Answer:
A(t) = 3/2t² + 24t + 96
Range = (96, ∞)
Explanation:
The equation for the side length of the cube s is given by
[tex]s(t)=\frac{1}{2}t+4[/tex]Where t is the number of hours. In the same way, the equation for the surface area is:
[tex]A(s)=6s^2[/tex]Then, the surface area as a function of time will be the composite function A(s(t)). So, replacing s by the equation of s(t), we get:
[tex]\begin{gathered} A(s(t))=6s(t)^2 \\ A(s(t))=6(\frac{1}{2}t+4)^2 \\ A(t_{})=6(\frac{1}{4}t^2+2(\frac{1}{2}t)(4)+4^2) \\ A(t)=6(\frac{1}{4}t^2+4t+16) \\ A(t)=6(\frac{1}{4}t^2)+6(4t)+6(16) \\ A(t)=\frac{3}{2}t^2+24t+96 \end{gathered}[/tex]Then, the range is the set of all the possible values that A(t) can take. Since t takes values greater than or equal to 0, the minimum value that A(t) will take is 96 because:
A(0) = 3/2(0)² + 24(0) + 96 = 96
Therefore, the range for the surface area will be (96, ∞)
Want to check if I got the correct answer, thank you
To find:
The division of the polynomial.
Solution:
The division in given in the image below:
Thus, the result is:
[tex]x^3+3x^2-1x-5-\frac{11}{x+3}[/tex]Option D is correct.
Nick knows that a + b < 0. Which statement is true?
I'll inform that to the tech team
Meanwhile I'll help here, ok?
I asked if this part of the question was right: a + b < 0
If a shape is dilated by a scale factor of 5, what is the resulting area?A.) The new area is 4Times the originalB.) The new area is 25times the originalC.) The new area isone-fourth theoriginalD.) The new area is 5times the original
If a shape is dilated by a scale factor of 5, the new dimensions would have increased by a factor of 5 on all sides. This means the new area is 25 times the original
The correct answer is option B
CAN SOMEONE HELP WITH THIS QUESTION?✨
Answer: [tex]48^{\circ}[/tex]
Step-by-step explanation:
Coterminal angles differ by integer multiples of [tex]360^{\circ}[/tex].
So, an angle coterminal with an angle of [tex]408^{\circ}[/tex] is [tex]408^{\circ}-360^{\circ}=48^{\circ}[/tex], which lies within the required interval.
Question 1 of 10‚Q(t) = Q¸e¯ktThe functionmay be used to model radioactive decay. Qrepresents the quantity remaining after tyears; k is the decay constant. Thedecay constant for plutonium-240 is k = 0.00011. What is the half-life, inyears?OA. 6,301 yearsOB. 1,512,321 yearsC. 0.076 yearsOD. 3,150 years
The half-life is 6300 years.
From the question, we have
t_1/2 = 0.693/k
where,
t_1/2 = half-life
k = decay constant = 0.00011
substituting the value, we get
⇒t_1/2 = 0.693/0.00011
⇒t_1/2 = 6300 years
Half Life Period:
One of the main terms used in physics to describe the radioactive decay of a specific sample or element over a predetermined amount of time is half-life, also known as half-life period. When studying the subject, nuclear physics students will frequently run into the phrase. The term "exponential decay" is also frequently used to refer to both exponential and non-exponential decay, which are both common forms of decay processes. In fields other than physics, the word is used to describe the biological half-life of specific substances in the human body or in medications.
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what is the simplest form for the ratio of 24:48 and how
For 24 / 48 simplest form find the maximum common divisor ( m.c.d)
In this special case ( but this not common) 24 divides exactly 48
so then 24/24 = 1. And 48/24= 2.
then the simplest form is 24/48= 1/2
What is the approximate area they will have to paint to fill in this tree?
The area is 18. 8 ft².
From the question, we have
Area of a triangle = 1/2 base × height
= 1/2 × 5 × 3
= 1/2 × 15
= 7. 5 ft²
In trapezoid,
a = 4ft
b = 0. 2ft
h = 5ft
Area of trapezoid = 1/2*(a+b)*h
= 1/2*(4+0.2)*5
= 1/2*4.2*5 = 10. 5 ft²
Area of rectangle = length × width
= 0. 2 × 4
= 0. 8 ft²
Total area of tree = area of triangle + area of trapezoid + area of rectangle
= 7. 5 + 10. 5 + 0. 8
= 18. 8 ft²
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
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I NEED HELP FINDING THIS ANSWER ASAP PLEASE AND THANK YOU
The coordinates of triangle after being reflected across y-axis: X"(-2, -5), Y"(-2, -2), Z"(-1, -4)
Given that the coordinates of triangle X(4, -5), Y(4, -2), Z(5, -4)
ΔXYZ is reflected across the line x = 3 and then reflects the image across the y-axis.
