We will have that Absolute Value is the magnitude of a value and is denotated as follows:
| x | : The absolute value of x.
When we speak about magnitude we refer just to possitive values. For example:
*The absolute value of 3:
| 3 | = 3
*The absolute value of -45:
| -45 | = 45
From this, we can clearly see that we "keep the number" but not the sign.
Please help I am stuck with this problem for homework. I am in the 6th grade.
Explanation
In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints
it is given by
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]then
Step 1
Let
[tex]\begin{gathered} P2=(4,3) \\ M=(4,7) \\ P1=unknown=(x_1,y_1) \end{gathered}[/tex]replace
[tex]\begin{gathered} (4,7)=(\frac{x_1+4}{2},\frac{y_1+3}{2}) \\ \text{hence} \\ 4=\frac{x_1+4}{2} \\ and \\ 7=\frac{y_1+3}{2} \end{gathered}[/tex]Step 2
now, we have to solve for x1 and y1
a)
[tex]\begin{gathered} 4=\frac{x_1+4}{2} \\ \text{Multiply both sides by 2} \\ 4\cdot2=\frac{x_1+4}{2}\cdot2 \\ 8=x_1+4 \\ \text{subtrac 4 in both sides} \\ 8-4=x_1+4-4 \\ 4=x_1 \end{gathered}[/tex]b)
[tex]\begin{gathered} 7=\frac{y_1+3}{2} \\ \text{Multiply both sides by 2} \\ 7\cdot2=\frac{y_1+3}{2}\cdot2 \\ 14=y_1+3 \\ \text{subtract 3 in both sides} \\ 14-3=y_1+3-3 \\ 11=y_1 \end{gathered}[/tex]therefore, the coordinates of the other end point is
[tex](4,11)[/tex]I hope this helps you
Which equation models the line on the graph?
(-1,4)
(3,2)
O A) y-2= -1/2(x-3)
O B) y + 2 = -1/2 (x+3)
O C) y-2=-2(x-3)
OD) y + 2 = -2(x+3)
Answer:
a i
gussed
Step-by-step explanation:
W. Checkpoint: Solve lines 1) Tell whether each equation has exactly one solution, infinitely many solutions, or no solutions no exactly one solution Infinitely many solutions solutions 7(x-2) 9x - 2 9x + 3 = 3(3x + 1) 3x + 2 = 7(x-2)
7(x-2) = 9x - 2
open the parenthesis
7x - 14 = 9x - 2
collect like term
9x - 7x = -14 + 2
2x = -12
Divide both-side of the equation by 2
x = -6
It has exactly one solution
9x+3 =3(3x+1)
9x + 3 = 9x + 3
Since the left-hand side is exactly the same as the right hand side, then it has infinitely many solutions
3x + 2 = 7(x-2)
open the parenthesis
3x + 2 = 7x - 14
collect like term
7x -3x = 2 + 14
4x = 16
Divide both-side by 4
x = 4
It has exactly one solution
Order these numbers from least to greatest. 143 7 7.116, 6.67 20
We are given the following numbers
[tex]7\frac{1}{9},\: 7.116,\: \frac{143}{20},\: 6.67[/tex]We are asked to arrange these numbers from least to greatest.
As you can see, the numbers are in different forms (decimal, fraction)
So, first we need to convert them into a single form then we can compare them
Let us convert all the numbers into decimals
[tex]\begin{gathered} 7\frac{1}{9}=\frac{7\cdot9+1}{9}=\frac{63+1}{9}=\frac{64}{9}=7.111 \\ \frac{143}{20}=7.15 \end{gathered}[/tex]So the order from least to greatest is
6.67, 7.111, 7.116, 7.15
Now write the numbers in their original form
[tex]undefined[/tex]3. Select all equations that have exactly one solution.
A 5x + 8 = 5x - 15
B. 3x +4= 7x-1
c. 3 (x - 12) = 4x - 36
D. 2 (x-1) + x = 2x - 7
E. 4 (2x - 5) - 3x = 5x-20
Answer:
Step-by-step explanation:
D the reason is because I said so
A school principal ordered s new electric pencil sharpeners. Each classroom received 2 of them. Write an expression that shows the number of classrooms.
y = x/2 is the expression that shows the number of classrooms. where y is No. of classrooms and x is the Total No. of sharpener ordered.
What is an Algebraic Expression? an algebraic expression is an expression composed of variables and constants as well as algebraic operations (addition, subtraction, etc.). Terms combine to form expressions.Algebraic expressions are used in mathematics to solve various and complex equations. Algebraic expressions can be found in computer programming, where they are utilized for inference tasks. In economics, algebraic expressions are employed to calculate revenue, cost, and so on.The study of algebra improves logical thinking and allows a person to break down an issue first and then solve it. Although theoretical algebraic difficulties may not be encountered on a daily basis, exposure to algebraic equations and problems at some time in life will develop your mind to reason logically.let assume y be the No. of class room,
x be the Total No. of electric sharpeners order
Each classroom received 2 of them
y = x/2
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What is the GCF of 12, 48, 36, 24, and 60. Will mark BRAINLIEST!!!!!
Answer: 6
Step-by-step explanation:
Answer: Hi the answer to your question would be
GCF = 12
for the values 12, 24, 36, 48, 60
Here is an explanation!
The factors of 12 are: 1, 2, 3, 4, 6, 12
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36
The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Then the greatest common factor is 12.
Hope this helps Ihsan!
(4.18 x 10-4)(9 x 10-4)Can you please explain how to do step by step?
Answer:
3.762 x 10^-9
Explanation:
Given the expression:
[tex]\mleft(4.18\times10^{-4}\mright)\mleft(9\times10^{-4}\mright)[/tex]First, we remove the brackets:
[tex]=4.18\times10^{-4}\times9\times10^{-4}[/tex]Next, we bring the powers of 10 together.
[tex]=4.18\times9\times10^{-4}\times10^{-4}[/tex]Next, we combine the powers of 10 by adding the exponents (since they are being multiplied).
[tex]\begin{gathered} =4.18\times9\times10^{-4+(-4)} \\ =37.62\times10^{-8} \end{gathered}[/tex]We then obtain our final result as follows:
[tex]\begin{gathered} =3.762\times10^{-1}\times10^{-8} \\ =3.762\times10^{-9} \end{gathered}[/tex]Refer to Problems 1-3 to solve Problems 4–6. The first one is done for you. 4. A scale factor between 0 and 1 produces a similar figure that is smaller than the original figure. 5. In Problem 2, YZ = _=4V5, and UV = v=2v5. The ratio of YZ to UV in simplest form is 6. If one polygon can be mapped to another by a series of then the polygons are Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility 218
The ratio of YZ to UV is 2:1
1) Considering that the distance between YZ is 4√5 and the distance between points U and V is 2√5 the ratio of YZ to UV can be found through this:
[tex]\frac{YZ}{UV}=\frac{4\sqrt[]{5}}{2\sqrt[]{5}}[/tex]2) Let's rationalize it by multiplying both numerator and denominator by √5 to simplify removing the radicals on the denominator.
[tex]\frac{YZ}{UV}=\frac{4\sqrt[]{5}}{2\sqrt[]{5}}\cdot\frac{\sqrt[]{5}}{\sqrt[]{5}}=\frac{4\sqrt[]{5^2}}{2\sqrt[]{5^2}}=\frac{4\cdot5}{2\cdot5}=\frac{2}{1}[/tex]3) So the ratio of YZ to UV is 2:1
Chloe had 200 beads.• She used 15 beads to make a Barrett.• She used all the remaining beads to make 5 bracelets.• She used the same number of beads to make each bracelet.Write an equation that can be used to find B, the number of beads Chloe used to make each bracelet?
Let B be the number of beads used to make each bracelet. Then the number of beads used to make 5 bracelets is 5B.
Number of beads to make a Barrett = 15
The sum of number of beads used to make 5 bracelets and Barett gives the total number of beads. So,
[tex]5B+15=200[/tex]If Jamal treated his family with a family brunch and the brunch costs $250 and the sales tax was 4%. If Jamal left an 18% tip on the $250. How much did he pay in total?
The total amount jamal paid is $305.
Given:
Jamal treated his family with a family brunch at the cost of $250.
The sales tax was 4%.
The tip is 18%.
to find the sales tax.
[tex]\begin{gathered} =250\cdot4\text{ \%} \\ =250\cdot\frac{4}{100} \\ =\frac{1000}{100} \\ =10 \end{gathered}[/tex]The amount he paid for sales tax is $ 10.
to find the tip.
[tex]\begin{gathered} =250\cdot18\text{ \%} \\ =250\cdot\frac{18}{100} \\ =\frac{4500}{100} \\ =45 \end{gathered}[/tex]Jamal left a tip of $45.
Thus the total amount paid by Jamal is,
[tex]250+10+45=305[/tex]Explain the error Andrew is using vector v to draw a copy of ∆ABC explain his error
We want to know the mistake is doing Andrew when he tries to draw a copy of ∆ABC using the vector v.
We see that the vector v is directed 3 units to the right, and 3 units down.
For translating the triangle ABC with the vector v, we should make the translation with every point of the triangle.
This means that you move the point A 3 units down and 3 units to the right, but Andrew just moved it 2 units down, and 3 units to the left. Also, we have:
0. The point B was moved two units down and four units to the right.
,1. The point C was moved three units down, and three units to the right
Thus, Andrew didn't move correctly the points A and B.
Using the following diagram below: Find the length of TT. Round youranswer to the nearest tenth.Note: The nearest tenth means you will round to one decimal place. YouMust Show Your Work.IPoints T, T', and 7" are shown.T"T'T
Let point T the origin
so
The coordinates of point T are (0,0)
therefore
The coordinates of point T' are (-2,1)
Find out the distance TT'
Applying the formula to calculate the distance between two points
[tex]d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]substitute given coordinates
[tex]\begin{gathered} TT^{\prime}=\sqrt{(1-0)^2+(-2-0)^2} \\ TT^{\prime}=\sqrt{1^2+-2^2} \\ TT^{\prime}=\sqrt{5} \\ TT^{\prime}=2.2\text{ units} \end{gathered}[/tex]The answer is TT'=2.2 unitsEFHNm FG=97m GH=117m EHG= 164GoAngle E:OAngle F:Angle G:Angle H:Blank 1:Blank 2:Blank 3:Blank 4:
Given a cyclic quadrilateral
As shown:
The measure of the arc FG = 97
The measure of the arc GH = 117
The measure of the arc EHG = 164
The measure of the arc is two times the measure of the inscribed angle opposite to the arc.
So, the measure of the angle E = 1/2 the measure of the arc FGH =
[tex]\frac{1}{2}(\text{arc FG + arc GH ) =}\frac{1}{2}(97+117)=\frac{1}{2}\cdot214=107\degree[/tex]The measure of the angle F = 1/2 the measure of the arc EHG =
[tex]\frac{1}{2}\cdot164=82\degree[/tex]For the cyclic quadrilateral, every two opposite angles are supplementary.
So,
[tex]\begin{gathered} m\angle E+m\angle G=180 \\ m\angle G=180-m\angle E=180-107=73\degree \end{gathered}[/tex]And:
[tex]\begin{gathered} m\angle F+m\angle H=180 \\ m\angle H=180-m\angle F=180-82=98\degree \end{gathered}[/tex]So, the answer will be:
[tex]\begin{gathered} \text{Blank}1\colon107\degree \\ \text{Blank}2\colon82\degree \\ \text{Blank}3\colon73\degree \\ \text{Blank}4\colon98\degree \end{gathered}[/tex]The linear function y = g(x) Is graphed in the xy-plane. If g(-3) = 4 and g(2) = 19,
what is the slope of line g?
The slope of the line g is 3.
What is the slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.By calculating the difference between the coordinates of the two points, (x₁,y₁) and (x₂,y₂), it is simple to calculate the slope of a straight line between them. The letter "m" is frequently used to denote slope.So, the slope of line g will be:
y₁ = f(x₁)y₂ = f(x₂)Sope formula: y₂ - y₁/x₂ - x₁
Now, calculate as follows:
y₂ - y₁/x₂ - x₁f(x₂) - f(x₁)/x₂ - x₁y = g(x)x₁ = -3x₂ = 2g(x₁) = g(-3) = 4g(x₂) = g(2) = 19Slope:
g(x₂) - g(x₁)/x₂ - x₁19-4/2-(-3)15/53Therefore, the slope of the line g is 3.
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Determine the value for x in the equation x over 6 and 4 tenths equals 3 and 6 tenths.
Answer:
x = 23.04
Step-by-step explanation:
You want to know the value of x such that x/6.4 = 3.6.
One-step equationWe can solve this equation by multiplying by the inverse of the coefficient of x.
The coefficient of x is 1/6.4, so multiplying by 6.4 will give ...
6.4(x/6.4) = 6.4(3.6)
x = 23.04
The value for x in the equation is 23.04.
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Rectangle ABCD with vertices A(1, 0),
B(7, 2), C(8, -1), and D(2, -3):
(a) Translation: (x, y) → (x-8, y - 3)
(b) Reflection: in the x-axis
The vertices after the transformations is A''(-7, 3), B''(-1, 1), C'' (0, 4), and D'' (-6, 6)
How to determine the vertices after the transformations(a) Translation: (x, y) → (x-8, y - 3)
The vertices of the rectangle are given as
A(1, 0), B(7, 2), C(8, -1), and D(2, -3)
The translation rule is given as
(x, y) → (x-8, y - 3)
When this rule is applied, we have
A'(1 - 8, 0 - 3), B'(7 - 8, 2 - 3), C' (8 - 8, -1 - 3), and D' (2 - 8, -3 - 3)
Evaluate
A'(-7, -3), B'(-1, -1), C' (0, -4), and D' (-6, -6)
(b) Reflection: in the x-axis
This rule can be represented as
(x, y) → (x, -y )
When this rule is applied, we have
A''(-7, 3), B''(-1, 1), C'' (0, 4), and D'' (-6, 6)
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What is 1/5 divided by 4. (Fraction)
Given the expression:
[tex]\text{ 1/5 }\div\text{ 4}[/tex]Let's determine the quotient:
Step 1: Transform the whole number into the fractional form.
[tex]\text{ 1/5 }\div\text{ 4 = }\frac{1}{5}\text{ }\div\text{ }\frac{4}{1}[/tex]Step 2: Transpose the division into multiplication and reciprocate 4/1.
[tex]\frac{1}{5}\text{ }\div\text{ }\frac{4}{1}[/tex][tex]=\text{ }\frac{1}{5}\text{ x }\frac{1}{4}[/tex][tex]\text{ = }\frac{1}{20}[/tex]Therefore, the answer is 1/20.
Yesterday jack drove 38 1/2 miles. He used 1 1/4 gallons of gasoline. What is the unit rate for mile per gallon
Answer:
the unit rate for miles per gallons is 32.4 miles per gallon
Step-by-step explanation:
From the information we have, Jack drove 401/2 miles and used a total of 1 1/4 gallons of gasoline.
We need to find out how many miles he travelled per each gallon.
40 1/2 miles can be written as 40.5 miles
1 1/4 gallons can be written as 1.25 gallons.
So now we form an equation.
40.5 = 1.25
x = 1
Where x is the number of miles per gallon
We cross multiply the equation
40.5 * 1 = 1.25 * x
40.5 = 1.25x
40.5 / 1.25 = x
32.4 = x
x = 32 .4
Hi! I just wanted to double check and make sure that I worked the question correctly
Statement Problem: A boat on the river is 700ft from the base of a dam. The dam is 2460ft above water level. Given that someone standing on the boat stands 5ft above water level, what is the angle of elevation from the individual standing on the boat to the top of the dam? State your answer in radian rounded to 4 decimal places.
Solution:
We would represent the information in a diagram as;
Applying the trigonometry ratio for tangent, we have;
[tex]\tan \theta=\frac{opposite}{adjacent}[/tex]Thus,
[tex]\begin{gathered} \tan \theta=\frac{2460}{700} \\ \theta=\tan ^{-1}(3.5143) \\ \theta=74.1161^o \end{gathered}[/tex]Now, we would convert the angle from degrees to radians. We have;
[tex]\begin{gathered} 74.1161^o\times\frac{\pi}{180}\text{rad} \\ =1.2936rad \end{gathered}[/tex]Solve the system of equations using elimination. −3x + 2y = 9 x + y = 12 (−3, 0) (1, 6) (3, 9) (5, 7)
The system of equations using elimination. −3x + 2y = 9 x + y = 12 is x = 4/7 and y = 48/7
We need to solve the system of equations using elimination method
-3x + 2y = 12....... equation 1
9x + y = 12...........equation 2
Multiply the 2nd equation with 2
18x + 2y = 24 ............equation 3
Now, subtracting equation 3 from equation 1
- 3x - 18x + 2y - 2y = 12 - 24
-21x = 12
x = 12/21 = 4/7
-3(4/7) + 2y = 12
-12/7 + 2y = 12
2y = 12 + 12/7
2y = 96/7
y = 48/7
Therefore, the system of equations using elimination. −3x + 2y = 9 x + y = 12 is x = 4/7 and y = 48/7
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Answer:
(3, 9)
Step-by-step explanation:
I did the test
Match the correct slope-internet form of an equation with the standard form of the same equation.
Given:
-x+y=2
x-y=2
x+y=-2
-x-y=-2
To match the correct slope-intercept form of an equation, we follow the process as shown below:
Standard Form: Ax+By=C
Conversion: y= -A/Bx+C/B
So,
For -x+y=2:
A=-1
B=1
C=2
Hence,
[tex]\begin{gathered} y=-\frac{A}{B}x+\frac{C}{B} \\ y=-\frac{-1}{1}x+\frac{2}{1} \\ Simplify \\ y=x+2 \end{gathered}[/tex]For x-y=2,
A=1
B=-1
C=2
So,
[tex]\begin{gathered} y=-\frac{A}{B}x+\frac{C}{B} \\ =-\frac{1}{-1}x+\frac{2}{-1} \\ Simplify \\ y=x-2 \end{gathered}[/tex]For x+y=-2,
A=1
B=1
C=-2
So,
[tex]\begin{gathered} y=-\frac{A}{B}x+\frac{C}{B} \\ y=-\frac{1}{1}x+\frac{-2}{1} \\ y=-x-2 \end{gathered}[/tex]For -x-y=-2,
A=-1
B=-1
C=-2
So,
[tex]\begin{gathered} y=-\frac{A}{B}x+\frac{C}{B} \\ =-\frac{-1}{-1}x+\frac{-2}{-1} \\ Simplify \\ y=-x+2 \end{gathered}[/tex]Therefore, the answers are:
-x+y=2----y=x+2
x-y=2-----y=x-2
x+y=-2----y= -x-2
-x-y=-2----y= -x+2
What is the equation of the line that passes through the point (-3,-6) and has a slope of 1/3
In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
How can I locate a slope?You may determine the slope of the line by determining the rise and the run using two of the line's points. The rise and the run are terms used to describe changes in height between two points. The increase divided by the run is the slope.The letter m is frequently used to represent slope; the reason for this usage is unclear, but it can be found in O'Brien's (1844) and Todhunter's (1888) expressions of the equation for a straight line as "y = mx + b" and "y = mx + c," respectively.Formula m = rise / run = y2 - y1 / x2 - x1m = slope
(x1, y1) = coordinates of first point in the line
(x2, y2) = coordinates of second point in the line
Point (-3, 6) (-3, 6) Summary: An equation for the line through the point, which has the undefined slope m specified. x = -3 at the location (-3, 6).To Learn more About line's slope refer to:
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i have to find the distance form the swings to fountain. help please
The first thing we have to do is locate the points where the swings and the fountain are located on the graph.
[tex]\begin{gathered} Fountain\to(-2,-2) \\ Swings\to(5,-2) \end{gathered}[/tex]To calculate the distance between the 2 points we use the following equation:
[tex]\begin{gathered} D(F,S)=\sqrt[]{(x_2-x_1)^2-(y_1-y_1)^2} \\ \end{gathered}[/tex]We replace the values of the points F and S:
[tex]\begin{gathered} D(F,S)=\sqrt[]{(5_{}-(-2)_{})^2-(-2_{}-(-2)_{})^2} \\ D(F,S)=\sqrt[]{(5_{}+2_{})^2-(-2_{}+2_{})^2} \\ D(F,S)=\sqrt[]{(7_{})^2-(0_{})^2} \\ D(F,S)=\sqrt[]{(7)^2} \\ D(F,S)=7 \end{gathered}[/tex]So the distance between the swings and the fountains is 7The next model of a sports car will cost 6.2% less than the current model. The current model costs $57,000. How much will the price decrease in dollars? What will be the price of the next model
Answer:
The price will decrease $3534
The price of the next model is $53466
Step-by-step explanation:
57000 divided by 100 and then time 6.2 = $3534
Then subtract 57000 - 3534 = $53466
Answer: 53,466
Step-by-step explanation:
Do 57,000 minus 6.2 or and get 53,466.
Write an equivalent expression by distributing the "−−" sign outside the parentheses:−(−8.4n−1)−(−8.4n−1)
GIven:
[tex]-(-8.4n-1)[/tex]To Determine: The equivalent of the given expression
Distributing the sign outside as shown below:
[tex]\begin{gathered} -(-8.4n-1) \\ =-\times-8.4n-\times-1 \\ =8.4n+1 \end{gathered}[/tex]Hence, the equivalent expression by distributing the sign outside the given expression is:
8.4n+1
3. (a) Using a pencil, ruler and a pair of compasses, construct a triangle ABC such d that AB = 5.5 cm, LABC = 90° and ZBAC = 60°. (Marks will be given for clearly drawn construction lines) [4] (b) Using the diagram constructed in part (a), measure the length of AC. [1]
To solve this question, follow the steps:
1) Draw the segment AB = 5.5 cm using a ruler.
2) Draw the segment BC knowing that the angle ABC is 90º.
3) Draw the segment AC knowing that the angle BAC is 60º.
4) Connect the segments BC and AC.
5) Measure the length of AC using a ruler.
The triangle can be observed below:
Answer: the length of the segment AC is 11 cm.
Find the measure of the angles between the hands of the clocks at a) 8:54 b) 5:11 and c) 8:03I have the answers, but I need an explanation
I will explain to you through a drawing on how to identify 3 types of angles :
You will find the angles by placing a protractor aligning the centre with 0:00 marking the hour and the minute will be your angle formed on the watch, you can twist and turn the protractor but it will always form a measured angle .
Geometry Match each segment, angle, or arc to its degree measure. segment ADsegment DKsegment AKsegment KLangle BDCangle DAKangle EMAangle FBAarc EJsegment DEsegment AFarc DCE
The given figure inscribed in the circle is a square.
We know from the properties of a square that all the sides and all the angles of a square are equal.
Also the diagonal bisects each other at 90 degrees.
From the figure we are given;
CD = 14.14
AJ = 10
arc BC = 90 degrees
From the figure and properties of polygons, we can say that;
arc BC = arc CD = arc DE = Arc EB = 90 degree
AJ = AK = AB = AC = AD = AE = 10 = Radius of circle
JL = EC = BD = 20 = diameter of circle (Since, diameter = 2 * radius)
BC = CD = DE = EB = 14.14 = sides of the squares
Thus, the given figure inscribed in the circle is a square.
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please help at the image and answer
Step-by-step explanation:
the figure is a combination of
1 half-circle with radius 30/2 = 15
1 inner rectangle 13 width, (13+20)= 33 length.
2 right-angled triangles with 20 being one leg, and (30-13)/2 = 17/2 = 8.5 the other leg.
the area of the half-circle is
pi×r²/2 = pi×15²/2 = pi×112.5 = 353.4291735...
the area of the inner rectangle is
13×33 = 429
the area of one triangle (because they are right-angled, their area is leg1 × leg2 / 2)
20 × 8.5 / 2
but we have 2 triangles, and their total area is then
20 × 8.5 = 170
in total the area of the combined figure is the sum of all 3 numbers :
952.4291735...
this should be the cut-off 3rd answer option 952.4.