Given
[tex]y=6x²+10x-3[/tex]Find
derivatives using increment method.
Explanation
Given
[tex]y=6x²+10x-3[/tex]replace x and y by
[tex]\begin{gathered} x+\Delta x \\ y+\Delta y \end{gathered}[/tex]so ,
[tex]\begin{gathered} y+\Delta y-y=6(x+\Delta x)^2+10(x+\Delta x)-3-(6x^2+10x-3) \\ \Delta y=6x^2+6\Delta^2x^2+12\Delta x^2+10x+10\Delta x-3-6x^2-10x+3 \\ \Delta y=12\Delta x^2+6\Delta^2x^2+10\Delta x \\ \end{gathered}[/tex]now divide by
[tex]\Delta x[/tex]so ,
[tex]\begin{gathered} y^{\prime}=\frac{12\Delta x^2+10\Delta x+6\Delta^2x^2}{\Delta x} \\ \\ y^{\prime}=12x+10+6\Delta x \end{gathered}[/tex]now taking limit
[tex]\begin{gathered} \lim_{\Delta x\to0}y^{\prime}=\lim_{\Delta x\to0}(12x+10+6\Delta x) \\ \\ y^{\prime}=12x+10 \end{gathered}[/tex]Final Answer
Therefore , the derivative of the function using increment method is 12x + 10
right answer gets brainlist pls help asap
Answer:
6 units
Step-by-step explanation:
count the units between the two points
square root 5(square root10+square root 2
Answer:
(Decimal: 10.233345)
Step-by-step explanation:
√5(√10+√2
√5(√10+√2)
=√10+5√2(Decimal: 10.233345)
scores on the wechsler adult intelligence scale for the age group from 20 to 34 are approximately normally distributed with mean 110 and standard deviation 15. how high must a person score to be in the top 10%? (hint: that means, 90% of adults in that age range have a score lower than this cut-off score.)
A person must score at least 129.24 to be in the top 10%.
Using the z-table, find the z-score that corresponds to the 90% probability.
probability = 0.90
z-score = 1.2825
For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.
The z-score can be calculated using the formula below.
z-score = (x – μ) / σ
where x = individual data value
μ = mean
σ = standard deviation
Plug in the values and find the score to be in the top 10%, x.
z-score = (x – μ) / σ
1.2825 = (x – 110) / 15
x – 110 = 19.2377
x = 129.24
Learn more about normal distribution here: https://brainly.com/question/4079902
#SPJ4
Find the inverse of:f (x) = 4x3 + 1
1. replace f(x) with y
[tex]y=4x^3+1[/tex]2. Replace every x with a y and replace every y with an x
[tex]x=4y^3+1[/tex]3. Solve for y:
[tex]\begin{gathered} 4y^3=x-1 \\ y^3=\frac{x-1}{4} \\ y=\sqrt[3]{\frac{x-1}{4}} \end{gathered}[/tex]4. Replace y with f−1(x):
[tex]f^{-1}(x)=\sqrt[3]{\frac{x-1}{4}}[/tex]Nutrition: A cat food manufacturer uses fish and beef by-products. The fish contains 12 g of protein and 3 g of fat per ounce. The beef contains 6 g of protein and 9 g of fat per ounce. Each can of cat food must contain at least 60 g of protein and 45 g of fat. Find a system of inequalities that describes the possible number of ounces of fish and beef that can be used in each can to satisfy these minimum requirements. Graph the solution set. Find its vertices.
A cat food manufacturer uses fish and beef by-products.
Let the number of ounces of fish = x
Let the number of ounces of beef = y
The fish contains 12 g of protein and 3 g of fat per ounce.
fish = 12x + 3y
The beef contains 6 g of protein and 9 g of fat per ounce.
Each can of cat food must contain at least 60 g of protein and 45 g of fat.
so,
[tex]\begin{gathered} 12x+6y\ge60 \\ 3x+9y\ge45 \end{gathered}[/tex]Beside the above inequalities both of x and y must be greater than 0
so, the system of inequalities will be:
[tex]\begin{gathered} x\ge0 \\ y\ge0 \\ 12x+6y\ge60 \\ 3x+9y\ge45 \end{gathered}[/tex]The following figure represents the solution of the system:
As shown in the graph, the vertices are:
( 0 , 10 ) , (3 , 4 ) , ( 15 , 0 )
A dinner set was marked $ 532 and a discount of 12% was offered on its marked price. Find the sale price of the dinner set.
