Answer:
52.33% is the correct answer.
Step-by-step explanation:
Given that:
Area of triangle = 24 sq units
Center of Circle is at (0, 0) and the circle passes through (1.2, 1.6).
To find: The percentage of triangle covered by circle.
Solution: To find the required percentage, we need to find the area of circle.
To find the area of circle, we need the radius of circle.
Radius of circle is the distance between the center of circle and any point that lies on the periphery of the circle.
We can use Distance formula :
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Radius = [tex]\sqrt{(1.2-0)^2+(1.6-0)^2} = \sqrt{1.44+2.56} = \sqrt{4} = 2\ units[/tex]
Now, area of circle is given by the formula:
Area = [tex]\pi r^{2}[/tex]
Area = 3.14 [tex]\times 2^{2}[/tex] = 12.56 sq units
Percentage of Triangle covered:
[tex]\dfrac{Area\ of\ circle}{Area\ of\ triangle}\times 100\\\Rightarrow \dfrac{12.56}{24}\times 100\\\Rightarrow 52.33\%[/tex]
Hence, 52.33% is the correct answer.
Answer:
52%
Step-by-step explanation:
Khan Academy.
What numbers do you need to determine the surface area of a right cone? ANSWERS: The radius of the base, r, and the altitude h. The altitude h and the slant height s. The radius of the base, r, and the slant height s. You must have all three numbers r, s, and h.
Answer:
The Radius of the base, r, and the altitude h
Step-by-step explanation:
Surface area of a right cone
[tex]a=\pi r\sqrt{h^{2}+r^{2} }[/tex]
R= Radius
H=Radius
Answer:
The radius of the base, r, and the slant height s.
Step-by-step explanation:
pf
Ama's age is two thirds that of her elder sister. Four years ago ama's age was half the sister's. How old is the sister?
Answer:
12
Step-by-step explanation:
Ama's sister is 12 now and Ama is 8. 8/12 simplified is 2/3.
Four years ago Ama's would have been 4 and her sister would have been 8. 4/8 simplified is 1/2.
The equations:
(Ama is a)
(Ama's sister is s)
a = (2/3)s
a - 4 = (1/2)(s - 4)
Step one:
You would substitute the first equation into the second equation to get
(2/3)s - 4 = (1/2)(s - 4)
Step two:
Multiply by 6 to get rid of the fractions to get
4s - 24 = 3(s - 4)
Step three:
Simplify to get
4s - 24 = 3s - 12
Step four:
Subtract 3s and add 24 to get
s = 12
Step five:
Input the s value into the first equation to get
a = (2/3)(12) = 8
If this helped please rate, thanks, and mark brainliest! Also, please comment if it's correct :)
Step-by-step explanation:
let ama's age be x
and ama's sister be y
according to question
3x=2y --------(1)
x-4=(y-4)/2 ---------(2)
after solving equation (1) and (2)
we get ama's age is 8 years and AMA'S SISTER AGE IS 12 years
if -5 is a root of the quadratic equation 2x2+px-15=0 and the quadratic equation p(x^2+x)+k=0 has equal roots. find the value of k
Answer:
[tex]$k=\frac{7}{4} $[/tex]
Step-by-step explanation:
[tex]2x^2+px-15=0[/tex]
Once [tex]x=-5[/tex]
[tex]2(-5)^2+p(-5)-15=0[/tex]
[tex]2(25)-5p-15=0[/tex]
[tex]50-5p-15=0[/tex]
[tex]35-5p=0[/tex]
[tex]p=7[/tex]
Quadratic Equation:
[tex]2x^2+7x-15=0[/tex]
[tex]p(x^2+x)+k=0 \Rightarrow 7(x^2+x)+k=0 \Rightarrow 7x^2+7x+k=0[/tex]
[tex]\Delta=b^2-4ac[/tex]
[tex]\Delta=7^2-4(7)k[/tex]
[tex]\Delta=49-28k[/tex]
The quadratic equation having two equal roots means that the discriminant is equal to zero.
[tex]0=49-28k[/tex]
[tex]-49=-28k[/tex]
[tex]$k=\frac{49}{28} $[/tex]
[tex]$k=\frac{7}{4} $[/tex]
Helps pls Three generous friends, each with some cash, redistribute their money as follows: Ami gives enough money to Jan and Toy to double the amount that each has. Jan then gives enough to Ami and Toy to double their amounts. Finally, Toy gives Ami and Jan enough to double their amounts. If Toy has $36 when they begin and $36 when they end, what is the total amount that all three friends have?
Answer:
The total amount that all three friends have = $258
Step-by-step explanation:
Three friends: let their initial money be Ami's money =A, Jan = B, Toy = C
Toy started with $36 and ended with same amount
C = $36
After Ami gives, She is left with= A-x
Jan becomes= 2B
Toy becomes= 2C = 2×36 = 72
After Jan gives, Jan is left with = 2B-y
Ami now has = 2(A-x)
Toy now has = 2(72) = 144
After Toy gives, Toy is left with= 144-z
Ami now has = 2(2)(A-x) = 4(A-x)
Jan now has = 2(2B-y)
Since Toy is left with $36 at the end:
36 = 144-z
z = 144-36 = 108
So Toy spent $108 to double his two other friend's money
Both Amy and Jan had $108 in total when Toy had $144
Difference between the deductions across = $108
The total amount that all three friends have = 144+108
The total amount that all three friends have= $258
Answer:
The answer is 252
Step-by-step explanation:
The tabletop below is made from right triangles, each the same size. Your company charges $0.20 per square inch for sanding the tabletop. Which of the following is closest to the tabletop’s area, in square inches28 1/4"*4+20*4=a. 550 b.950 c.2,800 d.3,950 e.5,600
Answer: The correct answer is c.
Step-by-step explanation:
You take the area of the square which is 20x20 = 400.
There is 5 squares 400x5 = 2000
There is 4 triangles--which is 1/2 the area of 1 square (In this case).
One triangle = 200
200x4 = 800
2000 + 800 = 2800
Hess Company's inventory records show the following data for the month of September: Units Unit Cost Inventory, September 1 100 $3.00 Purchases: September 8 450 3.50 September 18 300 3.70 A physical inventory on September 30 shows 150 units on hand. Calculate the value of ending inventory and cost of goods sold if the company uses LIFO inventory costing and a periodic inventory system.
Answer:
Yes
Step-by-step explanation:
Give the starting value a, the growth factor b, and the growth rate r if Q = abt = a(1 + r)t Write r as a percent. Q = 1750 (1.593) Superscript t a. a = 1750 b = 1.593 r = 0.593% c. a = 2787.75 b = 2.5376 r = 0.593% b. a = 1750 b = 1.593 r = 59.3% d. a = 2787.75 b = 1.593 r = 59.3%
Answer:
Option b.
Step-by-step explanation:
If the starting value a, the growth factor b, and the growth rate r, then
[tex]Q=ab^t=a(1+r)^t[/tex] ...(1)
It is given that
[tex]Q=1750(1.593)^t[/tex] ...(2)
On comparing (1) and (2), we get
[tex]a=1750, b=1.593[/tex]
Now, equation (2) can be rewritten as
[tex]Q=1750(1+0.593)^t[/tex] ...(3)
On comparing (1) and (2), we get
[tex]r=0.593[/tex]
[tex]r=(0.593\times 100)\%[/tex]
[tex]r=59.3\%[/tex]
Therefore, the correct option is b.
Which of the following is the first step in problem solving?
Answer:
process of elimination
Step-by-step explanation:
Answer:
The 1st step in problem solving is defining your variables.
Step-by-step explanation:
When you read the word problem, you have to make sure you know which variables are which, or else you will get lost. If you don't label your variables, then you will not be able to answer the question properly.
A triangle has sides 45, 4x and 2x−4. What is the possible range of x?
x>2
The greatest possible value cannot be stated as it is not mentioned whether it is a right angled triangle, which is hypotenuse, or which is the smallest/largest side.
Answer:
49/6 < x < 41/2.
Step-by-step explanation:
In any triangle, each side is shorter than the sum of two other sides.
It gives three independent inequality
45 < 4x + (2x-4), (1)
4x < 45 + (2x-4), (2)
2x-4 < 45 + 4x. (3)
From (1), 6x > 45 + 4 = 49 ---> x > 49/6
From (2), 2x < 45 - 4 = 41 ---> x < 4/2
From (3), 2x > -4 - 45 = -49 ---> x > -49/2
PLEASE HELP IM STUCK
Answer:
Vertex: (0, 12)
Direction: Upwards
Step-by-step explanation:
Easiest way to do this is to graph it. When you do so you should be able to see that your vertex is at (0, 12) and that the graph opens upwards (a is not negative, so no reflection over the x-axis).
Hey guys help me solve for x!!!
Answer:
X=10solution,
In a parallelogram, diagonal bisects angle into two equal parts. So,
<TVU=<TVW
or, 5x=50
or, X=50/5
X=10
Hope this helps..
Good luck on your assignment.
Answer:
[tex]x = 10[/tex]
Step-by-step explanation:
WVT angle = UTV angle (alternative angles)
* sum of the interior angles in a triangle =180° In UVT triangle,[tex]80 + 5x + 50 =1 80 \\ 130 + 5x = 180 \\ 5 x = 180 - 130 \\ 5x = 50 \\ \frac{5x}{5} = \frac{50}{5} \\ x = 10[/tex]
Diego paid $47 for 3 tickets to a concert. Andre paid $141 for 9 tickets to a concert. Did they pay at the same rate?
Answer:
They did pay at the same rate
Step-by-step explanation:
when dividing 47 by 3 you get 15.666... and when dividing 141 by 9 you also get 15.666... using this you can deduce that it is the same rate.
Answer:
Yes
Step-by-step explanation:
We can use ratios for this:
Diego:
47:3 tickets
Divide both sides by 3 so you get the price of one ticket
15.67: 1 ticket
Andre:
141: 9 tickets
Divide both sides by 9 so you get the price of one ticket
15.67: 1 ticket
What is a solution in math?
A solution is an assignment of values to the unknown variables that makes the equality in the equation true.
Answer:
what the variable is equal to
Step-by-step explanation:
for example, in a equation like 1x = 2x/2 the solution could be x=1
Which algebraic expression represents the phrase below?
five times the sum of a number and eleven, divided by three times the sum of the number and eight
5(x + 11) + 3(x + 8)
StartFraction 5 x + 11 Over 3 x + 8 EndFraction
Start Fraction 5 (x + 11) Over 3 (x + 8) EndFraction
5x + 11 + 3x + 8
Answer:
5(x+11)/3(x+8) = 5x+55/3x+24
Step-by-step explanation:
The Answer Happens to be:
c
Use addition to solve the linear system of equations. Include all of your work in your final answer. x-y=6 y=x-4
Answer:
no solutions
Step-by-step explanation:
x-y=6
y=x-4
Subtract x from each side
-x+y = x-4-x
-x+y = -4
Add this to the first equation
x-y=6
-x+y = -4
---------------
0x + 0y = 2
0=2
This is never true so there are no solutions
Answer:
No solutions.
Step-by-step explanation:
x - y = 6
y = x - 4
Solve for x in the first equation.
x = 6 + y
Put x as 6 + y in the second equation and solve.
y = (6 + y) - 4
y - y = 6 - 4
0 = -2
There are no solutions.
Select the correct answer from each drop-down menu.
Point C(3.6, -0.4) divides in the ratio 3 : 2. If the coordinates of A are (-6, 5), the coordinates of point B are ____
If point D divides in the ratio 4 : 5, the coordinates of point D are ____
(fraction)
Answer:
Coordinates of point B are (10,-4)
Coordinates of point D are (3.6,-0.4)
Step-by-step explanation:
1) Point C(3.6, -0.4) divides in the ratio 3 : 2. If the coordinates of A are (-6, 5), the coordinates of point B are ____
Let the coordinates of B be [tex](x_2,y_2)[/tex]
Coordinates of A =[tex](x_1,y_1)=(-6,5)[/tex]
Coordinates of C=(x,y)=(3.6,-0.4)
We will use section formula over here
[tex]x=\frac{mx_2+nx_1}{m+n} , y = \frac{my_2+ny_1}{m+n}[/tex]
m:n=3:2
[tex]3.6=\frac{3x_2+2(-6)}{3+2} , -0.4=\frac{3y_2+2(5)}{3+2}3.6 \times 5 = 3x_2-12, -0.4 \times 5 = 3y_2+10\\18+12=3x_2 , -2=3y_2+10\\30=3x_2 , -12=3y_2\\10=x_2, -4=y_2\\[/tex]
Coordinates of B = (10,-4)
2)If point D divides in the ratio 4 : 5, the coordinates of point D are ____
(fraction)
Let the coordinates of D be [tex](x,y)[/tex]
Coordinates of A =[tex](x_1,y_1)=(-6,5)[/tex]
Coordinates of B=[tex](x_2,y_2)=(10,-4)[/tex]
We will use section formula over here
[tex]x=\frac{mx_2+nx_1}{m+n} , y = \frac{my_2+ny_1}{m+n}[/tex]
m:n=3:2
[tex]x=\frac{3(10)+2(-6)}{3+2} , y=\frac{3(-4)+2(5)}{3+2}\\x=3.6,y=-0.4[/tex]
Coordinates of point B are (10,-4)
Coordinates of point D are (3.6,-0.4)
Answer:
B is (10, -4), and D is (58/9, -2)
Step-by-step explanation:
(5.3a−0.8)−(1.6−4.7a)=2a−(a−0.3)
Answer: a = 0.3
Step-by-step explanation:
First, distribute(-1)
5.3a-0.8-1.6+4.7a=2a-(a-0.3)
Then, distribute(-1)
5.3a-0.8-1.6+4.7a=2a-a+0.3
Then, combine like terms
10a-2.4=a+0.3
Then, add(2.4)
10a=a+2.7
Then, subtract(a)
9a=2.7
Then, divide(9)
a = 0.3
Hope it helps <3
Answer:
a = 0.3.
Step-by-step explanation:
(5.3a−0.8)−(1.6−4.7a)=2a−(a−0.3)
5.3a − 0.8 − 1.6 + 4.7a = 2a − a + 0.3
5.3a + 4.7a - 2a + a = 0.3 + 0.8 + 1.6
9a = 2.7
a = 0.3.
Given that [Image Display]
What is the domain of the function f ?
a.
only positive integers
c.
only negative integers
b.
All non zero real numbers.
d.
All real numbers including zero
Answer:
The answer is option D.
All real numbers including zero
Hope this helps
Answer:
all non zero real numbers is the answer to the question.
this is because 0 cannot be a function of f of x because you would have undefined as an answer so therefore the answer is all non zero real numbers
A total of $5900 is invested, part at 11% simple interest and part at 7%. If the total annual return from the two investments is $ 537.00, how much is invested at each rate?
How much was invested at 11% ? $____
Answer:
Step-by-step explanation:
y = 5900 - x
Simple interest = Prt
Simple interest on $x = x * 0.11 * 1 = 0.11x
Simple interest on $ (5900 - x) = (5900 - x) * 0.07 * 1
= (5900 - x) * 0.07
= 5900 * 0.07 - x * 0.07
= 413 - 0.07x
Return from tow investment = $ 537
0.11x + 413 - 0.07x = 537
Add the like terms
0.04x + 413 = 537
Subtract 413 for both sides
0.04x = 537 - 413
0.04x = 124
x = 124 /0.04
x = 3100
y = 5900 - 3100 = 2800
x = $ 3100
y = $ 2800
2 3 8 63 what number is next
Answer:
The answer is 3968
63 squared= 3969
3969-1 = 3968
The face of the triangular concrete panel shown has an area of 22 square meters, and its base is 3 meters longer than twice its height. Find the length of the base.
Answer:
The length of the base is 11 meters.
Step-by-step explanation:
The diagram of the triangle is not shown; However, the given details are enough to solve this question.
Given
Shape: Triangle
Represent the height with h and the base with b
[tex]b = 3 + 2h[/tex]
[tex]Area = 22[/tex]
Required
Find the length of the base
The area of a triangle is calculated as thus;
[tex]Area = \frac{1}{2} * b * h[/tex]
Substitute 22 for Area and 3 + 2h for b
The formula becomes
[tex]22 = \frac{1}{2} * (3 + 2h) * h[/tex]
Multiply both sides by 2
[tex]2 * 22 = 2 * \frac{1}{2} * (3 + 2h) * h[/tex]
[tex]44 = (3 + 2h) * h[/tex]
Open the bracket
[tex]44 = 3 * h + 2h * h[/tex]
[tex]44 = 3h + 2h^2[/tex]
Subtract 44 from both sides
[tex]44 - 44 = 3h + 2h^2 - 44[/tex]
[tex]0 = 3h + 2h^2 - 44[/tex]
Rearrange
[tex]0 = 2h^2 +3h - 44[/tex]
[tex]2h^2 +3h - 44 = 0[/tex]
At this point, we have a quadratic equation; which is solved as follows:
[tex]2h^2 +3h - 44 = 0[/tex]
[tex]2h^2 + 11h - 8h - 44 = 0[/tex]
[tex]h(2h + 11) - 4(2h + 11) = 0[/tex]
[tex](h - 4)(2h + 11) = 0[/tex]
Split the above
[tex](h - 4) = 0\ or\ (2h + 11) = 0[/tex]
[tex]h - 4 = 0\ or\ 2h + 11 = 0[/tex]
Solve the above linear equations separately
[tex]h - 4 = 0[/tex]
Add 4 to both sides
[tex]h - 4 + 4 = 0 + 4[/tex]
[tex]h = 0 + 4[/tex]
[tex]h = 4[/tex] ---- First value of h
[tex]2h + 11 = 0[/tex]
Subtract 11 from both sides
[tex]2h + 11 - 11 = 0 - 11[/tex]
[tex]2h = 0 - 11[/tex]
[tex]2h = -11[/tex]
Divide both sides by 2
[tex]\frac{2h}{2} = -\frac{11}{2}[/tex]
[tex]h = -\frac{11}{2}[/tex] ------ Second value of h
Since height can be negative, we'll discard [tex]h = -\frac{11}{2}[/tex]
Hence, the usable value of height is [tex]h = 4[/tex]
Recall that [tex]b = 3 + 2h[/tex]
Substitute 4 for h
[tex]b = 3 + 2(4)[/tex]
[tex]b = 3 + 8[/tex]
[tex]b = 11[/tex]
Hence, the length of the base is 11 meters
Michaela has three times as many folders as Alejandro. Michaela gives Alejandro 5 folders, but still has 8 more than Alejandro. How many folders did Michaela have originally? A) 9 B) 12 C) 22 D) 27
Answer:
there were 22 folders originally
Michaela originally has 27 folders. Hence option D) is correct.
Michaela has three times as many folders as Alejandro.
Michaela gives Alejandro 5 folders, but still has 8 more than Alejandro.
In mathematics it deals with numbers of operations according to the statements.
Now, let Alejandro has x folders corresponding Michaela has 3x folders
According to the condition
3x-5 = x+5+8
2x = 18
x = 9
now
Michaela = 3x
= 3 x 9
= 27
Thus, Michaela originally has 27 folders.
Learn more about arithmetic here:
brainly.com/question/14753192
#SPJ2
Henry has quarters, dimes, nickels and pennies in a coin jar. He says that the total amount of money is two dollars and forty-one cents. He also claims that there are exactly twenty-three pennies. Let q be the number of quarters, d be the number of dimes, and n be the number of nickels. Which equation represents the relationship expressed above?
a. q + d + n = 23
b.q + d + n + 23 = 241
c. 25q + 10d + 5n + 23 = 2.41
d.25q + 10d + 5n + 23 = 241
Answer: D
Step-by-step explanation:
All would add up to 241 instead of 2.41 because you are not using decimals for the constants (Example: 25q not .25q)
PLEASE HELP For a particular transformer, the voltage E in the circuits is related to the number of windings W of wire around the core by the equation E=40W. How many windings will produce a voltage of 760 V? A voltage of 760 V will be produced by ? windings.
Answer:
A voltage of 760V will be produced by 19 windings.
Step-by-step explanation:
Given the equation:
E = 40W
Where E is the Voltage in the circuits
and W is the number of windings
Given that E = 760V
To find: W = ?
Solution: Here, we have the given equation in 2 variables where value of 1 variable is given so other can be easily calculated by putting the value of given variable in the equation.
So, Putting the value of E in the given formula and finding W, the number of windings:
[tex]760=40 \times W\\\Rightarrow W = \dfrac{760}{40}\\\Rightarrow W = \dfrac{76}{4}\\\Rightarrow W = 19[/tex]
So, number of windings for a voltage E = 760V is 19.
A voltage of 760V will be produced by 19 windings.
solve for X 68=-52x+16
Answer:
-1
Step-by-step explanation:
Move the +16 onto the other side. We now have 52 = -52x. Divide each side by 54 to get x = -1.
Answer:
-1=x
Step-by-step explanation:
68=-52x+16
Minus sixteen on both sides
52=-52x
Divide -52 on both sides which will equal to -1
-1=x
21.
6
Which ratio can form a proportion with 6/9
12/8
8/12
10/12
8/13
Step-by-step explanation:
6/9 divide top and bottom by 3 to get 2/3
Now reduce each of the fractions to the lowest terms, and look for one that gives 2/3.
12/8 = 3/2 (divide by 4 top and bottom)
8/12 = 2/3 (divide by 4 top and bottom) This is a solution
10/12 = 5/6 (divide by 2 top and bottom)
8/13 (cannot be reduced)
Therefore the second fraction (8/12) forms a proportion with 6/9.
Answer:
8/12
Step-by-step explanation:
divide through by 2 6/9 = 2/3
also,
divide through by 4
8/12 = 2/3
6/9 = 8/12
A coin is tossed and a number cube is rolled. What is the probability that the coin shows heads and the number cube shows 5? a. 1/6 b. 1/12 c. 2/3 d. 1/4
Answer:
1/12
Step-by-step explanation:
P( coin = heads) = number of heads / total = 1/2
P( cube = 5) = number of 5's / total =1/6
P( heads, 5) =1/2 * 1/6 = 1/12
The coin toss and the number cube roll are independent events.
This is because the result of the coin toss does
not affect the result of the number cube roll.
To find the probability of two independent events, we first find the probability of each event, then we multiply the probabilities.
Since there is only one way to get heads when tossing a coin and there are 2 possible outcomes, tossing a heads or tails, the probability of getting heads is 1/2.
Since there is only one way to roll 5 on a number cube, there
is 1 favorable outcome but six possible outcomes.
So the probability of rolling a 5 is 1/6.
Now multiply.
So we have 1/2 · 1/6 which is 1/12.
Round the numbers to estimate the quotient.
29 1/5 ÷ 4 6/7
Nhich numbers should be used?
Answer:
≈ 5.8
Step-by-step explanation:
Step 1: Round the fractions
29 1/5 = 146/5 = 29.2 ≈ 29
4 6/7 = 34/7 = 4.85714 ≈ 5
Step 2: Divide
29/5 = 5.8
The answer is under
Which division expression is equivalent
Answer:
Step-by-step explanation:
the division expression equivalent to 4 1/3 / (-5/6) is
13/3 / (-5/6)
The solution is A
4 1/3 is 13/3
4x3= 12 + 1 = 13 which is 13/3
Parallel lines s and t are cut by a transversal r. Parallel lines s and t are cut by transversal r. Clockwise from top left, the angles formed with r and s are 1, 2, 3, 4; the angles formed with r and t are 5, 6, 7, 8. Which angles are corresponding angles? Angle3 and Angle7 Angle1 and Angle7 Angle4 and Angle6 Angle1 and Angle8
Answer:
Option A.
Step-by-step explanation:
Consider the below figure attached with this question.
Corresponding angles : If a transversal line intersect two parallel lines, then it makes 4 angles at each intersection point. The angles with same relative position at each intersection is know as corresponding angles.
From the clear figure it is clear that the pair of corresponding angles are:
[tex]\angle 1\text{ and }\angle 5[/tex]
[tex]\angle 2\text{ and }\angle 6[/tex]
[tex]\angle 3\text{ and }\angle 7[/tex]
[tex]\angle 4\text{ and }\angle 8[/tex]
Therefore, the correct option is A.
Answer:
a
Step-by-step explanation: