karen recorded her walking pace in the table below. what equation best represents this relationship
Answers
Given Data:
The table given here shows time taken in the first column and the distance travelled in the second column.
First check the ration of distance /time to verify if the speed of the man is constant or not.
[tex]\begin{gathered} \frac{8.75\text{ m}}{2.5\text{ h}}=3.5\text{ m/h} \\ \frac{14\text{ m}}{4\text{ h}}=3.5\text{ m/h} \end{gathered}[/tex]As both ratios are same it means the speed of the man is constant and the distance travelled is directly proportional to the time taken and varies linealy with the time.
Now to determine the relationship between m and h we will use the same ratio of m and h which comes in the previous step.
[tex]\begin{gathered} \frac{m}{h}=3.5 \\ m=3.5h \end{gathered}[/tex]Thus, option (D) is the required solution.
Related Questions
there are 12 questionsI got 7 right what did I make?
Answers
there are 12 questions
I got 7 right
the easiest way to solve this is by using a rule of three
Step 1
Let
[tex]12\text{ questiones }\Rightarrow100\text{ percent}[/tex]then
[tex]7\text{ questions }\Rightarrow x\text{ percent}[/tex]Step 2
do the relation and solver for x
[tex]\begin{gathered} \frac{12}{100}=\frac{7}{x} \\ 12\cdot x=100\cdot7 \\ 12\cdot x=700 \\ x=\frac{700}{12} \\ x=58.33 \\ \end{gathered}[/tex]so, you did the 58.33 %
41 increased by 4 is what number ?
Answers
The statement
41 increased by 4
The word increase mean adding to the given number 41
Hence,
The statement can be expressed as
[tex]41+4[/tex]Simplifying the result gives
[tex]41+4=45[/tex]Therefore, the answer is
[tex]45[/tex]41 + 4 = (41-1+4=44+1=45)
41 + 4 = 45 (40+5=45)
(41-1=40 4 + 1 = 5 + 40 = 45)
Therefore, 41 increased by 4 (41+4) would be 45. Please correct me if I’m wrong.
Jo borrowed $3800 for 8 months from a bank at 5.5% a. how much interest did jo pay the bank for the us of it's money?b. how much did he pay total?
Answers
Let's begin by listing out the given information:
Loan (p) = $3,800
Time (t) = 8 months = 8/12 year
Interest rate (r) = 5.5%
a)
We calculate it thus:
[tex]\begin{gathered} I=\frac{p\times r\times t}{100} \\ I=\frac{3800\times5.5\times\frac{8}{12}}{100}=139.33 \\ I=\text{\$}139.33 \end{gathered}[/tex]b)
The amount paid in total is:
[tex]\begin{gathered} A=p+I \\ A=3800+139.33=3939.33 \\ A=\text{\$}3939.33 \end{gathered}[/tex]find the zeros algebraically: f(x)=x^4-8x^3+5x^2+14x
Answers
The given equation is:
x^4-8x^3+5x^2+14x
In this question, we have to find the zeros algebraically. Hence, we need to find the values of x that satisfy the equation.
Note: The roots (values of x) are equal to the power of the equation. Therefore, the given equation will have 4 roots
Therefore,
x^4-8x^3+5x^2+14x = 0
or
x(x^3-8x^2+5x+14) = 0
=> x = 0 and x^3-8x^2+5x+14 = 0
Therefore, the first root is x = 0.
Now,
x^3-8x^2+5x+14 = 0
To simplify that, try putting different values of x (starting from 1 and -1). The value that makes both sides equal to zero would be the solution.
Let's start with (1):
For x = 1
(1)^3 - 8(1)^2 + 5(1) + 14 = 0
1 -8(1) + 5 + 14 = 0
-1 -8 +5 + 14 = 0
- 9 + 19 = 0
10 = 0
It is false, therefore, x = 1 is not the solution.
For x = -1
(-1)^3 - 8(-1)^2 + 5(-1) + 14 = 0
-1 -8(1) - 5 + 14 = 0
-1 -8 -5 + 14 = 0
- 14 + 14 = 0
0 = 0
hence, x = -1 is the second solution.
If x = -1 is the solution, (x + 1) should be the factor of x^3-8x^2+5x+14. Therefore, the whole equation can be divided by factor
x^3-8x^2+5x+14 / (x+1). = x^2 - 9x + 14. (using division)
Now, let's find the roots of x^2 - 9x + 14
x^2 - 9x + 14 = 0
x^2 - 7x - 2x + 14 = 0
x(x - 7) - 2 (x - 7) = 0
(x - 7) (x - 2) = 0
or
x - 7 = 0. and x - 2 = 0
x = 7 and x = 2
Therefore, the zeros of the given equation are, 0, -1, 2 and 7.
Write the slope-intercept form of the equation. Put your answer in y = mx + b form.Passing through (-4, -8) and (-8, -13)
Answers
Answer:
[tex]y=\frac{5}{4}x-3[/tex]Step-by-step explanation:
Linear functions are represented by the following equation:
[tex]\begin{gathered} y=mx+b \\ \text{where,} \\ m=\text{slope} \\ b=y-\text{intercept} \end{gathered}[/tex]The slope of a line is given as;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex](-4,-8) and (-8,-13):
[tex]\begin{gathered} m=\frac{-8-(-13)}{-4-(-8)} \\ m=\frac{5}{4} \end{gathered}[/tex]Use the slope-point form of a line, to find the slope-intercept form:
[tex]\begin{gathered} y_{}-y_1=m(x_1-x_{}) \\ y+8=\frac{5}{4}(x+4) \\ y+8=1.25\mleft(x+4\mright) \\ y=\frac{5}{4}x-13 \\ y+8=\frac{5}{4}x+\frac{20}{4} \\ y=\frac{5}{4}x+5-8 \\ y=\frac{5}{4}x-3 \end{gathered}[/tex]PMark for Review 1 Harold spent the summer working at a diner. He now pays for a monthly subscription to a magazine. The equation y -35x + 180 can be used to represent this situation, where y is the amount of money Harold has remaining after x months of paying for his monthly magazine subscription. Which statement best describes the amount of money Harold has, given this equation? - A) Harold started with $35 and he spends $180 per month on his magazine subscription. B) Harold started with $180 and he gets paid $35 per month. C) Harold started with owed $180 for magazines and he continues to spends $35 per month on his magazine subscription. D) Harold started with $180 and he spends $35 per month on his magazine subscription.
Answers
the option D is the correct answer
the equation is
y = 35x +180
that means he started with 180 $ and his monthly subscription is 35 $.
Quadrilateral MNOP is dilated by a scale factor of % to create quadrilateral M'N'O'P. The perimeter of quadrilateral MNOP is x units. What is the perimeter in units of quadrilateral M'N'O'P'? A. x units B. ( V2 x units COM X units D. 8/7 x units
Answers
If the perimeter of the quadrilateral MNOP is x
And a scale factor of a dilated image is
[tex]\frac{7}{8}[/tex]If the perimeter of M'N'O'P' = y
Then
[tex]\text{scale factor = }\frac{perimeter\text{ of y}}{perimeter\text{ of x}}\text{ = }\frac{7}{8}[/tex]Cross multiplying,
[tex]perimeterofy=M^{\prime}N^{\prime}O^{\prime}P^{\prime}=\frac{7}{8}\text{ x units}[/tex]The perimeter of M'N'O'P' = 7/8 x units
Option A is correct
12x÷4yif x=-8 and y=3
Answers
To solve 12x÷4y, first, let's evaluate the products on both sides of the ÷ symbol, we know that x = -8, then we have:
[tex]12\times(-8)=-96[/tex]We have -96 on the left side of the ÷ symbol.
We know that y = 3, then, on the right side, we have:
[tex]4\times3=12[/tex]Then, we have 12 on the right side of the ÷ symbol, now the expression looks like this:
-96 ÷ 12. what we have to do is to divide -96 by 12, then we get:
[tex]-96\text{ }\div12=\frac{-96}{12}=-8[/tex]Then, the answer is 8
Derivative of ln(x)cos(x)
Answers
The derivative of the given expression ln(x)cos(x) can be written as (cos(x))/x - sin(x)ln(x).
What is derivative?
In mathematics, the derivative of a function of a real variable measures how sensitive the function's value (or output value) is to variations in its argument (input value). The derivative is the fundamental tool in calculus. A measure of how quickly an object's position changes over time is its velocity, which is the derivative of that object's position with respect to time.
We can solve this derivation using multiplication property of derivatives:
i.e. [tex]\frac{d}{dx}(uv) = u\frac{dv}{dx} + y \frac{du}{dx}[/tex]
In the given question, lets consider ln(x) as u and cos(x) as v
putting the values from question.
[tex]\frac{d}{dx}(ln(x)cos(x)) = ln(x)\frac{d(cos(x))}{dx} + cos(x) \frac{d(ln(x))}{dx}[/tex]
[tex]= ln(x)(-sin(x)) + cos(x)(\frac{1}{x})[/tex]
= (cos(x))/x - sin(x)ln(x)
To know more about derivative, go to link
https://brainly.com/question/23819325
#SPJ13
Please Help!!!!! NOT FOR QUIZ!!!!!!!!
Answers
The graph of the line y [tex]=[/tex] -3x + 4 is a line that shows the set of all solutions to the equation , the correct option is (c) .
In the question ,
it is given that
the equation of the line is y [tex]=[/tex] -3x + 4 ,
we have to plot the line in the coordinate plane .
we plot the line ,w e need at least two points .
for the first point ,
for x = 0 , we have
y = -3(0) + 4
y= 0 + 4
y = 4
the first point is (0,4)
for the second point
for y = 0 , we have
0 = -3x + 4
-3x = -4
x = 4/3
the second point is (4/3 , 0)
so , from the graph plotted below , we can see that the line y [tex]=[/tex] -3x+4 shows the set of all solutions to the equations .
Therefore , The graph of the line y [tex]=[/tex] -3x + 4 is a line that shows the set of all solutions to the equation .
Learn more about Line here
https://brainly.com/question/23680294
#SPJ1
The scatter plot shows the median household income x in thousands of dollars, and the number of adults per 1,000 people with bachelors degree y of 50 U.S states. The line y=4.08x+63.13 is a good fit for this data
Answers
So,
The line:
[tex]y=4.08x+63.13[/tex]Is a good fit of the data given.
To predict the number of bachelor's degrees in Mississippi, we replace x by 40.6 and operate:
[tex]\begin{gathered} y=4.08(40.6)+63.13 \\ y=228.778 \end{gathered}[/tex]The number of bachelor's degrees per 1000 people when x=40.6 median income, is predicted as 228.778.
I really need help make sure that your answer is 7th grade appropriate
Answers
Examples:
1. Five increased by four times a number
[tex]5+4n[/tex]where n is the number
2.The product of 4, and a number decreased by 7
[tex]4(n-7)[/tex]Ramon has assets that sum up to $253,000. He has liabilities that sum up to $216,345. what is his net worth?
Answers
Net worth is equal to total assets minus total liabilities (debt).
So,
Total Assets = 253000
Total Liabilities = 216345
Hence,
Net Worth = 253000 - 216345 = $36,655
In shop, you make a table. The sides of the table measure 36" and 18". If the diagonal of the table measures 43", is the table "square"? (In construction, the term "square" just means the table has right angles at the corners.)
