Answer:
the next term will be 15
Step-by-step explanation:
a=81/25
r(common ratio)=t2/T1=5/3
so,t4=ar^(n-1)
=81/25×5/3^(4-1)
= 81/25×125/27
=15
pls answer fast
Eric is observing the velocity of a runner at different times. After one hour, the velocity of the runner is 5 km/h. After three hours, the velocity of the runner is 3 km/h.
Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the runner at different times. Show your work and define the variables used. (5 points)
Part B: How can you graph the equation obtained in Part A for the first 5 hours? (5 points)
(10 points)
Answer:
Step-by-step explanation:
Part A:
Let's assume that the velocity of the runner changes linearly over time. We can use the slope-intercept form of a linear equation, y = mx + b, to describe the velocity of the runner at different times. In this case, the y-axis represents the velocity in km/h and the x-axis represents time in hours. We can define:
y = velocity of the runner in km/h
x = time in hours
The velocity of the runner changes by -2/3 km/h for every hour that passes. This gives us a slope of -2/3. We can use the point-slope form of a linear equation to find the equation of the line:
y - 5 = -2/3(x - 1)
Simplifying this equation, we get:
3y - 15 = -2x + 2
Rearranging to standard form, we get:
2x + 3y = 17
So the equation in two variables in standard form that can be used to describe the velocity of the runner at different times is 2x + 3y = 17.
Part B:
To graph the equation obtained in Part A for the first 5 hours, we can simply plot points for different values of x and y. For example, we can use x = 0, 1, 2, 3, 4, and 5 to find the corresponding values of y using the equation 2x + 3y = 17. Then we can plot these points on a graph and connect them with a straight line.
Here are the values of y for different values of x:
x = 0, y = 17/3
x = 1, y = 5
x = 2, y = 13/3
x = 3, y = 3
x = 4, y = 7/3
x = 5, y = 1
Plotting these points and connecting them with a straight line, we get the graph of the equation 2x + 3y = 17 for the first 5 hours:
|
6.0 -| .
| .
5.5 -| .
| .
5.0 -| .
|.
4.5 -|
|
4.0 -| .
| .
3.5 -| .
| .
3.0 -| .
|.
2.5 -|
|
2.0 -| .
| .
1.5 -| .
| .
1.0 -|.
|
0.5 -|
|
--------------
0 1 2 3 4 5
The y-intercept of the line is 17/3, which represents the initial velocity of the runner at time 0. The slope of the line is -2/3, which represents the rate of change of the velocity over time.
Answer: CLICK THANKS IF YOU LIKE MY ANSWER. HAVE A GOOD DAY SIR/MAAM #KEEPSAFE
Part A:
Let v be the velocity of the runner in km/h and let t be the time elapsed in hours. We can use the two given data points to form a system of two equations:
v = 5 when t = 1
v = 3 when t = 3
To find the equation in standard form, we can first use point-slope form:
v - 5 = m(t - 1) (using the point (1, 5))
v - 3 = m(t - 3) (using the point (3, 3))
Simplifying both equations:
v - 5 = m(t - 1)
v - 3 = m(t - 3)
v = mt + (5 - m)
v = mt + (3m - 3)
Setting the right-hand sides equal to each other:
mt + (5 - m) = mt + (3m - 3)
Simplifying and rearranging:
-m = -2
m = 2
Substituting m = 2 into one of the equations above:
v = 2t + 3
This is the equation in two variables in standard form that describes the velocity of the runner at different times.
Part B:
To graph the equation v = 2t + 3 for the first 5 hours, we can plot points for different values of t and then connect them with a line. For example:
When t = 0, v = 3, so the point (0, 3) is on the line.
When t = 1, v = 5, so the point (1, 5) is on the line.
When t = 2, v = 7, so the point (2, 7) is on the line.
When t = 3, v = 9, so the point (3, 9) is on the line.
When t = 4, v = 11, so the point (4, 11) is on the line.
When t = 5, v = 13, so the point (5, 13) is on the line.
Plotting these points on a coordinate plane and connecting them with a line, we get the graph of the equation v = 2t + 3 for the first 5 hours:
|
15 +-------*
| |
13 + *
| |
11 + *
| |
9 + *
| |
7 + *
| |
5 + *
| |
3 +---------------*-----------*
0 1 2 3 4 5 6 7
The x-axis represents time (t) in hours, and the y-axis represents velocity (v) in km/h. The line starts at (0, 3) and has a slope of 2, indicating that the velocity is increasing by 2 km/h for every hour that passes.
