Answers
Related Questions
What is the arc length of a circle that has a 6-inch radius and a central angle that is 65 degrees? Use 3. 14 for pi and round your answer to the nearest hundredth
Answers
C=2π6
C=37.6991118431
That's the arc length of the whole circle, i.e. the arc length of 360°.
65° is 18.055555555555555555555555555556% of 360°, (65/360*100)
so 18.055555555555555555555555555556% of 37.6991118431 is
6.8067840827819444444444444444444. Rounded to the nearest hundredth, the answer is 6.81 inches.
That's real pi, lets see if it makes a difference to use "stupid pi".
C=2πr
C=2π6
C=37.68
That's the arc length of the whole circle, i.e. the arc length of 360°.
65° is 18.055555555555555555555555555556% of 360°, (65/360*100)
so 18.055555555555555555555555555556% of 37.68 is
6.803333333333333333333333. Rounded to the nearest hundredth, the answer is 6.80 inches.
Yep makes a difference. That's why you don't use stupid pi. 3.14159 is what we always used in engineering, or just the pi button and using a ton of digits.
Answer: 6.80 inches.
Alex has been serving 2/3 cup of lemonade to each student. If he has 1 1/3 cups of lemonade left, how many students can still get lemonade?
Question 2 options:
1
2
3
0
Answers
In this case, every student is served 2/3 cup of lemonade and Alex has 1 1/3 cups of lemonade left. Then you just need to divide the lemonade left with lemonade served per student. The calculation would be:
Number of students served= lemonade left / lemonade served per student
Number of students served= 1 1/3 cup / (2/3 student/cup) = 2 student
What is the area of the region completely bounded by the curve y=-x^2+x+6?
Answers
y = -1 (x² - x - 6)
y = -1 (x - 3)(x + 2)
From this, we can tell the x-axis intercepts are -2 and 3.
(To do this, simply equate any of the expressions involving x to 0 and rearrange to give x).
Now, integrate between the limits -2 and 3:
R = area of region bounded
R = ³∫₋₂ -x² + x + 6 .dx
R = ³[-1/3x³ + 1/2x² + 6x]₋₂
R = (-1/3(3)³ + 1/2(3)² + 6(3)) - (-1/3(-2)³ + 1/2(-2)² +6(-2))
R = (-9 + 9/2 + 18) - (8/3 + 2 - 12)
R = (27/2) - (-22/3)
R = 27/2 + 22/3 = 125/6 units²
To find the area of the region completely bounded by the curve y=-x^2+x+6, you can integrate the equation with respect to x and evaluate it between the x-values where the curve intersects the x-axis. By solving the quadratic equation -x^2+x+6=0, you can determine the x-values. Then, evaluate the definite integral between these x-values to find the area.
Explanation:The area of the region completely bounded by the curve y=-x^2+x+6 can be found by integrating the equation with respect to x and evaluating it between the appropriate bounds. The integral of the given equation is ∫(-x^2+x+6) dx. To find the area, we need to find the definite integral between the x-values where the curve intersects the x-axis. First, set the equation equal to zero and solve for x:
-x^2+x+6=0
This quadratic equation can be factored as: (x-2)(x+3). Therefore, the curve intersects the x-axis at x=2 and x=-3.
By evaluating the definite integral between x=-3 and x=2, we can find the area of the region:
Area = ∫-32 (-x^2+x+6) dx
Integrating this equation will give you the area of the region bounded by the curve y=-x^2+x+6.
The circumference of a circle is 19πinches. find the radius.c=2πr
Answers
c=2πr
19 = 2 π r
r = 19/ 2 π
r = 19/ (2×3.14) =19/6.28
r = 3.03 nches
Solve by factoring and list only the positive solution: 2x2 - 5x = 88
Answers
The general form of a quadratic equation is,
Ax² + Bx + C = 0
where A and B are numerical coefficients and C is the constant. If we are to express the given equation in this form,
2x² - 5x - 88 = 0
The sum of the roots, x₁ and x₂ is -B/A and the product is equal to C/A.
Sum: x₁ + x₂ = -(-5/2) = 5/2
Product: x₁x₂ = -88/2 = -44
The values of x₁ and x₂ are 8 and -11/2.
The factors are (x - 8) and (x + 11/2)
ANSWERS: 8 and -11/2.
Law of sines:
Triangle ABC has measures a = 2, b = 2, and m∠A = 30°. What is the measure of angle B?
15°
30°
45°
60°
Answers
since a and b are equal to number 2, they are the same value. Because A is 30 degrees, B is 30 degrees too.
Answer: Second option is correct.
Step-by-step explanation:
Since we have given that
ΔABC has measures a=2, b=2, m∠A=30⁰
As we know the "Law of sines " i.e.
[tex]\frac{a}{\sin A}=\frac{b}{\sin B}\\[/tex]
so, we put the given values in above formula:
[tex]\frac{2}{\sin 30\textdegree}=\frac{2}{\sin B}\\\\\implies \sin 30\textdegree=\sin B\\\\\implies B=30\textdegreee[/tex]
Hence, Second option is correct.
John translated parallelogram ABCD using the rule (x,y)→(x+3, y−2). If angle A is 110° and angle B is 70°, what is the degree measurement of angle A'?
Answers
Angle measurements are preserved when translations happen. Shifting a figure will not change the angle. So because angle A = 110 degrees, this means angle A' = 110 degrees as well.
Answer:
The correct answer is B. 110.
2x-5y=-6; 2x-7y=-14
Answers
2x-7y = -14
-2x+5y = 6
2x - 7y = -14
-2y= - 8
y = 4
What's 9080 each number in expanded notation
Answers
What is a rule for the total cost of the tickets ? Give the rule in words and as a algebraic expression
Answers
ur equation would be : y = 12x + 150....where x is the number of students and y is the total cost...but that is an equation, and u want an expression...so I guess the expression would be 12x + 150
the cost of each ticket (12) multiplied by the number of students (x), added to 150 will give u the total cost
so theh rule is 12s+150 where s is the number of students
Expand (2x-3y)^4 using Pascal's Triangle. Show work
Answers
1) let 2x = a and 3y = b
(a+b)⁴ = a⁴ + a³b + a²b² + ab³ + b⁴
Now let's find the coefficient of each factor using Pascal Triangle
0 | 1
1 | 1 1
2 | 1 2 1
3 | 1 3 3 1
4 | 1 4 6 4 1
0,1,2,3,4,.. represent the exponents of binomials
Since our binomial has a 4th exponents, the coefficients are respectively:
(1)a⁴ + (4)a³b + (6)a²b² + (4)ab³ + (1)b⁴
Now replace a and b by their real values in (1):
2⁴x⁴ +(4)8x³(3y) + (6)(2²x²)(3²y²) + (4)(2x)(3³y³) + (1)(3⁴)(y⁴)
16x⁴ + 96x³y + 216x²y² + 216xy³ + 81y⁴
Answer:
16x^4 - 96x^3y + 216x^2y^2 - 216xy^3 + 81y^4
Step-by-step explanation:
(2x - 3y)^4
Fifth line on a Pascal Triangle
1, 4, 6 4, 1
(1) 2x^4
2^4 = 16
2x^4 = 16x^4
16x^4
(4) 2x^3 (-3y)^1
2^3 = 8
-3^1 = -3
8 times -3 times 4 = -96
-96x^3y
(6) 2x^2 (-3y)^2
2^2 = 4
-3^2 = 9
4 times 9 times 6 = 216
216x^2y^2
(4) 2x^1 (-3y)^3
2^1 = 2
-3^3 = -27
2 times - 27 times 4 = -216
-216xy^3
(1) (-3y)^4
-3^4 = 81
81y^4
16x^4 - 96x^3y + 216x^2y^2 - 216xy^3 + 81y^4
On a floor plan drawn at a scale of 1:100, the area of a rectangular room is 30
c. what is the actual area of the room?
Answers
such that a*b=30.
Since the scale is 1:100, a represents 100a, and b represents 100b.
So the actual dimensions are 100a by 100b.
The area is 100a*100b=a*b*10,000=30*10,000=300,000 (square units)
Answer: 300,000 (square units)
A polynomial function, f(x), with rational coefficients has roots of –2 and square root of 3. The irrational conjugates theorem states that which of the following must also be a root of the function?
Answers
Answer:
Step-by-step explanation:
option b
Given a polynomial with rational coefficients, if √3 is a root, its irrational conjugate -√3 must also be a root due to the Irrational Conjugates Theorem, ensuring that the polynomial maintains rational coefficients.
Explanation:The subject of this question is a polynomial function with rational coefficients, which is encountered in mathematics, particularly in algebra. When a polynomial has rational coefficients and one of its roots is an irrational number, such as the square root of 3 (√3), the Irrational Conjugates Theorem states that its conjugate, in this case, the negative square root of 3 (-√3), must also be a root of the polynomial. Therefore, the polynomial function in question must include both √3 and -√3 as roots to have rational coefficients.
