Search for the numbers that divide all of the given set.
Notice that all three of them can be divided by two:
[tex]\begin{gathered} \frac{20}{2}=10 \\ \frac{12}{2}=6 \\ \frac{24}{2}=12 \end{gathered}[/tex]Therefore, 2 is the first common factor. Now, take the numbers 10, 6 and 12 and repeat the procedure. Notice that all of them are divisible by 2:
[tex]\begin{gathered} \frac{10}{2}=5 \\ \frac{6}{2}=3 \\ \frac{12}{2}=6 \end{gathered}[/tex]Therefore, 2 is the next common factor. Now, take the numbers 5, 3 and 6 and repeat the procedure. Notice that 3 is not divisible by 2 and 5 is not divisible by 3. Since there are no more numbers lower tan 3 that divide all of the numbers, there are no more common factors.
The common factors were 2 and 2. Multiply all the common factors to find the greatest common factor:
[tex]2\cdot2=4[/tex]Therefore, 4 is the greatest common factor of 20,12 and 24.
Find the zeros by using the quadratic formula and tell whether the solutions are real or imaginary. F(x)=x^2+14x+20.
Find the zeros by using the quadratic formula and tell whether the solutions are real or imaginary. F(x)=x^2+14x+20.
we have that
the quadratic formula is equal to
[tex]x=\frac{-b\pm\sqrt[\square]{b^2-4ac}_{}}{2a}[/tex]where
a=1
b=14
c=20
substitute the given values in the formula
[tex]\begin{gathered} x=\frac{-14\pm\sqrt[\square]{14^2-4(1)(20)}_{}}{2(1)} \\ \\ x=\frac{-14\pm\sqrt[\square]{116}_{}}{2} \\ \\ x1=\frac{-14+\sqrt[\square]{116}_{}}{2} \\ \\ x2=\frac{-14-\sqrt[\square]{116}_{}}{2} \end{gathered}[/tex]x1 and x2 are the zeros of the quadratic equation
The solutions are real numbers
What’s the range of grades on the fifth exam that results in earning a B is _. If the highest grade is 100 then _ .
Let x be the grade of the last exam, then the average is:
[tex]\frac{71+76+88+92+x}{5}=\frac{x+327}{5}[/tex]now, to get a B we need this to be greater or equal than 80 and less than 90, that is:
[tex]80\leq\frac{x+327}{5}<90[/tex]Solving for x we have:
[tex]\begin{gathered} 80\leq\frac{x+327}{5}<90 \\ 5\cdot80\leq x+327<5\cdot90 \\ 400\leq x+327<450 \\ 400-327\leq x<450-327 \\ 73\leq x<123 \end{gathered}[/tex]Therefore the range of grades on the fifth exam that results in earnings a B is
[tex]73\leq x<123[/tex]If the highest grade is 100, then
[tex]73\leq x\leq100[/tex]Answer:
73-100
Step-by-step explanation:
Steve has a pretty lenient grading system! (Usually 85-93 is a B.)
He needs at LEAST an 80 , so the average of his five scores must meet this
(71+76+88+92+x) / 5 = 80
solve for x = 73
If he scores less than a 90 average , he will still get a B
(71+ 76 + 88+92 +x) / 5 < 90 shows x < 123 ( which he cannot score)
so the range of scores on fifth test to get a final grade B is 73 - 100 .
Similarities and differences between compound event, mutually exclusive event, overlapping event, independent event, dependent event
Difference between Dependent and Independent event:
[tex]\begin{gathered} Dependent\text{ Event:} \\ The\text{ outcome of one event affects the outcome of the other.} \\ \text{If A and B are dependent events},\text{ then the probability of both occuring is:} \\ P(A\text{ and B)=}P(A)\times P(B|A) \end{gathered}[/tex][tex]\begin{gathered} \text{Independent Event:} \\ The\text{ outcome of one event does not affects the outcome of the other.} \\ \text{If A and B are independent events, then the probability }of\text{ both occuring is:} \\ P(A\text{ and B)=}P(A)\times P(B) \end{gathered}[/tex]2) During the month of January, the depth, d, of snow in inches at the base of one ski resortcould be approximated by d = -2t + 69, where t is the number of days since December31st. Graph the equation and use the graph to estimate the depth of snow on January 24th.
To find the depth of snow on january we need to calculate the number of days since december 31st, which will be equal to 24, this value will be used on t. We have:
[tex]d=-2\cdot24+69=-48+69=21[/tex]To graph the line we need another point. We can use december 31st as our second point, since t is the number of days since december 31st than for this t will be equal to 0.
