Find the area of the shaded region in the figure Type an integer or decimal rounded to the nearest TENTH
Answers
Answer:
The area of the shaded region is;
[tex]18.7\text{ }in^2[/tex]Explanation:
Given the figure in the attached image.
The area of the shaded region is the area of the larger circle minus the area of the smaller circle;
[tex]\begin{gathered} A=\frac{\pi D^2}{4}-\frac{\pi d^2}{4} \\ A=\frac{\pi}{4}(D^2-d^2) \end{gathered}[/tex]Given;
[tex]\begin{gathered} D=6 \\ d=3\frac{1}{2} \end{gathered}[/tex]Substituting the given values;
[tex]\begin{gathered} A=\frac{\pi}{4}(D^2-d^2) \\ A=\frac{\pi}{4}(6^2-3.5^2) \\ A=\frac{\pi}{4}(23.75) \\ A=18.65\text{ }in^2 \\ A=18.7\text{ }in^2 \end{gathered}[/tex]Therefore, the area of the shaded region is;
[tex]18.7\text{ }in^2[/tex]Related Questions
Write an exponential function in the form y = ab that goes through points (0,18) and (3,6174).
Answers
Using the first point given in the statement you can find a, like this
[tex]\begin{gathered} y=ab^x \\ \text{ Replace x = 0 and y = 18} \\ 18=ab^0 \\ 18=a\cdot1 \\ 18=a \end{gathered}[/tex]Now, since you already have the value of a, you can find the value of b using the second point, like this
[tex]\begin{gathered} y=ab^x \\ \text{ Replace x = 3 and y = 6174} \\ 6174=18\cdot b^3 \\ \text{ Divide by 18 into both sides of the equation} \\ \frac{6174}{18}=\frac{18\cdot b^3}{18} \\ 343=b^3 \\ \text{ Apply cube root to both sides of the equation} \\ \sqrt[3]{343}=\sqrt[3]{b^3} \\ 7=b \end{gathered}[/tex]Therefore, the exponential function that passes through the points (0,18) and (3,6174) is
[tex]y=18\cdot7^x[/tex]on one side of the balance scale, Henry placed gram weight. on the other side of the scale, he placed a ballet slipper. how many milligrams does the slipper weigh?
Answers
Solution
Step 1
Convert gram to milligram
1 gram = 1000 milligram
Step 2
Find the answer
Assuming it is 1 gram weight on one side of the balance scale then, the ballet slippers will weigh 1 gram for the scale to be balanced.
I gram = 1000 milligram
Hence the ballet slippers will weigh 1000 milligrams
Simplify a raised to the negative third power over quantity 2 times b raised to the fourth power end quantity all cubed.
Answers
[tex]\frac{1 }{8*a^{9}*b^{12}}[/tex].
Step-by-step explanation:1. Write the expression.[tex](\frac{a^{-3} }{2b^{4} } )^{3}[/tex]
2. Solve the parenthesis by multiplying the exponents with each part of the fraction.[tex]\frac{a^{(-3*3)} }{2^{(3)} b^{(4*3)} } \\ \\\frac{a^{(-9)} }{8b^{(12)} }\\ \\\frac{a^{-9} }{8b^{12} }[/tex]
3. Move a to the denominator (the negative sign of the exponent vanishes).[tex]\frac{1 }{8b^{12} *a^{9}}\\ \\\frac{1 }{8*a^{9}*b^{12}}[/tex]
4. Express your result.[tex](\frac{a^{-3} }{2b^{4} } )^{3}=\frac{1 }{8*a^{9}*b^{12}}[/tex].
A computer part costs $7 to produce and distribute. Express the profit p made by selling 300 of these parts as a function of the price of c dollars. (Do not include $ symbol in your answer)
Answers
Given:
Each part costs $7 to produce and distribute.
The total number of parts on selling is 300 to make the profit P.
To write the function expression in terms of sale price C and profit P:
As we know,
[tex]\text{Profit}=\text{Selling price-cost price}[/tex]So, if we produce 1 part and sell that part, then the profit is
[tex]P=C-7[/tex]For 300 parts, the profit is
[tex]\begin{gathered} P=300(C-7) \\ P=300C-2100 \end{gathered}[/tex]Hence, the function is expressed in terms of P and C is,
[tex]P=300C-2100[/tex]find the reference angle for -0.8pi
Answers
Answer:
What is Meant by the Reference Angle? In mathematics, the reference angle is defined as the acute angle and it is measuring less than 90 degrees. It is always the smallest angle, and it makes the terminal side of an angle with the x-axis.
how to write the rule for the rotation on #11?
Answers
#11
If the point (x, y) is rotated 180 degrees around the origin clockwise or anti-clockwise, then its image will be (-x, -y)
We just change the sign of the coordinates
From the attached picture we can see
The parallelogram MNOP where
M = (1, -2)
N = (3, -2)
O = (4, -4)
P = (2, -4)
The parallelogram M'N'O'P' where
M' = (-1, 2)
N' = (-3, 2)
O' = (-4, 4)
P' = (-2, 4)
Since all the signs of the coordinates are changed, then
M'N'O'P' is the image of MNOP by rotation 180 degrees around the orign
The rule of transformation is
[tex]R\rightarrow(O,180^{\circ})[/tex]Please help me with my calc hw, I'd be more than happy to chip in albeit with my limited knowledge.
Answers
Given:
[tex]F(x)=\int_0^x\sqrt{36-t^2}dt[/tex]Required:
To find the range of the given function.
Explanation:
The graph of the function
[tex]y=\sqrt{36-t^2}[/tex]is upper semicircle with center (0,0) and radius 6, with
[tex]-6\leq t\leq6[/tex]So,
[tex]\int_0^x\sqrt{36-t^2}dt[/tex]is the area of the portion of the right half of the semicircle that lies between
t=0 and t=x.
When x=0, the value of the integral is also 0.
When x=6, the value of the integral is the area of the quarter circle, which is
[tex]\frac{36\pi}{4}=9\pi[/tex]Therefore, the range is
[tex][0,9\pi][/tex]Final Answer:
The range of the function is,
[tex][0,9\pi][/tex]To produce g, function f was reflected over the x-axis andFunction g can be defined as
Answers
The graph of the functions f and g are given.
It is required to complete the statement concerning how to produce g.
The graph of the parent function f is shown:
Reflect the graph of f across the x-axis:
Translate the function 5 units vertically upwards:
The given parent function is y=f(x).
Reflect the graph across in the x-axis to get the equation y=-f(x).
Translate the graph 5 units up to get y=-f(x)+5
Answers:
To produce g, the function f was reflected over the x-axis and shifted up 5 units.
Function g is defined as g(x)=-f(x)+5.
A carpenter wants to cut a board that is 5/6 ft long into pieces that are 5/16 ft long. The carpenter will use the expression shown to calculate the number of pieces that can be cut from the board.5/6 divided by 5/16How many pieces can be cut from the board?
Answers
The expression which is used to calculate the number of pieces that can be cut from the board is:
[tex]\frac{5}{6}\div\frac{5}{16}[/tex]We solve this by changing the division sign to multiplication and taking the reciprocal of the second fraction.
Therefore:
[tex]\begin{gathered} \frac{5}{6}\div\frac{5}{16}=\frac{5}{6}\times\frac{16}{5} \\ =\frac{16}{6} \\ =2\text{ }\frac{4}{6} \\ =2\frac{2}{3}\text{ pieces} \end{gathered}[/tex]The carpenter can cut 2 2/3 pieces from the board.
5(3a-1) - 2(3a+2)=3(a+2) + vselect two expressions that are equivalent to v.
Answers
Let's solve the equation for v to identify the expressions:
[tex]\begin{gathered} 5(3a-1)-2(3a+2)=3(a+2)+v \\ 15a-5-6a-4=3a+6+v \\ 9a-9=3a+6+v \\ v=9a-3a-9-6 \\ v=6a-15 \\ v=3(2a-5) \end{gathered}[/tex]Therefore the equivalent expressions are D and E
What is the value of x in the equation −6 + x = −2? (5 points)84−4−8
Answers
Given the equation:
[tex]-6+x=-2[/tex]solving for x:
[tex]\begin{gathered} x=-2+6 \\ x=4 \end{gathered}[/tex]ANSWER
x = 4
find the width of a newer 48-in TV whose screen has an aspect ratio of 16:9what is the width?