We need to find the coordinates of triangle after mentioned geometric transformation.
i) when ΔXYZ is reflected across the line x = 3
the coordinates of ΔX'Y'Z' are:
X'(2, -5), Y'(2, -2), Z'(1, -4)
The green triangle in the following graph.
ii) when ΔX'Y'Z' is reflected across the y-axis
the coordinates of ΔX"Y"Z" are:
X"(-2, -5), Y"(-2, -2), Z"(-1, -4)
The orange triangle in the following graph.
Therefore, the coordinates of triangle after being reflected across y-axis: X"(-2, -5), Y"(-2, -2), Z"(-1, -4)
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I really need help I can’t seem to understand this at all
Given the sequence below
[tex]8,12,18,27[/tex]The sequence above is a geometric series, therefore the formula for the common ratio(r) is
[tex]r=\frac{2ndterm}{First\text{ term}}=\frac{Thirdterm}{2nd\text{ term}}[/tex]Therefore,
[tex]\begin{gathered} r=\frac{12}{8}=\frac{18}{12} \\ r=\frac{3}{2}=\frac{3}{2} \end{gathered}[/tex]Hence, the answer is
[tex]\frac{3}{2}\text{ \lparen Option 3\rparen}[/tex]An electric company calculates a person's monthly bill from the number of kilowatt-hours (kWh), x, used. The function b(x) = { x < 200 0.10x, 0.15(x – 200) + 20, x > 200 determines the bill. How much is the bill for a person who uses 800 kWh in a month? O A. $90 O B. $110 O C. $60 O D. $80
Since x = 800kWh which is greater than 200, we use the function
b(x) = 0.15(x - 200) + 20
b(800) = 0.15(800 - 200) + 20
=0.15(600) + 20
= 90 + 20
=$110
option B is the correct answer
120+m=203d+59=33c-87=-42
Let's solve the following equation
c - 87 =42
Adding 87 at both sides:
c - 87 + 87 = -42 + 87
c = 45
The total income for the Mr. Jones’s apartment building can be represented by the equation 2R minus C minus 2P, where r is the amount of rent paid by each tenant, C is the cost of the cable bill, P is the cost of the phone bill. If the rent is $700, the cable bill is $100 in the phone bill is $50, what is the total income for Mr. Johnson?
total income= 2R-C-2P
R= omoun tof rent paid by each tenant = $700
C= cable bill = $100
P = Phone bill = $50
Replace the values:
Total income = 2(700)-100-2(50)
total income= 1,400-100-100 = 1,400-200= $1,200
Total income =$1,200
Consider the following three systems of linear equations.(Please list what option it is.
We transform System A into System B by converting equation A2 into equation B2. We transform System B into System C by converting equation B2 into equation C2.
We are given three systems of linear equations. The first system of linear equations is A1 : -2x + 7y = -5 and A2 : 4x - 3y = -23. The second system of linear equations is B1 : -2x + 7y = -5 and B2 : 11y = -33. The third system of linear equations is C1 : -2x + 7y = -5 and C2 : y = -3. To convert the system A to system B, we transform the equation A2 to equation B2. To convert the system B to system C, we transform the equation B2 to equation C2.
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Morris borrowed $9,000 from a credit union at 13% simple interest for 42 months. What were his money installment payments (to the nearest whole cent)?$311.79 per month$307.89 per month$297.58 per month$377.12 per monthNone of these choices are correct.
Now the total interest for 42 months will be:-
[tex]\begin{gathered} S\mathrm{}I\mathrm{}=\frac{9000\times13\times7}{200} \\ =\frac{90\times13\times7}{2} \\ =45\times13\times17 \\ =4095 \end{gathered}[/tex]So the total amount he has to pay after 42 months will be = 9000+4095
= $13095
So
[tex]\begin{gathered} 42\text{ months = \$13095} \\ 1\text{ month =}\frac{13095}{42} \\ =311.79 \end{gathered}[/tex]So his monthly installment will be $ 311.79
So $ 311.79 is the correct option.