[tex]d=-2\cdot0+69=69[/tex]Now we can graph the equation.
What number is the opposite of 2.6?A. -2.6B. 6.2C. 26D. -6.2
Explanation
The opposite of a number is a number that is the same distance from 0 as another number,but in the opposite direction
they have the same value, but in opposite directions,hence the opposite of a positive number is its negative value.
then
[tex]\begin{gathered} 2.6 \\ 2.6\text{ is a positive number, so} \\ \text{its opposite is} \\ A)-2.6 \end{gathered}[/tex]so, the answer is
[tex]A)-2.6[/tex]I hope this helsp you
Write the quadratic function in standard form. f(x) = −2x2 − 8x f(x) = Give the vertex. (x, y) = Find the intercepts. (If an answer does not exist, enter DNE.) x-intercept (x, y) = (smaller x-value) x-intercept (x, y) = (larger x-value) y-intercept (x, y) =
Answer:
[tex]f\mleft(x\mright)=-2\left(x+2\right)+8[/tex][tex]\begin{gathered} x-\text{ intercept: \lparen-4,0\rparen \lparen0,0\rparen} \\ y-intercept:\text{ \lparen0,0\rparen} \\ \text{ Vertex: \lparen-2,8\rparen} \end{gathered}[/tex]Step-by-step explanation:
The quadratic function in standard form is represented as:
[tex]ax^2+bx+c=0[/tex]Therefore, for the given function:
If the vertex is (-2,8) the equation would be represented as;
[tex]\begin{gathered} f(x)=a(x+2)^2+8 \\ \text{ Use one of the given points on the graph:} \\ x-\text{ intercept: \lparen-4,0\rparen \lparen0,0\rparen} \\ y-intercept:\text{ \lparen0,0\rparen} \end{gathered}[/tex][tex]\begin{gathered} 0=a(-4+2)^2+8 \\ 0=4a+8 \\ 4a=-8 \\ a=-\frac{8}{4}=-2 \end{gathered}[/tex]Hence, the function of the quadratic in standard form is represented as:
[tex]f\mleft(x\mright)=-2\left(x+2\right)+8[/tex]Write a function g whose graph represents a vertical shrink by a factor of 1/2 of the graph of f(x) = 2x+6. g(x) =
Vertical shrink factor = 1/2
So, f(x) = 1/2 g(x)
[tex]\begin{gathered} g(x)=\frac{1}{2}f(x) \\ \text{ where, f(x)=2x+6} \\ g(x)=\frac{1}{2}(2x+6) \\ g(x)=x+3 \end{gathered}[/tex]Answer : g(x) = x + 3
which graph shows the line that has x-intercept -2 and y-intercept 4
You have to determine which graph shows a line with x-intercept -2 and y-intercept 4
The x-intercept is the point where the line crosses the x-axis, at this point, the y-coordinate is zero. So the x-intercept must have coordinates (-2,0)
The y-intercept is the point where the line crosses the y-axis, at this point the x-coordinate is zero. So the y-intercept of the line we have to identify has coordinates (0,4)
You have to determine the x and y-intercepts of each line graphed and compared with the given coordinates.
Assuming each dot corresponds to one unit:
Graph A
The line crosses the x-axis at point (2,0) and the y-axis at point (0,-4)
→ The x-intercept and y-intercept of this line do not correspond to the line we are looking for.
Graph B
The line crosses the x-axis at point (2,0) and the y-axis at point (0,4)
→ The x-intercept and y-intercept of this line do not correspond to the line we are looking for.
Graph C
The line crosses the x-axis at point (-2,0) and the y-axis at point (0,-4)
→ The x-intercept and y-intercept of this line do not correspond to the line we are looking for.
Graph D
The line crosses the x-axis at point (-2,0) and the y-axis at point (0,4)
→ The x-intercept and y-intercept of this line correspond to the line we are looking for.
So the line that has x-intercept -2 and y-intercept 4 is the one in graph D
Find the distance between the two points shown below. Round your answer to 2 decimal places.
A- (-4,-3)
B- (0,0)
The distance between the two points A- (-4,-3) and as B- (0,0) shown in the question is 5 units.
What is Distance ?Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are.
The distance formula in coordinate geometry is used to calculate the distance between two given points. The distance formula to calculate the distance between two points (x1,y1) ( x1 , y1 ) , and (x2,y2) ( x2 , y2 ) is given as, D=√(x2−x1)²+(y2−y1)².