Answer:
$468.16
Step-by-step explanation:
answer key
which expression is equivalent to (2x^2+4x-7)(x-3) pls help soon
Answer:
Since you do not have any answer choices, I will step-by-step solve the equation for you. Typically what happens with problems like this is the answer choices will match the work when solving. So, pay attention to my scratch-work and if any answers match the answer choices, then that is most likely the correct answer. (Hint: the solution to the equation is most likely the correct answer)
Write the equation:
(2x^2 + 4x – 7)(x – 3)
Simplify and Distribute:
(2x^2 + 4x – 7)(x – 3)
2(x – 3)^2 + 4x(x – 3) – 7(x – 3)
2x^3 – 6x^2 + 4x
(x – 3) – 7(x – 3)
2x^3 – 6x^2 + 4
x^2 – 12x – 7(x – 3)
2x^3 – 6x^2 + 4
x^2 – 12x – 7x + 21
Combine Like Terms:
2x^3 – 2x^2 – 12x – 7x + 21
2x^3 – 2x^2 – 19x + 21
Solution:
2x^3 – 2x^2 – 19x + 21
Hope that helps! Have an amazing rest of your day! Please consider awarding me the Brainliest! :)
How do properties of interger exponents help you write equivalent expressions
Answer:
The product of powers property says that when we multiply powers with the same base, we just have to add the exponents. So, xaxb = x(a + b). As you can see, we keep the base the same and add the exponents together.
Step-by-step explanation:
Select the correct answer from each drop-down menu.
Triangle XYZ, with vertices X(-2, 0), Y(-2, -1), and Z(-5, -2), undergoes a transformation to form triangle X′Y′Z′, with vertices X′(4, -2), Y′(4, -3), and Z′(1, -4). The type of transformation that triangle XYZ undergoes is a
.
Triangle X′Y′Z′ then undergoes a transformation to form triangle X′′Y′′Z′′, with vertices X″(4, 2), Y″(4, 3), and Z″(1, 4). The type of transformation that triangle X′Y′Z′ undergoes is a
.
Answer:
1. (x+6, y-2)
2. reflection across the x-axis
Step-by-step explanation:
The triangle on the right is a scaled copy of the triangle on the left. Identify the scale factor. Express your answer as a fraction in simplest form.
The identified scale factor of the triangles is 71 / 37.
How to find the scale factor of similar triangles?Scale factor is the ratio of corresponding sides on two similar figures.
The triangles are similar. Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.
Therefore, let's identify the scale factor of the triangles.
The triangle on the right is a scale copy of the triangle on the left.
Hence,
scale factor = 71 / 37 = 71 / 37
Therefore, the scaled factor of the triangles in fraction form is 71 / 37
learn more on triangle here: https://brainly.com/question/28752536
#SPJ1
find the volume of the rectangular prism. need an integer or decimal.
We will have the following:
[tex]V=(\frac{9ft\ast9ft}{2})(12ft)\Rightarrow V=486ft^3[/tex]So, the volume is 486 ft^3.
please help please pleaseeee
Answer: x=59
Step-by-step explanation:
360-296=(x-24)+29
64=x+5
59=x
a binomial experiment with probability of success and trials is conducted. what is the probability that the experiment results in or more successes? do not round your intermediate computations, and round your answer to three decimal places. (if necessary, consult a list of formulas.)
The probability that the experiment results in 9 or more successes = 0.0676
A binomial distribution is given by,
P(X = x) = ⁿCₓ pˣ (1-p)ⁿ⁻ˣ ,
where p is the probability of success and x is the random variable for success in n trials.
A binomial experiment has only two outcomes- success or failure.
Here, the number of trials, n = 10
Probability of success = 0.63
The probability for 9 or more success = P( X = 9, 10)
= P (X = 9) + P(X = 10)
So P( X = 9) = ¹⁰C₉ (0.63)⁹ (1-0.63)¹⁰⁻⁹
= 10 x 0.0156 x 0.37
= 0.05772
and P(X = 10) = ¹⁰C₁₀ (0.63)¹⁰(1-0.63)¹⁰⁻¹⁰
= 1 x 0.009849 x 1
= 0.009849
Hence probability for 9 or more success = 0.05772 + 0.009849
= 0.067569
= 0.0676
The question is incomplete. Find the complete question below:
A binomial experiment with probability of success 0.63 and 10 trials is conducted. What is the probability that the experiment results in 9 or more successes? Do not round your intermediate computations, and round your answer to three decimal places. (If necessary, consult a list of formulas.)
