2. Last year, Mr. Leon had a rectangular gardenwith an area of 208 square feet. This year thedimensions of the garden are the size of thedimensions of last year's garden. What is thearea of Mr. Leon's garden this year?A. 104 ft2B. 416 ft2C. 52 ft2D. 208 ft2
Answers
Answer:
C. 52 ft2
Step-by-step explanation:
Rectangle:
Has two dimensions, which are height(h) and base(b).
The area is: A = b*h
In this question:
We have that that A = b*h = 208.
New dimensions:
Both the dimensions are half(1/2) of last year.
So
A = (b/2)*(h/2) = (b*h)/4
Since b*h = 208
A = (b*h)/4 = 208/4 = 52
Related Questions
I need help on this math question and I NEED IT NOWWW
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The triangle contains two right triangles. The base of each right triangle is equal. Given that the length of the base of the triangle is 10, the base of each right triangle is
10/2 = 5
The diagram of the right triangle is shown below
We would find x by appying the pythagorean theorem which is expressed as
hypotenuse^2 = one leg^2 + other leg^2
From the diagram,
hypotenuse = 13
one leg = 5
other leg = x
By applying the pythagorean theorem,
13^2 = 5^2 + x^2
169 = 25 + x^2
Subtracting 25 from both sides of the equation, we have
169 - 25 = 25 - 25 + x^2
x^2 = 144
x = square root of 144
x = 12
Instructions: Determine which expressions can be simplified and if not, explain why not. If yes, simplify completely or rewrite as a simplified radical expression. Must show all work.Last expression that I wasn’t able to include in the picture is (x^4 y) 2/3
Answers
As 5 is a prime number, it is not in the power of 2. Then, the expression cannot be simplified,
______________________
[tex]\sqrt[3]{8}[/tex]Prime factorization of 8 is:
[tex]\begin{gathered} 8=2\times2\times2 \\ 8=2^3 \end{gathered}[/tex]Then, the expression can be simplified to get;
[tex]\sqrt[3]{8}=\sqrt[3]{2^3}=2[/tex]_________________-
[tex]\sqrt[]{3+5}[/tex]To simplify the expression first add numbers, and then use the prime factorization of result as follow:
[tex]=\sqrt[]{8}=\sqrt[]{2^3}=\sqrt[]{2^2\times2}=2\sqrt[]{2}[/tex]_____________
[tex]\sqrt[\square]{\frac{2x}{3y}}[/tex]As both parts of the fraction under the root are not power of two and both are prime numbers the expression cannot be simplified.
___________________-
[tex](x^4y)^{2/3}[/tex]Use the next property to rewrite the expression:
[tex]a^{n/m}=\sqrt[m]{a^n}[/tex][tex](x^4y)^{2/3}=\sqrt[3]{(x^4y)^2}[/tex]Expand the expression under the root and then simplifiy the expression as follow:
[tex]=\sqrt[3]{x^8y^2}=\sqrt[3]{x^6^{}x^2y^2}=x^2\sqrt[3]{x^2y^2}[/tex]5. If Ms. Yamagata uses 18-inch tiles, what are the least number of tiles that she needs to buy to cover the floor? A. 30 B. 45 C. 68 D. 102
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We will have the following:
*First: We determine the area:
[tex]A=7.5\cdot9\Rightarrow A=67.5[/tex]So, there is an area of 67.5 square feet, now we take that to square inches:
[tex]\Rightarrow A=67.5\cdot144\Rightarrow A=9720[/tex]So, there is an area of 9720 square inches in that bathroom.
*Second: We will determine the number of 18-inch tiles that can be accommodated in the length and width:
**Length: We take into account that for each foot there are 12 inches and that each tile has a side length of 8 inches, so:
[tex]L=\frac{9\cdot12}{18}\Rightarrow L=6[/tex]So, in the length, we can accommodate 6 18-inch tiles.
