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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Hi, can you help me answer this question please, thank you!
We were given the following information:
Sample of men = 80, 45% of the sample owned cats (36 men owned cats)
Sample of women = 80, 55% of the sample owned cats (68.75 women owned cats)
The significance level is 0.025
We will calculate the test statistics as shown below:
[tex]undefined[/tex]is 0.49 a rational or irrational number? Explain how you know. PLS HELP
For the polynomial below, -1 is a zero. g(x) = x2-3x² + 25x +29 Express g (x) as a product of linear factors.
Hello there. To solve this question, we'll have to remember some properties about polynomials.
We want to express the following 3rd degree polynomial as a product of linear factors:
[tex]g(x)=x^3-3x^2+25x+29[/tex]Knowing that -1 is a zero.
For this, there are two ways of determining the other roots and hence the linear factors.
Remember that a polynomial is written as a product of linear factors if
[tex]f(x)=a(x-x_1)(x-x_2)\cdots[/tex]Where x1, x2 ... are the roots of the polynomial.
It is also called the canonical form of the polynomial.
First way: divide g(x) by (x - (-1)), that is (x + 1)
We'll use the long division method for polynomials:
At the top of x + 1 in the diagram below, we add the terms that, when multiplied by the bottom expression, gives us a term that can be subtracted from g(x).
We have a x³ factor, so we want to multiply it first by x² in order to cancel out:
Now we have a -4x² factor, so we multiply it by -4x in order to cancel out:
Finally, multiply it by a 29 in order to cancel the first 29x term:
Hence we say that
[tex]x^3-3x^2+25x+29=(x+1)(x^2-4x+29)[/tex]Now, we want to factorize the quadratic expression in the right hand side, writing it as a product of linear factors as well:
As said before, we can take the roots of the expression and write it in canonical form. Since it is a quadratic expression, we have this easier formula to find the roots:
[tex]ax^2+bx+c=0\Rightarrow x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]Plugging a = 1, b = -4 and c = 29, we'll get
[tex]\begin{gathered} x=\dfrac{-(-4)\pm\sqrt{(-4)^2-4\cdot1\cdot29}}{2\cdot1} \\ \\ x=\dfrac{4\pm\sqrt{16-116}}{2}=\dfrac{4\pm\sqrt{-100}}{2} \\ \end{gathered}[/tex]Notice the radical is a negative number, hence it cannot be factored in terms of real linear factors.
We say that for an expression
[tex]x^2+\beta x+\gamma[/tex]It is not reducible over R (real numbers) if
[tex]\beta^2-4\gamma<0[/tex]Therefore the final answer is:
[tex](x+1)(x^2-4x+29)[/tex]We could also use the following method to find this answer:
It is called the Horner-Ruffini method, that we dispose the coefficients and the roots in the following manner
Multiply the first coefficient by the root and add it to the second number in the line. Repeat the process until you reach the last number.
Therefore the result of this division is the polynomial:
[tex]x^2-4x+29[/tex]As we found before.
En3. A financial advisor is paid $500 per week plus a 4% commission on all sales over $800. During oneweek, his total sales were $1,330. Find his gross earnings for the week..$541.20$531.20$521.20$551.20
For this problem we know that the salary per week is 500 and he gets a commission of 4% for each sale over 800. During one week the total sales are 1330 and we want to estimate the gross earnings for the week.
Taking in count the info given we can set up the following equation for the total amount recieved:
[tex]A=500+0.04S[/tex]Where A represent the amount recieved and S the sales. For this case S=1330 and replacing we got:
[tex]A=500+0.04\cdot1330=553.2[/tex]Work these out mentally2/5 of 10 mm3/4 of 40 km 5/6 of $12
This can be solved by multiplying.
- 2/5 of 10 mm
[tex]\frac{2}{5}\times10=\frac{20}{5}=4[/tex]Answer: 4 mm
- 3/4 of 40 km
[tex]\frac{3}{4}\times40=\frac{40\times3}{4}=\frac{120}{4}=30[/tex]Answer: 30 km
- 5/6 of $12
[tex]\frac{5}{6}\times12=\frac{5\times12}{6}=\frac{60}{6}=10[/tex]Answer: $10
Find the cube number
7 12
20
25
27
Answer:
712 = 360944128
20 = 8000
25 = 15625
27 = 19683
Step-by-step explanation:
A cube number is a number that is the product of three numbers which are the same. In other words, if you multiply a number by itself and then by itself again, the result is a cube number.
point a is to the left of point B on the horizontal number line what could be the valves of point a and point B
Answer:
If point A is to the left of point B, point A is less than B. Therefore, the values of point A and B could be:
A = 7 and B = 9
A = -8 and B = -5
A = -10 and B = 2
Because 7 is less than 9, -8 is less than -5, and -10 is less than 2.
Which of the following polynomials has an even degree and a negative leading coefficient?
The function has an even degree if the the number of turns is an odd number.
The function has a negative leading coefficient if the behavior of the graph goes to the negative infinity.
From the choices, only this graph satisfied the conditions.
The graph has 3 turns (an odd number)
and it goes to the negative infinity.
Claire bought 5 kg of apples and 2 kg of bananas and paid altogether $22 Dale bought 4 kg of apples and 6 kg of bananas and paid altogether $33 Use matrices to find the cost of 1 kg of bananas
Answer:
$3.5
Explanation:
Let the cost of 1 kg of apples = x
Let the cost of 1 kg of bananas =y
Claire bought 5 kg of apples and 2 kg of bananas and paid altogether $22.
[tex]5x+2y=22[/tex]Dale bought 4 kg of apples and 6 kg of bananas and paid altogether $33.
[tex]4x+6y=33[/tex]We set up the system of linear equations as a matrix below:
[tex]\begin{bmatrix}{5} & {2} & \\ {4} & {6} & {}{}\end{bmatrix}\begin{bmatrix}{x} & \\ {y} & {}{}\end{bmatrix}=\begin{bmatrix}{22} & \\ {33} & {}{}\end{bmatrix}[/tex]We then solve for the variables x and y as follows.
[tex]\begin{gathered} \begin{bmatrix}{x} & \\ {y} & {}{}\end{bmatrix}=\begin{bmatrix}{5} & {2} & \\ {4} & {6} & {}{}\end{bmatrix}^{-1}\begin{bmatrix}{22} & \\ {33} & {}{}\end{bmatrix} \\ =\frac{1}{30-8}\begin{bmatrix}{6} & {-2} & \\ {-4} & {5} & {}{}\end{bmatrix}\begin{bmatrix}{22} & \\ {33} & {}{}\end{bmatrix} \\ =\frac{1}{22}\begin{bmatrix}{6} & {-2} & \\ {-4} & {5} & {}{}\end{bmatrix}\begin{bmatrix}{22} & \\ {33} & {}{}\end{bmatrix} \end{gathered}[/tex]We proceed to simplify further.
[tex]\begin{gathered} =\begin{bmatrix}{\frac{6}{22}} & {-\frac{2}{22}} & \\ {-\frac{4}{22}} & {\frac{5}{22}} & {}{}\end{bmatrix}\begin{bmatrix}{22} & \\ {33} & {}{}\end{bmatrix} \\ =\begin{bmatrix}{\frac{6}{22}\times22-\frac{2}{22}\times33} & {} & \\ {\frac{-4}{22}\times22+\frac{5}{22}\times33} & & {}{}\end{bmatrix} \\ =\begin{bmatrix}{6-3} & {} & \\ {-4+7.5} & & {}{}\end{bmatrix} \\ =\begin{bmatrix}{3} & {} & \\ {3.5} & & {}{}\end{bmatrix} \end{gathered}[/tex]Therefore:
x=3 and y=3.5.
The cost of 1 kg of bananas is $3.5.
express (x-3)² as a trinomial in standard form
We will write it as follows:
[tex](x-3)^2=(x-3)(x-3)=x^2-3x-3x+9[/tex][tex]=x^2-6x+9[/tex]the difference b and 2 is less than 25
We are given the following word problem.
"The difference of b and 2 is less than 25"
Let us convert t
Write a linear function f with the values f(-1) = -3 and f (2) = 6. A function is f(x) =
Answer:
The linear equation is;
[tex]f(x)=3x[/tex]Explanation:
Given that the function f(x) is a linear function;
[tex]f(x)=mx+b[/tex]let us derive the values of m and b.
