Answers
On simplifying the given expressions we get-
a) [tex]5^{12}[/tex]
b) [tex]5^{18}[/tex]
Here, we are given two expressions in exponential form. Let us solve them one by one.
Firstly, we look at a property of exponentials as follows-
[tex]x^{a} x^{b} = x^{a+b}[/tex]
Theoretically, this means that when the bases are equal, the powers can be added in case of multiplication of exponentials.
Now, we have-
a) [tex]5^{2} 5^{10}[/tex]
here, the base is equal, that is, 5. So we just add the powers to get-
[tex]5^{2+10}[/tex]
= [tex]5^{12}[/tex]
b) [tex]5^{2} 5^{7} 5^{9}[/tex]
Here, we have 3 exponents, but the property will still remain the same. Bases are all equal to 5, thus the expression will become-
[tex]5^{2+7+9}[/tex]
= [tex]5^{18}[/tex]
Thus, on simplifying the given expressions we get [tex]5^{12}[/tex] and [tex]5^{18}[/tex] respectively.
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Related Questions
Solve 2(4x - 3) = 2(x + 2) + 8 for x.A) x = 3B) x = 4C) x = -2D) x = -5
Answers
Given: 2(4x - 3) = 2(x + 2) + 8
Required: The value of x
Explanation:
Opening the brackets
[tex]\begin{gathered} 2(4x-3)=2(x+2)+8 \\ 8x-6=2x+4+8 \end{gathered}[/tex]Further
[tex]\begin{gathered} 8x-2x=4+8+6 \\ 6x=18 \end{gathered}[/tex]So
[tex]x=3[/tex]Final Answer: Option A is correct.
Value of x = 3 that is option A
Here we are given with the equation as,
2(4x-3) =2(x+2) +8
Now solving both left hand side and right-hand side
taking left hand side,
2(4x-3)
2 X 4x + 2 X (-3)
8x - 6
Now solving right hand side,
2(x+2) +8
2x + 4 +8
2x+ 12
Now according to question equating both left hand side and right-hand side,
8x - 6 = 2x + 12
Now transposing variables and constants on left hand side and right-hand side respectively,
8x - 2x = 6 + 12
6x = 18
x= 12 / 6
x = 3
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6. Which ordered pair is a solution to this system of equations below ? *7х + 5y = 59Зх — 9y = 159О(( -17, -12)О (-17, 12)О(17, -12)(17,12)
Answers
Answer:
(17, -12)
Explanation:
The system of equations is
7x +5y = 59
3x - 9y = 159
An ordered pair satisfies the system if it satisfies both equations. So, for each option we need to replace the ordered pair on the given equations.
For (x, y) = (-17, -12)
7x +5y = 59
7(-17) + 5(-12) = 59
-119 - 60 = 59
-179 = 59
The equality is not satisfied, so (-17, -12) is not a solution to this system
For (x, y) = (-17, 12)
7x +5y = 59
7(-17) + 5(12) = 59
-119 + 60 = 59
-59 = 59
The equality is not satisfied, so (-17, 12) is not a solution to this system
For (x, y) = (17, -12)
7x +5y = 59
7(17) + 5(-12) = 59
119 - 60 = 59
59 = 59
3x - 9y = 159
3(17) - 9(-12) = 159
51 + 108 = 159
159 = 159
Since both equations are satisfied, so (17, -12) is a solution to the system of equations
Therefore, the answer is (17, -12)
simplify the product using a table [tex]( - 3h - 4)(4h - 3)[/tex]
Answers
1) Simplifying this product, using the distributive property
(-3h -4)(4h-3)
-12h²+9h-16h+12
-12h²-7h +12
2) Inserting the table, or better making a similar one, multiplying the row by the column number:
_____|4h | -3 |
-3h | -12h² | 9h |
------------------------------
-4 | -16h | 12
------------------------------
-12h² +9h -16h +12
-12h² -7h +12
3) So the answer is -12h²-7h +12
Differentiate. y 5 ody (AX (52 O dy 5 (4x - 52
Answers
ANSWER
[tex]\frac{dy}{dx}\text{ = }\frac{-5}{(4x-5)^2}[/tex]EXPLANATION
We want to differentiate y given:
[tex]y\text{ = }\frac{x}{4x\text{ - 5}}[/tex]To differentiate fractions as this, we first spllit the numerator and denominator as:
U = x
V = 4x - 5
Now, differentiate them separately.
