Answer:
Option c
Step-by-step explanation:
given that limit x tending to 4 of the function (3x-4) is 8
This implies for all values of x such that for epsilon >0 arbitrary small ,
[tex]||x-4||<\epsilon[/tex], we get
|f(x)-8|<3epsilon
this is equivalent to the option c.
Proof:
Consider
[tex]||x-4||<\epsilon\\3||x-4||<3\epsilon\\||3x-12||<3\epsilon\\||3x-4|-8| <3\epsilon[/tex]
Hence it follows that option C is right.
The correct statement to use when proving that limx→4(3x−4)=8 is option b: Given 0 < | x - 4 | < epsilon/3, then | (3x - 4) - 8 | < epsilon. This uses the formal definition of limit and abides the epsilon-delta parameters definition to provide the correct proof.
Explanation:To verify the given limit, we need to utilize the formal definition of a limit. This formal definition gives us a systematic method to prove a limit based on epsilon-delta parameters. The purpose is to show that as x gets closer and closer to 4 (with| x - 4 | being smaller than an arbitrary positive delta), the expression (3x-4) increasingly approaches 8 (with |(3x - 4) - 8| getting within an epsilon range).
The correct choice is: b. Given 0 < | x - 4 | < epsilon/3, then | (3x - 4) - 8 | < epsilon. In this case, 'epsilon/3' in | x - 4 | < 'epsilon/3' is the delta in the epsilon-delta definition of limit. Essentially, it captures the notion that for every epsilon > 0, there exists a delta > 0 such that 0 < | x - 4 | < delta implies | (3x - 4) - 8 | < epsilon, thereby proving the limit.
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The manager at a concert venue keeps track of the number of adult tickets and student tickets sold each day and the total money received. On Wednesday, a total of 74 tickets were sold, and the money collected was $994. If adult tickets are sold for $15 and student tickets are sold for $11, how many adult tickets and student tickets were sold? Give your answer as an ordered pair (x,y), where x is the number of adult tickets and y is the number of student tickets.
Answer: the number of adult and student tickets sold are (45, 29)
Step-by-step explanation:
Let x represent the number of adult tickets that were sold.
Let y represent the number of student tickets that were sold.
On Wednesday, a total of 74 tickets were sold. This means that
x + y = 74
x = 74 - y- - - - - - - - - - - - - - 1
If adult tickets are sold for $15 and student tickets are sold for $11 and the money collected was $994, it means that
15x + 11y = 994- - - - - - - - - - - - - - 2
Substituting equation 1 into equation 2, it becomes
15(74 - y) + 11y = 994
1110 - 15y + 11y = 994
- 15y + 11y = 994 - 1110
- 4y = - 116
y = - 116/ - 4
y = 29
Substituting y = 29 into equation 1, it becomes
x = 74 - 29 = 45
The number of adult tickets and student tickets sold is (x, y) = (45, 29)
To determine the number of adult tickets x and student tickets y sold, we need to solve the system of equations given by the following conditions:
1. The total number of tickets sold is 74:
x + y = 74
2. The total revenue from the tickets is $994, with adult tickets sold for $15 each and student tickets sold for $11 each:
15x + 11y = 994
We can solve this system of equations using the substitution or elimination method. Here, we will use the elimination method.
First, let's write the two equations clearly:
x + y = 74
15x + 11y = 994
To eliminate one of the variables, we can multiply the first equation by 11, so the coefficients of y in both equations will be the same:
[tex]\[ 11(x + y) = 11 \cdot 74 \][/tex]
11x + 11y = 814
Now we have:
11x + 11y = 814
15x + 11y = 994
Next, we subtract the first modified equation from the second equation to eliminate y
(15x + 11y) - (11x + 11y) = 994 - 814
15x + 11y - 11x - 11y = 180
4x = 180
x = 45
Now, substitute x = 45 back into the first original equation to find y
x + y = 74
45 + y = 74
y = 29
Therefore, the number of adult tickets and student tickets sold is:
(x, y) = (45, 29)
The temperature is 71 °F at 2:00 in the afternoon. If the temperature drops 8 °F every hour after that, what is the temperature at 6:00 in the evening?
Answer:
39 °F
Step-by-step explanation:
There's 4 hours difference between given times so the change in the temperature would be 4 × 8 = 32° F if the temperature drops 8 °F every hour therefore the temperature would be 71 - 32 = 39 °F
What is the probability that at least one of a pair of fair dice lands of 5, given that the sum of the dice is 8?
