the question i have says “which statement correctly compares the rates of change of the two functions” and i dont understand how to solve it
Answers
The rate of change of function A is 4
The rate of change of function B is 3 (option D)
Explanation:We are looking for the rate of change of two functions.
m is also known as the rate of change
[tex]\begin{gathered} \text{Function A is given as:} \\ y\text{ = 4x + 6} \end{gathered}[/tex]comparing the equation above to a linear function:
y = mx + b
m = slope , b = y -intercept
For function A:
m = slope = 4, b = 6
To get the rate of change of function B, we need to find the slope of any two points on the table.
For linear function, the slope is constant irrespective of the two points used in calculating it.
Formula for slope:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]using points; (1, 3) and (3, 9)
[tex]\begin{gathered} x_1=1,y_1=3,x_2=3,y_2\text{ = 9} \\ \text{slope = }\frac{9-3}{3-1} \\ \text{slope = }\frac{6}{2} \\ \text{slope = 3} \\ \text{Slope for function B is 3} \end{gathered}[/tex]The rate of change of function A is 4
The rate of change of function B is 3 (option D)
Related Questions
In a horse race with 6 horses, in a horse race you have 6 horses, you make a bet by predicting the ranking of all 6 horses. If you place your bet at random, whatis the probability that you will get the first and second horse correct and in the correct order?Give your answer as a fraction.
Answers
Answer
Probability that one will get the first and second horse correct and in the correct order = ½
Explanation
The probability of an event is given as
[tex]\text{Probability of an event = }\frac{Number\text{ of elements in that event}}{Total\text{ number of elements in the sample space}}[/tex]For this question, we need to calculate the probability of getting the first and second horse correctly.
Number of elements in the event = Number of predictions with the first and second horse correct in that order = 1 × 1 × 6 × 5 × 4 × 3 = 360
Total number of elements in the sample space = Total number of possible arrangements for the horses = 6 × 5 × 4 × 3 × 2 × 1 = 720
Probability that one will get the first and second horse correct and in the correct order = (360/720) = ½
Hope this Helps!!!
The Quadratic f(x)=x^2-2x-15Using the functions of your graphing calculator calculate the coordinates of the following points (as shown in the calculator videos in this lesson). If the parabola doesn't intersect the x-axis then write "none." If necessary, round to the nearest hundredths place (2 decimal places).a. The vertex using the min/max calculate function.b. X-intercept(s) using the zero calculate function.c. Y-intercept using the value calculate function (w/ a value of x=0).d. Now, copy down the t-table generated by your calculator for integer input values from-3≤x≤3.
Answers
Given: The function below
[tex]f(x)=x^2-2x-15[/tex]To Determine: The vertex, the x-intercept, the y-intercept, and the table for -3≤x≤3
Solution
The graph of the given function is as shown below
Hence:
The vertex is a minimum value at y = -16 and coordinate (1, -16)
(b) The X-intercepets is x = -3, x = 5, coordinates: (-3, 0) and (5, 0)
(c) The Y-intercept is at y = -15, coordinate: (0, - 15)
(d) The table showing the values of f(x) for -3≤x≤3 is as shown below
Answer the question below. Be sure to show your work
Answers
ANSWER:
We have to find new side-lengths of PQR triangle.
Original sides are.
[tex]\begin{gathered} PQ\text{ = 8cm} \\ QR=17\operatorname{cm} \\ RP=15\operatorname{cm} \end{gathered}[/tex]After multiplying by 2.5 we get
[tex]\begin{gathered} PQ^{\prime}=2.5\times PQ=(8\times2.5)cm=20\operatorname{cm} \\ QR^{\prime}=(17\times2.5)cm=42.5\operatorname{cm} \\ RP^{\prime}=(15\times2.5)cm=37.5\operatorname{cm} \end{gathered}[/tex]These are the new sides of the P'Q'R' triangle.
which fractions represent how to find the probability to rolling a number less than 5 and a number greater than 2?
