The rate of the current is 2.03 mph if the small motorboat travels 8mph in still water. It takes 3 hours longer to travel 44 miles going upstream than it does going downstream.
What is a quadratic equation?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] Where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
Let's suppose the rate of the current = r
The time it takes to go downstream + 4 hours = time to go upstream
As we know the:
[tex]\rm Time = \dfrac{Distance}{ Rate }[/tex]
Now,
[tex]\rm \dfrac{44}{ (8 + r)} + 3 = \dfrac{44}{ (8 - r)}[/tex]
After solving:
[tex]\rm \dfrac{44}{ (8 - r)}-\dfrac{44}{ (8 + r)} =3[/tex]
After cross multiplication
44(8+r) - 44(8-r) = 3(8+r)(8-r)
88r = 3(64 - r²)
3r² + 88r - 192 = 0
After solving the above quadratic equation, we get:
r = 2.03 or
r=−31.37 (reject as it is negative)
So, the r =2.03 mph
Thus, the rate of the current is 2.03 mph if the small motorboat travels 8mph in still water. It takes 3 hours longer to travel 44 miles going upstream than it does going downstream.
Learn more about quadratic equations here:
brainly.com/question/2263981
#SPJ1
Anyone know what -8x-y=5 ; y=x+4 is using yhe subtraction method? Please explain to! would help greatly
Answer:
The answer would be x = -1 and y = 3
Step-by-step explanation:
Work is as shown:
1) -8x - y = 5
y = x + 4
2) -8x - (x+4) = 5
3) -8x -x = 9
4) -9x/-9 = 9/-9
5) y = -1 + 4 = 3
If there are any questions or if i didn't answer the question reply with the question please.
Find the area of the composite figure. First, find the area of the triangle.
Please help acellus sucks
Step-by-step explanation:
Rectangle area= 40×30= 1200cm²
Triangle area= 20×20= 400cm²
Total are of composite figure= 1200+400=1600cm²
Can someone help me with this
Answer:
95% = Within two standard deviations from the mean
99.7% = Within three standard deviations from the mean
68% = Within one standard deviation from the mean
Step-by-step explanation:
I hope this helped! If it did, please click "Thanks" to help me out!
The height of a light pole in a magazine is 4 inches. The scale of the picture was given as 1 inch:24 inches. What would be the actual height of the light pole?
Answer:
96
Step-by-step explanation:
4 times 24 is 96
Write down the next two terms in the sequence: 3, 15, 75 , ___, ___
answer pleass
I need it now
☹️
Answer:
375, 1875,
Step-by-step explanation:
hope this helps :)
In which of the following functions would it be appropriate to use only positive integers for the domain? Select all that apply.
The function c(p) represents the cost for (P) people to attend the movies.
The function m(t) represents the miles driven over t hours.
The function t(m) represents the average high temperature for a given number of months.
The function p(w) represents the profit of a farmer who sells (w) whole watermelons.
The function (n) represents the number of person-hours it takes to assemble (n) engines in a factory.
Answer: The function c(p) represents the cost for (P) people to attend the movies.
The function t(m) represents the average high temperature for a given number of months.
Step-by-step explanation:
What is the product of the fraction below (3/x+2) (7/2x)
Answer:21x^2+14x over 2
Step-by-step explanation:
please help me in this question please
Step-by-step explanation:
here is your answer, this is how you do it
Answer:
[tex]\boxed{\bf G. \: x = {25}^{o}} [/tex]
[tex]\boxed{\bf H. \: x = {20}^{o} }[/tex]
Step-by-step explanation:
In the given figure, the linear pairs are supplementary angles, meaning they should add up to 180°.
G)
[tex]\bf 2x + 34 + x + 71 = 18 {0}^{o} [/tex][tex]\bf 3x + 105 = 18 {0}^{o} [/tex][tex]\bf 3x = 180 - 105[/tex][tex]3x = 75[/tex][tex]\boxed{\bf x = {25}^{o} }[/tex]H)
[tex]\bf 2x + 4x + 3x = {180}^{o} [/tex][tex]\bf 9x = 180[/tex][tex]\boxed{\bf x = {20}^{o} }[/tex]«••••••••••••»«•••••••••••••»
(2x)(2x)=(x+10)(2x-3) what is x?