Answer:
0.40
Step-by-step explanation:
to find out the probability that at least one of a pair of fair dice lands of 5, given that the sum of the dice is 8
Let A = sum of dice is 8
B = one lands in 5
P(B/A) = P(AB)/P(A) by conditional probability
P(AB) = sum is 8 and one is 5
So (5,3) or (3,5)
P(A) = sum is 8.
i.e. (2,6) (2,6) (3,5) (5,3) (4,4)
Required probability
= n(AB)/n(A)
=[tex]\frac{2}{5} =0.40[/tex]
Need help with this sheet (solve each equation using the quadratic formula)
Answer:
Step-by-step explanation:
A student translated the phrase below into an algebraic expression, and then evaluated it for g = one-fourth. Is the student's work correct? one-third more than the product of four and a number; evaluate when g = one-fourth The expression is StartFraction 4 Over g EndFraction + one-third; for g = one-fourth. StartFraction 4 Over 1 EndFraction divided by one-fourth + one-third = StartFraction 4 Over 1 EndFraction times StartFraction 4 Over 1 EndFraction + one-third = 16 + one-third = 16 and one-third.
Answer: D
Step-by-step explanation:
it makes the most sense ( do ont know how to explain but I do know it is right. )
Answer:
D.) No, product means multiplication, and the student wrote a division expression.
Step-by-step explanation:
did the assignment. good luck! <3
What is the measure of side FD?
3.4 units
5.9 units
5.8 units
72.4 units
A suncatcher has 6 sections. Each section is in the shape of a parallelogram witha base of 12 cm and a height of 8 cm. What is the total area of the sections?
Answer:
576 cm²
Step-by-step explanation:
Given:
Number of sections in a suncatcher (n) = 6
Each section is in the shape of a parallelogram.
Base of parallelogram = 12 cm
Height of parallelogram = 8 cm
Now, area of a parallelogram is given as:
Area of parallelogram = Base × Height
Area of 1 parallelogram = 12 cm × 8 cm = 96 cm²
Now, there are 6 parallelogram shaped sections.
So, area of the sections = area of 1 section × total number of sections
∴ Area of 6 sections = 96 cm² × 6 = 576 cm²
Therefore, the total area of the sections of a suncatcher is 576 cm².
What is x given triangleABC ~triangleDBE?
x = 37.5 (or) [tex]\frac{75}{2}[/tex]
Solution:
Given [tex]\triangle A B C \sim \triangle D B E[/tex].
Let us take BE = x and BC = 25 + x.
To determine the value of x:
If two triangles are similar then the corresponding angles are congruent and the corresponding sides are in proportion.
[tex]$\frac{AC}{DE}=\frac{B C}{B E}[/tex]
[tex]$\frac{50}{30} =\frac{25+x}{x}[/tex]
Do cross multiplication, we get
[tex]50x=30(25+x)[/tex]
[tex]50x=750+30x[/tex]
Subtract 30x from both sides of the equation.
[tex]20 x=750[/tex]
Divide by 20 on both sides of the equation, we get
x = 37.5 (or) [tex]\frac{75}{2}[/tex]
Hence the value of x is 37.5 or [tex]\frac{75}{2}[/tex].
Name 3 of the 4 features listed below for the function g (x) = log2 (x + 4) - 1 and include a description of how you found those answers using complete sentences. 1) Vertical Asymptote 2) Domain 3) X and Y Intercepts 4) Transformations compared to its parent function f (x) = log2 x
(1) Vertical asymptote: [tex]x=-4[/tex]
(2) Domain: [tex]x>-4[/tex]
(3) X intercept: [tex](-2,0)[/tex] and Y intercept : [tex](0,1)[/tex]
(4) The function g(x) is shifted 4 units to the left and shifted 1 unit down.
Explanation:
The parent function is [tex]f(x)=\log _{2} x[/tex]
The transformed function is [tex]g(x)=\log _{2}(x+4)-1[/tex]
(1) Vertical asymptote:
The vertical asymptote of a function can be determined by equating
[tex]x+4=0[/tex]
Thus, [tex]x=-4[/tex]
The vertical asymptote is [tex]x=-4[/tex]
(2) Domain:
The domain of a function is the set of all independent x-values.
