Answers
Answer:
option C.
Step-by-step explanation:
If we calculate average rate of change of a function over a certain interval, we’re computing the average number of units which the function moves up or down, per unit along on the xx-axis. We might alternatively argue that we’re measuring how much change occurs in our function’s value per unit on the xx-axis.
The equation for average rate of change is -
Δx/Δf =
f(x2) - f(x1) / x2 - x1
Answer:
C k(x)
Step-by-step explanation:
The average rate of change (m) of a function on an interval is the difference between the function values at the ends of the interval, divided by the interval width:
[tex]m_{ab}=\dfrac{f(b)-f(a)}{b-a}\qquad\text{average rate of change on interval $[a,b]$}[/tex]
__
simplificationHere, the interval of concern is the same for all of the functions. It is [a, b] = [0, 2] so the denominator of this fraction is 2-0 = 2 for all of the functions. That means we can determine the greatest average rate of change by simply looking at the differences f(2) -f(0) for each of the functions.
amount of changeA. j(2) -j(0) = 3(1.6²) -3 = 4.68
B. g(2) -g(0) = 25/2 -8 = 9/2 = 4.5
C. k(2) -k(0) = 9 -4 = 5 . . . . . . . . . . greatest amount of change
D. f(2) -f(0) = 1.5(2²) -1.5 = 4.5
solutionThe function k(x) has the greatest average rate of change over the interval [0, 2].
Related Questions
find the surface area of the pyramid
Answers
Answer:
20ft²
Step-by-step explanation:
X+1/2y=5 What is the rate of change of y with respect to x?
Answers
Answer:
I'll do it the answer to x is 5 0 the answer to y will be 0 10
(11-8)x3+7+27-3
(18÷3)+6+(14-8)x5
(11-7)x6+4+32-4
Answers
The results of the arithmetic evaluations as given in the task content are; 40,42 and 62.
What are the results of the arithmetic evaluations?The arithmetic operations above can be evaluated and simplified as follows;
(11-8)x3+7+27-3 = (3×3)+7+27-3 = 40.
(18÷3)+6+(14-8)x5 = (6)+6+(6)x5 = 42.
(11-7)x6+4+32-4 = (5×6) +4 +32-4 = 62.
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Solve for B:
1/5b=d+f
Answers
Answer:
b=5d+5f
solve for b by simplifying both sides and then isolating the variable.
376
Step-by-step explanation:
4.
The graph below shows the distance traveled by a person biking at a rate of 6
miles per hour.
The equation is d = 6t, where t is the number of hours and d is the distance traveled
Write an equation that represents the distance traveled by a person who can bike
at a rate of 8 miles per hour.
Answers
Answer:
d=8t
Step-by-step explanation:
The figure shows part of the concrete slab which is used to make drains and its cross-section. it is made up of a cuboid of dimensions 120 cm by 60 cm by 40 cm, with a half-cylinder horizontally carved out of it.
(i) find the area of the cross-section ABCDEFG.
(ii) find the volume of the concrete slab.
(iii) find the total surface area of the concrete slab.
(iv) find the mass of the concrete slab if the density of concrete is 2300 kg/cubic m, giving your answer in kg.
Answers
(i) The area of the cross section ABCDEFG is 1771.6cm³
(ii) The volume of the concrete lab is 212592 cm³
(iii) the total surface area of the concrete slab is 30284 cm²
(iv) The mass of the concrete slab is 40746.8 kg/m³.
Given, dimensions are 120 cm by 60 cm by
40 cm.
(i) area of cross section = 40 × 60 ₋ π(60 ₋10 ₋ 10)/2 . 1/2
= 1771.6 cm³
(ii) the volume of the concrete slab = 40 × 60 × 120 ₋ 1/2 π((60 ₋ 10 ₋10)/2)² . 120
= 212592 cm³
(iii) The total surface area is:
=40 × 120 × 2 ₊ 60 × 120 ₊ 1771.6 × 2 ₊ 10 × 120 × 2 ₊ 1/2 π(60 ₋ 10 ₋10) × 120
= 30284 cm²
(iv) Mass of the concrete slab given density is 2300 kg/m³
Mass = Volume × density
Mass = 17.716 m³ × 2300
= 40746.8 kg/m³
Hence we get the mass as 40746.8 kg/m³.