Answers
The width of the TV is 41.84-in
Explanations:The diagonal size of the TV, d= 48 in
The aspect ratio= 16 : 9
The aspect ratio is usually given in form of width : Height
Let the width = w
Let the height = h
The diagram looks like:
[tex]\begin{gathered} \frac{w}{h}=\text{ }\frac{16}{9} \\ h\text{ = }\frac{9w}{16} \end{gathered}[/tex]Using the Pythagoras theorem:
[tex]\begin{gathered} d^2=h^2+w^2 \\ 48^2\text{ = (}\frac{9w}{16})^2+w^2 \\ 2304\text{ = }\frac{81w^2}{256}+w^2 \\ \text{Multiply through by 256} \\ 589824=81w^2+256w^2 \\ 589824\text{ = }337w^2 \\ w^2\text{ = }\frac{589824}{337} \\ w^2\text{ = 1750.22} \\ w\text{ = }\sqrt[]{1750.22} \\ w\text{ = 41.84 } \end{gathered}[/tex]The width of the TV is 41.84-in
Cheng-Yu ordered a book that cost $24 from an online store. Hertotal with the shipping charge was $27. What was the percent ofmarkup charged for shipping?
Answers
Given:
Cost of book = $24
Total cost of book (shipping charge inclusive) = $27
The shipping charge is:
Total cost - cost of book = $27 - $24 = $3
The shipping charge is $3
To find the percentage markup charged for shipping, use the formula:
[tex]\frac{ship\text{ charge}}{Total\text{ cost}}\ast100[/tex][tex]\frac{3}{27}\ast100\text{ = }0.111\text{ }\ast\text{ 100 = }11.1percent^{}[/tex]Therefore, the percent of markup charged for shipping is 11.1%
ANSWER:
11.1%
Please help with the question below (please try to answer in maximum 5/10 minutes).
Answers
Given
Joshira can create 1 item in 3/4 of an hour.
To find:
How many items can she create in 8 hours?
Explanation:
It is given that,
Joshira can create 1 item in 3/4 of an hour.
That implies,
[tex]\begin{gathered} Number\text{ }of\text{ }items\text{ }created\text{ }in\text{ }\frac{3}{4}\text{ }hour=1 \\ Number\text{ }of\text{ }items\text{ }created\text{ }in\text{ }1\text{ }hour=1\div(\frac{3}{4}) \\ =1\times\frac{4}{3} \\ =\frac{4}{3} \end{gathered}[/tex]Therefore, number of items created in 8 hours is,
[tex]\begin{gathered} Number\text{ }of\text{ }items\text{ }created\text{ }in\text{ }8\text{ }hours=\frac{4}{3}\times8 \\ =\frac{32}{3} \\ =\frac{30+2}{3} \\ =\frac{30}{3}+\frac{2}{3} \\ =10+\frac{2}{3} \\ =10\frac{2}{3}\text{ }items \end{gathered}[/tex]Hence, she can create 10 2/3 items in 8 hours.
The inequality 3x +2> x+8 is equivalent to
A. x>-12
C. x > 3
B. x > 2/2/1
D. x <3
Answers
Answer: C
Step-by-step explanation:
3x + 2 > x +8
= 3x + 2 -2 > x + 8 -2
= 3x > x + 6
= 3x - x > x - x + 6
= 2x/2 > 6/2
= x > 3
Answer:
C
Step-by-step explanation:
It is the only one that makes sense.
pls mark brainlest with the crown
How do I solve this problem? 1 - 9/5x = 8/6
Answers
The given equation is
[tex]1-\frac{9}{5x}=\frac{8}{6}[/tex]Adding -1 on both sides, we get
[tex]1-\frac{9}{5x}-1=\frac{8}{6}-1[/tex][tex]-\frac{9}{5x}=\frac{8}{6}-1[/tex][tex]\text{Use 1=}\frac{6}{6}\text{ as follows.}[/tex][tex]-\frac{9}{5x}=\frac{8}{6}-\frac{6}{6}[/tex][tex]-\frac{9}{5x}=\frac{8-6}{6}[/tex][tex]-\frac{9}{5x}=\frac{2}{6}[/tex][tex]-\frac{9}{5x}=\frac{1}{3}[/tex]Using the cross-product method, we get
[tex]-9\times3=5x[/tex][tex]-27=5x[/tex]Dividing by 5 into both sides, we get
[tex]-\frac{27}{5}=\frac{5x}{5}[/tex][tex]x=-\frac{27}{5}=-5.4[/tex]Hence the required answer is x=-5.4.
In a recent year, 26.3% of all registered doctors were female. If there were 47,400 female registered doctors that year, what was the total number of registered doctors? Round your answer to the nearest whole number.
