What is the average rate of change over the interval [1,2]Type the numerical value for your answer as a whole number, decimal, or fractionMake sure answers are completely simplified
![What Is The Average Rate Of Change Over The Interval [1,2]Type The Numerical Value For Your Answer As](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/1we3Dj8amUyoRCRNBaGOMVlVHK7SnaUN.png)
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To calculate the average rate of change over the interval [1,2] we need to identify the points in the extremes of the interval.
This points are (1,50) and (2,25).
We calculate the average rate of change as the slope:
[tex]r=\frac{y_2-y_1}{x_2-x_1}=\frac{25-50}{2-1}=-\frac{25}{1}=-25[/tex]Answer: the rate of change over [1,2] is -25.
Related Questions
the circle below is centered at the point (2,-1 ) and had a radius of length 3 what is its equation
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The standard equation for a circle is
[tex]\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ \text{where} \\ a=2 \\ b=-1 \\ r=\text{radius}=3 \\ (x-2)^2+(y-(-1))^2=3^2 \\ (x-2)^2+(y+1)^2=3^2 \\ \end{gathered}[/tex]MP is the perpendicular bisector of the side AC of the triangle ABC, in which AB = AC. prove that angle APB = 2 angle B
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We have the following:
[tex]\begin{gathered} \frac{a}{\sin now,[tex]\begin{gathered}Find the lateral surface area of thiscylinder. Round to the nearest tenth.8ft4ftLSA = [ ? ] ft2—
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Solution
Step 1:
Write the lateral surface area or curved surface area of a cylinder:
[tex]Lateral\text{ surface area = 2}\pi rh[/tex]Step 2:
Write the given data
Height h = 8ft
Radius r = 4 ft
Step 3:
Substitute in the formula to find the lateral surface area.
[tex]\begin{gathered} Lateral\text{ surface area = 2}\pi rh \\ =\text{ 2 }\times\text{ 3.142 }\times\text{ 4 }\times\text{ 8} \\ =\text{ 201.1 ft}^2 \end{gathered}[/tex]Final answer
201.1
State the domain of the function.{-2,0, 1, 2, 3, 4){-4,0, 1, 2, 6){0, 1,2,3)(-2,4)
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D= {-2,0,1, 2,3,4}
1) Considering that the Domain is the set of entries of a function, on the x-axis, and examining that graph we can state
- The lowest value for that is given by x=-2
- The highest value for that is x= 4
- The points (-2,-4) (0,0), (1,1), (2,2), (3,1) and (4,6)
2) So, we can write the set, the Domain, after examining the options as:
D= {-2,0,1, 2,3,4}
Notice that we're considering the x-coordinates
3) So the answer is D= {-2,0,1, 2,3,4}
A diver starts out at 342 feet below the surface (or – 342 feet). She then swims upward 237 feet.Use a signed number to represent the diver's current depth.
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Given:
A diver starts at 342 feet below the surface, which means -342 feet.
Now, she swims 237 feet upward.
It shows that she is moving in a positive direction.
So, the current depth of diver is,
[tex]-342+237=-105[/tex]The depth is -105 feet, which shows that the diver is still 105 feet below the surface.
I don’t know how to find the value of x. Geometry is so confusing too me, i can never understand it no matter how many times i re-read my instructions.
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The value of x = 40°
Explanation:To solve for x, we will use an illustration:
When two lines intersect, the angles opposite each other are vertical angles. Vertical angles are equal.
The angles marked in magenta are equal.
The angle by the right in magenta colour will also be 52°.
The sum of angles in a triangle = 180°
x° + 52° + 88° = 180°
x + 140 = 180
subtract 140 from both sides:
x + 140 - 140 = 180 - 140
x = 40°
Yesterday, Diane had c baseball cards. Today, she gave 6 away. Using c, write and expression for the number of cards Diane has left.
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Answer:
The expression is c-6. She gave away 6 cards so subtract 6 from the original number which is c.
