Carmen scored 50%of the total number of items in second test, the number of items in the second test is, 75
What is the percentage?The percentage is a mathematical term, which means a number or a ratio which is represented in fractions of 100. We use the '%' symbol to represent the percentage.
Formula for percentage;
Percentage = (present quantity/whole quantity)×100
Given that,
In the first Summative Test,
Carmen scored 20 points which is 80% of the number of items
In the second test,
Carmen scored 30 points,
Her total score is 50% of the number of items
The total number of the items in the second test = ?
Suppose, total number of items in the first test = x
in the second test = y
⇒ 20 points = 80x/100
⇒ 20 points = 0.80x
⇒ x = 25
⇒ 0.5(x + y) = 20 + 50
⇒ x + y = 100
⇒ y = 75
Hence, the total number of items in the second test is 75
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what is the answer ??
If y varies inversely as x and y=9 when x=7, find y when x=6
If y varies inversely as x and y = 9 when x = 7, then the value of y = 10.5 when x = 6.
How do you find y when y varies inversely with x?If y fluctuates inversely of x, then y = kx, where k is a fixed value. According to the expressions "y varies inversely as x" and "y is inversely proportionate to x," y decreases as x increases or vice versa. There are two translations for this idea. For some constant k, referred to as the constant of proportionality, yx = k.
According to the expression "y varies inversely as x," y drops by the same amount that x grows. In other terms, xy = k means that the equation xy is constant.
Let the equation be x = k/y, then k be a constant
[tex]$$\begin{aligned}& x=k \times \frac{1}{y} \\& \Rightarrow k=x y=9 \times 7=63 \\& \Rightarrow x=\frac{63}{y}\end{aligned}$$[/tex]
So [tex]$y=\frac{63}{x}$[/tex]
At x = 6 we have
[tex]$y=\frac{63}{6}=10.5$$[/tex]
If y varies inversely as x and y = 9 when x = 7, then the value of y = 10.5 when x = 6.
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Which statements are true for the following expression? (11 + 7)(8 + 7) + (2 + 9) Check all that are true. All factors are the sum of two terms. 40 The solution is the sum of three terms. 40 It is not possible to find a solution. 4 The solution is the product of two factors, plus another number: 4 The solution is the difference between three terms.
Answer:
All of the following statements are true for the expression (11 + 7)(8 + 7) + (2 + 9): all factors are the sum of two terms, the solution is the sum of three terms, the solution is the product of two factors, plus another number, and the solution is the difference between three terms.
give me brainiest
What is a property of all rectangles? A. A rectangle only has two right angles. B. The opposite sides of a rectangle are parallel. C. The diagonals of a rectangle do not have equal length. D. The four sides of a rectangle have equal length.
Answer:
The answer would be B
Step-by-step explanation:
integer numstudents and doubles firststudent and laststudent are read from input. first, declare a vector of doubles named swimminglogs with a size of numstudents. then, initialize the first and last element in swimminglogs to firststudent and laststudent, respectively. ex: if the input is 10 10.88 92.42, then the output is: 10.88 0 0 0 0 0 0 0 0 92.42
Declare a vector of doubles named swimming logs with size of num students. Initialize first element to first student and last element to last student. Fill the middle elements with zeros.
Firstly, declare a vector of doubles named swimming logs with a size of num students. This is done by writing "vector swimming logs(num students);". This creates a vector with the size specified by num students, which can be read from input.
Next, initialize the first element of the vector to first student. This is done by writing "swimming logs[0] = first student;". This sets the first element of the vector to the value of first student, which can be read from input.
Then, initialize the last element of the vector to last student. This is done by writing "swimming logs[num students - 1] = last student;". This sets the last element of the vector to the value of last student, which can be read from input.
Finally, fill the middle elements of the vector with zeros. This is done by writing "for (int i = 1; i < num students - 1; i++) { swimming logs[i] = 0; }". This loop iterates from the second element to the second last element of the vector, setting each element to 0. This completes the initialization of swimming logs with the specified values.
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A right triangle has one interior angle that measures 38% Which of these is the measure of a different interior angle of the triangle?
The measure of a different interior angle of the triangle is 52 degrees.
What is the measure of the missing interior angle ?A right angled triangle is a triangle with one of the angles as 90 degrees.
The sum of the interior angle of a triangle is 180 degrees.
Given the data in the question;
Measure of angle a = 38 degreeMeasure of angle b = ?Measure of angle c = 90 degreeSince the sum of the interior angle of a triangle is 180 degrees.
