A company estimates that that sales will grow continuously at a rate given by the functions S’(t)=15e^t where S’(t) Is the rate at which cells are increasing, in dollars per day, on day t. find the sales from the 2nd day through the 6th day (this is the integral from one to six)
Answers
Given the function:
[tex]S^{\prime}(t)=15e^t[/tex]Where S’(t) Is the rate at which sales are increasing (in dollars per day). To find the sales from the second day through the 6th day, we need to integrate this function from t = 1 to t = 6:
[tex]\int_1^6S^{\prime}(t)dt=\int_1^615e^tdt=15\int_1^6e^tdt[/tex]We know that:
[tex]\int e^tdt=e^t+C[/tex]Then:
[tex]15\int_1^6e^tdt=15(e^6-e^1)\approx\text{\$}6010.66[/tex]The sales from the 2nd day through the 6th day are $6,010.66
Related Questions
find the first term when the 31st 32nd and 33rd are 1.40, 1.55, and 1.70
Answers
jadeymae06, this is the solution:
This is an arithmetic sequence, where d (common difference) = 0.15
(1.70 - 1.55) or (1.55 - 1.40)
•
,• a + 30d = 1.40
,• a + 30(0.15) = 1.4
,• a + 4.5 = 1.4
,• a = 1.4 - 4.5
,• a = -3.1
Jade, the first term is -3.1
In 2000, there were 750 cell phone subscribers in a small town. The number of subscribers increased by 80% per year after 2000. How many cell phone subscribers were in 2010? Round off the answer to the nearest whole number.
Answers
This is an exponential growth. We would apply the exponential growth formula which is expressed as
y = a(1 + r)^t
Where
a represents the imitial number of subscribers
r represents the growth rate
t represents the number of years
y represents the number of subscribers after t years
From the information given,
a = 750
r = 80/100 = 0.8
t = 9 (number of years between 2000 and 2010)
Thus,
y = 750(1 + 0.8)^9
y = 750(1.8)^9
y = 148769.48
Rounding to the nearest whole number, the number of cell phone subscribers in 2010 is
148769
Convert €3.2 per kilogram to unit price dollars per pound
Answers
We get 1.45 dollars per pound when we convert 3.2 Euros per kilogram to dollar per pound.
According to the question,
We have the following information:
3.2 Euros per kilogram
We need to convert its units into dollars per pounds.
We know that 1 Euro is approximately equal to 1 US dollar and 1 kilogram of weight is equal to 2.205 pounds.
(Note that there are various conversions from Euro to dollars which have 1 Euro equal to 1.00755 and many other values. In this case, we have rounded it off to 1 to avoid any confusion.)
(We know that per means the unit given is in divide.)
So, we have:
(3.2*1)/(1*2.205)
3.2/2.205
1.45 dollar per pounds
Hence, the conversion to dollars per pounds is 1.45 dollar per ponds from Euros per kilogram.
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What is an example of a situation from your professional or personal life that requires you to compare, understand, and make decisions based on quantitative comparison? Be sure to describe the types of quantitative comparisons you had to make, what decisions you made, and why.
Answers
An example of situation involving quantitative variables is given by:
The gameplan of an NFL coach.
What are qualitative and quantitative variables?The variables are classified as follows:
Qualitative variables are variables that assumes labels or ranks, such as good/bad, yes/no and so on.Quantitative variables are variables that Assume numerical values.In the context of this problem, we want to use quantitative variables, that is, numbers.
Multiple examples of this are given by the gameplan of NFL coaches, as the following example:
How often to blitz? The coach has to analyze the opposing offense statistics against the blitz or against standard pressure. For example, Patrick Mahomes is known to be a blitz killer, hence a coach should visualize the statistics and conclude that he has a better chance of stopping Mahomes playing standard coverage than blitzing.
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the fraction 1-2 equals?
Answers
The given fraction is 1/2.
IF we divide, we have
[tex]\frac{1}{2}=0.5[/tex]Therefore, the answer is 0.5.Referring to the figure, find the value of x in circle C.