**Width:
[tex]W=\frac{7.5\cdot12}{18}\Rightarrow W=5[/tex]So, in the width, we can accommodate 5 18-inch tiles.
*Third: We determine the number of tiles we will need by multiplying the number of tiles that can be accommodated in the length times the tiles that can be accommodated on the width, that is:
[tex]t=6\cdot5\Rightarrow t=30[/tex]So, she will need 30 18-inch tiles.
Help with math discussion precalculus Select any city in the world that interests you. Research the average high temperature of that city each month for two years. Next, plot that data. The x-axis should be months (1-24) and the y-axis should be temperature. Embed your graph and table into the discussion board by uploading the image.
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SOLUTION
The Picture below is a table showing the average high temperature for Dallas for two years.
From the graph
[tex]\begin{gathered} x_1=\text{ represents the months for 24 months} \\ y_1=\text{ represents the average high temperature for each month } \end{gathered}[/tex]The graph for the data is shown below
We can see that the graph is a sinusoidal graph. That is it follows a sine wave form.
How do I solve the following system of equations by substitution. I have to show all steps
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In order to solve this system by substitution, let's equate both functions, substitute the expressions for f(x) and g(x), and calculate the values of x:
[tex]\begin{gathered} f(x)=g(x)\\ \\ -x^2+2x+3=-2x+3\\ \\ -x^2+2x+2x+3-3=0\\ \\ -x^2+4x=0\\ \\ x^2=4x\\ \\ x=4\text{ or }x=0 \end{gathered}[/tex]Therefore the solutions are x = 0 and x = 4.
Represent the expression “A number, x, decreased by the sum of 2x and 5* algebraically. A. (2x + 5) - x B. x - (2x + 5) C. x - 2x + 5 D. (x + 2x) - 5
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We are given the following word problem
"A number, x, decreased by the sum of 2x and 5"
We are asked to translate the word problem into an algebraic expression.
Sum of 2x and 5 means (2x + 5)
Now we need to subtract (decrease) this sum (2x + 5) from x
So, the algebraic expression becomes
[tex]x-(2x+5)_{}[/tex]Therefore, the correct algebraic expression is option B
Find all real solutions of the equation by using the square root method.(3c+4)2−37=0 c= Leave answers that include radicals as a single fraction, and separate multiple solutions with commas.
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Given the equation in the question expressed as:
[tex](3c+4)^2-37=0[/tex]Add 37 to both sides of the equation
[tex]\begin{gathered} (3c+4)^2-37+37=0+37 \\ (3c+4)^2=37 \end{gathered}[/tex]Take the square root of both sides
[tex]\begin{gathered} \sqrt{(3c+4)^2}=\sqrt{37} \\ 3c+4=\sqrt{37} \end{gathered}[/tex]Subtract 4 from both sides
[tex]\begin{gathered} 3c+4-4=\sqrt{37}-4 \\ 3c=\sqrt{37}-4 \end{gathered}[/tex]Divide both sides of the resulting equation by 3
[tex]\begin{gathered} \frac{3c}{3}=\frac{\sqrt{37}-4}{3} \\ c=\frac{\sqrt{37}-4}{3} \end{gathered}[/tex]Evaluate the expression 6c-d when c=2 and d=10 I need help?
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To evaluate the expression 6c - d, in case c = 2 and d = 10, we can proceed as follows:
We need to substitute the value of c and d in the expression, that is
c = 2, d = 10
Then
6c - d
6 x (2) - 10
12 - 10 = 2
So, the evaluation of the expression 6c - d when c =2 and d = 10 is 2.
