If Washington Auto Repair originally paid its mechanics $40 per hour. Now that there is a new owner, mechanics make $30.90 per hour. The percent of decrease in pay is: 22.75%.
How to find the percent decrease?Using this formula to find or determine the percent decrease
Percent decrease = Original Value – New Value/Original value
Let plug in the formula
Percent decrease = $40 per hour - $30.90 per hour / $40 per hour
Percent decrease = $9.10 / $40 per hour × 100
Percent decrease = 22.75%
Therefore the percent decrease is 22.75%.
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Please Help Me. This is Urgent!!!
The Lush Landscaping Company is involved in a project for the city. They will be enlarging the garden in front of City Hall. The current dimensions of the garden are 24 feet long by 16 feet wide. The company plans to make the garden area larger by planting a border of flowers all the way around the existing garden. The border will have the same width around the entire garden.
a.) Let x represent the width of the border. Write expressions for the length and the width of the new garden space (after the border has been added) in terms of x.
length = ________
width = _______
b.)Write a trinomial that represents the area of the new garden space (after the border has been added).
c.) Write a polynomial expression that represents the area of the border of the landscape company plans to add.
a) length = 24 + 2x
width = 16 + 2x
b) The area of the new garden space = 384 + 48x + 4x².
c) The area of the border can be represented by the polynomial expression 32x+2x².
What is a polynomial expression?
A polynomial expression is a mathematical expression that is a sum of terms, each term consisting of a constant coefficient multiplied by one or more variables raised to a non-negative integer power.
a.) Let x represent the width of the border. The length of the new garden space would be 24 feet + 2x (since the border is added to both the length and width). The width of the new garden space would be 16 feet + 2x (since the border is added to both the length and width).
length = 24 + 2x
width = 16 + 2x
b.) The area of the new garden space can be represented by the trinomial (24+2x)(16+2x) = (24*16) + (48x) + (4x^2)
c.) The area of the border can be represented by the polynomial expression 2x(16+x) = 32x + 2x^2.
Hence,
a) length = 24 + 2x
width = 16 + 2x
b) The area of the new garden space = 384 + 48x + 4x².
c) The area of the border can be represented by the polynomial expression 32x+2x².
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Solve the given initial-value problem. Give the largest interval I over which the solution is defined.
L di/dt +Ri =E, i(0)=i0 L, R, E, i0 constants
The solution to the given IVP is.[tex]$i(t)-\frac{E}{R}+\left(i_0-\frac{E}{R}\right) e^{-\frac{R}{L}}$[/tex]
Initial value problems describe a type of problem in calculus. Initial value problems in calculus concern differential equations with a known initial condition that specifies the value of the function at some point. The purpose of these problems is to find the function that describes the system, which can be done by integrating the differential equation.
Consider the initial value problem,
L [tex]\frac{d i}{d t}+R i=E \text {. }[/tex]
The initial condition is. [tex]$i(0)=i_0$[/tex]
Rewrite the DE as,
[tex]\begin{gathered}L \frac{d i}{d t}+R i=E \\\frac{d i}{d t}+\frac{R}{L} i=\frac{E}{L}\end{gathered}$$[/tex]
This is a linear DE.
Compare the DE [tex]\frac{d i}{d t}+\frac{R}{L} i=\frac{E}{L}$[/tex] with the general DE [tex]\frac{d i}{d t}+P(t) i=Q(t)$[/tex]. Then [tex]$P(t)=\frac{R}{L}$[/tex] and [tex]$Q(t)=\frac{E}{L}$[/tex].
Find the integrating factor (IF).
[tex]$$\begin{aligned}I F & =e^{\int P(t) \vec{t}} \\& =e^{\int\left(\frac{\pi}{\mathrm{I}}\right) \mathrm{A}} \\& =e^{\frac{\pi}{l^2}}\end{aligned}$$[/tex]
Thus, the integrating factor is [tex]$I F=e^{\frac{R^2}{2^2}}$[/tex].
Now multiply both sides of the DE with the IF.
[tex]$$\begin{array}{r}e^{\frac{R}{\bar{L}^t}}\left(\frac{d i}{d t}+\frac{R}{L} i\right)=\frac{E}{L} e^{\frac{R}{L^t}} \\\frac{d i}{d t} e^{\frac{\pi}{L^t}}+\frac{R}{L} e^{\frac{R}{\bar{L}^t}} i=\frac{E}{L} e^{\frac{\pi}{\bar{L}^t}} \\{\left[i e^{\frac{R}{L^2}}\right]=\frac{E}{L} e^{\frac{R^L}{L^t}}}\end{array}$$[/tex]
Integrate on both sides.
