer:
P(prize)= 2/7
Step-by-step explanation:
The probability of getting a prize can be found by dividing the number of favorable outcomes by the total number of outcomes.
P (prize) = favorable / total
The favorable outcome is a prize and there are 10 prizes.
P (prize) = 10 / total
There are 10 prizes and 25 blanks. Add 10 and 25.
10 prizes + 25 blanks= 35 total outcomes
P (prize)= 10/35
This fraction can be simplified. Both the numerator and denominator can be evenly divided by 5.
P(prize)= (10/5) / (35/5)
P(prize) = 2 / (35/5)
P(prize)= 2/7
The probability of receiving a prize is 2/7
A solid cylinderical metal is melted and recast into cubes of metal of side 3cm. The base radius of the initial cylinderical metal is 10.5cm and height is 63cm.How many cubes will be made
Answers
Answer:
808
Step-by-step explanation:
First find the volume of the original cylinder. It is given by πr²h:
π * (10.5)² * 63 ≈ 21820.717 cm³
Next find the volume of each cube. It is given by lwh:
3 * 3 * 3 = 27 cm³
Finally, divide the volume of the original cylinder by the volume of each cube to determine the number of cubes:
21820.717 / 27 ≈ 808.1747
Partial cubes are not possible, so the answer is 808.
. In a class, 36 students offered physics, 46 offered chemistry
and 48 offered mathematics. Of these, 26 are in both
chemistry and mathematics, 24 are in both physics and
chemistry, 22 are in both mathematics and physics.12 have
offered all the three subjects. Find the number of students in
the class.
Answers
Answer:
70 students
Step-by-step explanation:
pls help me .question no 14
Answers
Question 14, Part (i)
Focus on quadrilateral ABCD. The interior angles add to 360 (this is true for any quadrilateral), so,
A+B+C+D = 360
A+90+C+90 = 360
A+C+180 = 360
A+C = 360-180
A+C = 180
Since angles A and C add to 180, this shows they are supplementary. This is the same as saying angles 2 and 3 are supplementary.
==================================================
Question 14, Part (ii)
Let
x = measure of angle 1
y = measure of angle 2
z = measure of angle 3
Back in part (i) above, we showed that y + z = 180
Note that angles 1 and 2 are adjacent to form a straight line, so we can say
x+y = 180
-------
We have the two equations x+y = 180 and y+z = 180 to form this system of equations
[tex]\begin{cases}x+y = 180\\y+z = 180\end{cases}[/tex]
Which is really the same as this system
[tex]\begin{cases}x+y+0 = 180\\0+y+z = 180\end{cases}[/tex]
The 0s help align the y terms up. Subtracting straight down leads to the equation x-z = 0 and we can solve to get x = z. Therefore showing that angle 1 and angle 3 are congruent. We could also use the substitution rule to end up with x = z as well.
Solve for w: -4(w+1)=-24 Please explain this like you would a 2 year old and please explain it so it is the easiest way to solve it and why I would do it like that like for example let’s say divde it by 4 like why would Divde it by 4 once again that was an example
Answers
Answer:
Step-by-step explanation:
The first step in solving an equation is to look at it. Identify where the variable is that you're interested in, and see what operations are being performed on that variable.
Here, the variable w has 1 added to it, and the sum is multiplied by -4. The variable is only on the left side of the equation, and is inside parentheses. Inside parentheses, the coefficient of the variable is 1.
These observations tell you that, in some order, you will need to undo the operations of multiplication and addition, and you will have to eliminate parentheses.
You also observe that the multiplication factor of the parentheses (-4) is a factor of the constant on the right side of the equation (-24). This means you have a couple of options for solving this equation:
eliminate parentheses first, using the distributive propertydivide by -4 first, to undo the multiplicationThe second method is actually faster. We'll illustrate that one first.
__
Divide both sides of the equation by -4 to undo the multiplication by -4.
