Members of the Lake Shawnee Club pay $40 per summer season plus$7.50 each time they rent a boat. Nonmembers pay $12.50 each timethey rent a boat. How many times would both a member and anonmember have to rent a boot in order to pay the same amounts
Answers
Answer: The number of times that a member has to rent a boat is 3 and a nonmember is 5 in order for them to pay the same amounts.
Explanation:
Let x be the number of times that a member rents a boat and y the number of times that a nonmember rents a boat, then we set the following equations:
[tex]\begin{gathered} C_m=7.50x+40. \\ C_n=12.50y\text{.} \end{gathered}[/tex]If they pay the same amounts, then:
[tex]7.50x+40=12.50y\text{.}[/tex]Solving for y:
[tex]\begin{gathered} y=\frac{7.50x}{12.50}+\frac{40}{12.50}\text{.} \\ y=\frac{3}{5}x+\frac{16}{5.}\text{.} \end{gathered}[/tex]Multiplying the last equation by 5 we get:
[tex]5y=3x+16[/tex]An integer solution to the above equation is x=3 and y=5.
Related Questions
List the domain and Range, and determine if it's a funtion or not
Answers
The graph is a function
Explanation:The domain are the x values of a function. They are the input of the function
From the graph, following the x axis:
The arrow on the line indicates it doesn't end.
As a result, it moves from negative infinity to positive infinity
[tex]Domain\colon(-\infty,\text{ }\infty)[/tex]Range are the y values of the function. They are the output of a function
From the graph, following the y axis:
the line starts from y = -3 towards the positive side of y axis.
Since there is an arrow on the line pointing upwards towards the y axis, it indicates positive infinity.
[tex]\text{Range = (-3, }\infty)[/tex]For it to be a function, the input will have only one output:
Each of the x values (input) gives only one y value (output)
The graph is a function
Please help me on number one It’s all one question
Answers
Given:
[tex]f(x)=2x^2+12x+10[/tex]a) Standard form of the function is,
[tex]\begin{gathered} f(x)=2x^2+12x+10 \\ f(x)=2(x^2+6x+5+9-9) \\ f(x)=2(x^2+6x+9-4) \\ f(x)=2(x+3)^2-8 \end{gathered}[/tex]Standard form is,
[tex]f(x)=2(x+3)^2-8[/tex]b) The vertex of the given function
The vertex of the parabola having form,
[tex]\begin{gathered} y=ax^2+bx+c \\ \text{Vertex}=\frac{-b}{2a} \\ f(x)=2x^2+12x+10 \\ \text{Vertex}=\frac{-b}{2a}=\frac{-12}{2(2)}=-\frac{12}{4}=-3 \\ \text{Put x=-3 in }f(x)=2x^2+12x+10 \\ f(x)=2(-3)^2+12(-3)+10=18-36+10=-8 \end{gathered}[/tex]Vertex is ( -3,-8)
c) x and y-intercept is,
[tex]\begin{gathered} Set\text{ y=0 that means f(x)=0} \\ f(x)=2x^2+12x+10 \\ 2x^2+12x+10=0 \\ 2(x^2+6x+5)=0 \\ x^2+6x+5=0 \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a},a=1,b=6,c=5 \\ x=\frac{-12\pm\sqrt{12^2-4\cdot\:2\cdot\:10}}{2\cdot\:2} \\ x=\frac{-12\pm\: 8}{4} \\ x=-1,x=-5 \end{gathered}[/tex]x- intercepts are (-1,0) and (-5,0).
