To find the distance the hula hoop rolls in 4 full rotations, we calculate the circumference as 2πr and then multiply by 4. The total distance is then rounded to the nearest centimeter, resulting in 880 cm.
The question asks us to calculate the distance a hula hoop travels in 4 full rotations given its radius. The distance traveled in one rotation is equal to the circumference of the hoop.
To find the circumference, we use the formula C = 2πr, where r is the radius. Since the radius is given as 35 cm, the circumference is 2π×35 cm. To find the total distance for 4 rotations, we multiply the circumference by 4. This gives us 4×2π×35 cm. Using the approximate value of π (3.1416), we can calculate the distance, and then round it to the nearest centimeter.
Circumference C = 2π×35 cm = 219.91 cm
Total distance for 4 rotations = 4×C = 4×219.91 cm = 879.64 cm
Rounded to the nearest centimeter: 880 cm
Point Y is the midpoint of segment XZ. If XY = 2(3x +1) and YZ = 5x + 22, find the value of x. x = 20 x = 24 x = 18 x =11
Answer:x=20
Step-by-step explanation:
2(3x+1) = 6x+2
since xy and yz are the parts of a midpoint they are equal to eachother
so 6x+2=5x+22
if you subtract 5x from both sides you get x+2 = 22 then you subtract 2 from both sides so you have x=20
Nolan made lanps to sell at the school art show. He made 9 lamps each week for 4 weeks. How many lamps did Nolan make?
Answer: The answer would be 36
Step-by-step explanation:
9×4=36
Find an exact value. sine of seventeen pi divided by twelve.
Answer:
4.45058959259........
And it still goes
The exact value of sin(17π/12) is -(√2 + √6)/4.
To find the exact value of sin(17π/12), we need to express 17π/12 as a sum or difference of angles for which we know the sine values. Since 17π/12 is not a standard angle, we'll use the angle addition formula.
17π/12 = (3π/4) + (2π/3)
Now, we'll use the sine addition formula:
sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
Here, A = 3π/4 and B = 2π/3:
sin(3π/4 + 2π/3) = sin(3π/4)cos(2π/3) + cos(3π/4)sin(2π/3)
Now, we need to find the sine and cosine values of 3π/4 and 2π/3:
sin(3π/4) = √2/2, cos(3π/4) = -√2/2
sin(2π/3) = √3/2, cos(2π/3) = -1/2
Plugging these values into the formula:
sin(17π/12) = (√2/2 * -1/2) + (-√2/2 * √3/2)
= -√2/4 - √6/4
= -(√2 + √6)/4
So, the exact value of sin(17π/12) is -(√2 + √6)/4.
Determine the product: (46.2 × 10–1) ⋅ (5.7 × 10–6). Write your answer in scientific notation.
Answer:
[tex]2.6334 \cdot 10^{-5}[/tex]
Step-by-step explanation:
[tex](46.2 \cdot 10^{-1})(5.7 \cdot 10^{-6})[/tex]
To multiply it , first we multiply the numbers.
46.2 times 5.7 is 263.34
Now we multiply the exponents. To multiply exponents we apply exponential property.
[tex]a^m \cdot a^n= a^{m+n}[/tex]
When the exponents with same base are in multiplication then we add the exponents
[tex]10^{-1} \cdot 10^{-6}=10^{-7}[/tex]
[tex](46.2 \cdot 10^{-1})(5.7 \cdot 10^{-6})[/tex]
[tex]263.34 \cdot 10^{-7}[/tex]
Now we write it in scientific notation. Move the decimal point after the first number. So we move decimal point 2 places to the left
[tex]2.6334 \cdot 10^2 \cdot 10^{-7}[/tex]
[tex]2.6334 \cdot 10^{-5}[/tex]
it cost $270 for 3 people to go on a fishing trip how much does it cost for 10 people to go on a fishing trip
Answer:
$900
Step-by-step explanation:
It cost each person $90 to go on the trip when you divide 270/3. You can find out how much it would cost for 10 people to go on the trip by multiply 10X90.
Kwan said that the product of 56 × 213 is 103. How can you tell that his answer is wrong?
Answer:
_______________________________________________________
Note that this multiplication problem has two (2) multiplicands; that is, two (2) numbers being multiplied by each other; which are: "56" and "213"
The "product" refers to the number obtained when multiplicands in a multiplication problem are multiplied together.
In this case, the product given is: " 103 " ; which is smaller than one of the "multiplicands" in the problem — specifically, "213" !
This does not make sense; and this along tells us that the answer — "213" ; is incorrect.
________________________________________________
Furthermore, if we multiply the two (2) given multiplicands:
56 * 213 ; we get: " 11,928 " ; which is much greater than: " 103 " .
________________________________________________
Hope this answer is of help to you!
Best wishes in your academic endeavors
— and within the "Brainly" community!
________________________________________________
Write an equation for the line that is parallel to the given line and passes through the given point.
Given line: y= 2x + 4 Given Point: (3, 8)
A.) y = 2x + 2
B.) y = 2x + 6
C.) y = -2x + 6
D.) y = - 1/2x + 2
Parallel lines have the same slope.
If y = 2x + 4, then parallel line has equal y = 2x + b.
The line passes throught the point (3, 8). Put the coordinates of the point to the equation of a line:
8 = 2(3) + b
8 = 6 + b subtract 6 from both sides
2 = b
Answer: A) y = 2x + 2What is the equation of the line passing through the points (2, –1) and (5, –10) in slope-intercept form?
A)
Y=3x-5
B)
Y=3x+5
C)
Y=3x-5
D)
Y=3+5
Answer:
y = -3x+5 This has a negative slope
Step-by-step explanation:
The first step is to find the slope. We can use the formula
slope = (y2-y1)/(x2-x1)
= (-10--1)/(5-2)
= (-10+1)/3
= -9/3
=-3
Next we will use the point slope form of the equation of a line
y-y1 = m(x-x1)
y--1 = -3(x-2)
y+1 = -3(x-2)
Distribute the -3
y+1 = -3x -3*(-2)
y+1 = -3x+6
Subtract 1 from each side
y+1-1 = -3x+6-1
y = -3x+5
This is in the slope intercept form of the equation.
My answer differs from the options because I have a negative slope
Apply the Pythagorean Theorem to find the distance between points A and B.
A)
11
units
B)
50
units
C)
61
units
D)
72
units
Answer:
c 61 units but it should be under a square root
Step-by-step explanation:
CA=6
CB=5
5^2+6^2=AB^2
61=AB^2
The Option C is partially correct , the answer must be under a square root as [tex]\;\sqrt {61} {\text{ units}}[/tex].
Further explanation:
The pythagorean theorem is used in the right angle triangle and it states that the square of the hypotenuse is equal to the sum of the squares of the perpendicular and base.
It can be mathematically expressed as,
[tex]{h^2} = {p^2} + {b^2}[/tex]
Here, [tex]h[/tex] is the hypotenuse, [tex]p[/tex] is the perpendicular and [tex]b[/tex] is the base.
Step by step explanation:
Step 1:
It is observed from given figure that after joining the points [tex]A,B{\text{ and C}}[/tex] it is established as right angle triangle.
First determine the perpendicular and the base of the triangle.
It can be seen that there are 5 boxes between the point [tex]A{\text{ and }}C[/tex] and 6 boxes between the point [tex]{\text{B and C}}[/tex].
Therefore, the perpendicular of the triangle [tex]AC[/tex] is [tex]{\text{6 units}}[/tex] and the perpendicular of the triangle [tex]AB[/tex] is .
Step 2:
Now use the Pythagoras theorem to find the distance between [tex]B{\text{ and }}A[/tex].
The distance between [tex]B{\text{ and }}A[/tex] is the length of the hypotenuse of the triangle [tex]ABC[/tex].
The length of the hypotenuse [tex]AB[/tex] can be calculated as,
[tex]\begin{aligned}{h^2}&= {p^2} + {b^2}\\{h^2} &= {6^2} + {5^2}\\{h^2} &= 61\\h &= \sqrt {61}\\\end{aligned}[/tex]
Therefore, the distance between [tex]B{\text{ and }}C[/tex] is [tex]\sqrt {61}[/tex] units.
Thus, option C is partially correct , the answer must be under a square root as [tex]\sqrt {61}[/tex] units.
Learn more:
Learn more about the distance between two points on the number linehttps://brainly.com/question/6278187 Learn more about the distance between two coordinates of the linehttps://brainly.com/question/10135690 Learn more about midpoint of the segment https://brainly.com/question/3269852Answer details:
Grade: Junior school
Subject: Mathematics
Chapter: Pythagoras theorem.
Keywords: Distance, Pythagoras theorem, points, base, perpendicular, hypotenuse, right angle triangle, boxes, units, squares, sum
PLEASE I NEED HELP FAST Ben used vector DE to translate triangle ABC. Ben made an error in his work. What is Ben’s error? If Ben had completed the translation properly, what would be the correct coordinates for each vertex (A’, B’, and C’) for the image?
Answer:
He translated them the wrong way.
It should of gone up 2 and right 2 not down 2 and left 2.
The correct coordinates would be (A' = 3,0) (B' = 3, -3) (C' = 2, -2)
Please mark brainliest would rly help.
Step-by-step explanation:
what is the slope of the line that passes through the points (2, 5) and (7, 3)?
ANSWER: [tex]\frac{2}{-5}[/tex]
EXPLANATION:
We can use the slope formula and input the x and y values to solve for the slope.
[tex]\text{Slope Formula}: \frac{y_{2}-y_{1} }{x_{2}-x_{1}}=m[/tex]
[tex]\frac{5-3}{2-7}=m\\\text{Simplify.}\\\frac{2}{-5} =m[/tex]
The slope of the line is [tex]\frac{2}{-5}[/tex]
The slope of the line that passes through the points (2, 5) and (7, 3) is -2/5.
Explanation:To find the slope of the line passing through the points (2, 5) and (7, 3), we can use the formula for slope:
The slope of the line that passes through the points (2, 5) and (7, 3) can be calculated using the formula:
Slope (m) = (y2 - y1) / (x2 - x1)
Plugging in the values, we get:
Slope (m) = (3 - 5) / (7 - 2) = -2/5
Therefore, the slope of the line is -2/5.
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if f(x)=3x-2 and g(x)=f(x)+3, write the equation for g(x)
g(x) = f(x) + 3
Since you know f(x) = 3x - 2, you can plug in (3x - 2) for "f(x)" in the equation:
g(x) = f(x) + 3
g(x) = (3x - 2) + 3
g(x) = 3x - 2 + 3
g(x) = 3x + 1
help me to solve this question...easier
Answer:
x = - 3 and x = - 4
Step-by-step explanation:
(a)
The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the value that x cannot be.
solve x + 3 = 0 ⇒ x = - 3
(b)
Equate f(x) to 5, that is
[tex]\frac{2x+3}{x+3}[/tex] = 5 ( cross- multiply )
5(x + 3) = 2x + 3 ( distribute left side )
5x + 15 = 2x + 3 ( subtract 2x from both sides )
3x + 15 = 3 ( subtract 15 from both sides )
3x = - 12 ( divide both sides by 3 )
x = - 4
Find the product of 83 and 3.
Hello!
Answer:
249
Step-by-step explanation:
83
3 x
___
249
Hope this helps! ~Pooch ♥
Kiara downloaded 264 pictures from her cell phone to her computer. These pictures took up 528 megabytes of space on her computer. Each picture took up the same amount of space. How many megabytes do 35 of these pictures take up?
Hello!
Divide 528 and 264. It will give you 2.
Now, multiply 35 and 2.
Answer: 70
Hope this helps! ~Pooch ♥
which of the binomials below is a factor of this trinomial 5x^2-18x+9
Answer:
5x-3 or x-3
Step-by-step explanation:
I don't know what are the choices, so I'll just factor the whole thing. Choose the ones that fit.
-3 + -15 = -18
-3 * -15 = 9*5
5x^2-15x-3x+9
5x(x-3)-3(x-3)
(5x-3)(x-3)
Answer:
5x - 3
Step-by-step explanation:
APEX
in the figure L1 L2 and L3 is a traversal what is the value of q-p
Answer:
q=135 degrees
p=45 degrees
Step-by-step explanation:
For q:
q is 135 degrees because alternate exterior angles are congruent when L1 is parallel to L2 intersected by L3.
For p:
p is 45 degrees because L2 is a straight line so it has a measurement of 180 degrees. So to find p you do 180 degrees-q.
Which is 180-135=45 degrees
The wholesale price of a lamp is $44 and will be marked up by 40 percent. What is the retail price of the lamp?
Answer:
61.60
Step-by-step explanation:
Answer:
The answer is $61.60
Step-by-step explanation
The wholesale price is 44$, but it will be marked up 40% which in decimal form is .40. You multiply that by 44 to get 17.6, and since its mark up you add that number to 44 to get $61.6
The number in the middle of a data set best describes
N/8 - 3 = -11 What does n equal?
Hey there!
Firstly, [tex]simplify[/tex] both sides of your equation[tex]\frac{1}{8}n+ (-3)[/tex] [tex]=-11[/tex][tex]\frac{1}{8}n -3[/tex][tex]=-11[/tex]Second, [tex]add[/tex] by the number [tex]3[/tex] on each of your sides[tex]\frac{1}{8}n - 3[/tex][tex]+3[/tex]Cancel: [tex]-3 +3[/tex] because it gives you the result of [tex]0[/tex]Keep: [tex]-11+3[/tex] because it has the number we need to solve for the answer[tex]-11 + 3 =[/tex] [tex]-8[/tex][tex]\frac{1}{8}n = -8[/tex]Third, [tex]multiply[/tex] by the number [tex]8[/tex] on each of your sides [tex]8(\frac{1}{8}n)[/tex] [tex]= 8(-8)[/tex]Cancel: [tex]8(\frac{1}{8})[/tex] because it doesn't give you what you're looking forKeep: [tex]8(-8) [/tex] because it gives you your answer[tex]8(-8)= -64[/tex]Answer↓[tex]\boxed{n = -64}[/tex]Good luck on your assignment and enjoy your day! ~[tex]LoveYourselfFirst:)[/tex]enrico buys 3/8 pound of cheddar cheese and 4/8 pound swiss cheese how many cheese does enrico buy in all
Answer:
They buy [tex]\frac{7}{8}[/tex] of cheese.
Step-by-step explanation:
When adding two fractions with the same denominator, you simply add the two numerators (numbers on top):
[tex]\frac{3}{8} + \frac{4}{8} = \frac{7}{8}[/tex]
So they buy [tex]\frac{7}{8}[/tex] of cheese.
Find a cubic function that has the roots 5 and 3-2i
Answer:
[tex]P(x)=x^3-11x^2+43x-65[/tex]
Step-by-step explanation:
If the complex number [tex]3-2i[/tex] is a root of a cubic function, then the complex number [tex]3+2i[/tex] is a root too. Thus, the cubic function has three known roots [tex]5,\ 3-2i,\ 3+2i[/tex] and can be written as
[tex]P(x)=(x-5)(x-(3-2i))(x-(3+2i)),\\ \\P(x)=(x-5)(x^2-x(3-2i+3+2i)+(3-2i)(3+2i)),\\ \\P(x)=(x-5)(x^2-6x+9-4i^2),\\ \\P(x)=(x-5)(x^2-6x+9+4),\\ \\P(x)=(x-5)(x^2-6x+13),\\ \\P(x)=x^3-11x^2+43x-65.[/tex]
the ordered pairs (1,6),(2,12),(3,18),(4,24) and (5,30) represent a function. what is a rule that represents this function?
y=6x
y=(x+6)^2
y=x^6
y=6x
One evening 1400 concert tickets were sold for the Fairmont Summer Jazz Festival. Tickets cost $20 for covered pavilion seats and $15 for lawn seats. Total receipts were $24,000. How many tickets of each type were sold?
To determine how many tickets of each type were sold, two equations were formulated and the system was solved using the elimination method, resulting in 600 covered pavilion seats and 800 lawn seats sold.
To solve this problem we need to set up a system of equations based on the information provided. Let's define two variables: x for the number of covered pavilion seats sold, and y for the number of lawn seats sold. We know that together, a total of 1400 tickets were sold and the total receipts from these sales were $24,000. We can set up the following equations:
1) x + y = 1400 (total number of tickets sold)
2) 20x + 15y = 24,000 (total revenue from ticket sales)
To solve the system of equations, you can use either substitution or elimination method. Let's use the elimination method by multiplying the first equation by -15 and adding it to the second equation to eliminate y.
-15x - 15y = -21,000
20x + 15y = 24,000
Add the two equations:
5x = 3,000
Divide both sides by 5:
x = 600
Now we can substitute x back into the first equation to solve for y:
600 + y = 1400
y = 800
Therefore, 600 covered pavilion seats and 800 lawn seats were sold.
What is the solution to
-x+3y=2
X+y=-2
Answer:
(-2, 0)
Step-by-step explanation:
Use elimination: add the two systems. Because the left is equal to right, you are adding the same thing and it's legal.
-x+3y=2
+ (x+y=-2)
Add each term
-x+x + 3y+y = 2+ -2
4y=0
y=0
x+y=-2
x+0=-2
x=-2
Answer:
x=-2, y=0
Step-by-step explanation:
-x+3y=2
X+y=-2
We can add these two equations together to eliminate x
-x+3y=2
x+y=-2
--------------
4y = 0
Divide each side by 4
4y/4 = 0/4
y=0
Now we still need to find x
x+y = -2
Substitute x=0
0+y = -2
y= -2
Identify a pattern in the given list of numbers. Then use this pattern to find the next number 5,9,14,20,27,35,____
Answer:
the answer is 44
Step-by-step explanation:
the pattern is 4,5,6,7,8 so then you would add 9 to get 44
Final answer:
The pattern in the given list of numbers is that each number increases by consecutively larger increments of 1. By continuing this pattern, adding 9 to the last number (35), we determine the next number in the series to be 44.
Explanation:
The given list of numbers is 5, 9, 14, 20, 27, 35, and we are asked to identify the pattern to find the next number in the series.
Let's look at the differences between consecutive terms: 9 - 5 = 4, 14 - 9 = 5, 20 - 14 = 6, 27 - 20 = 7, 35 - 27 = 8.
We can see that with each step, the difference increases by 1. This pattern suggests that the next difference should be 9.
To find the next number, we add 9 to the last number in the series: 35 + 9 = 44. Therefore, the next number in the series is 44.
What are the proofs in proving triangles are congruent?
ANSWER: SSS, SAS, ASA, AAS, or HL
EXPLANATION:
SAS: Three congruent sides on both triangles.
SAS: Two congruent sides and a congruent included angle on both triangles.
ASA: Two congruent angles and a congruent included side on both triangles.
AAS: Two congruent angles and a congruent side on both triangles.
HL: Two right triangles with one congruent leg and congruent hypotenuses.
The cost of belonging to a gym can be modeled by C(m)= 50m + 79.50, where C(m) is the total cost for m months of membership. State the meaning of the slope and y-intercept of this function with respect to the cost associated with the gym membership.
Answer:
The slope is 50, which is the cost per month of the gym membership, and 79.50 is the y intercept. It represents the initial cost to join the gym.
Step-by-step explanation:
C(m)= 50m + 79.50,
This is written in the form y= mx+b where m is the slope and b is the y intercept.
The slope is 50, which is the cost per month of the gym membership, and 79.50 is the y intercept. It represents the initial cost to join the gym.
The slope of the function represents the cost of each additional month of membership, while the y-intercept represents the initial cost of joining the gym.
Explanation:The slope of the function C(m) = 50m + 79.50 represents the cost of each additional month of gym membership. In this case, the slope is 50, meaning that for every additional month of membership, the cost increases by $50.
The y-intercept of the function, which is 79.50, represents the initial cost of joining the gym. This can be considered as the one-time fee or the cost for 0 months of membership.
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In a rectangle, the ratio of the length to the width is 5 : 2. The length of the rectangle is 13.875 feet greater than the width. What are the perimeter and the area of the rectangle?
The width of the rectangle is 5.55 ft and the length is 19.425 ft. The perimeter of the rectangle is 25.95 ft and the area is 107.95875 sq ft.
Explanation:To find the width of the rectangle, we can set up the equation
5/2 = 13.875 / width
Solving for width gives us width = 5.55 ft. Therefore, the length of the rectangle is 13.875 + 5.55 = 19.425 ft.
The perimeter of a rectangle is given by the formula 2(length + width). Substituting the given values, we get the perimeter to be 2(19.425 + 5.55) = 25.95 ft.
The area of the rectangle is given by the formula length * width. Substituting the given values, we get the area to be 19.425 * 5.55 = 107.95875 square feet.
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you roll a fair six-sided die twice. what is the probabilty of rolling an even number then rolling an odd number?
Answer:
Probability of rolling an even number then rolling an odd number = 1/4
Step-by-step explanation:
When we roll a fair six-sided die twice,
The pair of combinations are
(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)
(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)
(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)
(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)
(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)
(5,1),(6,2),(6,3),(6,4),(6,5),(6,6)
There are 36 possibilities
The odd numbers are 1,3 and 5
even numbers are 2,4 and 6
Possibilities of rolling an even number then rolling an odd number
(2,1),(2,3),(25)
(4,1),(4,3),(4,5)
(6,1),(6,3),(6,5)
There are 9 possibilities
Probability of rolling an even number then rolling an odd number = 9/36 = 1/4