The same process is used to build an inscribed square and an inscribed regular hexagon: creating the circle.
A square that fits inside a specific shape and has sides that are perpendicular to it is said to be inscribed. The sides of the square that is inscribed are as long as they can be while still fitting entirely inside the provided shape and being perpendicular to it.
A regular hexagon that fits inside another shape so that its vertices contact it is called an inscribed regular hexagon. The sides of the inscribed hexagon are as long as they can be while still fitting entirely inside the predetermined shape and being perpendicular to it.
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Sara's past year at work pushed her to the limit, and she needs to recharge. She wants to splurge by spending 13 of his savings on a monster vacation. Her financial planner suggests that she spend less than $2500 on the vacation. Let x be the amount of money Sara has in savings. a) Write an inequality that best represents this situation. b) Solve the inequality for x. c) What does the value of x in part b represent in this situation.
An inequality that best represents this situation is: x - 1300 > 2500.
How to solve for the inequality?a) Let x be the amount of money Sara has in savings. We know that the amount she wants to spend on vacation is $1300, so we have x - 1300 > 2500.
b) To solve for x, we can add 1300 to both sides: x > 3800.
c) The value of x in this situation represents the amount of money Sara has in savings.
The inequality x > 3800 means that Sara must have more than $3800 in savings in order to spend $1300 on a vacation while following the financial planner's suggestion to spend less than $2500.
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Luke charges $14 per hour for washing cars. If f represents Luke's total fee after working for h hours, which equation can be used to model this situation? (hint: you can make your own table and use x for hours and y for fees)
Answer: f = 14h (f is total fee, h is the hour luke worked)
Step-by-step explanation:
-9s = 19
solve for s
Answer:
s= 19/-9
s≈-2.111
Step-by-step explanation:
s is being multiplied by -9
so, to get s by itself we divide both sides by -9
s= [tex]\frac{19}{-9}[/tex]
if you need it in decimal form, s≈-2.111
Apply the distributive property to factor out the greatest common factor. 12+80=12+80=12, plus, 80, equals.
The greatest common factor of 12 and 80 is 12, so we can use the distributive property to factor that out.
Identify the greatest common factor (GCF). In this case, it's 12.
Rewrite the expression so the GCF is outside of the parentheses. 12 + 80 = 12(1 + 80/12).
Simplify the expression inside the parentheses. 1 + 80/12 = 7.
Substitute the simplified expression back into the original equation. 12 + 80 = 12(7).
Simplify the expression. 12 + 80 = 84.
Therefore, 12 + 80 = 84 after applying the distributive property to factor out the greatest common factor of 12.
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.A polling organization announces that the proportion of American voters who favor congressional term limits is 64%, with a 95%
confidence margin of error of 3%. Which of the following statements is a correct interpretation of 95% confidence?
A. If the poll were conducted again in the same way, there is a 95% chance that the fraction of voters favoring term limits in the
second poll would be between 61% and 67%.
B. There is a 95% probability that the true percent of voters favoring term limits is between 61% and 67%.
C. If the poll were conducted again the same way, there is a 95% probability that the percent of voters favoring term limits in the
second poll would be within 3% of the percent favoring term limits in the first poll.
D. Among 95% of the voters, between 61% and 67% favor term limits.
E. None of the above.
!URGENT HELP! 100 points to any whom are willing ^-^
Explain how the complex conjugate root theorem applies to each of these polynomial functions:
- f(x) = x^2 − 9
- f(x) = = x^2 + 3x − 10
- f(x) = x^3 − 5x^2 + 10x − 8
The quadratic equation x² - 9 has two real roots.
The quadratic equation x² + 3 · x - 10 has two real roots.
The cubic equation x³ - 5 · x² + 10 · x - 8 has two complex conjugate roots and a real root.
