Based on the information, I can notice that mathematics is used in various situations in daily life. Additionally, I wonder how to apply algebra in daily life.
What do we notice about mathematics?Based on what we have learned about mathematics, I have noticed that it is a very broad area that covers various types of operations and mathematical problems that allow us to solve various problems. For example: It helps us to know how to distribute a budget in our daily life, it helps us to divide the birthday cake in equal parts and to find the area of our house and our room.
What do we ask ourselves about mathematics?What we ask ourselves about mathematics is how we can apply the problems and formulas of algebra and other areas derived from mathematics in daily life. Sometimes it seems that these complex problems do not have an application in daily life.
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The solution to any system is where the graphs cross or touch?
true or false?
Where the graphs intersect or touch, the supplied statement is true, and that is the solution to any system.
What are the principles governing linear equations?One or two variables make up a linear equation. Neither the numerator nor the denominator of a fraction can be a variable in a linear equation raised to a power higher than 1. The lines that connect all the points on a coordinate grid when you identify the values that make a linear equation true are congruent.
A linear equation is what?An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. The above is sometimes referred to as "linear equation of two variables," where y and x are the variables.
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Find the volume of the solid
480 m³ is the volume of the given solid.
What is Volume?
The space that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.
The dimensions of the trapezoidal prism are given in the diagram.
The dimensions of the cuboidal cavity are also given.
Volume of the solid = Volume of trapezoidal prism - Volume of cuboidal cavity
Volume of trapezoidal prism = (1/2)[Sum of parallel sides][h]×length
= (1/2)×[13+8]×[5]×10
= 525 m³
Volume of cuboidal cavity = l×b×h
= 10×3×1.5
= 45 m³
Volume of the solid = 525 - 45 m³
= 480 m³
The volume of the solid is 480 m³.
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What is an equation for the quadratic function represented by the table shown? (table provided below in attachment file)
The quadratic function represented by the table is f(x) = -x² + 4x -1.
What is a quadratic function?A polynomial of degree two in one or more variables is referred to as a quadratic polynomial. The polynomial function that a quadratic polynomial defines is known as a quadratic function.
Here, we have
Given: we have three variables a, b, and c, we can solve this problem by taking three points, say:
(0,-1), (2,3), and (4,-1)
Since we know that the function of the table is a quadratic function, we can start writing this function as follows:
f(x) = ax² + bx + c
So these points must satisfy the equation of the function.
For, (0,-1)
-1 = a(0)² + b(0) + c
c = -1
For, (2,3)
3 = a(2)² + b(2) + c
3 = 4a + 2b -1
4 = 4a + 2b
2 = 2a + b....(1)
For, (4,-1)
-1 = a(4)² + b(4) + c
-1 = 16a + 4b - 1
4a + b = 0...(2)
Now, we have two equations to solve for a and b:
a = -1
b = 4
Now we put the value of a, b, and c in the given equation and we get
f(x) = (-1)x² + 4x + (-1)
f(x) = -x² + 4x -1
Hence, the quadratic function represented by the table is f(x) = -x² + 4x -1.
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In a blueprint, each square has a side length of 14
inch.
a. Ceramic tile costs $5 per square foot. How much would it cost to tile the bathroom?
It would cost $
to tile the bathroom.
b. Carpet costs $18 per square yard. How much would it cost to carpet the bedroom and living room?
Step-by-step explanation:
1 blue square on drawing is length 1/4 in but that means 4ft in reality.
so one blue square area correspongs to 4x4 = 16 square feet.
(a) there 6 tiles for the batrhroom = 6x16 sq.ft = 96 sq.ft and the cost will be $480
(b) bedroom + living area = 7x8-8 tiles = 48 tiles = 48 x 16 sq.ft. = 768 sq.ft = 85.33 sq. yards. So the cost will be 85.33*18=$1535.94
(c) unit cost for tile: $5/sq.ft
unit cost for carpet: $1535.94/768sq.ft = $2/sq.ft
The tile has a greater unit cost ($5 per sq.ft) than carpet ($2 per sq.ft)
Tiling the bathroom would cost $25. The price of five squares of tile, or the cost of tiling the bathroom, is: $5 x 5 squares is $25.
How much would it cost to tile the bathroom?a. To calculate the cost of tiling the bathroom, we must first calculate its square footage. Assume the restroom measures 8 feet by 10 feet. We now have the area of:
960 square inches are equal to 8 feet by 12 inches per foot and 10 feet by 12 inches per foot.
The area of the bathroom can be divided by the area of each square, which is 14 inches on the blueprint, to determine the number of squares required:
14 inches by 14 inches divided by 960 square inches equals 4.96 squares.
As we are unable to purchase a fractional quantity of tile, we will round up to 5 squares.
The price of five squares of tile, or the cost of tiling the bathroom, is:
$5 x 5 squares is $25.
Consequently, tiling the bathroom would cost $25.
How much would it cost to carpet the bedroom and living room?b. To calculate the cost of carpeting the bedroom and living room, we must first calculate the square footage of each space. Assume that the living room is 18 feet by 20 feet and the bedroom is 12 feet by 14 feet in size. These areas include:
Bedroom: 168 square feet (12 feet by 14 feet).
The living room is 360 square feet (18 feet by 20 feet).
Divide by 9 to convert square feet to square yards:
Bedroom 168 sq ft / 9 sq ft = 18.67 sq ft
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How much would it cost for a customer to purchase 20 subscriptions for each of their 20 employees after a free 30-day trial period, with each subscription costing $10 per month for a yearly commitment? Additionally, they will need 1 extra subscription for a different service for every two employees, with each of these subscriptions costing $5 per month for a yearly commitment. What would be the total cost for the customer for the entire year
The total cost for the customer for the entire year is $48,600.
How to the total cost for the customer for the entire yearThe customer wants to purchase 20 subscriptions for each of their 20 employees, so they need a total of 20 x 20 = 400 subscriptions.
Each subscription costs $10 per month for a yearly commitment,
so the cost for one subscription for a year would be $10 x 12 = $120.
Therefore, the total cost for 400 subscriptions for a year would be $120 x 400 = $48,000.
In addition, they need 1 extra subscription for a different service for every two employees, so they need 20 / 2 = 10 extra subscriptions.
Each extra subscription costs $5 per month for a yearly commitment, so the cost for one extra subscription for a year would be $5 x 12 = $60.
Therefore, the total cost for 10 extra subscriptions for a year would be $60 x 10 = $600.
Adding the cost of the extra subscriptions to the cost of the regular subscriptions, the total cost for the customer for the entire year would be $48,000 + $600 = $48,600.
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A restaurant offers a 13% discount on all of its food. What is the new total after the discount has
been applied to a bill of £39?
Give your answer in pounds and include the £ sign.
The new total after the 13% discount has been applied to a bill of £39 is £33.93.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
To calculate the new total after the discount, we need to first find the amount of discount applied to the original bill.
We can do this by multiplying the original bill by the discount rate (as a decimal):
Discount = 0.13 * £39 = £5.07
Therefore, the amount of the discount is £5.07.
To find the new total, we need to subtract the discount from the original bill:
New total = £39 - £5.07 = £33.93
Therefore, the new total after the 13% discount has been applied to a bill of £39 is £33.93.
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find the smallest number, which when is diminished by 7, is divisible by 18,72, and 86.
Answer: 1015
Step-by-step explanation: We will find the factors of all the given numbers by using the prime factorization method. Then we will multiply the factors with the highest degree to find the least common multiple of the given numbers.
Which of the diagrams below represents the contrapositive of the statement
"If it is a square, then it is a quadrilateral"?
not quadrilateral
not square
Figure A
OA. Figure A
OB. Figure B
not square
not
quadrilateral
Figure B
Figure B is the correct option which represents the the contrapositive of the statement "If it is a square, then it is a quadrilateral".
What is a contrapositive statement ?
A contrapositive statement is a statement formed by negating both the hypothesis and the conclusion of the original statement, and then switching them and negating the entire statement.
In other words, if the original statement is of the form "If A, then B", then the contrapositive statement is of the form "If not B, then not A". The contrapositive statement is logically equivalent to the original statement, which means that if the original statement is true, then the contrapositive statement is also true, and if the original statement is false, then the contrapositive statement is also false.
Finding the contrapositive statement -
We are given "if it is a square,then it is a quadrilateral ".
To determine the contrapositive of a conditional statement, we must switch the hypothesis and the conclusion and negate both.
The original statement is "If it is a square, then it is a quadrilateral." The hypothesis is "it is a square," and the conclusion is "it is a quadrilateral."
Contrapositive of our given statement is -
"if it is not a square,then it is not a quadrilateral "
Therefore, figure B is correct option.
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drew used these clues to describe a number he wrote.
One digit has a value of 7 x 100,000.
One digit has a value of 9 x 100
One digit has value of 8 x 0.01
Which could be the number Drew wrote?
The number that Drew wrote is 790,800.
What is number?Number is a mathematical object used to count, measure, and label. It is an abstract concept that can be represented with symbols, such as numerals, and words, such as "three" or "three hundred." Numbers can be used to represent quantities, distances, sizes, and other measurements. In mathematics, number theory is the study of the properties of numbers, such as addition, subtraction, multiplication, and division. Number theory is also used in other sciences, such as physics and computer science.
This is determined by taking the value of each digit and multiplying it by the exponential value that Drew described. The first digit has a value of 7 x 100,000, the second digit has a value of 9 x 100, and the third digit has a value of 8 x 0.01. Therefore, the number is 790,800.
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The sum of 4 consecutive integers is -326. Find the largest integer
[tex]x + (x+1) + (x+2) + (x+3) = -326\\[/tex]
[tex]4x + 6 = -326[/tex]
[tex]4x = - 326-6[/tex]
[tex]4x = -332[/tex]
[tex]x = -332/4 \implies x = - 83[/tex]
the integers are:
[tex]-83 < -82 < -81 < -80[/tex]
the largest integer is: -80
Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 26 feet and a height of 20 feet. Container B has a diameter of 36 feet and a height of 19 feet. Container A is full of water and the water is pumped into Container B until Container A is empty.
no websites or links
After the pumping of Container A's water into Container B, the volume of water in Container B is 6,286 feet³.
What is the volume?The volume refers to the amount of space in a container.
The volume of a container can be determined using the following formula: πr²h, where:
π = pi = 22/7r = radius = diameter/2h = height.Container A:Diameter = 26 feet
Height = 20 feet
The volume of water in Container A = πr²h
r = radius = diameter/2
= 20/2 = 10 feet
Volume = 22/7 x 10 x 10 x 20
= 22/7 x 100 x 20
=6,285.7
= 6,286 feet³
Container B:Diameter = 36 feet
Height = 19 feet
Thus, the volume of Container B after the pumping, which is equal to the volume of water in Container A, is 6,286 feet³.
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Question Completion:After the pumping of Container A's water into Container B, what is the volume of water in Container B?
Find the value of x
Answer:
x = 13
Step-by-step explanation:
We know that 5x, x+12, and 90 makes a straight line, which is 180 degrees
5x + x+12 + 90 = 180
Combine like terms.
6x+102=180
Subtract 102 from each side.
6x+102-102=180-102
6x = 78
Divide each side by 6
6x/6 = 78/6
x = 13
Answer:
x = 13
Step-by-step explanation:
Now we have to,
→ Find the required value of x.
We know that,
→ The angle of right angle is 90°.
Forming the equation,
→ (x + 12)° + (5x)° = 90°
Then the value of x will be,
→ (x + 12)° + (5x)° = 90°
→ x + 12 + 5x = 90
→ (x + 5x) + 12 = 90
→ 6x + 12 = 90
→ 6x = 90 - 12
→ 6x = 78
→ x = 78 ÷ 6
→ [ x = 13 ]
Hence, the value of x is 13.
What is the best estimation of the equation 7 8 − 6 11 ? Drag the numbers into the boxes. Numbers may be used once, twice, or not at all. 1/42011/21/8 − =
For the equation 7/8 - 6/11, the best estimation is obtained as (1) - (1/2) = 1/2
To estimate 7/8 - 6/11, we need to find a common denominator for the two fractions.
One way to do this is to multiply the numerator and denominator of each fraction by the denominator of the other fraction.
So, we have -
(7/8) x (11/11) - (6/11) x (8/8)
= 77/88 - 48/88
= (77 - 48)/88
= 29/88
To simplify this fraction, we can look for common factors in the numerator and denominator.
The fraction 7/8 is almost 1 and the fraction 6/11 is almost 1/2.
Therefore, the best estimation of the equation 7/8 − 6/11 is -
(1) - (1/2) = 1/2
Therefore, the equation is obtained as (1) - (1/2) = 1/2.
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Please help me anyone with this question ?!!!??!!
Answer:
Believe it's just a
Step-by-step explanation:
Because
Gabe missed three less than twice as many points as his friend Noah on their test if they missed a total of 18 points how many did gabe miss
Noah missed 7 points on the test. And Gabe missed 2x - 3 = 2(7) - 3 = 11 points on the test. So, Gabe missed 11 points on the test.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
Let x be the number of points that Noah missed on the test.
Then, the number of points that Gabe missed is 2x - 3, according to the problem.
The total number of points missed by both of them is given as 18.
So, we can write an equation based on the problem statement:
x + (2x - 3) = 18
Simplifying the equation, we get:
3x - 3 = 18
Adding 3 to both sides of the equation, we get:
3x = 21
Dividing both sides of the equation by 3, we get:
x = 7
Therefore, Noah missed 7 points on the test. And Gabe missed 2x - 3 = 2(7) - 3 = 11 points on the test. So, Gabe missed 11 points on the test.
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Company A Company B
8/10/14/4 10/6/16/3
a. Calculate the single equivalent discount rate for each company?
Note: Do not round intermediate calculations. Round your final answers to the ne.
Company A
Company B
Single
equivalent
discount rate
%
%
The single equivalent discount rate for Company A is 19.28%, and for Company B is 23.18%.
How to find the percentage from the total value?
Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is
[tex]\dfrac{a}{100} \times b[/tex]
We are given;
The measures of company A and B= 8/10/14/4 10/6/16/3
Now,
To calculate the single equivalent discount rate for each company, we can use the following formula:
Single equivalent discount rate = [(1 - (Discount % / 100)) ^ (365 / Average payment period) - 1] x 100
For Company A, the average payment period is:
(8 + 10 + 14 + 4) / 4 = 9
Using the formula, we can calculate the single equivalent discount rate for Company A:
Single equivalent discount rate = [(1 - (8/100)) ^ (365 / 9) - 1] x 100 = 19.28%
For Company B, the average payment period is:
(10 + 6 + 16 + 3) / 4 = 8.75
Using the formula, we can calculate the single equivalent discount rate for Company B:
Single equivalent discount rate = [(1 - (10/100)) ^ (365 / 8.75) - 1] x 100 = 23.18%
Therefore, by percentage the answer will be 19.28% and 23.18%.
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I just need my brain reworked on how to do this
The number of square feet of wallpaper that Austin will need for the large wooden storage boxes would be = 1,296 ft².
How to calculate the amount of wallpaper needed by Austin?To calculate the amount of wallpaper needed, we should find the area of the rectangular prism.
The formula for the area of rectangular prism = 2 (lh +wh + lw ).
Where;
Length (l) = 6ft
width (w) = 3ft
Height (h) = 6ft
area = 2( 6×6 + 3×6 + 6×3)
= 2( 36+18+18)
= 2( 72)
= 144 ft²
Therefore the amount of wallpaper needed = 144× 9 = 1296 ft².
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Determine whether the study is an experiment or an observational study, and then identify a major problem with the study.
In a survey, 1465 Internet users chose to respond to this question posted on a newspaper's electronic edition: "Is news online as satisfying as print and TV news?" 52% of the respondents said "yes."
Question content area bottom
Part 1
This is an
▼
experiment
observational study
because the researchers
▼
do not attempt to modify
apply a treatment to
the individuals.
Part 2
What is a major problem with the study?
A.
This is a convenience sample with voluntary response, which has a high chance of leading to bias.
B.
There is no blinding or replication, which has a high chance of leading to bias.
C.
The sample is not very large.
D.
The results apply only to Internet users.
This is an observational study because the researchers do not attempt to modify or apply a treatment to the individuals. Major problem with the study is A.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
This is a convenience sample with voluntary response, which has a high chance of leading to bias.
The survey relies on self-selection, meaning that only those who were interested in responding to the question chose to do so.
This can result in a biased sample that does not accurately represent the population of all internet users.
Additionally, the sample size is not known to be representative or sufficient for generalization, and there is no control group or experimental design to establish cause and effect.
Hence, this is an observational study because the researchers do not attempt to modify or apply a treatment to the individuals.
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Find the degree of this polynomial.
8t5 + 5t4
Answer:
5
Step-by-step explanation:
The degree of a polynomial is the highest degree of its terms.
Identify the term with the largest exponent on the variable
Identify the degree of each terms
The degree of 8t5 is 5
The degree of 5t4 is 4
Degree of polynomial = 5
The area of the triangle is 45.5 square units and the height of the triangle is given. What is the measurement of the base?
For the triangle which is mentioned above the measurement of the base will be 10 cm.
What is a Triangle?
With three sides, three angles, and three vertices, a triangle is a closed, two-dimensional object. A polygon also includes a triangle.
The area of a triangle is A=1/2b*h
Here, A is the area of triangle =45.5 square units
b will be the base(NEED TO FIND)
h will be the height = 9.1cm
Substituting, 45.5 = (1/2)×b×9.1
b= (45.5×2)/9.1
b= 10 cms
The base value will be: 10cms
The Complete Question: The area of the triangle is 45.5 square units and the height of the triangle is given as 9.1 cm. What is the measurement of the base?
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Determine whether the pair of lines are parallel, perpendicular, or neither.
12x + 4y = 9
12x = 36y + 48
The pair of lines 12x + 4y = 9 and 12x = 36y + 48 are perpendicular.
Determining whether the pair of lines are parallel, perpendicular or neitherFrom the question, we are to determine whether the pair of lines are parallel, perpendicular or neither
To determine whether the pair of lines are parallel, perpendicular, or neither, we need to compare their slopes.
We can rewrite both equations in slope-intercept form, y = mx + b,
Where m is the slope of the line:
12x + 4y = 9
4y = -12x + 9
y = (-3/1)x + 9/4
12x = 36y + 48
12x - 48 = 36y
(1/3)x - 4/3 = y
The slope of the first line is -3/1, and the slope of the second line is 1/3.
Parallel lines have the same slope, so these lines are not parallel.
Perpendicular lines have slopes that are negative reciprocals of each other, meaning their slopes multiply to -1. Therefore, these lines are perpendicular.
Hence, the given pair of lines are perpendicular.
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What is the product of 6 /square root 12 and 2/ square root 14 in simplest radical form?
The product of 6 √12 and 2√14 in simplest radical form is 24 √42 .
What is Radical?Radical - The √ symbol that is used to denote square root or nth roots. Radical Expression - A radical expression is an expression containing a square root.
We have to find the product of 6 √12 and 2√14 in simplest radical form.
So, 6 √12 x 2√14
= 12 x √12 x √14
= 12 x 2√3 x √14
= 24 x √3 x √14
= 24 √42
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At a restaurant, the bill comes to $76. If you decide to leave a 20% tip, how much total do you need to pay? Give your answer to the nearest dollar.
Answer:
$91
Step-by-step explanation:
bill = $76
tip = 20%
20% of bill = (20/100) * 76
= $15.2
total bill = $76 + $15.2
= $91.2
= $91
The scatterplot shows the number of students in each 8 different classrooms and the number of pencils needed for the entire school year.
Answer:
I think the answer is 50 pencils
The following figure has volume as indicated. Find the value of x.
V = 128
a) 8
b) 16/8
c) 4
d) 16
The value of x for the given cone will be 4. The correct option is C.
What is the volume of the cone?The area a cone takes up in a three-dimensional plane is known as its volume. A cone's base is circular, so it is made of a radius and a diameter.
Given that the volume of the cone is V = 128π and the height of the cone is h = 24 units.
The value of the radius x will be calculated as,
V = ( 1 / 3 )πr²h
128π = ( 1 / 3) π x r² x 24
r² = 16
r = 4 units
Therefore, the value of x will be 4 units.
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Keisha can ride her skateboard two and one half miles an hour how far can you ride in 3/4 of an hour
Answer:
1 and 7/8.
Step-by-step explanation:
Two and a half= 5/2
5/2 x 3/4 = 15/8 = 1 7/8
9feet to3 3/8inches ratio
Answer:
32 : 1
Step-by-step explanation:
dimensions of the parts of the ratio must be in the same units
convert 9 feet to inches
1 foot = 12 inches
then
9 feet = 9 × 12 = 108 inches
then ratio
9 feet : 3 [tex]\frac{3}{8}[/tex] inches
= 108 inches : 3 [tex]\frac{3}{8}[/tex] inches ( change mixed number to improper fraction )
= 108 : [tex]\frac{27}{8}[/tex] ( multiply both parts by 8 to clear the fraction )
= 864 : 27 ( divide both parts by 27 )
= 32 : 1
Find the value of k such that the line through (7, 1) and (k, 7) is parallel to the line y=3x.
The value of the k is 5
The slope of Parallel lines:The slope of a line is a measure of its steepness or inclination. It tells us how much the line rises or falls as we move horizontally along it.
Parallel lines will have the same slope. That means if two lines are parallel, they have the same steepness or inclination.
Here we have
Equation of the line is y = 3x --- (1)
Equation(1) is in the form y = mx + x
The slope of the line (1) = 3
Let y = m₁x + c is the line that is parallel to line (1)
Since the slope of the parallel lines are equal
=> y = 3x + c --- (2)
Given that the line passes through (7, 1)
=> 1 = 3(7) + c
=> c = - 21 + 1
=> c = - 20
Hence, the equation of the line is y = 3x - 20 --- (3)
It is given that the line will also pass through the point (k, 7)
=> 7 = 3k - 20
=> 3k = 27
=> k = 9
Therefore,
The value of the k is 9
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complete the number pattern 9;27;81?
Answer:
the full numbers is 9, 27, 81, 243.
Answer:
243
Step-by-step explanation:
How to do a area problem
Answer: 205
Step-by-step explanation:
ok, the height of this thing is 22 so lets start whit the top. So the height of this thing is 17 not including the triangles at the top. And 22-17=5 so the height of these triangles is 5 and the base is 10 because if you dd the two 5s and subtract it from the whole base you get 10 and 10 x 7 is 70 /2 is 35 now for the rectangle in the middle the height is 7 and we alr know the base which is 10 so 7x10 is 70 70+35=105 ok now the last one 10 x 20= 200 +105= 205
Answer:
Area=295cm²
Step-by-step explanation:
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