-4(w +1)/(-4) = -24/(-4) . . . . . we have indicated the division we want to do
w +1 = 6 . . . . . . . . . . . . . . . . here is the result of that division
Now, we can add the opposite of +1 to eliminate the constant from the left side. As with all operations on equations, we must do the same thing to both sides. This means we add -1 to both sides of the equation:
w +1 -1 = 6 -1 . . . . . . we have indicated the addition we want to do
w = 5 . . . . . . . . . . . here is the result of that addition
The solution of the equation is ...
w = 5
__
Often, when parentheses are involved, the numbers are such that the solution method is not as simple as what we just did. In those cases, you would take the approach of eliminating parentheses first. For this equation, it looks like this:
-4(w +1) = -24 . . . . . . . given
-4w -4 = -24 . . . . . . . . use the distributive property to eliminate parentheses
We want the variable term by itself, so we need to eliminate the constant -4 that is added on the left. To do that, we add its opposite. This means we add +4 to both sides of the equation.
-4w -4 +4 = -24 +4 . . . . . . indicating the addition of +4
-4w = -20 . . . . . . . . . . . . . the result of adding +4
Here, w is multiplied by -4. We want w by itself, so we want to undo that multiplication. That means we want to divide both sides of the equation by -4.
-4w/(-4) = -20/(-4) . . . . . . indicate the division
w = 5 . . . . . . . . . . . . . . . . the result of doing the division
The solution of the equation is ...
w = 5
_____
Our basic approach is to undo the operations done to the variable, in the reverse of the order in which they are done. In that process, we observe the rules of equality: whatever operation you do to one side of the equation must also be done to the other side. (My teacher called this last rule: "keep the equal sign sacred.")
You can always use the distributive property for factoring, collecting terms, or eliminating parentheses.
Plz help ASAP will mark brainlist
Answers
Answer:
[tex]\huge \boxed{\mathrm{C}}[/tex]
Step-by-step explanation:
The domain is the set of all possible values for x.
The function does not cross the line x = 1.
The domain is all real numbers except 1.
The range is the set of all possible values for y.
The function does not cross the line y = 0.
The range is all real numbers except 0.
Which group of expressions could represent the dimensions of a rectangular prism with a volume of 2y3 + 15y2 + 28y?
A. y, y + 4, 2y + 7
B. y, y + 7, 2y + 4
C. y, y + 2, 2y + 14
D. y, y + 14, 2y + 2
Answers
Answer:
C. y, y + 2, 2y + 14
Step-by-step explanation:
Given
[tex]Volume = 2y^3 + 15y^2 + 28y[/tex]
Required
Determine which set of dimensions is applicable
The volume of a rectangular prism is calculated as:
[tex]Volume = Length * Width * Height[/tex]
So, to solve this question, we have to test each options using the above formula
A. y, y + 4 and 2y + 7
[tex]Volume = y * (y + 4) * (2y + 7)[/tex]
Open brackets
[tex]Volume = y * (y * 2y+ 4* 2y + y * y+ 4* 7)[/tex]
[tex]Volume = y(2y^2+ 8y + y^2+ 28)[/tex]
[tex]Volume = 2y^3+ 8y^2 + y^3+ 28y[/tex]
Collect Like Terms
[tex]Volume = 2y^3 + y^3+ 8y^2+ 28y[/tex]
[tex]Volume = 3y^3+ 8y^2+ 28y[/tex]
B. y, y + 7, 2y + 4
[tex]Volume = y * (y + 7) * (2y + 4)[/tex]
Open brackets
[tex]Volume = y * (y * (2y + 4)+ 7* (2y + 4))[/tex]
[tex]Volume = y * (2y^2 + 4y+ 14y + 28)[/tex]
[tex]Volume = y * (2y^2 + 18y+ 28)[/tex]
[tex]Volume = 2y^3 + 18y^2+ 28y[/tex]
C. y, y + 2, 2y + 14
[tex]Volume = y * (y + 2) * (2y + 14)[/tex]
Open brackets
[tex]Volume = y * (y* (2y + 14) + 2* (2y + 14))[/tex]
[tex]Volume = y * (2y^2 + 14y + 4y + 28)[/tex]
[tex]Volume = y * (2y^2 + 18y + 28)[/tex]
[tex]Volume = 2y^3 + 18y^2 + 28y[/tex]
There's no need to check the last option because option c answers the question.