Step-by-step explanation:
Of the 40 learners in the class, 12 walks to school, twice the number who walk, come by car or taxi and the remainder cycle to school. What fraction does not cycle to school? Answer must be simplest form.
The fraction of learners who do not cycle to school is equal to 9/10.
How to evaluate for the fraction of learners.Given that the total number of learners is 40, 12 of which walk to school and twice of the number of learners who walk, come to school by car or taxi, then the remainder of learners who cycle to school is calculated as;
40 - [12 +2(12)] = 4
The number of learners who do not cycle to school is;
12 + 2(12) = 36
fraction of learners who do not cycle to school = 36/40
by simplification;
fraction of learners who do not cycle to school = 9/10.
Therefore, the fraction of learners who do not cycle to school is equal to 9/10.
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I will mark you brainiest!
If JL = 30, JK = 18, and LM = 6, then the value of LN is
A) 3
B) 6
C) 9
D) 15
Answer: LN = 15
Make a proportional relationship:
[tex]\dfrac{LN}{JL}=\dfrac{LM}{KL}[/tex]
Insert the values:
[tex]\longrightarrow\dfrac{LN}{30} =\dfrac{6}{30-18}[/tex]
cross multiply:
[tex]\longrightarrow LN=\dfrac{30(6)}{12}[/tex]
Simplify:
[tex]\text{LN}= \text{15}[/tex]Veronica walks dogs in her neighborhood for extra money during the summer. For each dog walk, she earns $5.25. On Monday, she completes 3 walks, and on Tuesday she completes 2 walks. She estimates that in order to save up for a new purse that costs $86, she needs to complete 12 more walks by the end of the week.
Answer:
Veronica is correct
Step-by-step explanation:
On Monday, Veronica earns 3 walks * $5.25 per walk = $15.75.
On Tuesday, Veronica earns 2 walks * $5.25 per walk = $10.50.
So far, Veronica has earned a total of $15.75 + $10.50 = $26.25.
To reach her goal of $86, Veronica needs to earn an additional $86 - $26.25 = $59.75.
Since Veronica earns $5.25 per walk, she needs to complete $59.75 ÷ $5.25 per walk = 11.38 walks.
Since Veronica cannot complete a fraction of a walk, she will need to complete 12 more walks (rounded up from 11.38) by the end of the week.
if walter eats 12 cookies, which represents 25% of the bag how many cookies where in the bag before any was eaten
Answer:
48 cookies were in the bag.
Step-by-step explanation:
It said 12 was 25%, so you want to multiply it by 4 to get 100% and 100% of the bag was 48 cookies.
2 over 3 plus 5 over 9 I need Steps MY PARENTS ARE GONNA GROUND ME HELP MEEEEEE
Answer: 11/9 or 1 2/9 or 11 over 9
Step-by-step explanation:
Firstly, you need to know what a fraction is.
A fraction is a segment (part of) a whole. To express a fraction, you write the numerator over the denominator. A numerator is the top part of the fraction, and it shows how much it is out of. The denominator shows how much it is out of.
Example: [tex]\frac{1}{3}[/tex]
That means it is 1 part out of 3 parts
Now you know what a fraction is, now let's add them.
Next, convert the word form into the number form:
2 over 3 is 2/3
plus is +
5 over 9 =is 5/9
Combine them:
2/3 + 5/9
Steps of the problem:
Firstly, you have to find the L.C.M (Lowest Common Multiple) of 3 and 9 because to add fractions, you need a common (same) denominator.
9 is the L.C.M of 3 and 9, as 9x1 = 9 and 3x3 = 9.
Mulitiply the numerator and denominator by 3:
2x3/3x3 = 6/9
Now, the equation is 6/9+5/9.
Add the numerators:
11/9
The answer is 11/9
If the question tells you to convert into a mixed number, then here's the following steps:
You have to find the highest number 11 goes into 9
It's 1.
Take the remainder (2) into the fraction:
2/9
Now, add 1 in front of it:
1 2/9
As a decimal, it is 1.2222222 (recurring).
If that helped you, please make me Brainliest!
Answer:
11 over 9 [tex](\frac{11}{9})[/tex]
Step-by-step explanation:
What is a fraction?A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.
To solve for [tex]\frac{2}{3} +\frac{5}{9}[/tex], we need to first convert these fractions so that they share a common denominator.
What is a common denominator?A common denominator consists of two or more fractions that have the same denominator. This makes it easier to perform numeric equations, and to solve them.
