Which exponential function is represented by the table below? x –2 0 2 4 y 16 4 1 14
Answers
An exponential function which is represented by the table above is: f(x) = 4(1/2)^x
What is an exponential function?An exponential function simply refers to a mathematical function whose values are generated by a constant that is raised to the power of the argument. Mathematically, an exponential function can be modeled by using this equation:
f(x) = abˣ
Where:
a represents the initial value.b represents the rate of change.From the table above, we would calculate the value of a and b:
At x = 0 and y = 4; the value of a (initial value) is 4.
Rate of change, b = Δy/Δx
Rate of change, b = 1/2
Substituting the parameters into the formula, we have;
f(x) = abˣ
f(x) = 4(1/2)^x
Check:
f(x) = 4 × (1/2)^x f(x) = 4 * ( 1/2 )^x
f(x) = 4 × (1/2)² f(x) = 4 × (1/2)⁻²
f(x) = 4 × 1/4 f(x) = 4 × 4
f(x) = 1 f(x) = 16
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Related Questions
Given: B is the midpoint of AC. Complete the statementIf AB = 28, Then BC =and AC =
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If B is the midpoint of AC, this means that point B divides the line AC exactly into 2 equal parts AB and BC, therefore,
[tex]AB=BC[/tex]Answer A
Thus, if AB = 28, BC = 28 too.
Answer B: Therefore, AC = 56
Suppose A is true, B is true, and C is true. Find the truth values of the indicated statement.
Answers
Solution:
If A is true, B is true, and C is true, then:
[tex]A\lor(B\wedge C)=\text{ T }\lor(T\wedge T)\text{ = T}\lor(T)\text{ = T }\lor\text{ T = T}[/tex]we can conclude that the correct answer is:
TRUE
write the exponential function for the data displayed in the following table
Answers
As per given by the question,
There are given that a table of x and f(x).
Now,
The genral for of the equation is,
[tex]f(x)=ab^x[/tex]Then,
For the value of x and f(x).
Substitute 0 for x and -2 for f(x).
So,
[tex]\begin{gathered} f(x)=ab^x \\ -2=ab^0 \\ -2=a \end{gathered}[/tex]Now,
For the value of b,
Substitute 1 for x and -1/3 for f(x),
So,
[tex]\begin{gathered} f(x)=ab^x \\ -\frac{1}{3}=ab^1 \\ ab=-\frac{1}{3} \end{gathered}[/tex]Now,
Put the value of a in above result.
So,
[tex]\begin{gathered} ab=-\frac{1}{3} \\ -2b=-\frac{1}{3} \\ b=\frac{1}{6} \end{gathered}[/tex]Now,
Put the value of a and b in the general form of f(x).
[tex]\begin{gathered} f(x)=ab^x \\ f(x)=-2\cdot(\frac{1}{6})^x \end{gathered}[/tex]Hence, the exponential function is ,
[tex]f(x)=-2(\frac{1}{6})^x[/tex]Amtrak's annual passenger revenue for the years 1985 - 1995 is modeled approximately by the formulaR = -60|x- 11| +962where R is the annual revenue in millions of dollars and x is the number of years after 1980. In what year was the passenger revenue $722 million?In the years ____ and ___, the passenger revenue was $722 million.
Answers
ANSWER
1987 and 1995
EXPLANATION
The revenue is modeled by:
[tex]R=-60|x-11|+962[/tex]To find the years that the revenue was $722 million, we have to solve for x when R is 722.
That is:
[tex]\begin{gathered} 722=-60|x-11|+962 \\ \Rightarrow722-962=-60|x-11| \\ -240=-60|x-11| \\ \Rightarrow|x-11|=\frac{-240}{-60} \\ |x-11|=4 \end{gathered}[/tex]We can split the absolute value equation into two different equations because the term in the absolute value is equal to both the positive and the negative of the term on the other side of the equality.
That is:
[tex]\begin{gathered} x-11=4 \\ x-11=-4 \end{gathered}[/tex]Solve for x in both:
[tex]\begin{gathered} x=11+4 \\ \Rightarrow x=15 \\ x=11-4 \\ \Rightarrow x=7 \end{gathered}[/tex]That is to say 7 and 15 years after 1980.
Therefore, in the years 1987 and 1995, the revenue was $722 million.
Question 3 (5 points) Convert the decimal 0.929292... to a fraction. O 92 99 O 92 999 O 92 100 92 1000
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Using data from the previous table, construct an exponential model for this situation.A ( t ) =What will be the value when t=8, rounded to 2 decimal places?
Answers
Answer
• Exponential model
[tex]A(t)=13.60(1+0.25)^{t}[/tex][tex]A(8)\approx81.06[/tex]Explanation
The exponential model equation can be given by:
[tex]A(t)=C(1+r)^t[/tex]where C is the initial value, r is the rate of growth and t is the time.
We can get the initial value by evaluating in the table when t = 0. In this case the value A(0) = 13.60. Then our equation is:
[tex]A(t)=13.60(1+r)^t[/tex]Now we have to get r by choosing any point and solving for r. For example, (3, 26.56). By replacing the values and solving we get:
[tex]26.56=13.60(1+r)^3[/tex][tex]\frac{26.56}{13.60}=(1+r)^3[/tex][tex](1+r)^3=\frac{26.56}{13.60}[/tex][tex]\sqrt[3]{(1+r)^3}=\sqrt[3]{\frac{26.56}{13.60}}[/tex][tex]1+r=\sqrt[3]{\frac{26.56}{13.60}}[/tex][tex]r=\sqrt[3]{\frac{26.56}{13.60}}-1\approx0.2500[/tex]Thus, our rate is 0.25, and we can add it to our equation:
[tex]A(t)=13.60(1+0.25)^t[/tex]Finally, we evaluate t = 8:
[tex]A(8)=13.60(1+0.25)^8=81.06[/tex]Put the following equation of a line into slope-intercept form, simplifying all fractions.
4x-3y=9
Answers
Answer:
y=4/3x+3
Step-by-step explanation:
we know that slope intercept form is y=mx+b, where m is the slope and b is the y intercept
for 4x-3y=9, we have to isolate y
we subtract 4x to both sides to get
-3y=-4x+9
to get y alone, we divide both sides by -3
y=4/3x+3
Answer:
Y=4/3x-3
Step-by-step explanation:
Y=4/3x-3
the other guy had the right idea but the two negatives make a positive!
Simplify the expression.
the expression negative one seventh j plus two fifths minus the expression three halves j plus seven fifteenths
negative 19 over 14 times j plus 13 over 15
negative 19 over 14 times j minus 13 over 15
negative 23 over 14 times j plus negative 1 over 15
23 over 14 times j plus 1 over 15
Answers
The expression is simplified to negative 23 over 14 times j plus negative 1 over 15. Option C
What is an algebraic expression?An algebraic expression can be defined as an expression mostly consisting of variables, coefficients, terms, constants and factors.
Such expressions are also known to be composed or made up of some mathematical or arithmetic operations, which includes;
AdditionSubtractionDivisionBracketMultiplicationParentheses. etcFrom the information given, we have that;
negative one seventh j = - 1/7jtwo fifths = 2/5three halves j = 3/2 jseven fifteenths = 7/15Substitute the values
- 1/7j + 2/5 - 3/2j - 7/15
collect like terms
- 1/7j - 3/2j + 2/5 - 7/15
-2j - 21j /14 + 6 7 /15
-23j/14 + -1/15
Hence, the correct option is negative 23 over 14 times j plus negative 1 over 15
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Hello! Need a little help on parts a,b, and c. The rubric is attached, Thank you!
Answers
In this situation, The number of lionfish every year grows by 69%. This means that to the number of lionfish in a year, we need to add the 69% to get the number of fish in the next year.
This is a geometric sequence because the next term of the sequence is obtained by multiplying the previous term by a number.
The explicit formula for a geometric sequence is:
[tex]a_n=a_1\cdot r^{n-1}[/tex]We know that a₁ = 9000 (the number of fish after 1 year)
And the growth rate is 69%, to get the number of lionfish in the next year, we need to multiply by the rate og growth (in decimal) and add to the number of fish. First, let's find the growth rate in decimal, we need to divide by 100:
[tex]\frac{69}{100}=0.69[/tex]Then, if a₁ is the number of lionfish in the year 1, to find the number in the next year:
[tex]a_2=a_1+a_1\cdot0.69[/tex]We can rewrite:
[tex]a_2=a_1(1+0.69)=a_1(1.69)[/tex]With this, we have found the number r = 1.69. And now we can write the equation asked in A:
The answer to A is:
[tex]f(n)=9000\cdot1.69^{n-1}[/tex]Now, to solve B, we need to find the number of lionfish in the bay after 6 years. Then, we can use the equation of item A and evaluate for n = 6:
[tex]f(6)=9000\cdot1.69^{6-1}=9000\cdot1.69^5\approx124072.6427[/tex]To the nearest whole, the number of lionfish after 6 years is 124,072.
For part C, we need to use the recursive form of a geometric sequence:
[tex]a_n=r(a_{n-1})[/tex]We know that the first term of the sequence is 9000. After the first year, the scientists remove 1400 lionfish. We can write this as:
[tex]\begin{gathered} a_1=9000 \\ a_n=r\cdot(a_{n-1}-1400) \end{gathered}[/tex]Because to the number of lionfish in the previous year, we need to subtract the 1400 fish removed by the scientists.
The answer to B is:
[tex][/tex]Given the diagram below which could be used to calculate AC
Answers
Cos a = adjacent side / hypotenuse
Where:
a= angle = 37°
adjacent side = 20
Hypotenuse = x (the longest side , AC)
Replacing:
Cos (37)=20/ x (option B)
The ratio of students polled in 6th grade who prefer lemonade to iced tea is 8:4, or 2:1. If there were 39 students in 6th grade polled, explain how to find the number of students that prefer lemonade and the number of students that prefer iced tea. Be sure to tell how many students prefer each.
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Since we know the ratio is 2:1, then to find the number of students who like iced tea we convert the ratio to a fraction:
[tex]\frac{1}{2}[/tex]this means that one of two students preferred iced tea.
To find the number of students who prefer iced tea we multiply the total number of students by the fraction, then:
[tex]39\cdot\frac{1}{2}=\frac{39}{2}=19.5[/tex]Since we can't have a fraction of a student, we conclude that 19 students prefer iced tea and 20 prefer lemonade.
One evening 1400 concert tickets were sold for the Fairmont Summer Jazz Festival. Tickets cost $30 for covered pavilion seats and $20 for lawn seats. Total receipts were $32,000. Howmany tickets of each type were sold?How many pavilion seats were sold?
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Let p be the number of pavilion seats and l be the number of lawn seats. Since there were sold 1400 tickets, we can write
[tex]p+l=1400[/tex]and since the total money was $32000, we can write
[tex]30p+20l=32000[/tex]Then,we have the following system of equations
[tex]\begin{gathered} p+l=1400 \\ 30p+20l=32000 \end{gathered}[/tex]Solving by elimination method.
By multiplying the first equation by -30, we have an equivalent system of equation
[tex]\begin{gathered} -30p-30l=-42000 \\ 30p+20l=32000 \end{gathered}[/tex]By adding these equations, we get
[tex]-10l=-10000[/tex]then, l is given by
[tex]\begin{gathered} l=\frac{-10000}{-10} \\ l=1000 \end{gathered}[/tex]Now, we can substitute this result into the equation p+l=1400 and obtain
[tex]p+1000=1400[/tex]which gives
[tex]\begin{gathered} p=1400-1000 \\ p=400 \end{gathered}[/tex]Then, How many tickets of each type were sold? 400 for pavilion seats and 1000 for lawn seats
How many pavilion seats were sold? 400 tickets
Quadrilateral HGEF is a scaled copy of quadrilateral DCAB. What is themeasurement of lin EG?
Answers
Answer:
14 units
Explanation:
If quadrilaterals HGEF and DCAB are similar, then the ratio of some corresponding sides is:
[tex]\frac{FH}{BD}=\frac{EG}{AC}[/tex]Substitute the given side lengths:
[tex]\begin{gathered} \frac{6}{3}=\frac{EG}{7} \\ 2=\frac{EG}{7} \\ \implies EG=2\times7 \\ EG=14 \end{gathered}[/tex]The measurement of line EG is 14 units.
what is 0.09 as a percentage?
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State which pairs of lines are:(a) Parallel to each other.(b) Perpendicular to each other.
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So first of all we should write the three equations in slope-intercept form. This will make the problem easier to solve. Remember that the slope-interception form of an equation of a line looks like this:
[tex]y=mx+b[/tex]Where m is known as the slope and b the y-intercept. The next step is to rewrite the second and third equation since the first equation is already in slope-intercept form. Its slope is 4 and its y-intercept is -1.