Answers
We are given the following information:
Table sides = 36 inches & 18 inches
Diagonal of table = 43 inches
We are to find out if the table is "square" (that is if the table follows the Pythagoras theorem). We will check this below:
[tex]\begin{gathered} \text{The Pythagoras Theorem is given by:} \\ c^2=a^2+b^2 \\ c=43in,b=36in,a=18in \\ \text{Substituting we have:} \\ 43^2=18^2+36^2 \\ 1849=324+1296 \\ 1849=1620 \\ \Rightarrow1849\ne1620 \\ \\ \therefore\text{ The table is not ''square''} \end{gathered}[/tex]Therefore, the table is not "square" (it does not have right angles at the corners)
Help please!!!!!!!!!!!!!!!!!!!!!!!!!Which is the best buy?a. $18.09 for 9 bottles of juiceb. $22.33 for 11 bottles of juice
Answers
Answer:
The correct option is option a.
$18.08 for 9 bottles is the better buy.
Explanation:
The best buy is the item with the lesser price tag.
Let us chech which of the given items has the lesser price tag.
a. $18.08 for 9 bottles of juice
Let us find how much one bottle costs.
1 bottle = 18.08/9
= 2.01
1 bottle of juice costs $2.01 approximately
b. $22.23 for 11 bottles of juice
1 bottle = 22.23/11
= 2.03
1 bottle of juice costs $2.03 approximately.
Comparing these prices per bottle of juice, we realise that the one with $18.08 for 9 bottles is the better buy.
What is 44 over 13 rounded to the nearest 10 tenths
Answers
we have that
44/13=3.38
rounded to the nearest tenths
3.38=3.4
the answer is 3.4Point X is (3, -6). Wgich point is 10 units away from Point X
Answers
If we find the point X on the plane we can see the following:
Notice that the point D and the point X are 10 units apart with respect the x-axis, therefore, the point that is 10 units away from X is point D
Calculate the area of the right triangle that has the following coordinates:
A: (-2,-1)
B: (1, 1)
C: (3,-2)
You must show all calculations to earn any credit. I suggest that you sketch this
triangle on graph paper so that the visual can help you.
Answers
The area of right triangle is [tex]\frac{1}{15}[/tex].
The given coordinates are [tex](-2,-1), (1, 1), (3,-2)[/tex].
We have to find the area of right triangle.
To find the area we first draw the graph using that coordinate.
The graph of the coordinate is
To find the area we use the formula
[tex]\angle ABC=\frac{1}{2}(|AB|)(|AC|)[/tex]
We first find the value of [tex](|AB|)[/tex] and [tex](|AC|)[/tex].
e coordinate of [tex]A[/tex] is [tex](-2,-1)[/tex] and [tex]B[/tex] is [tex](1,1)[/tex].
The slope of [tex](|AB|)=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
The slope of [tex](|AB|)=\frac{1-(-1)}{1-(-2)}[/tex]
The slope of [tex](|AB|)=\frac{1+1}{1+2}[/tex]
The slope of [tex](|AB|)=\frac{2}{3}[/tex]
The coordinate of [tex]A[/tex] is [tex](-2,-1)[/tex] and [tex]C[/tex] is [tex](3,-2)[/tex].
The slope of [tex](|AC|)=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
The slope of [tex](|AC|)=\frac{(-2)-(-1)}{3-(-2)}[/tex]
The slope of [tex](|AC|)=\frac{-2+1}{3+2}[/tex]
The slope of [tex](|AC|)=-\frac{1}{5}[/tex]
Now finding the area of right triangle by putting the values.
[tex]\angle ABC=\frac{1}{2}\times\frac{2}{3} \times(-\frac{1}{5})[/tex]
Area can't be negative so
[tex]\angle ABC=\frac{1}{2}\times\frac{2}{3} \times\frac{1}{5}\\\angle ABC=\frac{2}{30}\\\angle ABC=\frac{1}{15}[/tex]
Hence, the area of right triangle is [tex]\frac{1}{15}[/tex].
