It is given that the distance is 6 miles and the time is 2 hours upstream and one and a quarter hour downstream.
The time downstream is given by:
[tex]1\frac{1}{4}=\frac{4+1}{4}=\frac{5}{4}\text{ hours}[/tex]Since the distance is constant, it follows:
[tex]\begin{gathered} \text{ Speed=}\frac{\text{ Distance}}{\text{ Time}} \\ \text{ Distance=SpeedxTime} \end{gathered}[/tex]So the distance is constant hence:
[tex]\text{ Distance upstream=Distance Downstream}[/tex]Let the speed of kayak be x and speed of current be y so the speed downstream is x+y and speed upstream is x-y so it follows:
[tex]\begin{gathered} \frac{5}{4}(x+y)=2(x-y) \\ 4\times\frac{5}{4}(x+y)=4\times2(x-y) \\ 5x+5y=8(x-y) \\ 5x+5y=8x-8y \\ 5y+8y=8x-5x \\ 13y=3x \\ x=\frac{13}{3}y \end{gathered}[/tex]Use the individual equation to find x and y as follows:
[tex]\begin{gathered} 6=2(x-y) \\ 6=2(\frac{13}{3}y-y) \\ 3=\frac{13-3}{3}y \\ \frac{9}{10}=y \end{gathered}[/tex]Hence the speed of the water current is 9/10 miles per hour.
The speed of the kayak is given by:
[tex]\begin{gathered} x=\frac{13}{3}y \\ x=\frac{13}{3}\times\frac{9}{10} \\ x=\frac{39}{10}=3.9\text{ miles per hour} \end{gathered}[/tex]Hence the speed of the kayak without the water current is 3.9 miles per hour.
The time required without water current is:
[tex]\begin{gathered} \text{Time}=\frac{Dis\tan ce}{Speed} \\ t=\frac{6}{3.9}\approx1.5\text{ hours} \end{gathered}[/tex]Hence it will take approximately 1.5 hours without the current.
The measure of the supplement of an angle exceeds twice the measure of the complement of the angle by 20. Find the measure of half of the complement
The supplement is when two angles add up to 180° and complement is when two angles add up to 90°
let:
x = the angle.
180 - x = its supplement.
90 - x = its complement
then x = 2(90-x) + 20 means the measure of the supplement of an angle exceeds twice the measure of the complement of the angle by 20
Graph the equation after rewriting it in slope-intercept form. Y-3x=4
We have this equation
[tex]y-3x=4[/tex]The following is the slope intercept form
[tex]y=mx+b[/tex]add 3x on both sides of the equation
[tex]y-3x+3x=4+3x[/tex]simplify
[tex]y=4+3x[/tex]rearrange
[tex]y=3x+4[/tex]So, the above is the equation in slope-intercept form
Now, let's graph the equation
since this is a linear equation, we need to find 2 points and plot them in the chart
let's find point 1. Let's say x = 0 and replace: y = 3x+4 = 3*0 + 4 = 0 + 4 = 4
so, when x=0, then y = 4 , so our 1st point is (0,4)
now, let's suppose, y=0 , in that case, y = 3x + 4 = 0 , then 3x = -4 , so the value of x is -4/3 = -1.3333
in that case, our seconds point is (-4/3 , 0)
just to make sure, we can also plot a 3rd point, let's say we make x = 2, then y = 3*2 + 4 = 6 + 4 = 10
so, our 3rd point is (2, 10)
using the points above, we can plot something like this...
Christina's purchasing a new TV. She was approved to finance the TV with zero interest. If Christina gives a one-time payment of $300 and pays $65 per month, how much has she paid in 5 months? (show work)
Given:
One time payment, p = $300
Payment per month, q = $65
Number of months paid, n = 5
The objectiv is to find the amount she paid in 5 months.
Let x be the amount she paid in 5 months. Then the the formula is,
[tex]x=p+nq[/tex]Let's substitute the values.
[tex]\begin{gathered} x=300+5(65) \\ x=300+325 \\ x=625 \end{gathered}[/tex]Hence, total amount paid in 5 months is $625.
Simplify f(x) = 2x^5 for x = 0, 1, 3, 5
f(0) = 0, f(1) = 2, f(3) = 486, f(5) = 6250
Explanations:The given function is:
[tex]f(x)=2x^5[/tex]To get the value of f(x) for x = 0, 1, 3, and 5, it means we are going to find f(0), f(1), f(3), and f(5).