[tex]$$\begin{aligned}& \int\left[i e^{\frac{R}{L}}\right] d t=\int \frac{E}{L} e^{\frac{R}{L^t}} d t \\& i e^{\frac{R}{L^{\mathrm{r}}}}=\frac{E}{L} \int e^{\frac{\pi}{L^t}} d t \\& i e^{\frac{R}{\perp} r}=\frac{E}{L}\left[\frac{e^{\frac{R}{2}}}{\frac{R}{L}}\right]+C \\& i e^{\frac{R}{\Gamma}+}=\frac{E}{R} e^{\frac{R^2}{I^{+}}}+C \\& i(t)=\frac{\frac{E}{R} e^{\frac{R}{L^2}}+C}{e^{\frac{R}{D^2}}} \\& t(t)=\frac{E}{R}+C e^{-\frac{R}{L^t}} \\&\end{aligned}$$[/tex]
Thus, the general solution to the [tex]\mathrm{DE}[/tex] is [tex]$i(t)=\frac{E}{R}+C e^{-\frac{R}{t^*}}$[/tex].
Use the initial condition. [tex]$i(0)=i_0$[/tex]
Substitute [tex]$t=0$[/tex] and [tex]$i(0)=i_0$[/tex] in [tex]$i(t)=\frac{E}{R}+C e^{-\frac{R}{I^t}}$[/tex].
[tex]$$\begin{aligned}& i(0)=\frac{E}{R}+C e^{-\frac{R}{I}(0)} \\& i_0=\frac{E}{R}+C e^0 \\& i_0=\frac{E}{R}+C \quad \text { use } e^0=1 \\& C=i_0-\frac{E}{R}\end{aligned}$$[/tex]
Substitute [tex]$C=i_0-\frac{E}{R}$[/tex] in [tex]$i(t)=\frac{E}{R}+C e^{-\frac{R}{L^1}}$[/tex].
[tex]$$\begin{aligned}& i(t)=\frac{E}{R}+C e^{-\frac{R}{I}} \\& i(t)=\frac{E}{R}+\left(i_0-\frac{E}{R}\right) e^{-\frac{\pi}{t^t}}\end{aligned}$$[/tex]
Therefore, the solution to the given IVP is. [tex]$i(t)-\frac{E}{R}+\left(i_0-\frac{E}{R}\right) e^{-\frac{R}{L}}$[/tex].
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Please help! I know it's a lot of questions, I'm giving the best answer brainiest. Thank you, this will help me so much!
The total surface area of the hemisphere is 235.71cm²
What is a hemisphere?A hemisphere is simply called half of a sphere. A sphere is an object that is purely round in shape
The given parameters that will help to calculate to total surface area of the hemisphere are
Diameter =2r, This implies that r=10/2 = 5
taking the r as the radius = 5 then
The total surface area of the hemisphere is given by
Total surface area = 3пr²
Total surface area = (3*22*5*5)/7
TSA =1650/7
Therefore the total surface area = 235.71 cm²
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In QRS, s=4.2 cm, R-160° and S-8°. Find the length of r, to the nearest 10th of
a centimeter.
ΔQRS, r = 10.32 cm.
Solved by using the concept of triangle.
What is a triangle?Three straight sides and three angles make up a triangle, a two-dimensional form. Three vertices, three angles, and three sides define a triangle. In a triangle, the lengths of its two longest sides are always bigger than its third side's length.
A triangle seems to be a three-sided polygon with three vertices. There is a 180-degree angle created inside the triangle. In other words, a triangle's internal angles add up to 180 degrees.
Triangles can be categorized into one of three groups, namely Scalene, Isosceles, or Equilateral, depending on how long their sides are.
In ΔQRS,
given that,
s = 4.2 cm
∠R = 160°
∠S = 8°
From, ΔQRS
As we know,
r / sin A = s / sin B
∠Q = 180° - 160° - 8°
∠Q = 12°
now, putting the values we get -
r = 10.32 cm
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Paula is scuba diving her elevation changes by -37 4/5m in 4.5 min.
what rational number represents the average change in paula’s elevation each minute
SHOW YOUR WORK!