Answer:
x = 5/2 or x = 6
Step-by-step explanation:
(2x)(2x)=(x+10)(2x-3)
4x^2 = 2x^2 - 3x + 20x - 30
2x^2 - 17x + 30 = 0
(2x - 5)(x - 6) = 0
x = 5/2 or x = 6
What is the range of the following numbers: 2, 5, 5, 8, 4, 3
Answer: range is 6
Step-by-step explanation:
Smallest number is 2
largest number is 8
8-2=6
2 7.1.2 Exam: Semester 1 Exam
Question 7 of 7
A part-time caregiver made $8944.58 last year. If he claimed himself as an
exemption for $3650 and had a $5700 standard deduction, what was his
taxable income last year?
O A. $5294.88
B. $3244.58
C. $0
O D. $405.42
Answer:$0
Step-by-step explanation:
Consider the solution to the system of inequalities below
-7x+y≥12.5
v+0.3x2 <-1
Which of the following functions could be added to the system without changing the solution set?
y < –2.1
y > –2.1
y = 2.1
y > 2.1
Answer:
i just want to try this but i think its y<2.1
Step-by-step explanation:
Gravity is one of the four fundemental forces in the universe. Electromagnetism is another one. The Other two are the strong force and the weak force that happen at the subotamic level. Find some information on what role these two forces play inside each atom and why one is considered strong and the other weak
Answer:
gravity is the force that helps u stay on the earth
Which function has the greatest x-intercept?
Et
f(x) = 3x - 9
g(x) = (x + 31)
h(x) = 2x – 16
j(x) = -5(x - 2)2
Answer:
g(x) = (x + 31)
f(x)= 3x-9
3×x-9= -9+3×x
=-6x
g(x)=(x+31)
1×x+31=32+1×x
=32x
h(x)=2x-16
2×x-16= 16+2×x
=18x
j(x)= -5(x-2)2
(-5x+10)2
-10x+20= 10×x+20
=20-10×x
=10x
What is the sum of 1/2plus 1/4use fractions strip to help
Answer:
Step-by-step e6/8 or in simple terms, 3/4
Step-by-step explanation:
Answer:
3/4
Step-by-step explanation:
1/2 is just 2/4
2/4+1/4 = 3/4
=)
Based on the work provided, write the dividend as a product of two factors
Answer:
x4+2x3+x2+5x+b=x-2x3+x+3
Step-by-step explanation:
NEED HELP URGENTLY!!!!!
In two or more complete sentences, explain how to use ordered pairs of points in f(x) = 3x - 5 and g(z) = ²5 to
determine iff (z) andg(z) are Inverses of each other.
The functions are inverses if the reverse of every ordered pair on the f(x) list is on the g(x) list.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have:
f(x) = 3x - 5
Here, g(x) is not given clearly.
But we can identify the given function as an inverse of each other.
Let's suppose the ordered pairs are:
[x, f(x)] and [x, g(x)]
The functions are inverses if the reverse of every ordered pair on the f(x) list is on the g(x) list.
f(0) = -5 so for (0, -5) on the f(x) list then (-5,0) must be on the g(x) list
f(1) = -2 so for (1, -2) on the f(x) list then (-2, 1) must be on the g(x) list
f(2) = 1 so for (2, 1) on the f(x) list then (1, 2) must be on the g(x) list
Let's suppose:
g(x) = (x+5)/3
g(-5) = 0
g(-2) = 1
g(1) = 2
So the ordered pair (-5, 0), (-2, 1), and (1, 2) are in the list of g(x).
Thus, the functions are inverses if the reverse of every ordered pair on the f(x) list is on the g(x) list.
Learn more about the function here:
brainly.com/question/5245372
#SPJ1
x2 + y2 – 2y – 99 = 0
What is the center of this circle ?
],
What is the radius of this circle ?
units
Answer:
The center is at (h, k) : (0, -1) and the radius is 10. ... The radius is 10. That is, since r^2 = 100, r must be 10.
Step-by-step explanation:
hope this helps you!
Which statements are true about exponential functions? Check all that apply.
Answer:
The answer is A
Step-by-step explanation:
its a multiple answer choice. so A , D
Given x varies inversely as y and x = 6 when y = - 4, find y when x = 8 .
- - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - -
[tex]\blue\textsf{\textbf{\underline{\underline{Question:-}}}}[/tex]
Given that x varies inversely with y, x=6 when y=-4, find y when x=8.
[tex]\blue\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}[/tex]
If x varies inversely with y, we divide.
So the formula looks as follows:-
[tex]\bold{x=\displaystyle\frac{k}{y} }[/tex]
where k = constant of proportionality
Plug in the values:-
[tex]\bold{6=\displaystyle\frac{k}{-4}}[/tex]
Multiply both sides by -4:-
[tex]\bold{-24=k}[/tex]
Now find y when x=8:-
[tex]\bold{8=\displaystyle\frac{-24}{y}}[/tex]
Multiply both sides by y:-
[tex]\bold{8y=-24}[/tex]
Divide by 8 on both sides:-
[tex]\dashrightarrow\bigstar{\boxed{\boxed{\underline{\bold{y=-3}}}}\dashleftarrow[/tex]
Good luck.
- - - - - - - - - -- - --- - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - -
9. Two fair dice are rolled. Find the odds of rolling the following sums.
(a) 2
(b) 6
(c) 9
(d) Between 5 and 8 (exclusive; that is, not including 5 or 8)
(e) Not more than 5
Find the mean of each distribution.
Correct answers will be mark as BRAINLIEST and get 50 points
Wrong answers will be reported
Answer:
See below ~
Step-by-step explanation:
a)
Mean = 3(21) + 1(22) + 2(23) + 5(24) + 1(25) / 12Mean = 63 + 22 + 46 + 120 + 25 / 12Mean = 276/12Mean = 23b)
Mean = 4.3 + 4.8 + 5.1 + 5.1 + 5.2 + 5.5 + 5.7 + 6.6 + 6.9 + 7.3 + 7.4 / 11Mean = 63.9/11Mean = 5.81Answer:
a) 23 °C
b) 5.81 m² (2 dp)
Step-by-step explanation:
Part (a)This set of data is presented as a Dot Plot.
The frequency (how often a data value occurs) is represented by the number of dots above each data value.
For example, in this dot plot, there are 3 dots above the data value 21 °C and so this means that there are three of this particular data value in the set of data.
To find the mean, we need to multiply each data value by its frequency, add them up, then divide by the total frequency.
[tex]\begin{aligned}\textsf{mean}&=\dfrac{3 \times 21+1 \times 22+2\times 23+5\times 24+1\times 25}{3+1+2+5+1}\\\\ & = \dfrac{63+22+46+120+25}{12}\\\\& = \dfrac{276}{12}\\\\&=23^{\circ} \sf C\end{aligned}[/tex]
Part (b)This set of data is presented as a stem and leaf diagram, where the units and tenths are split. The units column is the 'stem' and the tenths become the 'leaf'.
Therefore, the first row of this stem and leaf diagram represents 2 data values: 4.3 and 4.8
To find the mean, sum the data values, then divide by the total frequency.
To find the total frequency, simply count the number of values in the leaf part of the diagram.
Data values = 4.3, 4.8, 5.1, 5.1, 5.2, 5.5, 5.7, 6.6, 6.9, 7.3, 7.4
Total frequency = 11
[tex]\begin{aligned}\textsf{mean} &=\dfrac{4.3 + 4.8 + 5.1+5.1+5.2+5.5+5.7+6.6+6.9+7.3+7.4}{11}\\ & = \dfrac{63.9}{11}\\\\& = 5.81\:\textsf{(2 dp)}\end{aligned}[/tex]
Janet is retiring after working for a major department store for 20 years. The company offered her a flat retirement benefit of $50 per year for each year of service. a. What was her monthly income in the fi rst year after retirement?
Answer:
$1000
Explanation:
If the employee has worked there for 20 years and for every year its 50 dollars. That would mean its 50x20 which eqauls 1000.
The monthly income in the first year after retirement is $1000.
What is monthly income?Average monthly income is the amount you earn each month. Depending on your source of income, you can subtract insurance payments, rent allowances and other costs, such as federal and state taxes, from your total income every month. Net worth is your debt subtracted from your total assets.
Given that, Janet is retiring after working for a major department store for 20 years. The company offered her a flat retirement benefit of $50 per year for each year of service.
After working for 20 years, Janet has decided to retire from her job at a major department store.
The company has offered her a flat monthly retirement benefit of $50 for each year of service, which means that her monthly income in the first year after retirement would be $50 multiplied by 20, which is equal to $1000.
Hence, the monthly income in the first year after retirement is $1000.
For more such questions on monthly income, click;
brainly.com/question/30157678
#SPJ1
Find the LCD of the rational expressions in the list
Answer:
30
Step-by-step explanation:
what number does 7 multiply by that also can be multiplied by 5? 30 is the least common denominator between 7 and 5.
cedric's fish tank is 2yd long by 21in wide by 3ft tall. What is the volume of Cedric's take in cubic in?
Answer:
129 cubic inches
Step-by-step explanation:
lxwxh L=Length W=Width H= Height
Length times width times height gives you the volume
1. convert all numbers to inches
2. Multiply them together(order does not matter)
If for a particular one-to-one function f(2) = 13, what are the corresponding input and output
values for the inverse function?
Answer:
[tex]f^{-1}(13) = 2[/tex].
Step-by-step explanation:
For function [tex]f[/tex], the notation [tex]f(2) = 13[/tex] means that when the input to the function is [tex]2[/tex], the output would be [tex]13[/tex].
The inverse function of a one-to-one function [tex]f[/tex] is commonly denoted as [tex]\!f^{-1}[/tex].
The inverse function undoes the action of the original function. In this question, [tex]f[/tex] maps [tex]2[/tex] to [tex]13[/tex]. Thus, [tex]f^{-1}[/tex] would need to map [tex]13\![/tex] back to [tex]2\![/tex]. Therefore, [tex]f^{-1}(13) = 2[/tex] should be the corresponding input and output values.
Can someone help me with this question?
Answer: CD segment
Step-by-step explanation:
Factor the polynomial completely. 2x^2-9x+7
The polynomial is a quadratic function, and the completely factored expression of 2x^2 - 9x + 7 is (2x -7)(x - 1)
How to factor the polynomial?The polynomial expression is given as:
2x^2 - 9x + 7
Expand
2x^2 - 9x + 7 = 2x^2- 2x - 7x + 7
Factorize the above expansion
2x^2 - 9x + 7 = 2x(x - 1) - 7(x - 1)
Factor out x - 1
2x^2 - 9x + 7 = (2x -7)(x - 1)
Hence, the completely factored expression of 2x^2 - 9x + 7 is (2x -7)(x - 1)
Read more about polynomials at:
https://brainly.com/question/4142886
#SPJ1
Solve the system using elimination.
Answer:
This equation has no solution
Step-by-step explanation:
if the same equation equals 2 different numbers then therefore there is no solution.
Given the two similar flags shown,find the perimeter of the larger flag
The sum of the external side of a figure is its perimeter. the perimeter of the larger flag is 48
Similar shapesShapes are known to be similar if the ratioof their similar sides is equal to a constant.
From the given diagram, find the scale factor of the large triangle
k = 12/4
k = 3
Determine the perimeter of the large flag
Perimeter = 3 * perimeter of small flag
Perimeter of large flag = 3 * 16 = 48
Hence the perimeter of the larger flag is 48
Learn more on similar shapes here: https://brainly.com/question/2644832
#SPJ1