Learn more about binomial experiment at https://brainly.com/question/9325204
#SPJ4
a researcher selects a sample and administers a treatment to the individuals in the sample. if the sample is used for a hypothesis test, what does the alternative hypothesis (h1) say about the treatment?
The alternative hypothesis(h1) says that the treatment causes a change in the scores.
What is a hypothesis test?
In statistics, hypothesis testing involves putting an analyst's presumption about a population parameter to the test. The data type used and the study's purpose will determine the methodology the analyst uses.
Using sample data, hypothesis testing determines whether a claim is plausible. These data could originate from a broader population or a process that creates data.
Hence, the alternative hypothesis(h1) says that the treatment causes a change in the scores
To learn more about hypothesis tests from the given link
https://brainly.com/question/28273511
#SPJ4
Hello may you please help me
The value of x for the given triangle is 30°.
According to the question,
We have the following information:
We have a triangle.
Three angles of the triangle are x°, 65° and (x+55)°.
We know that the sum of all the three angles of a triangle is 180°.
So, the sum of these angles will be 180°.
Now, adding three angles:
x° + 65° + (x+55)° = 180°
(2x+120)° = 180°
2x = 180-120
2x = 60
x = 60/2 (2 was in the multiplication on the left hand side. So, it is in the division on the left hand side.)
x = 30°
Hence, the value of x in the angles of the given triangle is 30°.
To know more about value here
https://brainly.com/question/14316282
#SPJ1
Consider the function y=(x−1)2+3.(a) Give the coordinates of the vertex of the graph of the function.(b) Graph the function on a window that includes the vertex.
Given function is
[tex]y=(x-1)^2+3[/tex]The vertex of the graph is at (1,3).
Complete the point-slope equation of the line through (-5,7)(−5,7)left parenthesis, minus, 5, comma, 7, right parenthesis and (-4,0)(−4,0)left parenthesis, minus, 4, comma, 0, right parenthesis.
Use exact numbers.
The point-slope equation of this line is y - 7 = -7(x + 5).
What is the point-slope form?Mathematically, the point-slope form of a line is given by this equation:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.Next, we would determine the slope of this line by using this formula:
Slope, m = Δy/Δx
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Substituting the given parameters into the formula, we have;
Slope, m = (0 - 7)/(-4 + 5)
Slope, m = -7/1
Slope, m = -7
At point (-5, 7), the point-slope equation of the line is given by:
y - y₁ = m(x - x₁)
y - 7 = -7(x - (-5))
y - 7 = -7(x + 5)
Read more on slope here: https://brainly.com/question/7748981
#SPJ1
Complete Question:
Complete the point-slope equation of the line through (-5, 7) and (-4, 0). Use exact numbers.
Evaluate the function.
f(x) = x² + 6x - 9
-
Find f(7)
Answer:
82
Step-by-step explanation:
Since x=7, you would put that value into the equation. i.e put that value, of 7, instead of x.
x² + 6x - 9
7² + 6(7) - 949 + 42 - 982x^2+5x−21=0
complete the square
The solutions to the quadratic equation using completing the square method are x = -(√109)/2 - 5/2 and x = (√109)/2 -5/2.
What is the solution to the quadratic equation?
Given the quadratic equation in the question;
x² + 5x - 21 = 0x = ?To solve using completing the square method, first add 21 to both sides
x² + 5x - 21 = 0
x² + 5x - 21 + 21 = 0 + 21
x² + 5x = 21
Next, create a trinomial square on the left side of the equation, determine the value that is equal to the square of half of b which is 5.
( b/2 )² = ( 5/2 )²
Now, add ( 5/2 )² to both sides of the equation
x² + 5x + ( 5/2 )² = 21 + ( 5/2 )²
Simplify
x² + 5x + 25/4 = 21 + 25/4
Add 21 and 25/4
x² + 5x + 25/4 = 109/4
Factor the perfect trinomial.
x² + 5x + 25/4 = 109/4
( x + 5/2 )² = 109/4
Solve for x by taking the square root of both sides.
x + 5/2 = ±√( 109/4 )
x = -5/2 ±√( 109/4 )
x = ±(√109)/2 -5/2
x = -(√109)/2 - 5/2, (√109)/2 -5/2
Therefore, the solutions to are x = -(√109)/2 - 5/2 and x = (√109)/2 -5/2.
Learn more about completing the square method here: https://brainly.com/question/12356597
#SPJ1
Round 34,582 to the nearest thousand.
Answer:
35000
Step-by-step explanation:
So the number is 34582
now look at the hundreds
if it is 5 or over then we add a thousand to and subtract what ever the lower than thosand
and in this case it is 5 so we round UP
and now we have 35000
The answer is 35,000.
