The dog moves quickly through 250-meter passes
What is unitary method?This technique allows us to calculate both the value of multiple units from the value of a single unit and the value of single unit from the value of multiple units.
A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique.
We typically utilize this technique for math calculations.
This approach will be helpful to you while tackling problems involving ratio and proportion, algebra, geometry, etc.
According to our question-
dog run =11 metres per second
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Solve for u
23= -8u-7+2u
Answer:
u = -5
Step-by-step explanation:
Isolate the variable, u. Note the equal sign, what you do to one side, you do to the other.
First, combine like terms. Like terms are terms that have the same amount of the same variables:
23 = -8u - 7 + 2u
23 = (-8u + 2u) - 7
23 = -6u - 7
Next, isolate the variable, u. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operations, and stands for:
Parenthesis
Exponsnts (& Roots)
Multiplications
Divisions
Additions
Subtraction
~
First, add 7 to both sides of the equation:
23 = -6u - 7
23 (+7) = -6u - 7 (+7)
23 + 7 = -6u
30 = -6u
Next, divide -6 from both sides of the equation:
-6u = 30
(-6u)/-6 = (30)/-6
u = 30/-6
u = -5
u = -5 is your answer.
~
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Answer:
[tex]u=-5[/tex]Step-by-step explanation:
[tex]23= -8u-7+2u[/tex]
[tex]-8u-7+2u=23[/tex]
[tex]-8u+2u-7=23[/tex]
[tex]-6u-7=23[/tex]
[tex]-6x-7+7=23+7[/tex]
[tex]-6u=30[/tex]
[tex]\cfrac{-6u}{-6}=\cfrac{30}{-6}[/tex]
[tex]u=-5[/tex]
The average temperature for a country during September 2013 was 58.1 degrees Farenheit. This is 5.6 degrees Farenheit above the 20th-century average temperature for September. What was the country's 20th-century average temperature for September
Answer:
52.5
Step-by-step explanation:
58.1 - 5.6= 52.5
Given points A (1, 5) and B (-7, -5), which of the following coordinates is the midpoint of AB? (-3, 0) (-4, 0) (-2, 0) (4, 0) (2, 0)
The midpoint of the points A (1, 5) and B (-7, -5) is found to be (-3, 0)
What is midpoint of a line?The midpoint of a line segment is the centroid of the segment. It is equally distant from both of the ends and hence cuts the section in half.
How to find midpoint of a line segmentThe formula to determine the center point of a straight line using the coordinates of its endpoints is known as the midpoint formula in coordinate geometry.
The formula is of the form
X= (x₂ + x₁)/2
Y = (y₂ + y₁)/2
Given points A (1, 5) and B (-7, -5)
X= (1 - 7)/2 = -3
Y = (5 - 5)/2 = 0
the midpoint is (-3, 0)
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What is the equation of the line that passes through the points (10, 10) and (-2,-5)? Write your answer in slope-intercept form.
it's too late for this nonsense-
Write an equation that represents the line.
Use exact numbers.
Answer:
-5x+5
Step-by-step explanation:
That would be the answer
Someone help please!! I only need the questions that are circled.
Answer:
Question 8: (-4,7)
Question 10: (5,2)
Step-by-step explanation:
What are equations?:
Two mathematical expressions are equal.⇒ Example; 2x + 5 = 25 is an equation, in which 2x + 5 and 25 are two expressions separated by an equal (=) sign.What is Substitution Method?:
The value of one variable from one equation is substituted in the other equation.y = -2x - 1
3x - 4y = -40
Question 8:
3x - 4(-2x-1) = -40
3x + 8x + 4 = -40
11x + 4 = -40
11x = -44
x = -4
To find y we can substitute x into the equation.
y = -2(-4) -1
y = 8 -1
y = 7
(-4,7)
Question 8 Solution - (-4,7)
Question 10:
2x - y = 8
x = 5
Since this equation already given x we can substitution to find y.
2(5) - y = 8
10 - y = 8
-y = -2
y = 2
(5,2)
Question 10 Solution - (5,2)
Lenvy~
A man who is 6 feet tall casts a shadow that is 4 feet long. At the same time, a nearby flagpole casts a shadow that is 18 feet long. How tall is the flagpole?
picture of answer options are below
hello i need help with my homeowkr math today please.
The point R(3, 3) is rotated 180 clockwise around the origin. what are the coordinates of the resulting point, R
4. You download a digital soccer game for $2.50. You can add new players for
$1.50 each to upgrade your team. The total cost e is a function of the number n
of new players that you add. Which of the following statements about the
domain and the graph of the function is correct?
A The domain is discrete, and the point (4, 6) lies on the graph.
B
The domain is continuous, and the point (4. 6) lies on the graph.
The domain is discrete, and the point (5, 10) lies on the graph.
D The domain is continuous, and the point (5, 10) lies on the graph.
The domain is discrete, and point (5, 10) lies on the graph. Then the correct option is C.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
You download a digital soccer game for $2.50. You can add new players for $1.50 each to upgrade your team.
The number of players will be in a whole number. Then the function is given by the greatest integer function.
Let 'y' be the total cost and 'x' be the number of players. Then the equations are given as,
y = 1.50 [x] + 2.5
The total cost for 5 new players will be given as,
y = 1.50 [5] + 2.5
y = 7.5 + 2.5
y = 10
The domain is discrete, and point (5, 10) lies on the graph. Then the correct option is C.
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Which of the following rational functions is graphed below?
On solving the question, we can say that second function has vertical asymptote at x=2
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found.
The function that represents the graph is f(x) = 1/x-2 .
The graph of the function
From the given graph , the vertical asymptote is at x=2
Lets find out the vertical asymptote of each function
To find out vertical asymptote we set the denominator =0
f(x) = 1/2x
2x = 0
x = 0
f(x) = 1/x-2
x-2 = 0
x = 2
The second function has vertical asymptote at x=2
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Let u = [ 14 -1] and v= [14 1] show that [h k] is in span {u,v} for all and k
How can it be shown that a vector b is in Span {u,v}? O A. Determine if the system containing u, v, and b is consistent. If the system is inconsistent, then bis in Span{u,v}. O B. Determine if the system containing u, v, and b is consistent. If the system is consistent, b might be in Span {u,V}. C. Determine if the system containing u, v, and b is consistent. If the system is consistent, then bis in Span{u,v}. O D. Determine if the system containing u, v, and b is consistent.
C. Determine if the system containing u, v, and b is consistent. If the system is consistent, then b is in Span{u,v} is correct.
To show that a vector b is in Span{u,v}, one way is to determine if it can be written as a linear combination of the vectors in the set, i.e., if there exist scalars h and k such that b = hu + kv. If this is the case, the system containing the equations hu + kv = b is consistent, meaning that there exist values of h and k that make the equation true. Therefore, if the system is consistent, it can be concluded that the vector b is in Span{u,v}.
Therefore, option C is the correct answer.
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Decimal Fraction
5,6+23,3
I need answer
A party of 300 people,54% will have someone to kiss when the clock strikes midnight.How many people will have someone to
kiss?
In a party of 300 people, 54% of the people who would have someone to kiss is 162 people.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100 in mathematics. If we need to calculate the percentage of a number, divide it by the whole and multiply by 100. As a result, the percentage denotes a part per hundred.
To determine the percentage of people with partners to kiss at midnight;
300 people present in party
54% will have someone to kiss = 0.54
Number of people that will have someone to kiss = 300 x 0.54 = 162
The 54% of people with someone to kiss are 162 in number.
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9. How many solutions does this system have? (1 point)
x-2y = 2
y=-2x+5
O infinitely many solutions.
Ono solutions
Otwo solutions.
one solution
The final statement is: The system of equations have unique solution.
What is the solution to a linear equation?The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.
Given here: x-2y = 2 & y=-2x+5
Solving these two equations by method of substitution we get
x-2(-2x+5)=2
x+4x-10=2
5x=12
x=2.4
∴ y=2×2.4+5
=4.8+5
=9.8
Hence, The system has one solution.
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Please solve this ill mark brainlest please actually asnwer no answer = report
Answer:
Step-by-step explanation:
∠ADB=360-90=270°
circumference of circle=2πr=2π×3=6π m
length of arc ADB
[tex]=\frac{270}{360} \times 6\pi \\=\frac{3}{4} \times 6\pi \\=\frac{9}{2} \pi \\\approx 14.137~m\\[/tex]
area of circle =πr²=π×3²=9π m²
area of shaded region
[tex]=\frac{270}{360} \times 9\pi \\=\frac{27}{4} \pi ~m^{2} \\\approx 21.206~m^2[/tex]
Francis buys a package of 450 plastic forks. He uses 315 of the plastic forks.
What percent of the plastic forks did Francis use? Show your work.
Francis purchases a package of 450 plastic forks but only uses 315 of them, therefore he uses 70% of the available supply.
what is percentage ?In math, a % is a number or ratio that is expressed as a fraction of 100. There are also sporadic uses of the abbreviations "pct.," "pct," and "pc." However, the percent sign "%" is frequently used to indicate it. The percentages' total quantity has no dimensions. Percentages are fundamentally fractions when the denominator is 100. Put a percent sign (%) next to a number to indicate that it is a percentage. For instance, if you successfully answer 75 out of 100 questions on a test (75/100), you get a 75%. Divide the money by the total to get percentages, then multiply the resulting number by 100. The formula (value/total) x 100% is used to calculate the percentage.
given
Francis purchases 450 plastic forks and
utilizes 315 of them, for
a percentage of 315/450*100
= 70%.
Francis purchases a package of 450 plastic forks but only uses 315 of them, therefore he uses 70% of the available supply.
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help im almost out of time
The domain and the range of this function shown in the graph include the following;
B. Domain: all real numbers.
Range = f(x) ≥ -11
How to identify the domain and range of this graph?In Mathematics, the horizontal extent of a graph represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.
Furthermore, the vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph of this function (see attachment), we can reasonably and logically deduce the following domain and range:
Domain = -∞ ≤ x ≤ ∞ or all real numbers.
Range = f(x) ≥ -11 or [-11, ∞].
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a single line divides a plane into two regions. two lines (by crossing) can divide a plane into four regions; three lines can divide it into seven regions. let pn be the maximum number of regions into which n lines divide a plane, where n is a positive integer recurrence formula
The P(n) represents the maximum no of regions into which n lines divide the plain then P(k) = P(k-1) + k. (b). The formula for P(n) is [tex]1+{ }^{n+1} c_2\end{aligned}$[/tex]. (c). The 5152 regions can divide the plane for 100 lines.
When no. lines are drawn, we get one plain region.
Let the number of regions when divided by lines be represented by
P(0), P(1), P(2), P(3), P(n)
Therefore P(0) = 1
P(1) = 2
P(1) = P(0) + 1
P(2) = P(1) + 2
P(3) = P(2) + 3
P(4) = P(3) + 4………………….
P(n) = P(n-1) + n
Therefore, if P(n) represents the maximum no. of regions into which n lines divide the plain
Then P(k) = P(k-1) + k
(b).
⇒ P(0) = 1
⇒P(n) = P(n-1) + n
= P(n-2) + (n-1)+n
= P(n-3) + (n-2) +(n-1)+n……..
= P(0) + 1 + 2+ 4=3 + 4 + 5 +……+n
= P(0) + (Sum of the first n natural numbers)
[tex]$$\begin{aligned}& =P(0)+\frac{n(n+1)}{2} \\& =1+{ }^{n+1} c_2\end{aligned}$$[/tex]
Therefore, the formula for P(n) is [tex]1+{ }^{n+1} c_2\end{aligned}$[/tex].
(c)
Compute the value for n=100
[tex]$$1+{ }^{n+1} c_2=1+{ }^{101} c_2=1+\frac{101 \times 102}{2}=5152$$[/tex]
Therefore, the 5152 regions can divide the plane for 100 lines.
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A single line divides the plane into two regions. Two lines (by crossing) can divide the plane into four regions; three lines can divide it into seven regions, etc. Let P(n) be the maximum number of regions into which n lines divide a plane, where n is a positive integer.
(a) Derive a recurrence relation for P(k) in terms of P(k-1) for all integers [tex]$k \geq 2$[/tex].
(b) Use iteration to find an explicit (closed) formula for P(n).
(c) Into how many regions can 100 lines divide the plane?
Which expression is represented by the model?
The provided model represents the expression 4x-3.
What is expression?An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. A number, a variable, or a combination of numbers, variables, and operation symbols constitutes an expression. An equation consists of two expressions joined by an equal sign.
Here,
You have 4 x's, then you minus 3,
=4x-3
The expression is represented by the model given is 4x-3.
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In ΔXYZ, y = 500 inches, mm∠Y=117° and mm∠Z=10°. Find the length of z, to the nearest inch.
if in ΔXYZ, y = 500 inches, mm∠Y=117° and mm∠Z=10° then length of z is 97.64 inches.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Given that ΔXYZ, y = 500 inches, mm∠Y=117° and mm∠Z=10°.
We have to find the length of z.
By using sine rule we find the length of z.
sin117/500=sin10/z
0.891/500=0.174/z
Apply cross multiplication
0.891z=0.174×500
0.891z=87
z=87/0.891
z=97.64 inches
Hence, if in ΔXYZ, y = 500 inches, mm∠Y=117° and mm∠Z=10° then length of z is 97.64 inches.
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Answer:
97
Step-by-step explanation:
What is the input for the function f(x)=4x-9 if the output is 11
Answer:
Input = 5
Step-by-step explanation:
Output = Answer a.k.a. f(x)
Input = x
We start by replacing f(x) with the output, which is 11
11 = 4x-9. I like making it opposite. It's easier in my eyes.
Making it opposite it's 4x-9 = 11
Now we need to get x by itself. The opposite of -9 is +9. So if we add 9 to each side, it deletes the 9 from the left and puts it on the other side, making it;
4x = 11 + 9. 11 + 9 is 20, so....
4x = 20.
Now 4x is the same as 4 times x. The opposite of times is divide. So let's divide by 4 on both sides. That gets rid of the 4 on the left side and puts it on the other side, making it;
x = 20/4. 20/4 is 5, so...
x = 5
Step-by-step explanation:
f(x) = 4x - 9
4x - 9 = 11
4x = 11 + 9
4x = 20
x = 20 ÷ 4
x = 5
Y=(x-2)^2+3 vertex form to standard form
The required vertex form of the given equation is y = x² - 4x + 7.
What is the equation?The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
here,
y = (x - 2)² + 3
Simplifying the expression,
y = x² -4x + 4 + 3 {since (a - b)² = a² + b² -2ab}
y = x² - 4x + 7
Thus, the required vertex form of the given equation is y = x² - 4x + 7.
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Nick has a checking account with the Park Slope Savings Bank. He writes both paper and electronic checks. For each transaction Nick enters the necessary information: check number, data, type of transaction, and amount. He uses E to indicate an electronic transaction. Determine the balance in his account after the Star Cable Co. check is written.
there is not enough information here to complete the problem.
Given this equation...
4x - 1 6
--------- = -----
3x + 7 5
What is the value of x in this
proportion?
Answer:
x=91
Step-by-step explanation:
Follow the steps in the image.
add 16 to both sides
subtract 3 from both sides
divide by 1x
Plug answer back into equation
-Hope this helped
f(x)=6-1/2x, h(x)=4(x-3)^2 Write f(h(x)) as an expression in terms of x
f(h(x)) = -2x^2 + 12x + (-12) in terms of x.
What is a function?
A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range.
To find f(h(x)), we first need to substitute h(x) into f(x).
f(h(x)) = f(4(x-3)²)
Now we can substitute 4(x-3)^2 into f(x)
f(h(x)) = 6 - 1/2(4(x-3)^2)
= 6 - 2(x-3)^2
= 6 - 2(x^2 - 6x + 9)
= 6 - 2x^2 + 12x - 18
Hence, f(h(x)) = -2x^2 + 12x + (-12) in terms of x.
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Consider the piecewise-defined function given by the graph. What are these values?
f(–3) =
f(–1) =
f(3) =
f (–3) = -1 , B) f (–1) = 2 , C) f (3) = 5, Mathematical equations that are described in the plane of cartesian coordinates are known as straight-line equations.
What are straight-line equations?
The general equation for every straight line is y = mx + c, where m is the gradient (or degree of steepness) of the line and c is the y-intercept (the point in which the line crosses the y-axis).
The variables x and y are related to coordinates on the line in the linear equation y = mx + c.
The formula y = mx + c yields a result for y when we enter a value for x.
As y depends on the value of x, it follows that x is an independent variable and y is a dependent variable.
According to our question-
m (x-x1) = y-y1 or
y = mx + c
Where,
Straight-line gradient, or m, is the line's slope.
The Cartesian coordinate that the line crosses is x1, y1.
the constant c
The calculation of the gradient (m) between any two locations on a line
m = Δy / Δx
f (-1) = Because x = -1, the function used is
y = 2, so f (-1) = 2 C) f (-3) = Because -3 -1,
the function used is y = -x-4, so f (-3) = - (- 3) -4 f (-3) = 3-4 f (-3) = -1 f (3) Since the function employed is
= -2x + 11 and x = 3, f (3) = -2 (3) +11, f (3) = -6 + 11, and f (3) = 5.
Hence, f (–3) = -1 , B) f (–1) = 2 , C) f (3) = 5, Mathematical equations that are described in the plane of cartesian coordinates are known as straight-line equations.