We have given the coordinates which is A- (-4,-3) and B- (0,0).
Now, we will determine the distance between these points,
Distance (d) = √(x2−x1)² + (y2−y1)²
(x1, y1) = Coordinates of the first point
(x2, y2) = Coordinates of the second point
Distance = √{0-(-4)}² + {0-(-3)}²
= √16 + 9 = √25
= 5
Hence the distance between the points AB is 5 units.
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A teacher received the following answer to a quiz question in which the student was asked to simplify the expression in Step 1:
Step 1: −5(x − 16y) + 7(−2x − 8y)
Step 2: −5x + 80y − 14x − 8y
Step 3: −5x − 14x + 80y − 8y
Step 4: (−14x − 5x) + (80y − 8y)
Step 5: −19x + 72y
Part A: Identify the step where the student made a mistake and explain the specific error that was made. Support your answer using the correct vocabulary. (6 points)
Part B: How would you correct the mistake? Show all your work.
The student made a mistake and explain the specific error that was made. Support your answer using the correct vocabulary. The mistake has been done in Step 2.
PART A: There is a mistake in Step 2, Distributive Property has been employed incorrectly.
7 has to multiply by both the terms inside the bracket, but it has been multiplied with the first term only.
7(-2 x-8 y)=-14 x-56 y and 7(-2 x-8 y) -14 x-8 y
Hence, -5(x-16 y)+7(-2 x-8 y)=-5 x+80 y-14 x-56 y
PART B :
The given equation is
-5(x-16 y)+7(-2 x-8 y)
Applying distributive property to the above equation that states A(B+C)=AB+AC, we get :
-5 x+80 y-14 x-56 y
Now, Writing the terms with the same variable together, we get
(-5 x-14 x)+(80 y-56 y)
Proceeding with solving terms inside the brackets according to BODMAS, we get,
-19 x+24 y
Hence , −5(x − 16y) + 7(−2x − 8y) = -19x +24y
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I am trying to do 0.03 squared but my calculator is giving me the answer 9E-4 what does this mean
Answer:
[tex]0.03^2=0.0009\text{ or 9}\times10^{-4}[/tex]Step-by-step explanation:
The E on the calculator means ''times ten to the power of''
Therefore, 0.03 square would be 9 times ten to the power of -4. That means:
[tex]0.03^2=0.0009\text{ or 9}\times10^{-4}[/tex]Give one example of how a learner on level 1 will define a rectangle.
Step-by-step explanation:
Level 1 Analysis: Describe shapes on the basis of their properties. Students learn what properties each shape has. Example: “All rectangles have 4 sides with opposite sides equal and parallel, and 4 right angles.” or “Perpendicular lines form a right angle.”
A learner on basic level one will define a rectangle by four straight lines at right angles.
A rectangle has four straight lines in which any two opposite sides are parallel and equal in length to each other and any two adjacent sides are perpendicular to each other making a right angle in between the sides.
It is a four-sided polygon having four angles in which all the internal angles are of 90 degree each. One can make a rectangle by taking 2 sets of two sticks different in length and arrange the equal sides opposite to each other making an angle of 90 degree between every adjacent side.
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A) What do you know for sure about a number with the following clues:
part of the expanded form includes 3 × 105
the expanded form includes only three powers of 10
the expanded form includes 103
B) When a number is given to you in expanded form using powers of 10, what do you know about the number?
Answer:
hi iiiiiii8888888888iiiiii55
13. Bethany buys a used car for $9,000. She puts $600 down and finances the rest for 4 1/2 years at 5%annual interest. At the end of years, the $9000 car will have cost her $
Answer :
$11,062.40
Explanation :
The formula for the future amount in a compounding interest is :
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where P is the present value
r is the rate of interest
n is the number of compounding in a year
t is time in years
From the given problem,
She puts a downpayment of $600 so the remaining will be :
9000 - 600 = 8400, which she will be financing for 4.5 years
So P = 8400
r = 5% or 0.05
n = 1 (Since it will only be compounding once in 1 year - annually)
t = 4.5 years
Using the formula above :
[tex]\begin{gathered} A=8400(1+\frac{0.05}{1})^{1(4.5)} \\ A=10462.40 \end{gathered}[/tex]The value of the $9000 car after 4.5 years will be the sum of the downpayment and the future amount.
[tex]600+10642.40=\$11,062.40[/tex]The answer is $11,062.40
17. The table shows the record high and
record low temperatures for certain U.S.
states. Which state in the list had the
greatest variation in temperature? the
least?