4) B) determine the scope of each of the following lines assume the dots are on integer coordinates
Given the following question:
Part B:
Point A: (-8, -2) = (x1, y1)
Point B: (3, 2) = (x2, y2)
Formula for slope:
[tex]m=\frac{y2-y1}{x2-x1}[/tex][tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ m=\frac{2--2}{3--8}=\frac{4}{11} \\ m=\frac{4}{11} \end{gathered}[/tex]Use the formula d = vt + 1672, where d is the distance in feet, v is the initial velocity in feet per second, and t is the time in seconds.An object is released from the top of a building 320 ft high. The initial velocity is 16 ft/s. How many seconds later will the object hit the ground?
We got to use the given formula:
[tex]d=v\cdot t+16t^2[/tex]The distance, d, given is 320 ft and the initial velocity, v, 16 ft/s. We want the time, t. So:
[tex]\begin{gathered} d=v\cdot t+16t^2 \\ 320=16t+16t^2 \\ 16t^2+16t-320=0 \\ \frac{16t^2}{16}+\frac{16t}{16}-\frac{320}{16}=\frac{0}{16} \\ t^2+t-20=0 \end{gathered}[/tex]Now, we have a quadratic equation, so we can use Bhaskara formula:
[tex]\begin{gathered} t=\frac{-1\pm\sqrt[]{1^2-4\cdot1\cdot(-20)}}{2\cdot1}=\frac{-1\pm\sqrt[]{1+80}}{2}=\frac{-1\pm\sqrt[]{81}}{2}=\frac{-1\pm9}{2} \\ t_1=\frac{-1-9}{2}=-\frac{10}{2}=-5 \\ t_2=\frac{-1+9}{2}=\frac{8}{2}=4 \end{gathered}[/tex]Because we can't have a negative time, we consider only the second one, which it t = 4s.
I vaguely remember how to do this although I am familiar with all. All I need is a quick review explanation and I’ll be good. Thanks!
We have to calculate the perimeter of a pen that has an area expressed as
A = 3x²-7x+2.
We assume it is a rectangular pen, so it will have two different sides.
The area will be the product of this two side lengths, while the perimeter will be 2 times the sum of the lengths of the two sides.
Then, we start by rearranging the expression of A as a product of two factors.
We can do it by factorizing A.
To do that, we calculate the roots of A as:
[tex]\begin{gathered} x=\frac{-(-7)\pm\sqrt[]{(-7)^2-4\cdot3\cdot2}}{2\cdot3} \\ x=\frac{7\pm\sqrt[]{49-24}}{6} \\ x=\frac{7\pm\sqrt[]{25}}{6} \\ x=\frac{7\pm5}{6} \\ \Rightarrow x_1=\frac{7-5}{6}=\frac{2}{6}=\frac{1}{3} \\ \Rightarrow x_2=\frac{7+5}{6}=\frac{12}{6}=2 \end{gathered}[/tex]Then, we can now express A as:
[tex]\begin{gathered} A=3(x-\frac{1}{3})(x-2) \\ A=(3x-1)(x-2) \end{gathered}[/tex]Then, we can consider the pen to be a rectangle (or maybe square, depending on the value of x) with sides "3x-1" and "x-2".
Then, we can now calculate the perimeter as 2 times the sum of this sides:
[tex]\begin{gathered} P=2\lbrack(3x-1)+(x-2)\rbrack \\ P=2(3x-1+x-2) \\ P=2(4x-3) \\ P=8x-6 \end{gathered}[/tex]Answer: we can express the perimeter as 8x-6.
Each chef at "Sushi Emperor" prepares 15 regular rolls and 20 vegetarian rolls daily. On Tuesday, each customer ate 2 regular rolls and 3 vegetarian rolls. By the end of the day, 4 regular rolls and 1 vegetarian roll remained uneaten.
How many chefs and how many customers were in "Sushi Emperor" on Tuesday?
Please Help!
Answer: 13 customers and 2 chefs
Step-by-step explanation:
What is the slope of the line created by this equation? Round your answer out to two decimal places. 10x+5y=3
Given the Linear Equation:
[tex]10x+5y=3[/tex]You can write it in Slope-Intercept Form, in order to identify the slope of the line.
