Answer:
the width of the rectangle is -5/3 inches.
Step-by-step explanation:
To find the perimeter of the rectangle, we add together the lengths of all four sides. Since the rectangle is 5 inches long and 2x inches wide, the perimeter is given by:
Perimeter = 5 + 2x + 5 + 2x = 10 + 4x
To find the area of the rectangle, we multiply the length by the width. The area is given by:
Area = 5 * 2x = 10x
Setting the perimeter equal to the area, we have:
10 + 4x = 10x
Subtracting 10 from both sides, we have:
4x = 10x - 10
Combining like terms, we have:
-6x = -10
Dividing both sides by -6, we have:
x = 10 / -6
Simplifying, we have:
x = -5/3
9. Bob Rowinski made a $4,000 deposit to a
savings account paying 1.6% annual interest
compounded semiannually. If he kept the money
on deposit for 6 months, what would his account
balance be after the interest payment is made?
The account balance of Bob Rowinski if he kept the money on deposit for 6 months is $4,032.00.
What is Bob Rowinski account balance the interest payment is made?The compound interest formula can be expressed as;
A = P(1 + r/n)^(n*t)
Where A is accrued amount, P is principal, r is interest rate, t is time elapsed.
Given the data in the question;
Principal P = $4,000Interest rate r = 1.6% = 1.6/100 = 0.016Compounded semi-annually n = 2Time t = 6 months = 0.5 yearAccrued amount A = ?Plug the given values into the above formula and solve for A.
A = P(1 + r/n)^(n*t)
A = $4000( 1 + 0.016/2 )^(2*0.5)
A = $4000( 1 + 0.008 )^(1)
A = $4000( 1.008 )
A = $4,032.00
Therefore, the accrued amount after half a year is $4,032.00
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It keeps saying I’m wrong
Answer:
translation of 2 squares left and 1 square down
Step-by-step explanation:
consider the top vertex of both figures
S → T
then shape T is a translation of shape S
by moving 2 squares to the left and 1 square down
2. Use the Pythagorean Theorem to solve for c.
5 feet
18 feet
The value of C using Pythagorean Theorem when a equal 5feet and b equals 18feet then, C = 18.68
Pythagorean theoremIn mathematics, the Pythagorean theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle and is written as a^2 + b^2 = C^2
Using the Pythagorean theorem a^2 + b^2 = C^2
from the question we are given 5 feet and 18feet respectively
to find c we substitute the value into the equation
a^2 + b^2 = C^2
a= 5feet and b= 18 feet
5^2 + 18^2 =C^2
25 + 324 = C^2
349 =C^2
Square root both side
C= [tex]\sqrt{349}[/tex]
C = 18.68
Therefore, C in the equation is C = 18.68
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Using Pythagoras theorem the value of c is 18.68 feet
Pythagoras TheoremPythagoras theorem or Pythagorean theorem is an important topic in Mathematics, which explains the relation between the sides of a right-angled triangle. The sides of the right triangle are also called Pythagorean triples.
The value of c can easily be calculated using Pythagoras theorem which is given as;
c² = 5² + 18²
where;
c = hypothenusec² = 25 + 324
c² = 349
c = √349
c = 18.68 feet
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CAN SOMEONE HELP WITH THIS QUESTION?✨
The equation of the transformed graph will be y = -3(2ˣ) + 2.
What is the transformation of a graph?Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.
If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).
Suppose the equation of the given graph is y = A 2ˣ + k.
Substitute,(0,-1)
-1 = A 2⁰ + k
A + k = -1 (1)
Substitute, (1,-4)
-4 = A 2¹ + k
2A + k = -4
A + k/2 = -2 (2)
Subtract 1 - 2 as
k - k/2 = -1 + 2
k/2 = 1
k = 2
And, A = -2 - 2/2
A = -3
Thus y = -3(2ˣ) + 2
Hence "The equation of the transformed graph will be y = -3(2ˣ) + 2 ".