A) What is the perimeter of the regular hexagon shown above?B) What is the area of the regular hexagon shown above?(see attached image)
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Remember that
A regular hexagon can be divided into 6 equilateral triangles
the measure of each interior angle in a regular hexagon is 120 degrees
so
see the attached figure to better undesrtand the problem
each equilateral triangle has three equal sides
the length of each side is given and is 12 units
Part A) Perimeter
the perimeter is equal to
P=6(12)=72 units
Part B
Find the area
Find the height of each equilateral triangle
we have
tan(60)=h/6
Remember that
[tex]\tan (60^o)=\sqrt[]{3}[/tex]therefore
[tex]h=6\sqrt[]{3}[/tex]the area of the polygon is
[tex]A=6\cdot\lbrack\frac{1}{2}\cdot(6\sqrt[]{3})\cdot(12)\rbrack[/tex][tex]A=216\sqrt[]{3}[/tex]alternate way to find out the value of happlying Pythagorean Theorem
12^2=6^2+h^2
h^2=12^2-6^2
h^2=108
h=6√3 units
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In a test of a sex-selection technique, results consisted of 284 female babies and 15 male babies. Based on this result, what is the probability of a female being born to
a couple using this technique? Does it appear that the technique is effective in increasing the likelihood that a baby will be a female?
The probability that a female will be born using this technique is approximately
(Type an integer or decimal rounded to three decimal places as needed.)
Does the technique appear effective in improving the likelihood of having a female baby?
O No
O Yes
Answers
The probability of the girl being born to a couple is 0.949. Yes, it is effective in increasing the likelihood that the baby will be a girl as the number of girls is more than the number of boys.
What is probability?
Probability means possibility. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
Given
In a test of sex-selection technique, results consisted of 284 female babies and 15 baby boys.
Total children = 284 + 15 = 299
The probability of the girl being born to a couple will be
[tex]P = \frac{284}{299}[/tex]
P = 0.9498
Thus, the probability of the girl being born to a couple is 0.9498.
Yes, it is effective in increasing the likelihood that the baby will be a girl as the number of girls is more than the number of boys.
To learn more about the probability link is given below.
brainly.com/question/795909
#SPJ1
Simplity 9 - [x - (7+ x)]
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First we resolve the part between the square brackets:
[tex]\lbrack x-(7+x)\rbrack=(x-7-x)=0x-7=-7[/tex]Then:
[tex]9-\lbrack x-(7+x)\rbrack=9-(-7)[/tex]Then you apply the opperation with the symbols knowin that:
[tex](+)(+)=+[/tex][tex](+)(-)=-[/tex][tex](-)(-)=+[/tex]And the final answer is:
[tex]9+7=16[/tex]Three friends rented a kayak. It cost $4 per hour per person to rent the kayak, plus $2 for each life jacket, and $3 to park the car. It cost $57 in all. How many hours did they spend kayaking? Write an equation and solve.
Answers
Answer:
13 hours
Step-by-step explanation:
Let y = the total cost
let x = hours
y = 4x + 5 5 = the one time fee of the jacket and the parking
57 = 4x + 5 Subtract 5 from both sides
52 = 4x Divide both sides by 4
13 = x
Which of the following represents the set of possible rational roots for thepolynomial shown below?2x3 + 5x2 - 8x - 20 = 0oa{=}, +2, +1, +2, +3, +3 + 1}O B. {+1, +2, +4, +5, +10, 20}O a {, +1, +2 +3 +4, + 3, +10, +20)02 (1.1,2,3,4,5,10,20)
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We will have that the set of rational roots for the expression will be:
[tex]\mleft\lbrace\pm\frac{1}{2},\pm1,\pm2,\pm\frac{5}{2},\pm4,\pm5,\pm10,\pm20\mright\rbrace[/tex][Option C].
Which statements about the graph of the exponential function f(x) are TRUE?The x-intercept is 1.The y-intercept is 3.The asymptote is y = -3The range is all real numbers greater than -3The domain is all real numbers.f(x) is positive for all x-values greater than 1As x increases, f(x) approaches, but never reaches, -3.
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1 The x-intercept is the value of x where the graph intersects the x-axis. The graph crosses the x-axis at x = 1. This statement is true.
2 The y-intercept is the value of y where the graph intersects the y-axis. The graph crosses the y-axis at y = -2. This statement is false.
3 The horizontal asymptote is the value of y to which the graph approaches but never reaches. This value seems to be y = -3, thus this statement is true.
4 The range is the set of values of y where the function exists. The graph exists only for values of y greater than -3. This statement is true.