Angle a + Angle b + Angle c = 180
38 + Angle b + 90 = 180
Angle b + 128 = 180
Angle b = 180 - 128
Angle b = 52 degrees.
Therefore, the measure of the second angle is 52 degrees.
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A bus company usually transports 12 000 people
per day at a ticket price of $1. The company
wants to raise the ticket price. For every $0.10
increase in the ticket price, the number of riders
per day is expected to decrease by 400. Calculate
the ticket price that will maximize revenue.
If a bus company usually transports 12 000 people per day at a ticket price of $1. The ticket price that will maximize revenue is $2 per ticket.
How to find the ticket price that will maximize revenue?Equation to find the ticket price is:
y = (12000 - 400x)(1 + .1x)
Take the derivative of the function by product rule
y' = (12000 - 400x)(.1) + (-400)(1 + .1x)
y' = 1200 - 40x - 400 - 40x
y' = 800 - 80x
Let y' = 0
0 = 800 - 80x
Solving for x
80x = 800
Divide both side by 80x
x = 800/80
x = 10
Point at x = 10
Substitute x with 10 for 1 + .1x
1 + .1(10)
= 1 + 1
= $2 per ticket
Therefore the ticket price is $2 per ticket.
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Problem 4.1
A tank of water breaks and begins draining at a constant rate.
Complete the table.
Time (minutes)
Change in Water
(liters)
Expression
Water in the Tank
(liters)
The table is completed as follows:
Time of 2 minutes, change of -14 liters, expression 770 + 2(-14), water is 742 liters.Time of 3 minutes, change of -14 liters, expression 770 + 3(-14), water is 728 liters.How to model the situation?The situation is modeled by a linear function, in slope-intercept format, as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change.b is the y-intercept, representing the initial capacity.The initial capacity is of 770 liters, decaying by 14 liters each minute, hence the parameters are given as follows:
b = 770, m = -14.
The function for this problem is defined as follows:
y = -14x + 770.
The numeric values are given as follows:
x = 2: y = -14(2) + 770 = 742 liters.x = 3: y = -14(3) + 770 = 728 liters.Missing InformationThe table is given by the image presented at the end of the answer.
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13. Solve for x. Please help
Answer:
x = 15
Step-by-step explanation:
The sum of the four angles of a quadrilateral add up top 360°
Given:
m∠A = (5x+14)°
m∠b = 109°
m∠C = (3x+8)°
m∠D = 109°°
Here we are given actual values for two angles as 109°. Their sum is: 109 + 109 = 218°
The sum of the remaining two angles which are expressions in x should be:
360 - 218 = 142°
This is the sum of m∠A an m∠C
Substituting the terms for the two angle measures we get
(5x+14) + (3x+8) = 142
5x+14 + 3x+8 = 142
Grouping like terms:
5x + 3x + 14 + 8 = 142
8x + 22 = 142
8x = 142- 22
8x = 120
x = 120/4
x = 15
A simple harmonic oscillator consists of a block of mass 2.00kg attached to a spring of spring constant 100N/m. When t=1.00s, the position and velocity of the block are x=0.129m and v=3.415m/s. (a) What is the amplitude of the oscillations? What were the (b) position and (c) velocity of the block at t=0s?
The oscillations have an amplitude of 0.129 m. The block is positioned at 0m and moving at 0m/s at time t=0s.
The maximum deflection of a simple harmonic oscillator from its equilibrium position is its amplitude. Since this is the displacement at time t=1.00s, the oscillations in this instance have an amplitude of 0.129m. The oscillator is in equilibrium at time t=0 s, therefore the block is located at location 0 m. Additionally, since the oscillator has not yet begun to move, these values can be determined by examining the oscillator's equation of motion. According to this equation, the oscillator's position is determined by the expression x=A*cos(t), where A stands for amplitude and for angular frequency. The equation becomes simpler to x=0m for A=0.129m and t=0s. Similar to that, v=-Asin(t) gives the velocity. The equation is again simplified to v=0m/s as A=0.129m and t=0s.
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In AQRS, m
angle, then classify AQRS by its angles.
Classify:
m
m
m
Using Angle Sum property, the measure of 3 angles is ∠Q = 35°, ∠R = 19°, ∠S = 126°.
According to the triangle's "angle sum property," a triangle's angles add up to 180 degrees. Three sides and three angles, one at each vertex, make up a triangle. The sum of the interior angles in a triangle is always 180o, regardless of whether it is acute, obtuse, or right.