Utah, nevada
State
Alaska
Idaho
Nevada
Utah
Record High
Temperature (°F)
100
118
125
117
Record Low
Temperature (
-80
-60
-50
-69
The highest variation in the temperature if found for Utah.
What is defined as the temperature variation?Temperature is the degree to which an object is hot or cold.In weather forecasting, daily temperature variation refers to the difference between a high and a low air temperature on the same day.There are many factors that contribute to temperature variations in the atmosphere. Temperature fluctuations are caused by four natural factors: latitude, altitude, location from the sea, as well as ocean currents.For the given question;
The maximum and minimum temperatures of the U.S states are given;
The variation in temperature is found by;
Temperature variation = Maximum temperature - Minimum temperature
Alaska = 100 - (-80) = 180
Idaho = 118 - (- 60) = 160
Nevada = 125 - (-50) = 175
Utah = 117 - (-69) = 186
Thus, the highest variation in the temperature if found for Utah.
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Write 243 as a power using the number 3 as the base
Answer:
[tex]3^5[/tex]
Step-by-step explanation:
Hello! Let's help you with your question here!
So, we want to know 243 as a power using the number 3 as the base. Well, there is an easy way in figuring out to what the power would be.
We have the total and we already have the base. In order to figure out what the power number is, we can essentially just divide 243 by our base number 3, until we get to a point where we can't divide the number by 3 without getting a decimal value! So it would look like this!
[tex]243/3=81[/tex]
[tex]81/3=27[/tex]
[tex]27/3=9[/tex]
[tex]9/3=3[/tex]
[tex]3/3=1[/tex]
Now, it's just a matter of counting how many times we divided by 3 and it turns out we divided the number by 3 5 times! Therefore, we can say that:
[tex]3^5=243[/tex]
Find the measure of an angle in a regular polygon with 28 sides.
The internal angle of a regular polygon with n sides is found as follows:
[tex]\frac{(n-2)\cdot180}{n}[/tex]Replacing with n = 28:
[tex]\frac{(28-2)\cdot180}{28}=167[/tex]167 degrees
solve for the variable X: X+7=-4 someone pls help what even is this
The equation to solve is:
[tex]X+7=-4[/tex]We need to solve for the variable X, which means to take X to one side and numbers to another.
In solving equations, remember this golden rule.
Side Change = Sign Change
Now, looking at the equation, we can keep X on the left hand side and take "+7" to the right hand side. So we are changing sides of "+7" so taking it to the right hand side, it becomes "-7", so:
[tex]\begin{gathered} X+7=-4 \\ X=-4-7 \end{gathered}[/tex]We know
-4 -7 = -11
Thus,
[tex]\begin{gathered} X=-4-7 \\ X=-11 \end{gathered}[/tex]The variable X is -11
In a survey, 100 people were asked if they smoke and whether or not they exercise regularly ( more than twice a week). The results are summarized in the table below.
Explanation:
a) The % of people that do not smoke, regardless of whether or not they exercise.
= No. of people that dont smoke/total number of people
= 76/100
Answer: 76% of people do not smoke.
b) % of people that do not exercise regularly, regardless of whether or not they smoke:
= 84/100
Answer = 84% do not exercise regularly
PLEASE HELP ME IM SO DESPERATE
Two linear functions with point (1,4) are given by:
y = 2x + 2.y = -2x + 6.The graph with these two functions is given at the end of the answer.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the rule presented below:
y = mx + b
In which the coefficients are described as follows:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the y-axis(x = 0).A line with slope of 2 is given by:
y = 2x + b.
Supposing that it goes through point (1,4), when x = 1, y = 4, hence we can find the intercept as follows:
4 = 2 + b
b = 2.
Hence the first equation is:
y = 2x + 2.
A line with slope of -2 is given by:
y = -2x + b.
Then the intercept is found as follows, supposing that it also goes through the point (1,4):
4 = -2 + b
b = 6.
Then the equation is:
y = -2x + 6.
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nt-Facing Task StatementHere is a scatter plot that shows the years when some used cars were madeand their prices in 2016, together with the graph of a linear model for therelationship between year and price.
The slope is positive
as the line moves from 2006 to 2016, it also goes up showing an incease in car prices.
Evan has $580 to spend at a bicycle store for some new gear and biking outfits.
Assume all prices listed include tax.
• He buys a new bicycle for $396.95.
• He buys 4 bicycle reflectors for $7.40 each and a pair of bike gloves for $22.94.
• He plans to spend some or all of the money he has left to buy new biking outfits
for $42.10 each.
Required inequality is 47.25x ≤ 194.02.
What is inequality?An inequality is created when two or more algebraic expressions are compared using the symbols <, >, or ≤. They represent mathematical formulas when neither side is equal.
Given Data
Evan has $580 to spend at a bicycle store for some new gear and biking outfits
He buys a new bicycle for $396.95.
• He buys 4 bicycle reflectors for $7.40 each and a pair of bike gloves for $22.94.
• He plans to spend some or all of the money he has left to buy new biking outfits for $42.10 each.
Money spend on reflectors = 4(17.33)
Money spend on reflectors = $69.32
Total money left = (580 -(285.41 + 69.32 + 31.25))
Total money left = $194.02
If she buy x biking outfits:
47.25x ≤ 194.02
Required inequality is 47.25x ≤ 194.02.
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You spend 25$ on supplies to make cookies abd plan to sell them for 0.75$ each ehat numbers of cookies can you sell in order to make profit
34 cookies must be sold to make a profit .
Profit is defined as the difference between an economic entity's revenue from its products and the financial costs of its inputs.
It is the total of all revenues less all outlays, which includes both outlays that are explicit and those that are not. Because it only refers to costs that are expressly listed on a company's financial accounts, it differs from accounting profit. Accounting profit is determined by deducting all explicit expenditures from the company's total revenue. An economist considers both apparent and implicit economic costs while analyzing a firm. Therefore, economic profit is lower than accounting profit. Economic theory states that a business can only be profitable if its whole revenue is greater than its opportunity cost.let the number of cookies to be sold is x.
Cost of x cookies = 0.75x
Now we know that 0.75x > 25 since the sell price is more than the cost price profit is made.
Now solving the inequality:
0.75x > 25
or, x > 33.33
Therefore the number of cookies needed to be sold is 34 .
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There are two bags containing only purple and white marbles.Bag A has 6 purple marbles and 4 white marbles.Bag B has 8 purple marbles and 8 white marbles.A marble is randomly chosen from each bag.List these events from least likely to most likely.Event 1: choosing a red marble from Bag A.Event 2: choosing a purple marble from Bag A.Event 3: choosing a white marble from Bag B.Event 4: choosing a purple or white marble from Bag B.Least likelyMost likelyEvent (1)EventEvent |Event
Given:
There are two bags containing only purple and white marbles.
Bag A has 6 purple marbles and 4 white marbles.
so, the probability of choosing purple = 0.6
and the probability of choosing white = 0.4
And Bag B has 8 purple marbles and 8 white marbles.
So, the probability of choosing purple = 0.5
And the probability of choosing white = 0.5
Now, we will find the probability of the following events:
Event 1: choosing a red marble from Bag A.
There are no red colors in the bags
So, the probability will be = 0
Event 2: choosing a purple marble from Bag A.
the probability of choosing purple = 0.6
Event 3: choosing a white marble from Bag B.
the probability of choosing white = 0.5
Event 4: Choose a purple or white marble from Bag B.
So, all the marbles are purple or white
so, the probability = 1
So, the events from least likely to most likely will be as follows:
Event 1
Event 3
Event 2
Event 4
Use the information to find a linear algebraic equation model to use to answer the question being asked. When typing your answers do not include any spaces between your characters.Meya and Eric are joking that their combined ages equal Sam’s age. If Meya is twice Eric's age and Sam is 69 yr old, what are Meya and Eric's ages?Let m= Meya's ageLet e= Eric's ageWhat equation can we make to represent the relationship between Meya's and Eric's ages? AnswerUse your relationship from the question above to create an equation to find Meya and Eric's ages: AnswerMeya's age is AnswerEric's age is Answer
Answer
Meya's age is 46 year
Eric's age is 23 years
Step-by-step explanation:
Let Meya age be m
Let Eric's age be e
The combination of Meya and Eric age is equal to Sam age
Sam age = 69 years
Meya is twice Eric's age
This implies that
m = 2e --------------- equation 1
Since the combination of their age will be equal to Sam age
m + e = 69 ------------ equation 2
To find Eric age, substitute the value of Meya age into the above equation
m = 2e
m + e = 69
2e + e = 69
3e = 69
Divide through by 3
3e/3 = 69/3
e = 23 year
Hence, Eric's age is 23 year
Since m = 2e
e = 23
m = 2(23)
m = 46 year
The parking fee at a carnival is $1.50 for kids and $3.00 for adults. The day of the event 1700 people showed up and $3,750.00 was collected. How many children and how many adults attended??
