The rate at which the area is increasing is 95cm/sec² .
Let us take the variable a to be the length of the rectangle and take the variable to b be the width of the rectangle.
We know that the area of the rectangle is given by A=a × b
Now differentiating with respect to t we get :
[tex]\frac{dA}{dt} = w\times\frac{da}{dt} +l\times\frac{db}{dt}[/tex]
Substituting the values we get that the rate of increase in the area is :
Rate of increase = (32 + 63) cm/sec² = 95 cm/sec²
A constant function is also regarded as linear in this sense because it is a polynomial of degree zero, or the zero polynomial.
A line segment represents the graph of a single variable.In this context, a function that is also a linearly map may be referred to as a homogeneous linear function or a linear form (the other meaning). In the context of linear algebra, the scalar-valued affine mappings are functions of degree 0 or 1.To learn more about area visit:
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PLS HELP ASAP
!!!!!!
What is the length of AC?
Answer:
126 units!
Step-by-step explanation:
I hope this helped!! c:
Graph, on a separate piece of paper, the equation of a line with a slope of −3 and a y-intercept of 2.
Select the points that appear on the graph.
Multiple select question.
cross out
A)
(0, 0)
cross out
B)
(0, 2)
cross out
C)
(1, 1)
cross out
D)
(1, −1)
cross out
E)
(2, 0)
Based on the slope of the line and the y-intercept, when graphed, the points that will appear on the graph will be:
B. (0, 2) D. (1, -1)How to graph the line?The equation of a line takes the form:
y = mx + b
m = slope
b = y - intercept
This line would therefore take the equation form:
y = - 3x + 2
When graphed, the graph would be as attached.
As shown by the graph, the points that will appear include:
(0 , 2) (1 , - 1)
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In the community of Greendale, a local restaurant donates 15% of the total sales to student-based clubs on certain funding nights.
A- Write an equation to represent the relationship between the dinner sales (d) and the amount (a) the organization will receive.
B- What is the constant of proportionality? Interpret the constant proportionally for the problem situation.
C- How much will the organization receive if dinner sales are $3600?
NEED BY 2:35 CENTRAL TIME!!! OFFERING 35 POINTS! MIDDLE SCHOOL MATH!
The equation that represents the relationship between dinner sales and the amount the organisation would receive is a = 0.15d
The constant of proportionality is 0.15.
Th amount the organisation will receive if dinner sales is $3600 is $540
What is the relationship between dinner sales and the amount the organisation would receive?The equation that would be used to represent the relationship between dinner sales and the amount the organisation would receive is a linear equation.
A linear equation is an equation that has one variable that is raised to the power of one. A linear equation can either be either be a positive function or a negative equation. When a linear equation is drawn on a graph, the graph is a straight line.
The form of the linear equation would be:
total amount received by the organisation = percentage x amount the restaurant receives.
a = 0.15d
0.15 is the constant of proportionality. It is the value that relates the amount the organisation would receive and the amount the restaurant would receive.
a = 0.15 x 3600
a = $540
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fine the value of x. please help
Answer:
141 degrees
Step-by-step explanation:
The total angle interior of a triangle is 180 degrees. And the 2 angles opposite of x equal it so x=103+38
Write an inequality, in slope-intercept form, for the graph below. If necessary,use "<=" for sor">=" for >.5(-3,0)5(0, -3)
we need to find the line equation for the dashed line. Since we have 2 points of the line, its slope is
[tex]\begin{gathered} m=\frac{-3-0}{0-(-3)} \\ m=\frac{-3}{3} \\ m=-1 \end{gathered}[/tex]where we used the slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Then, our searched line has the form:
[tex]y=-x+b[/tex]where b is the y-intercept. We can finde b by substituting point (0,-3) into the last equation:
[tex]\begin{gathered} -3=-(0)+b \\ b=-3 \end{gathered}[/tex]then, the searched line in slope-intercept form is
[tex]y=-x-3[/tex]Therfore, the given area can be modeled as
[tex]y>-x-3[/tex]because when a line is dashed it doesn't belong to the given area.
Find the derivatives of the following using increment method.1.y = 6x² +10x - 3
Given
[tex]y=6x²+10x-3[/tex]Find
derivatives using increment method.