Change in Paula's elevation/altitude per minute is 8.4m.
What is altitude?There are numerous variations of altitude.
True altitude is the distance from mean sea level. [Elevation of geographic locations shown on maps is actually true altitude; for example, the height of Mount Everest.]Absolute altitude: The height from the spot on the ground immediately beneath the position under consideration is known as absolute altitude. Alternatively, it could be the height above the ground.When the altimeter is set for the local barometric pressure at mean sea level, it gives the indicated altitude. [Aircraft use outside pressure to calculate their altitude.]Pressure Altitude: The elevation above a standard datum air-pressure plane is referred to as pressure altitude. the local barometric pressure at the MSL is set to 1 ATM, or 1.0132105 Pa, on the altimeter.Now,
Given Change in Paula's elevation in 4.5 minutes=-37 4/5 m or -189/5m
- shows decrease in elevation.
so, for change in one minute = 189/5*4.5=189/22.5=8.4m
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A car is rolling south at 8 miles per hour, and a man pushes the car north at 10 miles per hour. What is the resultant vector on the car
The resultant vector on the car would be a vector pointing north with a magnitude of 2 miles per hour.
The resultant vector is the net effect of two or more individual vectors on an object. It is the overall force or movement that is produced when all the individual vectors are combined. To find the resultant vector, you would add together all of the individual vectors using vector addition. The resultant vector would be represented by a single vector with a certain magnitude and direction.
If a car is rolling south at 8 miles per hour, and a man pushes the car north at 10 miles per hour, subtract the southward velocity from the northward velocity.
10 mph northward - 8 mph southward= 2 mph northward
Therefore, the resultant vector on the car is 2 mph northward.
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Randy divides (2x - 3x³ 3x² + 7x-3) by (x² - 2x + 1) as shown below. What error does Randy make?
2x²+x+3
x²–2x+1) 2x²-3x³-3x² +7x-3
2x4-4x³+2x²
x³-5x² +7x
x³-2x²+x
-3x²+6x-3
-3x²+6x-3
0
Randy's error is that he did not arrange the terms of the dividend in descending order of power
How to determine the error in the workingsFrom the question, we have the following parameters that can be used in our computation:
2x²+x+3
x²–2x+1) 2x²-3x³-3x² +7x-3
This means that
Dividend = 2x²-3x³-3x² +7x-3
Divisor = x²–2x+1
Quotient = 2x²+x+3
See that the terms of the dividend are not properly represented
The proper representation is -3x³-3x²+2x² +7x-3
Hence, the mistake is in the order of the dividend terms
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complete the problems using synthetic division
Answer:
Step-by-step explanation:
write k for the divisor
write the coefficients of the dividend.
Bring the leading coefficient down.
Multiply the leading coefficient by k.
Add the terms of the second column.
Multiply the result by k.
Repeat steps 5 and 6 for the remaining columns
what is -3+4p= -31
thankyou
Answer:-32
Step-by-step explanation:
p=-32
7Answer:
-7
-Step-by-step explanation:
Angie puts 1/3 of a gallon of gas in her lawn mower. she can mow the lawn 4 times before she needs to refill it. how many gallons of gas does it take to mow the lawn once? How many times can she mow the lawn with one gallon of gas
Answer:
To mow the lawn once, it takes 1/12 gallon.
She can mow the lawn 12 times with 1 gallon.
Step-by-step explanation:
Terry used 14 yards of fabric to make flags for one-third of the drill team. How much fabric, would terry need to make flags for the whole team?.
The fabric that Terry need to make flags for the whole team will be 42 yards.
How to illustrate the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
In this case, Terry used 14 yards of fabric to make flags for one-third of the drill team and we want to know the fabric that Terry would need to make flags for the whole team.
The fabric that Terry need to make flags for the whole team will be the total yards of fabric divided by the fraction given. This will be:
= 14 ÷ 1/3.
= 14 × 3
= 42 yards
Therefore, 42 yards will be needed for the whole team.
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2. A bag of pennies weighs 5100 grams. Each penny weighs 2.5 grams. How many pennies are in
the bag?
Answer: Divide
Step-by-step explanation: (Don't look at this if you are taking a test) :)
Hello! What you do to answer this question is divide 5100 grams by 2.5 grams. You would do this because you want to divide the weight of all the pennies by the weight of a single penny to find the number of pennies. This is because number of pennies multiplied by 2.5 grams (weight of a penny) = 5100 grams (weight of all pennies). You will be able to figure out what the answer is by dividing 5100 by 2.5.
