The critical points of the given function are p = 2 ± √13.
What are functions?A relation between a collection of inputs and outputs is known as a function.
A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
Each function has a range, codomain, and domain.
Critical function:
The key points are locations inside the function's domain where the function's nature changes.
The function stops increasing or decreasing at these places.
The function is: [tex]h(p)=\frac{p-2}{p^2+9}[/tex]
The derivative test will be applied here:
[tex]\begin{aligned}& \therefore h^{\prime}(p)=0 \\& \Rightarrow \frac{d}{d p}\left(\frac{p-2}{p^2+9}\right)=0 \\& \Rightarrow \frac{\frac{d}{d p}(p-2)\left(p^2+9\right)-\frac{d}{d p}\left(p^2+9\right)(p-2)}{\left(p^2+9\right)^2}=0 \\& \Rightarrow \frac{1 \cdot\left(p^2+9\right)-2 p(p-2)}{\left(p^2+9\right)^2}=0 \\& \Rightarrow \frac{-p^2+4 p+9}{\left(p^2+9\right)^2}=0 \\& \Rightarrow-p^2+4 p+9=0\end{aligned}[/tex]
Then,
[tex]\begin{aligned}& \Rightarrow p_{1,2}=\frac{-4 \pm \sqrt{4^2-4(-1) 9}}{2(-1)} \\& \Rightarrow p_{1,2}=\frac{-4 \pm \sqrt{52}}{-2} \\& \Rightarrow p_{1,2}=-\frac{-4 \pm \sqrt{52}}{2} \\& \Rightarrow p_{1,2}=-\frac{-4 \pm 2 \sqrt{13}}{2} \\& \Rightarrow p_{1,2}=2 \pm \sqrt{13}\end{aligned}[/tex]
Therefore, the critical points of the given function are p = 2 ± √13.
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Here is a data set:
1 2 3 3 4 4 4 4 5 5 6 7
What happens to the mean and standard deviation of the data set when the 7 is changed to a 70?
The mean of the dataset increases and the standard deviation of the data set increases when the 7 is changed to a 70
How to determine the effect of changing a data element?From the question, we have the following parameters that can be used in our computation:
Dataset: 1 2 3 3 4 4 4 4 5 5 6 7
As a general rule:
When a data item is changed (increased), the mean is increasedWhen a data item is changed (increased), the standard deviation is increasedWhen a data item is changed (decreased), the mean is decreasedWhen a data item is changed (decreased), the standard deviation is decreasedTo prove the above statements, the mean and the standard deviations are calculated using online calculators
So, we have
Original dataset
1, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 7
Mean = 4
Standard deviation = 1.58
New dataset
1, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 70
Mean = 9.25
Standard deviation = 18.36
This means that changing 7 to 70 would increase the mean and the standard deviation
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You select three cards from a deck of cards without replacement. The first card is a king, then queen, and lastly a jack. What is the probability you select those three cards in that order? Round answer to nearest hundredth and include percent sign.
PLEASE ASAP HURRY PLEASE
Mario set a goal to run 170 miles this month to prepare for a marathon. So far this month, he has run 85 miles. Write and solve an equation to show how many miles Mario has left to run this month to reach his goal.
A. m over 85 equals 170; m = 14,450 miles
B. m − 85 = 170; m = 255 miles
C. m + 85 = 170; m = 85 miles
D. 85m = 170; m = 2 miles
The equation to show how many miles Mario has left to run this month to reach his goal is C. m + 85 = 170; m = 85 miles.
How to illustrate the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement
In this situation, Mario set a goal to run 170 miles this month to prepare for a marathon and far this month, he has run 85 miles.
Let the remaining miles be m.
This will be illustrated as:
m + 85 = 170
Collect like terms
m = 170 - 85
m = 85
In conclusion, the correct option is C
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What is the percent of increase from 24 to 42?
Write your answer using a percent sign (%).
Submit
Answer:
42.86%
Explanation:
First, we subtract the two numbers.
42 - 24 = 18
Now we divide this to the original number.
18 / 42 = 0.4285714286
Multiply by 100:
42.85714286
So, the percent increase is approximately 42.86%
Show that if f is a function from S to T, where S and T are finite sets with |S| > |T |, then there are elements s₁ and s₂ in S such that f(s₁) = f(s₂), or in other words, f is not one-to-one.
The function f : S--> T is not a one to one function
Given :
f : S --> T
S and T are finite sets with |S| > |T|
To proof : f is not one-one function
Let us assume for the sake of contradiction that f is one to one function
Let n and m be positive integers such that |S| = n and |T| = m.
Note that these integers need to exist as S and T are finite sets
n > m
Let S = {s1 , . . . , sn} and T = { t1 , . . . , tm}
Without loss of generality , we can assume that f(si) = ti , for i = 1, 2, 3 ....
as each element needs to have a unique image ( since , f is one to one ) and we can rename the element t1 , . . . , tm if the order of the elements didnt match up the images.
Since , n > m we have a term sm+1 while we do not have a term t m+1 .
This implies that sm+1 needs to have a same image as some sk
f(sm+1) = f(sk) = tk
However , f(sm+1) = f(sk) = tk is then in contradiction with the fact that f is one-to-one.
Since , we derive a contradiction our assumption that f is one-to-one is incorrect and thus f is not one-to-one
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Draw a rectangle that has a golden ratio of its sides. Label the rectangle’s sides. Show how it has a golden ratio of the sides.
The golden ratio can be found using the following formula if we take x as the width, and y as the length of the rectangle:
[tex]\frac{y}{x} =\frac{x+y}{y} =1.618[/tex]
What is the golden ratio?
The golden ratio is a unique proportion between two values where the ratio of the two values equals the ratio of their sum to the bigger of the two values.
If we take a square of sides A,B,C,D.
Locate the midpoint of any one side of the square by bisecting it.
Connecting the midpoint (say) P to a corner of the opposite side.
Placing the compass on point P, and the width set to match the distance of P to one of the opposite sides, we draw an arc.
By extending the line where P sits, we see that the arc intersects at a point. say Q.
Extending the opposite line to P, we see that the point Q drawing parallel to the side, we see that it intersects at another point R.
Now, the rectangle AQRD is a golden ratio rectangle.
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Consider a rectangle that is inscribed with its base on the x-axis and its upper corners on the parabola y=C−x2, with C>0. What are the width and height that maximize the area of this rectangle? What is that maximal area?
The width of the rectangle that maximizes the area is C/2 and the height of the rectangle that maximizes the area is C/2. The maximal area of the rectangle is C2/4.
How do you determine a maximum area?The gap between a rectangle's length and width must be as small as possible for its area to be as large as possible. Therefore, the length in this scenario must be ceiling (perimeter / 4) and the width will be floor (perimeter /4). The greatest size of a rectangle with a given perimeter is therefore equal to ceiling(perimeter/4) * floor(perimeter/4)
What does "maximum area" mean?The average of the maximum areas of land planted to a specific crop over the Relevant Period is referred to as the "maximum area for a particular crop."
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what is the answer to this? solve for x
4x+4=24
Answer: x=5
Step-by-step explanation:
4x+4-4=24-4
4x=20
x=5
10. The total cost of shipping toys from a specific company is $5 plus $2.50 times the number of toys purchased
Answer:y=2.50x+5
Step-by-step explanation:
y=2.50x+5
that's all i can do with the information provided
If AC=26, find BC. in simplest radical from
BC=
The simplest radical from BC = 2/3.
Step by Step Explanation:AC = 26 and BC = 10.
Therefore, BC = 26 - 10 = 14.
we need to find the simplest radical from BC = 14. A simple radical is a fraction with no common factors other than 1 and itself. The simplest radical from BC = 14 is 2/3
What is simplest radical ?Simply put, simplifying a radical eliminates the need to find any further square roots, cube roots, fourth roots, etc. Additionally, it entails eliminating any radicals from a fraction's denominator.
The radical consists of three separate parts:
RadicandDegree SymbolThe Complete Question is :
AC = 26 and BC = 10 find the simplest radical from BC =
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Answer…………………………………….
what's the answer my friend needs help
The image by rotation of the triangle ABC with vertices A(x, y) = (8, - 9), B(x, y) = (5, - 4), C(x, y) = (7, - 1) is represented by vertices A'(x, y) = (- 9, - 8), B'(x, y) = (- 4, - 5) and C'(x, y) = (- 1, - 7). The transformation rule is R'(x, y) = (x · cos θ - y · sin θ, x · sin θ + y · cos θ).
How to find the transformation rule and image of a given figure
In this problem we have the case of triangle set on a Cartesian plane and that must be rotated 90° clockwise, the image can be found by using the following transformation rule:
R'(x, y) = (x · cos θ - y · sin θ, x · sin θ + y · cos θ)
Where:
x, y - Coordinates of the original point.
θ - Angle of rotation, in degrees.
If we know that A(x, y) = (8, - 9), B(x, y) = (5, - 4), C(x, y) = (7, - 1) and θ = - 90°, then the image of the triangle is:
A'(x, y) = (8 · cos (- 90°) - (- 9) · sin (- 90°), 8 · sin (- 90°) + (- 9) · cos (- 90°))
A'(x, y) = (- 9, - 8)
B'(x, y) = (5 · cos (- 90°) - (- 4) · sin (- 90°), 5 · sin (- 90°) + (- 4) · cos (- 90°))
B'(x, y) = (- 4, - 5)
C'(x, y) = (7 · cos (- 90°) - (- 1) · sin (- 90°), 7 · sin (- 90°) + (- 1) · cos (- 90°))
C'(x, y) = (- 1, - 7)
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a varies inversely as the square of b. If a is 1 when b is 3, find a when b is 5
The distance it takes to stop a car varies directly as the square of the speed of the car. If it takes 112 feet for a car traveling at 40 miles per hour to stop, what distance is required for a speed of 65 miles per hour?
*
a. The inverse variation relationship between a and b can be expressed as a = k/b^2, where k is a constant. We are given that a is 1 when b is 3, so we can substitute these values into the equation to find k: 1 = k/(3^2). Solving for k, we get k = 9.
Substituting this value of k back into the equation a = k/b^2, we can find a when b is 5: a = 9/(5^2) = 9/25 = 0.36. Therefore, a is 0.36 when b is 5.
b. To find the distance it takes for a car traveling at 65 miles per hour to stop, we can use the equation for direct variation: d = kv^2, where d is the distance, v is the speed, and k is a constant. We are given that it takes 112 feet for a car traveling at 40 miles per hour to stop, so we can substitute these values into the equation to find k: 112 = k(40^2). Solving for k, we get k = 0.0056.
Substituting this value of k back into the equation d = kv^2, we can find the distance it takes for a car traveling at 65 miles per hour to stop: d = 0.0056(65^2) = 2256 feet. Therefore, it takes 2256 feet for a car traveling at 65 miles per hour to stop.
The following is an incomplete flowchart proving that the opposite angles of parallelogram JKLM are congruent:
- Parallelogram JKLM is shown where segment JM is parallel to segment KL and segment JK is parallel to segment ML. - Extend segment JM beyond point M and draw point P, by Construction. - An arrow is drawn from this statement to angle MLK is congruent to angle PML, Alternate Interior Angles Theorem. An arrow is drawn from this statement to angle PML is congruent to angle KJM, numbered blank 1.
- An arrow is drawn from this statement to angle MLK is congruent to angle KJM, Transitive Property of Equality. - Extend segment JK beyond point J and draw point Q. - An arrow is drawn from this statement to angle JML is congruent to angle QJM, Alternate Interior Angles Theorem. - An arrow is drawn from this statement to angle QJM is congruent to angle LKJ, numbered blank 2. - An arrow is drawn from this statement to angle JML is congruent to angle LKJ, Transitive Property of Equality. - Two arrows are drawn from this previous statement and the statement angle MLK is congruent to angle KJM, Transitive Property of Equality to opposite angles of parallelogram JKLM are congruent.
Which reasons can be used to fill in the numbered blank spaces?
1Alternate Interior Angles Theorem 2Alternate Interior Angles Theorem
1Corresponding Angles Theorem 2Corresponding Angles Theorem 1Same-Side Interior Angles Theorem 2Alternate Interior Angles Theorem
1Same-Side Interior Angles Theorem 2Corresponding Angles Theorem
The reason (B) Corresponding Angles Theorem can be used to fill in the blanks in the given question.
What is a parallelogram?A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry.
A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.
So, extend segments JM and JK beyond points M and J, respectively, and draw points P and Q.
It is assumed that a parallelogram with segments JM parallel to segments KL and JK parallel to segments ML is presented.
Draw point P and extend segment JM past point M through construction.
Through construction also Continue segment JK draws point Q after point J.
Consequently, the Alternate Interior Angles Theorem ∠MLK≅∠PML and ∠JML≅∠QJM (1)
Then, the corresponding angles theorem ∠PML≅∠KJM and ∠QJM≅∠LKJ is applied (2)
Equations (1) and (2) and the transitive property of equality are used to create:
∠MLK≅∠KJM and ∠JML≅∠LKJ
As a result, the supplied parallelogram JKLM's opposite angles are congruent. So it was proved.
Therefore, the reason (B) Corresponding Angles Theorem can be used to fill in the blanks in the given question.
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Correct question:
The following is an incomplete flowchart proving that the opposite angles of parallelogram JKLM are congruent:
Parallelogram JKLM is shown where segment JM is parallel to segment KL and segment JK is parallel to segment ML. Extend segment JM beyond point M and draw point P, by Construction. An arrow is drawn from this statement to angle MLK is congruent to angle PML, Alternate Interior Angles Theorem. An arrow is drawn from this statement to angle PML is congruent to angle KJM, numbered blank 1. An arrow is drawn from this statement to angle MLK is congruent to angle KJM, Transitive Property of Equality. Extend segment JK beyond point J and draw point Q. An arrow is drawn from this statement to angle JML is congruent to angle QJM, Alternate Interior Angles Theorem. An arrow is drawn from this statement to angle QJM is congruent to angle LKJ, numbered blank 2. An arrow is drawn from this statement to angle JML is congruent to angle LKJ, Transitive Property of Equality. Two arrows are drawn from this previous statement and the statement angle MLK is congruent to angle KJM, Transitive Property of Equality to opposite angles of parallelogram JKLM are congruent.
Which reasons can be used to fill in the numbered blank spaces?
a. Alternate Interior Angles Theorem
b. Corresponding Angles Theorem
c. Same-Side Interior Angles Theorem
d. Same-Side Interior Angles Theorem
A standard normal distribution has the following characteristics O the mean and the variance are both equal to 1 O the mean and the variance are both equal to 0 O the mean is equal to the variance the mean is equal to 0 and the variance is equal to 1 the mean is equal to the standard
A standard normal distribution's characteristics are its mean is equal to 0 and the standard deviation is 1. Thus, the variance is equal to 1.
What is a standard normal distribution?A normal distribution that has a mean value of 0 and a standard deviation or a variance of 1 is said to be a standard normal distribution.
I.e., μ = 0 and σ² = 1
This is also called z-distribution.
Calculation:A standard normal distribution has μ = 0 and σ² = 1.
So, the probability of a normal random variable is calculated by using a z-score.
The z-score value is calculated by the formula
z = (X - μ)/σ
Where mean (μ) and standard deviation (σ) for the variable X
By using the standard normal distribution tables with the z-score and probabilities, the required values are calculated.
So, we can conclude that the major characteristics of a standard normal distribution are mean = 0 and variance = 1.
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a plumber cuts 2 3/4 feet from pipe. The pipe is now 13 1/4 feet long. Write and solve an equation of to determine the original length if the pipe
Answer:
x - 2 [tex]\frac{3}{4}[/tex] = 13 [tex]\frac{1}{4}[/tex]
x = 16
Step-by-step explanation:
x - 2 [tex]\frac{3}{4}[/tex] = 13 [tex]\frac{1}{4}[/tex]
x - [tex]\frac{11}{4}[/tex] = [tex]\frac{53}{4}[/tex] Add [tex]\frac{11}{4}[/tex] to both sides
x = [tex]\frac{53}{4}[/tex] + [tex]\frac{11}{4}[/tex]
x = [tex]\frac{64}{4}[/tex]
x = 16
Answer:
[tex]x-2 \frac{3}{4}=13 \frac{1}{4}[/tex]
(where x is the original length of the pipe).