If a common denominator just refers to 2 fractions having the same denominator, we can simply multiply the numerator and denominator of the fraction [tex]\frac{2}{3}[/tex] by a number. To solve for that number, we can divide 9 by 3.
9 ÷ 3 = 3Now that we know that the number is 3, multiply both by 3.
2 × 3 = 63 × 3 = 9Now the fraction looks like this: [tex]\frac{6}{9}[/tex].
We can now change the expression to this:
[tex]\frac{6}{9}+ \frac{5}{9}[/tex]When adding fractions with the same denominator, we can just add the 2 numerators and keep the common denominator the same.
6 + 5 = 11Now just insert 11 in as the numerator:
[tex]\frac{11}{9} = 1\frac{2}{9}[/tex]Therefore 2 over 5 plus 5 over 9 is 11 over 9.
How does the graph of g(x) = (x + 2)3 − 6 compare to the parent function of f(x) = x3? g(x) is shifted 2 units to the right and 6 units down. g(x) is shifted 6 units to the right and 2 units up. g(x) is shifted 2 units to the left and 6 units down. g(x) is shifted 6 units to the left and 2 units down.
Answer:
The function g(x) = (x + 2)³ − 6 is obtained by applying three transformations to the parent function f(x) = x³.
First, g(x) is shifted 2 units to the left by subtracting 2 from x inside the parentheses:
g(x) = (x + 2 - 2)³ − 6 = (x)³ − 6
This shows that option C, "g(x) is shifted 2 units to the left and 6 units down," is not correct.
Next, g(x) is shifted 6 units down by subtracting 6 from the entire function:
g(x) = (x + 2)³ − 6 - 6 = (x + 2)³ - 12
This shows that option A, "g(x) is shifted 2 units to the right and 6 units down," is correct.
Finally, g(x) is not shifted left or right by any additional units, but it is shifted 2 units up by adding 2 to the constant term:
g(x) = (x + 2)³ − 6 + 2 = (x + 2)³ - 4
This shows that option B, "g(x) is shifted 6 units to the right and 2 units up," is not correct.
Therefore, the correct answer is option A: g(x) is shifted 2 units to the right and 6 units down.
Solve the following quadratic-like equation.
[tex]y^\frac{1}{2} -6y^\frac{1}{4} +8=0[/tex]
Step-by-step explanation:
given quadratic equation is
simplification,
by using,
[tex]y^\frac{1}{2} -6y^\frac{1}{4} +8=0
\\ y^\frac{1}{2} -6y^\frac{1}{4} = - 8 \\
[/tex]
[tex]square[/tex]
[tex] \\ {(y^\frac{1}{2} -6y^\frac{1}{4})}^{2} = {(- 8)}^{2}[/tex]
[tex]y + 36 {y}^{ \frac{1}{2}} \: [/tex]
Rewrite the following equations in the form (x−p)2=q 0=x^2-18x+1 and the equation x^2+26x+167.5=0
For the first equation, we can complete the square to find its vertex form. Here's how we do it:
0 = x^2 - 18x + 1
0 = (x - 9)^2 - 80
So we have (x - 9)^2 = 80. This is in the form (x - p)^2 = q, where p = 9 and q = 80.
For the second equation, we can complete the square in a similar way:
x^2 + 26x + 167.5 = 0
x^2 + 26x = -167.5
x^2 + 26x + (26/2)^2 = -167.5 + (26/2)^2
(x + 13)^2 = 9.25
So we have (x + 13)^2 = 9.25. This is in the form (x - p)^2 = q, where p = -13 and q = 9.25.
I hope that helps!
A town has a population of 1900
people at time t=0 In each of the following cases, write a formula for the population P, of the town as a function of year t
(a) The population increases by 60
people per year.
P= X people x=?
Answer:
The formula for the population P, of the town as a function of year t, if the population increases by 60 people per year, is:
P(t) = 1900 + 60t
where t is the number of years elapsed since t=0.
The formula for the population P, of the town as a function of year t is
P = 1900 + 60t
We have,
If the population increases by 60 people per year, then we can use the following formula to find the population P as a function of time t (in years):
P = 1900 + 60t
Here, the initial population at t=0 is 1900 people, and the population increases by 60 people per year,
So we add 60t to the initial population to get the population at time t.
For example,
If we want to find the population after 5 years, we can substitute t=5 into the formula:
P = 1900 + 60(5) = 2200
So the population after 5 years would be 2200 people.