At x=-1, f(-1)=-3;
[tex]\begin{gathered} f(-1)=m(-1)+b=-3 \\ -m+b=-3\text{ --------1} \end{gathered}[/tex]At x=2, f(2)=6;
[tex]\begin{gathered} f(2)=m(2)+b=6 \\ 2m+b=6\text{ ---------2} \end{gathered}[/tex]subtract equation 1 from 2;
[tex]\begin{gathered} 2m-(-m)+b-b=6-(-3) \\ 3m=9 \\ m=\frac{9}{3} \\ m=3 \end{gathered}[/tex]let's substitute the value of m into equation 2;
[tex]\begin{gathered} 2m+b=6 \\ 2(3)+b=6 \\ 6+b=6 \\ b=6-6 \\ b=0 \end{gathered}[/tex]Therefore, since we have the values of m and b we can substitute to get the equation f(x);
[tex]\begin{gathered} f(x)=mx+b \\ f(x)=3x+0 \\ f(x)=3x \end{gathered}[/tex]The linear equation is;
[tex]f(x)=3x[/tex]Zena's Z-score on the chemistry final was 0.65. If the class mean on the final was 78, the the standard deviation was 12, and the distribution was normal, what was Zena's raw score?
Zena's raw score in the chemistry test is 85.8
How to determine the raw score of the test?From the question, the given parameters are
Mean score of the class = 78Standard deviation of the class = 12z-score of the test = 0.65The z-score of the distribution is calculated using the following z-score formula
z = (raw score - mean value)/standard deviation
Substitute the given parameters in the above equation
So, we have the following equation
0.65 = (Raw score - 78)/12
Cross multiply in the above equation
Raw score - 78 = 7.8
Add 78 to both sides
Raw score = 78 + 7.8
Evaluate
Raw score = 85.8
Hence, the raw score is 85.8
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Examine the structure of this question. state if there are infinitely many solutions, no solution, or one solution. If there is one solution, solve the equation and state the solution. If there are infinitely many solutions or no solution, justify why using the structure of the equation.
1) Examining this rational equation. And then solving it.
3/4(x-1) -1/2 =2(1-3x)
3/4x-3/4-1/2=2-6x
2)Combining like terms, let's isolate the x terms on the left side
3/4x+6x -3/4-1/2=2-6x+6x
3)To add these fractions let's calculate the Least Common Multiple of the denominators:
27/4x -5/4=2+0
27/4x -5/4+5/4=2+5/4
27/4x=13/4 Multiplying both sides by four to eliminate the fraction.
27x=13 Dividing both sides by 13 to get the value of x
x =13/27
S={13/27}
2) For those 2 equations there was a single solution for x. We can say that there is one solution to these equations.
(3.22x10^3)-(2.96x10^3)
The value of (3.22 - 2.96)×10³ is 0.26×10³.
What is scientific notation?We use scientific notation for writing large numbers in compact form.
Scientific notation is written in base multiplied by 10 raised to some power where 0 ≤base < 10 scientific notation also has an alternative name which is known as engineering notation.
We know when we have numbers in scientific notation with the same exponent value we can do arithmetic operations to the base.
∴ (3.22x10³) - (2.96x10³).
= (3.22 - 2.96)×10³.
= 0.26×10³.
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can you answer this ? Tavon has a gift card for $95 that loses $4 for each 30-day period it is not used. He has another gift card for $85 that loses $3.50 for each Ju-day period It Is not Write and solve an equation for the number or 30-dav periods unuthe value or the art cards will be equalD. What wil the value or each card be when thev have equa value?a. If x is the number of 30-day periods, then the equation can be used to find the number of 30-dav periods until the values of the aift(Type an equation. Use integers or decimals for any numbers in the equation.
If x is the number of 30 days period, the cost of gift cards after x days unused is,
[tex]95-4x[/tex]And for the second gift card:
[tex]85-3.50x[/tex]The equation for x is,
[tex]95-4x=85-3.50x[/tex]Solve the equation for x.
[tex]\begin{gathered} 95-4x=85-3.50x \\ 95-85=4x-3.50x \\ 10=0.5x \\ x=\frac{10}{0.5} \\ =20 \end{gathered}[/tex]So after 20 unused days, the value of cards are equal.
(b)
Substitute 20 for x in equation 95 - 4x to determine the value of the card.