Answers
From the problem statement we can write:
47,400 is 26.3% of total registered doctors
We need to convert this word equation to algebraic equation noting that,
• "is" means "="
,• "of" means "x"
Also, remember to convert the percentage to decimal by dividing by 100,
[tex]\frac{26.3}{100}=0.263[/tex]The algebraic equation, thus, is:
[tex]47,400=0.263\times\text{total}[/tex]We let total be "t" and solve :
[tex]\begin{gathered} 47,400=0.263t \\ t=\frac{47,400}{0.263} \\ t=180228.14 \end{gathered}[/tex]Rounding to the nearest whole number,
Total Registered Doctors = 180,228
Answer:
180,228Mai must choose a number between 49 and 95 that is a multiple of 3, 8, and 12. Write all the numbers that she could choose. If there is more than one number, seperate them with commas.
Answers
Answer:
72
Explanation:
To choose a number between 49 and 95 that is a multiple of 3, 8, and 12, the first step is to find the lowest common multiple of the three numbers.
Begin by expressing them as a product of their prime factors:
[tex]\begin{gathered} 3=3 \\ 8=2^3 \\ 12=2^2\times3 \\ \text{LCM}=2^3\times3=24 \end{gathered}[/tex]Next, we find multiples of the L.C.M in between 49 and 95.
[tex]\begin{gathered} 24\times2=48 \\ 24\times3=72 \\ 24\times4=96 \end{gathered}[/tex]The only number that she could choose is 72.
I need help on number 14!!! Please help and justify your answer!! PLEASE
Answers
as the rate of company B is greater, the company B will reach the top first
Explanationto solve this we can find the rate of each company and then compare
let
[tex]rate=\frac{finished\text{ length of construction}}{time\text{ taken}}[/tex]so
Step 1
convert the mixed number into fractions
remember how
[tex]a\frac{b}{c}=\frac{(a*c)+b}{c}[/tex]so
[tex]\begin{gathered} 5\text{ }\frac{1}{2}=\frac{(5*2)+1}{2}=\frac{11}{2} \\ 3\text{ }\frac{1}{2}=\frac{(3*2)+1}{2}=\frac{7}{2} \end{gathered}[/tex]Step 2
Find the rate of each company
A) Company A
replace
[tex]\begin{gathered} rate=\frac{finished\text{ length of construction}}{time\text{ taken}} \\ rate_A=\frac{550}{\frac{11}{2}}=\frac{1100}{11}=100\text{ ft per month} \end{gathered}[/tex]B) Company B
[tex]\begin{gathered} rate=\frac{finished\text{ length of construction}}{time\text{ taken}} \\ rate_B=\frac{385}{\frac{7}{2}}=\frac{770}{7}=110\text{ ft per month} \end{gathered}[/tex]Step 3
finally, compare
[tex]\begin{gathered} 110\text{ ft per month }>100\text{ ft per month} \\ hence \\ rate_B>rate_A \end{gathered}[/tex]as the rate of company B is greater, the company B will reach the top first
How much would you need to deposit in an account now in order to have $5000 in the account in 15years? Assume the account earns 8% interest compounded monthly.$
Answers
A(t) = amount in t years
P = Principal (original investment)
r = annual interest rate (in decimal form)
n = number of times that interest is compounded each year
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Substitute in the given values:
[tex]5000=P(1+\frac{0.08}{12})^{12\times15}[/tex][tex]5000=P(1.0067)^{180^{}}[/tex][tex]5000=P\times3.307[/tex][tex]P=1511.94[/tex]Hence the amount need to deposit is 1511.94 dollar.
find the Medina number of campsites.9,11,12,15,17,18
Answers
To find the median of the composite numbers, we will first have to sort the numbers
We will arrange from least to greatest.
By doing so, we will obtain
[tex]9,11,12,15,17,\text{ and 18}[/tex]Next, we will find the middle number of the set.
The median will be the average of the two numbers
[tex]\frac{12+15}{2}=\frac{27}{2}=13.5[/tex]The median of the numbers is 13.5
a recipe call for 3/4 cup of olive oil for every 1/2 cup of vinegar. how much vinigar is needed for 2 cups of olive oil? how do I solve this step by step?
Answers
The amount of vinegar needed is 1 (1/3) cups
What is Unitary method
Unitary method is a method of finding the value of 1 unit by using the value of multiple units or by the given quantity So that we can find the value of a given unknown quantity.
Here we have
A recipe requires 3/4 cup of olive oil for every 1/2 cup of vinegar
The amount of olive oil = 2 cups
Which means 3/4 cup of olive oil requires 1/2 cup of vinegar
then the vinegar required for 1 cup of Olive oil
= (vinegar Qty ÷ olive oil Qty) × 1 cup
= (1/2) ÷ (3/4) × 1
= 1/2 / 3/4 = 2/3
Therefore,
1 cup of olive oil requires 2/3 rd cup of vinegar
Then the amount of vinegar is needed for 2 cups of olive oil
= 2 × [ the amount of vinegar required for 1 cup of olive oil ]
= 2 × (2/3) = 4/3 = 1(⅓)
The amount of vinegar needed is 1 (1/3) cups
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7^2 × 7^8. 7^a------------ = -------- = 7^b7^4 7^4
Answers
We have to find the values of a and b:
[tex]\frac{7^2\cdot7^8}{7^4}=\frac{7^a}{7^4}=7^b[/tex]We can use the laws of exponents to write:
[tex]\begin{gathered} 7^2\cdot7^8=7^a \\ 7^{2+8}=7^a \\ 7^{10}=7^a \\ 10=a \end{gathered}[/tex]Then, we can solve for b as:
[tex]\begin{gathered} \frac{7^a}{7^4}=7^b \\ 7^{a-4}=7^b \\ a-4=b \\ 10-4=b \\ 6=b \end{gathered}[/tex]Answer: a=10 and b=6
Leila wrote an equation to represent the revenue of a parking lot for one day. She let x represent the number of cars that paid to park and y represent the number of trucks that paid to park. If a car costs $8 per day, a truck costs $10 per day, and the total revenue for the day was $830, which equation could Leila use to represent the number of cars and trucks that paid to park that day?
8 x + 10 y = 1,660
10 x + 8 y = 1,660
8 x + 10 y = 830
Answers
The equation that Leila can use to represent the number of cars and trucks that paid to park that day is C. 8 x + 10 y = 830
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario
Let x represent the number of cars that paid to park.
Let y represent the number of trucks that paid to park.
Therefore, the equation will be:
= (8 × x) + (10 × y) = 830
8x + 10y = 830
In conclusion, the correct option is C.
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Maria made 97% of her penalty kicks in soccer. Her teammates' percentages were uniformly distributed between 65% and 80%.Select all the statements that must be true?O A The mean would decrease by omitting Maria's score.B. The median would decrease by omitting Maria's score.O c The range would decrease by omitting Maria's score.D. The interquartile range would decrease by omitting Maria's score.E The standard deviation would decrease by omitting Maria's score,
Answers
Let's evaluate each statement to check wheter they are true or not.
A. "The mean would decrease by omitting Maria's score".
The mean is the sum of all the scores divided by the number of attempts. Since Maria had a higher score, if we omitted it then the sum would decrease and by extension the mean would decrease as well.
This option is true.
B. The median would decrease by omitting Maria's score.
The median is the value on the middle of the series, if we omit Maria's score, which was one of the highest then the middle of the series should move to the left, decreasing it.
This option is true.
C. The range would decrease by omitting Maria's score.
The range of a function are the values that said function can have as an output. If we omit Maria's score then the output of the function would be only the values scored by their team mates, which would go from 65 to 80, instead of 65 to 97. Therefore the range would decrease.
This option is true.
D. The interquartile range would decrease by omitting Maria's score.
The interquartile range are the values between the 25% values of the series and the 75% values of the series. Since Maria is the highest score between her teammates, she is not considered into the IQR and the value wouldn't change by removing her score.
This option is false.
E. The standard deviation would decrease by omitting Maria's score.
The standard deviation is the mean amount of variation in a series, since all her teammates are in the range of 65% to 80% and Maria is way above on the 97% score, by taking her score out we decrease the standard deviation, because there will be less variation in the serie.
This option is true.
A growing number of thieves are using keylogging programs to steal passwords and other personal information from Internet users. The number of keyloggingprograms reported grew approximately exponentially from 0.3 thousand programs in 2001 to 11.0 thousand programs in 2008. Predict the number of keyloggingprograms that will be reported in 2013
Answers
Exponential growth (EG):
2001 = 0.3
2008 = 11
2013 = ?