[tex]x+4>0[/tex]
Thus, [tex]x>-4[/tex]
The domain of a function is [tex]x>-4[/tex]
(3) X and Y intercepts:
To determine the x intercept, let us substitute y=0 in [tex]g(x)=\log _{2}(x+4)-1[/tex]
[tex]\begin{equation}\begin{aligned}\log _{2}(x+4)-1 &=0 \\\log _{2}(x+4) &=1 \\x+4 &=2^{1} \\x &=-2\end{aligned}[/tex]
Thus, the x intercept is [tex](-2,0)[/tex]
To determine the y intercept, let us substitute x=0 in [tex]g(x)=\log _{2}(x+4)-1[/tex]
[tex]\begin{equation}\begin{aligned}y &=\log _{2}(0+4)-1 \\&=\log _{2} 4-1 \\&=2-1 \\&=1\end{aligned}[/tex]
Thus, the y intercept is [tex](0,1)[/tex]
(4) To determine the transformation:
The transformed function [tex]g(x)=\log _{2}(x+4)-1[/tex] is shifted 4 units to the left and shifted 1 unit downwards.
A forest has 800800800 pine trees, but a disease is introduced that kills \dfrac{1}{4} 4 1 start fraction, 1, divided by, 4, end fraction of the pine trees in the forest every year.
The required function that represents the situation is [tex]y=800(\frac{1}{4} )^t[/tex]
Exponential functionThe standard exponential function is expressed as:
[tex]y=ab^x[/tex] where:
a is the initial pine treesb is the growth rate/declinet is the time takenGiven the following parameters:
a = 800
b = 1/4
Substitute into the formula to have;
[tex]y=800(\frac{1}{4} )^t[/tex]
Hence the required function that represents the situation is [tex]y=800(\frac{1}{4} )^t[/tex]
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Answer:
It's 800(3/4)^t
Step-by-step explanation:
A puzzle piece in the shape of a triangle has perimeter 25 centimeters. Two sides of the triangle are each twice as long as the shortest side. Find the length of the shortest side.
Answer: the shortest side is 10 centimeters.
The length of each of the other sides is 10 centimeters each.
Step-by-step explanation:
Let x represent the length of the shortest side of the triangle.
Two sides of the triangle are each twice as long as the shortest side. This means that the length of the two sides would be 2x.
The perimeter of a triangle is the sum of each side of the triangle.
The puzzle piece in the shape of a triangle has perimeter 25 centimeters. This means that
x + 2x + 2x = 25
5x = 25
x = 25/5
x = 5
The length of each of the two sides is
2x = 2 × 5 = 10
The length of the shortest side of the triangle is 5 centimeters.
Let's denote the length of the shortest side of the triangle as "x" centimeters. According to the problem, the other two sides are each twice as long as the shortest side. Therefore, the lengths of the other two sides are "2x" centimeters each.
Now, we can use the information given about the perimeter to set up an equation:
Perimeter = Sum of all sides
Given that the perimeter is 25 centimeters:
25 = x + 2x + 2x
Now, combine like terms on the right side:
25 = 5x
To solve for x, divide both sides by 5:
x = 25 / 5
x = 5
So, the length of the shortest side of the triangle is 5 centimeters.
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PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!!
Find m∠U.
Write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠U = °
Yo sup??
This question can be solved by applying trigonometric ratios
let angle U be x, then
tanx=4/7
x=29.7
Hope this helps
Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains liters of a dye solution with a concentration of g/liter. To prepare for the next experiment, the tank is to be rinsed with fresh water flowing in at a rate of liters/min, the well-stirred solution flowing out at the same rate.Find the time that will elapse before the concentration of dye in the tank reaches 1% of its original value.
Answer:
t = 460.52 min
Step-by-step explanation:
Here is the complete question
Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains 200 liters of a dye solution with a concentration of 1 g/liter. To prepare for the next experiment, the tank is to be rinsed with fresh water flowing in at a rate of 2 liters/min, the well-stirred solution flowing out at the same rate.Find the time that will elapse before the concentration of dye in the tank reaches 1% of its original value.
Solution
Let Q(t) represent the amount of dye at any time t. Q' represent the net rate of change of amount of dye in the tank. Q' = inflow - outflow.
inflow = 0 (since the incoming water contains no dye)
outflow = concentration × rate of water inflow
Concentration = Quantity/volume = Q/200
outflow = concentration × rate of water inflow = Q/200 g/liter × 2 liters/min = Q/100 g/min.
So, Q' = inflow - outflow = 0 - Q/100
Q' = -Q/100 This is our differential equation. We solve it as follows
Q'/Q = -1/100
∫Q'/Q = ∫-1/100
㏑Q = -t/100 + c
[tex]Q(t) = e^{(-t/100 + c)} = e^{(-t/100)}e^{c} = Ae^{(-t/100)}\\Q(t) = Ae^{(-t/100)}[/tex]
when t = 0, Q = 200 L × 1 g/L = 200 g
[tex]Q(0) = 200 = Ae^{(-0/100)} = Ae^{(0)} = A\\A = 200.\\So, Q(t) = 200e^{(-t/100)}[/tex]
We are to find t when Q = 1% of its original value. 1% of 200 g = 0.01 × 200 = 2
[tex]2 = 200e^{(-t/100)}\\\frac{2}{200} = e^{(-t/100)}[/tex]
㏑0.01 = -t/100
t = -100㏑0.01
t = 460.52 min
Samantha and her children went into a movie theater and will buy bags of popcorn and candies. Each bag of popcorn costs $6 and each candy costs $3.25. Samantha has a total of $50 to spend on bags of popcorn and candies. Write an inequality that would represent the possible values for the number of bags of popcorn purchased, bb, and the number of candies purchased, c.c.
Multiply the price of popcorn by the number of bags so 6b.
Multiply the price of candy by the number bought, so 3.25c
Add those together to get total :
6b + 3.25c
Now the most she can spend is 50 so set the equation to less than it equal to what she can spend:
6b + 3.25c <= 50
Final answer:
The inequality representing Samantha's budget for purchasing popcorn and candies is 6b + 3.25c ≤ 50.
Explanation:
To formulate the inequality representing the possible values for the number of bags of popcorn (b) and the number of candies (c) Samantha can purchase without exceeding her $50 budget, we can set up an expression based on the given prices for each item.
The cost of the popcorn bags is $6, and the cost of each candy is $3.25.
The inequality that represents this scenario would be:
6b + 3.25c ≤ 50
This inequality denotes that the total cost of b popcorn bags and c candies, which is the sum of $6 times the number of popcorn bags plus $3.25 times the number of candies, should be less than or equal to $50.
Samantha must choose combinations of b and c that satisfy this inequality to stay within her budget.
Which relationships would most likely be causal? Select two options. a negative correlation between the temperature and the amount of snow still on the ground a negative correlation between the number of digital photos uploaded to a website and the amount of storage space that is left a positive correlation between the length of the side of a pool and its depth a positive correlation between the height of a woman and the height of her brother a negative correlation between the volume of water in a pot and the amount of time that the water takes to boil
Answer:
a negative correlation between the temperature and the amount of snow still on the ground
a negative correlation between the number of digital photos uploaded to a website and the amount of storage space that is left
Explanation:
When it comes to "correlations," a negative one refers to an "inverse" relationship between two variables. So, this means that as one variable increases, the other decreases and vice-versa.
The question is asking for two options that are "casual" (common) when it comes to "negative correlation." So, the answers are:
a negative correlation between the temperature and the amount of snow still on the ground
This is a casual example of negative correlation because as temperature increases, the amount of remaining snow on the ground decreasesa negative correlation between the number of digital photos uploaded to a website and the amount of storage space that is left
This is a casual example of negative correlation because as the number of digital photos uploaded to a website increases, the amount of storage space left decreases.
Answer:
A negative correlation between the temperature and the amount of snow still on the ground.A negative correlation between the number of digital photos uploaded to a website and the amount of storage space that is left.Step-by-step explanation:
These are the two relationships that are most likely to be causal. Causal relationships are those in which one aspect is the cause of the second one being described. Moreover, a negative correlation is one in which one aspect of the relationship increases while the other one decreases. In the first example, as the temperature goes up, this causes the amount of snow on the ground to go down. In the second example, as you upload more pictures to a website, there is less storage space.
Dimitri determined that he ordered pair (2,-2) is a solution to the system of linear equations 7x +9y=-4 and 5x -2y=6 as shown What was dimitri's mistake?
Answer:
Therefore [tex](\frac{46}{59},-\frac{62}{59} )[/tex] is a solution of given liner equations.
