Calculating a rate of change
What is the vertical change form Point A to Point B?
What is the horizontal change from Point A to Point B ?
What is the rate of change shown on the graph? Give the answer as a decimal rounded to the nearest tenth, if necessary?
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Hello there. To solve this question, we'll have to remember some properties about rate of change.
Given the points A and B from a line, we want to determine the vertical change and the horizontal change between the points and then, using these values, determine the rate of change of the function (the line passing through them).
For this, we first find the coordinates of the points.
[tex]A=(2,1)\text{ and }B=(4,2)[/tex]The vertical change is the difference between the y-coordinates of the points, hence
[tex]y(B)-y(A)=2-1=1[/tex]The horizontal change is given by the difference between the x-coordinates of the points, therefore
[tex]x(B)-x(A)=4-2=2[/tex]The rate of change of this function is, finally, given by the ratio between the vertical (rise) and horizontal (run) changes of the function:
[tex]\dfrac{1}{2}=0.5[/tex]This is the rate of change of this function.
Related Questions
Marco is a newspaper boy who received a total piecework paycheck of $169.12. He receives 56 cents for every newspaper he delivers. How many newspapers did he deliver?
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if he receives 56 cents for each period it means that the multiplication must give the total paid
[tex]0.56\times P=169.12[/tex]where P is the number of newspapers
then, solve for p
[tex]P=\frac{169.12}{56}=302[/tex]he delivered 302 newspapers
A business woman buys a new computer for $4000. for each year that she uses it the value goes depreciates by $400 the equation below gives the value y of the computer after x years. What does the x intercept mean in this situation? Find the x intercept. After how many years will the value of the computer be $2000Y=-400x+4000
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Step 1: Write the equation
y = -400x + 4000
Step 2:
The intercept in the equation represents time in years.
x-intercept represents the total length of time taken in years for the computer to values to depreciate to $0.
step 3: Find the x-intercept
To find the x-intercept, you will have to find the time taken for the computer value to depreciate to $0.
y = $0
[tex]\begin{gathered} \text{From the equation.} \\ y\text{ = -400x + 4000} \\ 0\text{ = -400x + 4000} \\ 400x\text{ = 4000} \\ x\text{ = }\frac{4000}{400} \\ x\text{ = 10} \end{gathered}[/tex]The x-intercept = 10 years
Step 4:
To find the number of years take for the computer value to depreciate to $2000.
You will substitute the value of y = $2000 and find the value of x.
Therefore
[tex]\begin{gathered} y\text{ = -400x + 4000} \\ 2000\text{ = -400x + 4000} \\ 400x\text{ = 4000 - 2000} \\ 400x\text{ = 2000} \\ x\text{ = }\frac{2000}{400} \\ \text{x = 5 years} \end{gathered}[/tex]It will take 5 years for the value of the computer to depreciate to $2000.
Can someone help me with 7? I’m desperate
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Solve 2x - 8 < 7...........................................................................
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
2x - 8 < 7
Step 02:
inequality:
2x - 8 < 7
2x - 8 + 8 < 7 + 8
2x / 2 < 15 / 2
x < 15 / 2
The answer is:
x < 15 / 2
(-oo , 15/2)
There is a stack of plates in the backyard. There are 4 plates in the 1st layer, 8 in the second, 16 in the third, 32 in the fourth, and so on. There are total 10 rows/layers. How many total plates are in the stack?
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Given that
[tex]\begin{gathered} layer1=4plates \\ layer2=8plates \\ layer3=16plates \\ layer4=32plates \end{gathered}[/tex]Explanation
From the above, it is easy to see that the arrangement of the layers follows a geometric sequence where
[tex]\begin{gathered} first\text{ term = 4} \\ common\text{ ratio = }\frac{second\text{ }term}{first\text{ term}}=\frac{8}{4}=2 \end{gathered}[/tex]Since r>1, therefore the sum of 10 terms, which implies would give the total number of plates that are in the stack can be seen below.
