We have to calculate the average rate of change of the function f(x) in the first two seconds.
As the function is a line, the rate of change is constant and is equal to the slope, as the slope is defined as the quotient of the variation of y=f(x) and the variation of x.
Taking two point (x=0 and x=2), we will calculate the rate of change:
When x = 0, f(0) = 50.
When x = 2, f(2) = 100.
Then, we can calculate the slope (or rate of change) as:
\(m=\frac{f(x_2)-f(x_1)}{x_2-x_1}=\frac{100-50}{2-0}=\frac{50}{2}=25\)The average rate of change between 0 and 2 is 25.
find the missing angle
Answer:
? = 77°
Step-by-step explanation:
the 3 angles in a triangle sum to 180° , that is
? + 35° + 68° = 180°
? + 103° = 180° ( subtract 103° from both sides )
? = 77°
Answer:77
Step-by-step explanation:
180-103=77
Chase baked 4/5 dozen brownies in 3 hours ? What is her average of baking per hour ?
Answer:
\(3\frac{1}{5}\)brownies per hour
Step-by-step explanation:
Given parameters:
Number of brownies = \(\frac{4}{5}\) of a dozen
Time taken = 3hrs
Unknown:
Average baking per hour = ?
Solution:
The average baking per hour;
This is a rate problem;
Average baking per hour = \(\frac{number of baking}{time}\)
Number of brownies = \(\frac{4}{5}\) x 12 = \(\frac{48}{5}\)
Average baking per hour = \(\frac{48}{\frac{5}{3} }\)
= \(\frac{48}{5} x \frac{1}{3}\)
= \(\frac{16}{5}\)
= 3\(\frac{1}{5}\)brownies per hour
find the probability that a randomly selected point within the circle falls in the red shaded area 106
Answer:
0.29
Step-by-step explanation:
Knowing that the shaded angle is 106 degrees, and a circle's angle total is 360 degrees, we will know what fraction of the circle is shaded by dividing the shaded region's angle by the angle of an entire circle:
106/360 = 0.29
The fraction of the circle that is shaded is also the probability that a randomly selected point within the circle falls in the shaded region since we just divided the desired outcome by all of the possible outcomes.
A shark begins 172.5 meters below sea level and then swam up 137.1 meters,. Where is the sharks location now in relation to sea level
Answer:
35.4m below sea level
Step-by-step explanation:
172.5 - 137.1 = 35.4
The shark's location is now 35.4m below sea level.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.
+ Addition operation: Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.
For example 4 -2 = 2
Using the arithmetic operations of addition and subtraction, the shark's location is now in relation to sea level if the shark begins 172.5 meters below sea level and then swam up 137.1 meters.
Assume that distance below sea level is positive,
⇒ 172.5 - 137.1 = 35.4
Hence, the shark's location is now 35.4m below sea level.
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Which factored form of 10x + 120x + 320 reveals all the zeros of the function it defines?
A) 10(x + 6)^2 – 40
B) 10(x + 8) (x + 4)
C) 10x (x + 12) + 320
D) 10(x^2 + 12x +32)
Answer:
b
Step-by-step explanation:
QUESTION 17. 1200 centimetres = metres.
Answer:
12 Metres (Meters)
Step-by-step explanation:
5.607 is what percent of 89 step by step
Answer:
6.3%
Step-by-step explanation:
so 5.607 = x% * 89
to find the percent u need to divide : 5.607/89 which is : 0.063
to convert 0.063 to a percent multiply 0.063 by 100 = 6.3%
check :
6.3% *89 = 5.607
What’s the area? Please help :)
Answer:
252 sq. in.
Step-by-step explanation:
divide it into sections like this
12*15=180
3*6=18
6*9=54
then add it all together. sometimes it is more complicated, but as long as none of the divided parts overlap this will be correct for any shape, as long as you account for the whole shape.
Triangles DEF and D'E'F' are shown on the coordinate plane below: H F D D' 2 -8-7--5-4-3-2-1 1 2 3 4 5 6 7 8 T 20 F CO What rotation was applied to triangle DEF to create triangle D'E'F'?
What is the probability a student scored less than 75%. The μ=75 and the σ=10
P (x < 75) = ____ + _____ = ______
PLEASE FILL IN THE BLANKS!
On solving the provided question we can say that As a result, the probability of a student P(x < 75) = 75 + (-75 ) = 0 .
What is probability?Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% since there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many disciplines, including statistics, economics, science, and engineering.
z = (x - μ) / σ
z = (75 - 75) / 10 = 0
That is, a raw score of 75 equates to a z-score of 0.
P(z < 0) = 0.5
As a result, the likelihood of a student scoring less than 75% is 0 or 0%.
