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
calculate the volume of a ball having a radius of 8 cm
Answer:
267.9 [tex]cm^{3}[/tex]
Step-by-step explanation:
volume of a circle = 4/3 * π *[tex]r^{2}[/tex]
=4/3 *3.14 *[tex]8^{2}[/tex]
=12.56/3 *64
=803.84/3
=267.94
=267.9 [tex]cm^{3}[/tex]
Mr.Williams drew
△
A
B
C
on a coordinate grid and asked his students to determine the transformations that will result in a transformed figure
△
A
`
B
`
C
`
such that
△
A
`
B
`
C
`
is similar but NOT congruent to
△
A
B
C
.
Two student responses are shown below.
Student 1: Reflect
△
A
B
C
across the y-axis and then dilate it by a scale factor of 1 with the center of dilation at the origin.
Student 2: Dilate
△
A
B
C
by a scale factor of 2 and the center of dilation at the origin and then reflect it across the x-axis.
Which statement is true?
A.
Neither student 1 nor student 2, because dilations and reflections preserve both side lengths and angle measures.
B.
Both student 1 and student 2, because dilations and reflections preserve angle measures but not side lengths.
C.
Only student 2, because dilations preserve angle measures and side lengths are proportional.
D.
Only student 1, because this dilation preserves angle measures and side lengths.
Answer: Answer C , Only student 2, because dilation preserve angle measures and side lengths are proportional
The true statement is only student 2, because dilations preserve angle measures and side lengths are proportional.
What is Geometric Transformation?Transformation of geometrical figures or points is the manipulation of a given figure to some other way.
Different types of transformations are Rotation, Reflection, Glide reflection, Translation and Dilation.
Dilation is a type of transformation where the figure is enlarged or made smaller such that it preserves the shape but not size.
In Reflection the figure is flipped. In other words, a figure when undergoes reflection becomes it's mirror image.
Dilation preserves the angle measures, so the triangles will be similar.
Reflection, on the other hand, will result in congruent triangles.
Student 1 said that Reflect △ABC across the y-axis and then dilate it by a scale factor of 1 with the center of dilation at the origin.
If the scale factor is 1, then the dilated image will be the same as the original image.
So the resulting triangle will be congruent to the original triangle.
In the case of what student 2 said, scale factor is 2. Triangle is enlarged.
So the resulting image will be similar to the original one.
Hence student 2 is correct.
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What is the
equation of the graphed line written in
standard form?
O X=-3
O y=-3
O x+y=-3
x-y=-3
Answer:
x = -3
Step-by-step explanation:
This is a vertical line. The x value remains constant.
x = -3
Answer:
x= 5.45 or -5.45
Step-by-step explanation:
What is the first step when factoring the trinomial .,
Answer:
Step 1: Set up a product of two ( ) where each will hold two terms. Step 2: Find the factors that go in the first positions. Step 3: Find the factors that go in the last positions. We need two numbers whose product is 9 and sum is 2.p explanation:
Answer:
A❤️✌️❤️✌️❤️Aaaaaa
A fruit juice recipe uses three ingredients. Two of the ingredients use a ratio of 2 ounces of pineapple juice to 5 ounces of fruit punch. Part A: Grape a line on the coordinates plane to represent this relationship
Part B: Create an equation to represent this relationship. Let x represent ounces of pineapple juice. Let y represent ounces of fruit punch.
Answer:
(a) See attachment
[tex](b)\ y =2.5x[/tex]
Step-by-step explanation:
Given
[tex]x \to pineapple[/tex]
[tex]y \to fruit[/tex]
[tex]x : y =2 : 5[/tex]
Solving (a): The graph
First, we create an equation from [tex]x : y =2 : 5[/tex]
Express as fraction
[tex]\frac{x }{ y} =\frac{2 }{ 5}[/tex]
Cross multiply
[tex]2y = 5x[/tex]
See attachment for graph
Solving (b): An expression that represents the relationship
In (a), we have:
[tex]2y = 5x[/tex]
Divide by 2
[tex]y = \frac{5}{2}x[/tex]
[tex]y =2.5x[/tex]
Find two integers whose sum is -23 and product is 132
Step-by-step explanation:
Let x and y be two integers
x * y = 132
x + y = -23
x= -23 - y
y(-23 - y) = 132
-23y - y^2 = 132
y^2 +23y + 132 = 0
(y + 11) (y + 12) = 0
y = -11 or - 12
If y = -11 then x + (-11) = -23 -> x = -12
If y = -12 then x + (-12) = -23 -> x = -11
So the two integers are -11 and -12
In triangle ABC, if ∠A = 120°, a = 8, and b = 3, then ∠B =
Answer:
Step-by-step explanation:
Use the Law of Sines here:
[tex]\frac{sin120}{8} =\frac{sinB}{3}[/tex] and cross multiply to get
8sinB = 3sin120 and solve for B:
[tex]sinB=\frac{3sin120}{8}[/tex] and
sinB = .3247595264
Now hit the 2nd button and then sin to get
[tex]sin^{-1}([/tex]
on your display. After that open parenthesis, enter that decimal and hit enter to get that angle B = 18.95 which you can round to howeve many places you need.
which expressions represents 15 more than the product 6 and 8
Please i need help
Answer:
x-15 = 48
or
x= 15 + (6*8)
Step-by-step explanation:
Pls vote as brainliest
Hi,
The correct answer is x=15 + (6x8)
Identify the maximum value of the function y = -472 - 24x + -36.
Answer:
I assume that this is a quadratic equation, something like:
y = -47*x^2 - 24x + (-36)
we can rewrite it as:
y = -47x^2 - 24x - 36
Ok, this is a quadratic equation and we want to find the maximum value.
First, you can notice that the leading coefficient is negative.
This means that the arms of the graph will open downwards.
Then we can conclude that the vertex of the equation is the "higher" point, thus the maximum value will be at the vertex.
Remember that for a general function
y = a*x^2 + b*x + c
the vertex is at:
x = -b/2a
So, in our case:
y = -47x^2 - 24x - 36
The vertex will be at:
x = -(-24)/(2*-47) = -12/47
So we just need to evaluate the function in this to find the maximum value.
Remember that "evaluating" the function in x = -12/47 means that we need to change al the "x" by the number (-12/47)
y = -47*(-12/47)^2 - 24*(-12/47) - 36
y = -32.94
That is the maximum value of the function, -32.94
Find 3v - 4w if v = -3i and w=-i + 5j. Use < > for
vector notation.
Answer:
[tex]<-5, 20>[/tex]
Step-by-step explanation:
What we're given:
[tex]\vec{v}=-3i[/tex] [tex]\vec{w}=-i+5j[/tex]The vector [tex]3v-4w[/tex] is then [tex]3(-3i)-4(-i+5j)=-9i+4i-20j=-5i+20j\implies \boxed{<-5, 20>}[/tex]
I need help!!! Parallel lines p and q are cut by two non parallel lines m and n as shown in the figure the value of x is degrees and the value of y is degrees
Answer:
x = 78° , y = 115°
Step-by-step explanation:
The angle adjacent to x on the left side is corresponding to 102° , then
x = 180° - 102° = 78°
----------------------------------------
y and 115° are corresponding angles and congruent, then
y = 115°
find the lateral area of the prism
Answer:
We know that the lateral area of any prism is the sum of the areas of its side faces. Thus, the lateral area of a triangular prism is the sum of the side faces, that is the three rectangular faces. The formula to find the lateral area of a triangular prism is, (a + b + c) h or Ph.
so
20×6= 120 sq in
Answer:
120 sq in.
Step-by-step explanation:
LA = ah
LA = 20 × 6
A = 120
simplify the expressions √(x^2-6x+9) if x>3
Answer:
simplified expression for √x^2+6x+9 if x≥3
is x+3
Step-by-step explanation:
but given that x≥3
then we have to negate solution -(x+3)\
Then simplified expression for √x^2+6x+9 if x≥3
is x+3
The world record for the longest someone has held their breath
was 24 minutes. How many seconds are in 24 minutes? 60 seconds
= 1 minute 24 minutes = seconds
Answer:
1440seconds
Step-by-step explanation:
1min = 60sec
24min = ?
24/1 × 60
1440sec
In the diagram, If mÐAOB = (3x)° and mÐBOC = (5x – 6)°, then what is the value of x?
Answer:
X=12
Step-by-step explanation:
Given, OC⊥AD , ∠AOB=3x° & ∠BOC=(5x-6)° .
We Know ∠AOC=90
& ∠AOC=∠AOB + ∠BOC
90 = 3x + (5x-6)
90+6 = 8x
8x=96⇔x=12
(For Diagram,Please find in Attachment)
An apartment has 90 square meters of carpeting. How much is this in square feet? Use the following conversion: 1 square meter is 10.8 square feet.
An explanation on how to do it would also be amazing!
Answer:
Area = 972 square feet
Step-by-step explanation:
Let 90 square meter be = x square feet
Given :
square meter square feet
1 10.8
90 x
[tex]\frac{1}{90} = \frac{10.8}{x}\\\\1 \times x =10.8 \times 90 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ cross \ multiply \ ]\\\\x = 972[/tex]
Therefore , 90 square meter = 972 square feet
Drag the items to complete the sentences about the end behavior of the exponential function graphed.
Answer:
as x --> oo, f(x) = oo (infinite)
as x -- -oo, f(x) = 3
So sánh √144 và √169
Answer:
Step-by-step explanation:
√144 < √169
Answcăn169
Step-by-step explanat
ion:cvăn 144
15 POINTS!!! Please please help out!!! If you can!! I have other things on my account worth a lot of points so if you can help out that would be so helpful
Answer:
The maximum is -3
and the third one -3<f(x)≤ -3
Step-by-step explanation:
Let's start by expanding the exponent
-(x+7)²= -(x²+14x+49)= -x²-14x-49
simplify
-x²-14x-49-3= -x²-14x-52
To find the maximum/minimum take the first derivative
-x²-14x-52= -2x-14
set this equal to 0
-2x-14= 0
x= -7
We then plug in x= -7 into the equation to find the y value
Because the coeficcent for the degree is negative (it's -1) this is a maximum
-(-7+7)²-3 = -3
Because -3 is the highest point the graph's range is -∞<f(x)< -3
Therefore the maximum i
Question 16
Use the rule for order of operations to simplify the expression as much as possible:
Question Help: Video
Submit Question
ps://www.myopenmath.com/asset
1721&ald-80137968
Answer:
16
Step-by-step explanation:
[tex]5 + 9 \div 3 + 4 \times 2 \\ = 5 + 3 + 8 \\ = 16[/tex]
Multiplication and division are priority to addition and subtraction
Brainliest please
D 51° F E 17 m Find the length DE. O 10.7 m O 13.2 m O 13.8 m 0 21.0 m O 21.9 m 0 27.0 m
Which region represents the solution to the given system of inequalities?
{y < -1/2x }
[y ≥ 2x+3 }
A
B
C
D
The region D represents the solution of the given system of inequalities.
What is the system of linear inequalities?
A system of linear inequalities is a collection of linear inequalities in the same variables.
How to shade the graph of inequalities?Rearrange the equations so "y" is on the left and everything else on the right. Plot the "y≤ ,y≥ ,y> or y< " line.Shade above the line for a " greater then" and below for the "less than".According to the given equation.
We have system of inequalities.
[tex]y < \frac{-1}{2}x[/tex]
and [tex]y \geq 2x + 3[/tex]
Also, the graph of the inequalities.
Since, y is less than [tex]-\frac{1}{2} x[/tex] shade below the line.
And, for the second inequality.
y is greater than and equal to 2x + 3 therefore, shade the above the line.
So, the common region D we get after the shading.
Hence, region D represents the solution of the given system of inequalities.
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What are the coordinates of the point on the directed line segment from ( − 10 , 2 ) (−10,2) to ( − 10 , − 5 ) (−10,−5) that partitions the segment into a ratio of 6 to 1?
Answer: [tex](-10,-4)[/tex]
Step-by-step explanation:
Given
The points joining line segment are (-10,2) and (-10,-5)
Using section formula, a point joining segment [tex](x_1,y_1)\ \text{and}\ (x_2,y_2)[/tex] divides it in k:1 has coordinates
[tex]x=\dfrac{kx_2+1\cdot x_1}{k+1}[/tex], [tex]y=\dfrac{ky_2+y_1}{k+1}[/tex]
Ratio is 6:1
Coordinates are
[tex]\Rightarrow x=\dfrac{6(-10)+(-10)}{6+1}\\\\\Rightarrow x=-10[/tex]
[tex]\Rightarrow y=\dfrac{-5(6)+1(2)}{6+1}\\\\\Rightarrow y=\dfrac{-28}{7}\\\\\Rightarrow y=-4[/tex]
Thus, the coordinates are [tex](-10,-4)[/tex]
PLEASE HELP IM SORRY THE PIC IS BLURRY I NEED TO PASS SUMMER SCHOOL
Aswer:
c represnt the function hope it helps you make me brainlest pls
I need an in-depth explanation for Trigonometric Ratios, QUICK!
Answer:
See below
Step-by-step explanation:
For a right triangle, there are relationships between the sides and the angles of the triangle:
[tex]sin\theta=\frac{opposite}{hypotenuse}[/tex]
[tex]cos\theta=\frac{adjacent}{hypotenuse}[/tex]
[tex]tan\theta=\frac{opposite}{adjacent}[/tex]
I would study the attached image for a better understanding.
What is the product of the 4th square number and the 4th square number
Answer:
4×4=16
Step-by-step explanation:
four squared is a two dimension polygon with a four equal side of four length unit.
Answer:
4×4=16
Step-by-step explanation:
What is the product of (a+b) (a-b)
Answer:
[tex]a^{2}+b^{2}[/tex]
Step-by-step explanation:
(a+b)(a-b)
[tex]a^{2}[/tex]-ab+ab-[tex]b^{2}[/tex]
[tex]a^{2} + b^{2}[/tex]
А
E
F
B1
2
2x
135°
750
2x -15°
12
G
H
I
C3
D
Determine the value of x.
i wonder this is math problem or code word for treasure
Answer:
Step-by-step explanation:
(2x-15) = 45
Step-by-step explanation:
When two angles lie on a straight line, they are supplementary
what this mean is that the add up to equal 180 degrees
Mathematically, we have this as:
(2x-15) + 135 = 180
(2x-15) = 180-135
(2x-15) = 45
A grocery store sells a bag of 4 oranges for $2.84. If arianna spent &3.55 on oranges, how many did she buy?
Answer:
5 dollors i just tookthe test 4
Step-by-step explanation:
Arianna bought 0 bags of oranges. It's possible that she may have bought other items along with the oranges or there might be a pricing discrepancy.
To find out how many oranges Arianna bought, we can use the given price of a bag of 4 oranges and the total amount she spent on oranges.
Let's set up a proportion:
Price of a bag of 4 oranges = $2.84
Amount Arianna spent on oranges = $3.55
Let "x" be the number of bags of oranges Arianna bought.
Since each bag contains 4 oranges, the total number of oranges she bought is 4 times the number of bags (4x).
Now, we can set up the proportion:
(Price of a bag of 4 oranges) / (Amount spent on oranges) = (Number of bags bought) / 4x
$2.84 / $3.55 = 1 / 4x
To solve for "x," cross-multiply:
$2.84 * 4x = $3.55 * 1
11.36x = 3.55
Now, solve for "x":
x = 3.55 / 11.36
x ≈ 0.3125
Since we can't buy a fraction of a bag, we round the value of "x" to the nearest whole number:
x ≈ 0 (rounded to the nearest whole number)
So, Arianna bought 0 bags of oranges. It's possible that she may have bought other items along with the oranges or there might be a pricing discrepancy.
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help asap ------------------------------
Answer:
(0,-41)
Step-by-step explanation:
Let see if this table of values are proportional.
All x values decrease by -9.All y values decrease by -19.This mean that the function is proportional. This also gives us the slope which is 19/9.
This tell us that this function will be a linear function since we are trying to find the y intercept we would use this equation
We know the slope and we know a point so let use point slope form to find the intercept.
[tex]y - y _1= m(x - x _1)[/tex]
Let use points (-18,-79) and let m =19/9.
[tex]y + 79 = \frac{19}{9} (x + 18)[/tex]
[tex]y + 79 = \frac{19}{9} x + 38[/tex]
[tex]y = \frac{19}{9} x - 41[/tex]
This is in slope intercept form so the y intercept is
[tex] - 41[/tex]
The answer is -41.