dU/dx = 1
dV/dx = 4
Now, use formula:
[tex]\frac{dy}{dx}\text{ =}\frac{V\frac{du}{dx}\text{ - U}\frac{dV}{dx}}{V^2}[/tex]So, let us put those values in there:
[tex]\begin{gathered} \frac{dy}{dx}\text{ = }\frac{(4x\text{ - 5) }\cdot\text{ 1 - (x }\cdot\text{ 4)}}{(4x-5)^2} \\ \frac{dy}{dx}\text{ = }\frac{4x\text{ - 5 - 4x}}{(4x-5)^2} \\ \frac{dy}{dx}\text{ = }\frac{-5}{(4x-5)^2} \end{gathered}[/tex]That is the answer
What is the inverse of the function h(x) = 3 over 4 x+12
Answers
To answer this question we will set the equation y=f(x), then we will solve the equation for x, and finally, we will exchange x and y.
Setting y=f(x) we get:
[tex]y=\frac{3}{4}x+12.[/tex]Subtracting 12 from the above equation we get:
[tex]\begin{gathered} y-12=\frac{3}{4}x+12-12, \\ y-12=\frac{3}{4}x\text{.} \end{gathered}[/tex]Multiplying the above equation by 4/3 we get:
[tex]\begin{gathered} (y-12)\times\frac{4}{3}=\frac{3}{4}x\times\frac{4}{3}, \\ x=\frac{4}{3}y-16. \end{gathered}[/tex]Exchanging x and y in the above equation we get:
[tex]y=\frac{4}{3}x-16.[/tex]Therefore the inverse function of h(x) is:
[tex]h^{-1}(x)=\frac{4}{3}x-16.[/tex]Answer:
[tex]h^{-1}(x)=\frac{4}{3}x-16.[/tex]3) Yi-fei Wang inherited $20,000 which she invested in stocks and bonds. The stocks returned 6% and the bonds 8%. if the return on the bonds was $80 less than the return on the stocks, how much did she invest in each?
Answers
We know that
• The total amount of money invested is $20,000.
,• The stocks returned 6%.
,• The bonds returned 8%.
,• Bonds return $80 less than Stocks return.
Let's called x stocks and 20,000 - x bonds.
Using the given information, we can define the following equation.-
[tex]0.08(20,000-x)=0.06x-80[/tex]Now, we solve for x.
[tex]\begin{gathered} 1,600-0.08x=0.06x-80 \\ 1,600+80=0.06x+0.08x \\ 0.14x=1,680 \\ x=\frac{1,680}{0.14} \\ x=12,000 \end{gathered}[/tex]Stocks' investment was $12,000.Bond's investment was $8,000. (the difference).change 0.31 to a fraction
Answers
Problem
change 0.31 to a fraction
Solution
For this case we can do the following:
31/100
And the final answer for this case would be 31/100 the most simplified form
Which are the intercept points and vertex point for the function ƒ(x) = x^2 + 5x + 6?
Answers
Answer:
The intercept points are:
[tex]\begin{gathered} (-3,0) \\ (-2,0) \end{gathered}[/tex]The vertex is:
[tex](-\frac{5}{2},-\frac{1}{4})[/tex]Step-by-step explanation:
To find the intercept points, we equal the function to zero and solve for x, as following:
[tex]\begin{gathered} x^2+5x+6=0 \\ \rightarrow(x+3)(x+2)=0 \\ \\ \rightarrow x+3=0\Rightarrow x_1=-3 \\ \\ \rightarrow x+2=0\Rightarrow x_2=-2 \end{gathered}[/tex]Now, we know that the intercept points have an x-value of -3 and -2. Since we're talking about intercepts, the y-values will be 0.
Therefore, we can conlcude that the intercept points are:
[tex]\begin{gathered} (-3,0) \\ (-2,0) \end{gathered}[/tex]The vertex of any given quadratic function in the form:
[tex]f(x)=ax^2+bx+c[/tex]is:
[tex](-\frac{b}{2a},f(-\frac{b}{2a}))[/tex]This way, for the given function, we'll have that the vertex point is:
[tex](-\frac{5}{2},-\frac{1}{4})[/tex]Evaluate.
(2a−1/3)÷b/15 when a=−3/5 and b=−6.75
Answers
The simplified mixed number upon evaluation is [tex]3\frac{11}{27}[/tex].