So, P(x < 75) = 75 + (-75 ) = 0
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solve the question:-4x +5=13
Let's begin by identifying key information given to us:
\(\begin{gathered} -4x+5=13 \\ \text{Add ''4x'' to both sides, we have:} \\ -4x+4x+5=13+4x \\ 5=13+4x \\ \text{Subtract ''13'' from both sides, we have:} \\ 5-13=13-13+4x \\ -8=4x\Rightarrow4x=-8 \\ 4x=-8 \\ x=-\frac{8}{4}=-2 \\ x=-2 \end{gathered}\)i need the smallest value first
Smallest value first is -3
What is cubic equation ?To plot the curve of a cubic equation, we need cubic equation formula. This formula helps to find the roots of a cubic equation. If the degree of the polynomial is n, then there will be n number of roots. The roots of cubic equation are also called zeros.
\(x^3-x^2-9x+9\)
First factorize the polynomial to get;
\(\Rightarrow x^2(x-1)-9(x-1)\)
\(\Rightarrow (x-1)(x^2-9)\)
\(\Rightarrow (x-1)(x+3)(x-3)\) \(\because a^2-b^2=(a+b)(a-b)\)
So, x = 1 ,x = 3 and x = -3
Hence, smallest value first is -3
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Find the value of a and b in the following = a + b
Evaluate:
3xy^2+7x-2y for X= -1 y= 3
Answer:
-94
Step-by-step explanation:
(3 (-1) (3))² + 7(-1) - 2(3)
-9² - 7 -6
-81 - 13
-94
hope this helps :)
CAN SOMEONE HELP WITH THIS QUESTION?✨
The marginal revenue is 909 dollars per unit.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
R(q) = -2q² + 1000q _____(1)
Where q is the unit sold.
Now,
Substitute q = 91 in (1).
R(q) = -2q² + 1000q
R(q) = -2 x 91² + 1000 x 91
R(q) = -8281 + 91000
R(q) = $82719
Now,
91 units = $82719
1 unit = 82719/91
1 unit = $909
Thus,
909 dollars per unit is the marginal revenue.
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yo yo buddy i got yo bro yo buddy i
Answer: \(=1\frac{111}{125}\)
Step-by-step explanation:
\(=1+0.888\)
\(=1+\frac{111}{125}\)
\(=1\frac{111}{125}\)
yuhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
PLEASE ANSWER FAST
How much power is required to lift a 240 N table up 3 m in 20 seconds?
A. 1600 W
B. 0 W
C. 36 W
D. 720 W
Answer:
I am not sure but the answer may be 36 w
Answer:
A.1600
Step-by-step explanation:
I hope its help keep safe
go to my page and answer my questions a lot of points pls and ty
Answer:
ok will do
Step-by-step explanation:
a) (10 pts) Re-express the given differential equation as a first order differential equation by utilizing matrix
and vector notation and in accordance with ()
= () form.
b) (10 pts) Is the system obtained in (a) stable, neutrally stable of unstable? Determine this using matrix.
c) (10 pts) Compute the eigenvalues and eigenvectors of matrix.
d) (10 pts) Using the results computed in (c) find and matrices and show that =
−
relationship
(i.e., the diagonalization relationship) is a valid relationship.
a) To re-express the given differential equation as a first-order differential equation using matrix and vector notation, we can rewrite it in the form:
\(x' = Ax\)
where x is a vector and A is a square matrix.
b) To determine the stability of the system obtained in part (a), we need to analyze the eigenvalues of matrix A.
If all eigenvalues have negative real parts, the system is stable.
If at least one eigenvalue has a zero real part, the system is neutrally stable.
If at least one eigenvalue has a positive real part, the system is unstable.
c) To compute the eigenvalues and eigenvectors of matrix A, we solve the characteristic equation
\(det(A - \lambda I) = 0\),
where λ is the eigenvalue and I is the identity matrix.
By solving this equation, we obtain the eigenvalues.
Substituting each eigenvalue into the equation
\((A - \lambda I)v = 0\),
where v is the eigenvector, we can solve for the eigenvectors.
d) Once we have computed the eigenvalues and eigenvectors of matrix A, we can construct the diagonalization relationship as follows:
\(A = PDP^{(-1)}\)
where P is a matrix whose columns are the eigenvectors of A, and D is a diagonal matrix whose diagonal elements are the eigenvalues of A.
To show that this relationship is valid, we can compute \(PDP^{(-1)}\) and verify that it equals A.
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(50 Points!) Choose ALL answers that describe the polygon.
A. Parallelogram
B. Quadrilateral
C. Rectangle
D. Rhombus
E. Square
F. Trapezoid
The required shapes that describe the polygon;
Parallelogram, Quadrilateral, Rectangle, Rhombus.
What is polygon?A polygon with four sides and four angles is called a quadrilateral. When two pairs of parallel sides are equal in length, it is a parallelogram. If all four sides are equal in length, it is a rhombus. If all four angles are equal and equal to 90 degrees, it is a rectangle. If both conditions of equal sides and equal angles are met, it is a square. A trapezoid is a quadrilateral with exactly one pair of parallel sides.
According ot question:In this case,
IJ || KL and JK || LI,
so it is a parallelogram.
Additionally,
since ZI≈ ZK and ZJ≈ ZL,
it can be concluded that the opposite sides are equal in length, making it either a rectangle or a rhombus.