(3х2 - 10x + 4) + (10х2 – 5х +8) can we this as a performance as a operation
Answers
Starting with the expression:
[tex](3x^2-10x+4)+(10x^2-5x+8)[/tex]Ignore the parenthesis, since their coefficients are equal to 1:
[tex]=3x^2-10x+4+10x^2-5x+8[/tex]Use the commutative property of addition to change the order of the terms without changing the result of the sum. Bring like terms together:
[tex]=3x^2+10x^2-10x-5x+4+8[/tex]Add like terms:
[tex]=13x^2-15x+12[/tex]Therefore:
[tex](3x^2-10x+4)+(10x^2-5x+8)=13x^2-15x+12[/tex]Jeanne has a coupon for $1.95 off ajug of name-brand laundry detergent thatnormally costs $14.99. The store-brandlaundry detergent costs $11.53.How much will Jeanne save if she buys thestore-brand detergent instead of usingher coupon and buying the name-brand?
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Find the price of the name brand detergent if Jeanne uses its coupon by substracting the amount of the coupon to the cost of the name brand detergent.
[tex]14.99-1.95=13.04[/tex]To find how much will she save if she buys the store brand detergent instead of the name brand, substract the cost of the store brand detergent to the cost calculated above.
[tex]13.04-11.53=1.51[/tex]She will save $1.51 if she buys the store brand detergent.
Thandi starts a new business baking pies that she sells to a local Spaza shop. She uses the family kitchen to bake her pies. Thandi used this formula to calculate her profit: Profit = money received for sales - cost of ingredients Her profits are shown in the table. Week Number of pies sold Profit 1 2 3 4 5 25 34 39 42 40 R75 R102 R117 R126 R120 a) Write Thandi's profit per pie as a rate. (1)
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Answer:
Step-by-step explanation:ni
The cylinder below has a radius 3 inches and a height of 8 inches. If two points are located on the surface of the cylinder, what is the maximum straight line distance they could be a part?
Answers
Consider the two situations below:
1) Two points are located on opposite sides of a diameter; as in the next diagram
The distance between the two points is equal to the diameter of the circle; in other words, 2 times the radius. Thus, the distance between the two orange points above is 6in.
2) Consider two points on opposite faces of the cylinder
The distance between the two points is equal to 8in, in this situation.
Mixing both diagrams so as to obtain the maximum distance between two points on the cylinder,
Thus, the maximum distance is given by the Pythagorean theorem, as shown below
[tex]d_{max}=\sqrt{6^2+8^2}=10[/tex]Hence, the answer is 10in
Jimmy has a certain amount of money. If he spends $12, then he has one-fifth of the original amount. How much money did Jimmy have originally?
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Let x be the original amount of money Jimmy had. Since he spent 12 and has the fifth of x this we have:
[tex]\begin{gathered} x-12=\frac{x}{5} \\ x-\frac{x}{5}=12 \\ \frac{4}{5}x=12 \\ x=\frac{12}{\frac{4}{5}} \\ x=15 \end{gathered}[/tex]Then, he had $15 originally.
4a. Explain how we can tell that this graph represents the given equation.*1 point108(0,6)6packs of cardstock4(1,3)2(14,0)24 6.8 10 12 14 16 18sheets of stickers
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The points on hte graph are
(0,6), (7,3) and (14,0).
Recall the general line equation is
[tex]y=mx+b[/tex]where m is slope and b is the y-intercept.
The y-intercept is the point where the graph crosses the y-axis.
The point (0,6) is the intersection point of the line and y-axis.
So, we get b=6.
Consider the points
[tex](x_1,y_1)=(7,3)\text{ and }(x_2,y_2)=(14,0)[/tex]Recall that the formula for slope is
[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]Susbtitude\text{ }x_1=7,x_2=14,y_1=3\text{ and }y_2=0.[/tex][tex]m=\frac{0-3}{14-7}=\frac{-3}{7}[/tex][tex]\text{Substitute m=}\frac{-3}{7}\text{ and b=6 in the line equation, we get}[/tex]Hence the required equation is
[tex]y=-\frac{3}{7}x+6[/tex]For each ordered pair (x,y) determine whether it is a solution to the inequality y<-3x-6
Answers
We have 4 ordered pairs (x,y), for which we must satisfy that the following inequality is satisfied:
[tex]y<-3x-6[/tex]What we must do to solve this is to replace the variables "x" and "y" in the inequality and verify that it is fulfilled.
