Suppose that b>0 and that the average value of f(x)=5x−5 on [0,b] is 14. find the value of
b.
The value of b is [tex]\dfrac{38}{5}[/tex].
Linear equation
In this, the power of x is 1. And it consists of the variable and/or constant term only.
Given
f(x)=5x−5
The average of that is 14 for the [0, b]
To find
The value of b.
How to get the value of b?For the x = 0, the value of f(x) will be
f(0) = -5
For the x = b, the value of f(x) will be
f(b) = 5b - 5
The average of that is 14.
[tex]\begin{aligned} \rm Average &= \dfrac{f(0)+f(b)}{2} \\14 &= \dfrac{(-5)+(5b-5)}{2} \\28 &= 5b -5 -5\\28 +5 + 5 &= 5b\\5b &= 38\\b &= \frac{38}{5} \\\end{aligned}[/tex]
Thus, the value of b is [tex]\dfrac{38}{5}[/tex].
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Factor the quadratic function f(x) = 4x2 – x – 5 to determine the zeros of the function.
To find the zeros of the function f(x) = 4x2 – x – 5, we first set the equation to zero, factor it to find (4x - 5)(x + 1) = 0, and solve for x, finding the zeros to be 5/4 and -1.
Explanation:The first step in factoring the quadratic function f(x) = 4x2 – x – 5 is to set the equation to zero.
The factored form of a quadratic equation is generally represented as (ax + b)(cx + d) = 0, where x is the zeros of the function. So, the equation we have is 4x² - x - 5 = 0.
Now, we need to look for two numbers that multiply to (a*c) = -20 (4*-5) and add up to -1 which are -5 and 4. Hence, the middle expression -x can be expressed as -5x + 4x, so the equation becomes:
4x² - 5x + 4x - 5 = 0.
Factoring, we get the following:
x(4x - 5) + 1(4x - 5) = 0.
Or we could write as:
(4x - 5)(x + 1) = 0.
Now, to find zeros of the function, we set each factor equal to zero and solve for x:
4x - 5 = 0 implies, x = 5/4.
x + 1 = 0 implies, x = -1.
So, the zeros of the function are 5/4 and -1.
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Suppose you have a cache of radium, which has a half-life of approximately 1590 years. how long would you have to wait for 1/5 of it to disappear?
You would have to wait approximately 3691.86 years for 1/5 of the radium to disappear, considering its half-life of 1590 years.
The decay of a substance with a half-life can be modeled using the formula [tex]\(N(t) = N_0 \left(\frac{1}{2}\right)^{\frac{t}{T_{\text{half}}}}\)[/tex], where:
- [tex]\(N(t)\)[/tex] is the remaining quantity after time \(t\),
- [tex]\(N_0\)[/tex] is the initial quantity,
- [tex]\(T_{\text{half}}\)[/tex] is the half-life.
In this case, [tex]\(N(t) = \frac{1}{5}N_0\)[/tex] and [tex]\(T_{\text{half}} = 1590\)[/tex] years.
Substituting these values into the formula and solving for \(t\):
[tex]\[ \frac{1}{5}N_0 = N_0 \left(\frac{1}{2}\right)^{\frac{t}{1590}} \][/tex]
Solving this equation yields[tex]\(t \approx 3691.86\)[/tex] years.
Therefore, you would have to wait approximately 3691.86 years for 1/5 of the radium to disappear, considering its half-life of 1590 years.
How many rectangles are needed to draw the net of this object?
There's an image of the problem that I'm asking about attached.
Answer with explanation:
If you will count the faces of this three dimensional geometrical shape , there are 5 faces in which there are 2 triangles and 3 Quadrilaterals.
So,to draw the net of this solid , you need
⇒As there are 3 Quadrilaterals which is in the shape of parallelogram,
You need three rectangles ,to draw the net of this object.
Option C: 3
If (x2 – 4) ÷ (x + 2) = x – 2, which polynomial should fill in the blank below?
(x + 2) ´ ______ = x2 – 4
A.x2 – 4
B.x – 2
C. x + 2
D. x2 – 2
Answer:
Step-by-step explanation:
Alright, lets get started.
Given that:
[tex]\frac{(x^2-4)}{(x+2)}=(x-2)[/tex]
(x-2) could be written as [tex]\frac{x-2}{1}[/tex]
[tex]\frac{(x^2-4)}{(x+2)}=\frac{(x-2)}{1}[/tex]
Doing cross multiply
[tex](x+2)(x-2)=(x^2-4)*1[/tex]
[tex](x+2)(x-2)=(x^2-4)[/tex]
It means the blank part is (x-2) : Answer
Hope it will help :)
Bill is 6 years younger than amy.the sum of their ages is 22.how old will each of them be in 8 years
Combine like terms to make a simpler expression:
5k+(−2k)−(−1)
what is the measure of one interior angle of a regular convex 31-gon
Final answer:
The measure of one interior angle of a regular convex 31-gon is approximately 168.39 degrees, calculated by dividing the sum of the interior angles, 5220 degrees, by the number of sides.
Explanation:
The measure of one interior angle of a regular convex 31-gon can be calculated using the formula for the sum of the interior angles of a polygon, which is (n - 2) × 180°, where n is the number of sides. For a 31-gon, the sum of the interior angles is,
(31 - 2) × 180°
= 29 × 180°
= 5220°.
To find the measure of one interior angle, you divide the total sum by the number of sides, so it is 5220° ÷ 31 ≈ 168.39°.
Helpppppppppppppppppppppppppppppppppp
Scientists found the wreck of the titanic 3797 m below sea level. How many km below sea level is the wreck?
We are given that the titanic is found 3,797 m below sea level. This is simply equivalent to 3.797 km or 3.8 km when rounded off to one decimal.
We should take note that the letter k in km means kilo and a kilo is equivalent to 1000. So this means that for 1 km there is exactly 1000 m. So to convert, simply multiply a value with unit m with this conversion factor. Conversion factor = 1 km / 1000 m
Depth of titanic = 3,797 m (1 km / 1000 m)
Depth of titanic = 3.797 km = 3.8 km
What’s the derivative of 3g(x)
Is it just 3g’(x)
Final answer:
The derivative of 3g(x) is 3g'(x), obtained by taking the derivative of the function and multiplying it by the constant.
Explanation:
Derivative of 3g(x):
Yes, the derivative of 3g(x) is indeed **3g'(x)**.
When you have a constant multiplied by a function, you can simply take the derivative of the function and multiply it by the constant to find the derivative of the entire expression. In this case, the derivative of 3g(x) would be 3 times the derivative of g(x), which is 3g'(x).
If (3/4)x + (5/6)y = 12, what is the value of 9x + 10y
Consider the sequence of steps to solve the equation: x - 3 3 = x + 3 Step 1 ⇒ x - 3 = 3(x + 3) Step 2 ⇒ x - 3 = 3x + 9 Step 3 ⇒ x = 3x + 12 Step 4 ⇒ -2x = 12 Step 5 ⇒ x = -6 Identify the property of equality which yields Step 5. A) Division Property B) Addition Property C) Subtraction Property D) Multiplication Propert
Find the equation of the tangent line and normal line to the curve at a given point y=x^4+2e^x
The tangent line to the curve at (0, 2) is y = 2x + 2, and the normal line is y = -1/2x + 2.
To find the equations of the tangent line and normal line to the curve at the given point (0, 2) for the function y = [tex]x^{4} +2e^{x}[/tex], we first need to determine the derivative of the function at that point.
1. Differentiate the function y =[tex]x^{4} +2e^{x}[/tex] with respect to x:
dy/dx = [tex]4x^{3} +2e^{x}[/tex]
2. Evaluate the derivative at the given point (0, 2):
dy/dx |(0, 2) = [tex]4(0)^{3}[/tex] + 2[tex]e^{0}[/tex] = 2
3. The slope of the tangent line at the point (0, 2) is 2.
4. Use the point-slope form to find the equation of the tangent line:
y - 2 = 2(x - 0)
y = 2x + 2
5. The slope of the normal line is the negative reciprocal of 2, which is -1/2.
6. Use the point-slope form to find the equation of the normal line:
y - 2 = (-1/2)(x - 0)
Simplify:
y = -1/2x + 2.
Question- Find the equation of the tangent line and normal line to the curve at a given point y=[tex]x^{4} +2e^{x}[/tex], (0, 2).
Maria wants too convert 500 centimeters to meters how many meters does she have ?
Final answer:
Maria can convert 500 centimeters to meters by dividing by 100. So, she would end up with 5 meters since each meter contains 100 centimeters.
Explanation:
Maria wants to convert 500 centimeters to meters to determine how many meters she has. Conversion between centimeters and meters is a common mathematical process. Since there are 100 centimeters in a meter, Maria needs to divide the number of centimeters by 100 to get the measurement in meters. So, she would calculate 500 cm ÷ 100, which equals 5 meters.
