Round off 37.005 to the nearest 1sf,2dp,3dp,1dp,2sf
Answers
Answer:
37.005 to:
1sf: 40
2dp: 37.01
3dp: 37.005
1dp: 37
2sf: 37
Related Questions
State the order and type of each transformation of the graph of the function f(X)=4(X+9)^2 as compared to the graph of the base function
Answers
Using translation concepts, the function f(x) was evaluated by comparing to the graph of a base function g(x) = x².
stretched vertically by a factor of fourShifted 9 units to the left.What exactly is a translation?In mathematics, a translation is the movement of a shape to the left or right and/or down or up. The translated shapes appear to be the same size as that of the original shape, and thus the shapes are congruent. They were simply shifted in one or even more directions. There's no change in shape because it is simply moved from one location to another.A translation is signified by a change with in function graph, based on operations in its definition including such multiplication or sum/subtraction.
The base function g(x) = x² in this problem was.Multiplied by 4, such that, stretched vertically by a factor of four.Shifted 9 units to the left.Thus, the resultant function is obtained as (X)=4(X+9)²
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Q1] A hockey team plays 15 matches. Below is a list of the numbers of goals scored in these matches. 1, 0, 2, 4, 0, 1, 1, 1, 2, 5, 3, 0, 1, 2, 2. Find mean median mode and range.
Answers
Answer:
The mean is the average number from the group of numbers.
In this case, the average of the numbers 2, 4, 0, 3, 4, 1, 3, 1, 1, 5 is 2.4.
This is discovered by adding all the numbers together (which in this case is 24) and dividing that number by the amount of numbers in the group (in this case it's 10).
24 ÷ 10 = 2.4
Therefore the mean is 2.4.
(02.03 MC) Triangle DOG was rotated to create triangle D'O'G''. Describe the transformation using details and degrees. (10 points) Triangles DOG and D prime, O prime, and G prime are shown. D is at negative 2, 1. O is at negative 3, 3. G is at 1, 1. D prime
Answers
Answer and Step-by-step explanation: Rotation is a "movement" of a geometric figure in order to transform one in another. In rotation, the shape and size of the figure is the same, so they are congruent.
A geometric figure can be rotated clockwise or counterclockwise and by different angles.
One way to recognized the angle of rotation is comparing the points of the figure and its rotated image.
On the figure below, triangle DOG has coordinates:
D (-2,1)
O (-3,3)
G (1,1)
And its image:
D' (2,-1)
O' (3,-3)
G' (-1,-1)
Comparing both set of coordinates, we observe:
D (-2,1) → D' (2,-1)
O (-3,3) → O' (3,-3)
G (1,1) → G' (-1,-1)
that the coordinates for ΔDOG and ΔD'O'G' are opposite to each other, i.e.:
(x, y) → (-x,-y)
rotating counterclockwise.
Since coordinates are opposite and rotation is counterclockwise, ΔD'O'G' is rotated by 180° related to ΔDOG.
Which statements are correct? Check all that apply.?
The rate of change is 4.
The rate of change is 1.
The rate of change is 4/1.
The plant grows 4 cm in 1 week.
The plant grows 1 cm in 4 weeks.
Answers
Answer:
A C D
Step-by-step explanation:
Answer:
Step-by-step explanation:
it's A,C,D
What is the value of x?
Enter your answer in the box.
X=l_l
Answers
9514 1404 393
Answer:
x = 62
Step-by-step explanation:
The angle marked x° is shown as the complement of the angle marked 28°. This means ...
x = 90 -28 = 62
find the line of best fit for the set of data
Answers
The line of best fit for the set of data in this problem is given as follows:
y = 0.613x + 4.142.
How to find the equation of linear regression?To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) of the data-set in the calculator.
The points for this problem are given as follows:
(-2, 2.9), (-3.5, 2), (1.4, 4.8), (-4.2, 1.5), (0,4), (2.8, 6), (-1.5, 3.5).
Inserting these points into a calculator, the line of best fit is given as follows:
y = 0.613x + 4.142.
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What equation represents this sentence? 42 is the quotient of a number and 6.