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What is the independent variable in the equation y=-5x+2?
Answers
Answer: x
Step-by-step explanation:
For this equation, the variable y is dependent on the value of x. The value of y changes depending on the value of x. This means that x is the independent variable for this equation.
√m is an integer.
Given that the value of "m" lies between between 2929 and 3939
Write down the value of "m"
Answers
Answer:
There are 8 possible answers for the value of m
Step-by-step explanation:
3025 (55^2), 3136 (56^2), 3249 (57^2)...., 3844(62^2)
The square of the numbers 55-62 could be a solution set for m.
Part 1: complete the operations geometrically. vector operations to draw the resultant vector draw 2u + 4v.
Answers
Vectors are elements of the vector space, and they can be illustrated by diagrams.
How to draw the vector 2u + 4v?The vector expression is given as:
2u + 4v
Split the vector expressions, as follows:
y1 = 2u
y2 = 4v
Next, we have:
y = y1 + y2
See the attachment for the graph of 2u + 4v.
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HELP ASAP/NOW...NO LINKS OR JOKING PLS
Answers
Answer:
D. 0 < x < 20
Explanation:
Domain is in the x axis, Range lies in the y axis.
Here it is seen that function's domain lies between 0 to 20.
Open circle's are used for '<' and '>'Closed circle's are used for '≤' and '≥'Here, as the circle's are open. Domain: 0 < x < 20
Additionally,
Range: -10 < f(x) < 0Millie needs a total of 7.8 feet of ribbon for a school project. She needs 0.7 more feet of ribbon. How much ribbon, in feet, did Millie already have? Write and solve an equation to find the answer.
6.9
7.1
7.5
8.5
Answers
Subtraction is a mathematical operation that reflects the removal of things from a collection. The ribbon that Millie already had is 7.1 feet.
What is subtraction?Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.
Given Millie needs a total of 7.8 feet of ribbon for a school project. Also, She needs 0.7 more feet of ribbon. Therefore, the ribbon that Millie needs is,
Ribbon Millie had = Total Ribbon - ribbon that is needed
= 7.8 feet - 0.7feet
= 7.1 feet
Hence, the ribbon that Millie already had is 7.1 feet.
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Can someone help me with this, it’s geometry and it’s so confusing
Answers
Answer:
Draw a line from one point A to B into the XY line in a angle
Draw a line parallel to the lines
Point a dot in the middle and name it O
Step-by-step explanation:
Hope it helps
What is the quotient of the synthetic division problem below, written in
polynomial form?
3 -2 15
-22
-16
A.2xd 121xr 41
B=
2,219x15
C. 2y 1 9g
40
D
2y7 - 21x 40
Answers
The quotient of the synthetic division problem is "f(x) = -2x² + 9x + 5" (Option C).
What is Synthetic Division?
When a polynomial division is executed using the shorthand method, using a linear factor, one is said to have executed a Synthetic Division.
The synthetic division translates to
- 2 15 -22 -15
3 | -6 27 15
-2 9 5 0
Citing the coefficient of the quotient of the first three numbers:
- 2, 9, 5. The last number is given as the remainder.
Hence the remainder is zero.
Given that the coefficient of the quotient are three, the interpretation is that the polynomial greatest degree is 2.
Thus,
f(x) = -2x² + 9x + 5
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i need help finding this for clever
Answers
Answer:
The dog is 16 years old.