Given that the function already has -2 as a root, we know that (x + 2) is a factor of the polynomial. Additionally, because √3 is a root, the factors (x - √3) and (x + √3) will also be part of the polynomial. To find the roots of a quadratic equation or higher-order polynomials, one can set the function equal to zero and solve for x, either by factoring, applying the quadratic formula, or other algebraic methods.
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A jar of 57 coins contains only dimes and quarters. The value of all the coins in the jar is $10.05. How many dimes are in the jar?
Answers
The dimes are 28 dimes
what is Algebra?Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.
Given:
total coins = 57
So,
D + Q = 57
D= 57 - Q....(1)
0.10D + 0.25 Q = 10.05
Using (1), we get
0.10(57 - Q) + 0.25Q= 10.05
5.7 - 0.10Q + 0.25Q = 10.05
0.15Q = 4.35
Q= 29
So, dimes = 57- 29= 28 dimes
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Which phrases can be used to represent the inequality mr024-1.jpg? Check all that apply. The product of 6.5 and the sum of a number and 1.5 is no more than 21. The sum of 1.5 and the product of 6.5 and a number is no greater than 21. The product of 6.5 and a number, when increased by 1.5, is below 21. The product of 6.5 and the sum of a number and 1.5 is at minimum 21. The sum of 1.5 and the product of 6.5 and a number is at least 21. The product of 6.5 and a number, when increased by 1.5, is at most 21.
Answers
The product of 6.5 and a number, when increased by 1.5, is below 21.
6.5x + 1.5 < 21
The sum of 1.5 and the product of 6.5 and a number is at least 21.
6.5x + 1.5 ≥ 21
The product of 6.5 and a number, when increased by 1.5, is at most 21.6.5x + 1.5 ≤ 21
Answer:
b and c
Step-by-step explanation:
2020 edge assignment
Is it possible for a line segment to have more than one bisector?
Answers
Yes, it is possible to have more than one bisector in a line segment.
Bisector is a line that divides a line or an angle in to two equivalent parts. There are two types of Bisectors based on what geometrical shape it bisects.
Bisector of a Line Angle BisectorIn general 'to bisect' something means to cut it into two equal parts. The bisector is the one that doing the cutting process.
With a line bisector, we cut a line segment into two equal parts with another line - the bisector. Just imagine the line PQ is being cut into two equal lengths (PF and FQ) by the bisector line AB.
Whenever AB intersects at a right angle, it is called the "perpendicular bisector" of PQ. If it crosses at any other angle it is simply called a bisector. Drag the points A or B and see both types.
For obvious reasons, the point F is called the midpoint of the line PQ,
Two dice are rolled. Are the events, “rolling doubles” and “rolling an even sum”, mutually exclusive? Justify your response.
There are 8 students lined up at the classroom door. What is the probability that Laura and Kimiko will end up next to each other if the students arrange themselves blindfolded?
Answers
A specific example is if we rolled a pair of '3's an we get 3+3 = 6 as a result.
So in conclusion, the events "rolling doubles" and "getting an even sum" are not mutually exclusive. If the first event happens, then the second event definitely happens. The same can't be said the other way around.
-----------------------------------------------------
Problem 2)
We have 8 students. Of those 8, we have two students Laura and Kimiko that we want to keep together. In other words, we want them to be adjacent to each other. If we think of Laura and Kimiko as one student, then we have 8-2+1 = 7 "students", 6 of which are individuals who can move on their own and 2 (Laura and Kimiko) who are tied together as one "student".
There are 7! = 7*6*5*4*3*2*1 = 5040 ways to arrange these 7 "students". For any given permutation, we can have Laura on the left side or Kimiko on the left side. So there are 2 ways to arrange Laura and Kimiko.
In total there are 2*5040 = 10080 different ways to arrange all of the students where Laura and Kimiko will be next to each other.
This is out of 8! = 8*7*6*5*4*3*2*1 = 40320 ways to arrange the students where we don't worry about Laura and Kimiko sticking together.
Divide the two values: 10080/40320 = 1/4
Answer:
The answer as a fraction is 1/4
The answer as a decimal value is 0.25 (since 1/4 = 0.25)
In percent form, the answer is 25% (0.25 turns into 25% after moving the decimal 2 spots to the right)
A fence is to be installed around a rectangular field. the field's perimeter is 204204 feet. find the dimensions of the field if the length of the field is 8 feet more than the width.
Answers
204188 / 4 = 51,047
width = 51,047
length = 51,055
The solution is, the dimensions of the field if the length of the field is 8 feet more than the width is:
width = 51,047
length = 51,055
What is perimeter?A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications.
Here, we have,
given that,
A fence is to be installed around a rectangular field.
the field's perimeter is 204204 feet.
now, we have,
204204 - 16 = 204188
we get,
204188 / 4 = 51,047
so, we get,
width = 51,047
length = 51,055
Hence, The solution is, the dimensions of the field if the length of the field is 8 feet more than the width is:
width = 51,047
length = 51,055
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One bundle contains 500 $20 bills. what would be the total value of 44 bundles
Answers
let y = total amount
x = number of bundles
y = $20 * 500x
y = $10,000 per bundle * x
So, using this equation, we can determine the total amount of money by simply substituting the number of bundles that we have.
To solve our problem, let x = 44 bundles
y = $10,000 per bundle * 44 bundles
y = $440, 000
Therefore, the total amount is $440,000.
At a store, 2 gallons of milk cost $6. Which is the value of the ratio of dollars to gallons of milk?
Answers
Answer:
3:1 or 3/1
Step-by-step explanation:
We have the next information:
Gallons of Milk Cost
2 ⇒ $6
dividing both quantities by two, we get the price for a single gallon of milk:
Gallons of Milk Cost
1 ⇒ $3
We are asked for the ratio of dollars to gallons of milk (the order is important since dollars go first than gallons) so we will have the following:
dollars:gallons or dollars/gallons
and since $3 dollars pay for 1 gallon of milk, the ratio is:
3:1 or 3/1
What is the equation of the line that is parallel to y=-2/3x+4 and that passes through (–2,–2)?
Answers
-
-
-
y=-2/3x-4/3
y=-2/3x-10/3
y=-2/3x-2/3
y=-2/3x-17/4
Answers
y=-2x/3+b, using the point (-2,-2) we can solve for "b", the y-intercept.
-2=-2(-2)/3+b
-2=4/3+b
-6/3-4/3=b
-10/3=b so our line is:
y=-2x/3-10/3 (or more neatly in my opinion :P)
y=(-2x-10)/3
It's the second one down from the top :)
The equation of the line parallel to y=-2/3x+4 and passing through (-2, -2) is y = -2/3x - 10/3.
Explanation:To find the equation of a line parallel to y = -2/3x + 4 and passing through the point (-2, -2), we need to use the fact that parallel lines have the same slope. The given equation has a slope of -2/3, so the parallel line will also have a slope of -2/3. Using the point-slope form of a line, we can write the equation as:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope. Plugging in the values, we have:
y - (-2) = -2/3(x - (-2))
Simplifying the equation, we get:
y - (-2) = -2/3(x + 2)
y + 2 = -2/3x - 4/3
y = -2/3x - 4/3 - 2
y = -2/3x - 4/3 - 6/3
y = -2/3x - 10/3
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Approximately 31,000 citizens of a country died in automobile accidents in 2015 express this toll in deaths per hour
Answers
Answer:
4 deaths per hour
Step-by-step explanation:
We have been given that approximately 31,000 citizens of the country died in automobile accident in 2015.
Since we know that 1 year = 365 days,
1 day = 24 hours
In one year there are total hours = 365 × 24 = 8,760 hours
Death per hour = [tex]\frac{31000}{8760}[/tex] = 3.5388 ≈ 4
Therefore, the toll in deaths per hour is approximately 4 in 2015.
What equation is solved by the graphed systems of equations? Two linear equations that intersect at the point negative 1, negative 4.
Answers
To solve this problem, we have to manually solve for the value of x for each choices or equations. The correct equation will give a value of -1 since the linear equations intersects at point (-1, -4).
1st: 7x + 3 = x + 3
7x – x = 3 – 3
6x = 0
x = 0 (FALSE)
2nd: 7x − 3 = x – 3
7x – x = 3 – 3
6x = 0
x = 0 (FALSE)
3rd: 7x + 3 = x − 3
7x – x = - 3 – 3
6x = -6
x = -1 (TRUE)
4th: 7x − 3 = x + 3
7x – x = 3 + 3
6x = 6
x = 1 (FALSE)
Therefore the answer is:
7x + 3 = x − 3
In this exercise, we are going to solve using our knowledge of systems and in this way we will find that the equation that satisfies the points.
As we know that the equation that will satisfy will have to have the values of X=-1, we will solve each one of the alternatives as:
First equation is:[tex]7x + 3 = x + 3\\6x = 0\\x = 0[/tex]
We realize that the value of x is not what we want so it doesn't satisfy us.
second equation is:[tex]7x - 3 = x - 3\\7x- x = 3- 3\\6x = 0\\x = 0[/tex]
We realize that the value of x is not what we want so it doesn't satisfy us.
third equation is:
[tex]7x + 3 = x − 3\\6x = -6\\x = -1[/tex]
fourth equation is:[tex]7x − 3 = x + 3\\7x – x = 3 + 3\\6x = 6\\x = 1[/tex]
We realize that the value of x is not what we want so it doesn't satisfy us.
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Help? @texaschic101
Parabola and its vertex
Answers
f (x) = a(x-4)^2 - 1
15 = a(0-4)^2 - 1
15 = a(-4)^2 - 1
15 = a(16) - 1
15 +1 = 16a
16 = 16a
16/16 = 16a/16
1 = a
A must be equal to 1
y = (x-4)^2 - 1
y = x^2 - 8x + 16 - 1
y = x^2 - 8x + 15
Factor (find two number that summed give -8 and multiplied +15)
(x-3)(x-5) = 0
(x-3) = 0 -> x = 3
(x-5) = 0 -> x = 5
So answer is: (3;0) and (5;0)
The expression 4 square root of 81^3 can be rewritten as_____.
A. 81^3/4
B.81^4/3
C. 81^12
D. 81^1/12
Answers
Answer:
81^1/12
HAVE A GREAT DAY
The expression ''4 square root of 81³'' can be rewritten as,
⇒ [tex]81^{\frac{3}{4} }[/tex]
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.
Given that;
The expression to write is,
⇒ 4 square root of 81³
Now, It can be written as;
⇒ 4 square root of 81³
⇒ [tex]\sqrt[4]{81^{3} }[/tex]
By rule of exponent we get;
⇒ [tex]81^{\frac{3}{4} }[/tex]
Thus, The expression ''4 square root of 81³'' can be rewritten as,
⇒ [tex]81^{\frac{3}{4} }[/tex]
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The variable is Z is inversely proportional to X. When X is 6, Z has the value 0.5. What is the value of Z when X = 10
Answers
zα1/x
hence;
z=k/x
where k is the constant of proportionality;
this implies that:
k=xz
when x=6,z=0.5
thus;
k=0.5*6
k=3
hence;
z=3/x
when x=10,
z=3/10
the answer is 3/10
The probability that a flipped coin will show heads on four consecutive flips is
Answers
n!/r!(n - r)! * p^(n-r)*q^r, where
n is the number of total trials
r is the number of success in the trials
p is the probability of the an event happening in one trial
p is the probability of the an event not happening in one trial
In here there are 4 flips, so n=4. If you want to find how many heads in 4 flips, r=4 consecutive heads. Then, p = 1/2 because it could either be a head or a tail, while q=1/2 because p+q = 1. Substituting the values:
4!/4!(4 - 4)! * (0.5)^(4-4)*(0.5)^4 = 1/18 or 6.25%
Graph the ellipse with equation x squared divided by twenty five plus y squared divided by four = 1.
Answers
thus, check the picture below.
using the formula C=2TTr, find the circumference of a circle with a diameter of 28 in. round your answer to the nearest inch
A. 56in
B. 28 in
C. 44in
D.88in
Answers
radius = diameter/2
so 28/2=14
using 3.14 for PI
2*3.14*14 = 87.92 = 88 inches
so radius = 28/2 = 14
Circumference = 2 x pi x 14 = 28 pi
or from calculator = 87.96 inches ....correct to 2 decimal places
How to find where the tangent line is horizontal?
Answers
the tangent line is horizontal when the slope = zero.....(f'(x) =0)
Final answer:
To determine where the tangent line to a function is horizontal, find the derivative of the function, set it equal to zero, and solve for 'x'. This value of 'x' is where the slope is zero, indicating a horizontal tangent line.
Explanation:
How to Find Where the Tangent Line is Horizontal
To find where the tangent line to a curve is horizontal, you need to determine where the slope of the tangent (which is the derivative of the function) is zero. This involves calculating the derivative of the given function and solving for the value of 'x' where this derivative equals zero.
For example, if we have a function y = 4x - x², we first find its derivative: dy/dx = 4 - 2x. Setting this derivative equal to zero gives us 4 - 2x = 0. Solving for x gives us x = 2. This is the value of x where the tangent line is horizontal.
If we are given a graph, like in a velocity-time graph, a horizontal tangent indicates a moment where the velocity is zero, signifying a change in direction of the particle. At such points, we can see that the slope of the tangent line is zero, meaning it is a horizontal tangent.