To learn more about area of right triangle here link
https://brainly.com/question/27694270
#SPJ1
At the fast food restaurant, an order of fries costs $0.94 and a drink costs $1.04. Howmuch would it cost to get 3 orders of fries and 2 drinks? How much would it cost toget f orders of fries and d drinks?
Answers
Determine the total cost for 3 order of fries and 2 drinks.
[tex]\begin{gathered} T=3\cdot0.94+2\cdot1.04 \\ =2.82+2.08 \\ =4.9 \end{gathered}[/tex]Determine the expression for f orders of fries and d drinks.
[tex]\begin{gathered} T=f\cdot0.94+d\cdot1.04 \\ =0.94f+1.04d \end{gathered}[/tex]So cost of 3 order of fries and 2 drinks is $4.9.
The cost order for f orders of fries and d drinks is 0.94f + 1.04d.
Given the equations and the table below, what is the first x-value when the y-value of equation 2 is greater than the y-value of equation 1 after the functions first intersect?Equation 1: f(x)=5x^3Equation 2: f(x)=2x+3
Answers
the first x value, when the y-value of the equation is greater than the y value of equation one, is x=15
Because the y-value of equation 2 with x=15 is 32771, while the y-value of equation 1 is 16875
Corky writes four equations to show each of the properties of equality. Which of Corky's equation is incorrect? Explainwill send image.
Answers
6 + m = 12
A. This IS equivalent
6 + m - m = 12 - m ==> 6 = 12 - m ==> 6 + m = 12
B. This IS NOT equivalent
6 + m - 6 = 12 - 12 ==> m = 0
C. This IS equivalent
6 + m + 2 = 12 + 2 ==> 6 + m = 12
D. This IS equivalent
6 + m - 6 = 12 - 6 ==> m = 6 ==> 6 + m = 12
Answer:
B is not equivalent
Write a SITUATION that can be represented with this graph. Not an equation.
Answers
We need to think of something that will cool down 10 degrees in 5 hours to be more realistic. You may say that this graph describes the temperature profile of a fermentation broth after it is heated to 82 degrees is left on the tank to cool down to room temperature.
Yesterday, Alan had k baseball cards. Today, he gave 19 away. Using k, write an expression for the number of cards Alan has left.
Answers
Answer:
k-19
Step-by-step explanation:
If Alan had k baseball card and gave 19 away then he would have 19 less then k
Answer:
K - 19= X
Step-by-step explanation:
I hope this helps!
Need help asap !!!!!
Answers
The practical domain is 1 ≤ x ≤ 20 and the practical range is 13.61 ≤ C(x) ≤ 127.61
How to determine the practical domain?From the question, the given parameters are:
Charges = $7.61Reservation = $6Maximum number of windows = 20Total cost = CThe domain is dependent on the number of windows washed
Using the maximum as a guide, the minimum number of windows could be
Minimum = 1
The domain is then represented as
Minimum ≤ x ≤ Maximum
So, we have
1 ≤ x ≤ 20
How to determine the practical range?Using the given parameters in (a), we have
Total cost, C = Charges * Number of windows + Reservation
So, we have
C(x) = 7.61 + 6x
Where x is the number of windows
When x = 0, we have
C(1) = 7.61 + 6(1)
C(1) = 13.61
When x = 20, we have
C(20) = 7.61 + 6(20)
C(20) = 127.61
So, we have the range to be 13.61 ≤ C(x) ≤ 127.61
Read more about domain and range at
https://brainly.com/question/13146216
#SPJ1
Here are the numbers of times 13 people ate out last month.5, 3, 4, 6, 3, 4, 5, 6, 4, 7, 3, 7, 6Find the modes of this data set.If there is more than one mode, write them separated by commas.If there is no mode, click on "No mode."No modeX?.