Answers
Answer:
42= x/6
Step-by-step explanation:
Quotient means the answer of a division problem
sense we don’t know the ”number” in this situation it will be seen as a variable or x
x / 6 = 42
to find x we just do 42/6 to get 7
x=7
If these cylinders and prisms were broken into two separate groups, what would be an equivalent ratio to 8/2? i dont have much longer and btw it doesn't have a picture.
100 points?
Answers
The Equivalent ratio to 8/2 is 4/1, 24/6, 32/8 and 48/12.
We have,
Cylinder and prism.
Here we have to find the equivalent ratio to 8/2.
First simplifying the given ratio as
8/2
= (4 x 2)/2
= 4 /1
Now, some more ratios equivalent to 8/2.
1. 8/2 x 3/3 = 24/ 6
2. 8/2 x 4/4 = 32/8
3. 8/2 x 6/6= 48/12
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Can anyone help please?
Answers
The side w of the rectangle is 2.5 cm.
How to find the side of a 2 dimensional figure?The triangle and the rectangle have the same area.
Therefore,
area of a triangle = 1 / 2 bh
where
b = base of the triangleh = height of the triangleb = 5 cm
h = 6 cm
area of a triangle = 1 / 2 × 5 × 6
area of a triangle = 30 / 2
area of a triangle = 15 cm²
Therefore,
area of a rectangle = lw
where
l = lengthw = widthHence,
15 = 6w
w = 15 / 6
w = 5 / 2
w = 2.5 cm
Therefore, the side w is 2.5 cm.
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Together two ferries can transport a day's cargo in 7 hours. The larger ferry can transport cargo three times faster than the smaller ferry. How long does it take the larger ferry to transport a day's cargo working alone?
Answers
Answer:
9 hours, 20 minutes
Step-by-step explanation:
When two ferries work together, they transport a day's cargo in 7 hours
The speed proportion or ratio of larger ferry to smaller ferry is given as 3 : 1
The sum of the ratio = 4 (3 + 1)
This means that it will take the smaller ferry = 7 x 4 hours to work alone = 28 hours, since the larger ferry is faster by 3.
Therefore, when larger ferry works alone, it will take it (7 x 4)/3 = 9.33 hours.
9.33 hours = 9 hours, 20 minutes.
Please help its urgent!
Answers
Applying the midsegment theorem:
a. x = 17; y = 2
b. Length of DF is: 20 units.
How to Apply the Midsegment Theorem?According to the midsegment theorem:
Length of GH = half the length of EF
Given the following:
GH = x - 3EF = 28GH = 1/2(EF)
Substitute:
x - 3 = 1/2(28)
x - 3 = 14
x - 3 + 3 = 14 + 3
x = 17
DH = HF
DH = y + 8
HF = x - 7
Therefore:
y + 8 = x - 7
Plug in the value of x
y + 8 = 17 - 7
y + 8 = 10
y = 10 - 8
y = 2
Length of DF = y + 8 + x - 7
Plug in the values of x and y:
Length of DF = 2 + 8 + 17 - 7
Length of DF = 20 units.
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In a bank, 20 customers on the average, are served by a cashier in an hour. If
the service time has exponential distribution, what is the probability that;
(i) It will take more than 10 minutes to serve a customer?
(ii) A customer shall be free within 4 minutes
Answers
(i) The probability that it will take more than 10 minutes to serve a customer is approximately 0.1353.
(ii) The probability that a customer shall be free within 4 minutes is approximately 0.4866.
To solve this problem, we can use the exponential distribution formula. The exponential distribution is often used to model the time between events occurring at a constant average rate. In this case, we want to find the probability of specific service times.
Let's denote λ as the average number of customers served per hour. Given that 20 customers are served on average, we can determine λ by dividing the average number of customers by the time taken to serve them, which is 1 hour. Therefore, λ = 20 customers/hour.
Now, we can calculate the probability using the exponential distribution formula:
(i) To find the probability that it will take more than 10 minutes to serve a customer, we need to convert 10 minutes to hours, which is 10/60 = 1/6 hour. Let's call this value x.