What is a mixed number?Mixed numbers, also known as mixed fractions, are made up of a whole number and a proper fraction (a fraction whose numerator is less than its denominator). There are a few features that mixed numbers and decimals have in common. A decimal number is made up of a whole number and a fractional element separated by a decimal point. A mixed number is made up of a whole number and a proper fraction, but they are not separated by a decimal point.Given:
a = −3/5 and b = −6.75
We have to determine the value of (2a−1/3) ÷ b/15.
Substituting the values of a and b in the expression, we get
(2(−3/5)−1/3) ÷ (−6.75)/15
⇒ (-6/5 - 1/3) ÷ (-0.45)
⇒ (-23/15) ÷ (-0.45)
⇒ 23/15 × 100/45
⇒ 92/27
⇒ [tex]3\frac{11}{27}[/tex]
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If a polynomial with real coefficients is of degree 3. Can we say there must be at least 1 real root?a. Yes, because complex roots must appear in conjugate pairs, leaving one root real. b. No. we can’t say anything about this casec. Yes, because if there is one real root, there must be two additional real rootsd. No, because such a curve never crosses the x-axise. Sometimes yes and sometimes no
Answers
Solution
If we have a polynomial odf degree 3 it must have 3 roots
And one of then should be real the answer is true
And the correct choice is:
a. Yes, because complex roots must appear in conjugate pairs, leaving one root real.
Since we have two possible options:
1) (x-i)(x+i) (x-a) with 2 factors conjugate and 1 root real a and two other complex numebrs
2) (x-a)(x-b)(x-c) with 3 real roots a,b and c
So then we must have at least one root assuming that the coeffcients of the polynomial are not complex
please help me find the y-intercept in the graph!
Answers
Answer:
(0,9)
Step-by-step explanation:
A washer and a dryer cost $905 combined. The washer costs $55 more than the dryer. What is the cost of the dryer?sXХ5?
Answers
Solution:
Given:
Let the washer be represented by w.
Let the dryer be represented by d.
Hence,
[tex]\begin{gathered} A\text{ w}asher\text{ and a dryer cost \$}905 \\ This\text{ means;} \\ w+d=905.........................(1) \\ \\ \\ The\text{ washer costs \$55 more than the dryer} \\ w=d+55..........................(2) \end{gathered}[/tex]Substituting the equation (2) into equation (1);
[tex]\begin{gathered} d+55+d=905 \\ 2d+55=905 \\ 2d=905-55 \\ 2d=850 \\ d=\frac{850}{2} \\ d=425 \\ \\ \\ Hence,\text{ } \\ w=d+55 \\ w=425+55 \\ w=480 \end{gathered}[/tex]Hence, the cost of the dryer is $425 and the cost of the washer is $480.
Therefore, the cost of the dryer is $425.
Use the figure to find the measures of the numbered angles. Explain your reasoning
Answers
The measures of the numbered angles are as follows:
3.
m∠1 139°m∠2 = 41°m∠3 = 139° m∠4 = 139° m∠5 = 41°m∠6 = 139°m∠7 = 41°4.
m∠1 = 117° m∠2 = 63°m∠3 = 117°m∠4 = 63° m∠5 = 117° m∠6 = 63° m∠7 = 63° How to find measures of angles?When parallel lines are cut by a transversal line, angle relationships are formed such as alternate angles, corresponding angles, linear angles, vertically opposite angles etc.
Therefore, line a and b are parallel to each other. The transversal line t cut the parallel lines.
Hence,
3.
m∠1 = 180 - 41 = 139° (angles on a straight line)
m∠2 = 41° (vertically opposite angles)
Vertically opposite angles are congruent.
m∠3 = 139° (vertically opposite angles)
m∠4 = 180 - 41 = 139° (same interior angles)
Same interior angles are supplementary.
m∠5 = 41° (same interior angles)
m∠6 = 139° (vertically opposite angles)
m∠7 = 41° (vertically opposite angles)
4.
m∠1 = 117° (alternate exterior angles)
Alternate exterior angles are congruent
m∠2 = 180 - 117 = 63° (sum of angles on a straight line)
m∠3 = 117° (vertically opposite angles)
m∠4 = 63° (vertically opposite angles)
m∠5 = 117° (vertically opposite angles)
m∠6 = 180 - 117 = 63° (sum of angles on a straight line)
m∠7 = 63° (vertically opposite angles)
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helpppppppppppppppppppppppppp
Answers
Answer:
yes
Step-by-step explanation:
The final answer would be -126<-105
Use your calculator to find tan−1(5) to the nearest degree.