Step-by-step explanation:
Given system of equation are
7x+9y=-4..............(1)
5x-2y=6...............(2)
Equation (1)×5 - equation (2)×7
35x +45y-(35x-14y)= -20-42
⇔ 35x+45y-35x+14y = -62
⇔59 y = -62
[tex]\Leftrightarrow y =-\frac{62}{59}[/tex]
Putting the value of y in equation (1)
[tex]7x +9.(-\frac{62}{59} )= -4[/tex]
[tex]\Leftrightarrow 7x += -4+\frac{558}{59}[/tex]
[tex]\Leftrightarrow 7x = \frac{322}{59}[/tex]
[tex]\Leftrightarrow x =\frac{322}{59\times 7}[/tex]
[tex]\Leftrightarrow x =\frac{46}{59}[/tex]
Therefore [tex]x =\frac{46}{59}[/tex] and [tex]y =-\frac{62}{59}[/tex]
Therefore [tex](\frac{46}{59},-\frac{62}{59} )[/tex] is a solution of given liner equations.
Answer:
D.)He made a mistake in his calculations when substituting the ordered pair into the equation 5x – 2y = 6 and simplifying.
Step-by-step explanation:
I just got this right for the exam review on edge
Give an example of a research experiment, indicating the independent and dependent variables, as well as the experimental and the control groups.
Answer:
In a study to determine whether how long a student sleeps affects test scores, the independent variable is the length of time spent sleeping while the dependent variable is the test score. You want to compare brands of paper towels, to see which holds the most liquid.
hopes it helps
a car travels along a straight road heading east for one hour, then traveling for 30 minutes on another road that leads northeast. if the car has maintained a constant spead of 40 miles per hour, how far is it from the starting position/
Answer:
55.96 miles
Step-by-step explanation:
Distance = Speed X time
Car first moved east for 1 hr , distance = 40 x 1 = 40 miles
Car then moved north-east for 30 min, distance = 40 x 0.5 = 20 miles
From trigonometry,
sin 45 = [tex]\frac{y}{20}[/tex] ; y = 20 sin 45 ; y= 14.14 miles
cos 45 = [tex]\frac{x}{20}[/tex] ; x = 20 cos 45 ; x = 14.14 miles
using Pythagoras theorem;
[tex]z^{2}[/tex] = [tex]y^{2}[/tex] + [tex](40+x)^{2}[/tex]
= [tex]14.14^{2}[/tex] + [tex](40+14.14)^{2}[/tex]
= 3131.08
[tex]z^{2}[/tex] = [tex]\sqrt{3131.08}[/tex]
z = 55.96 miles
The scale on a model railroad train set is 3.5 millimeters to 1 foot. If the length of a model car in the set is 150 millimeters, what is the approximate length of the actual car?
Answer:
The approximate length of the actual car is 43 feet.
Step-by-step explanation:
Given:
The scale on a model railroad train set is 3.5 millimeters to 1 foot. If the length of a model car in the set is 150 millimeters.
Now, to find the approximate length of the actual car.
Let the actual length of the car is [tex]x.[/tex]
The length of a model car in the set is 150 millimeters.
As, given the scale on a model railroad train set is 3.5 millimeters to 1 foot.
So, 3.5 millimeters equivalent to 1 foot.
Thus, 150 millimeters to [tex]x[/tex].
Now, to get the actual length of the car by using cross multiplication method:
[tex]\frac{3.5}{1} =\frac{150}{x}[/tex]
By using cross multiplying we get:
[tex]3.5x=150[/tex]
Dividing both sides by 3.5 we get:
[tex]x=42.85\ feet.[/tex]
The approximate length of the actual car = 43 feet.
Therefore, the approximate length of the actual car is 43 feet.
Answer:
43ft
Step-by-step explanation:
The answer is B.
Here's another way to solve this problem.
1. Write the scale ratio
3.5 mm
1 ft
2. Choose a variable, such as r, to represent the approximate length of the actual railroad car
3. Write the ratio of the length of the model car to the length of the actual car:
150 mm
r ft
4. Write a proportion
3.5=150
1= r
5. Cross multiply
3.5
r=150
3.5
r=42.9, which rounds to 43.
so the, approximate length of the actual car is 43 feet
Write the sum using summation notation, assuming the suggested pattern continues. -9 - 3 + 3 + 9 + ... + 81
summation of the quantity negative nine plus six n from n equals zero to fifteen
summation of negative fifty four times n from n equals zero to fifteen
summation of negative fifty four times n from n equals zero to infinity
summation of the quantity negative nine plus six n from n equals zero to infinity
Answer:
Option A: [tex]$ \sum_{n = 1}^{15} {\textbf{- 9 + 6 n}} $[/tex]
Step-by-step explanation:
We are given with the series - 9 - 3 + 3 + 9 + . . . . + 81.
