When constructing an inscribed equilateral triangle, how many arcs will be drawn on the circle?
a. 3
b. 4
c. 5
d. 6
Answers
Perhaps a more usual method would be to start at D, draw an arc at E, then from there at B. Resetting the compass to have radius, DB, a third arc can be drawn at C using either B or D as the center. This method would give you
.. selection A: 3 arcs
If you didn't want to reset the compass, you could draw two more arcs, say from B to A, then from A to C. This method would give you
.. selection B: 4 arcs.
Related Questions
What is the value of 4.05 divide by 1.5?
Answers
The value of the expression 4.05 / 1.5 using the division property will be 2.7.
What is Algebra?Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.
The numbers are given below.
4.05 and 1.5
Then the division of the numbers 4.05 and 1.5 will be given by putting a division sign between them. Then we have
⇒ 4.05 / 1.5
⇒ 2.7
The value of the expression 4.05 / 1.5 using the division property will be 2.7.
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Final answer:
The result of dividing 4.05 by 1.5 is 2.7.
Explanation:
The value of 4.05 divided by 1.5 can be calculated by simply performing the division.
When you divide 4.05 by 1.5, you get 2.7.
This is because 4.05 is equivalent to 405 tenths, and when you divide 405 by 15 (since 1.5 is the same as 15 tenths), you end up with 27, or 2.7 when you adjust for the decimal placement.
1/6 of 3 yards=______feet
I know I just ask one but u get 17 points so plz help I'm stuck
Answers
In this question, first we have to see how many feets are in 1 yard .
And there are 3 feets in 1 yard.
So in 3 yards, there are 9 feets
Therefore we will get
[tex] \frac{1}{6}*3 yards= \frac{1}{6} * 9 feet = 1.5 feet [/tex]
Therefore the answer of the given question is 1.5 feet.
Final answer:
To find the equivalent feet for 1/6 of 3 yards, multiply 1/6 by 3 feet per yard to get 1.5 feet.
Explanation:
1/6 of 3 yards=_____feet
Step 1: 1 yard is equal to 3 feet.
Step 2: To find the equivalent feet for 1/6 of 3 yards, calculate 1/6 x 3 = 0.5 x 3 = 1.5 feet.
Which expression represents the sixth term in the binomial expansion of (5y+3)^10
Answers
[tex]\bf \stackrel{coefficient}{\left(\frac{n!}{k!(n-k)!}\right)} \qquad \stackrel{\stackrel{first~term}{factor}}{\left( a^{n-k} \right)} \qquad \stackrel{\stackrel{second~term}{factor}}{\left( b^k \right)}[/tex]
[tex]\bf \stackrel{coefficient}{\left(\frac{10!}{5!(10-5)!}\right)} \qquad \stackrel{\stackrel{first~term}{factor}}{\left( (5y)^{10-5} \right)} \qquad \stackrel{\stackrel{second~term}{factor}}{\left( (-3)^5 \right)} \\\\\\ 252(5y)^5(-3)^5\implies 252(5^5y^5)(-3)^5\implies -252(3125y^5)(243) \\\\\\ -191362500y^5[/tex]
Answer:
bb
Step-by-step explanation:
Please help me with questions 24
Answers
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After the translation, the triangle stays in quadrant IV. It then reflects over to quadrant I, only to rotate back to quadrant IV again. The size and shape does not change. These transformations are known as "rigid transformations" which preserve segment lengths (aka keep them the same). So the final triangle is congruent to the original triangle. All that has happened is that it has moved around.
A bathtub is filling with water at a rate of 60 liters per minute.How many liters of water are in the bathtub after t minutes?
Answers
Answer:
[tex]60t\text{ Liters}[/tex]
Step-by-step explanation:
We have been given that a bathtub is filling with water at a rate of 60 liters per minute. We are asked to find the water filled in the bathtub after t minutes.
To find the number of liters of water filled in tub after t minutes we will multiply rate of water filling by time.
[tex]\frac{60\text{ Liters}}{\text{Minute}}\times t\text{ minutes}[/tex]
[tex]60\text{ Liters}\times t[/tex]
[tex]60\times t\text{ Liters}[/tex]
[tex]60t\text{ Liters}[/tex]
Therefore, there were [tex]60t\text{ Liters}[/tex] of water in the bathtub after t minutes.
Elijah is going to spin a spinner that goes to 4 180 times.He predicts that 60 of those spins will result in the spinner landing on the section labeled 3. Based on the theoretical probability, which best describes Elijah’s prediction?
Answers
Answer:
A. Elijah’s prediction is exact because 180 divided by 3 = 60.
Step-by-step explanation:
Each blade on a windmill is in the shape of a triangle with a base of 7 ft and height of 4 ft if there are four blades on the windmill, what is the total area of the blades.
Answers
A=(1/2)b*h=(1/2)7*4=28/2=14
for four blades
14*4=56
Solution :
As per the problem we have
Each blade on a windmill is in the shape of a triangle with a base of 7 ft and height of 4 ft.
There are four blades on the windmill.
we have been asked to find the total area of the blades.
Area of one blade[tex] =\frac{1}{2}*base*height=\frac{1}{2}*7*4 =14 \ ft^2\\ [/tex]
Total are of blades[tex] =4*\text{Area of one blade}\\ [/tex]
Total are of blades[tex] =4*14=56 \ ft^2\\ [/tex]
A bond is a small, interest-bearing loan made by an individual to a corporate or government entity.
Please select the best answer from the choices provided
T
F
Answers
Answer: TRUE
Step-by-step explanation:
in 2012 the population of a city was 6.25 million the exponential growth rate was 3.22% per year
find the exponential growth function estimate the population of the city in 2018
Answers
[tex]F=A(1+r)^t[/tex]
F=final amount
A=initial amount
r=growth rate iin decimal form
t=time in years elapsed
so given
A=6.25 million
r=3.22%=0.0322
t=2018-2012=6
so
[tex]F=6.26(1+0.0322)^6[/tex]
[tex]F=7.57[/tex]
so it will be about 7.57 million in 2018
Translated these questions to a equation:
6 more than 9 times a number x is -12
the quotient of a number t and 7, plus 2, is -4
Answers
6 + 9x = -12
the quotient of a number t and 7, plus 2, is -4 ...
(t/7)+ 2 = -4
Hope this helps :)
A combination lock has a code consisting of 3 numbers, each of which can be 0 to 39, with numbers repeated. Jillian says that there are only 120 possible codes. Is Jillian correct? If not, explain her error.
Answers
Answer:
Jillian is not correct
Jillian has summed up the possible number of codes for each digit instead of multiplying it
Step-by-step explanation:
The lock has a code that consists of 3 number
It is given that the number in the lock code can be used between [tex]0[/tex] to [tex]39[/tex]
Thus, out of total [tex]40[/tex] set of numbers (i.e [tex]0-39[/tex]), the numbers can be repeated.
This means for all three code numbers the opportunity of choosing a number is same i.e. between [tex]0-39[/tex]
Now, the first digit of the code can be any number between [tex]0-39[/tex]
Like wise the second and third digit of the code can be any number between [tex]0-39[/tex]
Thus. the possible number of codes with repetition allowed are
[tex]40 * 40* 40\\64000[/tex]
Hence, Jillian is not correct
Jillian has summed up the possible number of codes for each digit instead of multiplying it
Answer:
No, Jillian is not correct. According to the fundamental counting principle, the total number of possible codes would be (40)(40)(40) = 64,000. Jillian multiplied by 3 instead of multiplying the number of possibilities for each digit.
Step-by-step explanation:
What is the slope of a line that is parallel to to the one shown? (-3, 2) (0, -2)
Answers
slope = (2 + 2)/(-3 - 0) = -4/3
parallel lines have same slope
so answer is -4/3
Let u = <6, -9>, v = <1, -4>. Find u - v.
A) <5, -5>
B) <10, -10>
C) <15, 5>
D) <7, -13>
Answers
In terms of a formula if we had the vectors u and v such that
u = <a,b>
v = <c,d>
then
u - v = <a-c, b-d>
Let's use that to get...
u - v = <6,-9> - <1,-4>
u - v = <6-1,-9-(-4)>
u - v = <6-1,-9+4>
u - v = <5,-5>
----------------------
Answer: A) <5,-5>
Final answer:
To find the difference between vectors u and v, subtract the components of v from the corresponding components of u, resulting in the vector A) <5, -5>.
Explanation:
The question involves finding the difference of two vectors u and v. To find the vector u - v, you subtract each corresponding component of vector v from vector u.
For the first component, subtract the x-component of v (1) from the x-component of u (6), which equals 5.For the second component, subtract the y-component of v (-4) from the y-component of u (-9), which equals -5.Thus, the vector u - v is A) <5, -5>.
In an office, the number of chairs, c , is equal to five more than twice the number of desks, d. Which equation matches the information?
Answers
d (unknown)
chair is 5 more than twice the number of desks
So if I'm not wrong
The answer should be
c = 5+2d
Please correct me if I'm wrong :D
Final answer:
The algebraic equation that represents the relationship between the number of chairs, c, and the number of desks, d, in an office, where the number of chairs is five more than twice the number of desks, is c = 2d + 5.
Explanation:
The student's question pertains to creating an algebraic equation based on a given word problem describing the relationship between the number of chairs (c) and desks (d) in an office. The problem states that 'the number of chairs, c, is equal to five more than twice the number of desks, d'.
To formulate the equation that illustrates this relationship, we apply the information provided:
Identify the number of chairs as c.Determine that c is 'five more than' something, which suggests addition.Recognize that 'twice the number of desks' means 2 times d, or 2d.Combine the above to conclude that the 'five more than' is added to the 'twice the number of desks', which gives us the equation c = 2d + 5.A bucket is put under a leaking ceiling. the amount of water in the bucket doubles every minute. after 8 minutes, the bucket is full. after how many minutes is the bucket half full? show work
Answers
The water in the bucket doubles every minute. After 8 minutes the bucket is full. This means a minute earlier (i.e. at 7th minute) the water in bucket was half as compared to water in bucket after 8 minute.
So, if after 8 minutes bucket is full, after 7 minutes bucket will be half full. So the answer is 7 minutes.
Help please ...........MATH
Answers
N=N0e^(-kt)
where
N is amount of C-14 at time t
N0 is the initial amount
k is the constant
t is the time taken
given that the amount found was 30% percent of the initial amount, the age of the mammal will be found as follows:
let N=x, N0=0.3x, k=0.0001, t=?
Plug in the formula we get:
0.3x=xe^(-0.0001t)
x will cancel and we shall remain with:
0.3=e^(-0.0001t)
introducing natural logs we get:
ln 0.3=-0.0001t
hence
t=ln0.3/(-0.0001)
t= 12039.7 years
One focus of a hyperbola is located at (−1, 7). One vertex of the hyperbola is located at (−1, 5). The center is (−1, −3). What is the equation of the hyperbola?
Answers
Answer:
C) (y+3)^2/64-(x+1)^2/36=1
Step-by-step explanation:
Just took the review in edg
To solve this problem, we just need to substitute the values into the equation and solve. the equation of hyperbola and solve. This will give
[tex]\frac{(y+ 3)^2}{64} - \frac{(x+1)^2}{36} =1[/tex]
Equation of a HyperbolaThe standard equation of a hyperbola is given as
[tex]\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1\\[/tex]
The data given are;
focus = (-1, 7)vertex = (-1, 5)center = (-1, -3)Let's substitute the values into the equation of hyperbola and solve. This will give
[tex]\frac{(y+ 3)^2}{64} - \frac{(x+1)^2}{36} =1[/tex]
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△ABC is reflected to form △A′B′C′ . The vertices of △ABC are A(3, 1) , B(1, 5) , and C(6, 9) . The vertices of △A′B′C′ are A′(−1, −3) , B′(−5, −1) , and C′(−9, −6) . Which reflection results in the transformation of △ABC to △A′B′C′ ?
Answers
Answer:
that would be a reflection across the y axis resulting in a -x
Step-by-step explanation:
Point R is located at (11,5).point S is located at (-1,5). what is the distance between point R and point S
Answers
d=√(x2-x1)² + (y2-y1)²
d=√(-1-11)² + (5-5)²
d=√(-12)² + 0
d=12
Sherri uses her credit card to pay for new transmission that ended up totaling $1,050.25. She can pay off up to $400 a month. The card has an annual rate of 18.5%. How much will she pay in interest?
Answers
Please tell Sherri that it is less expensive to get a bank loan than to use the credit card.
Principal, P=1050.25
interest rate, i = 18.5%/12 per month
Monthly Repayment, A = 400
We need to calculate the monthly balance to know how many months it takes her to pay off the debit, and hence the interest charge.
As usual, we assume the debit is made at the beginning of the month, and the $400 paid at the end of the month. In actual practice, all these debits and credits are calculated on a daily balance basis, and interest accumulated at the end of the month.
The monthly interest is calculated as the balance from last month multiplied by the interest rate, 18.5%/12. The amount owing (at the end of the month)
F=Balance(1+0.185/12)
month Owing Paid Balance Calculation of owing next month
0 1050.25 0 1050.25 1050.25*(1+0.185/12)=1066.44
1 1066.44 400 666.44 666.44(1+0.185/12)=676.72
2 676.72 400 276.72 276.72(1+0.185/12)=280.98
3 280.98 290.98 ................... loan paid off
Total interest paid = 400+400+290.98 - 1050.25 = 40.73
Sherri will pay approximately $30.69 in interest on her credit card debt of $1,050.25 with an 18.5% annual interest rate, assuming she makes payments of $400 per month and the interest compounds monthly.
To calculate how much interest Sherri will pay on her credit card debt, we need to know how the interest compounds. Typically, credit card interest is compounded daily, but since we do not have the compound frequency, we'll use a simplified approach to estimate the interest assuming the interest is compounded monthly.
The annual interest rate is 18.5%, which translates to a monthly rate of 18.5%/12 = 1.54%. Since Sherri can pay $400 a month, we can calculate the time it will take for her to pay off the principal without considering interest. This gives us $1,050.25 / $400 < 3 months.
Since the debt would be paid off in less than three months, we can estimate the interest for each month and sum it up:
First month interest: $1,050.25 < 0.0154 = $16.17Second month principal: $1,050.25 - $400 + $16.17 = $666.42Second month interest: $666.42 < 0.0154 = $10.26Third month principal: $666.42 - $400 + $10.26 = $276.68Third month interest: $276.68 < 0.0154 = $4.26Adding up these interest payments gives us approximately:
$16.17 + $10.26 + $4.26 = $30.69 in interest.
Please note, this is an estimation that assumes a linear payment model. Actual interest charges could be higher due to daily compounding.
how many radians are in a semicircle? a.2π, b.π, c.π/2, d.3π/2
Answers
A semicircle, which is half of a full circle, consists of half the total amount of radians in a full circle. Since a full circle has 2π radians, a semicircle contains π radians. Therefore, the correct answer is b.π.
Explanation:To answer your question, let's review the structure of a circle.It is divided by its radius into 360 degrees or by its diameter into a full rotation of 2π radians. Therefore, a semicircle, which is half of a circle, must consist of half the total amount of radians in a full circle.
In a full circle, there are 2π radians. Hence, in a semicircle, which is exactly half of the full circle, there would be 2π/2. This simplifies to π radians.
So, the correct answer to your question 'How many radians are in a semicircle?' is b.π.
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Ari thinks the perfect milkshake has 3 ounces of caramel for every 5 scoops of ice cream. Freeze Zone makes batches of milkshakes with 6 ounces of caramel and 8 scoops of ice cream. What will Ari think about Freeze Zone's milkshakes?
Answers
Answer: Ari thinks amount of caramel is more for perfect milkshake as there is only need for 4.8 ounces of caramel but Freeze Zone is using 6 ounces of caramel.
Step-by-step explanation:
Since we have given that
Ari has 3 ounces of caramel for every 5 scoops of ice-cream .
Freeze Zone makes batches of milkshakes with 6 ounces of caramel and 8 scoops of ice-cream.
According to Ari,
For every 5 scoops of ice-cream, he needs 3 ounces of caramel
For every 1 scoop of ice-cream, he needs
[tex]\frac{3}{5}\text{ ounces of caramel}[/tex]
For every 8 scoops of ice-cream, he needs
[tex]\frac{3}{5}\times 8=\frac{24}{5}=4.8\text{ ounces of caramel}[/tex]
So, Ari thinks amount of caramel is more for perfect milkshake as there is only need for 4.8 ounces of caramel but Freeze Zone is using 6 ounces of caramel.
Ari will think Freeze Zone's milkshakes have the perfect amount of caramel.
Explanation:To determine what Ari will think about Freeze Zone's milkshakes, we need to compare the ratio of caramel to ice cream in Ari's perfect milkshake to the ratio in Freeze Zone's milkshakes.
Ari's perfect milkshake has 3 ounces of caramel for every 5 scoops of ice cream, so the ratio is 3:5.
Freeze Zone's milkshakes have 6 ounces of caramel for every 8 scoops of ice cream, so the ratio is 6:8.
To simplify both ratios, we can divide the numbers by their greatest common divisor. The GCD of 3 and 5 is 1, so the simplified ratio for Ari's perfect milkshake is 3:5. The GCD of 6 and 8 is 2, so the simplified ratio for Freeze Zone's milkshakes is 3:4.
Since both ratios are the same, we can conclude that Ari will think Freeze Zone's milkshakes have the perfect amount of caramel.
Use Cavalieri’s Principle to calculate the exact volume of an oblique cylinder with a radius of 10 meters and a height of 11 meters
Answers
so, the volume of a cylinder is V = πr²h.
now, we know the radius is 10, and the height is 11, so then V = π10²*11 is its volume.
The exact volume of the oblique cylinder with a radius of 10 meters and a height of 11 meters is 110π cubic meters.
To calculate the exact volume of an oblique cylinder using Cavalieri's Principle, follow these steps:
1. Consider a right cylinder with the same base and height as the oblique cylinder. The volume of the right cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
2. Since the oblique cylinder and the right cylinder have the same base and height, their volumes are equal according to Cavalieri's Principle.
3. The formula for the volume of a right cylinder can be applied to the oblique cylinder, giving the volume as V = πr^2h.
4. Substituting the values of the radius (r = 10 meters) and height (h = 11 meters) into the formula gives V = π(10)^2(11) = 110π cubic meters.
5. Therefore, the exact volume of the oblique cylinder with a radius of 10 meters and a height of 11 meters is 110π cubic meters.
A rectangular prism has a length of 4 1/2 millimeters, a width of 4 1/2 millimeters, and a height of 6 millimeters.
Sally has a storage container for the prism that has a volume of 143 cubic millimeters.
What is the difference between the volume of the prism and the volume of the storage container?
Help Please?
Answers
V = (4 1/2)(4 1/2)(6)
Converting the fractions to mixed numbers we have
V = (9/2)(9/2)(6/1) = 486/4 = 121.5
The storage container has a volume of 143, so the difference is 143 - 121.5 = 21.5 cubic mm.
Answer:
21 1/2
Step-by-step explanation:
If $200 is put in the bank and each year the account earns 5% simple interest, then how much interest will be earned in two years?
Answers
Sal can mop a certain floor in 8 minutes by himself.If Sal and ben can mop the floor together in 6 minutes,how long does it take Ben to mop the floor alone?
Answers
The measure of angle E, the angle of elevation from point A to point B, is 5(x-2). The measure of angle D, the angle of depression from point B to point A, is (x+14). Find the measure of each angle.
Answers
5(x -2) = x +14
5x -10 = x +14 . . . . . . . eliminate parentheses
4x = 24 . . . . . . . . . . . . add 10-x
x = 6
The angles of elevation and depression are both (6+14)° = 20°.
Answer:
measure of angle E equals 20 degrees, measure of angle D equals 20 degrees
The scale on a map is 1 cm for every 400 km. If Maine and Japan are 22 cm apart on the map, what is the distance between Maine and Japan?
Answers
After losing 30 pounds, an individual weigh 110 pound more than one-third his previous weight
Answers
For an instance, x is the previous weight
"After losing 30 pounds" could be written as (x - 30)
"110 pounds more than one-third his previous" could be written as (110 + [tex] \frac{1}{3} [/tex]x)
Join the expression and solve for x
x - 30 = 110 + [tex] \frac{1}{3} [/tex]x
Move 1/3 x to the left side, and the constant of 30 to the right side, so like terms will be on equal side
x - [tex] \frac{1}{3} [/tex]x = 110 + 30
Equalize the denominators of the fractions
[tex] \frac{3}{3} [/tex]x - [tex] \frac{1}{3} [/tex]x = 140
[tex] \frac{2}{3} [/tex] = 140
x = 140 × [tex] \frac{3}{2} [/tex]
x = 420/2
x = 210
The previous weight was 210 pounds
The new weight is 210 - 30 = 180 pounds
Ruben has two congruent wooden dowels. He cuts one dowel in two in order to have three pieces to make a triangle. Explain why, despite having three sides, Ruben will not be able to make a triangle with his three pieces.
Answers
After cutting one of the dowels, the lengths will then be
x/2, x/2,x.
He cannot form a triangle using the three dowels because the triangle inequality requires that the sum of the two shorter sides of a triangle must be greater than the third side. Here x/2+x/2=x equals the third side, so a triangle cannot be formed.
By the way, if he cuts the long dowel a little shorter, he will then be able to make a triangle.
Answer:
The dowels are congruent, so they have the same length. If one is cut, the sum of the lengths of the two cut pieces will equal the length of the longer piece. If the pieces are to make a triangle, the sum of the lengths of the two cut pieces must be greater than the length of the third piece.
Step-by-step explanation: