If the slope of the line has two negative signs, then it is positive.
How to obtain the slope of a linear function?The slope of a linear function represents the rate of change of the linear function.
If we have two points on the linear function, then the slope is obtained by the division of the change in the output by the change in the input.
If both changes are negative, then we are dividing two negative numbers, meaning that the slope is positive, as the quotient of two negative numbers is positive.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
Matt has a piggy bank with 250 coins all dimes and quarter.The total dollar amount in the piggy bank is $39.25. How of each type of coin are in the piggy bank?
The piggy bank has 200 dimes and 50 quarters.
To find this, we can set up the following equation:
(number of dimes x $0.10) + (number of quarters x $0.25) = $39.25
We know that the piggy bank contains 250 coins, so we can substitute that in:
(x x $0.10) + (250-x x $0.25) = $39.25
Now we can solve for x, the number of dimes:
x0.10 + (250-x)0.25 = 39.25
x0.10 + 62.5 - x0.25 = 39.25
0.1x + 62.5 - 0.25x = 39.25
-0.15x = -23
x= 153
So there are 153 dimes in the piggy bank, and 250-153 = 97 quarters.
But we know that the piggy bank contains 250 coins, so we can check that 153 dimes + 97 quarters = 250 coins.
11) The dimensions, in feet, of a rectangle are represented by expressions, as shown in the
diagram below. Explain your work.
(2.5m) ft.
(4n+ 5) ft.
The area of the rectangle is and using the length and breadth
What is the area of the rectangle?In a two-dimensional plane, a rectangle area is a space it encloses. Known for having 4 sides and 4 vertices, a rectangleis a closed shape. The sum of the spaces occupied by a rectangle three sides is known as its area. The product of a rectangle breadth and length is the usual formula for calculating its area.The area that is included within the perimeter of a flat object or figure is generally considered to be the definition of the word "area." The square units used for measuring are square metres as the standard unit.area of rectangle = length × breadth
area of rectangle = 2.5m × (4n +5)
area of rectangle = 10mn + 12.5m
To learn more about Rectangle from the given link
https://brainly.com/question/20693059
#SPJ4
Question:
The dimensions, in feet, of a rectangle, are represented by expressions, as shown in the diagram below. The area of the rectangle is 10mn + 12.5m. Explain your work.
Identify whether or not each pair of terms can be combined to simplify the expression (−4t − 7) + (3t+8).
-4r and -7
3r and 8
-41 and 3r
Answer: (-4t - 7) + (3t + 8) cannot be simplified further as the terms have different variables.
(-4r and -7) and (3r and 8) cannot be combined as these terms have different variables.
(-41 and 3r) cannot be combined as these terms have different variables.
Step-by-step explanation:
Which of the following is equivalent to the expression j ^ 41 ?
The equivalent expression of i⁴¹ is i.
What are the equivalent expressions?Expressions that are equivalent to the same thing, even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).
Given:
An expression i⁴¹.
Simplifying,
i⁴¹ = {(i⁴)¹⁰} i
i⁴¹ = {(1)¹⁰} i {i⁴ = 1}
i⁴¹ = i
Therefore, the equivalent expression is i.
To learn more about the equivalent expression;
https://brainly.com/question/28170201
#SPJ1
99
2
12
. At the library, Herb spent 1/6 hour looking for a book,1/4 hour of
reading, and 1/2 hour doing research on the computer. How man
hours did Herb spend at thelibrary?
2
3
Herb spent 55 hours at the library.
What is a fraction?Fractions defines a part of a whole and are represented as a numerical value. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.
Parts of a FractionThe denominator indicates the number of parts in which the whole has been divided into. It is placed in the lower part of the fraction below the fractional bar.The numerator indicates how many sections of the fraction are represented or selected. It is placed in the upper part of the fraction above the fractional bar.Total time spent in the Library = 1/6 + 1/4 + 1/2
Total time spent = 11/12 x 60 mins
Total time spent = 55 hours
Learn more about fractions here: https://brainly.com/question/78672
#SPJ1
Three vertices of a parallelogram are shown in the figure below.
Give the coordinates of the fourth vertex.
(-5,-3)
(2,7)
(0, -1)
Step-by-step explanation:
it is a parallelogram.
in comparison to a rectangle one side is shifted a bit, but the endpoints of the shifted side are still positioned the same way relative to each other.
and particularly, their relative offset from each other must be the same as for the endpoints of the other, parallel side.
let's look at
(0, -1) and (2, 7).
their relative offset is given by
x + 2 (from 0 to 2)
y + 8 (from -1 to 7)
the missing point must have the same offset from (-5, -3), as this line is parallel to the one above :
-5 + 2 = -3
-3 + 8 = 5
so, the missing point is (-3, 5).
Let g(t) be the population in thousands of people) of Calculus City, as a function the time t (in years), where t = 0 corresponds to the year 2019. In 2019, the population was 10 thousand, and each year the population increases by by 30%. (a) Model the population by finding a formula for g(t), using the appropriate choice of a linear, polynomial, power, trigonometric, or exponential function, or a piecewise contbination thereof. (b) Evaluate the expression 9(6), and write a sentence explaining what this means. (c) Solve the equation g(t) = 16.9, and write a sentence explaining what this means.
The population of Calculus City can be modeled by an exponential function, g(t) = 10(1.3) ^t, where t is the number of years since 2019. Evaluating g (6) means calculating the population of Calculus City after 6 years, which is 10(1.3) = 39.5 thousand people.
(a) The population of Calculus City can be modeled by an exponential function, g(t) = 10(1.3) ^t, where t is the number of years since 2019.
(b) g (6) = 10(1.3) = 46.6 thousand. This means that the population of Calculus City will be 46.6 thousand in the year 2025.
(c) Solving the equation g(t) = 16.9 yields t = log1.3(16.9/10) = 4.7 years. This means that the population of Calculus City will be 16.9 thousand in the year 2023.7.
To learn more about functions:
brainly.com/question/5975436
#SPJ4
The sum of four consecutive integers; n = first integer of the four
The sum of four consecutive integers is,
⇒ 4n + 6
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
We have to given that;
⇒ n = first integer of the four.
Now, Let four consecutive integers with n is first integer of the four are,
⇒ n, n + 1, n + 2, n + 3
Hence, The sum of four consecutive integers is,
⇒ S = n + (n + 1) + (n + 2) + (n + 3)
= 4n + 6
Learn more about the addition visit:
https://brainly.com/question/25421984
#SPJ1
Determine whether the lines L₁ and L2 given by the vector equations are parallel, perpendicular, or neither.
L₁: r(t) = (-5+ 3t)i + (3 + t)j
L₂: r(s) = (2+2s)i + (4 - 6s)j
parallel
Operpendicular
neither
If the lines are not parallel, find their point of intersection. (If the lines are parallel, enter PARALLEL.)
The lines L₁ and L₂ given by the vector equations is perpendicular.
How are the lines perpendicular?In order to prove that the lines are perpendicular,
L₁: r(t) = (-5+ 3t)i + (3 + t)j
L₂: r(s) = (2+2s)i + (4 - 6s)j
To determine whether the lines L₁ and L2 are parallel, perpendicular, or neither, we need to compare their direction vectors.
The direction vector for L₁ is given by <3,1> and the direction vector for L₂ is given by <2,-6>.
The dot product of the direction vectors is (32) + (1-6) = -8. Since the dot product is zero, the vectors are perpendicular, and therefore the lines are perpendicular.
Therefore, the lines are PERPENDICULAR.
learn more about vectors: https://brainly.com/question/25705666
#SPJ1
Annual Tuition and Fees $6,125.00
Annual Room and Board $2,112.00
Annual Cost of Books and Supplies $1,250.00
Other One-Time Fee $750.00
Annual Scholarship and Grants $5,000.00
Using the information from the table, identify the equation in slope-intercept form that models the total cost of attendance. (4 points)
y = 5,237
y = 10,237x
y = 9,487x + 750
y = 4,487x + 750
The equation in slope-intercept form that models the total cost of attendance is y = 4487x + 750.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects
the y-axis at x = 0.
To find the equation in the slope-intercept form,
We'll sum all the annual fees and subtract the scholarship amount and 'x' will represent the number of years while the one-time fee will be our constant term.
So, (6125 + 2112 + 1250 - 5000).
= 4487.
Therefore, The equation in slope-intercept form is,
y = 4487x + 750.
learn more about lines and slopes here :
https://brainly.com/question/3605446
#SPJ1
A tank has a height of 10 feet. The area of the horizontal cross section of the tank at height h feet is given by the function A where A(h) is measured in square feet. The function A is continuous and decreases as h increases. Selected values for Ach) are given in the table. (a) Use a left Riemann sum with the three subintervals indicated to approximate the integral. Indicate correct units of measure. (b) Interpret your answer from part (a). What is being measured?
(C) Is your estimate of the integral in part (a) an overestimate or underestimate of the actual integral?! Justify your answer
So. the left Riemann sum is 23.74 ft^2.
Given the information in the table:
(a) To use a left Riemann sum with three subintervals to approximate the integral of A(h) with respect to h, we need to divide the interval of integration [0,10] into three equal subintervals. The width of each subinterval is (10-0)/3 = 3.33 ft. The left Riemann sum can be calculated as:
(A(0) * 3.33) + (A(2) * 3.33) + (A(5) * 3.33) = (50.3 * 3.33) + (14.4 * 3.33) + (6.5 * 3.33) = 16.80 + 4.78 + 2.16 = 23.74 ft^2
(b) This approximation represents the total area of the horizontal cross section of the tank up to a specific height h.
(c) The Riemann sum is an underestimate of the actual integral. This is because the Riemann sum uses the left endpoint of each subinterval to approximate the area under the curve, but the actual area under the curve is always greater than or equal to the area of the rectangles.
To learn more about Riemann sum
Visit; brainly.com/question/30241844
#SPJ4
complete the table by using your knowledge of the formula for simple interest. principle amount saved (dollars) 425, interest rate 7% time (years) 5 how many interest Earned (dollars)
Answer:
$ 148.75
Step-by-step explanation:
Simple interest:Principle = $ 425
Rate = 7%
Time = 5 yeats
[tex]\sf \boxed{Simple \ Interest = \dfrac{Principle*rate*time}{100}}[/tex]
[tex]= \dfrac{425*7*5}{100}\\\\=\dfrac{17*7*5}{4}\\\\\\=\dfrac{595}{4}\\\\=148.75[/tex]
A block of mass 2.20 kg is placed against a horizontal spring of constant k = 895 N/m and pushed so the spring compresses by 0.0750 m.
(a)
What is the elastic potential energy of the block-spring system (in J)?
J
(b)
If the block is now released and the surface is frictionless, calculate the block's speed (in m/s) after leaving the spring.
m/s
a) The block-spring system has an elastic potential energy equal to 2.517 joule.
b) The block has speed of approximately 1.513 meters per second.
How to analyze a spring-block system
In this problem we must analyze the energy and kinematics of spring-block system with no irreversibilites (no friction). Part A - Elastic potential energy is determined when spring is entirely deformed:
U = (1 / 2) · k · x²
Where:
k - Spring constant, in newtons per meter.x - Spring deformation, in meters.U - Elastic potential energy, in joule.If we know that k = 895 N / m and x = 0.0750 m, then the elastic potential energy of the block-spring system is;
U = (1 / 2) · (895 N / m) · (0.0750 m)²
U = 2.517 J
The elastic potential energy of block-spring system is 2.517 joule.
Part B - And the speed can be determined by principle of energy conservation and work-energy theorem:
K = U
Where K is translational kinetic energy, in joules.
(1 / 2) · m · v² = U
v² = 2 · U / m
v = √(2 · U / m)
If we know that U = 2.517 J and m = 2.20 kg, then the speed of the block is:
v = √[2 · (2.517 J) / (2.20 kg)]
v ≈ 1.513 m / s
The speed of the block after leaving the spring is approximately 1.513 meters per second.
To learn more spring-block systems: https://brainly.com/question/26311680
#SPJ1
John had a yard full of dogs and chickens. He counts 25 heads and 78 legs. How many dogs does John have?
In the problem, it is solved that the number of dogs John has is 14
How to solve for the number of dogs John hasThe problem is solved by expression the word problem into a simultaneous equation as follows
let d be the number of dogs and c d number of chickens
d + c = 25 (since all must have a head)
4d + 2c = 78 (2 legs for chicken and 4 legs for dog)
using calculator to solve gives
d = 14 and c = 11
hence the number of dogs is 14
Learn more on simultaneous equation :
https://brainly.com/question/148035
#SPJ1
4 ) 316 with work
(Division)
The value of dividing 316 by 4 will be 79.
How to calculate the expression?An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.
In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.
It should be noted that dividing 316 by 4 will be:
= 316 / 4
= 79
Learn more about expressions on
brainly.com/question/723406
#SPJ1
Complete question
Divide 316 by 4
What is the value of x?
Answer:
X = 11
Step-by-step explanation:
The total degrees of a line is 180
They gave us 39 and 13x-2
We can get rid of the 39 by subtracting it from 180
180-39=141
That means 13x-2 = 141
Now to find X. Adding 2 on both sides, gets rid of the 2 on the left side
13x = 143
Dividing 13 on both sides, we can get X alone
X = 11
Set B is the set of positive two-digit even numbers less than 36 that do not contain the digit 2 .
The required set of positive two-digit even numbers less than 36 that do not contain the digit 2 is 11,13,14,15,16,17,18,19,30,31,33,34,35.
What is an integer?An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Zero is not a fraction or decimal of any number. It is neither positive nor negative.
Given:
Set D is the set of positive two-digit even numbers less than 36 that do not contain the digit 2.
According to the given question, we have
2-digit numbers are numbers that have two digits and they start with the number 10 and end with the number 99.
Starting at 11 and going up the two-digit numbers even numbers less than 36 that do not contain the digit 2.
11,13,14,15,16,17,18,19,30,31,33,34,35.
Learn more details about integers here:
brainly.com/question/15276410
#SPJ1
You are given the following information about a simple regression model fit to 10 observations: 10 10 Στη = 20, = , Συ = 100, Sy=8. S = 2, k=1 You are also given that the sample correlation coefficient r = -0.98. Determine the predicted value of y when I = 5. Answer to the nearest integer. A. -10 B. -2 C. 11 D. 30 E. 37
The predicted value of y when I = 5 is equal to D) 30.
To determine the predicted value of y when I = 5, we can use the equation of the simple linear regression model:
y = b0 + b1x
where b0 and b1 are the regression coefficients and x is the predictor variable.
We can find b1 using the formula:
b1 = r(Sy/Sx)
where r is the sample correlation coefficient, Sy is the standard deviation of the y variable, and Sx is the standard deviation of the x variable.
Plugging in the given values:
b1 = -0.98(8/2) = -4
We can find b0 using the formula:
b0 = ybar - b1*xbar
where ybar and xbar are the mean of the y variable and the x variable respectively.
Plugging in the given values:
b0 = 10 - (-4)*10 = 50
Therefore, the equation of the simple linear regression model is:
y = 50 - 4x
So when I = 5, the predicted value of y is:
y = 50 - 4(5) = 50 - 20 = 30
The closest answer choice is D. 30.
For more questions like Regression model click the link below:
https://brainly.com/question/14983410
#SPJ4
Following is a statement of a theorem which can be proven using calculus or precalculus mathematics. For this theorem, a, b, and c are real numbers. Theorem If f is a quadratic function of the form f (x) = ax^2 + bx + c and a < 0, then the function f has a maximum value when x = -b/2a. Using only this theorem, what can be concluded about the functions given by the following formulas? ? (a) g (x) = -8x^2 + 5x - 2 (b) h (x) = -(1/3)x^2 + 3x (c) k (x) = 8x^2 - 5x - 7 (d) j (x) = -(71/99)x^2 + 210 (e) f (x) = 4x^2 - 3x + 7 (f) F (x) = -x^4 + x^3 + 9
(a) The maximum value of g(x) = -8[tex]x^2[/tex] + 5x - 2 is 5/16.
(b) The maximum value of h(x) = -(1/3)[tex]x^2[/tex] + 3x is 9/2.
(c) The maximum value of k(x) = 8[tex]x^2[/tex] - 5x - 7 is 5/16.
(d) The maximum value of j(x) = -(71/99)[tex]x^2[/tex] + 210 is 0.
(e) The maximum value of f(x) = 4[tex]x^2[/tex] - 3x + 7 is 3/8.
(f) The maximum value of F(x) = -[tex]x^4[/tex] + [tex]x^3[/tex] + 9 is 0/0. We cannot say anything about that function.
The general form of a quadratic function;
f(x) = a[tex]x^2[/tex] + bx + c and a < 0,
Then the function f has a maximum value when x = -b/2a
(a) The function is g(x) = -8[tex]x^2[/tex] + 5x - 2
We can find the maximum value at x = -b/2a.
On comparing with f(x) = a[tex]x^2[/tex] + bx + c, we get a = -8 and b = 5
Now putting the value at x = -b/2a
x = -5/2(-8)
x = (-5)/(-16)
x = 5/16
(b) The function is h (x) = -(1/3)[tex]x^2[/tex] + 3x
We can find the maximum value at x = -b/2a.
On comparing with f(x) = a[tex]x^2[/tex] + bx + c, we get a = -(1/3) and b = 3
Now putting the value at x = -b/2a
x = (-3)/2(-1/3)
x = (3×3)/2
x = 9/2
(c) The function is k(x) = 8[tex]x^2[/tex] - 5x - 7
We can find the maximum value at x = -b/2a.
On comparing with f(x) = a[tex]x^2[/tex] + bx + c, we get a = 8 and b = -5
Now putting the value at x = -b/2a
x = -(-5)/(2×8)
x = 5/16
(d) The function is j(x) = -(71/99)[tex]x^2[/tex] + 210
We can find the maximum value at x = -b/2a.
On comparing with f(x) = a[tex]x^2[/tex] + bx + c, we get a = -(71/99) and b = 0
Now putting the value at x = -b/2a
x = 0/2(-(71/99))
x = 0
(e) The function is f(x) = 4[tex]x^2[/tex] - 3x + 7
We can find the maximum value at x = -b/2a.
On comparing with f(x) = a[tex]x^2[/tex] + bx + c, we get a = 4 and b = -3
Now putting the value at x = -b/2a
x = -(-3)/(2×4)
x = 3/8
(f) The function is F(x) = -[tex]x^4[/tex] + [tex]x^3[/tex] + 9
We can find the maximum value at x = -b/2a.
On comparing with f(x) = a[tex]x^2[/tex] + bx + c, we get a = 0 and b = 0
Now putting the value at x = -b/2a
x = 0/0
We cannot say anything about that function.
To learn more about quadratic function link is here
brainly.com/question/27958964
#SPJ4
The complete question is given below:
A school staff meeting had 5 teachers in attendance, 60% of whom were first-year teachers.
How many first-year teachers were in the meeting?
Answer: 3
Step-by-step explanation: 60 x 5/100 = 3
There were three first-year teachers in the meeting.
show that, given one nth root of z, the others are obtained by multiplying it by the nth roots of unity. (z is complex number)
It is proven that the other nth roots of z can be found by multiplying the initial one by the nth roots of unity.
A complex number satisfying the equation [tex]z^{n-1} = 0[/tex] is known as the nth root of unity. There are about n nth roots of a unit, according to the fundamental theorem of algebra. We know that,[tex]1=e^{2\pi i}[/tex]. Then, the nth root is written as [tex]\omega=e^{2\pi i/n}[/tex].
The integer of powers of this root between 0 and n-1 provides the other nth roots. Then, the roots are [tex]1, \omega, \omega^2 ,\cdots \cdots, \omega^{(n-1)}[/tex]. Now, factorize the equation [tex]z^{(n-1)} = 0[/tex] we get the required identity as, [tex]z^{(n-1)} = (z- 1)(z^{(n-1)}+ z^{(n-2)} + \cdots \cdots+ z + 1) = 0[/tex].
This indicates that the equation [tex]1+\omega+ \omega^2+\cdots \cdots+ \omega^{(n-1)}[/tex] is true for all nth roots of unity other than 1.
Roots of unity also have the great quality of being periodic, which results from the fact that n = 1. It is equal to a power of that power mod n if the power is bigger than n.
When ω is a third root of unity, [tex]\omega^5 + \omega^4 + 1 = \omega^2 + \omega + 1 = 0[/tex].
To know more about complex numbers:
https://brainly.com/question/20566728
#SPJ4
240 people are going to a charity event.
3535 of the guests have ordered chicken for their meals.
Of the remaining guests, 12.5% have ordered gluten-free meals.
How many people haven't ordered their meals yet?
Answer:
First, find out how many guests have ordered chicken: 240 guests * 3535/10000 = 84 guests
Then subtract that number from the total number of guests to find the number of guests who haven't ordered chicken: 240 guests - 84 guests = 156 guests
Then find how many of those guests have ordered gluten-free meals: 156 guests * 12.5% = 19.5 guests
Then round down the number of guests who have ordered gluten-free meals to the nearest whole number to find the exact number of guests who ordered gluten-free meals: 19 guests
Then subtract that number from the number of guests who haven't ordered chicken to find the number of guests who haven't ordered their meals yet: 156 guests - 19 guests = 137 guests
So 137 people haven't ordered their meals yet.
Determine another point on the line given two points on the line.
(0, 5), (4, 1)
Another point on the line is (2, 3)
How to find another point on the lineTo find another point on the line the equation of the line will be solved as used to get other points
The slope, m of the lines is calculated the formula
m = (y₀ - y₁) / (x₀ - x₁)
where
m = slope
x₂ and x₁ = points in x coordinates
y₂ and y₁ = points in y coordinates
The slope, m of the linear function is calculated using the points (0, 5), (4, 1)
m = (y₀ - y₁) / (x₀ - x₁)
m = (5 - 1) / (0 - 4)
m = (4) / (-4)
m = -1
equation passing through point (0, 5)
(y - y₁) = m (x - x₁)
y - 5 = -1 (x - 0)
y - 5 = -x
y = -x + 5 equation of the line
for x = 2
y = -x + 5 = -2 + 5 = 3
the point is (2, 3)
Learn more about linear equation at:
https://brainly.com/question/30125370
#SPJ1
Lisa earns $215.20 a week. She is married and claims 3 allowances. Starting next week she will receive a $40 per week raise. After the raise, how much will she pay in federal income taxes Annually?
After the raise, Lisa much will pay $9 in federal income taxes Annually.
Explain the term federal income taxes?The federal tax is a tax that is levied on the yearly profits of people, companies, and some other legal entities. Federal income taxes are due on all compensation, including salaries, monetary gifts from employers, business profits, tips, winnings from gaming, bonuses, and unemployment benefits.For the stated question:
Lisa's salary = $215.20 a week.
After increment of $40 per week.
$215.20 + $40 = $255.2
She gets 3 allowances and is married.
After raise,
Federal income taxes = $9. (taken from the table)
Thus, After the raise, Lisa much will pay $9 in federal income taxes Annually.
To know more about the income taxes, here
https://brainly.com/question/30027168
#SPJ1
Example 1. 15+6x3 This problem is modeled after example 1. Find the requested pattern. (Enter the first three numbers of the pattern as a comma-separated list.) three pattern
Therefore, the 3 patterns are
3,6,9,3,6,9
Explanation:
Given that,
we will carry out the multiplications of succession counting number by 3 and if there is more than a single digit answer .we add the digits.
we are looking for is a pattern for there single digit numerals.
carryout the plan
1x3=3→3
2x3=6→6
3x3=9→9
4x3=12→1+2=3
5x3=15→1+5=6
and so on
continue with some additional at terms.
6x3=18→1+8=9
7x3=21→2+1=3
∵ Therefore the 3 patterns are
3,6,9,3,6,9
A pattern is defined in mathematics as a sequence of repeating objects, shapes, or numbers. A pattern can be associated with any type of event or object. A pattern has a rule that tells us which objects belong to the pattern and which objects do not belong to the pattern.
To learn more about pattern
https://brainly.com/question/14720576
#SPJ4
Find the average rate of change of each function on the interval specified for the real numbers b or h in the simplest form.
1) the rate change of function f(x) in given interval =4(b+1)
2) the rate change of function g(x) in given interval =1
3) the rate change of function j(x) in given interval =[tex]3h^2+9h+9[/tex]
To find out the average rate change of function on given interval is -
Use the graph of f to determine f (a) and f (b) for the provided range [a,b]. Remember that the graph of f's point with the y-coordinate of f (a) and the x-coordinate of an is called f. Similar to that, f ( b ) is the y-coordinate of the point on the f graph whose x-coordinate is b.
Step 2: Calculate the average rate of change of f over the range [a, b] using the average rate of change formula.
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
1)
[tex]f(x)=4x^2-7 \ on\ [1,b]\\\\f(1)=4-7=-3\\\\f(b)=4b^2-7\\\\the \ rate \ change =\frac{4b^2-7+3}{b-1}\\\\=4(b+1)[/tex]
2)
[tex]p(x)=3x+4 \ on\ [2,2+h]\\\\p(2)=10\\\\p(2+h)=10+h\\\\The\ average\ rate \ change= \frac{10+h-10}{2+h-2}\\\\=1[/tex]
3)
[tex]j(x)=3x^3 \ on \ [1,1+h]\\\\j(1)=3\\\\j(1+h)= 3(1+h)^3\\\\\\so, the\ rate\ change = 3h^2+9h+9[/tex]
The complete Question is: -
For the following exercises, find the average rate of change of each function on the interval specified for real numbers b or h in simplest form.
1. f(x)= 4x^2 - 7 on [1, b]
2. p(x)= 3x+4 on [2,2+h]
3. j(x)= 3x3 on [1, 1+h]
learn more about average rate.
https://brainly.com/question/12395856
#SPJ4
r Analysis A student was asked to find the tient (4x³ + x2 + 2x + 1) = (x + 2). The student's kis shown at right. Identify the student's error provide the correct quotient.
When you divide two numbers the answer is called the quotient.
How do I calculate the quotient?Divide the dividend by the divisor to find the quotient of a division problem.
This may be accomplished by using repeated subtraction or lengthy division.
The quotient of two numbers, two fractions, or two algebraic expressions can be found.
According to the remainder theorem, when a polynomial p(x) is divided by (x – a), the remainder Equals f. (a). This is demonstrated by Euclid’s Division Lemma. Using this, p(x) = q(x) (x – a) + r if q(x) is the quotient and r is the remainder.
To learn more about quotient to refer:
https://brainly.com/question/27796160
#SPJ1
You use beads to make design. Of the beads, 1/3 are red and 1/6 are blue. The rest are white. What fraction of the beads are red red or blue?
Answer:
One Half
Step-by-step explanation:
1/3 = 2/6
2/6 + 1/6 = 3/6 = 1/2
Tyrone went to a basketball game and bought a jersey that was on sale at a 30% discount. He also bought a hat that cost $37.89. Tyrone spent a total of $83.39. Write an equation to find the original cost of the jersey.
Answer: Let x be the original cost of the jersey.
We know that the jersey was on sale at a 30% discount, so the sale price is x - (30/100)*x = x(1- 0.3) = 0.7x
We also know that Tyrone spent a total of $83.39 and the hat cost $37.89, so the jersey cost is 83.39 - 37.89 = 45.5
So we can write the equation:
0.7x = 45.5
To find the original cost of the jersey, we can divide both sides by 0.7:
x = 45.5 / 0.7
x = 65
So the original cost of the jersey is $65.
Step-by-step explanation:
Answer the following
One can infer some information about a line's slope just by looking at its graph, especially in comparison to other lines plotted on the same coordinate plane.
What is Identify slope from a graph?Slope has a meaning in mathematics that is remarkably similar to what it means in everyday language. When describing the steepness and direction of lines in mathematics, slope is utilized. The three lines' graphs are displayed below; take a look:Lines A and B will be examined first. Line B is steeper than line A, if these lines were hills, in your mental model. Line A and line B have different slopes.Then, as you walk from left to right, observe how lines A and B incline up. Assuming a positive slope for these two lines. Between left and right, Line C slopes downward. It slopes down on line C. The rise and run of the line may be determined using two of its points, and the slope can be calculated. The rise and run are terms for the vertical and horizontal changes between two places, respectively. Divide the rise by the run to get the slope.
Rise / run = a slope.
A slope of 1.2 will be present on this line.regardless of the line's two points that you choose. Try calculating the slope between the point ( 6, 3 ) and the origin, ( 0, 0). The ascent will equal 3 and the run will equal 6. Rise run equals 3 / 6 plus 1 2 is the slope. It remains the same.The Complete Question is line's slope.
To Learn more About line's slope refer To:
https://brainly.com/question/16949303
#SPJ1