Step-by-step explanation:
258
because there are 360 degrees in a circle. 360 - 102 = 258
The diagram shows the entrance to a tunnel.
The circular arc has a radius of 3m and center O.
AB is horizontal and angle AOB = 120°.
During a storm the tunnel filled with water, to the level shown by the shaded area in the diagram.
Calculate the shaded area.
Step-by-step explanation:
it filled up half the circle (up to the center point) - if we had a full circle. but a little bit is cut off (below AB).
what we see is that the shaded area is the sum of the area of the triangle AOB and 2 equally sized circle segment areas left and right of AOB.
since we are dealing with a half-circle, we have 180° in total. 120° are taken by AOB, so, that leaves us with 180-120 = 60° for both circle segments (so, one has an angle of 30°).
and 2×30° = 1×60°, so we can calculate the area of one 60° segment instead of two 30° segments.
AOB is an isoceles triangle (the legs are equally long, and therefore also the 2 side angles are equal).
the area of this triangle AOB is
1/2 × a × b × sin(C) = 1/2 × 3 × 3 × sin(120) =
= 3.897114317... m²
a circle segment area of 60° is 60/360 = 1/6 of the full circle area (as a full circle = 360°).
so, it's area is
pi×r² × 1/6 = pi×3²/6 = pi×3/2 = 4.71238898... m²
so, the total area of the shaded area is
3.897114317... m² + 4.71238898... m² =
= 8.609503297... m²
The area of the shaded portion of the circle is A = 8.61 m²
What is a Circle?A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The perimeter of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle
Given data ,
Let the area of the shaded region be A
Let the radius of the circle be r = 3 m
The triangle ΔAOB is an isosceles triangle with side lengths = 3m
The area of the triangle ΔAOB = ( 1/2 ) x 3 x 3 x sin (120)
On simplifying the equation , we get
The area of the triangle ΔAOB = 3.897 m²
Now ,
There are 2 sectors , with sector angle = 30°
The area of the two sectors = 2 x ( 30/360 ) x π x 3²
On simplifying the equation , we get
The area of the two sectors = 2 x 2.357
The area of the two sectors = 4.714 m²
Now ,
The area of the shaded region of circle A = area of the two sectors + area of the triangle ΔAOB
Substituting the values in the equation , we get
The area of the shaded region A = 4.714 + 3.897
The area of the shaded region A = 8.611 m²
Therefore , the value of A is 8.611 m²
Hence , the area is 8.611 m²
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i'm burfunkled right now
Answer: what grade is this
Step-by-step explanation:
(20 points)
Find x:
(x−2)^2=25
pls show steps so I understand lol
Answer:
(-3, 7)
Step-by-step explanation:
ok so first take the square root of both sides, so you get (x-2)=5, since the square root gets rid of the power, and the square root of 25, is 5, and since we did a square root, we also have to do the - + thing, so the equation really is now x-2=(+-)5
subtract 2 from both sides, and you get x=(+-)5+2
Solving for x we get -5+2=-3
and also
5+2=7 since there was a positive, and a negative 5.
therefore x would equal (-3, 7)
hope this helps, please mark as brainliest.
Shane went bowling with his friends. The bowling alley charges $20 for an hour of group bowling plus a fee to rent each pair of shoes. Shane's group bowled for one hour, rented 4 pairs of shoes, and paid a total of $31. Which equation can you use to find the fee, x, to rent each pair of shoes?
Answer:
4x+20=31
Step-by-step explanation:
So one hour of bowling is 20 dollars and they bowled for one hour hence the 1x20 which is equal to 20. That is the base coast we add to the variable of x that is the cost of renting one pair of shoes. And since they rented 4 pairs of shoes you multiply x by 4 to get 4x. Add the 20 dollars they paid to bowl and it is 4x+20. They paid 31 dollars in total so equal the equation to 31. 4x+20=31. Solution is $2.75 per pair of shoes. (If you want an explanation as to how to get the answer, just ask
Rewrite each equation without using absolute value for the given conditions.
y=|x-3|+|x+2|-|x-5| if x>5
Answer:
x>5, so
let x=6
6-3=3
+
6+2=8
-
6-5=1
3+8-1=10
answer=10
don’t even know how i got this far in geometry lol
[tex]\qquad\qquad\huge\underline{{\sf Answer}}☂[/tex]
Let's find the Area of sector ~
[tex]\qquad \sf \dashrightarrow \: \dfrac{ \theta}{360} \times \pi{r}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{ 270}{360} \times \pi{6}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{ 3}{4} \times {36}^{} \pi[/tex]
[tex]\qquad \sf \dashrightarrow \:3 \times 9 \pi[/tex]
[tex]\qquad \sf \dashrightarrow \:27\pi \: \: ft {}^{2} [/tex]
I hate these types of problems
I was never taught this stuff
(07.02) Choose the polynomial that is written in standard form. (4x3 - 2x - 9) + (2x2 + 5x + 3). (1 point) Оа 6X - 3x - 6 Ob 2x - 7X – 12 oc 6x2 + 3x - 6 . 2x3 = 3x - 3
The standard form of a polynomial is: ax^n+ bx^n-1 + cx^n-2 + ......... + d
The standard form of the polynomial is 4x^3 + 2x^2 + 3x - 6
How to determine the polynomial in standard form?The polynomial is given as:
(4x^3 - 2x - 9) + (2x^2 + 5x + 3)
Remove the bracket
4x^3 - 2x - 9 + 2x^2 + 5x + 3
Collect like terms
4x^3 + 2x^2 - 2x + 5x - 9 + 3
Evaluate the like terms
4x^3 + 2x^2 + 3x - 6
Hence, the standard form of the polynomial is 4x^3 + 2x^2 + 3x - 6
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OMG I'M HAVING A BRAIN FART AND CAN"T SOLVE THIS FOR THE LIFE OF ME. HELPPPP!
Answer:
Step-by-step explanation:
Because a square has 4 equal sides:
P = 4x
A = [tex]x^{2}[/tex]
Step 1. Substitute 4x into perimeter equation
[tex]P=\frac{4x^2+4}{x^2-2x+1}[/tex] (original P equation)
[tex]4x=\frac{4x^2+4}{x^2-2x+1}[/tex] (substitute P = 4x)
Step 2. Solve for x[tex]4x(x^2-2x+1)={4x^2+4}[/tex] (multiply denominator on both sides)
[tex]4x^3-8x^2+4x={4x^2+4}[/tex] (distribute 4x)
[tex]4x^3-12x^2+4x-4=0[/tex] (combine like terms, set = to 0)
[tex]4(x^3-3x^2+x-1)=0[/tex] (factor)
Continue using quadratic formula to find x
Step 3. Plug x into area equation, [tex]x^{2}[/tex]Hope this helps! Cannot finish answer right now, so sorry
side=Perimeter/4
side:-
[tex]\\ \rm\Rrightarrow \dfrac{4(x^2+1)}{4(x^2-2x+19}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{x^2+1}{x^2-2x+19)}✓/tex]
Area=side ²
[tex]\\ \rm\Rrightarrow \left(\dfrac{x^2+1}{x^2-2x+19}\right)^2[/tex]
the surface area?
A - 216
B - 336
C - 438
Answer:
B
Step-by-step explanation:
Find the area. Round to the nearest hundredth when necessary. Be sure you are showing all work to find each figure.
Additional requirements in figure :-
Mark point :-
ABCDEDraw a straight line from E to AB .
And the point line joins mark it as "F" .
It will generate quadrilateral FBCD.
we get to know In quadrilateral left angle is 90°
How ?
{
proof :
As three angles are given 90° So third angle will also be 90°
Reason:
→ Sum of interior angles = 2 (no. of angles - 2 × 180°
→Sum of interior angles = (4-2 × 180°)
→Sum of interior angles = (2 × 180°)
→Sum of interior angles = 360°
}
✿Now let the left angle be x
90° +90° + 90° + x = 360° 180° + 90° + x = 360°270° + x = 360x = 360° - 270°x = 90°we know :
Area of rectangle = Length × Breadth
STEPS :
Area of rectangle = Length × BreadthArea of rectangle = 7 × 8Area of rectangle = 56 in²Now let's find EF :
EF = BD - ECEF = 7 - 4 EF = 3 inTo find A
F :
A•F = AB - CDA•F = 12 - 8A•F = 4 inIn triangle AFE:
EF is base of triangle A•F is height of triangleWe know :
Area of triangle =( Height × Base)/2
Steps :
Area of triangle = (Height × Base)/2Area of triangle = (4 × 3)/2Area of triangle = 12/2Area of triangle = 6 in²To find area of figure :
Area of figure = Area of rectangle + Area of triangleArea of figure = 56 + 6Area of figure = 62 in²______________________
~WindyMint
Answer:
[tex]\displaystyle 62\:in.^2[/tex]
Step-by-step explanation:
▽ [tex]\displaystyle \frac{hb}{2} = A, \frac{1}{2}bh = A, or\:\frac{1}{2}hb = A[/tex]
▯ [tex]\displaystyle hb = A[/tex]
All edges meet at right angles, therefore resulting in this:
[tex]\displaystyle 62 = 56 + 6 \Rightarrow 62 = 7 \times 8 + 4 \times 1\frac{1}{2}[/tex]
I am joyous to assist you at any time.
Shana spends $18 on some almonds. She pays for the almonds with two $10 bills. How much change does Shana get back? Enter your answer in the box. $
Answer:
$2
Step-by-step explanation:
2($10)=$20
$20-$18=$2
Yosef found this relationship between the quantities in the table.
x
1
2
3
4
5
y
80
160
240
320
400
Multiply x by 8 to get y.
Which error did Yosef make?
Yosef should have added 80 to the x-values to get the y-values.
Yosef should have added 8 to the x-values to get the y-values.
Yosef should have multiplied the x-values by 40 to get the y-values.
Yosef should have multiplied the x-values by 80 to get the y-values.
Yosef should have multiplied the x-values by 80 to get the y-values.
Functions and tablesTables are told used to arrange ungrouped data.
From the given table, we can find the equation by using the coordinate points (1, 80) and (1, 160)
Find the equation of the lineThe standard equation of a line is y = mx + b
m is the slope
b is the y-intercept
Slop = 160-80/2-1
Slope = 80
For the y-intercept
160 = 80(2) + b
b = 0
The required equation is y = 80x
This means that Yosef should have multiplied the x-values by 80 to get the y-values.
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Answer:
A
Step-by-step explanation:
Maggie takes three electives art, Spanish and creative writing She calculated the mean absolute deviation of the points she earned throughout the year in each class art: mean absolute deviation of 2.1 Spanish: mean absolute deviation of 0.8
creative writing: mean absolute deviation of 2.7
In which elective were her scores the most spread out?
creative writing
art
Spanish
Creative writing had the largest mean absolute deviation of 2.7, therefore, the elective where her scores are most spread out is: creative writing.
What is the Mean Absolute Deviaton?The mean absolute deviation is a measure of variability of a data distribution, which describes the average distance of each data value and the mean of the data set.
The larger the mean absolute deviation, the more spread out the data points are from the mean of the data set.
Therefore, since creative writing had the largest mean absolute deviation of 2.7, therefore, the elective where her scores are most spread out is: creative writing.
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Answer: creative writing
Step-by-step explanation: I did k12 and got 100% Good Luck i hope this helps man. please give me brainiest I'm trying my best to help everyone. thanks :)
Ivanna needs to buy some pencils. Brand A has a pack of 36 pencils for 8.52 . Brand B has a pack of 48 pencils for 9.98 . Find the unit price for each brand. Then state which brand is the better buy based on the unit price. Round your answers to the nearest cent.
Answer:
Brand B is better
Step-by-step explanation:
Brand A's unit price is $0.24
Brand B's unit price is $0.21
Question 6
Luna mixes 2 cup of orange juice with a cup of cranberry juice. She gives
cup of the juice to Mags. How much is left in Luna's glass?
Answer:
nothing
Step-by-step explanation:
2cups= orange juice
1 cup= cranberry juice
nothing the orange and juice was used to make the mixture of juice
Answer:
its nothing??
Step-by-step explanation:
you gave it to mags so its nothing
Given the box plots below, what is the median of group B? Comparing Box Plots Worksheet Question 8 options: 50 min 65 min 40 min 5 min
Answer:
40
Step-by-step explanation:
I answered by simply looking at the equation
Find the area of this triangle. round to the nearest tenth.
Answer:
67.5ft²
Step-by-step explanation:
1/2xhxb
1/2x9x15
4.5x15
67.5ft²
Hope this helps!!!!
You are given two offers for a monthly wage. Option A is to be paid one cent on the first day of the month, with your wages doubling each day (2 cents on day 2, 4 cents on day 3, 8 cents on day 4, etc.) for the rest of this 30 day month. Option B is to be paid $1 on the first day of the month, with your wages increasing $100 each day ($101 on day 2, $201 on day 3, $301 on day 4, etc.). Which option will give you more money by the end of the month? Make sure to support your answer. Also remember to find the equations for the exponential function and the linear function. Substitute 30 in for x and simplify.
Answer:
Step-by-step explanation:
Option B
Because if you start with one dollar and by day 3 you get 301 dollars and option A only gives you 8 cents on day 3 you get more money by the end of the month if you choose option B.
Answer: A is the correct answer
Step-by-step explanation:
Its a because the amount keeps doubling so you will start with =
.1 then go too .2 (which is double .1)
then after .2 you will get .4( which is double .2 i will show you the graph.
.1, .2, .4, .8, 1.6, 3.2, 6.4 etc. Then when you get to day 30 you will have
53.687 million dollars, buy the end of them month, you'd be a millionaire.
HELP PLEASE IM STRUGGLING
Step-by-step explanation:
Both are very correct,
[tex]5 { }^{ - 2} = \frac{1}{25} \: or \: \frac{1}{5 {}^{2} } [/tex]
because any number raised to the power of a negative
is given as
[tex]a {}^{ - x} = \frac{1}{a {}^{x} } [/tex]
if this helped pls give brainliest
Triangle ABC has an area of 25 square feet and a perimeter of 65.5 feet. △ABC is dilated by a factor of 5/2 to create △DEF. \
Calculate the area of ABC using the scale factor.
Calculate the perimeter of DEF using the scale factor.
Answer:
Solution. To find the perimeter of \triangle ABC we use the Pythagorean Theorem which tells us that |AB|^2 = |AC|^2 + |BC|^2. Since |AC| = 5 and |BC| = 12 we find that |AB| = \sqrt{169} = 13. The perimeter of \triangle ABC is then 5 + 12 + 13 = 30 units.
What is the simplified expression of (4-5r+8s)(5r-9)
Answer:
The simplified expression of (4-5r+8s)(5r-9) is
40r s-25r^2-72s+65r-36
(hope this helped)
The simplified expression of (4-5r+8s)(5r-9) is [tex]65r - 25r^2 + 9r + 40rs - 72s.[/tex]
The simplified expression of (4-5r+8s)(5r-9) step by step.
Understanding how to simplify expressions can be incredibly useful in algebra and will make solving equations much easier. By using the distributive property, we can multiply the terms inside the parentheses and then combine like terms to get the simplified expression.
To simplify the expression (4-5r+8s)(5r-9), we'll use the distributive property, also known as the FOIL method (First, Outer, Inner, Last). This property allows us to multiply each term in the first parentheses by each term in the second parentheses.
1. First, we multiply the term "4" in the first parentheses by each term in the second parentheses:
4 * 5r = 20r
4 * (-9) = -36
2. Next, we move to the second term in the first parentheses, "-5r," and multiply it by each term in the second parentheses:
-5r * 5r = -25r²
-5r * (-9) = 45r
3. Lastly, we move to the third term in the first parentheses, "8s," and multiply it by each term in the second parentheses:
8s * 5r = 40rs
8s * (-9) = -72s
Now, we have all the resulting terms:
20r - 36 - 25r² + 45r + 40rs - 72s.
To simplify further, we combine like terms. Like terms have the same variable(s) raised to the same power:
20r + 45r = 65r
-36 + 45r = 9r
So, the simplified expression is:
65r - 25r² + 9r + 40rs - 72s.
In mathematical terms, we applied the distributive property to multiply each term in the first parentheses by each term in the second parentheses. Then, we combined like terms to obtain the final simplified expression, 65r - 25r² + 9r + 40rs - 72s.
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The runner completed 26.2 miles in 4 hours. How far did he run in 1 hour?
Answer:
6.55 miles
Step-by-step explanation:
26.2 miles in 4 hours means 6.55 each hour adds up to the total.
Do ---> 26.2 divided by 4 to get hourly miles = 6.55
Find the area of the shaded region.
Answer:
40.5 square meters
Step-by-step explanation:
the first thing you should do is find the area of the entire square
that is 9 * 9 which is 81
then you have to find the area of the triangle 9 * 9 * 1/2 which is 40.5
81 - 40.5 is 40.5 so the shaded region is 40.5
It is given that AB CD Identify the postulate that proves the triangles are congruent
Answer:
i can't see the multiple choice
Step-by-step explanation:
angle c and b are equal
angle a and d are equal
and you have a common angle o
and ab = cd
The triangles ΔAOB and ΔDOC are congruent to each other by SSS and SAS postulates. Then the correct option is A.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
It is given that AB || CD. The side AB is congruent to the side CD.
The line AD and BC intersect at the mid-point. Then the line segment AO and OD will be congruent and the line segment CO and OB will be congruent.
And the angle ∠AOB and ∠COD will be congruent because they are vertically opposite angles.
The triangles ΔAOB and ΔDOC are congruent to each other by SSS and SAS postulates. Then the correct option is A.
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Simplify the expression:
3y + x - 2x + y + x + x
+
a. *° -2x + 4y4
X3
b. x + 3y4
C. 5x + y + 3y
d. x + y + 3y
+
Please help me!! I will mark you brainliest!
Answer:
Step-by-step explanation:
Right off the bat, you will know the lowest number is 52 and the highest number is 65, therefore there will act as the guides for your box and whisker plot. This eliminates answers B and C because they are not accurate to that.
Next, we find the median of the set of numbers by crossing out (writing it down, or imagining doing so) the numbers on either end consecutively to until you reach the center number, ours being 58. This eliminates answer A.
This leads us to belive answer D is the correct box and whisker plot.
Mariah is randomly choosing three books to read from the following: 5 mysteries, 7 biographies, and 8 science fiction novels. what is the complement of mariah choosing three mysteries?
The probability is the ratio of the favorable event to the total number of events. Then the probability of choosing three mysteries books is 0.877%.
What is probability?Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen.
Mariah is randomly choosing three books to read from the following: 5 mysteries, 7 biographies, and 8 science fiction novels.
The total number of books will be
Total books = 5 + 7 + 8
Total books = 20
The total number of the event will be
[tex]\rm Total \ event = \ ^{20}C_3 \\\\\\Total \ event = \dfrac{20!}{(20-3)!3!}\\\\\\Total \ event = 1140[/tex]
The favorable event will be
[tex]\rm Favorable \ event = \ ^{5}C_3 \\\\\\Favorable \ event = \dfrac{5!}{(5-3)!3!}\\\\\\Favorable \ event = 10[/tex]
The probability of choosing three mysteries books will be
[tex]\rm P = \dfrac{10}{1140}\\\\\\P = 0.00877 \ or \ 0.877\%[/tex]
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Answer:
D
Step-by-step explanation:
Mariah is randomly choosing three books to read from the following: 5 mysteries, 7 biographies, and 8 science fiction novels. What is the complement of Mariah choosing three mysteries?
not choosing a mystery
choosing at least one mystery
choosing three mysteries
not choosing all mysteries
D is the right answer
A shop increases all their prices by 9% A picture frame increases by £153 Find the new price of the picture frame.
The new price of the picture frame is £1853
Discounts and incrementsGiven the following parameters
Percentage increase = 9%
Increment = £153
Determine the original value if the frame
9% of x = £153
0.09x = £153
x = £153/0.09
x = £1700
New price = £1700 + £153
New price = £1853
Hence the new price of the picture frame is £1853
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Solve for all values of x by factoring.
x2 – 2x – 28 = -6x + 4
X
=
There are two answers
Answer:
{4,-8}
Step-by-step explanation:
x^2 -2x -28 = -6x +4
x^2+4x-32=0
(x-4)(x+8) =0
x=4 or -8