I will give you an example problem if you need help dividing decimals:
3000/1.5
Move the decimal space over one to get 3000/15
15 √3000
30 divided by 15 is 2
2
15√3000
15 x 2 = 30
200
15 √3000
- 30 bring down two zeroes
__________________
000
Since there are two extra zeroes that you took, down your answer is 200. Since you already moved the decimal space one space to the right, move it to the right again and you will get 2000. Your answer for the example problem is 2000.
Prove the property a × b = − b × a of this theorem.
Let a= (a1, a2, a3) and b= (b1, b2, b3)
Then,
a × b = xxxxx
= (−1) * xxxx
= − b × a.
Fill in for the italic x's
The property states that when two vectors a and b are multiplied together, the result is equal to the negative of b multiplied by a. This can be shown by multiplying the components of both vectors and then multiplying the result by -1.
a×b = (a2*b3 - a3*b2, a3*b1 - a1*b3, a1*b2 - a2*b1)
= (a2*b3 - a3*b2, a3*b1 - a1*b3, a1*b2 - a2*b1)
= (−1) * (a2*b3 - a3*b2, a3*b1 - a1*b3, a1*b2 - a2*b1)
= (−1) * (b2*a3 - b3*a2, b3*a1 - b1*a3, b1*a2 - b2*a1)
= − b × a.
The property a × b = − b × a states that when two vectors a and b are multiplied, the result is equal to the negative of b multiplied by a. This can be proven by first expanding the components of both vectors. For a vector a=(a1,a2,a3) and b=(b1,b2,b3), the expanded form of a×b is (a2*b3 - a3*b2, a3*b1 - a1*b3, a1*b2 - a2*b1). This can then be multiplied by -1 to get the expanded form of -b×a, which is (b2*a3 - b3*a2, b3*a1 - b1*a3, b1*a2 - b2*a1). Since this is equal to the original form of a×b, this proves the property.
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Write The equation of a line which is
Parallel to y=3x+2
Parallel to 2y+5x-1=0
Perpendicular to y=-2x+1 and passes through the point (4,-3)
The equation x = 77 can be found on the line perpendicular to the y-axis that passes through the coordinates (77,88).
Write the equation of a line ?The equation of the line passing through the point (2,4) and perpendicular to the line y= 1/3 x+6 is y = 3x - 2.The slope of the line connecting the coordinates (1, 4), (1, 3) is not known.
The graph is shown below, and the line's equation is x = -1.The equation of a line in slope-intercept form is:y = mx + cwhere the slope is m
C is the y-intercept.For the line that passes through the point and is perpendicular to the y-axis (77, 88)The slope is infinite and the equation is of the form x = k because the line is parallel to the y-axis.
Line that is perpendicular to the line has the equation y= 1/3 x+6 through the location (2,4). Line perpendicular to y= 1/3 x+6 has a slope of m = 3.
y - y1 = m is the equation of a line in point-slope form (x- x1)
y= -4 = 3(x-2) (x-2)
y= 3x - 6 +4\sy= 3x -2
Calculate m= -3 -4 /-1- to determine the slope of the line going through the points (1, 4), (1, 3). (1)
M is endless.Undefined is the slope of the line.x = -1 is the line's equation.As a result, x = 77 is the equation of the line parallel to the y-axis passing through the coordinates (77,88).
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evaluate the double integral. 6y 4x5 + 1 da, d = {(x, y) | 0 ≤ x ≤ 1, 0 ≤ y ≤ x2} d
The double integral of 6y * 4x^5 + 1 over the region D = {(x, y) | 0 ≤ x ≤ 1, 0 ≤ y ≤ x^2} is 20/3
A double integral is used to calculate the total amount of a quantity that is distributed over a two-dimensional region. In this case, the quantity being integrated is 6y*4x^5 + 1. To evaluate the integral, we need to integrate with respect to x and y.
The first step is to evaluate the inner integral with respect to y. The limits of integration for y are 0 and x^2.
∫(6y4x^5 + 1) dy from 0 to x^2 = ∫(6y4x^5) dy + ∫1 dy = [6/7y^74x^5] from 0 to x^2 + [y] from 0 to x^2 = (6/7)x^5x^2 + x^2 = (6/7)*x^7 + x^2The second step is to evaluate the outer integral with respect to x. The limits of integration for x are 0 and 1.