[tex]n\text{ = }a\times b^t[/tex]a = initial amount = 0.3
b= growth factor = ?
t = period = 7
n = 11
[tex]\begin{gathered} 11=0.3\times b^7 \\ b^7=\frac{11}{0.3} \\ b\text{ = }\sqrt[7]{\frac{11}{0.3}} \\ b=1.67 \end{gathered}[/tex]b = 1.67
Solving the number of keylogging programs that will be reported in 2013:
[tex]\begin{gathered} n\text{ = }0.3\times1.67^{12} \\ n=144.12 \end{gathered}[/tex]Subtract 9 1/4 - 4 3/4 . Simplify the answer and write as a mixed number.
Answers
Upon subtracting 9 1/4 from 4 3/4 we get 18/4.
Given
9 1/4 - 4 3/4
solution:
[tex]9\frac{1}{4}[/tex] can be written as 37/4 ( 9 * 4 + 1 thus 37/4) and
[tex]4\frac{3}{4}[/tex] can be written as 19/4 ( 4 * 4 + 3 thus 19/4)
37/4 - 19/4 as 4 is the common denominator for both the fractions so take 4 as the denominator
[tex]= \frac{37-19}{4}[/tex] = 18/4 if we further simplify 18/4 = 4.5
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A person randomly selects one of four envelopes. Each envelope contains a check that the person gets to keep. However, before the person can select an envelope, he or she must pay $ 15 to play. Determine the person's expectation if two of the envelopes contain $ 5 checks and two of the envelopes contain $ 35 checks.
Answers
The person's expectation if two of the envelopes contain $ 5 checks and two of the envelopes contain $ 35 checks is $5.
In the given question,
A person randomly selects one of four envelopes.
Each envelope contains a check that the person gets to keep.
However, before the person can select an envelope, he or she must pay $15 to play.
We have to determine the person's expectation if two of the envelopes contain $5 checks and two of the envelopes contain $35 checks.
As we know that when the person have to select envelope then they have to pay $15.
Total number of envelop = 4
From the 4 envelop 2 have $5 each and 2 have $35 each.
So the probability of getting envelop of $5 = 2/4 = 1/2
Probability of getting envelop of $35 = 2/4 = 1/2
Let x be the amount a person gets after selecting the envelop.
So E(x) = $5×1/2 + $35×1/2
Taking 1/2 common on both side
E(x) = 1/2 ($5+$35)
E(x) = 1/2×$40
E(x) = $20
But he have to pay $15 before selecting the envelop.
So required expectation = $20−$15 = $5
Hence, the person's expectation if two of the envelopes contain $ 5 checks and two of the envelopes contain $ 35 checks is $5.
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A card is drawn from a standard deck of fifty-two cards. What is the probability of selecting Jack or a red card?
Answers
Solution
Step 1:
In a pack or deck of 52 playing cards, they are divided into 4 suits of 13 cards each i.e. spades ♠ hearts ♥, diamonds ♦, clubs ♣. Cards of Spades and clubs are black cards. Cards of hearts and diamonds are red cards. The card in each suit, are ace, king, queen, jack , 10, 9, 8, 7, 6, 5, 4, 3 and 2.
Step 2:
Total possible outcomes = 52
Total number of jacks = 4
Total number of red cards = 26
Step 3:
The probability of selecting Jack or a red card
[tex]\begin{gathered} \text{Probability of any event = }\frac{n\text{umber of required outcomes}}{n\text{umber of possible outcomes}} \\ =\text{ }\frac{4}{52}\text{ + }\frac{26}{52} \\ =\text{ }\frac{30}{52} \\ =\text{ }\frac{15}{26} \end{gathered}[/tex]Final answer
[tex]\frac{15}{26}[/tex]Expand the following using the suitable identity.(-x + 2y - 3z)^2
Answers
Given the expression (-x + 2y - 3z)², we are to expand it using a suitable identity.
Using the square of the sum of trinomial identity expressed as:
[tex](a+b+c)^2=a^2+b^2+c^2+2\text{ab+2ac+2bc}[/tex]From the given expression;
[tex]\begin{gathered} a=-x \\ b=2y \\ c=-3z \end{gathered}[/tex]Substitute the parameters into the identity to expand as shown:
[tex](-x+2y-3z)^2=(-x)^2+(2y)^2+(-3z)^2+2(-x)(2y)+2(-x)(-3z)_{}+2(2y)(-3z)[/tex]
Simplify the result to have:
[tex](-x+2y-3z)^2=x^2+4y^2+9z^2-4xy+6xz_{}-12yz[/tex]This gives the correct expansion using a suitable identity