There are 900 children and 800 adults in attendance
How to determine the number of children and adults in attendance?The given parameters are:
Kids fee = $1.50 per kidAdult fee = $3.00 per adultNumber of people = 1700Amount collected = $3,750.00Let the kids be x and the adults be y
So, we have
x + y = 1700
1.5x + 3y = 1750
Make y the subject in x + y = 1700
y = 1700 - x
Substitute y = 1700 - x in 1.5x + 3y = 1750
1.5x + 3(1700 - x) = 3750
So, we have
1.5x + 5100 - 3x = 3750
Evaluate the like terms
1.5x = 1350
Divide
x = 900
Recall that
y = 1700 - x
So, we have
y = 1700 - 900 = 800
Hence, the number of children and adults in attendance are 900 and 800 respectively
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Please help me with this
The two triangles are congruent and it is by the HL rule because the triangles have the same hypotenuse and leg. Therefore, the correct option is HL.
What are congruent triangles?When two triangles are congruent they will have exactly the same three sides and exactly the same three angles.
In simpler terms, when two triangles are congruent they will have exactly the same three sides and exactly the same three angles.
There are techniques used to ascertain if triangles are congruent.
For example SSS, SAS, ASA, AAS, and HL
where
S = sideA = anglesHL is only applicable to right triangles.
where
Hypotenuse sideLeg of the right triangleTherefore, the triangles are congruent by HL because it has the same length of the hypotenuse and the same length for one of the other two legs.
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2. Which expression is equivalent to 15,314? A 806 x 19-13,314 B 807x19= 15,333 C 808 x 18 =147544 D 809 181450
ANSWER
[tex]B)4\frac{1}{8}\text{ cups}[/tex]EXPLANATION
We have that two ingredients are mixed to make a sauce.
The sauce contains 1/2 cup of chopped onions and 3 5/8 cups of crushed tomatoes.
To find the total number of cups of ingredients the sauce contains, we have to add the two fractions of ingredients.
That is:
[tex]\begin{gathered} \frac{1}{2}+3\frac{5}{8} \\ =3+\frac{1}{2}+\frac{5}{8} \\ =3+\frac{9}{8}=3+1\frac{1}{8} \\ =4\frac{1}{8}\text{ cups} \end{gathered}[/tex]The answer is option B.
If f (x) = 3x2 + 5x − 4, then the quantity f of the quantity x plus h end quantity minus f of x end quantity all over h is equal to which of the following?
If a function [f(x) = (3x² + 5x - 4)], then the expression [{f(x + h) - f(x)}/h] will be equal to (3h + 6x + 5).
As per the question statement, a function [f(x) = (3x² + 5x - 4)].
We are required to calculate the value of the expression [{f(x + h) - f(x)}/h].
Since, [f(x) = (3x² + 5x - 4)] given,
Then, [f(x + h) = {3(x + h)² + 5(x + h) -4}]...[substituting (x + h) in place of "x" in the equation {f(x) = (3x² + 5x - 4)}]
Or, [f(x + h) = {3(x² + 2xh + h²) + 5x + 5h - 4}]
Or, [f(x + h) = (3x² + 3h² + 6xh + 5x + 5h - 4)]
Or, [f(x + h) = (3x² + 5x + 3h² + 5h + 6xh - 4)]
Therefore, [{f(x + h) - f(x)}/h]
= [{(3x² + 5x + 3h² + 5h + 6xh - 4) - (3x² + 5x - 4)}/h]
= [{(3x² - 3x²) + (5x - 5x) - (4 - 4) + 3h² + 5h + 6xh}/h]
= [(3h² + 5h + 6xh)/h]
= [h(3h + 6x + 5)/h]
= (3h + 6x + 5)
That is, [{f(x + h) - f(x)}/h] will be equal to (3h + 6x + 5).
Function: In Mathematics, a function is an operator, which when fed with particular inputs, will perform a fixed set and sequence of operations on the input, and produce particular outputs.Expression: Expressions are mathematical statements that consist of a minimum of two terms containing numbers or variables, or both, connected by operator(s) in between, and formed as per arithmetic rules.To learn more about Functions and Expressions, click on the link below.
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Solve for n.
−2(n − 4.5) > 11
n > 1
n < 1
n > −1
n < −1
Answer:
D. n < −1
Step-by-step explanation:
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