Answers
Explanation
The probability of an event is the number of favorable outcomes divided by the total number of outcomes possible
Step 1
find the total of favorable possible
[tex]\begin{gathered} \text{for a dice, } \\ a\text{ number less than 5, it is, 1, 2, 3 or 4, ( 4 favorables outcomes}) \\ a\text{ number greater than 2, it is, 3,4 , 5 or 6} \\ \text{the numbers that have the two options are 3 and 4 ( 2 favorable outcomes)} \end{gathered}[/tex]favorable outcomes : 2 ( 3 and 4)
Step 2
find the total number of outcomes possilbe
the dice has 6 faces, (numbers, 1, 2, 3, 4, 5 or 6),
possible outcomes : 6 ( 1,2,3,4,5 and 6)
Step 3
finally replace
[tex]\begin{gathered} P=\frac{favorable\text{ outcomes}}{\text{possible outcomes}} \\ P=\frac{2}{6}=\frac{1}{3} \end{gathered}[/tex]To find the length of JK you’d set up and solve:
Answers
According to the statement, to find x, it is necessary to use the following expression:
[tex]7x=3x+14[/tex]This expression is set up thanks to the definition of a parallelogram. To solve it isolate x to one of the sides of the equation.
[tex]\begin{gathered} 7x=3x+14 \\ 7x-3x=14 \\ 4x=14 \\ x=\frac{14}{4} \\ x=3.5 \end{gathered}[/tex]x has a value of 14/4 or 3.5.
According to the figure JK measures 7 times x. Use this information to find JK:
[tex]\begin{gathered} JK=7x \\ JK=7(3.5) \\ JK=24.5 \end{gathered}[/tex]JK measures 24.5.
How many red squares will there be if there are 60 squares?
Answers
• There are 3 red squares.
,• There are 4 white squares.
To compare them and get the ratio, we can build the following relation:
[tex]\frac{3}{4}=\frac{x}{60}[/tex]where x is the number of red squares it will be when there are 60 white squares.
Solving for x:
[tex]x=\frac{3}{4}\cdot60[/tex][tex]x=45[/tex]Answer: C. 45
The equation of the line of best fit of a scatter plot is y = –7x − 2. What is the the y-intercept?
–7
–2
2
7
Answers
Answer:
The y-intercept of this line is -2.
A pair of shoes is on sale for 20% off. I paid $95. How much were the shoes originally? Write an equation and solve.
Answers
118.75
0.80 * x = 95
x = 95/ 0.80
x = 118.75
With x being the original cost of the shoes.
I'll give you the pic.
Answers
Let's use pythagorean theorem to calculate the remaining side:
[tex]\begin{gathered} c=\sqrt[]{a^2+b^2} \\ c=\sqrt[]{7^2+3^2} \\ c=\sqrt[]{21+9} \\ c=\sqrt[]{30} \end{gathered}[/tex]The area of a square is given by:
[tex]\begin{gathered} A=s^2 \\ \text{Where:} \\ s=\text{One of its sides} \\ A=(\sqrt[]{30})^2 \\ A=30 \end{gathered}[/tex]Equivalent equations have exactly the same solution set. Select Yes or No in thedropdowns to indicate whether each equation is equivalent to this equation.
Answers
The given equation is:
[tex]4x+3=\frac{5}{2}x-7[/tex]Solve the equation for x:
[tex]\begin{gathered} 4x+3=\frac{5}{2}x-7 \\ \text{Collect like terms:} \\ \Rightarrow4x-\frac{5}{2}x=-7-3 \\ \Rightarrow\frac{3}{2}x=-10 \\ \Rightarrow3x=-20 \\ \Rightarrow x=-\frac{20}{3} \end{gathered}[/tex]Next substitute the solution into each equation.
The equation that the solution satisfies is equivalent to the original equation.