The probability can be calculated as P(X > x) = 1 - P(X ≤ x), where X follows an exponential distribution with rate parameter λ.
P(X > 1/6) = 1 - P(X ≤ 1/6)
= 1 - (1 - \(e^{(-\lambda x))\) [Using the cumulative distribution function (CDF) of the exponential distribution]
= \(e^(- \lambda x)\)
= \(e^{(-20/6)\)
≈ 0.1353
(ii) To find the probability that a customer shall be free within 4 minutes, we convert 4 minutes to hours, which is 4/60 = 1/15 hour. Let's call this value y.
The probability can be calculated as P(X ≤ y), where X follows an exponential distribution with rate parameter λ.
P(X ≤ 1/15) = 1 - \(e^{(-\lambda y)\)
= 1 - \(e^{(-20/15)\)
≈ 0.4866
Therefore, the probability that a customer shall be free within 4 minutes is approximately 0.4866.
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A short order cook can prepare 40hamburgers in 30 minutes
Answers
Answer:1.33333333333 hamburgers every minute
Step-by-step explanation:40 burgers ÷ 30minutes = 1.333333 burgers every minute
Solve the following system of equations using an inverse matrix. You must alsoindicate the inverse matrix, A-1, that was used to solve the system. You mayoptionally write the inverse matrix with a scalar coefficient.X-9y = -4- 3+7y = 579A-112y =1
Answers
The given system of equations is,
\(\begin{gathered} x-9y=-4 \\ -x+7y=5 \end{gathered}\)A system of equations can be defined as,
\(AX=B\text{ ------(1)}\)Here, A is the ceofficient matrix, X is the variable matrix and B is the constant matrix.
Coefficient matrix gives the coefficients of the variables in the system of equations. Hence,
\(A=\begin{bmatrix}{1} & {-9} & {} \\ {-1} & {7} & {} \\ {} & {} & {}\end{bmatrix}\)Hence, equation (1) can be written as,
\(\begin{bmatrix}{1} & {-9} & {} \\ {-1} & {7} & {} \\ {} & {} & {}\end{bmatrix}\begin{bmatrix}{x} & {} & {} \\ {y} & {} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{-4} & & {} \\ {5} & & {} \\ {} & {} & {}\end{bmatrix}\text{ -------(2)}\)If a 2x2 matrix A is given by,
\(A=\begin{bmatrix}{a} & {b} & {} \\ {c} & {d} & \\ {} & {} & {}\end{bmatrix}\)Then, adj A is, Hence, the adjoint of the given matrix A is,
\(adjA=\begin{bmatrix}{d} & {-b} & {} \\ {-c} & {a} & \\ {} & {} & {}\end{bmatrix}\)The determinat of A is,
\(|A|=ad-bc\)Hence, the inverse of the given matrix A is,
\(\begin{gathered} A^{-1}=\frac{1}{|A|}adj\text{ A} \\ =\frac{1}{7\times1-(-9\times(-1))}\begin{bmatrix}{7} & {9} & {} \\ {1} & {1} & {} \\ {} & {} & {}\end{bmatrix} \\ =\frac{1}{7-9}\begin{bmatrix}{7} & {9} & {} \\ {1} & {1} & {} \\ {} & {} & {}\end{bmatrix} \\ =\frac{1}{-2}\begin{bmatrix}{7} & {9} & {} \\ {1} & {1} & {} \\ {} & {} & {}\end{bmatrix} \end{gathered}\)
Now, multiply equation (1) by inverse of A to solve for the variable matrix.