[tex]\begin{gathered} f(0)=2(0)^5 \\ f(0)\text{ = 2(0)} \\ f(0)\text{ = 0} \end{gathered}[/tex][tex]\begin{gathered} f(1)=2(1)^5 \\ f(1)\text{ = 2(1)} \\ f(1)\text{ = 2} \end{gathered}[/tex][tex]\begin{gathered} f(3)=2(3)^5 \\ f(3)\text{ = 2 (}243) \\ f(3)\text{ = 486} \end{gathered}[/tex][tex]\begin{gathered} f(5)=2(5)^5 \\ f(5)\text{ = 2(}3125) \\ f(5)\text{ = }6250 \end{gathered}[/tex]the parent function name for y=|x|
This function is an absolute type of function
Draw the reflection of the figure in the x-axis. Polygon + Move - Redo 5 4 3 2 1 4 -3 -2 -29 1 5
Answer
Explanation
To draw the image of this figure, we need to first obtain the coordinates of the edge of the image of this figure.
And to do that, we need to first write the coordinates of the edges of the original figure.
When a given coordinate A (x, y) is reflected across the x-axis, the coordinates become A' (x, -y).
The coordinates of the original image include (-2, -4), (1, -3) and (3, -4)
After the reflection, we will now have
(2
cole is studying ceramics and he was asked to submit 5 vessels from his collection to exhibit at the fair. he has 15. vessels that he thinks are show worthy. in how many ways can the vessels be chosen
Since he has 15 vessels and needs to choose 5, we can use a combination of 15 choose 5 to calculate the number of possible ways, since the order of the vessels inside the group of 5 is not important.
The formula to calculate a combination of n choose p is:
[tex]C(n,p)=\frac{n!}{p!(n-p)!}[/tex]Then, for n = 15 and p = 5, we have:
[tex]\begin{gathered} C(15,5)=\frac{15!}{5!(15-5)!}=\frac{15!}{5!10!}=\frac{15\cdot14\cdot13\cdot12\cdot11\cdot10!}{5\cdot4\cdot3\cdot2\cdot10!} \\ =\frac{15\cdot14\cdot13\cdot12\cdot11}{5\cdot4\cdot3\cdot2}=3003 \end{gathered}[/tex]So there are 3003 ways to choose the 5 vessels.
If 2 dogs cross over a road and 1 dog disappear in the road how did the other dog made it
Answer:
he was quick???
Step-by-step explanation:
Mark me brainliest!
Larry answered 8 out of every 10 questions correctly. The test had 70 questions. How many correct answers did Larry give?---What represents the "x" or unknown in this problem?
Representation of fractional numbers
Larry's rate of succesful questions is 8/10.
Then must find how many times is divided 70 in 10 questions
70/10 = 7
if there were a 100% succesful then 70 rresulted
but the rate is 8/10 , then multiply 8x 7 = 56 succesful questions for Larry.
Find the x-intercept and the y-intercept without graphing. Write the coordinates of each intercept. When typing the point (x,y) be sure to include parentheses and a comma between your x and y components. Do not put any spaces between your characters. If a value is not an integer type your answer rounded to the nearest hundredth.3x+8y=24the x-intercept is Answerthe y-intercept is Answer
We want to find the x and y-intercepts of
[tex]3x+8y=24[/tex]The x-intercept is where the graph cuts the x-axis, when y = 0. To find this in our equation, we just need to evaluate it at y = 0.
[tex]\begin{gathered} 3x+8\times0=24 \\ 3x=24 \\ x=\frac{24}{3}=8 \end{gathered}[/tex]Then, the x-intercept is (8, 0).
The y-intercept is where the graph cuts the y-axis, when x = 0. To find this in our equation, we just need to evaluate it at x = 0.
[tex]\begin{gathered} 3\times0+8y=24 \\ 8y=24 \\ y=\frac{24}{8}=3 \end{gathered}[/tex]The y-intercept is (0, 3).
May I please get help with this math problem please I have tried so many times but still could not get the right answers
We know that the sum of interior angles of a triangle equals 180, then, in this case we have the following:
[tex]90+2x+17+3x+28=180[/tex]solving for x, we get:
[tex]\begin{gathered} 90+2x+17+3x+28=180 \\ \Rightarrow135+5x=180 \\ \Rightarrow5x=180-135=45 \\ \Rightarrow x=\frac{45}{5}=9 \\ x=9 \end{gathered}[/tex]therefore, x = 9
What is the solution to 2x + 2(x – 5)=6,explainhow you solved the equation.explain with words
Answer
The solution to the equation is x = 4.
Explanation
We are told to find the solution to the equation
2x + 2(x - 5) = 6
The first step is to open the bracket by multiplying through by the number outside the bracket, that is, 2.
2x + 2x - 10 = 6
4x - 10 = 6
Add 10 to both sides to leave only 4x on the Left Hand Side.
4x - 10 + 10 = 6 + 10
4x = 16
Divide both sides by 4 to obtain the value of x.
(4x/4) = (16/4)
x = 4
Hope this Helps!!!
I need help on this equation. It’s algebra. SAT PREP.