Hence, the dimension is y, y + 2, 2y + 14
Khalid wants to buy a long sandwich for a party. Store A sells a
5-foot sandwich for $42.50. Store B sells a 6-foot sandwich for $49.50.
Which store has the better buy? Show your work.
Answers
Answer:
From our analysis stores B has the better buyStep-by-step explanation:
Hey there!!!
In this problem, to know actually the store that has the better buy we need to solve for the cost of 1 foot of sandwich from individual stores.
Stores A
if 5 foot cost $42.50
1 foot will cost x
cross multiplying
x= x= $42.50/5
x= $8.5
Stores B
if 6 foot cost $49.50
1 foot will cost x
cross multiplying
x= x= $49.50/6
x= $8.24
From our analysis stores B has the better buy
How many solutions does the system have?
2y = 4x + 6
y=2x + 6
Choose 1 answer:
A. Exactly one solution
B. No solutions
C. Infinitely many solutions
Answers
Answer:
the answer should be no solution.
Evaluate the expression when b= 2 and c = -2 -b+2c
Answers
Answer:
- 6
Step-by-step explanation:
Given
- b + 2c ← substitute b = 2 and c = - 2 into the expression
= - 2 + 2(- 2)
= - 2 - 4
= - 6
Express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression.
Answers
Answer:
1). |(-3) - 8|
2). 11 units
Step-by-step explanation:
If the given numbers are 'x' and 'y', distance between these numbers will be represented by the absolute value expression,
Distance = |x - y|
Given numbers are (-3) and 8.
Therefore, expression for the distance between these points will be,
Distance = |(-3) - 8|
Distance between these points will be = 11 units
What would be the slope for y=-7x + 2
Answers
Answer:
-7
Step-by-step explanation:
Hello!
This equation is in slope intercept form. The base equation is
y - mx +b
m is the slope
b is the y-intercept
Since -7 is in place of m -7 is the slope
The answer is -7
Hope this helps!
Answer:
-7x
Step-by-step explanation:
The formula for slope is y=mx+b, m being slope. And in the equation y=-7x+2, -7 is taking the place of m. Therefore, -7x is the answer.
i need help, please.
Answers
1). y-intercept: 7 and slope: 4
2). y-int: 8 and slope: -1/3
3). y-int: -6 and slope 1/9
4). y-int: -9 and slope: -5
5). y-int: -6 and slope: 2
6). y-int: -7 and slope: -2/3
Answer:
work shown and pictured
The perimeter of a rectangle is 80 inches. The length is 4 inches longer than twice the width. What are the dimensions of the rectangle?
Answers
Answer:
length = 28 cmwidth = 12 cmStep-by-step explanation:
Perimeter of a rectangle = 2l + 2w
where
l is the length
w is the width
From the question
Perimeter = 80cm
The length is 4 inches longer than twice the width is written as
l = 4 + 2w
Substitute this into the formula and solve for the width
That's
80 = 2( 4 + 2w) + 2w
80 = 8 + 4w + 2w
6w = 80 - 8
6w = 72
Divide both sides by 6
w = 12 cm
Substitute w = 12 cm into l = 4 + 2w
That's
l = 4 + 2(12)
l = 4 + 24
l = 28cm
Therefore
length = 28 cm
width = 12 cm
Hope this helps you
The value pi/16 is a solution for the equation 2cos^2(4x)-1=0
True or false?
Answers
Answer:
True
Step-by-step explanation:
The other person is wrong
The value π/16 is a solution for the equation 2cos²(4x) – 1 = 0, is true.
What is trigonometry?The connection between the lengths and angles of a triangular shape is the subject of trigonometry.