Answers
The tangent-secant theorem states that given the segments of a secant segment and a tangent segment that share an endpoint outside of the circle, the product of the lengths of the secant segment and its external segment equals the square of the length of the tangent segment.
Graphically,
[tex]PA\cdot PB=(PD)^2[/tex]In this case, we have:
[tex]3x\cdot5=10^2[/tex]Now, we can solve the equation for x:
[tex]\begin{gathered} 3x\cdot5=10^2 \\ 15x=100 \\ \text{ Divide by 15 from both sides of the equation} \\ \frac{15x}{15}=\frac{100}{15} \\ \text{Simplify} \\ x=\frac{20\cdot5}{3\cdot5} \\ x=\frac{20}{3} \\ \text{ or} \\ x\approx6.67 \end{gathered}[/tex]Therefore, the value of x is 20/3 or approximately 6.67.
19. The table below shows the population of Florida from 2010 to 2019.YearPopulation (millions)201018.7201119.1201219.3201319.6201419.9201520.2201620.6201721.0201821.2201921.5(a) Use a graphing calculator to build a logistic regression model that best fits this data, letting t=0 in 2010. Round each coefficient to two decimal places.Pt = (b) What does this model predict that the population of Florida will be in 2030? Round your answer to one decimal place. million people(c) When does this model predict that Florida's population will reach 23 million? Give your answer as a calendar year (ex: 2010).During the year (d) According to this model, what is the carrying capacity for Florida's population? million people
Answers
The formula for the logistic regression model that best fits the data is,
[tex]y_1=\frac{a}{1+b\cdot e^{t\cdot x_{1}}}[/tex]The graph, tables and details of the population data will be shown below
a) The equation that best fits the regression model is,
[tex]\begin{gathered} P_t=y_1 \\ t=x_1 \\ a=93.2861\approx93.29(2\text{ decimal places)} \\ b=3.98291\approx3.98(2\text{ decimal places)} \\ t=-0.0198742\approx-0.02(2\text{ decimal places)} \end{gathered}[/tex]Substitutes the data above into the equation
[tex]P_t=\frac{93.29}{1+3.98\cdot e^{-0.02t}}[/tex]Hence,
[tex]P_t=\frac{93.29}{1+3.98\cdot e^{-0.02t}}[/tex]b) In the year 2030, t = 20
[tex]\begin{gathered} P_{20}=\frac{93.29}{1+3.98\cdot e^{-0.02\times20}}=\frac{93.29}{1+3.98\cdot e^{-0.4}}=\frac{93.29}{1+3.98\times0.67032} \\ P_{20}=\frac{93.29}{1+2.6678736}=\frac{93.29}{3.6678736}=25.43435521\approx25.4(1\text{ decimal place)} \\ P_{20}=25.4million\text{ people} \end{gathered}[/tex]Hence, the answer is
[tex]P_{20}=25.4\text{million people}[/tex]c) Given that
[tex]\begin{gathered} _{}P_t=23\text{million people} \\ 23=\frac{93.29}{1+3.98\cdot e^{-0.02t}} \end{gathered}[/tex]Multiply both sides by 1+3.98e^{-0.02t}
[tex]\begin{gathered} 23(1+3.98e^{-0.02t})=1+3.98e^{-0.02t}\times\frac{93.29}{1+3.98\cdot e^{-0.02t}} \\ \frac{23(1+3.98e^{-0.02t})}{23}=\frac{93.29}{23} \\ 1+3.98e^{-0.02t}=4.056087 \end{gathered}[/tex]Subtract 1 from both sides
[tex]\begin{gathered} 1+3.98e^{-0.02t}-1=4.056087-1 \\ 3.98e^{-0.02t}=3.056087 \end{gathered}[/tex]Divide both sides by 3.98
[tex]\begin{gathered} \frac{3.98e^{-0.02t}}{3.98}=\frac{3.056087}{3.98} \\ e^{-0.02t}=0.767861055 \end{gathered}[/tex]Apply exponent rule
[tex]\begin{gathered} -0.02t=\ln 0.767861055 \\ -0.02t=-0.264146479 \end{gathered}[/tex]Divide both sides by -0.02
[tex]\begin{gathered} \frac{-0.02t}{-0.02}=\frac{-0.264146479}{-0.02} \\ t=13.20732\approx13(nearest\text{ whole number)} \\ t=13 \end{gathered}[/tex]Hence, the population will reach 23million in the year 2023.
d) The carrying capacity for Florida's population is equal to the value of a.