Check for the first equation:
[tex]\begin{gathered} 4x=\frac{5}{2}x-4;x=-\frac{20}{3} \\ \Rightarrow4(-\frac{20}{3})=\frac{5}{2}(-\frac{20}{3})-4 \\ \Rightarrow-\frac{80}{3}=-\frac{50}{3}-4 \\ \Rightarrow-\frac{80}{3}\ne-\frac{62}{4} \end{gathered}[/tex]Since the solution does not satisfy the equation, it follows that the equation is not equivalent to the original equation.
Hence, select NO for the first equation.
Use the same procedure to check for the other equations.
Only the third and fourth equations are equivalent to the original equation, so feel yes for them, but no for the first and second.
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a bakery. needs to pack 48 donuts, 12 pastries, and 24 cinnamon in identical quantities across all of the boxes. What is the maximum quantity of boxes she can utilize?
Answers
It requires maximum 12 boxes to put 4 donuts, 1 pastry and 2 cinnamon in each box using the Greatest comon factor.
What is Greatest common factor or GCF?The greatest common factor or GCF is the largest number that can be split into exactly two or more other numbers. It is the "best" thing for reducing the complexity of fractions. A factor is a number that, when multiplied by other numbers, produces the desired numbers in mathematics. Factors are another name for the total that results.
The largest factor that two or more numbers have in common is called the greatest common factor (GCF).
It is given that there are 48 donuts, 12 pastries and 24 cinnamon.
Find the greatest common factor of the given values.
Expand 48,12, and 24 in factors.
48= 2x2x2x2x3
12=2x2x3
24=2x2x2x3
Find the greatest common factors of the three factored-out numbers.
GCF=2x2x3=12
So, it requires maximum 12 boxes to put 4 donuts, 1 pastry and 2 cinnamon in each box using the GCF.
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Look at the construction. Which statement is false? XA = YA XP = PY XA = XY
Answers
XA = XY is false. XA and YA are both congruent segments, which means they are equal. The same goes for XP and PY.
drawing and explanation for areaof triangle where h=137 and base = 203
Answers
The area of triangle is 13905.5 cm square when height is 137 cm and bae is 203 cm.
Given that,
There is a triangle with height 137 cm and base 203 cm.
We have to find the area of triangle.
We know,
The entire area filled by a triangle's three sides in a two-dimensional plane is referred to as the triangle's area. A straightforward formula can be used to get the area of a triangle by multiplying the sum of the base and height by two.
Area of triangle =1/2×b×h
Area of triangle =1/2×137×203
Area of triangle =1/2×27811
Area of triangle =13905.5
Therefore, The area of triangle is 13905.5 cm square when height is 137 cm and bae is 203 cm.
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which of the following equations represent linear functions? A. x^2+y^2=1 B. x+y=14 C. y=6/x D. y=3(2x+1)
Answers
A linear function has this form:
[tex]y=ax+b[/tex]Notice that option A cannot be written in this form, because x and y have a square power. If you clear y you'll get:
[tex]y=\sqrt[]{1-x^2}[/tex]Option B you can write it in the form of a linear equation:
[tex]y=14-x[/tex]For this option, a = -1 and b = 14
Option C cannot be written in this form:
[tex]y=\frac{6}{x}[/tex]And option D can be written like that:
[tex]y=6x+3[/tex]Here, a=6 and b=3.
So, options B and D are linear equations
Katie rents a car when spending her vacation in Argentina while she returns the car she has driven 900 miles and used about 36 gallons of gas if you guess cost an average of $4.139 Per gallon estimate how much she spent on fuel
Answers
Given that Katie had driven 900 miles and used about 36 gallons of gas.
The average cost of gas per gallon = $4.139
The amount she spent on gas would be:
[tex]\text{ The average cost of gas per gallon x gallons of gas used}[/tex]Hence, the amount Katie spent on gas would be:
[tex]\begin{gathered} \text{ }\frac{\text{\$4.139}}{\text{gallon}}\times\text{ 36 gallons} \\ =\text{ \$149.004} \end{gathered}[/tex]She spent $149.004
Express the function graphed on the axes below as a piecewise function.10802-108-6-422246810-10
Answers
From the graph it is clear that the function is a horizontal line from -6 to -3 and an oblique line from -3 to 3 so the equation from -6 to -3 is:
[tex]f(x)=5[/tex]The equation of line using two point form from -3 to 3 is found by knowing the points.The line passes through (-2,6) and (0,4) so it follows:
[tex]\begin{gathered} \frac{y-6}{x+2}=\frac{4-6}{0+2} \\ y-6=-(x+2) \\ y=-x-2+6=-x+4 \\ y=f(x)=-x+4 \end{gathered}[/tex]Hence the piecewise function is given by:
[tex]f(x)=\begin{cases}5,-6\leq x<-3 \\ -x+4,-3Hence the function shown above is the required piecewise function. Two different functions are represented by this graph and this table:
Answers
Answer
Option B is correct.
Function B has the greater slope.
3 is greater than 2.
Explanation
For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as
[tex]Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]For function A, we will pick two points on the line
(x₁, y₁) and (x₂, y₂) are (-2, -1) and (0, 3)
[tex]\text{Slope = }\frac{3-(-1)}{0-(-2)}=\frac{3+1}{0+2}=\frac{4}{2}=2[/tex]For function B, we will pick the two most extreme points on the table
(x₁, y₁) and (x₂, y₂) are (0, 1) and (5, 16)
[tex]\text{Slope = }\frac{16-1}{5-0}=\frac{15}{5}=3[/tex]We can easily see that function B (3) has a greater slope than function A (2).
Hope this Helps!!!
Find the answers to fill in blank 1. And blank 2.
Answers
EXPLANATION:
We are given the linear equation;
[tex]y-4=3(x+1)[/tex]To graph this equation, we would begin by re-writing the equation in the slope-intercept form, which is;
[tex]y=mx+b[/tex]To do this, we first expand the parenthesis;
[tex]y-4=3x+3[/tex]Next we add 4 to both sides;
[tex]y-4+4=3x+3+4[/tex][tex]y=3x+7[/tex]We can now begin to plot the various points on the line. Starting from, x = -2 we would have;
[tex]\begin{gathered} x=-2: \\ y=3(-2)+7 \\ y=-6+7 \\ y=1 \end{gathered}[/tex]We can now go on and plot other points depending on the limit imposed by the graph page.
However, what we have here shows the coordinates from which we may begin;
ANSWER:
[tex]\begin{gathered} (-2,1) \\ That\text{ is;} \\ x=-2,y=1 \end{gathered}[/tex]Hello I am helping my son with independent variable and dependent
Answers
It is given that,
As a plane descends, the more time that passes, the lower the plane's altitude is.
So,
Here, x be the time and y the altitude of the plane.
According to the statement, x be the dependent variable and y be the independent variable.
So, the graph is,
From the waiting area, they walked another 0.1 miles to board the plane. The plane left the gate 45 min after they arrived at the waiting area. Part C: what was the length from the waiting area to the airplanes takeoff?
Answers
C) We have to calculate the distance from the waiting area to the plane.
From the waiting area they walked 0.1 miles to board the plane.
Answer: from the waiting area to the plane there is a distance of 0.1 miles.
CD = 69, BC = 10x + 3. AD = 18x + 44,and AB= 7x- 20. Find BC.
Answers
Answer: A) 83
Explanation:
Representing this segments in a number line, and supposing that they are arranged in alphabetical order:
Here we can see that if we sum all of the segments they must be equal to 18x+44:
[tex]7x-20+10x+3+69=18x+44[/tex]Combining like terms:
[tex]17x+52=18x+44[/tex]Now we move all of the terms with x to the right side and all of the independent numbers to the left side:
[tex]\begin{gathered} 52-44=18x-17x \\ 8=x \end{gathered}[/tex]And now that we know the value of x, we can find BC:
[tex]\begin{gathered} BC=10x+3 \\ BC=10(8)+3 \\ BC=80+3 \\ BC=83 \end{gathered}[/tex]Which is option A)
19. Which of the following is equal to V-24 ?O-2iV64i 166i-1/2O21 V6
Answers
The given value is,
[tex]\sqrt[]{-24}[/tex]We can write this as,
[tex]\sqrt[]{-24}=\sqrt[]{24\times-1}[/tex]As we know, 24 = 4 x 6 and,
[tex]\sqrt[]{-1}=i[/tex]the above expression can again be rewritten as,
[tex]\sqrt[]{-24\times-1}=\sqrt[]{4\times6}\times i=2i\sqrt[]{6}[/tex]Thus, the last option is correct.