\(\begin{gathered} A^{-1}AX=A^{-1}B \\ IX=A^{-1}B \\ \begin{bmatrix}{1} & {0} & {} \\ {0} & {1} & {} \\ {} & {} & {}\end{bmatrix}\begin{bmatrix}{x} & {} & {} \\ {y} & {} & {} \\ {} & {} & {}\end{bmatrix}=\frac{1}{-2}\begin{bmatrix}{7} & {9} & {} \\ {1} & {1} & {} \\ {} & {} & {}\end{bmatrix}\begin{bmatrix}{-4} & & {} \\ {5} & & {} \\ {} & {} & {}\end{bmatrix} \\ \begin{bmatrix}{x} & {} & {} \\ {y} & {} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{\frac{-7}{2}} & {\frac{-9}{2}} & {} \\ {\frac{-1}{2}} & {\frac{-1}{2}} & {} \\ {} & {} & {}\end{bmatrix}\begin{bmatrix}{-4} & & {} \\ {5} & & {} \\ {} & {} & {}\end{bmatrix} \\ \begin{bmatrix}{x} & {} & {} \\ {y} & {} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{\frac{-7}{2}\times(-4)+(\frac{-9}{2}\times5)} & & {} \\ {\frac{-1}{2}\times(-4)+(\frac{-1}{2}\times5} & {} & {} \\ {} & {} & {}\end{bmatrix} \\ \begin{bmatrix}{x} & & {} \\ {y} & & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{14-\frac{45}{2}} & & {} \\ {2-\frac{5}{2}} & & {} \\ {} & {} & {}\end{bmatrix} \\ \begin{bmatrix}{x} & {} & {} \\ {y} & {} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{\frac{-17}{2}} & & {} \\ {\frac{-1}{2}} & & {} \\ {} & {} & {}\end{bmatrix} \end{gathered}\)Here, I is identity matrix.
Therefore, the inverse of matrix A is,
\(A^{-1}=\frac{-1}{2}\begin{bmatrix}{7} & {9} & {} \\ {1} & {1} & {} \\ {} & {} & {}\end{bmatrix}\)x=-17/2 and y=-1/2.
What is 80.89 divided by 8.425?
Answers
Answer:
9.60 or 9.601 if you want the hundreths place
Step-by-step explanation:
Answer:
\(80.89 \div 8.425 = 9.60 \\ \\ or \\ \\ = \frac{80.89}{8.425} \\ \\ = 9.60\)
PLEASE HELP!! a bag contains 10 marbles. four of them are red, three blue, two white, and one yellow. A mare ke drawn at random. What is the probability that it is blue?
Answers
Answer:
The probability that one marble drawn at random is not blue is 70%
Shoppers in two states are asked whether their shopping decisions are made impulsively or after careful consideration. Forty randomly selected shoppers in state A and thirty-six randomly selected shoppers in state B are questioned Shopping Habit State Conscientious ImpulseA 24 16 B 30 6(a) Test at the 5% level whether shoppers in the two states differ with regards to shopping habits. State all assumptions. (b) Find the p-value.
Answers
The chi-square test is 5.02 higher than critical value 3.841 so the two states does not differ with regards of shopping habits, and p value is 0.025.
How to calculate test statistic?O = observed value
E = expected value
n = size of sample = 2
df = degree of freedom = n - 1 = 2 - 1
α = significance level = 5% = 0.05
Chi-square is a one of many test statistic, chi-square is a test to see the different from observed value and expected value.
Chi-square formula is,
\(\chi^2\) = \(\sum\frac{(O_i - E_i)^2}{E_i}\)
Since, in question only give us the observed value, we need to calculate the expected value first.
Expected value conscientious state A can be calculate by this formula
E(ca) = total of state A value × total of conscientious value ÷ grand total
Repeat this process to all observed value.
We use excel to simplified and for precise calculation. Then, we put the obtained value from excel formula to Chi-square formula,
\(\chi^2\) = 0.69 + 1.69 + 0.76 + 1.88
= 5.02
a) Critical value for df = 1 and α = 0.05 from chi-square table is 3.841
Since, the result is 5.02 higher than 3.841, it can be concluded that the two states does not differ with regards of shopping habits.
Assumptions for we use is the study group is independent and the each expected value is higher than 5.
b) We use chi-square p-value calculator with P(\(\chi^2\) > 5.02) and df = 1, α = 0.05. So, we get 0.025.
Thus, two states doesn't differ with regards of shopping habits since chi-square result is higher than critical value, and p value is 0.025.