Original length of the pipe = 16 feet
Step-by-step explanation:
Let x be the original length of the pipe.
Given a plumber cuts 2 3/4 feet from a pipe and now has a pipe that is 13 1/4 feet long, the equation that models this is:
[tex]\boxed{ x-2 \frac{3}{4}=13 \frac{1}{4}}[/tex]
To determine the length of the original pipe, solve the equation for x.
Add 2 3/4 to both sides of the equation:
[tex]\implies x-2 \frac{3}{4}+2 \frac{3}{4}=13 \frac{1}{4}}+2 \frac{3}{4}[/tex]
[tex]\implies x=13 \frac{1}{4}}+2 \frac{3}{4}[/tex]
When adding mixed numbers, partition the mixed numbers into fractions and whole numbers, and add them separately:
[tex]\implies x=13 +\dfrac{1}{4}}+2 +\dfrac{3}{4}[/tex]
[tex]\implies x=13 +2 +\dfrac{1}{4}}+\dfrac{3}{4}[/tex]
[tex]\implies x=15 +\dfrac{1+3}{4}[/tex]
[tex]\implies x=15 +\dfrac{4}{4}[/tex]
[tex]\implies x=15 +1[/tex]
[tex]\implies x=16[/tex]
Therefore, the original length of the pipe was 16 feet.
A taxi charges a flat 1.23 plus an additional 0.76 per mile. Brent has only 14.91 to spend on the ride. How many miles can Brent travel?
Will be reported by all 53 of my account if not a good answer
Answer:
18 miles
Step-by-step explanation:
To determine how many miles Brent can travel, we need to first determine the cost of the base fare and then subtract that from the total amount of money Brent has. The base fare is $1.23, so we can subtract that from the total amount of money Brent has to find out how much money he has left for the per-mile charge:
14.91 - 1.23 = 13.68
Now that we know how much money Brent has left for the per-mile charge, we can divide that amount by the per-mile charge to find out how many miles Brent can travel:
13.68 / 0.76 = 18 miles
Therefore, Brent can travel a maximum of 18 miles given the amount of money he has available to spend on the ride.
Help! Write the slope-intercept form given the graph. PLEASE I NEED A ANSWER
The linear equation written in the slope-intercept form is:
y = (-3/5)*x
The correct option is C.
How to write the line on the graph?A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
Here we can see that the line crosses through the poin (0, 0), so the y-intercept is 0.
b = 0
y = a*x + 0
y = a*x
To find the value of a, we can use another point on the graph.
We can see that the linear equation passes through (5, - 3), replacing these values:
-3 = a*5
-3/5 = a
Then the linear equation is just:
y = (-3/5)*x
The correct option is C.
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An architect is designing a home and needs to create a rectangular bedroom. The bedroom must be 425 ft2 and must be 8 ft longer than it is wide. What are the width and length of the bedroom?
The width of the bedroom is 17 feet. The length of the bedroom is 17 + 8 = 25 feet.
What is the area of the rectangle?
The area of the rectangle is length x breadth. The diagonals of the rectangle divide it into two equivalent right-angled triangles. Therefore, the area of the rectangle will be equal to the sum of the area of these two triangles.
Let w be the width of the bedroom and l be the length of the bedroom.
The width of the bedroom is 8 feet shorter than the length, so the length is w + 8.
The area of the bedroom is the product of its width and length, or w * (w + 8).
We can set up the equation 425 = w * (w + 8) and solve for w.
First, we can rewrite the equation as 425 = w^2 + 8w.
Then, we can complete the square by adding (8/2)^2 = 16 to both sides:
425 + 16 = w^2 + 8w + 16
441 = w^2 + 8w + 16
We can rewrite the left side of the equation as (w + 4)^2, which gives us:
(w + 4)^2 = 441
Taking the square root of both sides gives us:
w + 4 = 21
Subtracting 4 from both sides gives us:
w = 17
Therefore, the width of the bedroom is 17 feet. The length of the bedroom is 17 + 8 = 25 feet.
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Consider the following inequality:
−2(2z−3)≥2z+24
Step 1 of 2 : Write the solution using interval notation.