How to determine if complex conjugate root theorem is applicable to quadratic equation
According to complex conjugate root theorem, if a quadratic equation has a root of the form a + i b, where a, b are real numbers, then the other root is a - i b. In addition, roots of quadratic equations of the form a · x² + b · x + c, where a, b, c are real coefficients. By quadratic formula, the equation has complex conjugate roots if:
b² + 4 · a · c < 0
Now we proceed to check each quadratic equations:
Case 1: (a = 1, b = 0, c = - 9)
D = 0² - 4 · 1 · (- 9)
D = 36
The equation has no complex conjugate roots.
Case 2: (a = 1, b = 3, c = - 10)
D = 3² - 4 · 1 · (- 10)
D = 9 + 40
D = 49
The equation has no complex conjugate roots.
The latter case is represented by a cubic equation, whose standard form is a · x³ + b · x² + c · x + d, where a, b, c, d are real coefficients. The equation has a real root and two complex conjugate roots if the following condition is met:
18 · a · b · c · d - 4 · b³ · d + b² · c² - 4 · a · c³ - 27 · a² · d² < 0
Now we proceed to find the nature of the roots of the polynomial: (a = 1, b = - 5, c = 10, d = - 8)
D = 18 · 1 · (- 5) · 10 · (- 8) - 4 · (- 5)³ · (- 8) + (- 5)² · 10² - 4 · 1 · 10³ - 27 · 1² · (- 8)²
D = - 28
The equation has a real root and two complex conjugate roots.
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Can anyone help me solve this problem step by step?
Step-by-step explanation:
to solve an equation with a variable we want to transform the equation, so that in the end we have the variable alone on one side of the equation, and everything else on the other side.
so, when we look at
(n + 8)/2 - 4 = 16
what blocks us from reading the value of n ?
several things on the left side.
I would start with the "- 4".
to get rid of that from the side of the variable we need to add 4. and to keep the equality true, we need to add this on both sides :
(n + 8)/2 - 4 + 4 = 16 + 4
and we get
(n + 8)/2 = 20
what blocks us now ?
I would say the fraction, this division by 2.
how do we get rid of that ?
by multiplying everything by 2 :
2×(n + 8)/2 = 2×20
and we get
n + 8 = 40
still, something is blocking us from reading the value of n : the "+ 8".
how do we get rid of that ?
by subtracting 8 from both sides :
n + 8 - 8 = 40 - 8
and we get
n = 32
that's it. we are finished. goal achieved.
An equation is shown below.
√−x=x+6 Which of these statements are true? Choose all that are correct. A.x=−9 satisfies the equation.
в. This equation has exactly one solution. c. This equation has the same solution set as−x=x2+12x+36. D. This equation has the same solution set as−x=x2+36. E.x=−4
Given quadratic equation has same solution set as -x=x²+12x+36 i.e. C.
Quadratic equations: what are they?A second-degree algebraic equation in x is a quadratic equation. Ax2 + bx + c = 0 is the quadratic equation in its standard form, with a and b acting as coefficients, x acting as the variable, and c acting as the constant term.
The coefficient of x2 must not be zero (a 0) for an equation to qualify as a quadratic equation. The x2 term comes first, followed by the x term, and finally the constant term when stating a quadratic equation in standard form. Instead of being written as fractions or decimals, the numerical values a, b, and c are frequently expressed as integral values.
Now,
Given equation is √-x=x+6
-x = (x+6)²
-x = x² +36+12x
x² + 11x + 36 = 0
As it is same quadratic equation as given in option C.
Hence,
Given quadratic equation has same solution set as
-x = x² + 12x + 36.
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Long division method square root of 5508409
Answer:
2347
2347 * 2347 = 5508409
Step-by-step explanation:
Hope it helps! =D
find the equation of the tangent line to the curve 3x3 3y2−11=4xy−x at the point (1,−1).
The equation of the tangent line to the curve 3x3, 3[tex]y^{2}[/tex] - 11 = 4xy - x at the point (1,−1) , then the slope = [tex]-\frac{3}{2}[/tex].
The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
A slope graph looks like a line graph, but with an important difference: there are only two data points for each line.
Given that,
The equation of the tangent line to the curve 3x3 ,
3[tex]y^{2}[/tex] - 11 = 4xy - x
3[tex]y^{2}[/tex] - 4xy + x - 11 = 0
Differentiate both side with respect to 'x'
6y [tex]\frac{dy}{dx}[/tex] - 4 ( x [tex]\frac{dy}{dx}[/tex] + y ) - 1 = 0
For slope at point ( 1 , -1 ) put x = 1 and y = -1
6(1) [tex]\frac{dy}{dx}[/tex] - 4 ( 1 [tex]\frac{dy}{dx}[/tex] - 1 ) -1 = 0
6 [tex]\frac{dy}{dx}[/tex] - 4 [tex]\frac{dy}{dx}[/tex] + 4 -1 = 0
2 [tex]\frac{dy}{dx}[/tex] + 3 = 0
2 [tex]\frac{dy}{dx}[/tex] = 0 - 3
2 [tex]\frac{dy}{dx}[/tex] = - 3
[tex]\frac{dy}{dx}[/tex] = -3/2
slope = [tex]-\frac{3}{2}[/tex]
Therefore,
The equation of the tangent line to the curve 3x3, 3[tex]y^{2}[/tex] - 11 = 4xy - x at the point (1,−1) , then the slope = [tex]-\frac{3}{2}[/tex].
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Which ordered pair a solution of the equation? -x-4y=-10
Answer:
-10+4=-x
-x_=-6_
x=6
if you don't understand
negative x over negative x and negative x over 6 the negative will cancle the negative you will get x to be 6
consider the function f(x,y) = x 2y, defined on d, i.e., the region bounded by the parabolas y= 2x2 and y= 1 x2. a. sketch the region din the x−yplane. b. evaluate the integral ∫∫ df(x,y)dxdy.
the integral by substituting the limits of integration for x and y and integrating with respect to x first. We get: ∫∫ df(x,y)dxdy = ∫-2 to 2 x2(1x2-2x2)dx = ∫-2 to 2 x2(-x2)dx = ∫-2 to 2 -x4dx = [-x5/5]from -2 to 2 = -2^5/5 + 2^5/5 = 0
a. The region D in the x-y plane is illustrated in the figure below.
b. ∫∫ df(x,y)dxdy = ∫-2 to 2 ∫2x2 to 1x2 x2(y)dxdy = ∫-2 to 2 x2(1x2-2x2)dx = ∫-2 to 2 x2(-x2)dx = ∫-2 to 2 -x4dx = [-x5/5]from -2 to 2 = -2^5/5 + 2^5/5 = 0
a. The region D in the x-y plane is the area bounded by the two parabolas y= 2x2 and y= 1 x2. This can be seen in the sketch below.
b. To evaluate the integral ∫∫ df(x,y)dxdy, we need to evaluate the integral of the function f(x,y) = x2y over the region D. We can do this by setting up the integral as follows:
∫∫ df(x,y)dxdy = ∫-2 to 2 ∫2x2 to 1x2 x2(y)dxdy
Next, we can evaluate the integral by substituting the limits of integration for x and y and integrating with respect to x first. We get:
∫∫ df(x,y)dxdy = ∫-2 to 2 x2(1x2-2x2)dx = ∫-2 to 2 x2(-x2)dx = ∫-2 to 2 -x4dx = [-x5/5]from -2 to 2 = -2^5/5 + 2^5/5 = 0
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PLEASE HELP IM BEGGING YOU PLEASE!!!