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brainliest help fast plz
Answers
Answer:
\(\frac{5}{16}\)
Step-by-step explanation:
\(\frac{1}{2}-\frac{3}{16}=\frac{8}{16}-\frac{3}{16}=\boxed{\frac{5}{16}}\)
Answer:
hope this helps
Step-by-step explanation:
the answer is 5/16
Stephanie has a spinner with sections labelled 1, 2 and 3.
She spun it 100 times and recorded how many times it landed on each section in
the table below.
Work out the relative frequency of landing on an odd number, giving your answer
as
a) a fraction in its simplest form.
b) a decimal.
Section
1
Frequency 17
2
20
3
63
Answers
Answer:
\(\frac{4}{5}\)
0.8
Step-by-step explanation:
Happy to help:)
Twenty-seven minus 3/2 of a number (x) os not mpre than 36. What is the number?
Answers
Answer:
-6
Step-by-step explanation:
27-3/2x=36
53-3x=72
3x=-18
x=-6
Part E
1e. Subtract the binomial 12y2 – 4y3 from the trinomial 7y - 2y3 + 5y2
Answers
Answer:
2y^3-7y^2+7y
Step-by-step explanation:
7y - 2y^3 + 5y^2 - ( 12y^2 – 4y^3)
Distribute the minus sign
7y - 2y^3 + 5y^2 - 12y^2 + 4y^3
Combine like terms
2y^3-7y^2+7y
PLEASE HELP ME OUT CCCCCCCCCCCCCCCCCC;
Answers
Answer:
I think it's the last to they sound way more independent!!!
Is 319,292 divisible by 4?
Answers
Answer:
Yes
Step-by-step explanation:
When you divide it, it has no remainder.
Hope this helps
Answer:
yes it is as when you divide it it has no remainder
The following transactions were completed by Winklevoss Inc., whose fiscal year is the calendar year:
Year 1
July 1 Issued $71,900,000 of 20-year, 6% callable bonds dated July 1, Year 1, at a market (effective) rate of 7%, receiving cash of $64,222,669. Interest is payable semiannually on December 31 and June 30.
Oct. 1 Borrowed $420,000 by issuing a six-year, 5% installment note to Nicks Bank. The note requires annual payments of $82,747, with the first payment occurring on September 30, Year 2.
Dec. 31 Accrued $5,250 of interest on the installment note. The interest is payable on the date of the next installment note payment.
31 Paid the semiannual interest on the bonds. The bond discount amortization of $191,933 is combined with the semiannual interest payment.
Year 2
June 30 Paid the semiannual interest on the bonds. The bond discount amortization of $191,933 is combined with the semiannual interest payment.
Sept. 30 Paid the annual payment on the note, which consisted of interest of $21,000 and principal of $61,747.
Dec. 31 Accrued $4,478 of interest on the installment note. The interest is payable on the date of the next installment note payment.
31 Paid the semiannual interest on the bonds. The bond discount amortization of $191,933 is combined with the semiannual interest payment.
Year 3
June 30 Recorded the redemption of the bonds, which were called at 98. The balance in the bond discount account is $6,909,599 after payment of interest and amortization of discount have been recorded. Record the redemption only.
Sept. 30 Paid the second annual payment on the note, which consisted of interest of $17,913 and principal of $64,834.
Required:
1. Journalize the entries to record the foregoing transactions. Round all amounts to the nearest dollar. Refer to the Chart of Accounts for exact wording of account titles.
2. Indicate the amount of the interest expense in (a) Year 1 and (b) Year 2.
3. Determine the carrying amount of the bonds as of December 31, Year 2.
Answers
1. The journal entries recording the transactions for Winkelvoss Inc. are as follows:
Journal Entries:Year 1:
July 1: Debit Cash $64,222,669
Debit Bonds Discount $7,677,331
Credit Bonds Payable $71,900,000
Oct. 1: Debit Cash $420,000
Credit Bank Notes Payable $420,000
Dec. 31 Debit Interest Expense $5,250
Credit Installment Note Interest Payable $5,250
Dec. 31 Debit Interest Expense $2,708,433
Credit Cash $2,516,500
Credit Bond Amortization $191,933
Year 2:
June 30 Debit Interest Expense $2,516,500
Credit Cash $2,324,567
Credit Bond Amortization $191,933
Sept. 30 Debit Interest Expense $15,750
Debit Installment Note Interest Payable $5,250
Debit Notes Payable $61,747
Credit Cash $82,747
Dec. 31 Debit Interest Expense $4,478
Credit Installment Note Interest Payable $4,478
Dec. 31 Debit Interest Expense $2,708,433
Credit Cash $2,516,500
Credit Bond Amortization $191,933
Year 3:
June 30 Debit Bonds Payable $64,990,401
Debit Bond Redemption Premium $5,471,599
Credit Cash $70,462,000
Sept. 30 Debit Interest Expense $13,435
Debit Installment Note Interest Payable $4,478
Debit Notes Payable $64,834
Credit Cash $82,747
2. The amounts of the interest expense in Year 1 and Year 2 are as follows:
Year 1 Year 2
Total interest $2,713,683 $2,72,8661
3. The bond's carrying amount as of December 31, Year 2, is $64,798,468.
Transaction Analysis:Year 1:
July 1: Cash $64,222,669 Bonds Discount $7,677,331 Bonds Payable $71,900,000
Oct. 1: Cash $420,000 Bank Notes Payable $420,000
Dec. 31 Interest Expense $5,250 Installment Note Interest Payable $5,250
Dec. 31 Interest Expense $2,708,433 Cash $2,516,500 Bond Amortization $191,933
Year 2:
June 30 Interest Expense $2,516,500 Cash $2,324,567 Bond Amortization $191,933
Sept. 30 Interest Expense $15,750 Installment Note Interest Payable $5,250 Notes Payable $61,747 Cash $82,747
Dec. 31 Interest Expense $4,478 Installment Note Interest Payable $4,478
Dec. 31 Interest Expense $2,708,433 Cash $2,516,500 Bond Amortization $191,933
Year 3:
June 30: Bonds Payable $64,990,401 Bond Redemption Premium $5,471,599 Cash $70,462,000
Sept. 30 Interest Expense $13,435 Installment Note Interest Payable $4,478 Notes Payable $64,834 Cash $82,747
Interest Expenses:Year 1 Year 2
Bonds Payable $2,708,433 $2,708,433
Notes Payable $5,250 $15,750
Notes Payable $4,478
Total interest $2,713,683 $2,72,8661
Carrying amount of the bonds December 31, Year 2:July 1: $64,222,669
Dec. 31 Bond Amortization $191,933
June 30 Bond Amortization $191,933
Dec. 31 Bond Amortization $191,933
Dec. 31 Year 2 Carrying Amont = $64,798,468
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which law would you use
Answers
This graph represents the relationship between the x and y.
What is an equation showing the relationship between x and y?
Enter your answer in the box.
PLEASE ASAP!!! MARKING BRAINLIEST!! FIRST ANSWER!!
Answers
Answer:
Therefore, x is 1 and 2.
Step-by-step explanation:
As you plot both equations on the same graph, you will get something like this, shown in the graph.
Then, you have to find the x solutions where they intersect.
So, both equations intersect at x = 1 and 2.
A researcher compared the heights and shoe sizes for 50 men, selected at random. The equation shown describes a line of best fit for the data, where x is the shoe size and y is the height, in inches. Based on the equation, what is the approximate shoe size for a man having a height of 60 inches
Answers
Answer:
7 1/2
Step-by-step explanation:
Convert 7 1/2 to a decimal then multiply it by 1.6 to get 12.00 then add 48 to get 60.
P.S i got it right
Find the Product.
5(cos pi/4 + i sin pi/4) x 3(cos 5pi/3 + i sin 5pi/3)
Answers
Answer:
D. 15(cos(23π/12) +i·sin(23π/12))
Step-by-step explanation:
You want the product 5(cos(π/4 +i·sin(π/4))×3(cos(5π/3) +i·sin(5π/3)).
Complex productThe product is ...
A·cis(a) × B·cis(b) = AB·cis(a+b)
where "cis(x)" means (cos(x) +i·sin(x))
Application5·cis(π/4) × 3·cis(5π/3) = (5·3)·cis(π(1/4+5/3)) = 15·cis(23π/12)
The product is 15·(cos(23π/12) +i·sin(23π/12)).
Please help need answers
Answers
\(\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\)
\(\frak{Good\;Morning!!}\)
\(\pmb{\tt{Question\;1}}\)
\(\star\boldsymbol{\rm{Given-:}}\)
Side length = 7 cm,Side length = 5 cm.\(\star\boldsymbol{\rm{We're\;looking\;for-:}}\)
Side length = xThis is how it's done.
\(\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\)
There's a special formula that we can use if we need to find the longest side of a right triangle. Fortunately, all of these triangles are right ones! Good.
The formula is. \(\boldsymbol{\rm{a^2+b^2=c^2}}\). This formula is known as Pythagoras' Theorem. This formula only works for right triangles.
Since we have a and b, we can just put in the values (7 for a and 5 for b), And then simplify!
\(\boldsymbol{\rm{7^2+5^2=c^2}}\) | 7^2 simplifies to 49, and 5^2 simplifies to 25
\(\boldsymbol{\rm{49+25=c^2}}\). | add
\(\boldsymbol{\rm{74=c^2}}\) | square root both sides
\(\boldsymbol{\rm{8.6=c}}}\). | the answer is given to 1 decimal place, as the problem required
\(\orange\hspace{350pt}\above5\)
\(\pmb{\tt{Question\;2}}\)
Once more, we're given two sides, and asked to find the third one,
which is still the longest side.
\(\boldsymbol{\rm{a^2+b^2=c^2}}\) is still the formula used here
Put in 5 for a and 3 for b.
\(\boldsymbol{\rm{5^2+3^2=c^2}}\) | 5^2 simplifies to 25, and 3^2 simplifies to 9
\(\boldsymbol{\rm{25+9=c^2}}\) | add
\(\boldsymbol{\rm{34=c^2}}\) | square root both sides
\(\boldsymbol{\rm 5.8=c}}\) | once again it's given to one decimal place
\(\hspace{350pt}\above5\)
\(\pmb{\tt{Question\;3}}\)
This problem is solved the exact same way
\(\boldsymbol{\rm{a^2+b^2=c^2}}\)
\(\boldsymbol{\rm{8.2^2+4.7^2=c^2}}\)
\(\boldsymbol{\rm{67.24+22.09=c^2}}\)
\(\boldsymbol{\rm{89.33=c^2}}\)
\(\boldsymbol{\rm{9.5=c}}\), rounded to one D.P.
\(\orange\hspace{300pt}\above2\)
\(\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\equiv\bullet\)
\(\pmb{\tt{Question4}}\)
Here we have the longest side and one side length-:
\(\boldsymbol{\rm{4^2+b^2=7^2}}\) | 4^2 simplifies to 16 and 7^2 simplifies to 49
\(\boldsymbol{\rm{16+b^2=49}}\) | subtract 16 from both sides
\(\boldsymbol{b^2=33}\) | square root both sides
\(\boldsymbol{\rm{b=5.7}}\)
\(\orange\hspace{300pt}\above3\)
\(\pmb{\tt{Question\;5}}\)
\(\boldsymbol{\rm{3.8^2+b^2=7.9^2}}\)
\(\boldsymbol{\rm{14.44+b^2=62.41}}\)
\(\boldsymbol{\rm{b^2=47.97}}\)
\(\boldsymbol{\rm{b=6.9}}\)
\(\orange\hspace{300pt}\above3\)
\(\pmb{\tt{Question\;6}}\)
\(\boldsymbol{\rm{a^2+6.1^2=7.3^2}}\)
\(\boldsymbol{\rm{a^2+37.21=53.29}}\)
\(\boldsymbol{\rm{a^2=16.08}}\)
\(\boldsymbol{\rm{a=4.0}}\)
\(\pmb{\tt{done~!!!}}\)
\(\orange\hspace{300pt}\above3\)
5. What number is 10 times as great as 6,546 ? *
Answers
Answer: 65460
Step-by-step explanation: I just used a calculator lol, bc in middle school they let u use themm