By definition, the Slope-Intercept Form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope of the line and "b" is the y-intercept.
Therefore, you can rewrite the given equation in Slope-Intercept Form by solving for "y":
[tex]\begin{gathered} 5y=-10x+3 \\ \\ y=\frac{-10x}{5}+\frac{3}{5} \end{gathered}[/tex][tex]y=-2x+\frac{3}{5}[/tex]You can identify that:
[tex]\begin{gathered} m=-2 \\ \\ b=\frac{3}{5} \end{gathered}[/tex]Hence, the answer is:
[tex]m=-2[/tex]སྣ། Cookies maze -x-37 +32=2) x+4y + 3x tt 5x+2y-27=-34 -12
Step 1: Problem
-x - 3y + 3z = 21
x + 4y + 5z = -1
5x + 7y - 2z = -34
Step 2: Concept
Apply substitute method to solve the three systems of equation.
Step 3: Method
Name the system of equations
-x - 3y + 3z = 21 ------------------------------ 1
x + 4y + 5z = -1 ------------------------------- 2
5x + 7y - 2z = -34 --------------------------3
From equation 1, make r subject of relation and substitute into 2 and 3
x = -3y + 3z - 21
Next, substitute x in equations 2 and 3.
In 2
- 3y + 3z - 21 + 4y + 5z = -1
y + 8z = -1 + 21
y + 8z = 20 ----------------------------------- (4)
In 3
5(-3y + 3z - 21) + 7y - 2z = -34
-15y + 15z - 105 + 7y - 2z = -34
-8y + 13z = - 34 + 105
-8y + 13z = 71 ------------------------------------- (5)
from 4, make y subject and substitute in 5
y = 20 - 8z
In 5
-8(20 - 8z) + 13z = 71
-160 + 64z + 13z = 71
77z = 71 + 160
77z = 231
z = 231/77
z = 3
y = 20 - 8(3)
y = 20 - 24
y = -4
x = -3y + 3z - 21
x = -3(-4) + 3(3) - 21
x = 12 + 9 - 21
x = 0
Step 4: Final answer
x = 0, y = -4 z = 3
choose equation of a line perpendicular to the given equation and passing through the point p x-axis; P =(6,2)
To solve the question you have find the equation of the line that is perpendicular to the y axis and passes through the point (6,2), so in this case the equation of the line is y=2 as you can see in this picture
Remember that two lines are perpendicular when they form an 90 degrees angle between them
Suppose that the functions h and f are defined as follows h(x)=x^2 +2f(x)=7/9x, x ≠0Find the compositions h• h and f•f Simplify your answers as much as possible (h•h)(x)=(f•f)(x)=
1) First we compute:
[tex](h\circ h)(x)=h(h(x))=h(x^2+2)=(x^2+2)^2+2.[/tex]Simplifying we get:
[tex](h\circ h)(x)=x^4+4x^2+4+2=x^4+4x^2+6.[/tex]2)Computing the composition we get:
[tex](f\circ f)(x)=f(f(x))=f(\frac{7}{9x})=\frac{7}{(9(\frac{7}{9x}))}=\frac{7}{\frac{7}{x}}=x.[/tex]Answer:
[tex]\begin{gathered} (h\circ h)(x)=x^4+4x^2+6, \\ (f\circ f)(x)=x. \end{gathered}[/tex]The longest runaway at an airport has the shape of rectangle and an area of 2,057,000 square feet. This runaway is 170 feet wide how long is the run away ? The length of the runaway is ?
The runway is 12100 ft long
Explanation:The area of a rectangle is given as:
A = wl
Where w is the width and l is the length
Given that A = 2, 057,000 sq. ft
w = 170 ft
Using these, we can easily find l
2,057,000 = 170l
l = 2,057,000/170
= 12100
So in my class i am studying RatioThe question is:There are 7 red pens for every 10 pencils in the borrow bin So would the answer be Part to partPart to whole or Whole to part
Answer:
The ratio of red pens to pencils is 7/10
The ratio of pencils to red pens is 10/7
Step-by-step explanation:
Ratio:
The ratio of a to b is a/b
The ratio of b to a is b/a
In this question:
7 red pens
10 pencils
The ratio of red pens to pencils is 7/10
The ratio of pencils to red pens is 10/7
marisol has 4/12 cups of flour. A biscuit recipe she wants try requries 3/4 cup of flour for a single batch of biscuits. How many batch s of biscuits can Marisol make
The number of biscuit batches that Marisol can make from the given task content is; 4 / 9 batches.