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Suppose that $11,353 is invested at an interest rate of 5.7% per year, compounded continuously.
a) Find the exponential function that describes the amount in the account after time t, in years.
b) What is the balance after 1 year? 2 years? 5 years? 10 years?
c) What is the doubling time?
Answer:
Step-by-step explanation:
1)11357*(105.7/100)^t
2)1 year 12000.121 2 year 12684 5 year 14979.1 10 years 19763.3
3)11357*(105.7/100)^t=22714 so t+12.5
I need help with my home work
Answer:
Below
Step-by-step explanation:
If congruent then
x = y+5 and
x+3 = 3y <======sub in the first equation for 'x'
y+5 +3 = 3y
8 = 2y then y = 4 x = y+5 = 9
Question 1 One solution. 2x - 1 =_________x - 1
Answer:
2
Step-by-step explanation:
2x-1 = __x-1
Make both sides match to make the statement true.
2x-1 = 2x-1
Which fraction is equivalent to the given fraction model?
10/4
4/5
4/10
2/10
4/10 is the fraction that is equivalent to the given fraction model
What is an equivalent fraction ?
According to equivalent fractions, two or more fractions are considered to be equal if, following simplification, both provide the same fraction. Let's imagine that a/b and c/d are two fractions. If these fractions are simplified to produce comparable fractions, such as e/f, they are then equal to one another.
For instance, if we simplify 5/15, the resulting fraction is the same as 1/3, hence that is the equivalent fraction of 1/3.
The fractions with distinct numerators and denominators but the same value are said to be equivalent fractions. For instance, since 2/4 and 3/6 both equal the 12, they are identical fractions. An element of a whole is a fraction. The same amount of the whole is represented by equivalent fractions.
As in the given model 2 out of 5 blocks are in red color which means the equivalent fraction to the given model is 2/5 which is equal to 4/10
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Solve the equation without using a calculator
[tex]\bf\\\\log^2x+log^2(x+10)=log^211\\\\log(x+10)\neq 0[/tex]
[tex]\bf\\(\ lgx=log_{10}x=logx\ )[/tex]
The solution to the logarithmic expression log²x + log²(x + 10) = log²11 is;
x = -11 and 1
How to solve logarithm expressions?We are given the logarithmic expression as;
log²x + log²(x + 10) = log²11
By the power rule of logarithm, we know that; log²x = 2log x
Thus;
log²x + log²(x + 10) = log²11 can be expressed as;
2log x + 2log (x + 10) = 2log 11
Divide through by 2 to get;
log x + log (x + 10) = log 11
We know from product rule of logarithm that log (ab) = log a + log b. Thus; log x + log (x + 10) = log 11 is;
log x(x + 10) = log 11
Log cancels out to get;
x² + 10x - 11 = 0
Using quadratic equation calculator gives;
x = -11 and 1
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"Use the formula A=P(1+r/n)ⁿt to solve the compound interest problem
Find how long it takes for $ 900 to double if it is invested at 6 % interest compounded monthly.
The money will double in value in approximately years."
After 11.61 years the given principal amount of $ 900 will be double.
What is Compound interest?
Compound interest is interest charged on a loan and is determined by both the principal amount and the rate of interest compounding per year.
The formula for the Amount when compound interest is calculated is given by
Amount, A = P(1+r/n)^nt
P = Principal amount
r = Rate of interest
n = Number of compounds
t = Time period in years
Given:
Principal amount = $ 900
Rate of interest = 6% = 6/100 = 0.06
Number of compounds = 12 [ ∵ compounded monthly]
We need to find the time period
Assume that after 't' years the amount will be doubled
From the given data and formula,
Amount, A = 900(1+0.06/12)^12t
= 900(1+0.06/12)^12t
= 900(1 + 0.005)^12t
= 900 (1.005)^12t
As we assumed after 't' years the amount is double
=> 900 (1.005)^12t = 2 × 900
=> (1.005)^12t = 2
Applying log on both sides
=> log (1.005)^12t = log 2
=> 12t log(1.005) = log 2
=> 12t = log 2/log(1.005)
=> 12t = 0.30108/ 0.00216
=> 12t = 139.888
=> t = 11.61
Hence, after 11.61 years the given principal amount of $900 will be double.
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The rectangular floor of a classroom is 30 feet in length and 36 feet in width. A scale drawing of the floor has a length of 5 inches. What is the area, in square inches, of the floor in the scale drawing?
The scale drawing's representation of the rectangle floor's circumference is 68 inches.
What is unitary method ?Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.
Create a square on paper by using a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.
Imagine that your square is made up of smaller unit squares.
The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.
To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.
According to our question-
P = 2L + 2W
W = 5
P = 2L + 2(5) = 16
2L + 10 = 16
2L = 6
L = 3 ft
Hence, The scale drawing's representation of the rectangle floor's circumference is 68 inches.
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Which operations involving complex numbers have solutions represented by (-6, 7)? 2(1 − 2i) − (4 + 3i), 2(1 + 2i) + (-4 − 3i), 2(-1 + 2i) − (4 − 3i), (-2 + 4i) + (-4 + 3i) , (-2 − 4i) + (4 − 3i)
Option 3 and 4 are the operations involving complex numbers have solutions represented by (-6, 7).
What is a complex number ?Every complex number can be expressed in the form displaystyle a+bia + bi, where a and b are real numbers. A complex number is an element of a number system that extends the real numbers with a specific element denoted I also known as the imaginary unit, and satisfying the equation displaystyle i2=-1. René Descartes referred to me as an imaginary number since no actual number can satisfy the aforementioned equation. The real component of the complex number displaystyle a+bia+bi is referred to as a, and the imaginary part is referred to as b. The symbols C or displaystyle "mathbb "C" are used to represent the set of complex numbers.Complex numbers are crucial to many parts of the scientific explanation of the natural world, despite the historical appellation "imaginary," and are recognized in the mathematical sciences as just as "real" as real numbers.Find the attachment answer
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if 1+1+10 x 34 what is it
Answer:
408
Step-by-step explanation:
1+1+10 equals 12, then do 12 x 34, which equals 408
An area near a forest was monitored by researchers. The first graph shows the change in the amount of ground shade during a five-year period. The second graph shows how the population of milkweed changed over the same period.
Which hypothesis is supported by the data?
A. The milkweed population is a biotic factor that decreased as the amount of sunlight, an abiotic factor, decreased.
B. The milkweed population is an abiotic factor that decreased as the amount of sunlight, a biotic factor, decreased.
C. The milkweed population is a biotic factor that decreased as the amount of sunlight, an abiotic factor, increased.
D. The milkweed population is an abiotic factor that decreased as the amount of sunlight, a biotic factor, increased.
Option A is correct.
What is increasing and decreasing graphs?
Generally speaking, we are aware that if something is growing, it is moving upward, and if it is shrinking, it is moving downward. As a result, if we talk about a function's graph, an increasing function is one that is moving upward, and a decreasing function is one that is moving downward.
From the graph, we infer that the sunlight, that is the shaded area increased in the given time. Which means that the sunlight was less.
From the milkweed population graph, we see that the milkweed population decreased over time.
Hence the most supportive hypothesis would be option A.
The milkweed population is a biotic factor that decreased as the amount of sunlight, an abiotic factor, decreases.
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A data set lists the grade point averages of 10th grade students. Which of the following charts could be used to display the data, and why?
Circle graph; because the data is categorical
Circle graph; because the data is numerical
Box plot; because the data is categorical
Box plot; because the data is numerical
The chart that could be used to display the data is given as follows:
Box plot; because the data is numerical.
What are numerical and categorical data?A data-set can be classified as either numerical or categorical, depending on the values assumed by the data, as follows:
If the values assumed by the data are numbers, then the data-set is numeric.If the values assumed by the data are labels, then the data-set is categorical.The correct charts for each type of data are given as follows:
Numeric: box plot.Categorical: circle graph.The grade point average assumes numeric values, hence it is a numeric data and should be shown on a box plot, meaning that the last option is correct.
The box plot will show the number of grades in each range of the grade point averages, for example, how many grades between 0 and 1, how many between 1 and 2, and so on.
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If the functions are combined using addition, which statements describe the resulting graph h(x)? Check two options. domain: x ≥ –2 domain: x ≥ 2 The point (2, 2) is on h(x). The point (–2, 0) is on h(x). The point (0, –3) is on h(x).
Answer:
(25,-5)
Step-by-step explanation:
Write a rule for the translation of ABC to A’B’C’
Answer:
Below
Step-by-step explanation:
x,y => ( +4 , -3) because it is shifted 4 units to the right and down 3 units
Find the most general antiderivative of the function f(x) = 7 sin(x) - 4 sec(x) tan(x) on the interval
[tex]( - \frac{\pi}{2} \: \: \frac{\pi}{2} )[/tex]
The most general antiderivative of the function is -7cosx-4secx+C on the interval (-π/2,π/2) is not defined.
Given that,
We have a function f(x)=7sinx -4secx tanx.
We have to find the most general antiderivative of the function on the interval (-π/2, π/2).
We know that,
Take the function,
f(x)=7sinx -4secx tanx.
The antiderivative is
= [tex]\int {7sinx-4secxtanx} \, dx[/tex]
= [tex]7\int{sinx} \, dx -4\int {secxtanx} \, dx[/tex]
= 7(-cosx)-4[tex]\int {sinx/cos^{2}(x) } \, dx[/tex]
Take cosx =u
-sinxdx=du
= -7cosx-4[tex]\int {-1/u^{2} } \, du[/tex]
= -7cosx-4(1/u)+C
=-7cosx-4(1/cosx)+C ( since we know u=cosx)
= -7cosx-4secx+C
Now for the interval (-π/2,π/2)
= -7(cosπ/2-cos(-π/2))-4(secπ/2-sec(-π/2))+C
= -7(0-0)-4(∞-∞)+C
=not defined
Therefore, The most general antiderivative of the function is -7cosx-4secx+C on the interval (-π/2,π/2) is not defined.
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how much more would it cost a family of 5 to get the jets game ($105.66) than a Lions game ($79.19?
Answer:
The answer is 26.47.
Step-by-step explanation:
To get this answer, you simply need to subtract $105.66, by $79.19. You would get the answer of 26.47.
Step 1. [tex]$105.66 x 5 = 528.3[/tex]
Step 2. [tex]$79.19 x 5 = 395.95[/tex]
Step 3. [tex]528.3 - 395.95 = 132.35[/tex]
Thus, with all these steps it would cost $132.35 more to go to the jets game than to go to the lions game.
PLEASE HELP!!!!
Which graph is linear?
Answer:
the second
Step-by-step explanation:
the second is a linear graph
Answer:
The second Graph
Step-by-step explanation:
The question is asking what graph is linear.
The first graph is of an absolute value function which is not linear.
The second is of a line. This is linear.
The third looks to be either an exponential or a logarithmic function. Both of which are not linear.
Write the fractional values under each note. Verify that the sum of the fractions is 1 for each measure.
Answer:
1/8, 1/8, 1/4, 1/4, 1/16, 1/16, 1/16, 1/16 = 1
1/2, 1/2 = 1
Step-by-step explanation:
from left to right
is this music class or math class lol?
If Corey scored higher than the mean on his SAT, but Jerry scored lower than the mean on his SAT, how will both Z scores differ? Jerry's Z score will be positive, while Corey's Zscore will be negative Jerry's Z score will be negative, while Corey's Z score will be positive Both Jerry and Corey's Z scores will be positive Both Jerry and Corey's Z scores will be negative
Based on the provided information, Jerry's Z score will be negative, while Corey's Z score will be positive.
A Z-score refers to a numerical measurement that defines the raw value's relationship to the mean of a group of values. It is measured in terms of standard deviations from the mean. If a Z-score is 0, it means that the data point's score is identical to the mean score. A negative z-score indicates that the data point is below average or mean and a positive z-score indicates that the data point is above average or mean. Consider the formula for z score which is given by:
z = (x - µ)/σ where x is the given data value, µ is the mean, and σ is the standard deviation.
Hence, if the x < µ, the z score will be negative while if x > µ, the z score will be positive. As Corey scored higher than the mean on his SAT, his z score will be positive, and Jerry scored lower than the mean on his SAT, his z score will be negative.
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a) Work out the minimum number of hikers who could have walked between 6 miles and 17 miles.
b) Work out the maximum number of hikers who could have walked between 6 miles and 17 miles.
a) minimum of nine hikers might have covered the distance between 6 and 17 miles because it falls within the standard interval of 10 ≤ x ≤ 15.
b) The maximum no. of hikers who might have covered the distance between 6 and 17 miles is 19.
What do minimum and maximum value mean?
Rearrange the function using fundamental algebraic concepts to get the value of x when the derivative equals 0. This response gives the x-coordinate of the function's vertex, which is where the maximum or minimum will occur. To find the minimum or maximum, rewrite the solution into the original function.
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Construct a polynomial function with the following properties: fifth degree, 2 is a zero of multiplicity 4, −5 is the only other zero, leading coefficient is 4.
The required equation of the polynomial is p(x) = 4(x - 2 )⁵(x+5).
What is a polynomial?A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.
Given the following properties: fifth degree, 2 is a zero of multiplicity 4, −5 is the only other zero, and the leading coefficient is 4.
The general form of the polynomial will be written as,
p(x) = 4(x - 2 )⁵(x+5).
Therefore, the required equation of the polynomial is p(x) = 4(x - 2 )⁵(x+5).
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not sure why its saying 109 is wrong as its the max
The Class limit of the data is shown below.
What is Frequency?Frequency tables or charts are used to represent frequency distributions. Frequency distributions can display the proportion of observations or the actual number of observations that fall inside each range. The distribution is known as a relative frequency distribution in the latter case.
Given:
From the data the class limit will be
45 - 54
55 - 64
65 - 74
75 - 84
85 - 94
95 - 104
105 - 114
class Boundary
44.5 - 54.5
54.5 - 64.5
64.5 - 74.5
74.5 - 84.5
84.5 - 94.5
94.5 - 104.5
104.5 - 114.5
Midpoint
49.5
59.5
69.5
79.5
89.5
99.5
109.5
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( i only need number one and number 7 )
someone please i’m desperate i have so much work i need done by monday even if you only do one of them it is greatly appreciated
Answer:
1. x-intercept = (1, 0), y-intercept = (0, -2)
7. y + 4 = -6( x - 7)
Step-by-step explanation:
Question 1Given point-slope equation:
[tex]y-2=2(x-2)[/tex]
The x-intercept is when y = 0:
[tex]\begin{aligned}y=0\implies 0-2 &=2(x-2)\\-2&=2x-4\\2&=2x\\x&=1\end{aligned}[/tex]
The y-intercept is when x = 0:
[tex]\begin{aligned}x=0\implies y-2 &=2(0-2)\\y-2&=2(-2)\\y-2&=-4\\y&=-2\end{aligned}[/tex]
Therefore, the intercepts are:
x-intercept = (1, 0)y-intercept = (0, -2)To graph the equation, plot the intercepts and draw a straight line through them. (See attachment 1).
---------------------------------------------------------------------------------
Question 7[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]
Given:
m = -6(x₁, y₁) = (7, -4)Substitute the given slope and point (7, -4) into the formula to write the equation of the line in point-slope form:
[tex]\implies y-(-4)=-6(x-7)[/tex]
[tex]\implies y+4=-6(x-7)[/tex]
To graph the line, find the value of y when x = 6 and when x = 8:
[tex]\begin{aligned}x=6\implies y+4 &=-6(6-7)\\y+4 &=-6(-1)\\y+4&=6\\y&=2\end{aligned}[/tex]
[tex]\begin{aligned}x=8\implies y+4 &=-6(8-7)\\y+4 &=-6(1)\\y+4&=-6\\y&=-10\end{aligned}[/tex]
To graph the equation, plot the points (6, 2) and (8, -10) and draw a straight line through them. (See attachment 2).
----------------------------------------------------------------------------------------------
Please note that I have drawn the graphs using the same size 7x7 grids as shown in your question paper. If you wish to graph more of the line, please change the scale from those I have used.
what is 3/4 - 1/4ygkfmvkbkmbkvmmf
Answer:
1/2
Step-by-step explanation:
Find AE on the rhombus below when AD=4 x+2, DC=7 x-13 and BD=34 .
Note: Write your answer in simplest radical form. In the first blank put the number in front of the v. And in the second blank. put the number that is inside the . ** If there is no number in front of the v, enter a 1 in the blank **
The length AE of the rhombus is √195 units
How to determine the length AE of the rhombus?From the question, we have the following parameters that can be used in our computation:
AD = 4x + 2
DC = 7x - 13
BD = 34
All the four sides of a rhombus are congruent
This means that
DC = AD
Substitute the known values in the above equation, so, we have the following representation
7x - 13 = 4x + 2
Evaluate the like terms
3x = 15
Divide both sides by 3
x = 5
Substitute x = 5 in AD = 4x + 2
So, we have
AD = 4 x 5 + 2
AD = 22
The length AE of the rhombus is then calculated as
AE² = AD² - (BD/2)²
Substitute the known values in the above equation, so, we have the following representation
AE² = 22² - (34/2)²
Evaluate
AE² = 195
Take the square roots
AE = √195
Hence, the length is √195 units
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find the zeros f(x) = x 3 - 3x 2 – 5x +15
Answer:
x = ± [tex]\sqrt{5}[/tex] x = 3
Step-by-step explanation:
to find the zeros set f(x) = 0 , that is
x³ - 3x² - 5x + 15 = 0 ( factor the first/second and third/fourth terms )
x²(x - 3) - 5(x - 3) = 0 ← factor out (x - 3) from each term
(x - 3)(x² - 5) = 0
equate each factor to zero and solve for x
x - 3 = 0 ⇒ x = 3
x² - 5 = 0 ( add 5 to both sides )
x² = 5 ( take square root of both sides )
x = ± [tex]\sqrt{5}[/tex]
the zeros of f(x) are then
x = - [tex]\sqrt{5}[/tex] , x = [tex]\sqrt{5}[/tex] , x = 3
Three sides of a triangle have lengths 4, 5, and 6. The angle between the two sides 5 and 6 is nearest: a. 83° b. 56°C. 41° d. 32°
In the given triangle, the angle between the two sides 5 and 6 is nearest 41°.
The term triangle means the polygon which has three sides and three angles and three vertices,
Here we have given that three sides of a triangle have lengths 4, 5, and 6.
And here we need to find the angle between the two sides 5 and 6
According to the given values, let us consider a = 4, b = 5 and c = 6
So, the angle between 5 and 6 can be written as ∠b
And it can be calculated as the following is one way to perform the calculation and it may not be the best way.
∠B = arc cos(a² + c² - b²)/2ac
When we apply the values one the formula, then we get
=> 0.72273 rad
The approximate degree is written as
=> 41.41°
When we round off it then we get the resulting value,
=> 41°
Therefore, option (c) is correct.
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