Step-by-step explanation:
X/4 + 6 = X/8 + 8
X/4-X/8 = 8-6
0.125X = 2
X = 2/0.125
X = 16
Answer:
16 years old
Step-by-step explanation
Dividing the dog’s age by 4 and adding 6
D÷4 + 6
dividing the dog’s age by 8 and adding 8
D÷8 + 8
equating both
D÷4 + 6 = D÷8 + 8
=> D÷4 - D÷8 = 2
multiplying by 8 both sides
=> 2D - D = 16
=> D = 16
hence, the dog is 16 years old
a town B is 12km from another town A on a bearing of 47degree and another C is 8km from town B on a bearing of 124degree.how far is town A from town C?what is the bearing of A from C
Answers
Answer:
Distance between A and C = 16km
Bearing of A from C = 257°
Step-by-step explanation:
please see photo for detailed analysis
Translate each description into an algebraic expression. Then, evaluate the expression
using the value shown in the box for the variable.
EXAMPLE: the quotient of 112 and a added to 25 = (112 + a) + 25 = 53
a = 4
w = 10
b=3
x = 11
c = 9
y = 7
d=2
z = 5
1. the difference of 100 and the product of y and 12 =
2. b times the sum of 15 and 37 =
3. 27 added to the product of z and 12 =
4. 135 divided by the product of c and 5 =
5. w to the second power times the quotient of 12 and 4 =
6. 12 times d divided by the difference of 25 and 19 =
7. the product of x and 5 added to 13 =
Answers
The value of each algebraic expressions are:
1. 16
2. 156
3. 87
4. 3
5. 300
6. 4
7. 68
What is an Algebraic Expression?An algebraic expression is a mathematical statement involving variables and digits. It is evaluated by plugging in the value of the variables.
1. Product of y and 12 is 12y
100 - 12y
Plug in the value of y
100 - 12(7) = 16
2. b(15 + 37) = b(52) = 3(52)
= 156
3. Product of z and 12 is 12z
12z + 27 = 12(5) + 27
= 87
4. 135 ÷ 5c = 135/5(9)
= 3
5. w²(12/4) = 3w²
= 3(10²)
= 300
6. 12d ÷ (25 - 19)
12d/6 = 12(2)/6
= 4
7. 13 + 5x
13 + 5(11)
= 68
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Again, simple questions! asap help please!
15 points!
Answers
Answer:
3) r = 1.5
7) y = 18
11) x = -10
Step-by-step explanation:
3) Isolate the variable by dividing each side by factors that don't contain the variable.
7) Solve for y by simplifying both sides of the equation, then isolating the variable.
11) Move all terms that don't contain x to the right side and solve.
Solve using a formula. Please don't guess, I would like professionals to take a look
Answers
Let's take this problem step by step:
What we know:
[tex]x+y=4\\xy=-2[/tex]
Before we solve, let's do one thing that will help us out greatly later down the road:
[tex]x+y=4\\(x+y)^2=4^2\\x^2+2xy+y^2=16\\x^2+2(xy)+y^2=16\\x^2+2(-2)+y^2=16\\x^2+4+y^2=16\\x^2+y^2=20[/tex]<--- useful equation
Let's rearrange the problem a little bit:
[tex]x+\frac{x^3}{y^2}+\frac{y^3}{x^2} +y=\frac{x^3}{x^2} +\frac{x^3}{y^2}+\frac{y^3}{x^2}+\frac{y^3}{y^2}[/tex]
Combine fractions of common denominators:
[tex]\frac{x^3+y^3}{x^2} +\frac{x^3+y^3}{y^2} =(x^3+y^3)*(\frac{1}{x^2}+\frac{1}{y^2} )[/tex]
Now's let factor everything apart:
[tex](x^3+y^3)=(x+y)(x^2-xy+y^2)\\\\\frac{1}{x^2}+\frac{1}{y^2} =\frac{x^2+y^2}{x^2y^2}[/tex]
Let's use what we know and our useful equation:
[tex](x+y)*(x^2-xy+y^2)*(\frac{x^2+y^2}{x^2y^2} )\\=4*(x^2+y^2-xy)*(\frac{20}{(xy)^2} )\\=4*(20-(-2))*\frac{20}{(-2)^2} \\=4*22*5\\=440[/tex]
The value is 440
Answer: 440
Hope that helps!
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complete the square to solve the equation below. check all that apply.
x^2 + 8x - 1 = 19
Answers
Answer:
B and D
Step-by-step explanation:
First take the equation and subtract 19 on both sides. You get x^2+8x-20=0
using the quadratic formula you get x= (-8 + or - root (8^2 -4(1)(-20)))/ 2(1)
simplify it and you get x= (-8 +or- 12) / 2
Separate the equation into two and you get (-8 + 12) / 2 and (-8 - 12) / 2
first one gives: 4/2=2
second gives -20/2=-10
answer x=-10,2
can someone please help meee
Answers
Answer:
-10
Step-by-step explanation:
y2- y1 -7 -3
---------- ----------
x2 - x1 -6 6
Given the functions below, find g(5) + h(2).
g(x) = 2x - 5
h(x) = 4x + 5
Answers
h(2)=4(2)+5=13
So, g(5)+h(2)=13+5=18.
Answer:
18
Step-by-step explanation:
substitute x = 5 into g(x) and x = 2 into h(x)
g(5) + h(2)
= 2(5) - 5 + 4(2) + 5
= 10 - 5 + 8 + 5
= 5 + 13
= 18
vanessa deposited money into a bank account yhat earned 1.25% simple interest after each year. after 1/2 year she earned $5 in interest on the account. how much was her initial deposit
Answers
The initial amount is $800.
What is interest?
Interest is the price you pay to borrow money or the cost you charge to lend money.
Given:
Simple interest = 1.25% = 0.0125
So, interest in half a year.
=0.0125 ÷ 2
= 0.00625
Now,
=5 / 0.00625
= 800
Hence, the initial deposit was $800
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Question 3(Multiple Choice Worth 5 points)
(06.03 LC)
Determine the equation of the graph, and select the correct answer below.
(-1, 3)
Answers
The heights of adult men in the united states are approximately normally distributed with a mean of 70 inches and a standard deviation of 3 inches. use this information together with the 68-95-99.7 rule to make three statements about the height of adult men in the united states.
Answers
Answer:
Use the graphing calculator to graph the system of equations and find the solution where x is the total hats sold and y is the total t-shirts sold.
x + y = 152,
8.5x + 12y = 1,656
How many hats were sold?
hats
Step-by-step explanation:
a) 74.857% of adult men are shorter than Michael
b) 84.134% of adult men are taller than Jack
c) 58.991% of adult men are of height between Jack and Michael
What is 68-95-99.7 rule?Within one standard deviation of the mean is 68% of the population. Within two standard deviations of the mean, 95% of the population is located. The median is within 3 standard deviations for 99.7% of the population.
Given:
µ = 70in, σ = 3in.
We know Z = (x-µ)/σ
a) Actor Michael B. Jordan is 6’0” (72”) tall.
Z = (72-70)/3 = 0.67
So, the probability of an adult man having a height of 0-72 inches, and no greater is 74.857%
b. Comedian Jack Black is 5’7’ (67”) tall.
Z = (67-70)/3 = -1
The corresponding value is .15866 which can be the probability of an adult man having a height of 0-67 inches, and no greater.
But the percentage of those taller than jack is = 1 – .15866 = 0.84134
c) P(X < 72) – P(x < 67)
= 0.74857 – 0.15866
= 0.58991
= 58.991%
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The Question attached here is incomplete, the complete question is
a. Actor Michael B. Jordan is 6’0” (72”) tall. What percentage of adult men are shorter than Michael?
b. Comedian Jack Black is 5’7’ (67”) tall. What percentage of adult men are taller than Jack?
c. What percentage of adult men are of height between Jack and Michael?
HELP! WILL GIVE BRAINLEST
Examine the following diagram: in the photo I attached of the question
What is the measure of DBC?
2°
6°
41°
49°
Answers
Answer:
Option C: 41
Step-by-step explanation:
<ABD+<CBD=90
<ABD=8x+1
<CBD=6x+5
(8x+1)+(6x+5)=90
Combine like terms
(8x+6x)+(1+5)=90
14x+6=90
14x=90-6
14x=84
divide both sides by 14
x=6
Now we plug that value into <DBC = 6x+5
6(6)+5=
36+5
41
Let's take this problem step by step:
∠ABC is 90 degrees
⇒ made up of two angles ⇒ ∠ABD and ∠DBC
⇒ in mathematical equation form:
[tex]ABD + DBC= ABC[/tex]
Since ∠ABD = 8x + 1 and ∠DBC = 6x+5
[tex]8x + 1+6x + 5=90\\14x+6=90\\14x=84\\x=6[/tex]
Let's plug it into ∠DBC = 6x+5
∠DBC = 6x+5 = 6(6)+5=41
Answer: ∠DBC = 41
Hope that helps!
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Help me please I can’t do this and I need this for the exam tomorrow?
Answers
The value of the x will be 25. The force involved vertically to the surface of an object per unit area is pressure.
What is pressure?The force applied perpendicular to the surface of an item per unit area across which that force is spread is known as pressure.
The given data in the problem is;
The base of the block of metal is a rectangle of 20 cm by x cm.
The block exerts a force of 1500 newtons on the ground. The pressure on the ground is 3 newtons/cm²
The area of the rectangle;
A = L × B
A=20 × x
[tex]\rm P = \frac{F}{A}\\\\ 3 N / cm^2 = \frac{1500 N}{20 \times x } \\\\ x= 25[/tex]
Hence the value of the x will be 25.
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Before opening night, the cast of Wicked put on a matinee and evening dress rehearsal at the Gershwin Theatre. At the Saturday matinee, 350 people attended the show. For the Saturday evening performance, 40% more people attended the performance. If the average cost of tickets was $182, how much money did the Gershwin Theatre collect from ticket sales of the Saturday performance?
Answers
The Gershwin Theatre collected the money from ticket sales of the Saturday performance would be $89180.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
At the Saturday matinee, 350 people attended the show.
The total number of people who watched the show on Saturday = 350
For the Saturday evening performance, 40% more people attended the performance.
350 x 40%
= 350 x 0.4
= 140
Total people will be = 350 + 140 = 490
If the average cost of tickets was $182
For 490 people = 490 x 182 = $89180
Hence, the Gershwin Theatre collected the money from ticket sales of the Saturday performance would be $89180.
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if the ratio of the sides of a triangle are 13:14:15 and its perimeter is 84 cm, find the area of the triangle.
Answers
Answer:
The ratio of sides of triangle = 13:14:15
perimeter = 84 CM
perimeter of a triangle = Sum of all sides
let the sides of a triangle be 13x, 14x and 15x
84 = 13x + 14x + 15x
84 = 42x
x = 2
13x = 13* 2 = 26 CM
14x = 14*2 = 28 CM
15x = 15*2 = 30 CM
This probability distribution shows
the
typical grade distribution for a Geometry
course with 35 students.
Grade
B
F
Frequency
5
10
15
3
2
Find the probability that a student earns
a
grade of B or C.
p=[?]
Answers
Answer:
The probability that a student earns a grade of A is 1/7.
Let E be an event and S be the sample space. The probability of E, denoted by P(E) could be computed as:
P(E) = n(E) / n(S)
As the total number of students = n(S) = 35
Students getting the grade A = n(E) = 5
So, the probability that a student earns a grade of A:
P(E) = n(E) / n(S)
= 5/35
= 1/7
Hence, the probability that a student earns a grade of A is 1/7.
Keywords: probability, sample space, event
solve the inequality 5x+3> 48
Answers
Answer:
x > 9
Step-by-step explanation:
for this inequality, we want to isolate x, so that we know the inequality of x
5x + 3 > 48
- 3 -3 {subtract 3 from both sides to get x alone}
5x > 45
/5 /5 {divide both sides by 5 to find 1x}
x > 9
So , x > 9 is the inequality in terms of x {is the solution}
hope this helps! :)
Answer:
[tex]\huge\boxed{\sf x > 9}[/tex]
Step-by-step explanation:
Given inequality:5x + 3 > 48
Subtract 3 to both sides
5x > 48 - 3
5x > 45
Divide 5 to both sides
x > 9
[tex]\rule[225]{225}{2}[/tex]