Answers
79 degree
Explanation:
When typing tan^-1 (5), click on the function that allows you to access the tan^-1 (generaly above the tan option),
can you help me with this, this is not for a test or quiz, i accept brainlys community guidelines.
Answers
The depth od the underwater camerais proportional to the time, this means that the depth varies the same amount of meters for every unit of time (second) that passes.
Let "y" represent the depth and "x" represent the time, you can express the relationship between both variables as
[tex]y=kx[/tex]Where k is the coefficient fo variation, ie. is the amount of meters the depth veries for every second that passes by.
Using the paired values (100, -5) we can calculate the coefficient of variation as
[tex]\begin{gathered} k=\frac{y}{x} \\ k=-\frac{5}{100} \\ k=-0.05 \end{gathered}[/tex]This means that fo every passing second the depth increases -0.05, we can establis the relationship as:
[tex]y=-0.05x[/tex]Now using this expression we can calculate the missing values of time and depth
For depth y= -1m
[tex]\begin{gathered} -1=-0.05x \\ x=-\frac{1}{-0.05} \\ x=20s \end{gathered}[/tex]For time x=60s
[tex]\begin{gathered} y=-0.05\cdot60 \\ y=-3m \end{gathered}[/tex]For time x=240s
[tex]\begin{gathered} y=-0.05\cdot240 \\ y=-12m \end{gathered}[/tex]Kindly help me with this question.
1. Given that f(x) = 2x-1, g(x) =(1/3) x 2 find:
i)(f o g(x)) ii) (g o f(x)) iii) (f o f(x)) iv) ( g o g(x)) v)confirm that f -1
(f(x))=x
Answers
Graph one complete cycle of y = -sec(2)+3. and list out your critical values points. Include asymptotes, if any.
Answers
Solution:
Given:
[tex]y=-sec(\frac{x}{4})+3[/tex]The graph of the above equation is shown below:
The critical values points are
[tex][/tex]A student entering a doctoral program in educational psychology is required to select three courses from the list of courses provided as part of his or herprogram(a) List all possible three-course selections.(6) Comment on the likelihood that EPR 669, EPR 634, and EPR 679 will be selectedClick the icon to view the course list(a) Select all the possible three-course selections below.A. 669,644, 679C. 669,634, 644DE 669.669, 634G. 669, 679, 6561669,634, 656K. 669, 669M. 634, 644,679(b) There is a chance that these courses will be selected.(Simplify your answer)B. 634, 644, 656D. 669. 644, 656OF 634, 679,656DH. 669,634, 679J. 656, 612, 656OL. 644,679, 656N. 644, 656, 644
Answers
(a) We need to find the number of combinations of selecting 3 courses of a group of 5 courses.
The number of combinations of n things chosen r at a time is found using:
[tex]_nC_r=\frac{n!}{r!(n-r)!}[/tex]Substituting with n = 5 and r = 3, we get:
[tex]_nC_r=\frac{n!}{r!(n-r)!}=\frac{5!}{3!(5-3)!}=\frac{5\cdot4\cdot3!}{3!2!}=\frac{5\cdot4}{2\cdot1}=10[/tex]The 10 possible combinations are:
• 669, 644, 679
,• 669, 634, 644
,• 669, 679, 656
,• 669, 634, 656
,• 634, 644, 679
,• 634, 644, 656
,• 669, 644, 656
,• 634, 679, 656
,• 669, 634, 679
,• 644, 679, 656
(b) There is a 1 in 10 chance that these courses will be selected
Geena's hair grew 1 1/8 inches in 3 months. How many inches will her hair grow in 1 month?
Answers
If Geena's hair grew 1 1/8 inches in 3 months then in one month Geena's hair grew 1 1/8 inches long.
What is Equation?Two or more expressions with an equal sign is called as Equation.
Given that,
Geena's hair grew 1 1/8 inches in 3 months.
We need to find how many inches grow in one month.
Let x be the hair grown in one month.
Let us convert 1 1/8 inches to improper fractions
1 1/8= 9/8
Let us form a equation with the given data.
nine by eight by three equal to x by 1.
9/8/3=x/1
Twenty seven by eight equal to x by one.
27/8=x/1
Apply cross multiplication
27=8x
x=27/8
x=3 3/8
Hence in one month Geena's hair grew 1 1/8 inches long.
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What is the range of the relation (-2,3) (0,3) (2,5) (2,9)
Answers
The range of a relation is given by the values of y the relation can assume.
Looking at the ordered pairs in the relation, the y-values that can be assumed are 3, 5 and 9.
Therefore the range is:
[tex]range=\mleft\lbrace3,5,9\mright\rbrace[/tex]what is the answer to the equation 14=-2-6-3
Answers
14 = -2c - 6 - 3c
14 + 6 = -2c - 3c
20 = -5c
c = 20/-5
c = -4
A linear function f(x) contains the coordinates (-9,4) and (6,4). Joy says f(x) is a horizontal line, and Lu says f(x) is a vertical line. Which student correctly described the function? Explain.
Answers
The student whose name is Joy has described the function correctly as the line is horizontal line.
What are the coordinates ?
Coordinates are a set of values which helps to show the exact position of a point in the coordinate plane.
The given coordinates of the linear function f(x) are (-9, 4) and (6,4).
The y-coordinates for both of these points will be the same if we plot them on the graph.
Additionally, if the y-coordinates on the graph are the same, then the line connecting these points is horizontal in nature.
So , we can conclude that , Joy is saying correct by saying it is a horizontal line.
Therefore , the student whose name is Joy has described the function correctly as the line is horizontal line.
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Elsa, Chau, and Felipe served a total of 100 orders Monday at the school cafeteria. Chau served 3 times as many orders as Felipe. Felipe served 5 more orders than Elsa. How many orders did they each serve?
Answers
Answer:
Chau served 63 orders.
Elsa served 16 orders.
Felipe served 21 orders.
Step-by-step explanation:
Given information:
Elsa, Chau, and Felipe served a total of 100 orders.Chau served 3 times as many orders as Felipe. Felipe served 5 more orders than Elsa.Define the variables:
Let e = number of ordered Elsa served.Let c = number of ordered Chau served.Let f = number of ordered Felipe served.Create a system of equations from the given information and defined variables:
[tex]\begin{cases}e+c+f=100\\c=3f\\e=f-5\end{cases}[/tex]
Substitute the second and third equations into the first equation and solve for f:
[tex]\implies e+c+f=100[/tex]
[tex]\implies (f-5)+3f+f=100[/tex]
[tex]\implies 5f-5=100[/tex]
[tex]\implies 5f=105[/tex]
[tex]\implies f=21[/tex]
Substitute the found value of f into the second equation and solve for c:
[tex]\implies c=3f[/tex]
[tex]\implies c=3(21)[/tex]
[tex]\implies c=63[/tex]
Substitute the found value of f into the third equation and solve for e:
[tex]\implies e=f-5[/tex]
[tex]\implies e=21-5[/tex]
[tex]\implies e=16[/tex]
Therefore:
Chau served 63 orders.Elsa served 16 orders.Felipe served 21 orders.Let us assume that,
→ Elsa = x
→ Felipe = x + 5
→ Chau = 3x + 15
Now the required value of x,
→ x + x + 5 + 3x + 15 = 100
→ 5x + 20 = 100
→ 5x = 100 - 20
→ x = 80/5
→ [ x = 16 ]
Then the orders each serve is,
→ Elsa = x = 16
→ Felipe = x + 5 = 16 + 5 = 21
→ Chau = 3x + 15 = 48 + 15 = 63
Hence, the above one is correct.
Vijay earned some money doing odd jobs last summer and put it in a savings account that earns 6% interest compounded continuously. After 1 year, there is $400.00 in the account. How much did Vijay earn doing odd jobs? Round your answer to the nearest cent.
Answers
The interest is 6%, compounded continuously.
After 1 year there is $400.
The continuous compound formula is
[tex]A=P\times e^{i\times t}[/tex]Where P is the principal, A is the final amount, i is the interest and t is the time in years.
Replacing all the given information, we have.
[tex]\begin{gathered} 400=P\times e^{0.06\times1} \\ P=\frac{400}{e^{0.06}} \\ P\approx376.71 \end{gathered}[/tex]Hence, Vijay earned $376.71 doing odd jobs.What is the domain of this function? (assume there are arrows at the ends of the graph) The answer has the form [A, B] Where A = and B = What is the range of this function? The answer has the form Select an answer Where A = and B = On what interval is the function increasing? The answer has the form Select an answer Where A = and B = On what interval is f(x) >= 0? The answer has the form Select an answer Where A = and B =
Answers
SOLUTION
From the question, we want to find
(a) The domain of the function.
The domain is gotten from the x-values. Looking at the x-values from the graph whether the curve is expanded or not, it would satisfy infinitely the value of any x-values. That is whatever x-value will make the function defined.