[tex]\begin{gathered} S_n=\frac{a(r^n-1)}{r-1} \\ therefore; \\ S_{10}=\frac{4(2^{10}-1)}{2-1}=\frac{4(1024-1)}{1}=4(1023)=4092 \end{gathered}[/tex]Answer: 4092
help meeeeeeeeee pleaseee !!!!!
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For the given functions, the two compositions are:
(f o g)(x) = 9x² + 5
(g o f)(x) = 3*x² + 15
How to find the compositions of the functions?Here we have two functions which are:
f(x) = x² + 5
g(x) = 3x
Now we want to find the compositions:
(f o g)(x) = f( g(x) )
So we just need to evaluate f(x) in g(x), we will get:
f( g(x) ) = g(x)² + 5
f( g(x) ) = (3x)² + 5 = 9x² + 5
The other composition is:
(g o f)(x) = g(f(x))
And we can get this in a similar way:
g(f(x)) = 3*f(x) = 3*(x² + 5) = 3*x² + 15
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what is the surface area of the rectangular prism? 1.8 ft 2/5 ft 1/2 ft
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Each face of a rectangular prism has a rectangle shape. To calculate the surface area we need to calculate the area of all the faces. Each face appears twice on the prism, on opposite sides so we only need to make three calculations. These are done using the formulas below:
[tex]\begin{gathered} A_1=height\cdot width_{} \\ A_2=length\cdot width_{} \\ A_3=length\cdot height_{} \end{gathered}[/tex]Using the data from the problem we can calculate these areas.
[tex]\begin{gathered} A_1=\text{ 1.8}\cdot\frac{2}{5}=0.72\text{ square ft} \\ A_2=\frac{1}{2}\cdot\frac{2}{5}=0.2\text{ square ft} \\ A_3=1.8\cdot\frac{1}{2}=0.9\text{ square ft} \end{gathered}[/tex]The surface area of the prism is the sum of the areas above multiplied by two.
[tex]\begin{gathered} A_{\text{surface}}=2\cdot(A_1+A_2+A_3) \\ A_{\text{surface}}=2\cdot(0.72+0.2+0.9)=2\cdot1.82=3.64\text{ square ft} \end{gathered}[/tex]Drag the factors to the correct locations on the image. Not all factors will be used.What is the factored form of this expression?27 m 3 + 125n39m + 25n9m2 - 15mn + 25n23m + 5n9m2 + 15mn + 2523m2 – 8mn + 5123m - 5n
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The surface area of the solid cone requiring paint rounded to the nearest whole number is how many square centimeters?
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In order to calculate the surface area of the cone, first let's calculate its slant height.
If the diameter is 5 cm, the radius is 2.5 cm. Now, using the Pythagorean theorem, we can calculate the slant height s:
[tex]\begin{gathered} s^2=h^2+r^2 \\ s^2=11.4^2+2.5^2 \\ s^2=129.96+6.25 \\ s^2=136.21 \\ s=11.67\text{ cm} \end{gathered}[/tex]Now, we can calculate the surface area using the formula below:
[tex]\begin{gathered} S=\pi rs+\pi r^2^{} \\ S=\pi\cdot2.5\cdot11.67+\pi\cdot2.5^2 \\ S=29.175\pi+6.25\pi \\ S=35.425\pi \\ S=111.29\text{ cm}^2 \end{gathered}[/tex]Rounding to the nearest square centimeter, we have a surface area of 111 cm².