One of the most commonly applied properties in geometry is the triangle's angle sum property. Most often, the unknown angles are calculated using this attribute.
As given the measure of 3 angles is -
∠Q = 4x - 17
∠R = x + 6
∠S = 10x - 4
We know that by angle - sum property,
The sum of 3 angles of triangle = 180°
⇒ 4x - 17 + x + 6 + 10x - 4 = 180
⇒ 15x -15 = 180
⇒ 15x = 180 + 15
⇒ 15x = 195
⇒ x = 13
∠Q = 4x - 17 = 4 × 13 - 17 = 35°
∠R = x + 6 = 13 + 6 = 19°
∠S = 10x - 4 = 10 × 13 - 4 = 126°
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Complete question -
two-finger morra is a game in which two players each hold up one or two fingers. the payoff, in dollars, is the total number of fingers shown. r receives the payoff if the total is even, and c receives the payoff if the total is odd. write the payoff matrix.
Payoff matrix: R (row player) receives payoff if total number of fingers shown is even, C (column player) receives payoff if total number of fingers shown is odd.
Two-finger morra is a game in which two players take turns holding up either one or two fingers. The payoff for the game is the total number of fingers shown, with the player whose total is even (R) receiving the payoff, and the player whose total is odd (C) receiving the payoff. This game can be represented in a payoff matrix, which is a table that shows the payoffs for each player in each possible situation. For two-finger morra, the payoff matrix would have two rows and two columns, representing the two players, R and C. The top row would show the payoffs for R when the total number of fingers is even, and the bottom row would show the payoffs for R when the total number of fingers is odd. Similarly, the left column would show the payoffs for C when the total number of fingers is even and the right column would show the payoffs for C when the total number of fingers is odd.
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3. Marcus makes $3,000 each month. He pays a total of 28% in taxes and 5% for *
retirement
Retirement
Net Monthly
Income
Taxes
Gross monthly
income
$3,000
оооо
$840
ооос
$150
оооо
$2,010
о
Help
The amount you make each month before taxes and other deductions is known as your monthly gross income so monthly gross income is 3000.
What is net income?Marcus makes $3,000 each month. He pays a total of 28% in taxes and 5% for
It's rather easy to figure out net income. Simply deduct expenses like taxes, insurance, and retirement contributions from your gross income, which is the entire amount of money you have made. Deductions from gross income equal net income.
Gross income – deductions = net income.
3000 - 840 - 150 = 2010.
The amount you make each month before taxes and other deductions is known as your monthly gross income. In other words, it is your annual income divided by 12.
monthly gross income = 3000.
The amount you make each month before taxes and other deductions is known as your monthly gross income so monthly gross income is 3000.
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based on the information in the graphic, which of the following claims would an opponent to the decision in citizens united v. federal elections commission (2010) most likely make? choose 1 answer:
The opponent to Citizens United v. Federal Elections Commission (2010) would most likely argue that corporate and special interest influence in elections should be limited to prevent corruption and maintain a fair and level playing field for all candidates.
The opponent to Citizens United v. Federal Elections Commission (2010) would most likely argue that the decision to allow unrestricted corporate and special interest spending in elections has had a negative impact on the integrity of the democratic process. They would point to the increased influence of money in politics and the dangers of corruption that come with it. They would argue that the decision has allowed wealthy entities to have an outsized influence in elections, creating an unfair and unequal playing field for candidates. Furthermore, they would argue that the decision has weakened the regulation of campaign spending and has allowed for the creation of so-called "dark money" groups, which can spend money on elections with little to no transparency. In short, the opponent to Citizens United v. Federal Elections Commission (2010) would argue that allowing unlimited corporate and special interest spending in elections has created an unequal playing field and should be limited in order to protect the integrity of the democratic process.
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Simplify the expression. Assume that the denominator does not equal zero.Write any variables in alphabetical order.
12m−3n62m−7n
The simplified expression is 14m -10n
How to simplify the expressionFrom the question, we have the following parameters that can be used in our computation:
12m−3n62m−7n
Express properly
So, we have the following representation
12m - 3n + 2m - 7n
Collect the like terms
This gives
12m + 2m - 3n - 7n
Evaluate the like terms
So, we have the following representation
14m - 10n
Hence, the solution is 14m - 10n
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A cell phone carrier charges a fixed monthly fee plus a constant rate for each minute used.
Part 1. In January, the total cost for 100 minutes was $47 while in February, the total cost for 350 minutes
was $52. The constant charge for each minute used is:
O 0.02
O 0.04
O 0.03
The required constant charge for each minute used is $0.02.
What is linear equation of two variable?Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions. For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.
According to question:Let fixed charge of monthly be x and constant rate of each minute used is y.
So,
In january
x + 100y = 47--------(1)
and in February
x + 350y = 52-----------(2)
equation(2) - equation(1)
(x + 350y) - (x + 100y) = 52 -47
250y = 5
y = 0.02
Thus, $0.02 used per minutes.
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Mr. Williams pays $40 a month for city
water, no matter how many gallons of water he uses in
a given month. Let x represent the number of gallons
of water used per month. Let y represent the monthly
cost of the city water in dollars. What is the equation
of the line that represents this information? What is
the slope of the line?
y = $40 is the equation of the line that represents the information. The line has no slope.
What is the equation and the slope?A linear equation can be used to represent the equation that represents Mr. Williams' total payment for city water. A linear equation is one that is composed of a single variable raised to the power of one.
A linear equation takes the following form:
y = ax + b
Where: a = slope = which measures the equation's rate of change
b = the intercept
y = $40 + (x × 0)
y = $40
A linear equation can have an upward, downward, or zero slope when plotted on a graph.
The equation of the line that represents the information is y = $40. There is no slope to the line.
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how to find the anser to 1999+888999
890998
Step-by-step explanation:
1999+888999 = 890998
Find the missing coordinate to complete the ordered pair for the equation 3x- 4y = 12: When the following are given (0, ?) and (?, 3)
The missing coordinates on the ordered pairs of the linear equation are:
(0, -4) and (8, 3)
How to find the missing coordinates?Here we have the linear equation:
3x - 4y = 12
And we want to find the missing coordinates for the given points (0, ?) and (?, 3) where these points belong to the line.
The first point is (0, ?), this means that the value of x is zero, then we can evaluate the equation in x = 0 then we will get:
3*0 - 4y = 12
-4y = 12
y = 12/-3 = -4
So the point is (0, -4)
For the other point (?, 3) we need to evaluate in y = 3.
3*x - 4*3 12
3x - 12 = 12
3x = 12 + 12
3x = 24
x = 24/3 = 8
So we have the point (8, 3)
These are the missing coordinates.
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objects a and b are both positively charged. both have a mass of 300 g , but a has twice the charge of b. when a and b are placed 50 cm apart, b experiences an electric force of 0.38 n . part a what is the charge on a? express your answer to two significant figures and include the appropriate units.
The charge on the object a is 0.00017 micro Coulombs (0.00017 μC) to two significant figures.
The electric force between two objects is given by Coulomb's law: F = k[tex]q_1[/tex][tex]q_2[/tex] /[tex]r^2[/tex], where k is the Coulomb constant, [tex]q_1[/tex]and [tex]q_2[/tex] are the charges of the two objects, and r is the distance between them.
We have , [tex]q_2[/tex] = b
r = 50cm = 0.5m
k = 9 x [tex]10^9[/tex] [tex]Nm^2/C^2[/tex]
We know that b has a mass of 300 g and that a has twice the charge of b. So we can substitute these values and solve for [tex]q_1[/tex]:
[tex]q_1[/tex]= 2 * [tex]q_2[/tex]
[tex]q_2[/tex] = 0.38 N * [tex]0.5^2[/tex] / k
Substituting the values in Coulomb's law we get,
[tex]F = k q_1 q_2/r^2[/tex]
0.38 N = k * [tex]q_1[/tex] * [tex]q_2[/tex] / [tex]0.5^2[/tex]
[tex]q_2[/tex] = 0.38 N * [tex]0.5^2[/tex] / (9 x [tex]10^9[/tex])
[tex]q_2[/tex] = 0.00085 * [tex]10^{-6}[/tex]
then we can multiply [tex]q_2[/tex] by 2 to find the charge on object a:
[tex]q_1[/tex] = 2 * [tex]q_2[/tex]
[tex]q_1[/tex]= 0.00017 x [tex]10^{-6}[/tex] C
So, the charge on the object a is 0.00017 micro Coulombs (0.00017 μC) to two significant figures.
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A triangle has a perimeter of 11ft. Side b is twice as long as side a. Side c is 3 more than side a.
What is the length of each side?
The length of sides a,b and c of triangle are 2, 4 and 5 respectively whereas the perimeter is 11ft.
A perimeter is defined.A one-dimensional length, a two-dimensional shape, or both can have perimeters that are closed paths that contain, surround, or define them. A circle's or an ellipse's perimeter is measured by its circumference.