So the domain is all real numbers or negative infinity to positive infinity Written as
[tex]\begin{gathered} (A,B) \\ where\text{ } \\ A=-\infty\text{ and B = }\infty \end{gathered}[/tex](b) The range is the y-values that satisfy the function. Looking at the curve, the y-values would have infinitely number of negative values, but does not exceed 1, which is the maximum value.
So the range is negative infinity to 1.
Written as
[tex]\begin{gathered} (A,B] \\ where\text{ } \\ A=-\infty\text{ and B = 1} \end{gathered}[/tex](c) The function is increasing from infinite negative values of x, up to where x is -3, before it starts decreasing of sloping downwards
Hence the function is increasing between negative infinity to negative 3, written as
[tex]\begin{gathered} (A,B) \\ where\text{ } \\ A=-\infty\text{ and B = -3} \end{gathered}[/tex](d) Interval where f(x) >= 0
For f(x), that is y to be greater than or equal to zero, this must take place at the x-intercept, that is where the graph cuts the x-axis plane. Looking at the graph, this is at -4 and -2
hence the answer is between -4 and -2, written as
[tex]\begin{gathered} [A,B] \\ where\text{ } \\ A=-4\text{ and B = -2} \end{gathered}[/tex]Yesterday, Charmaine went on a bike ride. Her average speed was 10 miles per hour. Today, she went on another ride, this time averaging 13 miles per hour. In
the two days, she biked for a combined total time of 12 hours.
Let x be the number of hours she biked yesterday. Write an expression for the combined total number of miles she biked in the two days.
total number of miles biked
Answers
The base of an 8-foot ladder is placed 2 feet away from a wall. How high up the wall will the ladder reach?
Answers
The height up the wall will be 7.74 feet the ladder reach when an 8-foot ladder is placed 2 feet away from a wall.
The base of an 8-foot ladder is placed 2 feet away from a wall.
This is a simplistic Pythagoras problem since the wall forms a right angle with the ground.
Let a be the height up the wall.
Let b be the distance from the wall.
Let c be the length of the ladder.
According to Pythagoras's theorem,
a² + b² = c²
Here b = 2 and c = 8
a² + 2² = 8²
a² + 4 = 64
a² = 64 - 4
a² = 60
a = √60
a = 7.74 feet
Thus, the height up the wall will be 7.74 feet the ladder reach.
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What’s the correct answer answer asap for brainlist
Answers
Answer:
B. There is not much to add to this answer
Answer:
Step-by-step explanation:
B.
The valence electrons are known as the outermost elections which are usually stored in something called "valence electron shel"
6.25 ft7.14 am25 cm11 am8.9 m21.6 m
Answers
For figure 6
In figure 6 we have a circle and a rectangle. The shaded area will be the difference between the area of the rectangle of side 25ft and the area of the ciercle of diameter 25ft.
The radius of the circle will be 25ft/2 = 12.5ft
Then, the area will be:
[tex]\begin{gathered} \text{Area}=(25ft)\cdot(25ft)-\pi\cdot(12.5ft) \\ \text{Area}=625ft^2-490.87ft^2=134.13ft^2 \end{gathered}[/tex]For figure 7
In figure 7 we have a rectangle and a triangle. The shaded area will be the area of the rectangle minus the area of the triangle. The sides of the triange are 25cm and 14cm, while the triangle has a base of 25cm and a height of 11cm. We can say 11cm is the height because according to the figure this height forms a right triangle with the base.
Then, the area will be:
Area = 350cm^2 - 137.5cm^2
Area = 212.15cm^2
For figure 8
The figure 8 has a triangle and a semicircle. The shaded area will be the difference between the area of the semicircle and the area of the triangle.
We can say this is a righ triangle because his hypotenuse is the diameter of a circle and the hycks join in the circumference.
The hypotenuse is calculated with hicks 9m and 21.6m
[tex]h=\sqrt[]{(9m)^2+(21.6m)^2}=\sqrt[]{81m^2+466.56m^2}=\sqrt[]{547.56m^2}=23.4m[/tex]The area of the triangle could be calculated with the base 21.6m and the height 9m., and the area of the semicircle could be calculated considering his radius as the half of diameter: 23.4/2 = 11.7m
Then the area will be:
[tex]\text{Area = }\pi\cdot(11.7m)^2-\frac{(21.6m)\cdot(9m)}{2}[/tex][tex]\text{Area}=215.02m^2-97.2m^2=117.82m^2[/tex]