write a quadratic equation in the form of ax²bx+c=0
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The general form of a quadratic equation is expressed as
ax^2 + bx + c = 0
In order to write the equation, we would substitute values for a, b and c. If a = 3, b = 8, c = 25, the equation would be
3x^2
Solve the System of Equations8x + 15y = -1174x + 9y=-75Write your answer as an ordered pair: (x,y)
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We have to solve the system of linear equations:
[tex]\begin{gathered} 8x+15y=-117 \\ 4x+9y=-75 \end{gathered}[/tex]We can substract 2 times the second equation for the first equation and solve for y:
[tex]\begin{gathered} (8x+15y)-2(4x+9y)=-117-2(-75) \\ 8x+15y-8x-18y=-117+150 \\ 0x-3y=33 \\ y=\frac{33}{-3} \\ y=-11 \end{gathered}[/tex]Now, we can solve for x:
[tex]\begin{gathered} 4x+9y=-75 \\ 4x+9(-11)=-75 \\ 4x-99=-75 \\ 4x=-75+99 \\ 4x=24 \\ x=\frac{24}{4} \\ x=6 \end{gathered}[/tex]Answer: (x,y)=(6,-11)
What is the answer for 5p+10 = 8p+1
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The equation is given to be:
[tex]5p+10\: =\: 8p+1[/tex]We can solve for p using the following steps:
Step 1: Subtract 10 from both sides of the equation
[tex]\begin{gathered} 5p+10-10=8p+1-10 \\ 5p=8p-9 \end{gathered}[/tex]Step 2: Subtract 8p from both sides of the equation
[tex]\begin{gathered} 5p-8p=8p-9-8p \\ -3p=-9 \end{gathered}[/tex]Step 3: Multiply both sides by -1
[tex]\begin{gathered} -1\times(-3p)=-1\times(-9) \\ 3p=9 \end{gathered}[/tex]Step 4: Divide both sides by 3
[tex]\begin{gathered} \frac{3p}{3}=\frac{9}{3} \\ p=3 \end{gathered}[/tex]ANSWER:
[tex]p=3[/tex]See attached pic for problem. Only need help with #2
Answers
SOLUTION
Part 1
The independent variable are the predicting varaible for which other variable are depends on. The are the x- values
Hence
The indepedent varibles is school year
The dependent variable are the responses variables. They are the y-values for which depends on othere values,
Hence
The dependent variable for the data given is
The Tution
Part 2
To find the function, we need to set up the data as given in the table below.
The years has an interval of 1 and each fees difer by 4, the to obtain the x-values we use the mid-point
[tex]x=\frac{\text{lower}+\text{higher}}{2}\text{ for each }[/tex]Hence
The data plot will be
The linear is given by the form
[tex]\begin{gathered} y=ax+b \\ \text{Where }^{} \\ a=561.043,\text{ b=-0.0000}010994 \\ \text{Hence } \\ y=561.043x-0.0000010994 \end{gathered}[/tex]THerefore
The linear regression is y = 561. 043x -0.0000010994
Then for exponenetial we have
[tex]\begin{gathered} y=e^{ax+b} \\ \text{Where } \\ a=0.0286229,b=-47.2727 \\ \text{Hence } \\ y=e^{0.029x-47.27} \end{gathered}[/tex]Hence
The exponential regression is y = e^(0.029x-47.27)
For the power represion we have
[tex]\begin{gathered} y=ab^x \\ \text{Where } \\ a=2.9495\times10^{-21,}b=1.02904 \\ \text{Hence } \\ y=2.9495\times10^{-21,}(1.02904)^x \end{gathered}[/tex]Hence
The power regression is
y= 2.9495 x 10^-21 (1.02904)ˣ
Part 3
The graoh lot for linear function is given below
The graph for the exponential plot is
The graph for the power regression plot is given below as
Express the sum of the angles of this triangle in two different waysX3/2X1/2X
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1) Since the sum of these angles is written in terms of x, we can write it out:
[tex]\begin{gathered} x+\frac{3}{2}x+\frac{1}{2}x\text{ } \\ \frac{2x+3x+x}{2} \\ \frac{6x}{2} \\ 3x \end{gathered}[/tex]Notice that to sum these fractions we had to take the LCM(2, 1) = 2 and rewrite it as a sum.
2) Another way of writing the sum of these angles is writing it as a sum of decimal numbers since we can rewrite fractions as decimal numbers.
3/2 = 3÷2 = 1.5
1/2 = 1÷2 =0.5
1
[tex]\begin{gathered} x+1.5x+0.5x \\ x+2x \\ 3x \end{gathered}[/tex]if cos ∅=sin 46° find ∅
Answers
Answer:
∅ = 44°
Step-by-step explanation:
cos∅ = sin46°
∅ = (90 - 46)°
∅ = 44°
Hope this helps
The pie chart below shows how the annual budget for a certain company is divided by department. If the amount budgets forceditoral and sales combined is12,500,000, what is the total annual budget
Answers
Explanation
We are asked to find the total annual budget given that the combined amount for sales and editorial is $12,500,000
To do so, let the total combined amount be x
If we check for the combined percentages for the amount for sales and editorial, we will have
[tex]21\text{ \%}+4\text{ \% = 25\%}[/tex]Thus, we can set up the equation
[tex]25\text{ \% of x = 12,500,00}[/tex]Solving for x
[tex]\begin{gathered} \frac{25}{100}\times x=12500000 \\ \\ \frac{x}{4}=12500000 \\ \\ x=4\times12,500,000 \\ \\ x=50,000,000 \\ \end{gathered}[/tex]Therefore, the total annual budget will be $50,000,000
(3x10⁴) (2x10⁵)Find the answer by simplifying
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The given expression (3x10⁴) (2x10⁵)
we seperate the terms and collect like terms:
[tex]\begin{gathered} \mleft(3\times10^{4}\mright)(2\times10^{5})\text{ = 3}\times10^{4}\times2\times10^{5} \\ =\text{ 3}\times2\times10^{4}\times10^{5} \end{gathered}[/tex]When multiplying exponent (power) of the same base, the exponenet of the two numbers (base) are added together.
[tex]\begin{gathered} \text{Base = 10 , exponent = 4 and 5} \\ =3\times2\times10^{4+5} \\ =\text{ 6}\times10^9 \end{gathered}[/tex]
PLS HELP ASAP WILL GIVE BRAINLIST
Answers
Answer:
65
Step-by-step explanation:
[tex]-4a + 65 = 2a + 5\\60 = 6a\\a = 10\\[/tex]
KJN = 25 degrees
MJN = 25 degrees
KJM = KJN + MJN = 25 + 25 = 50 degrees
total angles = 360 degrees
JKL = (360 - 50 - 50 )/2 = 130 degrees
LKN is half of JKL = 130/2 = 65
If I complete this review, then I will do well on the test. If I do well on the test. If I do well on the test, then I will get an “A” on my progress report. Make a conclusion using the law of syllogism
Answers
Law of syllogism:
If p, then q
If q, then r
Conclude:
If p, then r
Given situation:
p: complete this review
q: do well on the test
r: get an “A” on my progress report
If p, then q: If I complete this review, then I will do well on the test
If q, then r: If I do well on the test, then I will get an “A” on my progress report
Conclusion:
If p, then r: If I complete this review, then I will get an “A” on my progress report
You buy a new commercial stove for $9,000 and estimate that it will enable you to deliver 20 additional meals per night at an average price of $20. Assuming 25% food cost and no additional costs to using the new stove, how long will it take the stove to pay for itself?
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Assuming 25 % food cost and no additional costs to using the new stove, The time it will take the stove to pay for itself is 30 days.
Determining the number of daysProfits per meal = $20 - ( 0.25 x20)
Profits per meal = $20 -$5
Profits per meal = $15
Profits for 20 meals = $15 x 20
Profits for 20 meals =$300
Now let determine the number of days
Number of days =$9000 / $300 days
Number of days =30 days
Therefore we can conclude that 30 days is the days that it will take.
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0.4(2-) 0.2(9 + 7) A)-3 B - 1 C) 3 D) all real numbers
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Let us solve the equation to arrange the steps
[tex]-3(4+3x)+5x=-16[/tex]In the first step, we must multiply the bracket by -3 (distributive property)
[tex](-3)(4)_{}+(-3)(3x)=-12-9x[/tex]Then the equation is
[tex]-12-9x+5x=-16[/tex]Now add the like terms on the left side
[tex]\begin{gathered} -12+(-9x+5x)=-16 \\ -12x+(-4x)=-16 \\ -12-4x=-16 \end{gathered}[/tex]Next step, add 12 to both sides
[tex]undefined[/tex]You have 1/4 of a quiche left over from lunch. If you sent 4/6 of the leftover quiche home with your brother, how much of the quiche do you have left in the dish?
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Answer:
[tex]\frac{1}{12}[/tex]
Step-by-step explanation:
If the brother took home 4/6, that means that you still have 2/6.
[tex]\frac{1}{4}[/tex] x [tex]\frac{2}{6}[/tex] = [tex]\frac{2}{24}[/tex] which is the same as 1/12
que es el producto para (x+5) (2x-1)?
Answers
the given expression is,
(x+ 5) (2x -1)
so the answer is
[tex]\begin{gathered} \mleft(x+5\mright)(2x-1)=2x^2-x+10x-5 \\ \end{gathered}[/tex][tex]=2x^2+9x-5[/tex]so the answer is
2x^2 + 9x - 5
For which equation would x = 12 not be a solution?96 ÷ x = 89 x - 7 = 101x + 4 = 105 + 4 x = 53
Answers
Notice that:
1)
[tex]\frac{96}{12}=8.[/tex]Therefore x=12 is a solution to
[tex]96\div x=8.[/tex]2)
[tex]9*12-7=108-7=101.[/tex]Therefore x=12 is a solution to:
[tex]9x-7=101.[/tex]3)
[tex]12+4=16\ne10.[/tex]Therefore x=12 is not a solution to:
[tex]x+4=10.[/tex]4)
[tex]5+4*12=5+48=53.[/tex]Therefore x=12 is a solution to:
[tex]5+4x=53.[/tex]Answer: Third option:
[tex]x+4=10.[/tex]An earthquake in California measured 3.6 on the Richter scale. Use the formula R=log(A/Ao) to determine approximately how many times stronger the wave amplitude of the earthquake was than .
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The correct option regarding how many times stronger the wave amplitude of the earthquake was than the standard wave Ao is given by:
A = 3981Ao.
Ratio of A and AoTo find the ratio of A and Ao, measuring how many times a earthquake measuring R in the Richter scale was than Ao, we have to solve the following logarithmic function:
R=log(A/Ao)
The power of 10 in inverse to the logarithm, hence it is applied to both sides of the expression, as follows:
10^R = 10^log(A/Ao).
Since they are inverses, we can remove the power and the logarithm as follows:
A/Ao = 10^R
Hence the formula for how many times stronger and earthquake is than Ao is given as follows:
A = 10^R Ao
In this problem, the Richter measure of the earthquake was of:
R = 3.6.
Hence the ratio is:
A = 10^(3.6)Ao
A = 3981Ao.
Missing informationThe problems asks how many times stronger the earthquake was than Ao.
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A committee must be formed with 4 teachers and 4 students. If there are 7 teachers to choose from, and 9 students, how many different ways could the committee be made?
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ANSWER
4,410
EXPLANATION
The number of ways we can choose 4 teachers from 7 teachers is,
[tex]_7C_4=\frac{7!}{(7-4)!\times4!}=\frac{7\times6\times5\times4!}{3!\times4!}=\frac{7\times6\times5}{3\times2}=\frac{7\times6\times5}{6}=7\times5=35[/tex]There are 35 ways of choosing 4 teachers out of 7.
And the number of ways we can choose 4 students from 9 students is,
[tex]\begin{gathered} _9C_4=\frac{9!}{(9-4)!\times4!}=\frac{9\times8\times7\times6\times5\times4!}{5!\times4!}=\frac{9\times8\times7\times6\times5}{5\times4\times3\times2} \\ _9C_4=\frac{9\times8\times7}{4}=\frac{9\times(2\times4)\times7}{4}=9\times7\times2=126 \end{gathered}[/tex]There are 126 ways of choosing 4 students out of 9.