For y-intercept , set x=0
[tex]\begin{gathered} f(x)=2x^2+12x+10 \\ y=2x^2+12x+10 \\ y=2(0)+12(0)+10 \\ y=10 \end{gathered}[/tex]y-intercept is (0,10)
d) the graph of the function is,
e) The domain and range of the function is,
[tex]\begin{gathered} \text{For range of the function f(x)=ax}^2+bx+c\text{ with vertex (x,y)} \\ \text{If a}<0\text{ range is }f(x)\leq y \\ \text{If a>0, range is f(x)}\ge\text{y} \end{gathered}[/tex]For the given function,
[tex]\begin{gathered} f(x)=2x^2+12x+10\text{ with vertex (-3,-8)} \\ a=2>0,\text{ range is f(x)}\ge\text{-8} \\ \text{Domain is -}\inftyTherefore,[tex]\begin{gathered} \text{Domain of f is (-}\infty,\infty) \\ \text{Range of f is \lbrack-8,}\infty) \end{gathered}[/tex]write an equation in point slope form of the line that passes through the given points or with the given characteristics
Answers
The equation of a line in point-slope form is
[tex](y-y_1)=m(x-x_1)[/tex]At m = -2 and (-3 , 5) we have,
[tex]\begin{gathered} (y-5)=-2(x--3) \\ (y-5)=-2(x+3) \end{gathered}[/tex]That is the equation in point-slope form.
Jack had a box Good and plenty candy. The ratio of pink to white candy's was 5:7 If Jack buys a bigger bag of candy with the same pink to white ratio and a total of 120 candies, how many candy's are white?
Answers
Thus, the number of white candies are:
[tex]\begin{gathered} \frac{7}{12}\times120 \\ 7\times10=70\text{ candies} \end{gathered}[/tex]Hence, there are 70 white candies in the bigger bag
Choose the inequality that represents this situation. During a summer afternoon, the water in the tank was used at a rate of 300 gallons per hour. During the winter the rate was less than half that. How many gallons were used in h hours on February 3rd? A f < ½ x (300 x h)B f ≤ ½ x (300 x h)C ½ x f < (300 x h)D f > ½ x (300 x h)
Answers
f < ½ x (300 x h)
f is the number of gallons used
since it was stated that it was less than. we will use the symbol <
Identify the rational function whose graph is given below. The y-intercept is (0,−1/2).
Answers
The numerator relates to the x-intercepts:
(-1,0) means (x+1) is a factor in the numerator.
The denominator relates to the vertical intercepts:
x = -2 as a VA means (x+2) is a factor in the denominator.
x = 1 as a VA means (x-1) is a factor in the denominator.
Since the x-intercept crosses and the VA's are "one up, one down", we know these all have odd multiplicities.
So, we think the function could be [tex]r(x) = \dfrac{x+1}{(x+2)(x-1)}[/tex]
Checking the y-intercept with this function
[tex]r(0)= \dfrac{0+1}{(0+2)(0-1)} = \dfrac{1}{-2}=-\dfrac{1}{2}[/tex]
This checks out. That's your function: [tex]r(x) = \dfrac{x+1}{(x+2)(x-1)}[/tex]
A cyclist rode for 3.5 hours and completed a distance of 60.9 miles. If she kept the same average speedfor each hour, how far did she ride in 1 hour?Part AEstimate the quotient. Include an equation to show your work. Explain your thinking.Math symbols+.808(.)O=<>+$?Part BFind the exact distance she rode in 1 hour by completing the division Enter the answer in the box10 of 14 Answered
Answers
We know that the cyclist rode for 3.5 hours and completed a distance of 60.9 miles.
We can estimate the average speed as the quotient between the distance and the time:
[tex]\bar{v}=\frac{d}{t}=\frac{60.9\text{ miles}}{3.5\text{ hours}}[/tex]We have now to estimate the distance she will ride in one hour.
We can estimate the average speed as:
[tex]\frac{60.9}{3.5}\approx\frac{60\cdot2}{3.5\cdot2}=\frac{120}{7}\approx17[/tex]She will ride 17 miles in an hour.
If we solve the quotient 60.9 / 3.5 with a calculator, we get 17.4 miles per hour.
Answer:
a) We can estimate that she will ride 17 miles in an hour.
b) 17.4 miles per hour.
Answer:
17.4
Step-by-step explanation:
How do you know when to factor a negative square root number and when to just find it’s imaginary number
Answers
sqrt(-44)
This has a perfect square inside the square root
4 is a perfect square
sqrt(-1 * 4 * 11)
sqrt(-1) sqrt(4) sqrt(11)
We know the square root of 4 is 2
2 sqrt(11) sqrt(-1)
2 sqrt(11) i
sqrt(-30)
sqrt( 6*5* -1)
There is no perfect square for 30
Another example with a perfect square inside would be
sqrt(-54)
sqrt( -1 * 27*2)
sqrt( -1 * 9 *6)
9 is a perfect square
sqrt( -1) * sqrt(9) sqrt(6)
3 i sqrt(6)
Try to break down larger numbers and see if there is a perfect square that is a factor
If a sample mean is 96, which of the following is most likely the range ofpossible values that best describes an estimate for the population mean?A. (82, 114)B. (76,108)O C. (78, 110)D. (80, 112)
Answers
Ok! I understand.
So, we have to find the average of each option between these points.
Let's start with A.
Average will be: (82+114)/2 which is equal to 98.
98 is not equal to 96, so that's not the answer.
Let's see B.
Average will be (76+108)/2 which is equal to 92.
92 is not equal to 96, so that's not the answer.
Let's see C.
Which of the following is the inverse of f(x) = - 19x + 13?OA.− 19 (x − 13)f¹(x) =OB. f¹(x) = 19 (x − 13)-OC. f-¹(x) = 130219OD. f¹(x) = x+1319
Answers
Step 1
Given;
Step 2
[tex]\begin{gathered} y=f(x) \\ Thus, \\ y=-19x+13 \\ \mathrm{A\:function\:g\:is\:the\:inverse\:of\:function\:f\:if\:for}\:y=f\left(x\right),\:\:x=g\left(y\right)\: \\ replace\text{ y with x and x with y} \\ x=-19y+13 \end{gathered}[/tex]Solve for y
[tex]\begin{gathered} 19y=13-x \\ \frac{19y}{19}=\frac{13-x}{19} \\ y=\frac{13-x}{19} \\ f^{-1}(x)=\frac{13-x}{19} \end{gathered}[/tex]Answer; Option C
[tex]f^{-1}(x)=\frac{13-x}{19}[/tex]Identify the independent and dependent variable of the following graph. Indicate whether the graph rises, faconstant.wAnnual gross income in relation to number of years.Annual Income
Answers
Given data:
The given graph.
The annual can can be written as,
[tex]\text{Annual income =f(time)}[/tex]The independent variable is time, the dependent variable is Annual income.The annual income graph rises steadily then drop off sharply before begining to rise again.
Thus, the option (d) is correct.
This is one practice problem that I need help on It asks to solve logarithmic equations, and It includes a question within it. Please note that this is a lengthy problem. & I have enlarged the equations for better view.
Answers
The Solution:
We are required to solve each of the following logarithmic equations:
a.
[tex]\begin{gathered} 1.\text{ }\log _464=m \\ \text{cross multiplying, we get} \\ 64=4^m \\ 4^3=4^m \\ m=3 \end{gathered}[/tex][tex]\begin{gathered} 2.\text{ }\log _8n=3 \\ \text{Cross multiplying, we get} \\ n=8^3=512 \end{gathered}[/tex][tex]\begin{gathered} 3.\text{ }\log _p4096=3 \\ \text{Cross multiplying, we get} \\ 4096=p^3 \\ \text{ Equalising the base in both sides, we get} \\ 16^3=p^3 \\ 16=p \\ p=16 \end{gathered}[/tex][tex]\begin{gathered} 4.\text{ }\log _{32}q=3 \\ \text{cross multiplying, we get} \\ q=32^3=32\times32\times32=32768 \end{gathered}[/tex]b.
Given the equation below:
[tex]\log _{4^x}2^a=3[/tex]We are required to express a in terms of x.
[tex]\begin{gathered} \log _{4^x}2^a=3 \\ \text{Cross multiplying, we get} \\ 2^a=(4^x)^3 \\ \text{Equalizing the base, we get} \\ 2^a=(2^{2x})^3 \\ 2^a=2^{6x} \\ a=6x \end{gathered}[/tex]Find the derivative of y=3x/(x^2 + 1)
Answers
To find the derivative of
[tex]y=\frac{3x}{x^2+1},[/tex]we will use the division rule for derivatives.
The division rule states that:
[tex](\frac{f(x)}{g(x)})^{\prime}=\frac{f^{\prime}(x)g(x)-g^{\prime}(x)f(x)}{g(x)^2}.[/tex]Therefore, the derivative of the given quotient is:
[tex]y^{\prime}=\frac{(3x)^{\prime}(x^2+1)-(x^2+1)^{\prime}(3x)}{(x^2+1)^2}.[/tex]Simplifying the above result we get:
[tex]\begin{gathered} y^{\prime}=\frac{3(x^2+1)-(2x\cdot3x)}{(x^2+1)^2}=\frac{3(x^2+1)-6x^2}{(x^2+1)^2}=\frac{3(x^2+1-2x^2)}{(x^2+1)^2} \\ =\frac{3(1-x^2)}{(x^2+1)^2}. \end{gathered}[/tex]Answer:
[tex]y^{\prime}=\frac{3(1-x^2)}{(x^2+1)^2}.[/tex]Find - 34 + 21 - 39 - ( - 3 )
Answers
-49
Explanation:[tex]-34\text{ + 21 - 39 -(-3)}[/tex]Expanding the parenthesis:
[tex]\begin{gathered} mu\text{ltiplication of asme sign gives a positive number:} \\ -34\text{ + 21 - 39 + 3} \end{gathered}[/tex]simplify:
[tex]\begin{gathered} =-34\text{ - 39 + 21 + 3} \\ -34\text{ - 39 = - 7}3 \\ 21\text{ + 3 = 24} \end{gathered}[/tex][tex]\begin{gathered} -39\text{ - 39 + 21 + 3 = -73 + 24}| \\ =\text{ }-49 \end{gathered}[/tex]OOnly question 4For questions 1 – 5, answer the questions about triangles.**When answers are not a whole number, please write the exact answer (radical form) AND a decimal approximation**
Answers
SOLUTION:
Case: Trigonometry
Method:
Step 1: Start with the diagram
From te diagram above, theline representing the altitude sis a perpendicular bisector.
We will aply Pythagoras' therrem to solve the problem ioffindin g 'h'
Step 2:
[tex]\begin{gathered} 11^2+h^2=22^2 \\ 121+h^2=484 \\ h^2=484-121 \\ h^2=363 \\ h=\sqrt{363} \\ h=\sqrt{121\times3} \\ h=11\sqrt{3}(exact\text{ }value) \\ h=19.05(2\text{ }decimal\text{ }places) \end{gathered}[/tex]Final answer:
[tex]\begin{gathered} h=11\sqrt{3}(exact\text{ }value) \\ h=19.05(2\text{ }dp) \end{gathered}[/tex]Write the fraction as a percent. Round to the nearest tenth of a percent if necessary.7/11A) 63.6%B) 57.8%C) 6.4%D) 110%
Answers
To express a fraction as a percent, divide the numerator by the denominator, then multiply by 100.
7 / 11 = 0.636
0.636 x 100 = 63.6 %
Answer:
A) 63.6 %
Explain how the Quotient of Powers Property was used to simplify this expression. 5 to the fourth power, over 25 = 52By simplifying 25 to 52 to make both powers base five and subtracting the exponentsBy simplifying 25 to 52 to make both powers base five and adding the exponentsBy finding the quotient of the bases to be one fifth and cancelling common factorsBy finding the quotient of the bases to be one fifth and simplifying the expression
Answers
We need to know how the given expression was simplified.
"5 to the fourth power, over 25 = 52":
[tex]\frac{5^4}{25}[/tex]First, we need to convert 25 into a number with power
5²= 25
Then:
[tex]\frac{5^4}{5^2}[/tex]Simplify by subtracting exponents:
[tex]\frac{5^{4}}{5^{2}}=5^4\ast5^2=5^{4-2}=5^2[/tex]Hence, we used the first option method.
The correct answer is the first one.
Which inequality is true?O A /> 2B. 7 +8 < 11C. 37 > 9D. 21 – 1 < 5SUBMIT
Answers
Verify eact option
Option A
we have
pi/2 > 2
remember that
pi=3.14
so
pi/2=1.57
1.57 > 2 -------> is not true
Option B
we have
pi+8< 11
3.14+8 < 11
11.14 < 11 ------> is not true
Option C
we have
3pi > 9
3(3.14) > 9
9.42 > 9 -------> is true
Option D
we have
2pi-1 < 5
2(3.14)-1 < 5
5,28 < 5 ------> is not true
Shane made a scale drawing of a hotel. A room in the hotel, which is 18 feet wide in real life, is 51 inches wide in the drawing. What is the scale of the drawing?17 inches :____Feet
Answers
We know that 18 feet in real life are 51 inches in the drawing. And we must find hoy many feet are 17 inches
We can write the next equation for the situation
[tex]\frac{18\text{feet}}{51\text{inches}}=\frac{\text{x }}{17\text{ inches}}[/tex]Then, we must solve it for x
[tex]x=\frac{18\text{ feet }\cdot17\text{ inches}}{51\text{ inches}}=6\text{ feet}[/tex]Finally, the answer is
17 inches : 6 Feet
A farm has 5 brown cows and 10 white cows. A fence is open and a cow escapes. What is the probobility that it will be a brown cow? A. 50%B.1/2C.33%D.20%
Answers
A farm has 5 brown cows and 10 white cows
Total of cows:
[tex]5+10=15[/tex]Probability is represented by:
[tex]P=\frac{NU\text{MBER OF FAVOURABLE OUTCOMES}}{\text{TOTAL NUMBER OF FAVOURABLE OUTCOMES}}[/tex]So, the probability of a brown cow escapes:
[tex]\begin{gathered} P=\frac{5}{15}=0.33\text{ (decimal form)} \\ P=0.33\cdot100=33\text{ percent} \end{gathered}[/tex]Solve equation: 2x^2-50=0
Answers
Given:
[tex]2x^2-50=0[/tex]To solve for x:
[tex]\begin{gathered} 2x^2-50=0 \\ 2x^2=50 \\ x^2=25 \\ x=\pm5 \end{gathered}[/tex]Hence, the solution is x=-5, 5.
Answer:
[tex]x=[/tex] ± [tex]5[/tex]
Step-by-step explanation:
[tex]2x^{2} -50=0[/tex]
[tex]2x^{2} =50[/tex]
[tex]x^{2} =\frac{50}{2}[/tex]
[tex]x^{2} =25[/tex]
[tex]x=\sqrt{25}[/tex]
[tex]x=[/tex] ± [tex]5[/tex]
There are 2 solutions for x: 5 positive and 5 negative. If you square them they result in 25
Hope this helps
how would I find slope
Answers
the formula to find a slope between two points is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]if the equation of a line is given
y = mx +c
then m is the slope of the line.
simplify 3x squared minus 6x plus 12 minus 6x plus 10
Answers
Given:
[tex]3x^2-6x+12-6x+10[/tex]Let's simplify:
Collect like terms and evaluate
[tex]3x^2-6x-6x+12+10[/tex][tex]3x^2-12x+22[/tex]ANSWER:
[tex]3x^2-12x+22[/tex]Graph -9x + 5y = 45. Intro y Unit Test skills 9 8+ 7+ 6 CO 5 4 3 No 1 1 х -9-8-7 -6 -5 -4 -3 -2 1 2 3 4 5 6 7 8 9 -2 -3 -4 -5 -6 -7 -8 -9
Answers
Here, we want to graph the given line
Firstly, we write the equation in the standard form
The standard form is;
[tex]y\text{ = mx + b}[/tex]where m represents the slope and b is the y-intercept
We have this as;
[tex]\begin{gathered} 5y\text{ = 9x + 45} \\ \text{divide through by 5} \\ y\text{ = }\frac{9}{5}x\text{ + }\frac{45}{5} \\ \\ y\text{ = 1.8x + 9} \end{gathered}[/tex]we have the y-intercept, this is 9, so we mark the point (0,9)
What is left is to get the possible x-intercept
As the value of y at this point is zero
We have it that;
[tex]\begin{gathered} 0\text{ = 1.8x + 9} \\ 1.8x\text{ = -9} \\ x\text{ = }\frac{-9}{1.8} \\ x\text{ = -5} \end{gathered}[/tex]The x-intercept is -5, which in the coordinate form is (-5,0)
So, by joining the points (-5,0) and (0,9), we have the graph of the line
A plot is shown below;
Why must the first and last term of a perfect square trinomial be both positive?
Answers
Given:
The objective is to provide the reason for first and last term of a perfect square trinomial be both positive
Explanation:
Consider the following equations,
[tex]\begin{gathered} (a+b)^2=(+a)^2+2(a)(b)+(+b)^2\text{ . . . . . . . (1)} \\ (a-b)^2=(+a)^2+2(a)(b)+(-b)^2\text{ . . . . . . . (2)} \\ (-a+b)^2=(-a)^2+2(a)(b)+(+b)^2\text{ . . . . . . . (3)} \end{gathered}[/tex]From equations (1), (2) and (3), the first and last term are always perfect squares. So, even when those numbers are negative integer, square of the number will get converted into poitive integer.
Hence, the first and the last term of a perfect square trinomial must be positive.
Write an equivalent unit rate to eating 4 hot dogs in 1/3 of a minute
Answers
To write an equivalent unit rate, we have to divide the number of hot dogs by the number of minutes, as follows:
[tex]\frac{4\text{ hot dogs}}{\frac{1}{3}\text{ minutes}}=3\cdot4\frac{\text{ hot dogs}}{\text{ minute}}=12\frac{\text{ hot dogs}}{\text{ minute}}[/tex]help me find the slope plss
Answers
the perimeter of a rectangle is 54 inches the length is three more than twice the width what are the dimensions of the rectangle
Answers
Perimeter of a rectangle = (2x length) + ( 2 x width)
if the length is 3 more than twice the width then
length = 3 +( 2x width)
substituting for the perimeter which is given as 54 inches and the length derived as above in to the equation for the perimeter. we have
54 = 2(3+(2 x w)) + 2w
54 = 6 +4w +2w
54 =6 +6w
6w = 48
6w/6 = 48/6
w = 8 inches
Substituting for w in the equation for length gives us
length = 3 + (2 x8)
L= 3+16
L = 18 inches
The dimesnsions of the rectangle are therefore
W = 8 inches
and
L = 18 inches
A line connects points A and B as shown below. If a third point, C, is plotted six units to the right of point B, what will be the area of the resulting right triangle?O 48O 24O 30O 18
Answers
ANSWER
EXPLANATION
We are given the two points A and B connected by a line.
A third point C is plotted 6 units to the right of B.
So, we have:
Use the given scale factor and the side lengths of the scale drawing to determine the side lengths of the real object. Scale factor: 2:1 5 in 10 in 6 C с 13 in Scale drawing Object O A. Side a is 11 inches long, side bis 8 inches long, and side cis 3 inches long. O B. Side a is 26 inches long, side bis 20 inches long, and side cis 10 inches long. O C. Side a is 2.5 inches long, side bis 5 inches long, and side cis 6.5 inches long. D. Side a is 15 inches long, side bis 12 inches long, and side 7
Answers
If the scale factor is 2: 1
a = 5/2 = 2.5 inches
b = 10/2 = 5 inches
c = 13/5 = 6.5 inches