[tex]\begin{gathered} 95-4\cdot20=95-80 \\ =15 \end{gathered}[/tex]So the value of cards, when they are equal, is $15.
Can someone help me with this, please?
if a (9,18) and b = (1,12) what is the length of ab
To calculate the lenght of AB we'll use the formula for distance between two points.
Remember that the disnatce between points
[tex]\begin{gathered} (x_1,y_1) \\ \text{and} \\ (x_2,y_2) \end{gathered}[/tex]is:
[tex]\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Using this, and the data given,
[tex]\begin{gathered} AB=\sqrt[]{(1_{}-9)^2+(12-18)^2} \\ \rightarrow AB=\sqrt[]{(-8)^2+(-6)^2} \\ \rightarrow AB=10 \end{gathered}[/tex]This way, the lenght of AB is 10 units
The percentage of adult height attained by a girl who is x years old can be modeled byf(x)=61+35 log (x-3)where x represents the girl's age (from 5 to 15) and f(x) represents the percentage of her adult height. Complete parts (a) and (b) below.a. According to the model, what percentage of her adult height has a girl attained at age 12?A girl has attained% of her adult height by age 12.(Do not round until the final answer. Then round to the nearest tenth as needed.)b. Why was a logarithmic function used to model the percentage of adult height attained by a girl from ages 5 to 15, inclusive?O A. Height increases rapidly at a young age, and then increases more slowly.OB. Height increases at a steady rate, regardless of one's age.OC. Height increases rapidly at a young age, stops increasing at a certain age, and then starts decreasing.O D. Height increases rapidly at a young age, and continues to increase even faster as one gets older.
The percentage of her adult height has a girl attained at age 12 is 94.39 %
The percentage of adult height attained by a girl who is x years old can be modeled by
f(x) = 61 + 35 log (x - 3)
where x represents the girl's age and f(x) represents the percentage of her adult height.
The percentage of her adult height a girl attained at age 12
f(12) = 61 + 35 log (12 -3) = 61 + 35 log 9
f(12) = 61 + 35 *0.954 = 94.39
Now, f(12) = 94.39 %
The logarithmic function used to model the percentage of adult height attained by a girl from ages 5 to 15, inclusive, Height increases rapidly at a young age and then increases more slowly.
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A line includes the point (7,5)has a slope of 1.What is its equation in slope intercept form?
Given:
Point( 7, 5)
x = 7 and y=5
slope(m) = 1
We need to first find the intercept.
Substitute x=7, y=5 and m=1 into y=mx + b and solve for intercept(b)
5 = 1(7) + b
5 = 7 + b
5 - 7 = b
-2 = b
Now, form the equation by substituting the value of the slope and intercept into y=mx + b
y = x - 2
Kevin needs to rent tables for his party. There will be 26 people at his party. Each table can seat 4 people. How many tables does Kevin need to order? Write a multiplication and division sentence that will help you answer the question. Use n for the unknown. __ x __ =___ ___÷___=____
Answer:
6.5
Step-by-step explanation:
Well if you do 4 x n=26 26/4=n
Subjects in an experiment take either an aspirin or a placebo as part of a study on heart attack prevention. The use of a placebo is an example of incorporating what aspect of successful experimental design?
Given the definitions of
blocking is the arranging of experimental units in groups (blocks) that are similar to one another
replication experiment is typically performed by obtaining test results on 20 samples of the same material and then calculating the mean, standard deviation, and coefficient of variation
randomized experiments are the experiments that allow the greatest reliability and validity of statistical estimates of treatment effects
in Control Experiment all variable factors have been kept constant and which is used as a standard of comparison to the experimental component in a controlled experiment
since
the sampling group could be either in group a or b (aspirin or placebo)
this expample is a blocking experiment
Correct answer
option A
4 sheets of paper cost's $14 how much will with be for 11 1/2 sheets of paper?
4 sheets of paper cost's $14 how much will with be for 11 1/2 sheets of paper?
we have that
Applying proportion
14/4=x/11 1/2
Convert 11 1/2 to an improper fraction
11 1/2=23/2
substitute
14/4=x/(23/2)
x=(23/2)*(14/4)
x=$40.25
therefore
teh answer is $40.25
Find the area of the shaded region.6005 cmA = [?] cm2Enter a decimal rounded to the nearest tenth.