The required solution of the given inequality is z ≤ 9.
Given that,
To determine the solution of the inequality −2(2z−3)≥2z+24.
Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
−2(2z−3)≥2z+24
-4z + 6 ≥ 2z + 24
-2z ≥ 18
z ≤ 9
Thus, the required solution of the given inequality is z ≤ 9.
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Teacher's Salary The average teacher's salary in a particular state is $54,137.
If the standard deviation is $10,450, find the salaries corresponding to the following z scores.
The salary corresponding to z=1 is $64587 if the average teacher's salary in a particular state is $54,137.
What is z-score?A Z-score is a metric that quantifies the connection between a value and the mean of a set of values. The Z-score is measured as the standard deviations from the mean. If the Z-score is 0, A data point's score is the same as the mean score. In statistics, a raw score's value that deviates or surpasses the mean of the phenomenon being observed or measured is referred to as the standard score. Raw scores above the mean are given positive standard scores, whilst raw values below the mean are given negative standard ratings.
The pay is 1 standard deviation above the mean, according to a z score of 1.
Therefore, the salary for a z-score of 1 is:
$54,137 + 1($10,450) = $64587
Therefore, the salary corresponding to z=1 is $64587
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Stephen's current average weekly net pay is $354.76. The van he wants to purchase has monthly payments of $325.00. Which inequality correctly shows the comparison between 15% of Stephen's average monthly net pay and the monthly van payment? (4 points)
$212.86 ≥ $325.00
$212.86 ≤ $325.00
$230.59 ≤ $325.00
$230.59 ≥ $325.00
Stephen's current average weekly net pay is $354.76. The van he wants to purchase has monthly payments of $325.00. the inequality that correctly shows the comparison between 15% of Stephen's average monthly net pay and the monthly van payment is $212.86 ≤ $325.00
How to find the inequalityInformation given in the question
Stephen's current average weekly net pay is $354.76
The van he wants to purchase has monthly payments of $325.00.
the inequality that compares 15% of Stephen's average monthly net pay and the monthly van payment = ?
A weekly pay of $354.76 getting the monthly pay is
= 4 * $354.76
= $1419.04
15% of the monthly pay
= 0.15 * $1419.04
= 212.856
= $212.86
This amount is less than $325.00 which is monthly payment for the van hence $212.86 ≤ $325.00
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1. A basketball player made 12 out of 15 free throws she attempted. She wants to know how many consecutive free throws she would have to make to raise the percent of successful free throws to 85%. (a) Write an equation to represent this situation. (b) Solve the equation. How many consecutive free throws would she have to make to raise her percent to 85%? Answer:
Basketball player have to make 5 successful consecutive throws to make to raise her percent to 85%.
What is percentage?Percentage is a part of the whole number. It is denoted by % sign.
1 %= 1/100.
Given that,
Basketball player makes 12 out of 15 free throws she attempted.
The percentage of successful throws = (12/15)x100 = 75%
Let n consecutive free throws she has to make to increase the percentage of successful throws to 85%,
Implies that,
(12+n)/ (15+n) = 85/100
(12+n)/ (15+n) = 17 /20
240 + 20n = 255 + 17n
3n = 15
n = 5
Basketball player have to make 5 successful consecutive throws to make to raise her percent to 85%.
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Find the value of x. Hint: use the Exterior Angle Theorem
The value of x using Exterior Angle Theorem is 9.
What is the exterior angle of theorem?
The measure of an exterior angle is equal to the sum of the measures of the two opposite(remote) interior angles of the triangle, according to the external angle theorem. A triangle contains three internal angles, all of which add up to 180 degrees. This theorem is applied to each of the outer angles, which total six. As they constitute a linear pair of angles, take note that an exterior angle is supplementary to the neighbouring interior angle. Exterior angles are those that are created between a polygon's side and its extended neighbouring side.Interior 2 angle = exterior angle
32° + (6x -2)° = 9x + 3
32° + 6x -2° = 9x + 3
30° - 3° = 9x - 6x
3x = 27°
x = 9
Hence, the value of x using Exterior Angle Theorem is 9.