What is the number of biscuit batches that can be made from the 4/12 cups of flour?It follows from the task content that the number of batches of biscuit that can be made from the given 4/12 batches of biscuit be determined.
By proportion, since it is given that the one biscuit recipe requires 3/4 cups of flour, it consequently can be inferred that;
In 4/12 cups of flour, the number of batches she can make is;
= 4/12 ÷ 3/4
= 4/12 × 4/3
= 16 / 36
= 4 / 9 batches of biscuits.
Ultimately, the number of batches of biscuits she can make is; 4 / 9 batches of biscuits.
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I need help with this practice problem Having trouble solving it If you can use Desmos to graph it
The graph of the function:
[tex]f(x)=\cot (x+\frac{\pi}{6})[/tex]is shown below:
By graphing at least one full period of the function, we would take the limit of the function as:
[tex]-\pi\le x\le\pi[/tex]Hence, the graph of at least one full period is:
A bottle rocket is launched straight up. Its height in feet (y) above theground x seconds after launch is modeled by the quadratic function: y =-16x2 + 116x + 7.What was the maximum height of the rocket?
1) Looking at the function y= -16x² + 116x + 7
The maximum height is the vertex described by the parabola. The Vertex follows that formula:
[tex]\begin{gathered} V=(\frac{-b}{2a},\frac{-\Delta}{4a}) \\ \end{gathered}[/tex]2) Since the question wants only the height, let's keep with the y-coordinate of the Vertex. Let's call it Yv
[tex]Y_V=\frac{-(116^2-4(-16)(7))}{4(-16)}\Rightarrow\frac{-(13904)}{-64}=\text{ 217.25}[/tex]So the maximum height of that rocket is 217.25 feet above the ground.
The graph shows the distance ofa remote control drone above theground as it flies west to east. Thex-axis represents the distance from acentral point and the y-axis representsthe distance above the ground, in m.411-21021. What is the range of the functionand what does it represent?
Part 1
For this question we need to remember that the range is defined as:
[tex]\text{Range}=\text{Max}-Mi[/tex]And if we look at the function we see that Min =0 and Max= 5 so then we have:
[tex]\text{Range}=5-0=5[/tex]And the range represent the lenght of the codomain of a function
Part 2
The domain for this case is given by:
[tex]\text{Domain}=\left\lbrack -4,4\rbrack\right?[/tex]And it represent all te possible values of x that the function can assume
Part 3
For this case we identify two intervals where the height is increasing:
[-4,-2] and [0,4]
But the longest interval is :[0,4]
Part 4
The x intercept represent the values when the function satisfy that y=0 and we have:
x intercepts: x=-4, x=0
Part 5
The average rate of change between [-4,4] is given by:
[tex]m=\frac{3-0}{4-(-4)}=\frac{3}{8}[/tex]And then the answer for this case would be 3/8
The steps for deriving the Quadratic formular are shown. Which best choose for the missing reason?
In the part inside the yellow circle, we multiplied by 1 the term -c/a, that is
[tex]-\frac{c}{a}=-\frac{c}{a}\times1=-\frac{c}{a}(\frac{4a}{4a})=-\frac{4ac}{4a^2}[/tex]where 1 was written as 4a/4a.
Since we must add this result to
[tex]\frac{b^2}{4a^2}[/tex]the answer is option C, change to LCD ( Least Common Denominator) because both terms must have the same denominator, which is 4a^2.
Matt needs to find the volume of this rectangular pyramid. What answer should he arrive to?
Given:
• Length of the pyramid, l = 17 units
,• Width of the pyramid, w = 7 units
,• Height of the pyramid, h = 13 units
Let's find the volume of the given rectangular pyramid.
To find the volume, apply the formula:
[tex]V=\frac{l*w*h}{3}[/tex]Where:
l is the length = 17 units
w is the width = 7 units
h is the height = 13 units
Thus, we have:
[tex]\begin{gathered} V=\frac{17*7*13}{3} \\ \\ V=\frac{1547}{3} \\ \\ V=515.67\text{ cubic units} \end{gathered}[/tex]Therefore, the volume of the rectangular pyramid is 515.67 cubic units.
Matt's answer should be 515.67 cubic units.
ANSWER:
515.67 cubic units.