To determine the area of the shaded region we first need to calculate the area of the whole circle, then we need to calculate the area of the circular sector of 60º, then finally we will calculate the area of the triangle and subtract the area of the triangle from the area of the circular sector, this will be the area of the part that isn't painted. Finally we can subtract the area that isn't painted by the area of the circle to determine the shaded region.
To calculate the area of the circle we will do as follows:
[tex]A_{\text{circle}}=\pi\cdot r^2=\pi\cdot5^2=25\cdot\pi=78.5[/tex]The circular sector can be calculated by the following expression:
[tex]A_{\text{sector}}=\frac{60\cdot\pi\cdot r^2}{360}=\frac{\pi\cdot5^2}{6}=\frac{25\cdot\pi}{6}=13.08[/tex]All of the sides of the triangle are equal, so we can use the following expression:
[tex]A_{\text{triangle}}=\frac{l^2\sqrt[]{3}}{4}=\frac{5\cdot\sqrt[]{3}}{4}=2.163[/tex]Now we will subtract the area of the triangle from the area of the sector to determine the area that isn't shaded.
[tex]A_{\text{blank}}=13.1-2.163=10.937[/tex]To finish we will subtract the area that isn't shaded from the area of the circle.
[tex]A_{\text{shaded}}=78.54-10.937=67.6[/tex]The area of the shaded region is 67.6 cm²
if 150 bars equals 350 hars, and 200 gars equals 25 hars, how many bars is 112.5 hars
Answer:
48.214 bars
Step-by-step explanation:
112.5 hars * (150 bars / 350 hars) = 48.214 bars
Is hollow a double consonant
Is HALLOW is double consonant. Yes, HALLOW is double consonant.
Given that,
We have to prove is HALLOW is double consonant.
What is double consonant?
A double consonant is a term that contains two consecutive consonant letters. For instance, the double consonant "nn" in tunnel. Words with a suffix, like "beginning," are usually found to have double consonants.
In conclusion, if a word has:
Syllable count: 2
Vowel one is short.
between each vowel, only one consonant sound is made.
Double that consonant after that! Like any other spelling rule in English literacy, this spelling strategy should be taught to pupils to help them learn how to double consonants together with other rules.
Here,
In hallow there is "ll"
Therefore, HALLOW is double consonant.
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Joy's investment of $3600 grows to $4800 in 48 weeks. What simple interest did she earn?
Answer:
answer
down
below
8 294 400
Statistics$ 9 45%ХIntFlorinchantemeraldataPositive and negative linear associations from scatter plots80/12so SanThe plot shown below describes the relationship between theaverage income in a city and the average rent for a 1-bedroomapartment in hat city.18001600100Average rent for a 10 dollars per month
Using the given scatter plot, let's describe the relationship between the average income in a city and the average rent for a 1-bedroom apartment in that city.
Here, the average income is represented on the x-axis while the average rent is represented on the y-axis.
Using the scatter plot, we can see that as the average income increases, the average rent also increases.
Since one variable increase as the other increases, and the points show a straight line pattern, we can say the relationship between them is a positive linear association.
Therefore, the relationship between the average income and the average rent for a 1-bedroom apartment in that city is a positive linear association.
ANSWER:
A. Positive linear association.
Answer to this question
Answer:
Either B or D
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
the general form of the absolute value function is
y = a | x - h | + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
here (h, k ) = (2, 3 ) then
y = a | x - 2 | + 3
to find a substitute any other point on the graph into the equation
using (1, - 1 ) , then
- 1 = a | 1 - 2 | + 3
- 1 = a | - 1 | + 3
- 1 = a + 3 ( subtract 3 from both sides )
- 4 = a
then
f(x) = - 4 | x - 2 | + 3
A certain group of women has a 0.97% rate of red/green color blindness. If a woman is randomly selected, what is the probability that she does not have red/green color blindness?
The probability that a randomly selected women does not have red/ green color blindness is 0.9903.
The probability of a woman has red/ green color blindness is,
P (Color blindness) = 0.0097.
The probability that a randomly selected women does not have red/ green color blindness is,
P (No Color blindness) = 1 - P (Color blindness)
= 1 - 0.0097
= 0.9903
Thus, the probability that a randomly selected women does not have red/ green color blindness is 0.9903.
Hence the probability that the women does not have red/green color blindness is 0.9903.
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