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Answer:-1
2
5
Step-by-step explanation:
simple answer
NO LINKS!!! Part 3
Find an exponential function y = ab^x form that satisfies the given information
f. passes through (-1, 72.73) and (3, 106.48)
g. passes through (-2, 351.56225) and (3, 115.2)
h. passes through (4, 405) and (9, 98415)
Answer:
[tex]\text{f)} \quad y=80(1.1)^x[/tex]
[tex]\text{g)} \quad y=225(0.8)^x[/tex]
[tex]\text{h)} \quad y=5(3)^x[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]
Part (f)Given points:
(-1, 72.73)(3, 106.48)Substitute the given (x, y) points into the exponential function formula to create two equations:
[tex]\implies 72.73=ab^{-1}[/tex]
[tex]\implies 106.48=ab^3[/tex]
Divide the second equation by the first equation to eliminate a:
[tex]\implies \dfrac{106.48}{72.73}=\dfrac{ab^3}{ab^{-1}}[/tex]
[tex]\implies \dfrac{106.48}{72.73}=\dfrac{b^3}{b^{-1}}[/tex]
Solve for b:
[tex]\implies \dfrac{106.48}{72.73}=b^3 \cdot b^{1}[/tex]
[tex]\implies \dfrac{106.48}{72.73}=b^{3+1}[/tex]
[tex]\implies \dfrac{106.48}{72.73}=b^4[/tex]
[tex]\implies b=1.09998968...[/tex]
[tex]\implies b=1.1[/tex]
Substitute the found value of b into one of the equations and solve for a:
[tex]\implies 72.73=a \cdot (1.09998968...)^{-1}[/tex]
[tex]\implies a=80.0022499...[/tex]
[tex]\implies a=80[/tex]
Substitute the found values of a and b into the exponential function formula:
[tex]\implies y=80(1.1)^x[/tex]
---------------------------------------------------------------------------------------
Part (g)Given points:
(-2, 351.56225)(3, 115.2)Substitute the given (x, y) points into the exponential function formula to create two equations:
[tex]\implies 351.56225=ab^{-2}[/tex]
[tex]\implies 115.2=ab^3[/tex]
Divide the second equation by the first equation to eliminate a:
[tex]\implies \dfrac{115.2}{351.56225}=\dfrac{ab^3}{ab^{-2}}[/tex]
[tex]\implies \dfrac{115.2}{351.56225}=\dfrac{b^3}{b^{-2}}[/tex]
Solve for b:
[tex]\implies\dfrac{115.2}{351.56225}=b^3 \cdot b^{2}[/tex]
[tex]\implies \dfrac{115.2}{351.56225}=b^{3+2}[/tex]
[tex]\implies \dfrac{115.2}{351.56225}=b^5[/tex]
[tex]\implies b=0.800000113...[/tex]
[tex]\implies b=0.8[/tex]
Substitute the found value of b into one of the equations and solve for a:
[tex]\implies 115.2=a(0.800000113...)^3[/tex]
[tex]\implies a=224.999904[/tex]
[tex]\implies a=225[/tex]
Substitute the found values of a and b into the exponential function formula:
[tex]\implies y=225(0.8)^x[/tex]
---------------------------------------------------------------------------------------
Part (h)Given points:
(4, 405)(9, 98415)Substitute the given (x, y) points into the exponential function formula to create two equations:
[tex]\implies 405=ab^4[/tex]
[tex]\implies 98415=ab^9[/tex]
Divide the second equation by the first equation to eliminate a:
[tex]\implies \dfrac{98415}{405}=\dfrac{ab^9}{ab^4}[/tex]
[tex]\implies 243=\dfrac{b^9}{b^4}[/tex]
Solve for b:
[tex]\implies 243=b^9 \cdot b^{-4}[/tex]
[tex]\implies 243=b^{9-4}[/tex]
[tex]\implies 243=b^{5}[/tex]
[tex]\implies b=3[/tex]
Substitute the found value of b into one of the equations and solve for a:
[tex]\implies 405=a \cdot 3^4[/tex]
[tex]\implies 81a=405[/tex]
[tex]\implies a=5[/tex]
Substitute the found values of a and b into the exponential function formula:
[tex]\implies y=5(3)^x[/tex]
Create a problem in which you add three different five digit numbers to get a sum of 93852
?+?+? =93,852
Answer:
50,000+30,000+13852=93,852
2. The figure shows a small rectangle cut out of a big rectangle. Find the area of the shaded figure.
7 cm
8 cm
3 cm
3 cm
Area of the shaded figure:
Area of the shaded figure:
square centimeters
The area of shaded figure rectangle is 7.5m²
How to find the area of rectangle?The amount of space occupied by a flat surface with a particular shape is referred to as the area. It is calculated using the "number of" square units (square centimeters, square inches, square feet, etc.) The amount of unit squares that can fit inside a rectangle is its area. The flat surfaces of laptop monitors, blackboards, canvas, etc. are a few examples of rectangular shapes.
step1:
The formula for the area of the Rectangle is:
A= a+ b/2*h= 3+3/2*7=31.5
step2:
The formula for the area of the rectangle is:
A=w l=3*8=24
Now you rest 31.5 -24 and it gives you 7.5
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