To round to the nearest thousand, we look at the last three digits. If these digits are 500 or greater, then we round the thousands digit up, and if they are less than 500, then we round down, keeping the thousand's digit the same.
Since in this case the last three digit consists of 582 which is greater than 500 so we round the thousands digit up i.e. from 4 to 5 in this case.
To learn more about rounding off visit : brainly.com/question/2100597
Half of the smaller of two consecutive even integers is equal to two more than the larger integer find the smaller even integer
SOLUTION
Let the first even integer be 'a'.
Let the second integer be (a + 2) since the second is a consecutive even integer.
Half of the smaller (i.e. a) is equal to two more than the larger (i.e. a + 2). In other words:
[tex]\frac{a}{2}=(a+2)+2[/tex]Evaluate for a
Simplify
[tex]\begin{gathered} \frac{a}{2}=a+2+2 \\ \frac{a}{2}=a+4 \end{gathered}[/tex]Multiply all through by 2
[tex]\begin{gathered} 2\times\frac{a}{2}=2\times a+2\times4 \\ a=2a+8 \end{gathered}[/tex]Collect like terms
[tex]\begin{gathered} -8=2a-a \\ -8=a \\ \therefore a=-8 \end{gathered}[/tex]Hence, the smaller even integer is
[tex]-8[/tex]The number of alligators in a wildlife preserve inLouisiana can be shown with the exponential functionf(0) = 3450(1.04)++! Find the average growth rate ofchange from the 4th year to the 7th year.
Given data:
The given function is f(x)=3450(1.04)^(x+1).
The
Heraldo starts a push-up challenge, and on the first day does 10 pushups, the second day he does 13, the third day he does 16, and so on.
Write the recursive definition for this sequence, and then find how many pushups he should do on the 20th day, if he continues.
Answer:
Day 20 = 67 pushups (64+3)
Step-by-step explanation:
Day 1 = 10 pushups Day 2 = 13 pushups (10+3) Day 3 = 16 pushups (13+3)
He does three more pushups each day.
So day 4 = 19 pushups (16+3)
Day 5 = 22 pushups (19+3)
Day 6 = 25 pushups (22+3)
Day 7 = 28 pushups (25+3)
Day 8 = 31 pushups (28+3)
Day 9 = 34 pushups (31+3)
Day 10 = 37 pushups (34+3)
Day 11 = 40 pushups (37+3)
Day 12 = 43 pushups (40+3)
Day 13 = 46 pushups (43+3)
Day 14 = 49 pushups (46+3)
Day 15 = 52 pushups (49+3)
Day 16 = 55 pushups (52+3)
Day 17 = 58 pushups (55+3)
Day 18 = 61 pushups (58+3)
Day 19 = 64 pushups (61+3)
Day 20 = 67 pushups (64+3)
Leo wants to buy two pairs of shoes. He found the shoes at two different stores at different prices and discounts. Store X is offering 10% off the price of the shoes. Store Y is offering $6 off the price of the shoes. For each shoe price listed in the table, indicate which store offers the lowest discounted price. Select the correct answer in each row.
The correct option regarding the discounts is given as follows:
Store Z has the best sale price of $28.
How to calculate the discount?The discount can be a percentage or an amount off, and the calculations are explained as follows:
Percentage: the original price is multiplied by the subtraction of one and the equivalent decimal of the discount.Amount off: the equivalent amount is given by the original amount subtracted by the amount off. ($6 off, the amount is subtracted by $6).Considering the discount plans and the original price of $35, the discounted prices in this problem are as follows:
Store X: 0.85 x 35 = $29.75.Store Y: 35 - 5 = $30.Store Z: 4/5 x 35 = 0.8 x 35 = $28.Hence the correct statement is given as follows:
Store Z has the best sale price of $28.
Missing information
The complete problem is:
Leo wants to buy some shoes. He found the shoes at three different stores for a price of $35. The stores are each having a sale:
Store X is offering 15% off the price of the shoes.Store Y is offering $5 off the price of the shoes.Store Z is offering a ⅕ discount off the price of the shoes.Which statement about the sale price of these shoes is true?
Store X has the best sale price of $20.Store Z has the best sale price of $28.Store Y has the best sale price of $30.More can be learned about discounts at https://brainly.com/question/7459025
#SPJ1
I need to find the value of x in this figure. I need to do it so that whatever x is, it can be substituted into the expressions
Remember: all the angles of a triangle = 180 degrees and other geometry stuff
please help :)
Answer:
x = 42
see below for the angle measures.