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The relationship between altitude and the boiling point of a liquid is linear. At an altitude of 8200 ft, the liquid boils at 199.42°F. At an altitude of 4700 ft, the liquid boils at 206.07°F. Write an equation giving the boiling point b of the liquid, in degrees Fahrenheit, in terms of altitude a, in feet. What is the boiling point of the liquid at 2500 ft?
Write an equation.
b=nothing
Answer:
The boiling point of the liquid it 210.25°F
Step-by-step explanation:
Linear Modeling
Some real-life events can be modeled as linear functions. If we are in a situation where a linear model is suitable, then we need two sample points to build the model and predict unknown behaviors.
The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:
\(\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\)
We are given the following points (H,A) where A is the altitude and P is the boiling point of a certain liquid: (8200,199.42) and (4700,206.07)
Applying the formula:
\(\displaystyle B-199.42=\frac{206.07-199.42}{4700-8200}(A-8200)\)
Calculating:
\(\displaystyle B-199.42=\frac{6.65}{-3500}(A-8200)\)
\(\displaystyle B-199.42=-0.0019(A-8200)\)
\(\displaystyle B-199.42=-0.0019A+15.58\)
\(\displaystyle B=-0.0019A+15.58+199.42\)
The equation is:
\(\displaystyle B=-0.0019A+215\)
Finally, we calculate the boiling point at A=2500 ft:
\displaystyle B=-0.0019*2500+215
B = 210.25°F
The boiling point of the liquid it 210.25°F
Which number is less than it’s square?
9/10
12/11
15/16
13/13
The number which is lesser than its square is 12/11
What is a square number ?When a number is multiplied by itself, the result is a square number. For instance, 25 is a square number as it is composed of 5 lots of 5, or 5 × 5.
The opposite of squaring an integer is finding its square root. The result of multiplying a number by itself yields its square value, whereas the square root of a number may be found by looking for a number that, when squared, yields the original value. It follows that a a = b if "a" is the square root of "b." Every integer has two square roots, one of a positive value and one of a negative value, because the square of any number is always a positive number. For instance, the square roots of 4 are both 2 and -2. However, the square root of a number is typically only expressed as the positive value.
The numbers are
9/10 , 12/11 , 15/16 and 13/13
The squares are
81/100, 144,121, 225/256, 1
here
81/100 < 9/10 abd
225/256 < 15/16
144/121 > 12/11
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Which statement is true about the measure of angle R’??
Answer:
Angle R is an Angle
Step-by-step explanation:
This question has no photo or context
-2log (6x + 1) = -6.
A line is perpendicular to y = 6x +3
and intersects the point (6, 1).
Find the equation for this line.
y-1=-(x-[?])
Answer:
1
Step-by-step explanation:
Perpendicuar lines have slopes that are opposite reciprocals: 6 ==> -1/6
y=mx+b
y=-x/6 + b ==> plug in slope -1/6 into slope equation
1 = -6/6 + b ==> plug in x and y values into slope equation
1 = -1 + b
1 + 1 = -1 + 1 + b
b = 2 ==> solve for b
y = -x/6 + 2 ==> plug in the value of b into the equation
y - 1 = -x/6 + 2 - 1
y - 1 = -x/6 + 1
y - 1 = -(x/6-1) ==> answer: 1
Write an equation of the line with slope 2/3 and y-intercept -9
Answer:
y=2/3x - 9
Step-by-step explanation:
Zach is repainting his bedroom. The area of one wall is 96 square feet. The length of his wall is 12 feet. What is the height of Zach’s bedroom wall?
Answer:
8 feet
Step-by-step explanation:
Let's start by remembering what we know about rectangles. The area of a rectangle is equal to the length multiplied by the height:
A = l x h
To find the height of the wall, we will divide the area by the length to isolate the unknown variable on one side of this equation:
h = 96/12 = 8 feet
Hope this helped!
A triangle has vertices of (-3,3),(-3,2), and (1,-2). What are the coordinates after dilating from the origin by a scale factor of 1/2?
Answer:
The coordinates after a dilating the triangle by a factor of 1/2 would be (-1.5, 1.5), (-1.5, 1) and (0.5, -1), respectively.
Step-by-step explanation:
Since we are dilating from the origin of the graph, (0, 0), all we need to do is multiply each vertex by the given scale factor.
find each angle measure to the nearest degree
Find m.
E
F
1.25 m
3 m
D
if correct will mark brainless :))
EF=2.73m;m<D
=65;m<F=25*
Hope this helps
HELP ME PLEASE I DONT KNOW WHAT TO DO!!!!!!!!
Answer:
I would have to guess c because it show a decrease in the number line
Step-by-step explanation:
Step-by-step explanation:
ɪᴛs ᴛʜᴇ ʟᴀsᴛ ᴏᴘᴛɪᴏɴ D
ᴀs ᴛʜᴇ ᴅᴏᴛ ɪs ᴘᴏɪɴᴛᴇᴅ ʙᴇᴛᴡᴇᴇɴ -15 ᴀɴᴅ -20