[tex]\begin{gathered} \text{where,} \\ a=93.29\text{ million people} \end{gathered}[/tex]Hence, the carrying capacity fof Florida's population is
[tex]93.29\text{million people}[/tex]
Draw a figure to use for numbers 13 - 15. Points A. B. and C are collinear and Bis the midpoint of AC. 13. If AB = 3x - 8 and BC = x + 4, find the length of AB 14. If BC = 6x - 7 and AB = 5x + 1. find the length of AC 15. If AB = 8x + 11 and BC = 12x - 1. find the length of BCAnswer 13
Answers
13.
Given:
AB = 3x - 8, BC = x + 4
A, B and C are collinear
B is a midpoint of AC
Since B is the midpoint, we can write:
[tex]\text{length of AB = Length of BC}[/tex]Hence, we have:
[tex]3x\text{ - 8 = x + 4}[/tex]Solving for x:
[tex]\begin{gathered} \text{Collect like terms} \\ 3x\text{ -x = 4 + 8} \\ 2x\text{ = 12} \\ \text{Divide both sides by 2} \\ x\text{ = 6} \end{gathered}[/tex]Hence, the length of AB is:
[tex]\begin{gathered} =\text{ 3x - 8} \\ =\text{ 3}\times\text{ 6 -8} \\ =\text{ 18 -8} \\ =\text{ 10} \end{gathered}[/tex]Answer:
The length of AB is 10 unit
A. What is the common ratio of the pattern?B. Write the explicit formula for the pattern?C. If the pattern continued how many stars would be in the 11th set?
Answers
Given:
The sequence of number of stars is 2,4,8,16
a) To find the common ratio of the pattern.
[tex]\begin{gathered} \text{Common ratio=}\frac{2nd\text{ term}}{1st\text{ term}} \\ r=\frac{4}{2} \\ r=2 \end{gathered}[/tex]Hence the common ratio is 2.
b) To find the explicit formula for the pattern.
The general for a geometric progression sequence is,
[tex]a_n=a_1(r)^{n-1}_{}_{}[/tex]Hence, the formula for the above pattern will be,
[tex]a_n=2(2)^{n-1}[/tex]c) To find the number of stars in 11th set.
Substitute n=11 in the explicit formula of the pattern.
[tex]\begin{gathered} a_{11}=2(2)^{11-1} \\ a_{11}=2(2)^{10} \\ a_{11}=2(1024) \\ a_{11}=2048 \end{gathered}[/tex]Hence, the number of stars in 11th set will be 2048.
How many possible values for y are there where y = Cos-lo? O A. O Ο. O B. Infinite O C. 1 O D. 2
Answers
Answer:
B. Infinite
Explanation:
Given that:
[tex]y=\cos ^{-1}(0)[/tex]This implies that:
[tex]\cos (y)=0[/tex]From the graph of f(x)=cos(x), we observe that:
[tex]\cos (x)=0\text{ for }x=\frac{\pi}{2}+k\pi\text{ for any }k\in\Z,\text{ }\Z\text{ being the set of integers}[/tex]Therefore, there are infinitely possible values of y.
I need help with finding the rational approximation of 37 using perfect squares
Answers
SOLUTION
For rational approximation of 37, it means we are to obtain the close estimate for the square root of 37.
using perfect squares,
The perfect square number immediately lower than 37 is
[tex]36[/tex]The perfect square number immediately higher than 37 is
[tex]49[/tex]Then we set up the problem as in the image below
The distance between 36 to 37 is lower than the distance between 49 to 37, hence the rational aproximation of 37 will be closer to the square root of 36 than the square root of 49.
This accouunt for the sqaure root of 37 in the image above
[tex]\sqrt[]{37}=6.08\approx6.1[/tex]Therefore
The rational aprosimation of 37 using perfect square is 6.1
The GCD of two numbers is 11 and their LMC is 220. One of the numbers is 55. find the other number.
Answers
If the GCD of two numbers is 11 and their LCM is 220 and one of the number is 55, then the second number is 44
The one number = 55
Consider the second number as x
GCD is the greatest common divisor
LCM is the least common multiple
The greatest common divisor of two numbers = 11
The least common multiple of two numbers = 220
We know
The product of two numbers= The product of GCD and LCM
55 × x = 11 × 220
55x = 2420
x = 44
Hence, If the GCD if two numbers is 11 and their LCM is 220 and one of the number is 55, then the second number is 44
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2+2=im in kendergardenin. pls help.
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The addition is the operation that puts together two quantities of numbers. It is represented by the signal "+". To add the two numbers we can use a visualization method as shown below:
We have two sticks on the left and two sticks on the right, we need to add them both, this is the same as joining them together, the result is 4 sticks. The answer is 4.
Answer:
the answer is 11
duuuh
Step-by-step explanation:
Carlos is saving money to buy a new Nintendo Switch game. He has $25. After he receives his allowance (n), he will have $45. Which of the following equations models this situation?
Answers
ANSWER
25 + n = 45
EXPLANATION
We have that Carlos already has $25.
His allowance is n. After receiving it, he now has $45.
This means that if we add the amount he had and his allowance, we will have $45.
Therefore:
25 + n = 45
This equation models the situation accurately.
Find the solution to following system of equations A+ 10C = 54 A +9C = 50 A. A=10 C= 4 B. A= 14 C= 4 C. A=4 C= 14 D. A= 10 C= 6
Answers
Answer:
B. A = 14
C = 4
Explanation:
The system of equation is:
A + 10C = 54
A + 9C = 50
So, we can solve for A using the first equation:
A + 10C = 54
A + 10C - 10C = 54 - 10C
A = 54 - 10C
Now, we can replace A by (54 - 10C) on the second equation, so:
A + 9C = 50
(54 - 10C) + 9C = 50
54 - 10C + 9C = 50
54 - C = 50
54 - C + C = 50 + C
54 = 50 + C
54 - 50 = 50 + C - 50
4 = C
Then, we can replace C by 4 and calculate A, so:
A = 54 - 10C
A = 54 - 10(4)
A = 54 - 40
A = 14
Therefore, the solution of the system is:
A = 14
C = 4
Hello! I'm hitting a bit of a snag on this. I think I'm reading it too many times
Answers
The solution:
Given:
[tex]\begin{gathered} \text{ A sphere of radius 4m.} \\ \\ A\text{ cube of side 6.45m} \end{gathered}[/tex]Required:
To compare the volume and area of bot shapes.
The Sphere:
[tex]\begin{gathered} Area=4\pi r^2=4(4)^2\pi=64\pi=201.062m^2 \\ \\ Volume=\frac{4}{3}\pi r^3=\frac{4}{3}\times\pi\times4^3=268.083m^3 \end{gathered}[/tex]The Cube:
[tex]\begin{gathered} Area=6s^2=6\times6.45^2=249.615m^2 \\ \\ Volume=s^3=6.45^3=268.336m^3 \end{gathered}[/tex]Clearly, we can see that:
Both shapes have approximately the same volume.
But the cube has a greater volume than that of the sphere.
Therefore, the correct answer is [option 4]
How many different choices of shirts does the store sell
Answers
Answer:
11
Explanation:
From the probability tree:
• There are 3 choices of small shirts.
,• There are 3 choices of medium shirts.
,• There are 3 choices of large shirts.
,• There are 2 choices of X-Large shirts.
Therefore, the number of different choices of shirts the store sells:
[tex]\begin{gathered} =3+3+3+2 \\ =11 \end{gathered}[/tex]There are 11 choices of shirts.
A scale drawing of a rectangular park is 4 inches wide and 8 inches long. The actual park is 320 yards long. What is the perimeter of the actual park, in square yards?
Answers
Given:
• Width of scale drawing = 4 inches
,• Length of scale drawing = 8 inches
,• Length of actual park = 320 yards
Let's find the perimeter of the actual park.
Let's first find the width of the actual park.
To find the width of the actual park, we have:
[tex]\begin{gathered} \text{ width of actual = }\frac{\text{ length of actual}}{\text{ length of scale}}*\text{ width of scale} \\ \\ \\ \text{ width of actual = }\frac{320}{8}*4 \\ \\ \text{ width of actual = 40 * 4 = 160 yards} \end{gathered}[/tex]The width of the actual park is 160 yards.
Now, to find the perimeter of the actual park, apply the formula do perimeter of a rectangle:
P = 2(L + W)
Where:
P is the perimeter
L is the length = 320 yards
W is the width = 160 yards
Thus, we have:
P = 2(320 + 160)
P = 2(480)
P = 960 yards
Therefore, the perimeter of the actual park is 960 yards.
ANSWER:
960 yards
which are thrwe ordered pairs that make the equation y=7-x true? A (0,7) (1.8), (3,10) B (0,7) (2,5),(-1,8) C (1,8) (2,5),(3,10)D (2,9),(4,11),(5,12)
Answers
In order to corroborate that the points belong to the equation, we must subtitute the points into the equation.
If we substitute the points from option A, we get
[tex]\begin{gathered} 7=7-0 \\ 7=7 \end{gathered}[/tex]for (1,8), we have
[tex]\begin{gathered} 8=7-1 \\ 8=6\text{ !!!} \end{gathered}[/tex]then, option A is false.
Now, if we substitute the points in option B, for point (2,5), we have
[tex]\begin{gathered} 5=7-2 \\ 5=5 \end{gathered}[/tex]which is correct. Now, for point (-1.8) we obtain
[tex]\begin{gathered} 8=7-(-1) \\ 8=8 \end{gathered}[/tex]Since all the points fulfil the equation, then option B is an answer.
Lets continue with option C and D.
If we substitute point (1,8) from option C, we have
[tex]\begin{gathered} 8=7-1 \\ 8=6\text{ !!!} \end{gathered}[/tex]then, option C is false.
If we substite point (4,11) from option D, we get
[tex]\begin{gathered} 11=7-4 \\ 11=2\text{ !!!} \end{gathered}[/tex]then, option D is false.
Therefore, the answer is option B.
Rewrite the function by completing the square.
g(x)=x^2 − x − 6
g(x)= _ ( x + _ )^2 + _
Answers
The completed square function is (x - 1/2)² = 25/4
Square function:
A square function is a 2nd degree equation, meaning it has an x². The graph of every square function is a parabola.
Given,
Here we have the function g(x) = x² - x - 6
Now, we need to convert this into the complete square function.
In order to solve this we have to do the following:
Add 6 to both sides of the equation,
x² - x = 6
To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of b.
(b/2)² = (-1/2)²
Add the term to each side of the equation.
x² - x + (-1/2)² = 6 + (-1/2)²
When we simplify the equation, then we get,
x² - x + 1/4 = 25/4
Factor the perfect trinomial square into,
(x - 1/2)² = 25/4
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Is this continous or discrete?Fees for Overdue Books
Answers
The following graph is given, representing the fees due for Overdue books:
I would like to make sure my answer is correct ASAP please
Answers
step1: Write out the formula for exponential growth
[tex]y=a(1+r)^n[/tex][tex]\begin{gathered} a=\text{initial population} \\ r=\text{rate} \\ n=\text{years} \end{gathered}[/tex]Hence we have
[tex]a=800,r=3\text{ \%, n=x}[/tex]Step2: substitute into the formula in step 1
[tex]\begin{gathered} y=800(1+\frac{3}{100})^x \\ y=800(1+0.03)^x \\ y=800(1.03)^x \end{gathered}[/tex]Hence the right option is A
What does the slower car travel at Then what does the faster car travel at
Answers
Given that two cars are 188 miles apart, travelling at different speeds, meet after two hours.
To Determine: The speed of both cars if the faster car is 8 miles per hour faster than the slower car
Solution:
Let the slower car has a speed of S₁ and the faster car has a speed of S₂. If the faster speed is 8 miles per hour faster than the slower car, then,
[tex]S_2=8+S_1====\text{equation 1}[/tex]It should be noted that the distance traveled is the product of speed and time. Then, the total distance traveled by each of the cars before they met after 2 hours would be
[tex]\begin{gathered} \text{distance}=\text{speed }\times time \\ \text{Distance traveled by the faster car after 2 hours is} \\ =S_2\times2=2S_2 \\ \text{Distance traveled by the slower car after 2 hours is} \\ =S_1\times2=2S_1 \end{gathered}[/tex]It was given that the distance between the faster and the slower cars is 188 miles. Then, the total distance traveled by the two cars when they meet is 188 miles.
Therefore:
[tex]\begin{gathered} \text{Total distance traveled by the two cars is} \\ 2S_1+2S_2=188====\text{equation 2} \end{gathered}[/tex]Combining equation 1 and equation 2
[tex]\begin{gathered} S_2=8+S_1====\text{equation 1} \\ 2S_1+2S_2=188====\text{equation 2} \end{gathered}[/tex]Substitute equation 1 into equation 2
[tex]\begin{gathered} 2S_1+2(8+S_1)=188 \\ 2S_1+16+2S_1=188 \\ 2S_1+2S_1=188-16 \\ 4S_1=172 \end{gathered}[/tex]Divide through by 4
[tex]\begin{gathered} \frac{4S_1}{4}=\frac{172}{4} \\ S_1=43 \end{gathered}[/tex]Substitute S₁ in equation 1
[tex]\begin{gathered} S_2=8+S_1 \\ S_2=8+43 \\ S_2=51 \end{gathered}[/tex]Hence,
The slower car travels at 43 miles per hour(mph), and
The faster car travels as 51 miles per hour(mph)
what is 3/8 * 1/5 and 6/10 * 3/4
Answers
Answer
(3/8) × (1/5) = (3/40)
(6/10) × (3/4) = (9/20)
Explanation
We are asked to solve the given expressions
(3/8) × (1/5)
And
(6/10) × (3/4)
For (3/8) × (1/5)
[tex]\frac{3}{8}\times\frac{1}{5}=\frac{3\times1}{8\times5}=\frac{3}{40}[/tex]For (6/10) × (3/4)
[tex]\begin{gathered} \frac{6}{10}\times\frac{3}{4}=\frac{6\times3}{10\times4}=\frac{18}{40} \\ We\text{ can now reduce this to the simplest form} \\ \text{Divide numerator and denominator by 2} \\ \frac{18}{40}=\frac{9}{20} \end{gathered}[/tex]Hope this Helps!!!
Find the first five terms in sequences with the following 3n+2
Answers
To determine the first five terms of the sequence we substitute n by 1, 2, 3, 4, and 5.
For n=1, we get:
[tex]3(1)+2=3+2=5.[/tex]For n=2, we get:
[tex]3(2)+2=6+2=8.[/tex]For n=3, we get:
[tex]3(3)+2=9+2=11.[/tex]For n=4, we get:
[tex]3(4)+2=12+2=14.[/tex]For n=5, we get:
[tex]3(5)+2=15+2=17.[/tex]Answer: The first five terms of the sequence are:
[tex]5,\text{ 8, 11, 14, 17.}[/tex]Find the real solutions of the equation by graphing. 4x^3-8x^2+4x=0
Answers
x = 0,1 are the real solutions of the equation .
What are real solutions in math?
Any equation's solution that is a real number is known as a "real solution" in algebra.Discriminant b2 - 4ac is equal to zero when there is only one real solution. One solution, x = -1, exists for the equation x2 + 2x + 1 = 0.There are a number of solutions to the given quadratic equation depending on whether the discriminant is positive, zero, or negative. The existence of two unique real number solutions to the quadratic is indicated by a positive discriminant. A repeating real number solution to the quadratic equation is indicated by a discriminant of zero.4x³ - 8x² + 4x = 0
x( 4x² - 8x + 4 ) = 0
x( 4x² - 4x - 4x + 4 ) = 0
x ( 4x ( x - 1) -4 ( x - 1 )) = 0
x ( ( 4x - 4 ) ( x - 1 ) ) = 0
x = 0
4x - 4 = 0 ⇒ x = 1
x - 1 = 0 ⇒ x = 1
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How many soultions?x + 3 = 2x - 18A single solutionInfinite solutionsNo solution
Answers
The given equation is expressed as
x + 3 = 2x - 18
Subtracting x from both sides of the equation, it becomes
x - x + 3 = 2x - x - 18
3 = x - 18
Adding 18 to both sides of the equation, it becomes
3 + 18 = x - 18 + 18
21 = x
x = 21
Since there is only one value for x, the correct option is
a. A single solution
Given slope of m=2/3 and y-intercept b=1 graph the line
Answers
ok! to graph your first point, you know the y-intercept is 1, so your point is (0,1)
graph that
because we knkow the slope is 2/3 and it's y change/x change, move up 2 and left 3 for your next point, which is (2,4)
we can graph a third point for accuracy, and move up 2 and left 3 again to get (4,7)
create a line connecting all the points
Find the perimeter and area of the polygon with given vertices
Answers
Let's begin by listing out the information given to us:
[tex]\begin{gathered} A(-3,3),B(-3,-1),C(4,-1),D(4,3) \\ AB=3-(-1)=3+1=4_{} \\ BC=|-3-4|=|-7|=7 \\ CD=|-1-3|=|-4|=4 \\ AD=|-3-4|=|-7|=7 \\ \\ Perimeter=2(l+w)=2(7+4)_{}=2(11)=22 \\ Perimeter=22unit \\ \\ Area=lw=7\cdot4=28unit^2 \\ Area=28unit^2 \end{gathered}[/tex]Tools Pencil Guideline Eliminator Sticky Notes Formulas Graphing Calculator Graph Paper Х y 5 Clear Mark 3 -4.5 5 -9.5 7 - 14.5 9 - 19.5 What are the slope and the y-intercept of the graph of this function? A Slope = 2, y-intercept = -4.5 5 B Slope = y-intercept = 3 2 © Slope = 2, y-intercept = -5 D Slope = 2 5 y-intercept = 3
Answers
Explanation:
The equation for a line in the slope-intercept form is:
[tex]y=mx+b[/tex]Where 'm' is the slope and 'b' is the y-intercept.
We can find both with only two points from the line. The slope is:
[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_1-y_2}{x_1-x_2}[/tex](x1, y1) and (x2, y2) are points on the line.
With only one of these points, once we know the slope, we can find the y-intercept by replacing x and y by the point. For example:
[tex]y_1=mx_1+b[/tex]And then solve for b.
In this problem we can use any pair of points from the table. I'll use the first two:
• (3, -4.5)
,• (5, -9.5)
The slope is:
[tex]m=\frac{-4.5-(-9.5)}{3-5}=\frac{-4.5+9.5}{-2}=\frac{5}{-2}=-\frac{5}{2}[/tex]And the y-intercept - I'll use point (3, -4.5) to find it;
[tex]\begin{gathered} -4.5=-\frac{5}{2}\cdot3+b \\ -4.5=-\frac{15}{2}+b \\ b=-4.5+\frac{15}{2}=-\frac{9}{2}+\frac{15}{2}=\frac{6}{2}=3 \end{gathered}[/tex]Answer:
• Slope: -5/2
,• y-intercept: 3
The correct answer is option B