Step-by-step explanation:
The angle marked 2x - 9 is sort of outside the triangle. It is called an exterior angle. The other two angles are called remote interior angles. "Remote" means that they are away from the exterior angle. When you have this set up, the two remote angles added together EQUAL the exterior one.
x+5 + 28 = 2x - 9
x + 33 = 2x - 9
Subtract x.
33 = x - 9
Add 9.
42 = x
So x = 42° which if you put that back into the expressions you can find the measures of the one remote interior angle (the other we know is 28°) and the exterior angle.
remote int angle:
x+5
= 42 + 5
= 47°
Exterior angle:
2x - 9
= 2(42) - 9
= 84 - 9
= 75°
(You can also then find the completely unmarked angle which is 180°- 75° which is 105°)
a marksman has a probability of 0.268 for hitting a certain long-range target. what is the probability that it takes 5 shots for the marksman to hit the long-range target? (round your answer to three decimal places, if necessary.)
The probability of the marksman hitting the long-range target in 5 shots is 0.1429.
The geometric distribution is a Bernoulli experiment that predicts the likelihood of the first success after a certain number of failures. Negative-binomial and binomial distributions are two different forms of Bernoulli trials.
P = 0.268
x = 5
Use the geometric probability mass function below to calculate the probability:
P(X = x) = [tex](1 - P)^{(x-1)}[/tex]× P
P(X = x) = [tex](1 - 0.268)^{(3-1)}[/tex]× 0.268
P(X = x) = 0.1429
The probability that it takes 5 shots for the marksman to hit the long-range target is 0.1429.
Learn more about binomial distributions at
https://brainly.com/question/28823380?referrer=searchResults
#SPJ4
If cosA is equal to sin65 find the value of A
Answer:
A = 25Step-by-step explanation:
We know that:
cos A = sin (90 - A)Apply it to the given to get:
90 - A = 65A = 90 - 65A = 25Answer fast
Which of the following is used to identify outliers in a set of data?
1.5(IQR)
1.5(range)
2(mean)
2(median)
The Interquartile range i.e 1.5 (IQR) is used to identify outliers in a set of data which is the correct answer would be option (A).
What is the Interquartile range (IQR)?We may build up a "fence" outside of Q1 and Q3 by using the Interquartile range (IQR) method of spotting outliers. Outliers are values that fall outside of this range.
To construct this barrier, we take 1.5 times the IQR, deduct it from Q1, and add it to Q3. This provides us with the lowest and maximum fence posts against which we will compare each observation.
Outliers are observations that are greater than 1.5 IQR below or above Q1. Minitab's default strategy for identifying outliers is this.
Therefore, the Interquartile range (IQR) is used to identify outliers in a set of data.
Hence, the correct answer would be option (A).
To learn more about the Interquartile range (IQR) here:
brainly.com/question/4102829
#SPJ1
Analysis questions: 1. Find the slope of the line that goes through donuts 1-12. Find the slope of the line that goes from donuts 13-25. Are they the same or not?| 2. What if we only buy in amounts of baker's dozens? Is there a line for those? What points are on this line? What is the slope? 3. How much money do you save with the baker's dozen deal on 30 donuts? Where can this amount be seen on the graph?
1. Find the slope of the line that goes through donuts 1-12.
take the points
(1, 1.05) and (2, 2.10)
m=(2.10-1.05)/(2-1)
m=1.05/1
m=1.05
Find the slope of the line that goes from donuts 13-25
take the points
(14,14.05) and (15, 15.10)
m=(15.10-14.05)/(15-14)
m=1.05/1
m=1.05
so
The slope is the same
2. What if we only buy in amounts of baker's dozens? Is there a line for those? What points are on this line? What is the slope?
the points are
(13,13.00) and (24,24.55)
m=(24.55-13.00)/(24-13)
m=11.55/11
m=1.05
the equation in point slope form is
m=1.05
(x1,y1)=13,13)
y-13=(1.05)(x-13)
y-13=1.05x-13.65
y=1.05x-0.65
For x=30 donuts
y=1.05(30)-0.65
y=30.85
therefore
Do you save $0.65
Ciara how’s it going with the total area of (3x^2+4x) Square feet.What is the length and the width of the garden? explain
Ok, since we know that the area of a rectangle is given by the product of the width times the length, and the area is given to us by the function 3x^2+4x, we then factor the function of area:
[tex]3x^2+4x=x(3x+4)[/tex]By the previous definition, we will have that the lenght of the garden will be 3x+4 and the widht of the garden will be x.