Four students graphed the system of equations shown below. Which graph is correct?
Answers
Explanation
Step 1
Let
[tex]\begin{gathered} y_1=-\frac{3}{4}x+4 \\ y_2=\frac{1}{2}x-1 \end{gathered}[/tex]a) graph y1, to draw the line, we need 2 points ( coordinates)so
i)when x=0
[tex]undefined[/tex]Find the x-intercept and y-intercept of the line. - 6x + 4y= 15 Write your answers as exact values. Do not write your answers as ordered pairs. x-intercept: 1 Х ? y -intercept: 1
Answers
The equation of a line is line is given as y = mx + c where m is the slope and c is the y-intercept
From the equation
-6x + 4y = 15
Changing into the form of the general equation
4y = 6x + 15
Divide both sides by 4
y = 6y/4 + 15/4
y = 3y/2 + 15/4
the x intercept is 0 while the y intercept is 15/4.
Given that segment AD is congruent to segment BC, and angle DAB is congruent to CBA; Prove: triangle ABE is isosceles
Answers
Statement | Reason
AD ≅ BC | Given
∠DAB ≅ ∠CBA | Given
AB ≅ AB | Reflexive property of congruence
ΔADB ≅ ABC | SAS postulate
∠DBA ≅ ∠CAB | CPCTC
ΔABE is isosceles | Any triangle with 2 congruent angles is isosceles
Sketch the graph of the equation. y= 1/2x− 3/2.
Use the graphing tool to graph the line.
Answers
The graph of the line is given below:
What is graph?
The collection of ordered pairings where f(x)=y exists is the graph of a function f. These pairs are Cartesian coordinates of points in two-dimensional space and so form a subset of this plane in the typical situation when x and f(x) are real integers.
The graph of the given equation is,
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Please Help! Functions and Relations The graph shows the absolute value parent function. which statement best describes the function?
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The function is increasing when, if xa > xb, then f(xa) > f(b).
Let's choose values for x < 0 and for x > 0.
First, let's compare x = -2 and x = -1
-1 > -2
f(-1) < f(-2)
Then, the function is decreasing for x < 0.
Second, let's compare x = 1 and x = 2.
2 > 1
f(2) > f(1)
Then, the function is increasing for x > 0.
Answer: c. The function is increasing when x >0.
The slope of the line below is 2 Write the point-slope equation of the line using the coordinates of the labeled point.
Answers
As per given by the question,
there are given that,
The slope of the line is 2, and the point is (3, 10).
Now,
For finding the point slope equation;
From the formula for point slope equation of the line,
[tex]y-y_1=m(x-x_1)[/tex]Here,
[tex]x_1=3,y_1=10,\text{ and m=2}[/tex]Then put the value in above formula,
[tex]undefined[/tex]The set consisting of all integers between -2 and -1 will be empty
Answers
It is true that the set consisting of all integers between -2 and -1 is empty.
Integers are numbers that are not fraction. They are simply the whole numbers on the number line.
There are positive and negative integers.
Positive Integers are: 1, 2, 3, 4, 5, and so on
Negative Integers are: -1, -2, -3, -4, -5, and so on.
Between -2 and -1, there are no integers. Therefore, the set consisting of all the integers between them is empty.
Determine the coordinates of the midpoint of the segment with given endpoints. J(-3, 2), K(7,10) Midpoint: