Answers
Average rate of change is calculated using the slope of the line linking the interval's ends on the graph of the function. The average rate of change, in simplest form, is -1/6.
What is meant by average rate of change?It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.
The formula for calculating the gradient of a function exists expressed as:
[tex]$m=\frac{d y}{d x}=\frac{y_2-y_1}{x_2-x_1}[/tex]
Using the coordinate points from the table (6, 53) and (24, 50).
Substitute the coordinate into the expression:
[tex]$m=\frac{50-53}{24-6} \\[/tex]
[tex]$&m=\frac{-1}{6} \\[/tex]
Therefore, the average rate of change, in simplest form is -1/6.
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Related Questions
14. A can of vegetables has a paper label that covers the lateral surface are can, 4 in. 2.6 in. What is the lateral surface area of the can onded to the
Answers
We will have that the lateral area will be the following:
*First, we can see that if we were to cut a straight vertical line and unfold the label, we would get a rectangle, thus the surface area of the label will be given by:
[tex]S_A=h\cdot C[/tex]Here h is the height of the label and C is the circumference of the base, that is:
[tex]S_A=h\cdot2\pi r[/tex]Now, we determine the radius of the base, that is:
[tex]r=\frac{2.6}{2}\Rightarrow r=1.3[/tex]Now, we replace the values and solve for the surface area:
[tex]\Rightarrow S_A=(4)\cdot(2)\pi(1.3)\Rightarrow S_A\approx32.7[/tex]So, the surface area of the label on the can is approximately 32.7 squared inches.
pls help!!
6cm, 5cm, 9cm
Answers
Explanation: (image below)
what is the median of this data set?[13,13,13,15,15,16,16,17,17]
Answers
Given the following data set:
[13,13,13,15,15,16,16,17,17]
Let's determine the median.
Step 1: Arrange the data points from smallest to largest.
The set is already arranged in ascending order.
[13,13,13,15,15,16,16,17,17]
Step 2:
a.) If the number of data points is odd, the median is the middle data point in the list.
b.) If the number of data points is even, the median is the average of the two middle data points in the list.
There are 9 data in the set, it is odd. The middle data is the 5th data.
[13,13,13,15,15,16,16,17,17]
The 5th data is 15.
Therefore, the median of the given set of data is 15.
Graph the line by plotting any two ordered pairs with integer value coordinates that satisfy the equation.- 6x + 9y = 0AnswerKeypadKeyboard ShortcutsPoints can be moved by dragging or using the arrow keys. Any lines or curves will be drawn once allrequired points are plotted and will update whenever a point is moved.
Answers
Explanation
Step 1
get the slope-intercep form_
we need to use the function to graph the line,so let's convert the given equation in the slope-intercept form,to do that, isolate y
so
[tex]\begin{gathered} -6x+9y=0 \\ \text{add 6x in both sides } \\ -6x+9y+6x=0+6x \\ 9y=6x \\ \text{divide both sides by }9 \\ \frac{9y}{9}=\frac{6x}{9} \\ y=\frac{2}{3}x \end{gathered}[/tex]
so, the equation of the line is
[tex]y=\frac{2}{3}x[/tex]Step 2
now, let's use the equation to find 2 coordiantes of the line
a) for x =0
[tex]\begin{gathered} y=\frac{2}{3}x \\ \text{replace} \\ y=\frac{3}{2}(0)=0 \\ \text{hence, } \\ \text{ Point 1 ( 0,0)} \end{gathered}[/tex]b) for x= 3
[tex]\begin{gathered} y=\frac{2}{3}x \\ \text{replace} \\ y=\frac{2}{3}(3)=2 \\ \text{hence, } \\ \text{ Point 1 ( 3,2)} \end{gathered}[/tex]Step 3
finally, draw a line that passes through the points (0,0) and (3,2)
I hope this helps you
The coordinates of the vertices of a quadrilateral are P (5,2), S (5,-6), H(-6-1), and B (-6,4). The figure is rotated 360° counterclockwise with the origin as the center of rotation to create quadrilateral P'S'H'B'
What are the coordinates of the vertices of quadrilateral P’S’H’B’?
P’ =
S’ =
H’ =
B’ =
Answers
P’ = (5,2)
S’ = (5, -6)
H’ = (-6, -1)
B’ = (-6, 4)
Reason
The rotation of a point (x, y) by 360 degrees does not change its coordinates, it makes a complete circle or rotation around the origin. This rotation is represented by the coordinate transformation rule
(x, y) → (x, y)
one thousand two hundred and seventy deer are living on an island that is eight hundred and thirty square kilometers in size. what is the population density of the deer per square kilometer?
Answers
you divide the population by the size, and in turn you would get 1.53
hope this helped!! :)
lia has taken a mathematics exam, and she wants to calculate an 88% confidence interval to represent the exam scores within her group of friends. what are the z statistics that fall at each line marking the middle 88% of scores in the distribution?
Answers
In the given scenario, in order to calculate an 88% confidence interval, the z statistics that fall at each line marking the middle 88% of scores in the distribution would be +/- 1.555 (from the table).
In a case of seeking 88% confidence interval, the implication is that there is 12% chance that the interval does not contain the true value i.e., α=0.12 Assuming a two-sided test, it means that there should be 6% chance attributed to each tail of the z statistics (distribution). Thus, zα/2= z0.06.This z value at α/2=0.06 is the coordinate of the Z-curve that has 6% of the distribution's area to its right, and thus 94% of the area to its left. It is determined by z-value by reverse-lookup in a z-table. Find the closest value in the table to 0.9400 as possible, then see what its row and column is. From observation, it is seen that 0.9394 and 0.9406 are in the table with z -values of 1.55 and 1.56 respectively.We use liner interpolation to find the experimental z-score:0.9400 is (0.9400-0.9406)/(0.9394-0.9406) = ½ way from 0.9406 to 0.0394So, the z-score for 0.9400 is approximately ½ way from 1.56 to 1.55, hence
Z score = 1.56+((1.55-1.56)*1/2 = 1.5550
Hence the z score = 1.5550
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Mrs. brown is putting different colored sand into cups for 4 daughters to make sand art bottles . pink is 3/4 and purple is 1/2. each color is divided equally among the daughters how much more pink sand will be available than purple sand for each girl
Answers
Using mathematical operations, we can say that the extra pink sand avaliable to each girl is 1/16.
What are mathematical operations?A function in mathematics known as an operation is one that transforms zero or more input values into a clearly defined output value. The operation's complexity is determined by its operand count. The rules that specify the order in which we should perform several operations to solve an expression are known as the order of operations. Parentheses, Exponents, Multiplication, Division (from left to right), Addition, and Subtraction are in the following order: PEMDAS (from left to right).So, more pink sand is available to each girl:
Pink sand is 3/4 and purple sand is 1/2.Sand available to each girl:
Pink: 3/4 ÷ 4 ⇒ 3/4 × 1/4 ⇒ 3/16Purple: 1/2 ÷ 4 ⇒ 1/2 × 1/4 ⇒ 1/8Pink sand more to each girl:
3/16 - 1/83 - 2/161/16Therefore, using mathematical operations, we can say that the extra pink sand avaliable to each girl is 1/16.
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HELP ME PLEASE I NEED HELP I DONT KNOW HOW TO DO THIS
Answers
Answer:
convert miles to kilometers by multiply by 1.61 covert kilometers to miles by devide by 0.62(if am not wrong)
At basketball practice you made 21 out of 80 shots.
Which choice is closest to the percentage of shots you made?
Answers
Answer: 26.25% basketball practice
Step-by-step explanation: At basketball practice I made 21 out of 80 shots.
Therefore the percentage of shots I made is = 21/80×100%
=26.25%
2(x + 7) = 6x + 9 - 4x
Answers
EXPLANATION
Given the equation:
2(x+7) = 6x + 9 -4x
Applying distributive property:
2x + 14 = 6x + 9 -4x
Adding similar terms:
2x + 14 = 2x + 9
Subtracting -2x to both sides:
14 ≠ 9
--->The equation hasn't got solution.
What are the lengths of the major and minor axes of the ellipse?
(x−3)212+(y+4)224=1
Drag a value to the boxes to correctly complete the table.
Answers
The lengths of the major and minor axis of the ellipse, [tex] \displaystyle{ \frac{ {(x - 3)}^{2} }{12} +\frac{ {(y + 4)}^{2} }{24} = 1}[/tex] are;
Length of major axis; 4•√6Length of minor axis; 4•√3What is an ellipse in coordinate geometry?An ellipse describes the locus of a point on a curve, such that the sum of the distance from two focal points from the points on the curve is a constant.
The given given function of the ellipse can be presented as follows;
[tex] \displaystyle{ \frac{ {(x - 3)}^{2} }{12} +\frac{ {(y + 4)}^{2} }{24} = 1}[/tex]
The above equation can be compared to the standard equation of an ellipse as follows;
[tex] \displaystyle{ \frac{ {(x - h)}^{2} }{ {b}^{2} } +\frac{ {(y - k)}^{2} }{ {a}^{2} } = 1}[/tex]
Where;
(h, k) = The coordinates of the center of the ellipse
a = The length of the semi major axis
b = The length of the semi minor axis
By comparison, we have;
(h, k) = (3, -4)
a = √(24) = 2•√6
b = √(12) = 2•√3
The length of the major axis = 2•a
The length of the minor axis = 2•b
The length of the major axis is therefore;
2•a = 2 × 2•√6 = 4•√6
The length of the minor axis is therefore;
2•b = 2 × 2•√3 = 4•√3
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2 ÷ 125.1
Round the answer to 3 decimals
Answers
2/125.1 = 0.01598721023
Round that to 3 decimal places:
0.016
HOWEVER - If you need the answer to 3 significant figures, it would be:
0.0160
What is the absolute value of -6? Use the number line to help answer the question.
-6
07
6543210
st
4+
3+
2+
7777777
Answers
Answer:
your answer is in the screenshot
Step-by-step explanation:
Morgan can make 4 cupcakes with 1 cup of flour. How many cupcakes can she make with 18 cups of flour?
Answers
Answer: She can make 72 cupcakes.
Step-by-step explanation:
a rectangle has a length that is twice the size of its width. if the perimeter of the rectangle is 48 inches, what is the area of the rectangle in square inches?
Answers
The area of the rectangle is, 128 square inches.
What is perimeter, area?
The area of a shape or figure is the area it occupies, whereas the perimeter of a shape is the distance it encircles on all sides.
The square unit or unit2 is used as the unit of area, and the unit is also used for the perimeter.
Given: A rectangle has a length that is twice the size of its width. The perimeter of the rectangle is 48 inches.
Suppose the width of the rectangle is x.
So, the length is 2x.
As perimeter is 48 inches.
So, x + x + 2x + 2x = 48
6x = 48
x = 8 inch.
The width of the rectangle is 8 inches.
Therefore, the length of the rectangle is 2x = 2(8) = 16 inches.
Now to find area of the rectangle,
Since,
Area of rectangle = length x width
= 16 x 8
Area of rectangle = 128 inch^2.
Therefore, the area of the rectangle is 128 square inches.
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How many vertices does a triangle prima have?
Answers
A triangle prima has six vertices. A triangular prism has five faces, three rectangular and two triangular, nine vertices, and six edges.
What is triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points determine a unique triangle and, by stretching, a unique aircraft. Triangles are three-sided polygons with three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The sum of the triangle's three angles equals 180 degrees. You've seen that a triangle is a simple closed curve made up of three line segments. It is made up of three vertices, three sides, and three angles.To learn more about triangle, refer to:
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Draw a reference triangle and find the trig ratio for the angle (if possible) without a calculator.
Answers
Recall the definition of the cosecant function in terms of the sine function:
[tex]\csc (x)=\frac{1}{\sin (x)}[/tex]Draw the angle -210º in the unit circle to find a reference triangle for that angle:
Notice that a 30-60-90 triangle is formed:
Since the side opposite to the 30º angle has a length of 1/2, then:
[tex]\sin (30º)=\frac{1}{2}[/tex]On the other hand, notice that since the angle of -210º lies in the second quadrant, then the value of sin(-210º) is positive:
[tex]\sin (-210º)=\sin (30º)=\frac{1}{2}[/tex]Use the definition of the cosecant function to find csc(-210º):
[tex]\csc (-210)=\frac{1}{\sin (-210º)}=\frac{1}{(\frac{1}{2})}=2[/tex]Therefore, the value of csc(-210º) is equal to 2.
Help me please i need help with my math hw
Answers
Answer:
answer of 1st picture
second is not under standing much
which is an equation of the line through the origin and (-5,6)
Answers
The equation of a line through the origin and (-5,6) is y = -1.2x
How to determine the equationIt is important to note that the equation of a line is expressed as;
y = mx + c
Where;
y is the point on the y - axism is the slope of the linex is the point on the x - axisc is the intercept on the y axisFrom the information given, we have the points;
(0, 0) and ( -5, 6)
The formula for slope is given as;
slope, m = y₂ - y₁/ x₂ -x₁
slope, m = 6 - 0/ -5 - 0
slope, m = 6/ -5
slope, m = - 1. 2
To determine the intercept, we have;
6 = -1. 2(-5) + c
expand the bracket
c = 6 - 6
c = 0
The equation is given as;
y = -1.2x
Hence, the equation is y = -1.2x
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Which of the following statements is true about congruent angles?
Answers
Answer: Congruent angles are the angles that have equal measure. So all the angles that have equal measure will be called congruent angles. They are seen everywhere, for example, in equilateral triangles, isosceles triangles, or when a transversal intersects two parallel lines.
Step-by-step explanation:
B. Write S if the expression is a sum of two cubes, D if a difference of two cubes, and N if neither.
1. 27x⁶ + y³=
2. 81 - b¹⁵=
3. 64x³ - 9z⁹=
4. 36m¹² - n⁶
5. 1 - d¹²=
6. 729 - y²⁹=
7. 343 - y⁶=
8. 4x³ + 8 =
9. 144 -125y² =
10. 64j⁶- k⁹=
Answers
Answers:
SNNNDNDNND==========================================================
Explanation:
Question 1
27x^6 = (3x^2)^3 which is one cube and y^3 is another cube
Therefore 27x^6+y^3 is a sum of two cubes.
It might help to think of it like A^3+B^3 where in this case A = 3x^2 and B = y.
----------------------------------------
Question 2
81 isn't a perfect cube since 81^(1/3) = 4.3267 approximately, which isn't a whole number. We need 81^(1/3) to be a whole number if we wanted 81 to be a perfect cube.
We don't even need to check b^15 since 81 being a non-perfect cube means the entire expression cannot be a sum of two cubes, nor a difference of cubes.
----------------------------------------
Question 3
64x^3 = (4x)^3 is a perfect cube
but 9z^9 is not a perfect cube
We can see this if we computed 9^(1/3) and the result is a non-whole number.
The answer here is the same as the previous question.
----------------------------------------
Question 4
36^(1/3) is not a whole number, so 36 isn't a perfect cube. By extension 36m^12 isn't a perfect cube either. The answer is the same as questions 2 and 3.
----------------------------------------
Question 5
1 is a perfect cube since 1 = 1^3
d^12 is a perfect cube because d^12 = (d^4)^3
Therefore, we have a difference of two cubes.
----------------------------------------
Question 6
729^(1/3) = 9 which rearranges to 9^3 = 729, showing 729 is a perfect cube.
However y^29 is not a perfect cube since the exponent 29 is not a multiple of 3.
The overall expression is "neither".
----------------------------------------
Question 7
343^(1/3) = 7 rearranges to 7^3 = 343, showing 343 is a perfect cube
y^6 is a perfect cube since (y^2)^3, i.e. the exponent 6 is a multiple of 3.
We have a difference of cubes.
----------------------------------------
Question 8
4 isn't a perfect cube since 4^(1/3) results in some decimal value that isn't a whole number. The entire expression is neither a sum nor difference of cubes.
----------------------------------------
Question 9
144^(1/3) isn't a whole number, so we get a similar result to problem 8.
----------------------------------------
Question 10
64j^6 = (4j^3)^3 is one cube
k^9 = (k^3)^3 is another cube
We have a difference of cubes
A bicycle company has designed and built a new model of sports bicycle. They have determined that the profit for the sale of the bicycles can be modeled by the function ��(��) =− 2�� , where x is the price of each bicycle. Which of the 2+ 920�� + 84, 000 following is a sale price for the bicycles that will allow the company to achieve a profit of $189,800?
A. $210
B. $230
C. $250
D. $270
Answers
A sale price for the bicycles that would allow this company to achieve a profit of $189,800 is: B. $230.
How to determine the sale price for the bicycles?In order to determine the sale price for the bicycles that would make it possible for this company to achieve a profit of $189,800, we would simply evaluate the profit function by substituting the value of the profit as follows:
P(x) = −2x² + 920x + 84,000
189,800 = −2x² + 920x + 84,000
Re-arranging the profit function by collecting like terms, we have:
2x² + 920x + 189,800 - 84, 000 = 0
2x² - 920x + 105,800 = 0
Dividing both sides by 2, we have:
x² - 460x + 52,900 = 0
Next, we would solve the quadratic equation by using factorization method:
x² - 230x -230x + 52,900 = 0
x(x - 230) + 230(x - 230) = 0
(x - 230)(x + 230) = 0
x = 230 or -230
Since the price cannot be negative, the required sale price for this company is equal to $230.
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Complete Question:
A bicycle company has designed and built a new model of sports bicycle. They have determined that the profit for the sale of the bicycles can be modeled by the function P(x) = −2x² + 920x + 84,000, where x is the price of each bicycle. Which of the following is a sale price for the bicycles that will allow the company to achieve a profit of $189,800?
A. $210
B. $230
C. $250
D. $270
Help da brother out.
Answers
Answer:
y=2x+5, y=4x, y=-3+9/2x
Step-by-step explanation:
8x+4y=20 turns into:
y=2x+5
3y-12x=0 turns into:
y=4x
9x-2y=6 turns into:
y=-3+9/2x
Which of the following is a disadvantage of using a check casher, compared to a bank?
Responses
You wait longer to get your money at a check casher than at a bank
You wait longer to get your money at a check casher than at a bank
You pay a higher fee to cash checks at a check casher than at a bank
You pay a higher fee to cash checks at a check casher than at a bank
You can only cash checks worth more than $500 at a check casher
You can only cash checks worth more than $500 at a check casher
You can cash fewer checks at a check casher than at a bank
Answers
The main disadvantage of using a check cashier is that, 'You pay a higher fee to cash checks at a check casher than at a bank'
Check casher;
A check casher is someone who works in the check-cashing industry, with the exception of someone who doesn't cash checks for others on any one day that total more than $1,000 in cash, money, or other assets.
Disadvantage of Check cashers;
Fees for cash checking services can be as low as $1 or as much as 2% of the check amount depending on where you are. These costs reduce one's capacity to make ends meet or have extra money available. Always be aware of the prices and fees before using a check cashing service.
That is,
The main disadvantage of using a check cashier is that, 'You pay a higher fee to cash checks at a check casher than at a bank'
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-5x8+x²+6 please help
Answers
Answer:[tex]\left(x^2+1\right)\left(5x^6-5x^4+5x^2-6\right)[/tex]
Step-by-step explanation:
How do you find average speed from aHow do you find average speed from a distance time graph?\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ distance time graph?
Answers
An average speed can be calculated from a distance time graph through the division is change in distance and change in its corresponding time.
What is distance time graph?A distance time graph is a type of graph that show the distance covered by an object with respect to time.
When plotting a distance time graph, the distance is plotted in the y-axis while time is plotted of the X -axis and a suitable scale of used to fill in the observed figures.
Speed is the product of distance travelled by an object with respect to its time. Therefore, an average speed can be calculated through the division is change in distance and change in its corresponding time.
That is ; average speed= ∆speed/∆ time
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Given mn, find the value of x.
(2x-5)°
(3x-22)°
Answers
If m || n and line t cuts them, the value of x is 17 degree
Given that, the line m || line n. and we need to find the value of x
If two lines are parallel and a transversal cuts them then the corresponding alternate interior angles are equal.
Here, line m and line are parallel anf the transversal t cuts them, so the alternate interior angles will be same
2x - 5 = 3x - 22
2x - 3x = - 22 + 5
- x = - 17
x = 17
Therefore, if m || n and line t cuts them, the value of x is 17 degree
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Determine the relative frequency for the third class as a simplified fraction
Answers
GIVEN:
We are given a frequency distribution table showing different classes of hours of study and the frequency of each class of data.
Required;
To determine the relative frequency for the third class
Step-by-step solution;
For a relative frequyency, we need to find the number of times an event occurs and express it as a fraction of the total events that occured in the survey/experiment.
The events in this case are hours of study and the occurrence is the total frequency for all classes of hours of study.
The total frequency is;
[tex]3+10+6+15+6=40[/tex]The relative frequency for the third class therefore would be;
[tex]\begin{gathered} Relative\text{ }Frequency_3=\frac{6}{40} \\ \\ Relative\text{ }Frequency=\frac{3}{20} \end{gathered}[/tex]ANSWER:
The relative frequency of the third class therefore is
[tex]\frac{3}{20}[/tex]If mDH =(11x + 7) degrees , mGF = (5x + 9) degrees , and mEF = (10x - 22) degrees, find mDH
Answers
For this problem we use the arcs and chords theorem we know that
[tex]\begin{gathered} \measuredangle H\text{EF=}\frac{1}{2}(mGF+mDH) \\ \text{Substituting }\measuredangle HEF=10x-22,\text{ mGF=5x+9 and mDH=11x+7 we get} \\ 10x-22=\frac{1}{2}(5x+9+11x+7) \end{gathered}[/tex]Solving for x we get:
[tex]\begin{gathered} 10x-22=\frac{1}{2}(16x+16)=8x+8 \\ 2x=30 \\ x=15 \end{gathered}[/tex]Finally, we substitute x for mDH=(11x+7) degrees=(11*15+7) degrees=172 degrees.
mDH=172 degrees.