The perimeter calculation has a lot of useful applications. Calculated perimeter is the term used to describe the size of fence required to completely surround a yard or garden. How far a wheel or circle can go in one spin is determined by its circumference, which measures its perimeter. Similar to this, a spool's circumference is inversely related to the length of thread that is wound around it; if the string were exactly the same length, the circumference would be equal.
Given that
b = 2a
c = 3 +a
We know that the perimeter is equal to the sum of all the sides
Perimeter = a+b +c
11 = a +2a + a+3
8 = 4a
a = 2
Hence, sides a ,b and c are 2, 4, 5 respectively.
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If the equation of the function f(x) is written in standard form f(x) = ax2 + bx + c, what is the value of b?
03
06
O 16
O 22
Answer: b is the coefficient of the x term. In the standard form f(x) = ax^2 + bx + c, b is the value of the coefficient of the x term. So the value of b is 0.
Step-by-step explanation:
The value of b in the given function is 12.
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
For example, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
Given that, a table defining the function, we need to form an equation and compare with the standard form of a quadratic function,
We can use the vertex form of a quadratic function, which is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.
Since, we know the vertex of this parabola from the table, we can use that information to write the equation in vertex form: f(x) = a(x + 6)^2 + 8
Expanding this, we get f(x) = a(x² + 12x + 36) + 8
Comparing this with the standard form, we see that a = 1, b = 12, and c = 8.
Therefore, the value of b is 12.
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The complete question is :-
The table represents a quadratic function f(x). x f(x) −10 24 −9 17 −8 12 −7 9 −6 8 −5 9 −4 12 If the equation of the function f(x) is written in standard form f(x) = ax2 + bx + c, what is the value of b?
what is 1/5 of 99.
hwelp meh im confused
Answer:
19.8
Step-by-step explanation:
Answer:
Do 99 divided by 5
Step-by-step explanation:
Use cross multiplication
NO LINKS!!
Solve each equation. Be sure to check for extraneous solutions. Part 2
k. log₇(x + 12) + log₇(x + 1) = log₇(42)
l . log₄(x + 3) + 1 = 2log₄(x)
Answer:
k) x = 2
l) x = 6
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{8cm}\underline{Log laws}\\\\Product law:\quad\:$\log_axy=\log_ax + \log_ay$\\\\Power law:\quad\;\;\;\:$\log_ax^n=n\log_ax$\\\\Equality Law:\; If $\log_ax=\log_ay$ then $x=y$\\\\Same base as number:\;\;\;$\log_aa=1$\\$\end{minipage}}[/tex]
Part k[tex]\begin{aligned}\log_7(x + 12) + \log_7(x + 1) &= \log_7(42)\\\log_7\left[(x + 12)(x+1)\right]&= \log_7(42)\\(x + 12)(x+1)&=42\\x^2+13x+12&=42\\x^2+13x-30&=0\\x^2+15x-2x-30&=0\\x(x+15)-2(x+15)&=0\\(x-2)(x+15)&=0\\\\\implies x&=2\\\implies x&=-15\end{aligned}[/tex]
As logs of negative numbers cannot be taken, x = -15 is an extraneous solution. Therefore, the only valid solution is x = 2.
Part l[tex]\begin{aligned}\log_4(x + 3) + 1 &= 2\log_4(x)\\\log_4(x + 3) + \log_44 &= \log_4(x^2)\\\log_4\left[4(x + 3)\right] &= \log_4(x^2)\\4(x + 3)&=x^2\\4x+12&=x^2\\x^2-4x-12&=0\\x^2-6x+2x-12&=0\\x(x-6)+2(x-6)&=0\\(x+2)(x-6)&=0\\\\\implies x&=-2\\\implies x&=6\end{aligned}[/tex]
As logs of negative numbers cannot be taken, x = -2 is an extraneous solution. Therefore, the only valid solution is x = 6.
which of the following lists is in order from smallest to largest? 25%, 0.04, 0.04, 25%, , 0.04, 25% , 25%, 0.04
The order of the numbers from the smallest to the largest is: 0.04, 25%
What is increasing order?It can be said that the ascending or increasing order is the one where the values, elements or numbers of a group or set are ordered starting from the one with the smallest value to the one with the highest value of all.