The committee is formed by 4 teachers and 4 students. The number of ways it can be made is,
[tex]_7C_4\times_9C_4=35\times126=4,410[/tex]Hence, there are 4,410 ways to choose 4 students and 4 teachers out of 9 students and 7 teachers.
create a system of equations to represent this situation. be sure to explain the meaning of each variable. graph the system of equations. determine the break even point for Chuck E Cheese and Bright Child, Adventure Plex and Bright Child, Adventure Plex and Chuck E Cheese.
Answers
For them, let x = number of children of the party and
A=Adventure Plext cost
B= Bright Child cost
C= Chuck E Cheese cost
So,
[tex]\begin{gathered} A=300+12x \\ B=180+15x \\ C=18x \end{gathered}[/tex]Then, graphing each equation of the system of equations
Now, for determine the break even point for Chuck E Cheese and Bright Child you have
[tex]\begin{gathered} 180+15x=18x \\ 180=18x-15x \\ 180=3x \\ \frac{180}{3}=x \\ 60=x \end{gathered}[/tex]That is, the break even point for Chuck E Cheese and Bright Child occurs when x = 60 children.
For determine the break even point for Adventure Plex and Bright Child you have
[tex]\begin{gathered} 300+12x=180+15x \\ 300+12x-180=180+15x-180 \\ 120+12x=15x \\ 120+12x-12x=15x-12x \\ 120=3x \\ \frac{120}{3}=\frac{3x}{3} \\ 40=x \end{gathered}[/tex]That is, the break even point for Adventure Plex and Bright Child occurs when x = 40 children.
Finally, For determine the break even point for Adventure Plex y Chuck E Cheese you have
[tex]\begin{gathered} 300+12x=18x \\ 300+12x-12x=18x-12x \\ 300=6x \\ \frac{300}{6}=\frac{6x}{6} \\ 50=x \end{gathered}[/tex]That is, the break even point for Adventure Plex and Chuck E Cheese occurs when x = 50 children.
Solve for w.4w+6= -22Simplify your answer as much as possible.W8DDХ5?
Answers
w= -7
Explanation
[tex]\begin{gathered} 4w+6=-22 \\ \end{gathered}[/tex]
Step 1
The addition property of equality and subtraction property of equality are similar. Adding or subtracting the same number to or from both sides of an equation keeps both sides equal, so we can use this fact to isolate w
a) subtract 6 in both sides of the equation
[tex]\begin{gathered} 4w+6=-22 \\ 4w+6-6=-22-6 \\ 4w=-28 \\ \end{gathered}[/tex]Step 2
The division property of equality states that when we divide both sides of an equation by the same number, the two sides remain equal.so
b) divide both sides by 4
[tex]\begin{gathered} 4w=-28 \\ \frac{4w}{4}=\frac{-28}{4} \\ w=-7 \end{gathered}[/tex]therefore, the answer is
w= -7
I hope this helps you
Suppose the cost per ton f(x) to build an oil platform of x thousand tons is approximated byf(x)= 62,500 ______ x+125What is the cost per ton for x=30?
Answers
Given that
The cost per ton f(x) to build an oil platform of x thousand tons is approximated by
[tex]f(x)=\frac{62500}{x+125}[/tex]The cost per ton for x = 30, i.e f(30) will be
[tex]\begin{gathered} f(x)=\frac{62500}{x+125} \\ f(30)=\frac{62500}{x+125}=\frac{62500}{30+125}=\frac{62500}{155} \\ f(30)=\frac{62500}{155}=403.226\text{ (3 d.p)} \\ f(30)=403.226\text{ (3 d.p)} \end{gathered}[/tex]Hence, the answer is 403.226 (3 d.p)
Why might It be more useful to have a square root in simplest form rather than a large number under the root or the approximate Value?
Answers
Problem
Why might It be more useful to have a square root in simplest form rather than a large number under the root or the approximate Value?
Solution
One possible answer is that if we have the square root in the simplest form we can simplify expression add, subtract and multiply/divide by other quantities. Also with the simplification is easire to understand the value of interest.