First-order pair
[tex]\begin{gathered} (7,-27) \\ -27<-3\cdot(7)-6 \\ -27<-21-6 \\ -27=-27 \end{gathered}[/tex]This order pair is not a solution to the inequality
Second-order pair
[tex]\begin{gathered} (-9,25) \\ 25<-3\cdot(-9)-6 \\ 25<27-6 \\ 25>21 \end{gathered}[/tex]This order pair is not a solution to the inequality
Third-order pair
[tex]\begin{gathered} (6,-26) \\ -26<-3\cdot(6)-6 \\ -26<-18-6 \\ -26<-24 \end{gathered}[/tex]This order pair is a solution to the inequality
Fourth-order pair
[tex]\begin{gathered} (-3,-2) \\ -2<-3\cdot(-3)-6 \\ -2<9-6 \\ -2<3 \end{gathered}[/tex]This order pair is a solution to the inequality
Finally, we have that only the following ordered pair are a solution for the inequality:
[tex]\begin{gathered} (6,-26) \\ (-3,-2) \end{gathered}[/tex]Explain how you know whether a relationship between two quantities is or is not a function
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In order to know whether a relationship is a function or not, follow these steps:
1. Identify the input values, usually grouped as the values for the independent variable "x"
2. Identify the output values, usually grouped as the values for the dependent variable "y"
3. If each input value leads to only one output value, classify the relationship as a function. If any input value leads to two or more outputs, do not classify the relationship as a function.
Find the distance between the points (0, 10) and (–9, 1).A. 14.21B. 12.73C. 16.23D. 20.22
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We have the next formula to calculate the distance between 2 points
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]in our case
(0,10)=(x1,y1)
(-9,1)=(x2,y2)
we substitute the values
[tex]d=\sqrt[]{(1-10)^2+(-9-0)^2}[/tex]then we simplify
[tex]d=9\sqrt[]{2}=12.7279[/tex]Therefore the correct choice is B. 12.73
Which expression is equivalent to 18-2V14r8 67704, if x + 0? O A. 12.142 OB. 3.42 O C.3.147 OD. 3.02 Reset Next
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We will simplify the expression thus:
[tex]\frac{18x^2\sqrt[]{14x^8}}{6\sqrt[]{7x^4}}[/tex][tex]\frac{18x^2\times\sqrt[]{14}\times x^{8\times\frac{1}{2}}}{6\times\sqrt[]{7}\times x^{4\times\frac{1}{2}}}[/tex]Simplifying further will give us:
[tex]\begin{gathered} \frac{3x^2\times\sqrt[]{2}\times x^4}{x^2} \\ \frac{3\times\sqrt[]{2}\times x^4}{1} \\ =3x^4\sqrt[]{2} \\ \text{The correct answer is option B.} \end{gathered}[/tex]For the graph shown, identify a) the point(s) of inflection and b) the intervals where the function is concave up or concave down X . 110 ! a) The point(s) of inflection is/are (Type an ordered pair. Use a comma to separate answers as needed.)
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We have the following:
Therefore:
a.
The point (0,5)
b.
therefore:
Concave up:
[tex](-4,0)[/tex]Convace down:
[tex](-2,\frac{3}{2})[/tex]a.
(0,5)
determine the axis of symmetry of the quadratic functionA) y = 2B) x = 2C) x = 0D) y = 1
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SOLUTION:
Case: Axis of symmetry of quadratic function
Given: A graph with a turning point
Required: To find the axis of symmetry of the quadratic function
Method:
Use a vertical on the divide the graph into two equal parts
Final answer:
The axis of symmetry is at x=2
Find the length of the 3rd side using the simplest radical form
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Given a right angled triangle, we shall solve for the unknown side by applying the Pythagoras' theorem which is;
[tex]c^2=a^2+b^2[/tex]Where c is the hypotenuse (side facing the right angle) and then a and b are the other two sides.
Substituting for the given values, we shall now have the following;
[tex]\begin{gathered} c^2=a^2+b^2 \\ c^2=5^2+5^2 \\ c^2=25+25 \\ c^2=50 \end{gathered}[/tex]Take the square root of both sides;
[tex]\begin{gathered} \sqrt[]{c^2}=\sqrt[]{50} \\ c=\sqrt[]{50} \end{gathered}[/tex]We can now re-arrange the the right side of the equation;
[tex]\begin{gathered} c=\sqrt[]{2\times25} \\ c=\sqrt[]{2}\times\sqrt[]{25} \\ c=5\sqrt[]{2} \end{gathered}[/tex]ANSWER:
The third side of the triangle would now be;
[tex]5\sqrt[]{2}[/tex]solve the equation 3x = 2x +5. what can you do to isolate the variable on one side of the equation 1. add 5 negative unit tiles to both sides.2. add 5 positive unit tiles to both sides.3. add 2 negative x-tiles to both sides 4. add 2 positive x-tiles to both sides
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To isolate only one variable on one side of the equation, you'll need to subtract -2x from both sides of the equation. So only option 3 from the given choices suffice this condition.
I'll send a pic of the Homework
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given the value of a and b in each set:
Set 1 :
[tex]\begin{gathered} a=-\frac{1}{2},b=6 \\ \\ \end{gathered}[/tex]We will find the value of the following :
[tex]\begin{gathered} -a=-1\cdot-\frac{1}{2}=\frac{1}{2} \\ \\ -4b=-4\cdot6=-24 \\ \\ -a+b=\frac{1}{2}+6=6\frac{1}{2} \\ \\ a\div-b=\frac{1}{2}\div-6=\frac{1}{2}\cdot-\frac{1}{6}=-\frac{1}{12} \\ \\ a^2=(-\frac{1}{2})^2=\frac{1}{2}\cdot\frac{1}{2}=\frac{1}{4} \\ \\ b^3=6^3=216 \end{gathered}[/tex]The expression with the largest value = b^3 = 216
The expression with the smallest value = -4b = -24
the expression which is closest to zero = a ÷ -b
May I please get help with this. For I am confused as I have tried many times and many ways to get the correct answers but still could not find the right answers or how to plot it in the graph
Answers
From the graph, the point marked with a large dot is located at (-7, -6)
Translation 5 units to the right transforms the point (x, y) into (x+5, y). Applying this rule to the point, we get:
(-7, -6) → (-7+5, -6) → (-2, -6)
Translation 7 units up transforms the point (x, y) into (x, y+7). Applying this rule to the point, we get:
(-2, -6) → (-2, -6+7) → (-2, 1)
In the final figure, the point is (-2, 1)
how do you solve for x in the following problem? 4x + 16 equals 24
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Let's begin by listing out the information given to us:
[tex]\begin{gathered} 4x+16=24 \\ \text{Subtract 16 from both sides, we have:} \\ 4x+16-16=24-16_{} \\ 4x=8 \\ \text{Divide both side by 4, we have:} \\ \frac{4x}{4}=\frac{8}{4}\Rightarrow x=2 \\ x=2 \end{gathered}[/tex]Just give best explanation and give answer to both questions
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If the two triangles are similar then their angles have the same measure. This also implies that the quotient between a side of one triangle and its corresponding side in the other one is the same for the three pairs of sides. The sides of the large triangle are 9, 2+y and 12 and their corresponding sides in the small triangle are 3, 2 and x. Then since the quotient between corresponding sides is always the same we get:
[tex]\begin{gathered} \frac{9}{3}=\frac{2+y}{2}=\frac{12}{x} \\ 3=\frac{2+y}{2}=\frac{12}{x} \end{gathered}[/tex]So for x we get:
[tex]3=\frac{12}{x}[/tex]We multiply both sides by x and we get:
[tex]\begin{gathered} 3\cdot x=\frac{12}{x}\cdot x \\ \\ 3x=12 \end{gathered}[/tex]And we divide both sides by 3:
[tex]\begin{gathered} \frac{3x}{3}=\frac{12}{3} \\ x=4 \end{gathered}[/tex]Then for y we get:
[tex]3=\frac{2+y}{2}[/tex]We can multiply both sides by 2:
[tex]\begin{gathered} 3\cdot2=\frac{2+y}{2}\cdot2 \\ 6=2+y \end{gathered}[/tex]And we substract 2 from both sides:
[tex]\begin{gathered} 6-2=2+y-2 \\ y=4 \end{gathered}[/tex]So x=4 and y=4. Then the answer to part 1 is option A and the answer to part 2 is option B.
4: Random numbers are useful for ______ real-world situations that involve chance.
Answers
Real world situations that involve chance can be modeled by the use of random numbers.
The answer is option A.
What should be the check digit for the UPC of a tic-tac package whose first 11 digitsare: 0-09800-23798-d?(The check digit is d so determine what that digit should be by using the UPC method.)
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The Universal product code (UPC) is an 11-digit set of numbers and the check digit is located to the far right..
To calculate this 12th digit (the check digit), follow the stesp shown;
[tex]\begin{gathered} (1)\text{ Multiply each of the 1st, 3rd, 5th and 7th digits by }3\text{ and then add the results all together} \\ (0\times3)+(9\times3)+(0\times3)+(2\times3) \\ 0+27+0+6 \\ 33 \\ \text{Take the remaining digits (not included above) and }add\text{ them to the total (33)} \\ 0+8+0+3+7+9+8=35 \\ 35+33=68 \\ \text{Next you divide this new total by 10 } \\ \frac{68}{10} \\ 6\text{ rem 8} \\ To\text{ get the check digit, you now subtract the remainder (8) from 10} \\ Check\text{ digit=10-8} \\ \text{Check digit=2} \end{gathered}[/tex]The calculations show that the check digit is 2.
Find the domain of this without using the graphical method
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By definition, the domain of a function is the complete set of possible values of the independent variable (x, usually).
We must find the domain of the following function:
[tex]f(x)=\sqrt[5]{x^2-7x+2}\text{.}[/tex]We see that the function is the odd root of a polynomial. Odd roots are defined for all real numbers, so this function is defined for all real numbers. The domain of the function is:
[tex]\text{Domain }=(-\infty,\infty).[/tex]Answer
[tex]\text{Domain }=(-\infty,\infty).[/tex]If f(x) varies directly with x and f(x)= 64 when x=29 , find the value of f(x) when x=8.Round you final answer to the nearest whole number.
Answers
18
Explanation
Direct variation describes a simple relationship between two variables, it can be defined by the expression
[tex]\begin{gathered} f(x)=kx \\ \text{where} \\ f(x)=\text{ y, } \\ \text{and k is a constant} \end{gathered}[/tex]Step 1
find the k value,
set the equation and solve for k
so
let
f(x)=64 when x=29
so
[tex]\begin{gathered} f(x)=kx \\ \text{replace} \\ 64=k\cdot29 \\ to\text{ solve for k, divide both sides by 29} \\ \frac{64}{29}=\frac{k\cdot29}{29} \\ \frac{64}{29}=k \end{gathered}[/tex]Step 2
now, set the equation:
with k=64/29 , the function would be
[tex]\begin{gathered} f(x)=kx \\ f(x)=\frac{64}{29}x \end{gathered}[/tex]finally, to check the f(x) when x= 8, just replace and calculate
[tex]\begin{gathered} f(x)=\frac{64}{29}x \\ f(8)=\frac{64}{29}\cdot8 \\ f(8)=\frac{512}{29} \\ f(8)=17.655 \\ \text{rounded} \\ f(8)=18 \end{gathered}[/tex]threfore, the answer is
18
I hope this helps you