Explanation
Given
[tex]y=6x²+10x-3[/tex]replace x and y by
[tex]\begin{gathered} x+\Delta x \\ y+\Delta y \end{gathered}[/tex]so ,
[tex]\begin{gathered} y+\Delta y-y=6(x+\Delta x)^2+10(x+\Delta x)-3-(6x^2+10x-3) \\ \Delta y=6x^2+6\Delta^2x^2+12\Delta x^2+10x+10\Delta x-3-6x^2-10x+3 \\ \Delta y=12\Delta x^2+6\Delta^2x^2+10\Delta x \\ \end{gathered}[/tex]now divide by
[tex]\Delta x[/tex]so ,
[tex]\begin{gathered} y^{\prime}=\frac{12\Delta x^2+10\Delta x+6\Delta^2x^2}{\Delta x} \\ \\ y^{\prime}=12x+10+6\Delta x \end{gathered}[/tex]now taking limit
[tex]\begin{gathered} \lim_{\Delta x\to0}y^{\prime}=\lim_{\Delta x\to0}(12x+10+6\Delta x) \\ \\ y^{\prime}=12x+10 \end{gathered}[/tex]Final Answer
Therefore , the derivative of the function using increment method is 12x + 10
Using the drawing tools to form the correct answer on the provided graph
Horizontal line with the given function: y = 4
Explanation:
Since the midline of a sine function is the horizontal centerline about which the functions oscilliart above and below, the corresponding line here is y = 4 with x = 0.
NB:
The midline is parrallel to y = 0 ~ the x-axis.
5/3x+1/3x=11 1/3+8/3x
Answer:
-111/2
Step-by-step explanation:
Please look at the attachment below! :D
if the work required to stretch a spring 3 ft beyond its natural length is 15 ft-lb, how much work (in ft-lb) is needed to stretch it 18 in. beyond its natural length? give your answer in decimal form.
The amount of work needed to stretch the spring 18 in. from its natural position is 3.75 ft-lb.
According to the Hooke's Law, the work done on the spring is:
W = 1/2. k . x²
Where:
k = spring constant
x = displacement.
Notice that the work done is directly proportional to x².
Hence,
W₁ : W₂ = x₁² : x₂²
Parameters given:
W₁ = 15 ft-lb
x₁ = 3 ft
x₂ = 18 in. = 1.5 ft
Plug the above parameters into the ratio equation:
15 : W₂ = 3² : (1.5)²
W₂ = (1.5)² . 15 / 3² = 15/4 = 3.75 ft-lb
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For her science fair project, Madelyn is growing crystals with sugar water. She wants to know if the size of the container has an effect on crystal growth. To start, Madelyn pours a sugar-water mixture into a small bowl. Then she pours triple the amount of the mixture into a large bucket. She decides to add red coloring so the crystals are more visible. Madelyn adds the same amount of red coloring to both containers. Which container's sugar water mixture is a darker shade of red?
The container whose sugar water mixture is a darker shade of red is: A. the small bowl's mixture is a darker shade of red.
What is a ratio?A ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.
In this scenario, the ratio of the sugar water mixture in the small bowl (S) to the sugar water mixture in the large bucket (L) can be represented by this mathematical expression:
S:L = 1:3
Also, when red coloring is added to both containers, we have:
S:L = 1r:3r
In this context, we can reasonably and logically deduce that the mixture in the small bowl would have a darker shade of red because it is less diluted in comparison with the sugar water mixture in the large bucket.
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Complete Question:
For her science fair project, Madelyn is growing crystals with sugar water. She wants to know if the size of the container has an effect on crystal growth. To start, Madelyn pours a sugar water mixture into a small bowl. Then she pours triple the amount of the mixture into a large bucket. She decides to add red coloring so the crystals are more visible. Madelyn adds the same amount of red coloring to both containers. Which container's sugar water mixture is a darker shade of red?
answer choices
The small bowl's mixture is a darker shade of red.
The large bucket's mixture is a darker shade of red.
Neither. The mixtures are the same shade of red.
Please answer attached question with diagram :)
The translation observed by shape A after reflection is
x direction -5y direction -2What is translation?Translation refers to a linear movement used in describe repositioning of image during transformation
Transformation is the generally the repositioning of an image. Transformations are usually described in a cartesian plane for ease of comprehension.
The shape A after reflection had a new position. The new position was moved downwards, in the y direction by 2 units representing -2
The shape was further moved to the left 5 units in the x direction representing -5
Hence we say that c = -5 and d = -2
This describes the position of the image now labeled shape B
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WILL MARK BRAINLIEST FOR THE BEST AND MOST ANSWERED OUT REPLY
1. A recent election poll claims that Candidate A is projected to win the election with 53% of the vote. If a sample of 2436 voters is polled, determine if Candidate A can be guaranteed a win with 95% confidence.
Select an answer
a. yes
b. no
c. Not enough information
Explain why or why not using two sentences.
Using percentages we can conclude that 95% of votes that is 2,314 votes (B) cannot be guaranteed which is 1,023 votes more than the projected 53% winning votes (1,291 votes).
So, candidate A has a projection of winning 53% votes.
A sample of 2436 voters is pulled, then:
2436/100 × 53 = 1,291 votesCan candidate A be guaranteed 95% votes which are:
2436/100 × 95 = 2,314 votesDifference: 2,314 - 1,291 = 1,023
Therefore, using percentages we can conclude that 95% of votes that is 2,314 votes (B) cannot be guaranteed which is 1,023 votes more than the projected 53% winning votes (1,291 votes).
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Here is a sketch of the unique triangles that can be
made with angle measures 80° and 20° and side
length 5.
PLEASE HELPPPP
ASAAAAPPPPP DUE AT END OF TODAY
Option (B) describes the correct unique possibilities of the given triangle.
What are triangles?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. △ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane. A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon. There are three sides and three angles in every triangle, some of which may be the same. Triangles can be divided into three types based on the lengths of their sides, and these are Scalene, Isosceles, and Equilateral.So, according to the given image:
We can easily observe that the triangle is an isosceles triangle with base angles being equal and the third angle being the smallest.Then, the correct option about the triangle will be an option (B).Therefore, option (B) describes the correct unique possibilities of the given triangle.
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Determine the rate at which the sloth travels.
Justify your answer.
Distance (ft)
987654MN-
6.
3-
2
1
0
Speed of a Sloth
1 2
3 4
Time (min)
The rate at which the sloth travels as required in the task content is; -22ft/min.
Speed as a rate of distance with respect to time.It follows from the task content that the rate at which the sloth travels is to be determined.
Since the correct representation of the data is such that the distance and corresponding time pairs are as follows;
(98, 1) , (76, 2) , (54, 3), (32, 4).
Hence, the rate of distance change per time is the speed of the sloth and hence, the rate of distance change is;
Rate = ∆Distance/∆time.
Rate, R = (98 - 76)/(1 - 2)
Rate, R = 22/-1
R = -22 ft/min.
Ultimately, the rate at which the sloth travels is therefore; -22 ft/min.
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what are the coordinates of a’?
Need help solving this problemNote for part A I got 4/22 and it was incorrect
First, we need to find the total frequency. This is given by adding all the given frequencies. That is,
[tex]\begin{gathered} f_{\text{total}}=4+6+7+5 \\ f_{\text{total}}=22 \end{gathered}[/tex]and the relative frequency is the division of the frequency of the corresponding interval by the total frequency,
[tex]f_{\text{rel}}=\frac{f_{\text{ interval}}}{f_{total}}[/tex]Therefore, the answers are:
a) 4/22 but written in simple form:
[tex]\frac{2}{11}[/tex]b)
[tex]\frac{5}{22}[/tex]Simplify 6 + 2(5 – 8)2 + 7
The answer is very simple. .
6 + 2 (5 - 8 ) ² + 7
Firstly we solve what is inside the parenthesis
[tex]6\text{ + 2}\cdot(-3)^2\text{ + 7}[/tex][tex]6\text{ + 2 (9) +7}[/tex]Then we solve the multiplications
[tex]6\text{ + 18 + 7 }[/tex]Finally we solve the sums.
[tex]\text{ 6 +18 + 7 = }31[/tex]That is the solution.
2x + y = 2
Step 2 of 2: Determine the missing coordinate in the ordered pair (?, -3) so that it will satisfy the given equation.
Answer:
2.5
Step-by-step explanation:
Plug is -3 for y and solve for x
2x -3 = 2 Add 3 to both sides
2x = 5 Divide both sides by 2
x = [tex]\frac{5}{2}[/tex] o r 2[tex]\frac{1}2}[/tex] or 2.5
100 brainly!! Which of the following values are in the range of the function graphed below? Check all that apply.
Answer:
B
Step-by-step explanation:
find the value of x in each case
Answer:
x=23
Step-by-step explanation:
The amount of degrees in a triangle is 180 degrees.
line AC and line DF are straight angles meaning that the opposite angles are equal to each other. That means that angle FBC is also equal to x. Because line AC and EF are parallel we know that FBC and BFE are equal. Therefore, BFE is equal to x. The sum of the values of each angle of the triangle should add up to 180. 5x+65=180
5x=115
x=23
If f(x) = 12x and g(x) = -4x-12, find (f ·g)(x).
A.) -48x^2 - 12x
B.) -48x^2 - 144x
C.) -4x^2 - 144x
D.) -192x^2
Answer:
[tex]-48x^2 - 144x[/tex]
Step-by-step explanation:
[tex](f \cdot g)(x)=f(x) \cdot g(x) \\ \\ =12x(-4x-12) \\ \\ =-48x^2-144x[/tex]
PLEASE HELP!!!!!
Which of the following equations represents the line that passes through the point (4, 3) and has a slope of 1/2?
A) 2x-3y=-18
B)2x-3y=17
C)3x-2y=-17
D)3x-2y-18
The equation of a line that passes through the point (4, 3) and has a slope of 1 / 2 is y = 1 / 2 x + 1.
How to find the equation of a line?The equation of a line that passes through a point can be describe as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the line passes through (4, 3) and the slope is 1 / 2.
Hence, let's find the y-intercept using (4, 3)
y = 1 / 2 x + b
3 = 1 / 2 (4) + b
3 = 2 + b
b = 3 - 2
b = 1
Therefore, the equation of the line is y = 1 / 2 x + 1.
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What are the coordinates of the midpoint of segment whose endpoints are A(-2,7) and B(4,-2)?
can someone help me out with this?
Answer:
area of triangle is length *breathe
4.5 * 5.5 = 24.75
Britany is bringing birthday cake and cookies to her office. She has already spent $10.00 on the cake. Cookies cost $0.70 each, and she does not wish to spend more than $34.50 for all desserts. If x represents the number of cookies she can buy, which of the following inequalities symbolizes this situation?
A.
$10.00x + $0.70 < $34.50
B.
$0.70x + $10.00 < $34.50
C.
$0.70x + $10.00 < $34.50
D.
$10.00x + $0.70 < $34.50
Considering the definition of an inequality, the correct answer is option C. the inequiality $0.70x + $10.00 < $34.50 symbolize this situation
Definition of inequalityAn inequality is the existing inequality between two algebraic expressions, connected through the signs:
greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.The solution of an inequality is the set of numbers that make the inequality true.
Inequality in this caseIn this case, you know that:
Britany has already spent $10.00 on the cake. Cookies cost $0.70 each. She does not wish to spend more than $34.50 for all desserts.Being "x" the number of cookies Britany can buy, the inequality that expresses the previous relationship is
10 + 0.70x <34.50
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Divide. Enter the correct answer.
17+2=
the d score is a standardized measure of the degree to which the independent variable caused a change in the dependent variable. this is also known as the
The standardized measure of the degree to which the independent variable caused a change in the dependent variable is a standard change.
What is a dependent variable?A dependent variable is what is determined in an experiment or test and is the one that is influenced throughout the experiment. The dependent variable is affected by the independent variable.
In mathematical modeling, statistical modeling, and experimental sciences, dependent and independent variables are variables. Dependent variables are so named because their values are explored in an experiment under the assumption or requirement that they are dependent, by some law or rule, on the values of other variables.
In conclusion, the standard change illustrates the change.
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You want to go on a swamp tour. How long does it take a swamp vehicle that travels at 3.2 miles per hour to travel across the swamp, from point Z to point S ?
If the swamp vehicle that travels at 3.2 miles per hour to travel across the swamp, then the time taken to travel from point Z to point Y is 1.56 hours
The speed of the swamp vehicle = 3.2 miles per hour
From the figure we can see the two triangles ΔXVM and ΔXYZ
Here we have to use the ratio of the two similar triangles
The ratio will be
VW/WX = YZ/ZX
Substitute the values in the equations
10/6 = YZ/3
We have to find the distance from point Z to point Y
YZ = (10/6)×3
= 5 Miles
We know
Speed = Distance / Time
Time = Distance / speed
= 5/3.2
= 1.56 hours
Hence, if the swamp vehicle that travels at 3.2 miles per hour to travel across the swamp, then the time taken to travel from point Z to point Y is 1.56 hours
The complete question is
You want to go on a swamp tour. How long does it take a swamp vehicle that travels at 3.2 miles per hour to travel across the swamp, from point Z to point Y ?
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Orlando is getting balloons for his grandmother's birthday party. he wants each balloon string to be 6 feet long. at the party store, string is sold by the yard. if orlando wants to get 72 balloons, how many yards of string will he need?
144 yards of string will need to use balloons for the party.
Given,
The length of balloon string Orlando wanted = 6 feet
Number of balloons = 72
We have to find the total length of strings wanted for 72 balloons in yards.
1 yard = 3 feet
Now,
Total length of strings Orlando needs = length of one string x number of balloons = 6 x 72 = 432 feet
Now convert 432 feet into yard
That is,
432 / 3 = 144 yards
So,
144 yards of string will need to use balloons for the party.
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