5 We can give x any real value and the function exists, i.e., any vertical line would eventually intersect the graph. This statement is true.
To find the domain of a function when we are given the graph, we use the vertical line test. This consists of drawing an imaginary vertical line throughout the x-axis. If the line intersects the graph, that value of x is part of the domain.
This imaginary exercise gives us the centainty that there is no value of x that won't intercept the graph, thus the domain is the set of all the real values.
6 We can see the graph is positive exactly when the function has its x-intercept, thus This statement is true.
7 As x increases, y goes to infinity. The value of -3 is not a number where f(x) approaches when x increases, but when x decreases. This statement is false.
The triangles formed by two ladders leaning against a wall are similar. How long is the shorter ladder?
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To solve this problem we must use proportions
[tex]\begin{gathered} \text{ }\frac{x}{8}\text{ = }\frac{42}{24} \\ \text{ x = }\frac{8\text{ x 42}}{24} \\ \text{ x = }\frac{336}{24} \\ \text{ x = 14} \end{gathered}[/tex]The length of the shortest ladder is 14.
letter B is the correct answer.
Find the volume round to the nearest 10th necessary. Use three. 144 pi and a calculator to get your answers.
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The diameter of the cylinder is 24 mm.
Therefore, the radius is given by:
[tex]\frac{24}{2}=12mm[/tex]The height of the cylinder is given as 5 mm.
The formula for the volume V of a cylinder with radius r and height h is given by:
[tex]V=\pi r^2h[/tex]Substitute r = 12mm and h = 5 mm into the formula for volume:
[tex]V=\pi\left(12\right)^2\left(5\right)\approx2261.9[/tex]Therefore, the volume of the cylinder is approximately 2261.9 mm².
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i inserted a picture of the questions 19 and 20 that i need help with.
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WE are given that 9 tickets have a total cost of $94.50. To determine the price for each ticket we must find the quotient between the total amount spent and the number of tickets, like this:
[tex]\frac{94.50}{9}[/tex]Solving the operations we get:
[tex]\frac{94.50}{9}=10.5[/tex]Therefore, each ticket has a price of $10.50
According to projections through the year 2030, the population y of the given state in year x is approximated byState A: - 5x + y = 11,700State B: - 144x + y = 9,000where x = 0 corresponds to the year 2000 and y is in thousands. In what year do the two states have the same population?The two states will have the same population in the year
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The x variable represents the year in question. The year 2000 is represented by x = 0, 2001 would be repreented by x = 1, and so on.
The year in which both states would have the same population can be determined by the value of x which satisfies both equations.
We would now solve these system of equations as follows;
[tex]\begin{gathered} -5x+y=11700---(1) \\ -144x+y=9000---(2) \\ \text{Subtract equation (2) from equation (1);} \\ -5x-\lbrack-144x\rbrack=11700-9000 \\ -5x+144x=2700 \\ 139x=2700 \\ \text{Divide both sides by 139} \\ x=19.4244 \\ x\approx19\text{ (rounded to the nearest whole number)} \end{gathered}[/tex]Note that x = 19 represents the year 2019
ANSWER:
The two states will have the same population in the year 2019
2x - 6(x-3) ≥ 5
solve for x.
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Answer:
It’s siu
Step-by-step explanation:
Answer:x≤4.6
Step-by-step explanation: 2x-6(x-3)≥5. 1).combine the like terms. 2x+x=3x & -6+-3=-9. 2). isolate the "x". 3x-9≥5. 3x≥14. 3). divide both sides by your coefficient. 3x≥14/ 3
x≥4.6
4) flip your sign. x≤4.6
I need help figuring out if what I got is rigjt
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The figure in the picture shows 3 squares that form a right triangle. Each side of the triangle is determined by one side of the squares.
The only information we know is the area of two of the squares. The area of a square is calculated as the square of one of its sides
[tex]A=a^2[/tex]So to determine the side lengths of the squares, we can calculate the square root of the given areas:
[tex]\begin{gathered} A=a^2 \\ a=\sqrt[]{A} \end{gathered}[/tex]For one of the squares, the area is 64m², you can determine the side length as follows:
[tex]\begin{gathered} a=\sqrt[]{64} \\ a=8 \end{gathered}[/tex]For the square with an area 225m², the side length can be calculated as follows:
[tex]\begin{gathered} a=\sqrt[]{225} \\ a=15 \end{gathered}[/tex]Now, to determine the third side of the triangle, we have to apply the Pythagorean theorem. This theorem states that the square of the hypothenuse (c) of a right triangle is equal to the sum of the squares of its sides (a and b), it can be expressed as follows:
[tex]c^2=a^2+b^2[/tex]If we know two sides of the triangle, we can determine the length of the third one. In this case, the missing side is the hypothenuse (c), to calculate it you have to add the squares of the sides and then apply the square root:
[tex]\begin{gathered} c^2=225+64 \\ c=\sqrt[]{225+64} \\ c=\sqrt[]{289} \\ c=17 \end{gathered}[/tex]So the triangle's sides have the following lengths: 8, 15 and, 17
Now that we know the side lengths we can calculate the perimeter of the triangle. The perimeter of any shape is calculated by adding its sides:
[tex]\begin{gathered} P=8+15+17 \\ P=40m \end{gathered}[/tex]consider the line y=2/5x. What is the slope of a line perpendicular to this line?
What is the slope of a line parallel to this line?
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Answer:
- 5/2
Step-by-step explanation:
If the slope of a line is m then the slope of the perpendicular line is -1/m
The slope of y = 2/5 x is 2/5
Slope of perpendicular line = - 5/2
The director of a film festival received 9 submissions, 7 of which were sci-fi films. If the director randomly chose to play 6 of the submissions on the first day of the festival, what is the probability that all of them are sci-fi films? Write your answer as a decimal rounded to four decimal places .
Answers
Given data:
9 submissions out of which 7 were sci-fi
If the director randomly chose to play 6 of the submissions on the first day of the festival
Then, the probability that all of them are sci-fi films will be obtained as follows
At the first selection, it will be: 7/9
At the second selection, it will be: 6/8
At the third selection, it will be: 5/7
At the fourth selection, it will be: 4/6
At the fifth selection, it will be: 3/5
At the sixth selection, it will be: 2/4
Thus, the probability will be
[tex]\frac{7}{9}\times\frac{6}{8}\times\frac{5}{7}\times\frac{4}{6}\times\frac{3}{5}\times\frac{2}{4}=\frac{5040}{60480}[/tex]=>
[tex]\frac{5040}{60480}=\frac{1}{12}[/tex]=>
[tex]\frac{1}{12}=0.0833[/tex]Answer = 0.0833
The sides of an L-shaped figure meet all the right angles
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ANSWER:
24 ft²
STEP-BY-STEP EXPLANATION:
To determine the area of the figure, we must divide the L-shaped figure into two rectangles just like this:
We calculate the area of each rectangle and the sum of both areas would be the area of the L-shaped figure, in the following way:
[tex]\begin{gathered} A_1=L\cdot W=6\cdot2=12\text{ ft}^2 \\ \\ A_2=L\cdot W=3\cdot4=12\text{ ft}^2 \\ \\ \text{ Therefore:} \\ \\ A_t=A_1+A_2=12+12 \\ \\ A_t=24\text{ ft}^2 \end{gathered}[/tex]The area of the L-shaped figure is equal to 24 ft².