To visualize this, imagine you have a ruler that measures in centimeters. If you laid out rulers end to end until you reached 500 centimeters, you would have the equivalent length of 5 meters because every 100 centimeters make up 1 meter.
Example:
If we had 200 cm, we would divide by 100 and find that 200 cm equals 2 m. Comparing this to a meter stick, which measures 1 meter, we can see that 200 cm is greater than 1 m and would require using the meter stick twice to measure the entire length.
What is the quotient when −3x3 + 5x + 14 is divided by x − 2?
−3x2 − 6x − 7
− 3x2 − x + 12
−3x2 + 6x − 7 + 28 over the quantity of x minus 2
−3x2 − x + 12 + 28 over the quantity of x minus 2
Answer:
[tex]-3x^{2} -6x-7[/tex]
Step-by-step explanation:
The given expression is :
[tex]\frac{-3x^{3}+5x+14}{x-2}[/tex]
Factoring [tex]-3x^{3}+5x+14[/tex]
Factor out common term -1
[tex]3x^{3}-5x-14[/tex]
Now dividing leading coefficients of numerator and divisor.
[tex]\frac{3x^{3}}{x}=3x^{2}[/tex]
Multiplying x-2 with [tex]3x^{2}[/tex] = [tex]3x^{3}-6x^{2}[/tex]
Subtracting [tex]3x^{3}-6x^{2}[/tex] from [tex]3x^{3}-5x-14[/tex]
we get [tex]6x^{2} -5x-4[/tex]
Therefore, [tex]\frac{-3x^{3}+5x+14}{x-2}[/tex] = [tex]3x^{2} +\frac{6x^{2}-5x-14}{x-2}[/tex]
Now repeating these same steps until (x-2) is factored out, we get the quotient as :
[tex]-3x^{2} -6x-7[/tex]
From the statement select the related given statement. If B is between A and C, then AB + BC = AC
A.) Plane R is parallel to plane S; Plane T cuts planes R and S.
B.) △ABC with ∠1 = ∠2.
C.) Point B is between points A and C.
D.) Line l; point P not on l.
E.) △ABC with midpoints M and N.
Answer:
C.) Point B is between points A and C.
Step-by-step explanation:
The simplest way to analyze this is as a line.
This line goes from A to C and somewhere in the middle, is B.
But they tell you that AB + BC = AC.
The distance from A to B plus the distance from B to C is the same as the distance from A to C.
Option A about planes is not the correct one because there's no mention of planes.
Option B about angles is not correct because they only talk about some points of a line. You don't know if there's some angle in between.
The same happed with options D and E.
Write the following question expression in simplest binomial form 4(3x-2)-2(4x+5)
The expression 4(3x-2)-2(4x+5) in it's simplest binomial form is 4x - 18.
What are the types of algebraic expressions?We can classify algebraic expressions in terms of how many terms they have. If an algebraic expression has only one term we call it a monomial, having two terms makes it a binomial and having more than two terms makes it a polynomial
We know a binomial consists of two terms separated by any of the arithmetic operations.
Given, 4(3x-2)-2(4x+5).
First, we will distribute the terms.
= 12x - 8 - 8x - 10.
= 4x - 18.
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The organizers of a drama club wanted to sell 350 tickets to their show.The actual sales were no more than 35 tickets from his goal.Write an d solve an absolute value inequality to find the range of the number of tickets that could have been sold
Is the product of two positive mixed numbers ever less than 1?
WILL BE AWARDED 68 POINTS. Solve for x. Round your answer to 2 decimal places. (5 points)
to find x divide 16 by the sin of 30
16 / sin(30) = 32
if you need 2 decimal places it would be 32.00
Answer:
16 sin30 = 32
Step-by-step explanation:
Name a line that contains point A
The line which contains point A is line l.
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
Now from the given diagram, lines l and m lie in plane P.
And the point lies on the line l are A, B and C.
The point lies on the line m are B and D.
Point E lies in plane P.
Thus, the line which contains point A is line l.
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Find the vertex and the axis of symmetry of the graph of f(x)=3(x+1)^2
One difference between the z-distribution and t-distributions is the t-distribution tends to be
Find the solutions to the given system of equations
x^2+y^2=15 and y= -x - 6
A. No solution
B. (-2,5)
C. (-1,-2) and (5, -5)
D. (-1,2) and (2,-11)
9x^2+3x - 35=y and 3x-1=y
A. (-2,5)
B. (2,7)
C. (2,7) and (-2,-5)
D. (2,-5) and (-2,-5)
Four balls of wool will make 8 knitted caps. How many balls of wool will Malcolm need if he wants to make 6 cups
A group consists of 6 men and 5 women. five people are selected to attend a conference. in how many ways can 5 people be selected from this group of 11? in how many ways can 5 men be selected from the 6 men? find the probability that the selected group will consist of all men.
To compute for combinations, we will use the method nCr = n! / r! * (n - r)!
Where: n signifies the number of items, and r signifies the number of items being selected at a time.
Solution
1. 11C5 = 11!/ 5! * (11-5)! = 462 ways
2. 6C5 = 6!/ 5! * (6-5)! = 6 ways
3. 6/462 = 1/77 or 0.1230 is the probability that the selected group will consist of all men.
The calculation involves using combinations to find the total number of ways to select 5 people from 11, and then to find the probability of selecting 5 men by dividing the number of ways to select 5 men from 6 by the total number of selections.
Explanation:The student's question deals with the topic of combinatorics, specifically the selection of groups and calculation of probabilities using the hypergeometric distribution. To find how many ways 5 people can be selected from a group of 11 (6 men and 5 women), we use the combination formula [tex]C(n, k) = n! / (k!(n-k)!).[/tex]
For the first part of the question, selecting 5 people out of 11, the calculation is C(11, 5). To calculate the number of ways 5 men can be selected from 6 men, we use C(6,5).
Lastly, to find the probability that the selected group will consist of all men, we divide the number of ways to select 5 men by the total number of ways to select 5 people from the whole group:
Calculate the number of ways to choose 5 people from 11 (C(11, 5)).Calculate the number of ways to choose 5 men from 6 (C(6,5)).Divide the number of ways to choose 5 men by the total number of ways to choose 5 people to get the probability of selecting all men.Learn more about hypergeometric distribution here:https://brainly.com/question/35126689
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In May, there were 157 people living in Kristin's neighborhood. By August, the population had increased 21%. How many people were in Kristin's neighborhood by August?
A.330
B.190
C.33
D.1900
N a triangle, the measure of the first angle is twicetwice the measure of the second angle. the measure of the third angle is 68 degrees68° more than the measure of the second angle. use the fact that the sum of the measures of the three angles of a triangle is 180degrees° to find the measure of each angle.
Use slopes to determine if the triangle whose vertices are left parenthesis negative 4 comma 4 right parenthesis(−4,4), left parenthesis 1 comma 5 right parenthesis(1,5), and left parenthesis 2 comma 0 right parenthesis(2,0) is a right triangle. find the slope for the side of the triangle between the vertices left parenthesis negative 4 comma 4 right parenthesis(−4,4) and left parenthesis 1 comma 5 right parenthesis(1,5). mequals= one fifth 1 5 (type an integer or a simplified fraction.) find the slope for the side of the triangle between the vertices left parenthesis 1 comma 5 right parenthesis(1,5) and left parenthesis 2 comma 0 right parenthesis(2,0). mequals= negative 5−5 (type an integer or a simplified fraction.) find the slope for the side of the triangle between the vertices left parenthesis negative 4 comma 4 right parenthesis(−4,4) and left parenthesis 2 comma 0 right parenthesis(2,0). mequals= negative two thirds− 2 3 (type an integer or a simplified fraction.) is the triangle a right triangle?
Final answer:
By calculating slopes of the triangle's sides and identifying that two of them are negative reciprocals of each other, it's confirmed that the triangle with vertices (-4, 4), (1, 5), and (2, 0) is a right triangle.
Explanation:
To determine if the triangle with vertices (-4, 4), (1, 5), and (2, 0) is a right triangle, we calculate the slopes of all three sides. The slope of the line between points (-4, 4) and (1, 5) is calculated using the slope formula m = (y2 - y1) / (x2 - x1). Using the coordinates, the slope is (5 - 4) / (1 - (-4)) = 1 / 5. Similarly, the slope between points (1, 5) and (2, 0) is (0 - 5) / (2 - 1) = -5. Lastly, the slope of the line between (-4, 4) and (2, 0) is (0 - 4) / (2 - (-4)) = -4 / 6, which simplifies to -2 / 3. A right triangle has one 90-degree angle, and the slopes of perpendicular lines are negative reciprocals of each other. Therefore, if two of these slopes are negative reciprocals, the triangle is a right triangle. In this case, the slopes -5 and 1/5 are negative reciprocals, confirming that the triangle is a right triangle.