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Find the difference (7/8x-8)-(1/8x-12
The expressions are given to solve and reduce the answer to their simplest form.The x is 1/8.
Find the difference (7/8x-8)-(1/8x-2 ?We move all terms to the left:
7/8x-8-(1/8x-2)=0
Domain of the equation: 8x!=0
x!=0/8
x!=0
x∈R
Domain of the equation: 8x-2)!=0
x∈R
We get rid of parentheses
7/8x-1/8x+2-8=0
We multiply all the terms by the denominator
2*8x-8*8x+7-1=0
We add all the numbers together, and all the variables
2*8x-8*8x+6=0
By multiply elements
16x-64x+6=0
We add all the numbers together, and all the variables
-48x+6=0
We move all terms containing x to the left, all other terms to the right
-48x=-6
x=-6/-48
x = 1/8
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Math probability question
Answer:
9.
[tex] \frac{1}{6} [/tex]
10.
[tex] \frac{1}{3} [/tex]
Find the 10th term of the geometric sequence whose common ratio is 1/3 and whose first term is 7.
The 10th term of the geometric sequence whose common ratio is 1/3 and whose first term is 7 is [tex]\frac{7}{19683}[/tex].
What is geometric sequence?
A unique kind of sequence is a geometric sequence. Every term in the series (apart from the first term) is multiplied by a fixed amount to determine the following term. In other words, we multiply the current phrase in the geometric sequence by a constant term (called the common ratio), and then divide the current term in the geometric sequence by the same common ratio to discover the previous term in the geometric sequence.
nth term of geometric series
a(n) = a(1) * r^(n-1)
You are given a(1) = 7, r = 1/3 and n = 10.
a(10) = 7 * 1/3^(10-1)
[tex]7\left(\frac{1}{3}\right)^{10-1}$$[/tex]
Apply exponent rule: [tex]$\left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}$[/tex]
[tex]$$\begin{aligned}& \left(\frac{1}{3}\right)^{10-1}=\frac{1^{10-1}}{3^{10-1}} \\& =7 \times \frac{1^{10-1}}{3^{10-1}}\end{aligned}$$[/tex]
[tex]$$\begin{aligned}& 1^{10-1}=1 \\& =7 \times \frac{1}{3^{10-1}} \\& 3^{10-1}=19683 \\& =7 \times \frac{1}{19683}\end{aligned}$$[/tex]
Convert element to fraction: [tex]$\quad 7=\frac{7}{1}$[/tex]
[tex]=\frac{7}{1} \times \frac{1}{19683}$$[/tex]
Apply the fraction rule: [tex]$\frac{a}{b} \times \frac{c}{d}=\frac{a \times c}{b \times d}$[/tex]
[tex]=\frac{7 \times 1}{1 \times 19683}$$[/tex]
Multiply the numbers: [tex]$7 \times 1=7$[/tex]
[tex]=\frac{7}{1 \times 19683}$$[/tex]
Multiply the numbers: [tex]$1 \times 19683=19683$[/tex]
[tex]=\frac{7}{19683}[/tex]
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can yall help me with this question
give the component from the following vectors shown
Answer:
[tex](-3, 4)[/tex]
Step-by-step explanation:
The horizontal component is [tex]-3[/tex] and the vertical component is [tex]4[/tex]
The component (-3, 4) from the given vectors are shown in the graph.
What are vectors linearly independent and dependent?Let A = v 1, v 2,..., v r be a collection of vectors from Rn. If r > 2 and at least one of the vectors in A can be expressed as a linear combination of the others, A is said to be linearly dependent. The rationale for this description is straightforward: at least one of the vectors is dependent (linearly) on the others. If no vector exists in A, the set is said to be linearly independent. It is also usual to state "the vectors are linearly dependent (or independent)" rather than "the set comprising these vectors is linearly dependent (or independent)."
We have been given that the graph in the question
Here v = -3i + 4j
This means the component (-3, 4) of the provided vectors.
Therefore, the required component (-3, 4) from the provided vectors are depicted in the graph.
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What is the answers to this?
Answer:
5x^2
4x
-20x
Step-by-step explanation:
5x(x) = 5x^2
4(x)= 4x
5x(-4)= -20x