65+ (blank) =180
11x + (blank)=180
11x =
x =
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Answer:
sorry if this is wrong
I just answered it according to the question you gave not the pic
Step-by-step explanation:
x = 65
11x + x = 180
12x = 180
x = 180 ÷ 12
= 15
fine one value of x for which f(x) = 4 and find f(0)look at the graph below
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To find the value of x for which f(x) = 4 we must find the point (x, 4), first, let's draw a horizontal line at y = 4:
As we can see the horizontal line touches the graph, then it touches the graph we draw a vertical line until we reach the x-axis, where we reach it, it's the value of x:
As we can see, the vertical line reaches x = -4, therefore, f(-4) = 4
[tex]f(-4)=4[/tex]Our final answer will be x = -4
b)
Now for f(0) = ?, we must do the same logic, but now we start with a vertical line at x = 0, and goes up until we reach the graph
As we can see it touches the graphic at y = 2, hence, f(0) = 2
[tex]f(0)=2[/tex]To find the value of x for which f(x) = 4 we must find the point (x, 4), first, let's draw a horizontal line at y = 4:
As we can see the horizontal line touches the graph, then it touches the graph we draw a vertical line until we reach the x-axis, where we reach it, it's the value of x:
As we can see, the vertical line reaches x = -4, therefore, f(-4) = 4
[tex]f(-4)=4[/tex]Our final answer will be x = -4
b)
Now for f(0) = ?, we must do the same logic, but now we start with a vertical line at x = 0, and goes up until we reach the graph
As we can see it touches the graphic at y = 2, hence, f(0) = 2
[tex]f(0)=2[/tex]Which answer shows how to solve the given equation using the quadratic formula? 22 - 3. - 4= 0 3+, 22-4(2)(-4) 2(2) -(-3)=1/(-3)2-4(2)(-4) 2(2) 4+/(-3) -4(2)(-4) 2 3+1/32-4(-3)(-4) 2(2)
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hello
the question here is a given quadratic equation and we're required to use quadratic formula to solve it.
[tex]2x^2-3x-4=0[/tex]now, to solve this, let's bring out quadratic formula first
[tex]x=-b\pm\frac{\sqrt[]{b^2-4ac}}{2a}[/tex]now from our equation given, we can easily identify a, b and c.
[tex]\begin{gathered} 2x^2-3x-4=0 \\ a=2 \\ b=-3 \\ c=-4 \end{gathered}[/tex]next we plug in the variables into the equation and solve
[tex]undefined[/tex]solve for r 2r + 7 = 4r - 13
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2r + 7 = 4r - 13
subtract 4 from both-side of the equation
2r - 4r + 7 = 4r - 4r - 13
-2r + 7 = -13
subtract 7 from both-side of the equation
-2r + 7 = -13 - 7
-2r = -20
divide both-side of the equation by -2
r = 10
Let the graph of f(x) be given below. Find the formula of f(x), a polynomial function, of least degree.
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To detrmine the formula of the polynomial, we check for the roots on the graph:
when y = 0, x = -2
when y = 0, x = 4
We have two roots.
x = -2
x + 2 = 0
x = 4
x - 4 = 0
3rd factor is x = 0
Hence, we have two factors: x(x + 2) and (x - 4)
The polynomial function using the factors:
[tex]f(x)\text{ = ax(x + 2)(x - 4)}[/tex]Next, we find the value of a:
To get a , we pick a point on the graph. let the point be (0, -4)
substitute the point in the function above:
[tex]\begin{gathered} f(x)\text{ = y = -4, x = 0} \\ -4\text{ = a(0 + 2) (0 - 4)} \\ -4\text{ = a(2)(-4)} \\ -4\text{ = -8a} \\ a\text{ = -4/-8} \\ a\text{ = 1/2} \end{gathered}[/tex]The formula of the polynomial becomes:
[tex]f(x)\text{ = }\frac{1}{2}x(x\text{ }+2)(x-4)[/tex]Can u guys simplify this?
(2x^-3y^5)^2*(x^7y^-11)
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In a scale drawing of a rectangularswimming pool, the scale is 2 inch: 4feet. Find the perimeter and area ofthe swimming pool.15 in.3.5 in.
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The given scale is
[tex]2in\colon4ft[/tex]This means each two inches of the scale represents 4 feet of the actual size (or each inch is equivalent to two feet).
So, if the dimensions of the scale are 15 inches by 3.5 inches, then the actual dimensions would be 30 feet by 7 feet.
The perimeter would be
[tex]P=2(w+l)=2(30+7)=2(37)=74ft[/tex]The area would be
[tex]A=w\cdot l=30.7=210ft^2[/tex]Therefore, the perimeter is 74 feet, and the area is 210 square feet.A length of 48 ft. gave Malama an area
of 96 sq. ft. What other length would
give her the same area (96 sq. ft.)?
4
Answers
My explanation:
Easy explanation ⬇️
Given length: 48ft
Total area is 96sq. ft
48 + 48 = 96
Second explanation:
Formula to find missing length ⬇️
Area = length x width
96 sq. ft = 48ft x w
96 sq. ft = 48ft x 2
(2 x 48 = 96)
So 2 (probably 48) should be your answer!