Note that the second term is obtained by adding 6 to the first term.
Each consecutive term is obtained by adding 6 to its previous term.
Therefore, we should be adding six two times to get the third term from the first term.
Putting it Mathematically, we get: - 9 + 6n
This gives all the terms of the sequence. Since, we have to add all the terms we take the summation.
Also, note that 81 is the 15 th term.
Therefore, - 9 - 3 + 3 + 9 + . . . . + 81 = [tex]$ \sum_{n = 1}^{15} {- 9 + 6 n} $[/tex]
Hence, the answer.
Final answer:
The sequence -9, -3, 3, 9, ..., 81 increases by 6 each time and follows the arithmetic sequence formula -9 + 6(n-1), which simplifies to -15 + 6n. The summation notation that represents this sequence is the sum of -15 + 6n from n = 0 to 15.
Explanation:
The given sequence is -9, -3, 3, 9, ..., 81, and we can see that it is increasing by 6 each time (an arithmetic sequence). The nth term of an arithmetic sequence can be written as a + (n-1)d, where a is the first term and d is the common difference. Here, the first term a is -9 and the common difference d is 6. Plugging these values into the formula gives us the nth term as -9 + 6(n-1). We can simplify this to -9 + 6n - 6, which further simplifies to -15 + 6n.
To find the last term which is 81, we can set the nth term equal to 81: -15 + 6n = 81. Solving for n gives us n = 16, meaning there are 15 terms before it (since we start counting from n = 0).
The summation notation for the given sequence is then the sum of the terms from n = 0 to n = 15 of the general term -15 + 6n.
Please help
Julie takes her kids to a playground that has the shape shown.
A. While her kids are playing, Julie wants to get some exercise. If she does 2 laps around the playground, how much distance has she covered?
B. The park service is creating a flyer for the playground and wants to list the area that the playground covers. How much area does the playground cover?
Answer:
a=128 feet b=256 feet
Step-by-step explanation:
hope i got it
Answer:
A.) 128FT
B.) A=256
Step-by-step explanation:
A.)
16 x 4 = 64FT
62 x 2 = 128FT
So, 2 Laps Would Equal Up To 128FT.
B.)
Find the length of one of the sides (as each side is the same length) and then multiply this by itself to find the area.
Naledi climbed up a mountain. Her initial altitude was 40 meters above sea level, and it increased by 10 meters each hour.Let )g(n)be Naledi's altitude at the beginning of the nth hour of her climb.G is a sequence. What kind of sequence is it? Answer
Answer:
ARITHMETIC SENTENCE
Step-by-step explanation:
Final answer:
Naledi's altitude sequence is an arithmetic sequence because it increases by a constant amount each hour.
Explanation:
Naledi's altitude at the beginning of the nth hour of her climb can be described by the function g(n), where g(n) is the altitude at that hour. Since she starts at 40 meters above sea level and increases her altitude by 10 meters every hour, the sequence representing her altitude over time is an arithmetic sequence. This is because each term in the sequence increases by a constant value, which is the definition of an arithmetic sequence.
The general formula for the nth term of an arithmetic sequence is aₙ = a₁ + (n - 1)d, where a₁ is the first term and d is the common difference between terms. In Naledi's case, a₁ is 40 meters (her initial altitude), and d is 10 meters (the constant increase each hour).
Please Help!!!
What is a polynomial function in standard form with zeroes 1, 2, -3, and -1 ?
Answer:
[tex]p(x) = {x}^{4} + {x}^{3} - 7 {x}^{2} - x + 6[/tex]
Step-by-step explanation:
The polynomial function has zeros
x=1, x=2,x=-3,x=-1
This means the factored form of the polynomial is
[tex]p(x) = (x - 1)(x + 1)(x + 3)(x - 2)[/tex]
We expand to get:
[tex]p(x) = ( {x}^{2} - 1)( {x}^{2} + x - 6)[/tex]
We expand further to get:
[tex]p(x) = {x}^{2}( {x}^{2} + x - 6) - 1({x}^{2} + x - 6)[/tex]
[tex]p(x) = {x}^{4} + {x}^{3} - 6 {x}^{2} - {x}^{2} - x + 6[/tex]
This simplifies to:
[tex]p(x) = {x}^{4} + {x}^{3} - 7 {x}^{2} - x + 6[/tex]
This is the standard form of the polynomial since it is written in descending powers of x.
