Given:
[tex]\begin{gathered} -x^2+x-7 \\ x+1 \end{gathered}[/tex]Required:
To find the quotient and remainder using synthetic division.
Explanation:
Consider
[tex]\begin{gathered} x+1=0 \\ x=-1 \end{gathered}[/tex][tex]\begin{gathered} -1|-1\text{ }+1\text{ }-7 \\ \text{ }|\text{ }+1\text{ }-2 \\ ------------------- \\ \text{ }-1\text{ }+2\text{ }-9 \\ \end{gathered}[/tex][tex]-x+2-\frac{9}{x+1}[/tex]Here the quotient is
[tex]-x+2[/tex]And the remainder is
[tex]-9[/tex]Final Answer:
Quotient :
[tex]-x+2[/tex]Remainder : -9.
The perimeter of a rectangular garden is 72 meters. The length is 6 meters longer than
twice the width. Find the dimensions of the garden.
P = 2L + 2W
P = 72
L = 12W (that's an odd way to put it -- 6x 2x)
P = 2(12W) + 2W
P = 24W + 2W
72 = 26W
W = 2.769
an ice cream shop sells small and large sundaes . one day, 30 small sundaes and 50 large sundaes were sold for $420.another day, 15 small sundaes and 35 large sundaes were sold for $270. sales tax is included in all prices .
Using equation, the cost of small sundae and large sundae are 4 dollars and 6 dollars respectively.
How to solve for the cost of small and large sundae that were sold?The ice cream shop sells small and large sundaes .
One day, 30 small sundaes and 50 large sundaes were sold for $420. Another day, 15 small sundaes and 35 large sundaes were sold for $270.
Therefore,
let
x = cost of each small sundae
y = cost of each large sundae
Therefore,
30x + 50y = 420
15x + 35y = 270
multiply equation(ii) by 2
30x + 50y = 420
30x + 70y = 540
subtract equation(i) from equation(ii)
20y = 120
y = 120 / 20
y = 6
Hence,
30x + 50(6) = 420
30x + 300 = 420
30x = 420 - 300
30x = 120
x = 120 / 30
x = 4
Therefore,
cost of small sundae = 4 dollars
cost of large sundae = 6 dollars
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What graph represents the system of linear inequalities? y>3x+1 y≤−2x−4
Answer:
Step-by-step explanation:
y>3x+1
y≤-2x-4
For each set of points below, determine the distance between them using the distance formula. each answer in this problem will be an integer
Distance between two coordinates:
[tex]\text{ Distance=}\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Given point: b) (10, -5) and ( -6, 7)
[tex]x_1=10,y_1=-5,x_2=-6,y_2=7[/tex]Substitute the value in the expression of distance formula
[tex]\begin{gathered} \text{ Distance=}\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{Distance}=\sqrt[]{(-6-10)^2+(7-(-5))^2} \\ \text{Distance}=\sqrt[]{(-16)^2+(12)^2} \\ \text{Distance}=\sqrt[]{256+144} \\ \text{Distance}=\sqrt[]{400} \\ \text{Distance = 20 unit} \end{gathered}[/tex]The distance between coordinates (10,-5) & (-6,7) is 20 unit
Gary applied the distributive property using the greatest common factor to determine the expression that is equivalent to 66 + 36. His work is shown below.
Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
66 + 36 = 3 (22 + 12)
What statement best describes Gary’s error?
Gary did not use correct factors for 66 in the equation.
Gary did not use correct factors for 36 in the equation.
Gary did not use two equivalent expressions in the equation.
Gary did not use the greatest common factor in the equation. pls hurry 10 mins left
A statement which best describes Gary’s error is that: Gary did not use correct factors for 66 in the equation.
What is the distribution property of multiplication?The distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a given numerical value or factor, the same output would be produced as when each addend is multiplied respectively by the numerical value or factor, and the products are added together.
Mathematically, the distributive property of multiplication is given by this expression:
a(b + c) = ab + ac.
Also, the correct greatest common factor of 66 and 36 is given by:
Greatest common factor (GCF) = 6
By applying the distributive property of multiplication, we have:
66 + 36 = 6(11 + 6)
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For each equation, determine whether it shows a direct variation (that is, shows directly proportional variables).If it does, find the constant of variation and write it in simplest form.-Click on Picture for the questions! More understandable-
(a) 2y=8x
[tex]\begin{gathered} 2y=8x \\ y=\frac{8x}{2} \\ y=4x\Rightarrow y=kx\Rightarrow y\propto x\text{ \lbrack}direct\text{ }variation] \\ k=4 \end{gathered}[/tex](b) 7x=-2y-7 [ not direct variation ]
[tex]\begin{gathered} 7x=-2y-7 \\ 7x+7=-2y \\ 7(x+1)=-2y \\ (x+1)=\frac{-2y}{7} \\ x=\frac{-2y}{7}-1 \end{gathered}[/tex]We couldn't express in the form x=ky , hence variation is not direct. OR we can say we couldn't express in the form y=kx ....hence variation is not direct
what percentage grade should a road have if the angle of elevation of the road is 44 degrees? (the percentage grade is defined as the change in the altitude of the road over a 100100 -foot horizontal distance. for example a 5%5% grade means that the road rises 55 feet for every 100100 feet of horizontal distance.)
For a 44° elevation angle, the grade will be 96%.
Given that,
if the angle of elevation of the road is 44 degrees,
The difference in the road's altitude over a horizontal distance of 100 feet is what is referred to as the percentage grade. For instance, a road with a 5% slope will rise 5 feet for every horizontal 100-foot distance.)
A tangent ?
One of the six basic trigonometric functions is tangent, denoted as tan().
The ratio of the opposite side length to the adjacent side length is the definition of the tangent value of the one sharp angle,, in a right triangle.
[tex]tan \alpha = sin\alpha /cos \alpha[/tex]
The tangent of the angle is the ratio of rise to run.
tan(angle) = grade
tan(44°) ≈ 0.96 = 96%
Therefore, The grade will be 96% for an angle of elevation of 44°.
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Question 1
A triangle has sides of length 2 cm, 8 cm and 9 cm.
Calculate the value of the largest angle in this triangle.
Answer: You have to use a calculator
Step-by-step explanation:
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if the flow rate in an artery has been reduced to 8.5% of its normal value by a blood clot and the average pressure difference has increased by 20.5%, what percent of the original is the radius of the reduced artery?
Percent of the original is the radius of the reduced artery is 0.070 times the original radius.
Given that,
A blood clot has lowered the flow rate in an artery to 8.5% of its usual value, and the average pressure difference has increased by 20.5%.
p1 = 8.5 % ,
p2 = 20.5 %
The equation is using here is From Poiseuille's equation
Q = \Delta p \pi r4 / 8 \eta L
now
Q1 = \Delta p1\pi r14 / 8 \eta L
and
Q2 = \Delta p2\pi r24 / 8 \eta L
Q1 = \Delta p1\pi r14 / 8 \eta L / Q2 = \Delta p2\pi r24 / 8 \eta L
Q1 / Q2 = \Delta p1 ro4 / \Delta p2 r24
r24 = ( 0.085 Q1 / Q1 ) ( \Delta p1 / \Delta p1 + 0.20 \Delta p1 ) ro4
r24 = 0.085 X ( 1 / ( 1 + 0.20 ) ro4
r2 = 0.070 ro
As a result, the shortened artery's radius is 0.070 times its original radius, or percent of the original.
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Given the information above, what is the size of the wedge to the nearest whole degree foraqua pencils?options:55°12°61°43°
the size of the wedge for aqua pencils is 43°
Explanation:Given:
A table showing the pencil collection
To find:
the portion that represents the aqua pencils in degree
The total number of pencils = 23 + 106 + 62 + 47 + 32
The total number of pencils = 270
In degrees:
Total angle in a circle = 360°
Size of the wedge for aqua = number of aqua pencils/total pencils × 360°
[tex]\begin{gathered} Size\text{ of the wedge = }\frac{32}{270}\text{ }\times360° \\ \\ Size\text{ of the wedge = 42.67\degree} \end{gathered}[/tex]To the nearest degree, the size of the wedge for aqua pencils is 43°
the dial on a combination lock contains markings which represent the numbers from 0 to 39. how many 3- number combinations are possible if the first and the second must be different odd numbers, while the third number must not be an odd number?
The dial for the standard combination lock is fastened to a spindle. The spindle travels through many wheels and a drive cam inside the lock. Every number has one wheel, hence the number of wheels in a wheel pack depends on how many numbers are in the combination.
The lock uses the numbers 0 to 39 and has 64,000 distinct combinations.
How many possible three-number combinations are there?
You have 10 options for the first digit, 9 options for the second digit, and 8 options for the third digit, giving you 10x9x8 = 720 if you want all three possible numbers with no duplication of the digits.
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Given the costs for several of the same grocery items in two countries, find the rate of the total cost for these items in the United Kingdom to that of the total cost of
items in Australia.
Using ratios and assuming the given values, the rate of the total cost for items in the United Kingdom to that of the total cost of items in Australia is 2/3.
How do you calculate the ratio?A ratio shows how often one number is contained in another. The ratio of oranges to lemons, for instance, is eight to six if there are eight oranges and six lemons in a bowl of fruit.The ratio of oranges to all fruits is 8:14, whereas the ratio of lemons to oranges is 6:8.A ratio is a comparison of two items when it is expressed in numbers or amounts. For instance, the boy-to-girl ratio in a room with 10 males and thirty girls is 1:3, or one to three.Assume that the costs are:
United Kingdom = 10.78Australia = 21.23The ratio would be:
Ratio = United Kingdom: AustraliaSo, we have:
Ratio = 10.78:21.23Simplify:
Ratio = 2 : 3Express as rate
Rate = 2/3Therefore, using ratios and assuming the given values, the rate of the total cost for items in the United Kingdom to that of the total cost of items in Australia is 2/3.
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pls help me asap! due in 30 minutes :(
Answer:
(x+6)+x=20 Andy
Step-by-step explanation:
X represents Andy
X+6 represents juana who did 6 more problems
(X+6)+x=20
2x+6=20
2x=14
X=7
B. Write S if the expression is a sum of two cubes, D if a difference of two cubes, and N if neither.
1. 27x⁶ + y³=
2. 81 - b¹⁵=
3. 64x³ - 9z⁹=
4. 36m¹² - n⁶
5. 1 - d¹²=
6. 729 - y²⁹=
7. 343 - y⁶=
8. 4x³ + 8 =
9. 144 -125y² =
10. 64j⁶- k⁹=
Answers:
SNNNDNDNND==========================================================
Explanation:
Question 1
27x^6 = (3x^2)^3 which is one cube and y^3 is another cube
Therefore 27x^6+y^3 is a sum of two cubes.
It might help to think of it like A^3+B^3 where in this case A = 3x^2 and B = y.
----------------------------------------
Question 2
81 isn't a perfect cube since 81^(1/3) = 4.3267 approximately, which isn't a whole number. We need 81^(1/3) to be a whole number if we wanted 81 to be a perfect cube.
We don't even need to check b^15 since 81 being a non-perfect cube means the entire expression cannot be a sum of two cubes, nor a difference of cubes.
----------------------------------------
Question 3
64x^3 = (4x)^3 is a perfect cube
but 9z^9 is not a perfect cube
We can see this if we computed 9^(1/3) and the result is a non-whole number.
The answer here is the same as the previous question.
----------------------------------------
Question 4
36^(1/3) is not a whole number, so 36 isn't a perfect cube. By extension 36m^12 isn't a perfect cube either. The answer is the same as questions 2 and 3.
----------------------------------------
Question 5
1 is a perfect cube since 1 = 1^3
d^12 is a perfect cube because d^12 = (d^4)^3
Therefore, we have a difference of two cubes.
----------------------------------------
Question 6
729^(1/3) = 9 which rearranges to 9^3 = 729, showing 729 is a perfect cube.
However y^29 is not a perfect cube since the exponent 29 is not a multiple of 3.
The overall expression is "neither".
----------------------------------------
Question 7
343^(1/3) = 7 rearranges to 7^3 = 343, showing 343 is a perfect cube
y^6 is a perfect cube since (y^2)^3, i.e. the exponent 6 is a multiple of 3.
We have a difference of cubes.
----------------------------------------
Question 8
4 isn't a perfect cube since 4^(1/3) results in some decimal value that isn't a whole number. The entire expression is neither a sum nor difference of cubes.
----------------------------------------
Question 9
144^(1/3) isn't a whole number, so we get a similar result to problem 8.
----------------------------------------
Question 10
64j^6 = (4j^3)^3 is one cube
k^9 = (k^3)^3 is another cube
We have a difference of cubes
What’s the answer plss
Answer:
B.15.9
Step-by-step explanation:
Trigonometry
7.7/SIN(29)=15.9
Answer:
3.7 cm
Step-by-step explanation:
See attached worksheet
if a child is 120cm tall, but they grow 4% bigger in a year, how tall will they be?
Answer
The height of the child in a year time = 124.8 cm
Explanation
The child is currently 120 cm tall.
The child grows 4% bigger in 1 year.
We now need to calculate how tall the child is in that 1 year.
New height for the child = (Current height) + (Increase in height)
Current height = 120 cm
Increase in height = 4% of 120 cm = 0.04 × 120 = 4.8 cm
New height for the child = (Current height) + (Increase in height)
= 120 + 4.8
= 124.8 cm
Hope this Helps!!!
PLEASE ANSWER ASAP GIVING CROWN (don't know what its called)
Which point is not included in the solution set for the inequality?
(–2, 1)
(1, 3)
(4, 3)
(5, –1)
Answer: The answer is B. At least that is what I think the answer would be.
Step-by-step explanation: I hope this helps.
NEED HELP ASAP THIS IS OVERDUE !!!
Answer:
A
Step-by-step explanation:
The slope goes up by 11 and over by 1.
Answer: D
Step-by-step explanation:
y= [tex]\frac{1}{55}[/tex]×
Part A Write the multiplication expression shown by the model. Do not solve the problem. Part B
Explain the expression written in Part A. Include the final product and how it is shown with the model.
Part A: The multiplication expression is L×w
Part B: The expression is written as N= r+ g + w + b
The final product = 200 boxes
How to determine the expressionIt is crucial to note that the formula for determining the area of a rectangle is expressed as;
Area = lw
Given that;
l represents the length of the rectanglew represents the width of the rectangleThe area can be calculated by multiplying the length and the width and also by then adding the number of boxes.
We have the expression as;
10( 4 + 5 + 4 + 7)
Also,
L × w = r + g + w + b
Hence, we have that L×w is a multiplication expression.
Total number of boxes for the length = 20
Total number of boxes for the width = 10
Total area = L×w = 20×10=200
Number of available red boxes = 46Number of available green boxes = 46Number of available blue boxes = 46Number of available white boxes = 62We have;
N= r+ g + w + b
but r = g = b
Also,
L×B = 3r + w
Hence, a multiplication expression is an expression that has its variables or numbers being multiplied.
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can you help show me the steps to solve this?
Answer:69
Step-by-step explanation8966966969996^996969969969699696996996969699696969699696699696966969669669669669669669669669
Find three consecutive even integers such that one less than four times the third is equal to five more than the sum of the first two.
The three consecutive even integers such that one less than four times the third is equal to five more than the sum of the first two is -4,-2,0.
What is an integer?An integer is a whole number irrespective of the sign that the integer is all whole numbers that are going from 0 to infinite or 0 to minus infinite.
Integer ; ....-2 , -1 , 0 , 1 , 2 , .....
Integers are non-decimal numbers and all integers are rational numbers.
Let's assume that first, even integer is x
Then the second and third will be x + 2,x + 4 respectively.
As per the given,
1 less than 4 times the third → 4(x+4) - 1
It is equal to the 5 more than the sum of x and x + 2
So, x + x + 2 + 5
Therefore, 4(x+4) - 1 = x + x + 2 + 5
4x + 16 - 1 = 2x + 7
4x + 15 = 2x + 7
2x = 7 - 15
x = -4
So integers are -4,-2,0
Hence "The three consecutive even integers such that one less than four times the third is equal to five more than the sum of the first two is -4,-2,0".
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If mDH =(11x + 7) degrees , mGF = (5x + 9) degrees , and mEF = (10x - 22) degrees, find mDH
For this problem we use the arcs and chords theorem we know that
[tex]\begin{gathered} \measuredangle H\text{EF=}\frac{1}{2}(mGF+mDH) \\ \text{Substituting }\measuredangle HEF=10x-22,\text{ mGF=5x+9 and mDH=11x+7 we get} \\ 10x-22=\frac{1}{2}(5x+9+11x+7) \end{gathered}[/tex]Solving for x we get:
[tex]\begin{gathered} 10x-22=\frac{1}{2}(16x+16)=8x+8 \\ 2x=30 \\ x=15 \end{gathered}[/tex]Finally, we substitute x for mDH=(11x+7) degrees=(11*15+7) degrees=172 degrees.
mDH=172 degrees.
Which statement about the data in the table is true?
O The data represent a proportional relationship, and the constant of proportionality is $10.
The data do not represent a proportional relationship, but the rate of change of the data is $5 per shirt.
There is not a constant rate of change for these data.
The data represent a proportional relationship, and the constant of proportionality is $5.
B) The data does not represent a proportional relation, but it has constant rate of change of $5 per shirt.
A)
Take number of T-shirts up to 3 and calculate their proportions.
2/1 = 15/10 = 1.5 (3/2) = 20/15 = 1.33
Clearly the rate of T- shirts is not proportional.
B)
From option (A) we found the given data is not proportional but from the table given in question the rate of change of T- shirts is indeed $5.
C)
No, there is a constant rate of change of $5 as shown in the table below.
D)
No, the data does not represent a constant proportionality. The rate varies.
2/1 = 15/10 = 1.5 (3/2) = 20/15 = 1.33
What is rate of change ?Rate of change is the rate that describes how one quantity changes relative to another quantity. If x is the independent variable and y is the dependent variable, then
rate of change change=change in y / change x
Rate of change can be positive or negative. This corresponds to an increase or decrease in the y-value between two data points. If a quantity does not change over time, it is called zero rate of change.
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Please help me out with this!
Answer:
10
Step-by-step explanation:
I am not absolutely sure but i think that is correct
Think the length of a rectangle is 5 inches longer than its width if the perimeter of the rectangle is 42 inches find it’s area
The area of the rectangle is 104 inches²
Define Area of Rectangle
The area of a rectangle is the space occupied by the rectangle inside its perimeter.
Given that, the perimeter is 42 inches
we know, the formula of perimeter of rectangle = 2(L + W)
so, the first equation will be
2(L + W) = 42
or, 2L + 2W = 42 ----------eq(i)
Next, the length of a rectangle is 5 inches longer than its width, so
L = W + 5
or, L - 5 = W --------------eq(ii)
Now, the eq(i) is
2L + 2W = 42
Put W value from eq(ii),
2L + 2(L- 5) = 42
=> 2L + 2L - 10 = 42
=> 4L - 10 = 42
=> 4L = 52
=> L = 13
We got, L = 13 put this value in any of the equation
I'm putting the value in eq(ii) as it easy for to solve
=> 13 - 5 = W
=> W = 8
If you want to cross verify the values of L and W , then simply put the values in both the equation and LHS = RHS like that
2(13) + 2(8) = 42 (correct)
13 - 5 = 8 (correct)
Now, we got length and width so now just put the values of L and W in area of rectangle formula,
Area of rectangle = Length * width
= 13 * 8
Area of rectangle = 104 inches²
Hence, The area of the rectangle is 104 inches²
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can someone help me understand the working of how to get the answer??
A) The ingredient she needed = Fruit juice = 21 litres
Lemonade = 14 litres
B) The extra punch she can make = 20litres
C) The ratio of fruit juice and lemonade for second batch = 7:6
What is Ratio?
A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. Similarly, the ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8.
A)
Let 3x be fruit juice and 2x be the lemonade
3x + 2x = 35litres
5x = 35
x = 35/5
x = 7
Then, required ingredient she needed
Fruit juice = 3x7 = 21 litres
Lemonade = 2x7 = 14 litres
B)
According to question
The amount of fruit juice she had = 12litre
Let x be 12litre
as we know that the ratio of fruit juice to the lemonade is 3 : 2
Thus,
Fruit juice = 3(x) = 12 litres
x = 12/3
x = 4
Fruit juice = 3 x 4 = 12litres
putting the value in lemonade
Lemonade = 2(4) = 8 litres
So, The extra punch she can make :
12 + 8 = 20litres
C)
The ratio for new second batch she added 4litres in lemonade
Then it become :
Fruit juice = 21 litres
Lemonade = 14 litres + 4litres = 18
The ratio will be
21:18
7:6
Thus, the ratio of fruit juice to lemonade in second batch will be 7:6
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ALTAThe graph shown compares the rent Andrew and Dave pay for renting bikes from different stores,Andrew's and Dave'sBike Rentalsу13DaveAndrew11Rent Paid (dollars)2319117HoursAfter how many hours would the amount Andrew and Dave pay for the rentals be equal?
We have the following:
The first thing is to calculate the equation by means of the graph.
For Andrew, we can see that he starts at $ 3 and every hour that passes, he charges $ 2, therefore the equation is:
[tex]y=3+2x[/tex]where x is the number of hours.
For Dave, we can see that he starts at $ 6 and every hour that passes, he charges $ 1.5, therefore the equation is:
[tex]y=6+1.5x[/tex]where x is the number of hours.
to calculate the number of hours when the value is equal, we must match the equations like this
[tex]\begin{gathered} 3+2x=6+1.5x \\ 2x-1.5x=6-3 \\ 0.5x=3 \\ x=\frac{3}{0.5}=6 \end{gathered}[/tex]Which means that at 6 hours they have the same price
you constructed a pairwise ranking of four events w, x, y, and z and came up with the following assessment: x is more likely than z y is more likely than x w is more likely than x what needed information is missing that prevents you from completing this analysis?
The relation between the events Y and W prevents us from completing the analysis.
The relation between the events Y and W prevents us from completing the analysis.
Case 1: W is more likely than Y then we have the following analysis:
Z, X, Y, and W are arranged in ascending order of more likeliness.
Case 2: Y is more likely than W then we have the following analysis:
Z, X, W, and Y are arranged in ascending order of more likeliness.
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Which of the following values are solutions to the inequality 9 ≤ -7+ 4x?
I. - 4
II. O
III. 4
Answer: Inequality Form: x ≥ 4
lll. 4
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Answer:
Your answer is x ≥ 4
Step-by-step explanation:
a) Simplify both sides of the inequality.
9 ≤ 4x − 7
b) Flip the equation.
4x − 7 ≥ 9
c) Add 7 to both sides.
4x − 7 + 7 ≥ 9 + 7
4x ≥ 16
d) Divide both sides by 4.
4x/4 ≥ 14/4
x ≥ 4
A jet ski rental charges a flat rate of $75, plus an additional $10 per hour. You only have $200 to spend. How many hours can you rent the jet ski?
PLS HELP ME
Answer:
12.5 hours
Step-by-step explanation:
The flat rate is the base, in which no matter how long you rent it for, they'll still charge you that much. You have 200 dollars, and negative 75 is 125 dollars, which you can spend on the hours. Assuming you can rent the jet ski for half an hour, you can divide 125 by 10 for the amount of hours, and the answer is 12.5 hours. However, if you can't rent the jet skis for half an hour, the answer is 12 hours.