Answers
The mode is the number that appears most or occurs most frequently. Therefore, the mode of the data set below can be calculated below
[tex]5,3,4,6,3,4,5,6,4,7,3,7,6[/tex]Let's rearrange the data
[tex]3,3,3,4,4,4,5,5,6,6,6,7,7[/tex]The mode will be
[tex]\mleft\lbrace3,4,6\mright\rbrace[/tex]For each ordered pair, determine whether it is a solution to 3x + 5y=-17. Is it a solution? X 6 ? No (-8,3) (-4, -1) (6, 7) (7,2)
Answers
Determine whether is a solution for:
[tex]\begin{gathered} 3x+5y=-17 \\ To\text{ determine if it's a solution, we can isolate y and see if the statement} \\ is\text{ true:} \\ 5y=-17-3x \\ y=-\frac{17}{5}-\frac{3}{5}x \end{gathered}[/tex]For, x=-8, y has to be 3:
[tex]\begin{gathered} y=-\frac{17}{5}-\frac{3}{5}(-8) \\ y=\frac{7}{5}=1.4 \end{gathered}[/tex](-8, 3) is not a solution for the equation.
For x=-4, y has to be -1:
[tex]\begin{gathered} y=-\frac{17}{5}-\frac{3}{5}(-4) \\ y=-1 \end{gathered}[/tex](-4, -1) is a solution for the equation.
For x=6, y has to be -7:
[tex]\begin{gathered} y=-\frac{17}{5}-\frac{3}{5}(6) \\ y=-7 \end{gathered}[/tex](6, -7) is a solution for the equation.
For x=7, y has to be 2
[tex]\begin{gathered} y=-\frac{17}{5}-\frac{3}{5}(7) \\ y=-\frac{38}{5}=-7.6 \end{gathered}[/tex](7, 2) is not a solution for the equation.
the ratio of men to woman working for a company is 5 to 4. if there is 225 employees total how many women work for the company
Answers
Given:
The ratio of men to women = 5: 4
Total number of employees = 225
The total ratio is:
[tex]\begin{gathered} =\text{ 5 + 4} \\ =\text{ 9} \end{gathered}[/tex]The number of women is the ratio of women to the total ratio times the number of employees
[tex]\begin{gathered} =\frac{4}{9}\times225 \\ =\text{ 100} \end{gathered}[/tex]Answer:
100 women
Put the following equation of a line into slope-intercept form, simplifying allfractions.2x + 8y = 24
Answers
Devon is 30 years old than his son, Milan. The sum of both their ages is 56. Using the variables d and m to represent the ages of Devon and Milan, respectively, write a system of equations to describe this situation. Enter the equations below, separated by a comma.How old is Devon?
Answers
Let's set d as the age of Davon and m as the age of Milan.
Devon is 30 years old than his son Milan, it is represented by the equation:
[tex]d=m+30\text{ Equation (1)}[/tex]The sum of both ages is 56, the equation that represents the situation is:
[tex]d+m=56\text{ Equation (2)}[/tex]To find Devon's age, in equation 1, solve for m in terms of d:
[tex]m=d-30[/tex]Now, replace in equation 2 and solve for d:
[tex]\begin{gathered} d+(d-30)=56 \\ 2d-30=56 \\ 2d=56+30 \\ 2d=86 \\ d=\frac{86}{2} \\ d=43 \end{gathered}[/tex]Devon is 43 years old.
What is the measure of the exterior angle of the triangle? A. 23°B. 149°C. 180°D. 31°
Answers
Solution
The diagram below will be of help
From the image above
We know that the sum of angle in a triangle is 180 degrees
That is
[tex]\begin{gathered} 63+86+y=180 \\ 149+y=180 \\ y=180-149 \\ y=31^{\circ} \end{gathered}[/tex]Now, to find x
We also know that the sum of angle in a straight line is 180 degrees
That is
[tex]y+x=180[/tex]We now solve for x
[tex]\begin{gathered} x=180-y \\ x=180-31 \\ x=149^{\circ} \end{gathered}[/tex]Therefore, the value of x = 149 degrees
Option B