Dont worry I gotchu
Answer: 33.7°
help ill give brainless
Answer: c
Step-by-step explanation:
quite easy because y=mx+b (y=3x-1)
the -1 is the y-intercept. (Where the line meets the y line. c is the only one where the y-intercept is -1
It wa jake and am birthday. There were 26 preent. Jake an am wanted to plit them evenly but didnt know how. Can you help them
we have 4 women and 5 men and want to create a committee with 2 women and 2 men. in how many ways we can do this? a.6 b.10 c.30 d.60
The number of unique committees is 240 / 4 = 60. So the answer is d. 60.
What is the combination?
The permutation is to select an object and then arrange it and it cares about the orders while Combination is about only selecting an object without caring about the orders.
To form a committee with 2 women and 2 men, we have 4 choices for the first woman, 3 choices for the second woman, 5 choices for the first man, and 4 choices for the second man.
Therefore, the number of ways to form a committee is 4 * 3 * 5 * 4 = 240. This is the total number of combinations, and to find the number of unique committees,
we need to divide by the number of ways to arrange the members within each committee.
As the members are distinguishable, the number of arrangements is simply 2! * 2! = 4.
Therefore, the number of unique committees is 240 / 4 = 60. So the answer is d. 60.
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Bowler World charges $5. 00 to rent shoes and $1. 10 per game. Lucky Spares charges $3. 00 for shoes and $1. 50 per game.
Part A
Drag numbers to complete a system of equations to represent the situation, using g for number of games and c for cost. Numbers may be used once, more than once, or not at all.
Bowler World: c = ?g + ?
Lucky Spares: c = ?g + ?
(Numbers: 1, 1. 1, 1. 5, 2. 6, 3, 5, 8)
The number of games that would make the cost equal in both locations is 5. The total cost is $10.50.
The equation that can be used to determine the total cost of renting shoes at both locations is:
total cost = fixed cost + variable cost
Total cost of renting at Bowler World = $5 + $1.1x
Total cost of renting at Lucky Spares = $3 + $1.50x
Where
x = number of games played
In order to determine the number of games that would make the cost
equal in both locations, the following steps would be taken:
$5 + $1.1x = $3 + $1.50x
Combine similar terms
$5 - $3 = $1.50x - $1.1x
$2 = $0.40x
Divide both sides of the equation by $0.4
x = 2 / 0.4
x = 5 games
Total cost = $5 + $1.1(5) = $5 + $5.5 = $10.50
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30 points! Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
Slope of the line: ___
Answer:
m = 5/4
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Pick 2 points (0, -3) (4,2)
We see the y increase by 5 and the x increase by 4, so the slope is
m = 5/4
when multiplying and dividing integers what would (-98)÷14 equal it would equal 7 but would it be positive or negative?
Answer: -7
Step-by-step explanation:
Here we will show you step-by-step with detailed explanation how to calculate 98 divided by 14 using long division.
Instead of saying 98 divided by 14 equals 7, you could just use the division symbol, which is a slash, as we did above.
Also note that all answers in our division calculations are rounded to three decimals if necessary.
Here are some other ways to display or communicate that 98 divided by 14 equals 7:
98 ÷ 14 = 7
98 over 14 = 7
98⁄14 = 7
The easiest way we found to answer the question "what 98 divided by 14 means", is to answer the question with a question: How many times does 14 go into 98?
If the side ratio is 9:16, the perimeter ratio is
The perimeter ratio of the figures is given as follows:
9:16.
How to obtain the perimeter ratio?Considering the side length ratio of a:b, the perimeter ratio has the proportion given as follows:
a:b.
This is because both the side lengths and the perimeter are measured in units, hence the perimeter ratio is the same as the side length ratio.
Considering that the area is measured in square units and the volume in cubic units, their ratios would be given as follows:
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Please help me I have no idea how to do this it’s about Multiples
Answer:
Step-by-step explanation:
The area of a circle is more than 2 square units but less than 4 square units.
The range between which the radius of the circle lies is -
[tex]$\sqrt{\frac{2}{\pi } } < r < \sqrt{\frac{2}{\pi } }[/tex] .
What is inequality?Inequality in mathematics is a relation that is used to compare two or more expressions in mathematics. For example -
(ax + b) > (cx + d)
kx < 6
Given is the inequality statement as -
"The area of a circle is more than 2 square units but less than 4 square units".
The area of a circle is -
{A} = πr²
Mathematically, we can write the inequality statement as -
2 < {A} < 4
2 < πr² < 4
(2/π) < r² < (4/π)
[tex]$\sqrt{\frac{2}{\pi } } < r < \sqrt{\frac{2}{\pi } }[/tex]
Therefore, the range between which the radius of the circle lies is -
[tex]$\sqrt{\frac{2}{\pi } } < r < \sqrt{\frac{2}{\pi } }[/tex] .
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Why do we use a pooled estimate of the population?
By merging information from several sources, a pooled estimate of the population is utilised to gain a better picture of the population mean as a whole.
When a person or organisation needs to combine data from several sources to better understand a population, they utilise a pooled estimate of the population. This can be accomplished in a number of ways, such as by integrating data from several surveys, data from various time periods, or data from various geographical regions .A more complete and accurate view of the population can be acquired by combining the data from several sources. Because it enables a more precise assessment of a population's needs and traits, this is particularly helpful for making judgements about policy or resource distribution. The comparison of several populations or the analysis of changes across time can both be done using pooled estimates. This is necessary to comprehend population change and determine the most effective resource allocation.
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Find the period of this function:
A. 2
B. 4
C. 6
D. 8
Answer:
is 2
because it's below for and two is the closest answer to the function variable answer to this question that you have here
Can someone PLEASE help me with this and show work?
The measure of the angle ∠DBC, m∠DBC, found by writing an equation based on the angle addition postulate is m∠DBC = 30°
What is an equation?An equation consists of two expressions that are specified as being equivalent, by joining them by an equals to '=' sign.
The specified information are;
m∠ABD = (3·x+ 15)° and m∠DBC = (2·x)°, m∠ABC = 90°
The angle addition postulate indicates that we get;
m∠ABC = m∠ABD + m∠DBC
m∠ABC = 90° = (3·x+ 15)° + (2·x)° (substitution property)
90° = (3·x+ 15)° + (2·x)° = (5·x+ 15)°
(5·x + 15)° = 90°
5·x = 90° - 15° = 75°
5·x = 75°
x = 75°/5 = 15°
x = 15°
m∠DBC = 2·x
Therefore, m∠DBC = 2 × 15° = 30°
m∠DBC = 30°
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PLEASE ANSWER WILL GIVE BRAINLIEST!!!
The box plot shows the times for sprinters on a track team. A horizontal number line starting at 40 with tick marks every one unit up to 59. The values of 42, 44, 50, 54, and 56 are all marked by the box plot. The graph is titled Sprinters' Run Times, and the line is labeled Time in Seconds. Which value does 50% of the data lie above, and what is it called? 54, the upper quartile 44, the lower quartile 50, the median 42, the median
The value that 50% of the data, is 50 the median.
What is the Box Plot?An illustration of variation in a set of data is called a box and whisker plot. A histogram analysis usually gives an adequate display, but a box and whisker plot can add more detail while enabling the display of different sets of data on the same graph.
Given Data: 42, 44, 50, 54, and 56
The median can be referred to as the second quartile (Q2) or 50th percentile of the data set.
The median value shows that 50% of the data set is above it while 50% is below it also.
So, 50 is the median, and this means that 50% of the data lie above 50.
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PLEASE HELP
Which of the following functions has the same horizontal asymptote as the function graphed below
A function which has the same horizontal asymptote as the function graphed above include the following: A. f(x) = 4^{x + 2} - 3.
What is a horizontal asymptote?In Mathematics, a horizontal asymptote simply refers to a horizontal line (y = b) where the graph of a function approaches the line as the input values (domain or independent value) approach negative infinity (-∞) to positive infinity (∞).
In this context, the line passing through the ordered pair (0, 3) on the graph of this exponential growth function represents a horizontal asymptote and it has an equation of y = 3, as shown in the image attached below.
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Write a division problem with 1/4
as the dividend and 3 as the divisor. Then, find the quotient.
(GIVING 20 POINTS)
When 1/3 is the dividend and 3 is the divisor, the quotient is 1/12.
What is meant by dividend?The amount that needs to be split up into a specific number of equal pieces in a division problem is known as the dividend. Similar to the example given above, the dividend is the number 20 and the divisor is the number 5 when we divide a group of 5 individuals into a group of 20 apples.A number is divided by any other number in division to get a new number. Thus, the dividend is the number that is divided in this context. The divisor is the quantity that divides the provided quantity. The resultant number is what is known as the quotient. When a number is divided partially by a divisor, the result is known as the remainder.Dividend/Divisor is the quotient.
Divide the dividend by the divisor to obtain the quotient.
Here, Dividend = 1/4
Divisor = 3
Divisor/Dividend =(1/4)/3 = 1/12
So, when 1/3 is the dividend and 3 is the divisor, the quotient is 1/12.
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Suppose that ????(1)=8, ????(4)=7, ???? '(1)=9, ???? '(4)=−3, and ???? '' is continuous. Find the value of the definite integral ∫x????″(x) ????x on the interval [1,4].
The value of the definite integral ∫[tex]x????"(x)????(x) dx[/tex] on the interval [tex][1,4][/tex] is -5.
What do you mean by integration?Integration is a fundamental concept in calculus that deals with finding the area under a curve and calculating the accumulation of values over an interval. Integration can be thought of as the reverse of differentiation, which is the process of finding the rate of change of a function at a given point.
There are two main types of integration: definite and indefinite integration. Definite integration involves finding the exact area between a curve and the x-axis over a specified interval. Indefinite integration involves finding the general antiderivative of a function, which is a function that, when differentiated, will yield the original function.
The process of integration can be represented symbolically as ∫ (the integral symbol) and the result of an integration is typically represented as an antiderivative. The fundamental theorem of calculus states that differentiation and integration are inverse operations, so the derivative of an antiderivative is the original function.
Given that ????(1) = 8, ????(4) = 7, ???? '(1) = 9, and ???? '(4) = -3, we can use the method of integrating by parts to evaluate the definite integral ∫[tex]x????"(x)????(x) dx[/tex] on the interval [1, 4].
Let u = ????(x) and dv = x dx. Then du = ???? '(x) dx and v = x^2/2.
Using the method of integrating by parts, we have:
∫[tex]x????"(x)????(x) dx= x????(x)[/tex] ×[tex]\frac{x}{2} -[/tex]∫[tex](\frac{x^{2} }{2} )????'(x) dx[/tex]
We can use the same method of integrating by parts to evaluate the second integral on the right-hand side. Let [tex]u=\frac{x^{2} }{2}[/tex] and [tex]dv=????'(x) dx[/tex]. Then [tex]du=x dx[/tex] and [tex]v=????(x)[/tex].
So we have:
∫[tex]x????"(x)????(x) dx = x????(x)[/tex]× [tex]\frac{x}{2} - \frac{x}{2} ^{2}????(x) + c[/tex]
Where C is an arbitrary constant of integration.
We can use the given values of ????(1) and ????(4) to evaluate the definite integral:
∫[tex]x????"(x)????(x) dx[/tex] = 4????(4) * 4/2 - (4^2/2)????(4) + 4????(1) * 1/2 - (1^2/2)????(1)
= 28 - 14 * 7/2 + 4 * 8/2 = 28 - 49 + 16 = -5.
Therefore, the value of the definite integral ∫[tex]x????"(x)????(x) dx[/tex] on the interval [1, 4] is -5.
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A diagonal of a square mirror is 10 inches long. What is the length, in inches, of each side of the mirror?.