∫((6/7)*x^7 + x^2) dx from 0 to 1 = [x^8/7 + x^3/3] from 0 to 1 = 1/7 + 1/3 = 20/21 + 10/21 = 30/21 = 20/3Therefore, the double integral of 6y*4x^5 + 1 over the region D = {(x, y) | 0 ≤ x ≤ 1, 0 ≤ y ≤ x^2} is 20/3.
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9 Emily was given $600 for her high school graduation. She invested it in
an account that earns 2.4% interest per year. If she does not make any
deposits or withdrawals, which expression can be used to determine the
amount of money that will be in the account after 4 years?
The expression that can be used to determine the amount of money that will be in the account after 4 years is 600 + (600 × 2.4% × 4).
How to illustrate the expression?An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. in this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.
In this case, Emily was given $600 for her high school graduation. She invested it in an account that earns 2.4% interest per year
The expression to find the amount of money will be:
600 + (600 × 2.4% × 4)
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Which dot plot corresponds to the values in the table?
A dot plot that corresponds to the values in the table include the following: dot plot B.
What is a dot plot?In Mathematics, a dot plot can be defined as a type of line plot that is typically used for the graphical representation of a data set above a number line, especially through the use of dots.
Based on the values contained in the table, the high school students' essays score on a scale of 0 to 10 should be plotted on a dot plot as follows:
An essay score of 3 would have 1 dot.
An essay score of 4 would have 1 dot.
An essay score of 5 would have 2 dots.
An essay score of 6 would have 5 dots.
An essay score of 7 would have 4 dots.
An essay score of 8 would have 7 dots.
An essay score of 9 would have 3 dots.
An essay score of 10 would have 2 dots.
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What are the properties of a logarithmic graph?
A logarithmic graph has a curved shape, with its vertical axis increasing exponentially, and its horizontal axis increasing in a logarithmic scale. The graph is useful for plotting data with a wide range of values, as it can be used to compress the data into a smaller range.
A logarithmic graph is a type of graph that is used to represent data with a wide range of values. It has a curved shape, with its vertical axis increasing exponentially and its horizontal axis increasing in a logarithmic scale. This scale compresses the data into a smaller range, which makes it easier to visualize and compare values that span a large range. It is useful for plotting data that grows or decreases exponentially, such as population growth or exponential decay. Logarithmic graphs are also used to graph values that have a very large range, such as the size of galaxies. The graph helps to compress the data into a smaller range, making it easier to visualize and compare values.
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HELPPPPPP PLEASEeeeeeeeeeeeeee
As a result, you are turning the entire trapezium figure 90 degrees clockwise in order to change the trapezoid LMNQ into L′M′NQ′.
The trapezoid is what?In American and Canadian English, a trapezoid is a quadrilateral with at least one set of parallel sides. In British and other versions of English, the word is a trapezium. A trapezoid is always a convex quadrilateral in Euclidean geometry. The parallel sides of the trapezoid are referred to as its bases.
Given: When (-7,-2) to L, L becomes L' (-2,7)
You will often obtain a rotation of 90 degrees clockwise or 270 degrees counterclockwise around the origin (0,0), as well as a reflection across the x-axis and across the line of symmetry of the image, if you have (x,y) and it becomes (y,-x).
The entire graphic is therefore rotated 90 degrees in a clockwise orientation.
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Last season, the Eagles scored seven less than twice the number of touchdowns that the Cowboys scored. If the two teams scored 71 touchdowns combined, how many did the Eagles score?
The number of scores by the Eagles is 45.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Cowboys scores = x
Eagles scores = y
y = 2x - 7 _____(1)
Now,
x + y = 71 ______(2)
From (1) and (2) we get,
x + 2x - 7 = 71
3x - 7 = 71
3x = 71 + 7
3x = 78
x = 26
Now,
y = 2x - 7
y = 2 x 26 - 7
y = 52 - 7
y = 45
Thus,
The eagles scored 45.
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At the beginning of the year, Valeria had $20 in savings and saved an additional $15 each week thereafter. Jackson started the year with $70 and saved $5 every
week. Let V represent the amount of money Valeria has saved t weeks after the beginning of the year and let J represent the amount of money Jackson has saved t
weeks after the beginning of the year. Graph each function and determine at what week do Valeria ands Jackson have the same amount of money?
A graph of each function is shown in the image attached below.
The number of weeks after which Valeria and Jackson would have the same amount of money is 5 weeks.
How to write and solve the equation graphically?In order to graphically solve the equation, we would write an equation that models the situation by assigning variables to the amount of money Valeria and Jackson have saved respectively, and then translate the word problem into algebraic equation as follows:
Let the variable V represent the amount of money Valeria has saved t weeks after.Let the variable J represent the amount of money Jackson has saved t weeks after.Since Valeria had $20 in savings and saved an additional $15 each week at the beginning of the year, an equation which models this situation is given by;
T = 15V + 20
Since Jackson had $70 in savings and saved an additional $5 each week at the beginning of the year, an equation which models this situation is given by;
T = 5J + 70
Next, we would use an online graphing calculator to plot the above system of equations with a point of intersection at (5, 95) as shown in the image attached below.
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Find the area between the graph of y=x^2-2 and the x-axis, between x=0 and x=7.
Round your answer to 3 decimal places.
45.500 square units make up the region between the graph of y=x2-2 and the x-axis between x=0 and x=7.
The area between the graph of y=x^2-2 and the x-axis between x=0 and x=7 is calculated by first finding the area beneath the graph. This can be done by using the formula
A = ∫f(x)dx.
This integral is equal to
A = ∫(x^2-2)dx,
which when solved yields
A = (x^3/3)-2x.
Plugging in the values for x=0 and x=7 yields
A = (343/3)-(14)= 45.500.
To find the area between the graph and the x-axis, we subtract the area beneath the x-axis from the area beneath the graph. The area beneath the x-axis is 0, so the final answer is 45.500.This area is calculated by finding the area beneath the graph and subtracting the area beneath the x-axis.
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Two students, Ai Mi and Malika, line up one behind the other. How
many different ways can they stand in line?
Answer:
Submit Answer
FOU
attempt 1 out of 2
Answer:
2
Step-by-step explanation:
Say that 1 represents Ai Mi and 2 represents Malika. It could go like 1 2 or 2 1. Because there is only two of them, there isn't any other way that they could stand. Hope this helps!
calculate the average value of f(x) = 8x sec2(x) on the interval [0, π/4].
The average value of f(x) = 8x sec^2(x) on the interval [0, π/4] is -4/3.
To find the average value of a function f(x) on an interval [a, b], we need to evaluate the definite integral of the function over that interval and divide it by the length of the interval.
The definite integral of f(x) = 8x sec^2(x) over the interval [0, π/4] is given by:
∫[0,π/4] 8x sec^2(x) dx
This integral can be evaluated by substitution. Let u = sec(x) and du = sec(x)tan(x)dxmthen the integral becomes:
∫[0,π/4] 8x sec^2(x) dx = ∫[1,sec(π/4)] 8xu^2du
= 8/3u^3 evaluated at u = sec(π/4) - 8/3u^3 evaluated at u = 1
= 8/3sec^3(π/4) - 8/3 = 8/3(1/cos^3(π/4)) - 8/3 = 8/3*(1/1/2) - 8/3 = 4/3 - 8/3 = -4/3
Thus, The average value of f(x) = 8x sec^2(x) on the interval [0, π/4] is -4/3.
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A coordinate grid with 2 lines. The first line is labeled y equals negative StartFraction 7 over 4 EndFraction x plus StartFraction 5 over 2 EndFraction and passes through the (0, 2.5) and (2.2, negative 1.4). The second line is labeled y equals StartFraction 3 over 4 EndFraction x minus 3 and passes through (0, negative 3, 0.14) and (2.2, negative 1.4)
Which is the best approximate solution of the system of linear equations y = 1.5x – 1 and y = 1?
The solution of the system of linear equations are,
1) (2.2, -1.4).
2) (1.33, 1)
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Here, We have to given that;
Two lines, with their corresponding equations are given and we have to find the solution to the system of equations.
The given lines are:
Equation of Line 1 is,
⇒ y = - 7/4x + 5/2
And, This line passes through the points (0, 2.5) and (2.2, -1.4).
Equation of Line 2 is,
⇒ y = 3/4x - 3
And, This line passes through the points (0, -3) , (2.2, -1.4)
By looking at the graph/given data we have to find the solution of these linear equations as;
Remember that the solution of linear equations is an ordered pair, through which both the lines pass i.e. the point at which both the given lines intersect is the solution of the linear equations.
So, From the given data we can see that both the lines pass through one common point, (2.2, -1.4).
Since, both lines pass through this point, this means this is the point of intersection of the lines and hence there solution.
So, The answer to this questions is (2.2, -1.4)
For the second question;
The given equations are:
⇒ y = 1.5x - 1 .. (i)
⇒ y = 1 .. (ii)
Now, We can solve these equations by method of substitution.
So, Substituting the value of y from Equation 2, in Equation 1, we get:
1 = 1.5x - 1
1 + 1 = 1.5x
2 = 1.5x
x = 2/1.5
x = 1.33
And, y = 1
Thus, The solution of the given linear equations is, (1.33, 1)
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hurry please and thank you #3
Looking at the triangles in the figure, the difference in the x coordinates of points Q and R is 10
What are similar triangles?This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent
Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions
Examining the figure shows that pair of equivalent sides are
ST and QR, UT and SR.
The solution is worked out using sides ST and QR, UT and SR.
ST / QR = UT / SR
5 / QR = 3 / (4 - (-2))
5 / QR = 3 / 6
cross multiplying
3 * QR = 30
QR = 10
hence QR = 10
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Geometry find length of third side help
The length of the third side of the triangle is 10 units long.
What is Pythagorean theorem in Euclidean geometry?In mathematics, the Pythagorean theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.Mathematically -(base)² + (perpendicular)² = (hypotenuse)²
Given is a right angle triangle.
We can write -
(base)² + (perpendicular)² = (hypotenuse)²
(√51)² + (7)² = (hypotenuse)²
(hypotenuse)² = 49 + 51
(hypotenuse)² = 100
(hypotenuse) = 10
Therefore, the length of the third side of the triangle is 10 units long.
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find the general solution of the given system. dx dt = 4x + 5y dy dt = 10x + 9y
The general solution will be y(t) = (4c1 + 5c2)*e^((2+sqrt(5))t) + (10c1 + 9c2)*e^((2-sqrt(5))t).
What is differentiate ?
Differentiation is a concept in calculus that involves finding the rate of change of a function with respect to one of its variables. It is represented by the symbol ∂/∂x or ∂/∂y or ∂/∂t (where x, y and t are the variables of the function). The process of differentiation allows us to find the slope of a curve, the instantaneous rate of change, and the maximum or minimum points of a function.
The general solution of the system of differential equations dx/dt = 4x + 5y and dy/dt = 10x + 9y is given by ,
x(t) = c1e^((2+sqrt(5))t) + c2e^((2-sqrt(5))t)
y(t) = (4c1 + 5c2)*e^((2+sqrt(5))t) + (10c1 + 9c2)*e^((2-sqrt(5))t)
Where c1 and c2 are arbitrary constants determined by the initial conditions,
The general solution will be y(t) = (4c1 + 5c2)*e^((2+sqrt(5))t) + (10c1 + 9c2)*e^((2-sqrt(5))t).
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Please help me! Find the area of the figure. Round to nearest hundredth if nessary.
Answer:
140 square meters
Step-by-step explanation:
A= lw
A= 10 times 14 = 140
Kayla had 20 candies. Kayla have 1/5 of the candies to her sister. Of the amount left , she gave 3/8 of her friend. How many candies does Kayla have left for herself ?
10 candies treats is Kayla still keeping for herself when Kayla had twenty candies. Kayla gave her sister one-fifth of the candies.
Given that,
Kayla had twenty candies. Kayla gave her sister one-fifth of the sweets. She gave her pal 3/8 of the remaining funds.
We have to find how many treats is Kayla still keeping for herself.
We know that,
20 candies are in Kayla's candy collection.
The amount Kayla gave her sister was equal to 1/5 of 20.
= 1/5 ×20
= 4 candies
The number of sweets Kayla has left over after sharing them with her sister = 20-4 = 16 candies
From the leftover candies, the friend received 3/8 of 16 candies.
= 3/8 × 16
= 6 candies
Kayla has 16 candies left after subtracting 6 for herself.
= 10 candies.
Therefore, 10 candies treats is Kayla still keeping for herself when Kayla had twenty sweets. Kayla gave her sister one-fifth of the sweets.
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