Ordering the numbers from the smallest to the largest , we have:
25% is equal to 25/100 = 0.25, so 0.25 is largest than 0.04
0.04 < 0.25
0.04 < 25%
The correct option is:
0.04, 25% = correct order
25%, 0.04 = incorrect order
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3 Select the correct answer. Triangle is reflected across the y-axis and then dilated by a factor of centered at the origin. Which statement correctly describes the resulting image, triangle ? Image of right triangle ABC in a graph with vertices A (minus 4, minus 2), B (4, minus 2), and C (4, 4) A. Both the reflection and dilation preserve the side lengths and angles of triangle . B. The reflection preserves the side lengths and angles of triangle . The dilation preserves angles but not side lengths. C. The dilation preserves the side lengths and angles of triangle . The reflection does not preserve side lengths and angles. D. Neither the reflection nor the dilation preserves the side lengths and angles of triangle .
The reflection preserves the side lengths and angles of the triangle. The dilation preserves angles but not side lengths. Therefore, option B is the correct answer.
What is a dilation?Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image.
Given that, triangle is reflected across the y-axis and then dilated by a factor of centered at the origin.
The triangle ABC in a graph with vertices A (-4, -2), B (4, -2), and C (4, 4)
A reflection across the y-axis changes the coordinates of the triangle from (x, y) to (-x, y) without changing the side lengths and angles.
The dilation of the triangle by a factor an then centered at the origin increases the side length of the triangle but the angles in the triangle remain the same since the ratio of the sides before and after dilation are the same.
Therefore, option B is the correct answer.
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a square fountain in the center of a shopping mall has an area of (4x^2+12x+9)ft^2. The dimensions of the fountain are of the form cx + d, where c and d are whole numbers. Find an expression for the perimeter of the fountain. Find the perimeter when x=2 ft.
A. An expression for the perimeter of the fountain is 8x + 12 ft.
B. The perimeter when x=2 ft. is 28 ft
How do we determine the values?The area of the fountain is given as 4x^2 + 12x + 9 square feet. Since the fountain is a square, we know that the length and the width of the fountain are equal. This means that we can express the area of the fountain in the form of (cx + d)^2.
Expanding (cx + d)^2 gives:
(cx + d)^2 = cx^2 + 2cxd + d^2
We can equate this to the given area of the fountain:
cx^2 + 2cxd + d^2 = 4x^2 + 12x + 9
To find the expression for the perimeter of the fountain, we need to find the dimensions (length and width) of the fountain. This can be done by factoring the area expression:
4x^2 + 12x + 9 = (2x + 3)(2x + 3)
So the dimensions of the fountain are (2x + 3) ft
The perimeter of a square is the sum of all four sides, so we can find the perimeter of the fountain by multiplying the length of one side by 4:
Perimeter = 4(2x + 3) ft = 8x + 12 ft
When x = 2 ft, the perimeter of the fountain is:
8(2) + 12 = 28 ft
So when x = 2 ft, the perimeter of the fountain is 28 ft.
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Find the length of the arc of a circle of diameter 10
meters subtended by a central angle of π3
radians.
Round your answer to two decimal places.
The length of the arc of a circle with given radius and central angle is 5.23 meters.
What is the circle?A circle is a two-dimensional figure formed by a set of points that are at a constant or at a fixed distance (radius) from a fixed point (center) on the plane. The fixed point is called the origin or center of the circle and the fixed distance of the points from the origin is called the radius.
Given that, a circle of diameter 10 meters subtended by a central angle of π/3 radians or 60°.
We have, radius of a circle = 5 meters
We know that, arc length of a circle is θ/360° ×2πr
Now, 60°/360° ×2×3.14×5
= 1/6×2×3.14×5
= 5.23 meters
Therefore, the length of the arc of a circle with given radius and central angle is 5.23 meters.
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15% off of a total $41.10 what s discounted total price
Answer:
34.94
Step-by-step explanation:
Answer: 34.94
Step-by-step explanation:
What is the area of the shaded region below?
Step-by-step explanation:
the easiest way might be the approach to calculate the area of the whole rectangle and then subtract the area of the triangle.
the area of the whole rectangle is
18×16 = 288 m²
the area of a triangle is
baseline × height / 2
in a case like this (right-angled triangle) we can use one leg as baseline, and the other leg (90°) as height.
so, the height is the same as the width of the rectangle : 16 m.
how long is the baseline ?
it is on the 18 m length of the rectangle, and there are two 3 m "gaps", one left, and one right.
so, what's left for the baseline of the triangle itself ?
baseline = 18 - 3 - 3 = 12 m
therefore the area of the triangle is
12×16/2 = 12×8 = 96 m²
so, the total area of the shaded region is
288 - 96 = 192 m²