So let's rewrite equation (ii). We can begin with substracting 4 from both sides of the equation:
[tex]\begin{gathered} 8y+4=-2x \\ 8y+4-4=-2x-4 \\ 8y=-2x-4 \end{gathered}[/tex]Then we can divide both sides by 8:
[tex]\begin{gathered} \frac{8y}{8}=\frac{-2x-4}{8} \\ y=-\frac{2}{8}x-\frac{4}{8} \\ y=-\frac{1}{4}x-\frac{1}{2} \end{gathered}[/tex]So its slope is -1/4 and its y-intercept is -1/2.
For equation (iii) we can add 8x at both sides:
[tex]\begin{gathered} 2y-8x=-2 \\ 2y-8x+8x=-2+8x \\ 2y=8x-2 \end{gathered}[/tex]Then we can divide both sides by 2:
[tex]\begin{gathered} \frac{2y}{2}=\frac{8x-2}{2} \\ y=\frac{8}{2}x-\frac{2}{2} \\ y=4x-1 \end{gathered}[/tex]Then its slope is 4 and its y-intercept is -1. As you can see this equation is equal to equation (i).
In summary, the three equations in slope-intercept form are:
[tex]\begin{gathered} (i)\text{ }y=4x-1 \\ (ii)\text{ }y=-\frac{1}{4}x-\frac{1}{2} \\ (iii)\text{ }y=4x-1 \end{gathered}[/tex]It's important to write them in this form because when trying to figure out if two lines are parallel or perpendicular we have to look at their slopes:
- Two lines are parallel to each other if they have the same slope (independently of their y-intercept).
- Two lines are perpendicular to each other when the slope of one of them is the inverse of the other multiplied by -1. What does this mean? If a line has a slope m then a perpendicular line will have a slope:
[tex]-\frac{1}{m}[/tex]Now that we know how to find if two lines are parallel or perpendicular we can find the answers to question 4.
So for part (a) we must find the pairs of parallel lines. As I stated before we have to look for those lines with the same slope. As you can see, only lines (i) and (iii) have the same slope (4) so the answer to part (a) is: Lines (i) and (iii) are parallel to each other.
For part (b) we have to look for perpendicular lines. (i) and (iii) are parallel so they can't be perpendicular. Their slopes are equal to 4 so any line perpendicular to them must have a slope equal to:
[tex]-\frac{1}{m}=-\frac{1}{4}[/tex]Which is the slope of line (ii). Then the answer to part (b) is that lines (i) and (ii) are perpendicular to each other as well as lines (ii) and (iii).
Meghan measures the heights and arm spans of the girls on her basketball team. She plots the data and makes a scatterplot comparing heights and arm spans, in inches. Meghan finds that the trend line that best fits her results has the equation y=x+2 . if a girl on her team is 64 inches tall, What should Meggan expect her span to be?
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EXPLANATION
Let's see the facts:
The equation is given by the following expression y= x + 2
---> 64 inches tall
As we can see in the graph of arm span versus height, and with the given data the arm span should be:
arm span = y = 64 + 2 = 66 inches
So, the answer is 66 inches. [OPTION C]
How do I do this ? I need to find the solution for it
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given equations
[tex]\begin{gathered} y=-\frac{4}{3}x \\ y=\frac{3}{2}x \end{gathered}[/tex]STEP 2: Define the point that is the solution for the given functions on the graph
The solution of such a system is the ordered pair that is a solution to both equations. To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect.
STEP 3: Determine the solution for the system of equations
It can be seen from the image below that the two lines intersect at the origin and hence they are given as the solutions to the given system of equations.
Hence, the solutions are:
[tex]x=0,y=0[/tex]Use the graph to evaluate the function for the given input value. 20 f(-1) = 10 f(1) = х 2 -10 -20 Activity
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we have that
[tex]f(-1)=-8,f(1)=-12[/tex]Two liters of soda cost $2.50 how much soda do you get per dollar? round your answer to the nearest hundredth, if necessary.
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If two litters of soda cost $2.50;
Then, a dollar would buy;
[tex]\begin{gathered} =\frac{2}{2.5}\text{litres of soda} \\ =0.80\text{ litres of soda} \end{gathered}[/tex]11. Suppose that y varies inversely with x. Write a function that models the inverse function.x = 1 when y = 12- 12xOy-y = 12x
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We need to remember that when two variables are in an inverse relationship, we have that, for example:
[tex]y=\frac{1}{x}[/tex]In this case, we have an inverse relationship, and we have that when x = 1, y = 12.
Therefore, we have that the correct relationship is:
[tex]y=\frac{12}{x}[/tex]In this relationship, if we have that x = 1, then, we have that y = 12:
[tex]x=1\Rightarrow y=\frac{12}{1}\Rightarrow y=12[/tex]Therefore, the correct option is the second option: y = 12/x.
Graph the system below. What is the x-coordinate of the solution to the system of linear equations?y= -4/5x + 2y= 2/3x + 2A. -4B. 2C. 3D. 0
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The solution is (x,y) = (0,2)
Uptown Tickets charges $7 per baseball game tickets plus a $3 process fee per order. Is the cost of an order proportional to the number of tickets ordered?
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The cost of an order is proportional to the number of tickets if the relation between them is constant.
Then, if we order 1 ticket the cost will be $7 + $3 = $10
And if we order 2 tickets, the cost will be $7*2 + $3 = $17
So, the relation between cost and the number of tickets is:
For 1 ticket = $10 / 1 ticket = 10
For 2 tickets = $17/ 2 tickets = 8.5
Since 10 and 8.5 are different, the cost of an order is not proportional to the number of tickets ordered.
Answer: they are not proportional
Need some help thanks
Answers
In the given equations, the value of variables are:
(A) a = -10(B) b = -0.2(C) c = 0.25What exactly are equations?When two expressions are equal in a mathematical equation, the equals sign is used to show it.A mathematical statement is called an equation if it uses the word "equal to" in between two expressions with the same value.Using the example of 3x + 5, the result is 15.There are many different types of equations, such as cubic, quadratic, and linear.The three primary categories of linear equations are point-slope, standard, and slope-intercept equations.So, solving for variables:
(A) 1/5a = -2:
1/5a = -2a = -2 × 5a = -10(B) 8 + b = 7.8:
8 + b = 7.8b = 7.8 - 8b = -0.2(C) -0.5 = -2c:
-0.5 = -2cc = -0.5/-2c = 0.25Therefore, in the given equations, the value of variables are:
(A) a = -10(B) b = -0.2(C) c = 0.25Know more about equations here:
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Hello! I need some help with this homework question, please? The question is posted in the image below. Q4
Answers
a) f(0) = -1
b) f(1) = 1
c) f(4) = 7
d) f(5) = 121
Explanation:
. Since for every value between -2 (excluded) and 4 (included)
~ 0 , 1 and 4
You have to use the first equation
=> f(0) = 2 * 0 - 1 = -1
=> f(1) = 2 * 1 - 1 = 1
=> f(4) = 2 * 4 - 1 = 7
. For values between 4 (exclude) and 5(included)
~ 5
You have to use the second equation
=> f(5) = 5^3 - 4 = 121
Use a system of equations to solve the following problem.The sum of three integers is380. The sum of the first and second integers exceeds the third by74. The third integer is62 less than the first. Find the three integers.
Answers
the three integers are 215, 12 and 153
Explanation:
Let the three integers = x, y, and z
x + y + z = 380 ....equation 1
The sum of the first and second integers exceeds the third by 74:
x + y - 74 = z
x + y - z = 74 ....equation 2
The third integer is 62 less than the first:
x - 62 = z ...equation 3
subtract equation 2 from 1:
x -x + y - y + z - (-z) = 380 - 74
0 + 0 + z+ z = 306
2z = 306
z = 306/2
z = 153
Insert the value of z in equation 3:
x - 62 = 153
x = 153 + 62
x = 215
Insert the value of x and z in equation 1:
215 + y + 153 = 380
368 + y = 380
y = 380 - 368
y = 12
Hence, the three integers are 215, 12 and 153
57-92=17 -2c-ust +1 8x1322-1) = 677343 (x + 55-22-20 K 54+32--1 5x+363) = -1 5x+aen -6 8+2=6 2:6-8 -44)-5)-(2) 16-3942=12 18-y-18 -x-57-3222 - (-1)-sy-5633=2 2-35-17 = 2 2.3.3 -Byzo yo TARE 3) -x - 5y + z = 17 -5x - 5y +56=5 2x + 5y - 3z=-10 4) 4x + 4y + 2x - 4y+ 5x - 4y
Answers
ANSWER:
[tex]\begin{gathered} x=4 \\ y=2 \\ z=0 \end{gathered}[/tex]STEP-BY-STEP EXPLANATION:
We have the following system of equations:
[tex]\begin{gathered} 4x+4y+z=24\text{ (1)} \\ 2x-4y+z=0\text{ (2)} \\ 5x-4y-5z=12\text{ (3)} \end{gathered}[/tex]We solve by elimination:
[tex]\begin{gathered} \text{ We add (1) and (2)} \\ 4x+4y+z+2x-4y+z=24+0 \\ 6x+2z=24\text{ }\rightarrow x=\frac{24-2z}{6}\text{ (4)} \\ \text{ We add (1) and (3)} \\ 4x+4y+z+5x-4y-5z=24+12 \\ 9x-4z=36\text{ (5)} \\ \text{ replacing (4) in (5)} \\ 9\cdot(\frac{24-2z}{6})-4z=36 \\ 36-3z-4z=36 \\ -7z=36-36 \\ z=\frac{0}{-7} \\ z=0 \end{gathered}[/tex]Now, replacing z in (4):
[tex]\begin{gathered} x=\frac{24-2\cdot0}{6} \\ x=\frac{24}{6} \\ x=4 \end{gathered}[/tex]Then, replacing z and x in (1):
[tex]\begin{gathered} 4\cdot4+4y+0=24 \\ 16+4y=24 \\ 4y=24-16 \\ y=\frac{8}{4} \\ y=2 \end{gathered}[/tex]Identify all points and line segments in the picture below.Points: A, B, C, DLine segments: AB, BC, CD, AD, BD, ACPoints: A, B, C, DLine segments: AD, AC, DC, BOPoints: A, B, C, DLine segments: AB, AD, AC, DC, BCPoints: A, BLine segments: AB, AC, DC, BC
Answers
Option C
Points: A, B, C, D
Line segments: AB, AD, AC, DC, BC
Geometry Problem - Given: segment AB is congruent to segment AD and segment FC is perpendicular to segment BD. Conclusion: Triangle AEG is isosceles. (Reference diagram in picture)
Answers
As the triangle AEF has 2 angles with the same measure, triangle AEF is isosceles.
An independent third party found the cost of a basic car repair service for a local magazine. The mean cost is $217.00 with a standard deviation of $11.40. Which of the following repair costs would be considered an “unusual” cost?
Answers
Given
An independent third party found the cost of a basic car repair service for a local magazine.
The mean cost is $217.00 with a standard deviation of $11.40.
To find: The repair costs which would be considered an “unusual” cost.
Explanation:
It is given that, the mean is 217.00, and the standard deviation is 11.40.
Consider, the distribution as a Normal distribution.
Then, the first range is defined as,
[tex]\begin{gathered} First\text{ }range:mean\pm SD \\ \Rightarrow X_1=mean+SD \\ =217.00+11.40 \\ =228.4 \\ \Rightarrow X_2=mean-SD \\ =217.00-11.40 \\ =205.6 \end{gathered}[/tex]And, the second range is defined as,
[tex]\begin{gathered} Second\text{ }range:mean\pm2SD \\ \Rightarrow X_3=217.00+2(11.40) \\ =217.00+22.8 \\ =239.8 \\ \Rightarrow X_4=217.00-2(11.40) \\ =217.00-22.8 \\ =194.2 \end{gathered}[/tex]Hence, the answer is option a) 192.53 since it does not belongs to the above ranges.
in this problem you will use a ruler to estimate the length of AC. afterwards you will be able to see the lengths of the other two sides and you will use the pythagorean theorem to check your answer
Answers
Answer:
5.124
Explanation:
Given the following sides
AB = 6.5cm
BC = 4.0cm
Required
AC
Using the pythagoras theorem;
AB^2 = AC^2 + BC^2
6.5^2 = AC^2 + 4^2
42.25 = AC^2 + 16
AC^2 = 42.25 - 16
AC^2 = 26.25
AC = \sqrt{26.25}
AC = 5.124
Hence the actual length of AC to 3dp is 5.124