Thus,
The formula for the population P, of the town as a function of year t is
P = 1900 + 60t
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john put three gallons into his truck
An appliance store decreases the price of a 19-in. television set 28% to a sale price of $435.60.What was the original price?
Answer:
Step-by-step explanation:
Let x be the original price of the television set.
The sale price is 28% off the original price, which means that the sale price is equal to 100% - 28% = 72% of the original price.
So we can write an equation based on this information:
0.72x = 435.60
Solving for x, we get:
x = 435.60 / 0.72
x ≈ $605
Therefore, the original price of the television set was approximately $605.
Find the perimeter of a rectangle with w=5 and l=9
Answer:
28 units
Step-by-step explanation:
The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width.
Substituting l = 9 and w = 5, we get:
P = 2(9 + 5) = 2(14) = 28
Therefore, the perimeter of the rectangle is 28 units.
What is 2 +2 -6 + 9 divided by 4
Answer:0.25
Step-by-step explanation:
3/10=
19/50=
5/10=
1/5=
14/25=
3/25=
Answer:
3/10 = 0.3
19/50 = 0.38
5/10 = 0.5
1/5 = 0.2
14/25 = 0.56
3/25 = 0.12
Enlarge the picture below by a scale factor of 3.
Answer:
21 feet by 15 feet
hope this helps
PLEAS HELP!!!
Find the volume of the pyramid. Write your answer as a fraction or mixed number.
The volume of the triangular pyramid is 26 2/3 yd³
How to determine the volumeThe formula for calculating the volume of a triangular pyramid is expressed with the equation
A = 1/3bh
Such that the parameters in the equation are;
A is the area of the triangular pyramid.b is the base area of the triangular pyramid.h is the height of the pyramid.The base area of the pyramid is;
Area = 1/2 × 4 × 5
Multiply the values
Base area =20/2
Base area = 10 yd
Substitute the value
Volume = 1/3 × 10 × 8
Multiply the values
Volume = 80/3
Divide the values
Volume = 26 2/3 yd³
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A, B, and C started a business with Rs 60,000. Amount invested by 'A' and 'C' together is twice that of 'B', while the amount invested by 'A' and 'B' together is thrice that of 'C'. 'A' invested for 6 months, 'B' for 9 months, and 'C' for a year. Find the share of 'B' (in Rs) out of the total profit of Rs 3400.
Answer:
Step-by-step explanation:
Let the amount invested by A, B, and C be denoted by a, b, and c respectively.
From the given information,
a + b + c = 60000 ---(1)
a + c = 2b ---(2)
a + b = 3c ---(3)
Multiplying equation (2) by 3 and equation (3) by 2, we get:
3a + 3c = 6b
2a + 2b = 6c
Adding these two equations, we get:
5a + 5b + 5c = 0
a + b + c = 0
This is not possible as the sum of the investments cannot be zero. Therefore, there must be an error in the problem statement.
Without further information or correction, it is not possible to find the share of B in the profit.
Please anyone help me with number 2 ? Thank you:))
Answer:
subtract 20; 80, 60, 40
The pattern is to subtract 20 from the previous term.
Next three terms: 20, 0, -20.
Therefore, the sequence continues as follows:
80, 60, 40, 20, 0, -20.
What is the scale of dilation?
Answer:
1/4
Step-by-step explanation:
First, Pick a point
A (-4, 8) → A' (-1, 2)
We see that to get from A to A' we time 1/4
So, the scale of dilation is 1/4
It Quiz: Graphs and Measurement
Diana is making enough soup to feed 9 people. She plans to serve all of the soup to her guests in 6-ounce bowls.
In order to make enough soup, she needs to add a total of 4.75 cups of water. There are 8 ounces in a cup.
How many total ounces of water did Diana add to her soup? What is the total number of ounces of the other
ingredients in her soup? Explain how you found your answers.
Type your answer in the box below.
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Answer:
1. 57/16 or 3.5625 ounces of water
8 : 4.75
1 : 19/32 -----> divide both by 8
19/32x6=57/16 = 3.56 ounces
2. 2.4375 ounces of other ingredients
6-3.5625=2.4375
According to Okun's law, if the unemployment rate goes from 3% to 7%, what
will be the effect on the GDP?
Answer: decrease in the GDP by 2.5%.
Step-by-step explanation:
What are the first three terms of the sequence defined by the following equation? a_n= 7 + (n - 1) 5
7, 2, -3
7, 12, 17
7, 35, 175
12, 17, 22
Answer:
7, 12, 17 which is the second choice
Step-by-step explanation:
The given sequence is expressed by the equation
[tex]a_n = 7 + (n - 1)5\\\\(n - 1)5 = 5n - 5\\\\a_n = 7 + (n - 1)5= 7 + 5n - 5\\\\= 2 + 5n\\\\a_n = 5 + 2n\\\\a_1 = 2 + 5(1) = 2 + 5 = 7\\\\a_2 = 2 + 5(2) = 2 + 10 = 12\\\\a_3 = 2 + 5(3) = 2 + 15 = 17\\\\[/tex]
So the first three terms are
7, 12, 17 which is the second choice
add me
1111111111111111111111111111111
The value οf the variable y is 9 when k is -3 in the given question.
What is variable?In mathematics and statistics, a variable is a quantity οr a characteristic that can take οn different values οr attributes. Variables can be classified as either quantitative οr categοrical, depending οn the type οf data they represent.
A quantitative variable is a variable that represents a numerical measurement οr quantity. Examples οf quantitative variables include height, weight, temperature, and incοme.
A categοrical variable is a variable that represents a grοup οr categοry. Examples οf categοrical variables include gender, race, and type οf car.
Given: y=k x
where, x= -3 and k= -3
we can find the value of y by multiplying k with x,
so, y=k x
now, putting values as follows:
we get, y = -3 × -3
= 9
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Helppppp me please!!!! I'm in algebra 2 high school.
[tex]f(-x)[/tex] is not equal to f(x), the function [tex]f(x) = 5x^3 + x[/tex] is neither even nor odd.
What type of function have both an odd and even value?If a function meets the requirements for both odd and even, then the answer is yes. The function is both even and odd if [tex]f(-x) = f(x)[/tex] and [tex]f(-x) = -f(x)[/tex] for every x in the domain of f.
These functions are known as the zero function or identically zero function because they imply that f(x) = 0 for all x in the domain of f.
The given function is [tex]f(x) = 5x³ + x.[/tex]
To know that a function f(x) is even if f(-x) = f(x) for all x in the domain of f.
A function f(x) is odd if f(-x) = -f(x) for all x in the domain of f.
Thus,
[tex]f(-x) = 5(-x)³ + (-x) = -5x³ - x[/tex]
[tex]f(x) = 5x³ + x[/tex]
Comparing f(-x) with f(x), we get:
[tex]f(-x) = -5x³ - x[/tex]
[tex]f(x) = 5x³ + x[/tex]
Since f(-x) is not equal to f(x), the function f(x) = 5x^3 + x is neither even nor odd.
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Write the equation of the line
Answer:
Below
Step-by-step explanation:
Pick two convenient integer coordinate sets on the line
like 0,0 and 10,4
find slope, m = ( y1-y2) / (x1-x) = ( 4-0) / ( 10-0) = 4/10 = 2/5
b = y axis intercept = 0
Slope - intercept equation of a line is of the form : y = mx + b
substitute in the m and b values found above to get
y = 2/5 x + 0
or just y = 2/5 x
Find d/dx (cos(x) + e^5x) using derivative rules.
O-sin(x) +5e^5x
O-sin(x) + 5xe^(5x-1)
O-sin(x) +e^5x
None of the answers listed is correct.
O sin(x) +e^5x
Answer:
1st one.-sin(X)+5e^5x
Which of the following expressions are equivalent to 18x - 24y? Select all that apply.
3(6x-8y)
O2(9x+12y)
6(3x-4y)
6(18x-4y)
(6x-24y)3
O-2(-9x+12y)
how you can find the most common and least common on a line plot
giving away 100 points whoever gets it right, if your not trying to help and just get the points leave.
Answer:
siuuuuuuuuuuuuuuuuuuuuuuuuuu
find the areas of the sectors formed by angleDFE. Round your answers to the nearest hundredth
The area of the sector formed by angle DFE is approximately 3.29 square feet.
What is area of the sector?
To find the area of a sector of a circle, we need to know the central angle that defines the sector and the radius of the circle. We can then use the formula:
Area of sector = (central angle / 360 degrees) x π x (radius)²
In this case, we are given that the radius of the circle is 4 feet and the central angle that defines the sector is 75 degrees. Therefore, the area of the sector can be calculated as:
Area of sector = (75 / 360) x π x (4)²
= (0.2083) x π x 16
= 3.29 square feet (rounded to the nearest hundredth)
Therefore, the area of the sector formed by angle DFE is approximately 3.29 square feet.
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