The value π/16 is a solution for the equation 2cos²(4x) – 1 = 0.
Put x = π/16, we have
2cos²(4x) – 1 = 0
2cos²[4 (π/16)] – 1 = 0
2cos²(π/4) – 1 = 0
We know that cos (π/4) = 1/√2
2(1/√2)² – 1 = 0
2 (1/2) – 1 = 0
1 – 1 = 0
0 = 0
Thus, the statement is true.
More about the trigonometry link is given below.
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The formula for the time it takes to travel a distance of d at an average speed v is (d)/(v)
Tessa ran a 100-meter dash at a speed of about 7.5 meters per second.
What calculation will give us the estimated duration of Tessa's dash in seconds?
Answers
Answer:
100/7.5
Step-by-step explanation:
It takes 13.3 s to reach 100 meter.
How to find the time?
The formula for the time it takes to travel a distance of d at an average speed is t = d / v
t = 100 / 7.5
t = 13.33
To calculate time, divide the distance by using pace. To get the gap, multiply pace by time. you could see those equations simplified as s = d / t, wherein s is speed, d is distance, and t is time.
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A calculator is sold for Rs 230 at a profit of 15%.find cp
Answers
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{ \: Rs \: 200}}}}}[/tex]
Step-by-step explanation:
Given,
Selling price ( SP ) = Rs 230
Profit % = 15 %
Cost price ( CP ) = ?
Finding the Cost price
[tex] \boxed{ \sf{cost \: price = \frac{selling \: price \times 100}{100 + profit \: \%}}} [/tex]
plug the values
⇒[tex] \sf{ \frac{230 \times 100}{100 + 15 \: }} [/tex]
Muliply the numbers : 230 and 100
⇒[tex] \sf{ \frac{23000}{100 + 15}} [/tex]
Add the numbers : 100 and 15
⇒[tex] \sf{ \frac{23000}{115} }[/tex]
Divide 23000 by 115
⇒[tex] \sf{200}[/tex]
Cost price ( CP ) = Rs 200
Hope I helped!
Best regards!!
Find the product. √5(2+√7)
A)2√5+√35 B)√45 C)2√5+2√7 D)√10+√35
Answers
Answer:
A. 2√5 + √35
Step-by-step explanation:
Product means multiplication
√5(2+√7)
= 2 × √5 + √5 × √7
= 2√5 + √35
Option A is correct
B. √45
√5(2+√7)
=√5 * 2 + √5 * √7
=√10 + √35
=√45
Option B is incorrect
C. 2√5 + 2√7
√5(2+√7)
=2√5 + 2√7
Option C is incorrect
D. √10 + √35
√5(2+√7)
=√5 * 2 + √5*√7
=√10 + √35
Option D is incorrect
It is the parallelogram that has its unequal contiguous sides and the four right angles. A) Square B) Rhombus C) Rectangle D) Rhomboid
Answers
Answer:
Rhomboid is the parallelogram that has its unequal contiguous sides and the four right anglesHope it helps you Mark it as brainliest and follow me My account you can see here below (hardik 60)Look at the diagram below. If ∠A and ∠C are complementary, what's the measurement of ∠C?
Answers
Answer:
∠A + ∠C=90°(Right angle triangle)
37+∠C=90°
∠C=90°-37°
∠C=53°
Hope it helped you:)
Answer:
∠A + ∠C=90°(Right angle triangle)
37+∠C=90°
∠C=90°-37°
∠C=53°
Step-by-step explanation:
a + 2 = 6
Solving One and Two step Equations
Answers
Answer:
a = 4
Step-by-step explanation:
a + 2 = 6
Subtract 2 from both sides
a + 2 - 2 = 6 - 2
a = 4
Answer:
4
Step-by-step explanation:
6 - 2 = 4
which inequality does the graph represent?
Answers
Answer:
I believe the answer is B.
Step-by-step explanation:
Explanation:
+ 1 is the y-intercept
-x is the slope where it rise one and run to the left one (1/-1)