Given the lines, AB and CD, determine the slope of line CD. Type a numerical answer in the space provided. If necessary, use the / key to represent a fraction bar. Do not put spaces in your answer.
A(0,-1)
B(5,3)
C(2,3)
D(6,2)
Answer:
The slope is = -1/4
Step-by-step explanation:
We are looking for the slope of the line CD. You are given the coordinates for each point as follows:
A(0,-1) B(5,3) C(2,3) D(6,2)
To find the slope of a straight line, you use the formula:
slope (m) = (y2 - y1)/(x2 - x1)
In other words the slope is the "rise over run":
rise (change in y) over the run (change in x) between two coordinates of the points:Remember: the coordinates of a point are (x;y). Choose one of the points to be point 1 and the other to be point 2. I would suggest that you follow the order they have given you ie. CD:
So if our points are C (2; 3) and D (6, 2) we can say point C is point 1 and point D is point 2. Plug into the formula:
slope (m) = (y2-y1)/(x2-x1)
y1 = 3
y2 = 2
x1 = 2
x2 = 6
∴ m = (2-3)/(6-2)
= -1/4
Mandi learned that each 10% of charge on her cell phone gave her an hour and twenty minutes of use. While playing a game today on her phone, she noticed the charge drop from 81% to 57% how long did mandi play the game?
Answer:
3hrs 12 mins
Step-by-step explanation:
For every 10% charge she gets 1hr 20mins (or 80 mins)
Charge drop = (81% - 57%) = 24%
Since 10% gives 80 mins;
24% gives (24/10) x 80 mins = 192 mins
since 1hr = 60 mins
192 mins = 192/60 = 3hrs 12 mins
Final answer:
Mandi played the game on her phone for 3 hours and 12 minutes, as she experienced a 24% drop in battery charge, with each 10% equating to 1 hour and 20 minutes of playtime.
Explanation:
The student's question involves calculating the duration of time Mandi played a game on her phone based on the percentage drop in battery charge. Mandi’s phone loses 10% charge for every 1 hour and 20 minutes of use. The charge dropped from 81% to 57%, which is a 24% drop. To find out how long she played the game, we calculate the number of 10% intervals in 24% and then multiply by the duration of one interval.
First, we determine how many 10% intervals are in 24%, which is calculated as 24% ÷ 10% = 2.4 intervals. Each interval equates to 1 hour and 20 minutes (which is the same as 80 minutes). Therefore, Mandi played for 2.4 intervals × 80 minutes per interval:
2.4 intervals × 80 minutes/interval = 192 minutes.
To convert minutes into hours and minutes, we divide by 60:
192 minutes ÷ 60 minutes/hour = 3 hours and 12 minutes.
So, Mandi played the game for 3 hours and 12 minutes.
Divide using synthetic division
(3x³ - 17x² + 15x - 25)/(x - 5) =
= (3x³ - 15x² - 2x² + 0x + 5x - 25)/(x - 5)
= [3x²(x - 5) - 2x(x - 5) + 5(x - 5)]/(x - 5)
= (3x² - 2x + 5)(x - 5)/(x - 5)
= 3x² - 2x + 5
(5x³ + 18x² + 7x - 6)/(x + 3) =
= (5x³ + 5x² + 13x² + 13x - 6x - 6³)/(x + 3)
= [5x²(x + 1) + 13x(x + 1) - 6(x + 1)]/(x + 3)
= (x + 1)(5x² + 13x - 6)/(x + 3)
= (x + 1)(5x² + 15x - 2x - 6)/(x + 3)
= (x + 1)[5x(x + 3) - 2(x + 3)]/(x + 3)
= (x + 1)(5x - 2)(x + 3)/(x + 3)
= (x + 1)(5x - 2)
(4x³ + 8x² - 9x - 18)/(x + 2) =
= [4x²(x + 2) - 9(x + 2)]/(x + 2)
= (4x² - 9)(x + 2)/(x + 2)
= (4x² - 9)
= (2x - 3)(2x + 3)
(9x³ - 16x - 18x² + 32)/(x - 2) =
= [x(9x² - 16) - 2(9x² - 16)]/(x - 2)
= (9x² - 16)(x - 2)/(x - 2)
= 9x² - 16
= (3x - 4)(3x + 4)
(- x³ + 75x - 250)/(x + 10) =
= ( - x³ + 5x² - 5x² + 25x + 50x - 250)/(x + 10)
= [ - x²(x -5) - 5x(x - 5) + 50(x - 5)]/(x + 10)
= - (x - 5)(x² + 10x - 5x - 50)/(x + 10)
= - (x - 5)[x(x + 10) - 5(x + 10)]/(x + 10)
= - (x - 5)(x - 5)(x + 10)/(x + 10)
= - (x - 5)²
(3x³ - 16x² - 72)/(x - 6) =
= (3x³ - 18x² + 2x² - 72)/(x - 6)
= [3x²(x - 6) + 2(x² - 36)]/(x - 6)
= [3x²(x - 6) + 2(x - 6)(x + 6)]/(x - 6)
= [3x² + 2(x + 6)](x - 6)/(x - 6)
= 3x² + 2x + 12
Find an explicit formula for the geometric sequence -8,-40,-200,-1000
Step-by-step explanation:
The given geometric sequence:
- 8, - 40, - 200, - 1000
Here, first term(a) = - 8, common ration(r) = [tex]\dfrac{-40}{-8}[/tex] = 5
To find, an explicit formula for the given geometric sequence = ?
We know that,
The explicit formula for the geometric sequence
[tex]a_{n} =ar^{n-1}[/tex]
∴ An explicit formula for the given geometric sequence
[tex]a_{n} =(-8)(5)^{n-1}[/tex]
[tex]a_{n} =\dfrac{-8}{5} (5)^{n}[/tex]
∴ An explicit formula for the given geometric sequence, [tex]a_{n} =\dfrac{-8}{5} (5)^{n}[/tex]
Answer:
what the guy above me said
Step-by-step explanation:
Farmer Jones raises ducks and cows. He looks out his window and sees 54 animals with a total of 122 feet. If each animal is "normal", have many of each type of animal does he have
Answer:
47 ducks and 7 cows
Step-by-step explanation:
Ducks have 2 legs and cows have 4 legs.
If all the animals are ducks,
number of legs= 54(2)= 108
Difference in number of legs= 122 -108= 14
Difference in no. of legs per animal= 4 -2 = 2
Number of cows=14 ÷2 = 7
Number of ducks= 54-7= 47
Thus, he have 47 ducks and 7 cows.
Let's check:
Total number of feet= 7(4)+ 47(2) = 122 ✓
You could also first assume that all the animals are cows. The answer would be the same.
(50 Points & Brainliest, please show work)
The function f(x) = 2x + 210 represents the number of calories burned when exercising, where x is the number of hours spent exercising.
The function g(x) = 2x + 125 represents the calorie deficit that occurs when following a particular diet, where x is the number of hours spent exercising.
What is (f + g)(3)?
Show all work and explain your answer
Answer:
(f+g)(3) = 347 calories
Step-by-step explanation:
f(x) = 2x + 210
g(x) = 2x + 125
(f+g)(x) is the sum of the functions
(f+g)(x) = 2x+210 + 2x+125
Combining like terms
=4x+335
Now let x = 3
(f+g)(3) = 4*3 +335
= 12 +335
= 347
(f+g)(3) = 347 calories
Answer:
347
Step-by-step explanation:
f(x) = 2x + 210
g(x) = 2x + 125
we know that (f+g)(x)=f(x)+g(x)
so (f+g)(x)= 2x + 210 + 2x + 125 = 4x + 335
(f+g)(3) simply means that x=3
therefore
(f+g)(3) = 12 + 335 = 347
Samantha and Luke got married. They received $4,500 in gift money and deposited it into a savings account that pays 2.85% simple interest. How much will they have in savings after 3 years?
Group of answer choices
$384.75
$4,884.75
$9,000.00
$38,475.75
Answer: $4,884.75
Step-by-step explanation:
The formula for determining simple interest is expressed as
I = PRT/100
Where
I represents interest paid on the amount deposited.
P represents the principal or amount deposited.
R represents interest rate
T represents the duration of the savings in years.
From the given information,
P = 4500
R = 2.85
T = 3 years
I = (4500 × 2.85 × 3)/100 = $384.75
The total amount that they will have in savings after 3 years is
4500 + 384.75 = $4884.75