Answer:
c. 36·x
Step-by-step explanation:
Part A
The details of the circle are;
The area of the circle, A = 12·π cm²
The diameter of the circle, d = [tex]\overline {AB}[/tex]
Given that [tex]\overline {AB}[/tex] is the diameter of the circle, we have;
The length of the arc AB = Half the the length of the circumference of the circle
Therefore, we have;
A = 12·π = π·d²/4 = π·[tex]\overline {AB}[/tex]²/4
Therefore;
12 = [tex]\overline {AB}[/tex]²/4
4 × 12 = [tex]\overline {AB}[/tex]²
[tex]\overline {AB}[/tex]² = 48
[tex]\overline {AB}[/tex] = √48 = 4·√3
[tex]\overline {AB}[/tex] = 4·√3
The circumference of the circle, C = π·d = π·[tex]\overline {AB}[/tex]
Arc AB = Half the the length of the circumference of the circle = C/2
Arc AB = C/2 = π·[tex]\overline {AB}[/tex]/2
[tex]\overline {AB}[/tex] = 4·√3
∴ C/2 = π·4·√3/2 = 2·√3·π
The length of arc AB = 2·√3·π cm
Part B
The given parameters are;
The length of [tex]\overline {OF}[/tex] = The length of [tex]\overline {FB}[/tex]
Angle D = angle B
The radius of the circle = 6·x
The measure of arc EF = 60°
The required information = The perimeter of triangle DOB
We have;
Given that the base angles of the triangles DOB are equal, we have that ΔDOB is an isosceles triangle, therefore;
The length of [tex]\overline {OD}[/tex] = The length of [tex]\overline {OB}[/tex]
The length of [tex]\overline {OB}[/tex] = [tex]\overline {OF}[/tex] + [tex]\overline {FB}[/tex] = [tex]\overline {OF}[/tex] + [tex]\overline {OF}[/tex] = 2 × [tex]\overline {OF}[/tex]
∴ The length of [tex]\overline {OD}[/tex] = 2 × [tex]\overline {OF}[/tex] = The length of [tex]\overline {OB}[/tex]
Given that arc EF = 60°, and the point 'O' is the center of the circle, we have;
∠EOF = The measure of arc EF = 60° = ∠DOB
Therefore, in ΔDOB, we have;
∠D + ∠B = 180° - ∠DOB = 180° - 60° = 120°
∵ ∠D = ∠B, we have;
∠D + ∠B = ∠D + ∠D = 2 × ∠D = 120°
∠D = ∠B = 120°/2 = 60°
All three interior angles of ΔDOB = 60°
∴ ΔDOB is an equilateral triangle and all sides of ΔDOB are equal
Therefore;
The length of [tex]\overline {OD}[/tex] = The length of [tex]\overline {OB}[/tex] = The length of [tex]\overline {DB}[/tex] = 2 × [tex]\overline {OF}[/tex]
The perimeter of ΔDOB = The length of [tex]\overline {OD}[/tex] + The length of [tex]\overline {OB}[/tex] + The length of [tex]\overline {DB}[/tex] = 2 × [tex]\overline {OF}[/tex] + 2 × [tex]\overline {OF}[/tex] + 2 × [tex]\overline {OF}[/tex] = 6 × [tex]\overline {OF}[/tex]
∴ The perimeter of ΔDOB = 6 × [tex]\overline {OF}[/tex]
The radius of the circle = [tex]\overline {OF}[/tex] = 6·x
∴ The perimeter of ΔDOB = 6 × 6·x = 36·x
(x – 3) (x + 6) ayudaaaaaaaaaaa
[tex]\longrightarrow{\green{ \: {x}^{2} + 3x - 18 }}[/tex]
[tex]\sf\purple{Step-by-step\:explanation:}[/tex]
[tex](x - 3)(x + 6)[/tex]
➼ [tex] \: x(x + 6) - 3(x + 6)[/tex]
➼ [tex] \: {x}^{2} + 6x - 3x - 18[/tex]
➼ [tex] \: {x}^{2} +3x - 18[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{☂}}}}}[/tex]
2 Kenedi has a piece of ribbon that measures
24 inches long. She cuts the ribbon into
15 equal pieces to attach to her dance
costume. Kenedi uses the expression shown to
calculate the length of each piece of ribbon she
uses on her costume.
241 - 15
Which of the following expressions CANNOT be
used to determine the length of each piece of
ribbon?
15
F99=
G (242) (15)
H7+15
J 241-15
Answer:
The length of each ribbon is 1.6 inches
Step-by-step explanation:
From the question, we are told that:
Kenedi has a piece of ribbon that measures 24 inches long. She cuts the ribbon into 15 equal pieces to attach to her dance costume
Hence, the expression that can be used to show how to calculate the length of each piece of ribbon is given as:
24 inches ÷ 15 pieces
= 24 ÷ 15
= 1.6 inches
Therefore, the length of each ribbon is 1.6 inches
A square has an area of 36 ft^2. What is the perimeter of the square? Show or explain your
answer.
Answer:
24 ft
Step-by-step explanation:
The area of a square is given by
A = s^2
36 = s^2
Take the square root of each side
sqrt(36) = sqrt(s^2)
6 = s
The perimeter of a square is
P = 4s
P = 4(6)
P = 24
I need help with these 4
Answer:
dude if they have a pattern they are a function figure it out from there
answer in detail & explain well plzz !!!
Step-by-step explanation:
my answer is in the image above
Analyze the diagram below and complete the statement that follows.
The perimeter of the square is
A. 42
B. 60
C. 110.25
D. 112.5
Answer:
A: 42
Step-by-step explanation: 10.5x4=42
Answer:
your answer is A 42
Step-by-step explanation:
make me brainliest
I understand the problem
Answer:
c.100
Step-by-step explanation:
first draw a figure of rhombus EFGH to avoid confusions
given
angle E= 3x+5
angle H= 4x
here,
E=G and H=F ( opposite angles of rhombus are equal)
now,
E+G+H+F= 360 ( sum of interior angles in a rhombus)
3x+5+3x+5+4x+4x= 360
x= 25°
we know that,
F= H
F= 4x
F= 4 × 25
F= 100
What’s the perimeter
Answer:
60 cm
Step-by-step explanation:
Perimeter = 2(12) + 2(18)
Perimeter = 2(30) = 60
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer:
60cm
Step-by-step explanation:
(diagram with colors below)
The two red sides can be visualized as the same length as the length, so the two red segments add up to 18cm. The same thing can be said with the blue segments and the width. We can say the perimeter can be:
18 + 18 + 12 + 12 = 60cm
Increase £854 by 89%
Give your answer rounded to 2 DP
Answer:
[tex]{ \tt{ = (100 + 89)\%}} \\ = { \tt{(189\% \times £854)}} \\ = £1614.06[/tex]
Find the value of p (x) = 4x^3 - 7x^2 - 5x + 43 if x= -3
Answer:
[tex]p(x) = {4x}^{3} - {7x}^{2} - 5x + 43 \\ \\ p( - 3) = {4( - 3)}^{3} - {7( - 3)}^{2} - 5( - 3) + 43 \\ p( - 3) = - 113[/tex]
Answer:
- 113
Step-by-step explanation:
Substitute x = - 3 into p(x) and evaluate , that is
p(- 3) = 4(- 3)³ - 7(- 3)² - 5(- 3) + 43
= 4(- 27) - 7(9) + 15 + 43
= - 108 - 63 + 58
= - 171 + 58
= - 113
HELP ASAPPPP!!!!!!!
Find the y-intercept of the line y-7x= -3
Answer:
y - intercept = - 3
Step-by-step explanation:
The equation of a line is typically written as y=mx + b where m is the slope and b is the y-intercept.
Given :
y - 7x = - 3
y = 7x - 3 [ convert to standard line equation form ]
Therefore , y - intercept = - 3
Answer:
-3
This is the y intercept because when you re-arrange the equation to form y=mx+c, the y-intercept( c) is -3.
ReeeeeeeeeeeereEeeeeereeeee
Answer:
22
Step-by-step explanation:
B racket
I ndices
D division
M multiplication
A addition
Subtraction
Work out answer using the BIDMAS order
WILL GET BRAINLIEST
Which does NOT represent the interior angle measures of a triangle? A.5°, 75°, 100°B.10°, 80°, 90°C.20°, 60°, 100°D.45°, 45°, 45°E.50°, 50°, 80°
Answer:
3 * 45 = 135 which is NOT 180
45, 45, 90 would work
Step-by-step explanation:
hope it helps!
pl help me I will give u branist and also follow u and give u like plz help me
Answer:
Dividend
Step-by-step explanation:
Dividend is the profit earned from investing in stock
Dylan has a bank that sorts coins as they are dropped into it. A panel on the front displays the total number of coins inside as well as the total value of these coins. The panel shows 80 coins with a value of $16.25 inside of the bank.
Answer:
The equations
[tex]x + y = 80[/tex]
[tex]0.25x + 0.1y = 16.25[/tex]
The solution
55 dimes and 25 quarters
Step-by-step explanation:
Given
Let
[tex]x \to[/tex] quarters
[tex]y \to[/tex] dimes
[tex]Total = 80[/tex]
[tex]Worth = \$16.25[/tex]
Required
Set up a system of equation to calculate the number of each coin
The total coin of 80 implies that:
[tex]x + y = Total[/tex]
[tex]x + y = 80[/tex]
A dime = $0.1
A quarter = $0.25
So, the worth of the coin is:
[tex]0.25 * x + 0.1 * y = Worth[/tex]
[tex]0.25x + 0.1y = 16.25[/tex]
So, the equations are:
[tex]x + y = 80[/tex]
[tex]0.25x + 0.1y = 16.25[/tex]
Next, solve for x and y
Multiply the second equation by 4
[tex]0.25x + 0.1y = 16.25[/tex] by 4
[tex]x + 0.4y = 65[/tex]
Subtract from [tex]x + y = 80[/tex]
[tex]x- x + y - 0.4y = 80 - 65[/tex]
[tex]0.6y = 15[/tex]
Solve for y
[tex]y = 25[/tex]
We have:
[tex]x + y = 80[/tex]
[tex]x = 80 - y[/tex]
[tex]x = 80 - 25[/tex]
[tex]x = 55[/tex]
Hence, there are 55 dimes and 25 quarters
Use the Law of Sines. Find the indicated measure to the nearest tenth
In ADEF, mZF" - 43°, d - 16 mm, and f - 24rom. Find MZD.
a. 23.6
C. 27.0
b. 31.7
d. 19.50
here is the answer bae. Feel free to ask for more.
What is 9/12a = 1 ? Also what is 6/5b = 1 ? And Finaly what is 12c = 1 ?
Step-by-step explanation:
hope I understand your question
a = 9/12
b = 6/5
c = 1/12
please simplify the fractions by yourself
calculate the area of the shape
Answer:
which shape tho and it's easy if there is more than one shape than find the formula for each shape and combine them!
Answer:
the formula for the rectangle is LxW or BxH (however your teacher taught it) which is just 4x15=60. The triangle is bxh÷2 which means 4x15=60 then 60÷2= 30. Add 30+60 which gives you Area=90formula for a circle πxr^27.5 as an improper fraction in its simplest form
Answer:
7.5 as an improper fraction in its simplest form would be 15/2
1. What is the value of the digit 7 in the number 176 354?
Answer:
7 thousand because in word it is 0me hundred and seventy six thousand three hundred and fifty four
Answer:
tens of thousands
Step-by-step explanation:
Tiana has 8 purple daisies. In all, she counts 128 petals on all her flowers. If each flower has the same number of petals, how many petals are on one flower?
Answer:
the answer is 16 dividing 128 by 8 to get the petals in each flower.
Answer:
There are 16 petals per flower
Step-by-step explanation:
Take the number of petals and divide by the number of flowers
128/8
16
There are 16 petals per flower
pls pls help ez middle school math
Step-by-step explanation:
[tex]\sqrt{x^2-6x + 9} = \sqrt{(x - 3)^2}= x - 3[/tex]
Please help me figure out how to solve functions
Answer:
f(6) = 24
Step-by-step explanation:
To evaluate f(6) substitute x = 6 into f(x) , that is
f(6) = 6² - 2(6) = 36 - 12 = 24
Points D, C, B, and A are collinear.
What is the slope of DC in simplest form?
Answer:
if DA line is lineer
Step-by-step explanation:
you can use small triangle.. it's slopes ⅕ slope of DC=⅕
It takes 26 pounds of seed to completely plant a 3-acre field. How many pounds of seed are needed per acre?
Answer:
3.25 pounds per acre
Step-by-step explanation:
We want to find how much pounds of seed is need per acre. In division, with a numerator and denominator, this works perfectly, with how much we need (of seed) per acre translating into [tex]\frac{26 pounds}{3 acres}[/tex] , with the line representing the per. We can plug this into a calculator to get 3.25 pounds per acre, or [tex]\frac{3.25 pounds}{1 acre}[/tex]
Find the area of the circle shown Use pi=3.14
Answer:
50.24 sq cm
Step-by-step explanation:
radius is 4 (half of 8)
A=(3.14)4^2
A=50.24
Answer:
B) 50.24 sq.cm
Step-by-step explanation:
equation for area of circle is [tex]\pi r^{2}[/tex]
radius is half of diameter
radius = 4 cm
[tex]\pi (4)^2[/tex] = 50.24 sq.cm
if bottled water costs 3.00 and a pack of 6 water's cost 4.50 which has the lower unit rate
Answer:
The pack of water has the lower unit rate.
Step-by-step explanation:
The unit rate per bottle for individual bottles is 3.00. The unit rate for the pack is 0.75 per bottle.
"which of the numbers below can be classified as an integer" and the options are . 10÷2 , -0.3 ,√20 ,. 0.4
Answer:
The number 10/2 = 5 is an integer.
Step-by-step explanation:
An integer is a whole number which cannot be expressed in fractions. For example, 1, 2, 3...
Integer can be positive, negative of zero.
[tex]\frac{10}{2}=5[/tex]
It is a whole number so it is an integer.
- 0.3
It is not an integer as it has a fractional part.
[tex]\sqrt20[/tex]
It also has a fractional part, so it is not an integer.
0.4
It also has a fractional part, so it is not an integer.
Please help me with this
Answer:
(x+3)² = 64
Step-by-step explanation:
(x+a)² = b
so, let's see the details of the square calculation :
x² + 2ax + a² = b
so, now we have in our problem the specific equation
x² +3x - 69 = -3x - 14
now, let's group and combine all expressions of x
x² + 6x - 69 = -14
compare to the general square equation.
x² is in both expressions. nothing else needs to be done for that part.
2ax must be equal to 6x.
=> 2a = 6
a = 3
so, our general swathe square equation turns then into
(x+3)² = b. or
x² + 6x + 3² = b
x² + 6x + 9 = b
now bring this again into our specific equation and see how we have to transform the remaining numbers to keep the equation true, and to show us b :
x² + 6x + 9 - 78 = -14 (because 9-78 is again -69)
x² + 6x + 9 = 64
=> b = 64
so, the form (x+a)²=b for our specific equation is
(x+3)² = 64
Prove or disprove that the vector V1=(1,2,3) v2=(1,1,1) and V3=(1,1,0) are linearly indepwndent in vector space R^2?
Answer:
The equations are linearly independent in vector space R²
Step-by-step explanation:
The given vectors are;
V₁ = (1, 2, 3), V₂ = (1, 1, 1), V₃ = (1, 1, 0)
For the vectors to be linearly dependent, we have;
a₁·V₁ + a₂·V₂ + a₃·V₃ = 0
Where;
a₁, a₂, and a₃ are not all zero
We get;
[tex]\left[\begin{array}{ccc}1&2&3\\1&1&1\\1&1&0\end{array} \right][/tex]
The vectors are linear dependent, if the following system of equation has a unique set of solution
x + y + z = 0...(1)
2·x + y + z = 0...(2)
3·x + y = 0...(3)
From equation (1), we have;
x = -(y + z)
∴ y + z = -x
Plugging in the value of y + z in equation (2) gives;
2·x + y + z = 0
2·x + y + z = 2·x - x = x = 0
x = 0
From equation (3), we get;
3·x + y = 0, where x = 0, therefore;
3 × 0 + y = 0
∴ y = 0
From equation (1), we have;
x + y + z = 0
Where, x = 0, and y = 0, we get;
0 + 0 + z = 0
z = 0
The vectors, V₁, V₂, and V₃ are linear independent in R³
In two dimensional space, we have
x + y = 0...(1)
2·x + y = 0...(2)
x + y = 0...(3)
Subtracting equation (1) from equation (2) gives;
2·x + y - (x + y) = 2·x - x + y - y = x = 0
∴ x = 0
From equation (1), we get
x + y = 0
∴ 0 + y = 0
∴ y = 0
Therefore, the equations are also linearly independent in vector space R²