Answer:
r = 1.14
Explanation:
The value of a product (A) over time with an increasing rate "i" can be calculated as follows:
A = C(1+i)^t
where:
C is the value of the product at time 0;
A is the value of the product at time t;
i is the increasing rate.
If we compare the expression V=300r^t with A = C(1+i)^t. We can observe that:
r = 1+i
r = 1+0.14
r = 1.14
A state sales tax of 6% and a local sales tax of 1% are levied in Tampa, Florida. Suppose the price of a particular car in Tampa is $15,000, and an oil change at a certain auto center is $29.Which statement is true another total cost of the car and the oil change after sales tax has been calculated?Select the correct answer
We have the following:
What we must do is calculate the total cost of the car by adding its original value plus the cost of taxes, 6% and 1%
We know that the initial value is $15000, if to that we add 6% of those $15000 and equal 1%, we have
[tex]15000+15000\cdot0.06+15000\cdot0.1=15000+900+150=16050[/tex]We do the same procedure for the oil change
[tex]29+29\cdot0.06+29\cdot0.01=29+1.74+0.29=31.03[/tex]Therefore the correct statement is the last
Hello for this particular problem can I change the final results to a whole number? or it is not possible?
We are asked which of the given combinations will produce a number that is less or equal to 25.
For A we have:
[tex]A=3(8\frac{3}{4})[/tex]Let's remember that for a mixed fraction we have:
[tex]a\frac{b}{c}=a+\frac{b}{c}[/tex]Therefore, we can change the mixed fraction and we get:
[tex]A=3(8\frac{3}{4})=3(8+\frac{3}{4})[/tex]Solving the operations:
[tex]A=26.25[/tex]Since we get a number greater than 25 this is not a trail he can ride.
For B we have:
[tex]B=2(10\frac{1}{4})[/tex]Changing the mixed fraction:
[tex]B=2(10\frac{1}{4})=2(10+\frac{1}{4})[/tex]To solve the operation we will apply the distributive property:
[tex]B=20+2\times\frac{1}{4}[/tex]Now, we simplify the fraction:
[tex]B=20+2\times\frac{1}{4}=20+\frac{1}{2}[/tex]Now, we use the fact that 1/2 = 0.5:
[tex]B=20+\frac{1}{2}=20+0.5=20.5[/tex]Since we get a number that is less than 25 this is a train he can ride.
For C we have:
[tex]C=2(7\frac{1}{2})+10\frac{1}{4}[/tex]Changing the mixed fraction:
[tex]C=2(7+\frac{1}{2})+10+\frac{1}{4}[/tex]Now, we apply the distributive property:
[tex]C=14+1+10+\frac{1}{4}[/tex]Solving the operations. We use the fact that 1/4 = 0.25:
[tex]C=25+0.25=25.25[/tex]Since we get a number greater than 25 this is not a trail he can ride.
For D.
[tex]D=7\frac{1}{2}+2(8\frac{3}{4})[/tex]Now, we change the mixed fractions:
[tex]D=7+\frac{1}{2}+2(8+\frac{3}{4})[/tex]Now, we use the distributive property:
[tex]D=7+\frac{1}{2}+16+2\times\frac{3}{4}[/tex]Simplifying the fraction:
[tex]D=7+\frac{1}{2}+16+\frac{3}{2}[/tex]Now, we add the fractions, we have into account that when fractions have the same denominator we can add the numerators and use the common denominator, like this:
[tex]D=7+\frac{4}{2}+16[/tex]Simplifying the fraction we get:
[tex]D=7+2+16[/tex]Solving the operations:
[tex]D=25[/tex]Since we get 25 this is a trail that he can ride.
8. MOVIE TICKETS Tickets to a movie cost $25 for adults and 5.50 formodents A group of friends purchased 8 tickets for $52.75 a Write a system of equations to represent the station
Tickets for adults --> $25
Tickets for formodents --> $5.50
The equations that would represent the number of adults and formodents in th group of friends:
Let x be adults
Let y be formodents
$25x+$5.50y=$52.72
x+y=8
1f(x) =X-24g(x)ХFind: (fog)(x) =
We have the functions:
[tex]undefined[/tex]s
what is the equation of a line that passes through point (-1,5) and has the slope of m=4
The general equation of a line is given as;
[tex]y=mx+b[/tex]In this question, the slope (which is m) is given as 4. Also we have the points x and y, given as (-1, 5). That is;
[tex]x=-1,y=5[/tex]Therefore the next step is to find the y-intercept (that is b in the equation).
We substitute for the known values as follows;
[tex]\begin{gathered} y=mx+b \\ 5=4(-1)+b \\ 5=-4+b \\ \text{Add 4 to both sides} \\ 5+4=-4+4+b \\ 9=b \end{gathered}[/tex]Now we know the value of b and m, we can substitute them as follows;
[tex]\begin{gathered} y=mx+b \\ m=4,b=9 \\ y=4x+9 \end{gathered}[/tex]Select all the pairs that represent alternate interior angles.See image for instruction
Alternate means on the opposite side of the transversal, or line n
interior means inside of the parallel lines l and m
The alternate interior angles are 4 and 5
and 3 and 8
Check the boxes for both pairs
For the problem below, find the reference angle, to the nearest 10th (if necessary), and also the two possible quadrants in which θ could lie.tan(θ)=−3
The two possible quadrants are the second and the fourth
can someone please help me solve and graph this the past few have been incorrect and this is my homework and i really need help
step 1
Solve the inequality
[tex]\begin{gathered} 3x+8\leq11 \\ 3x\leq11-8 \\ 3x\leq3 \\ x\leq1 \end{gathered}[/tex]the solution for the first inequality is the interval
(-infinite, 1]
step 2
Solve the inequality
[tex]\begin{gathered} 3x+8\text{ > 20} \\ 3x\text{ > 20-8} \\ 3x\text{ > 12} \\ x\text{ > 4} \end{gathered}[/tex]the solution for the second inequality is the interval
(4, infinite)
step 3
the general solution for the first inequality or the second inequality is
(-infinite, 1] U (4, infinite)see the attached figure to better understand the problemReally need help solving this practice from my ACT prep guide It’s a trig practice
Given:
- The amplitude of the Sine Function:
[tex]A=10[/tex]- The midline:
[tex]y=4[/tex]- And the period:
[tex]Period=2[/tex]- You know that the function does not have a Phase shift.
• You need to remember that, by definition, the General Equation for a Sine Function has this form:
[tex]y=Asin\mleft(B\mleft(x+C\mright)\mright)+D[/tex]Where "A" is the amplitude, "C" is the phase shift, "D" is the vertical shift and this is the period:
[tex]Period=\frac{2\pi}{B}[/tex]Since the midline is given by the vertical shift, you can identify that, in this case:
[tex]D=4[/tex]And, knowing the period, you can set up that:
[tex]2=\frac{2\pi}{B}[/tex]Solving for "B", you get:
[tex]\begin{gathered} 2B=2\pi \\ \\ B=\frac{2\pi}{2} \\ \\ B=\pi \end{gathered}[/tex]• It is important to remember the following Transformation Rule for Functions:
When:
[tex]-f(x)[/tex]The function is reflected over the x-axis.
Therefore, knowing all the data, you can set up this equation:
[tex]f(x)=-10\sin (\pi x)+4[/tex]Hence, the answer is: First option.
Any math tutors available to help me ? I need help
Hello!
First of all, let's write the initial temperature:
• 6am: 58ºF
In next 5 hours, the temperature rose 1ºF per hour, so:
• 7am: 59ºF
,• 8am: 60ºF
,• 9am: 61ºF
,• 10am: 62ºF
,• 11am: 63ºF
In the next 3 hours, it rose 3ºF per hour:
• 12pm: 66ºF
,• 1pm: 69ºF
,• 2pm: 72ºF
The temperature stayed steady until 6pm:
• In this part, we'll have a constant line until 6pm (it will be 72ºF in all).
In the next 4 hours, the temperature dropped 2ºF per hour:
• 7pm: 70ºF
,• 8pm: 68ºF
,• 9pm: 66ºF
,• 10pm: 64ºF
Dropped steadily until 63ºF at midnight
• 12am: 63ºF
Now, let's make the graph!
7(-a-3)=3(2a-6) I have the answer but I need help checking it.
SOLUTION:
Step 1:
In this question, we are meant to solve the following:
[tex]7\text{ ( - a - 3 ) = 3 ( 2a - 6 )}[/tex]Step 2:
Simplifying, we have that:
[tex]\begin{gathered} -7a\text{ - 21 = 6a - 18} \\ \end{gathered}[/tex]collecting like terms, we have that:
[tex]\begin{gathered} -21\text{ + 18 = 6 a + 7a} \\ 13\text{ a = -3} \\ \text{Divide both sides by 13, we have that:} \\ a\text{ = }\frac{-3}{13} \end{gathered}[/tex]Step 3:
To verify that:
[tex]a\text{ =}\frac{-3}{13}[/tex]is a solution, we have that:
[tex]7\text{ ( - a - 3 ) = 7 \lbrack -(}\frac{-3}{13}\text{ ) - 3 \rbrack}[/tex][tex]7\lbrack\text{ }\frac{3}{13}\text{ - 3\rbrack = 7 \lbrack }\frac{3}{13}\text{ - }\frac{39}{13}\text{ \rbrack = 7 x }\frac{-36}{13}\text{ = }\frac{-252}{13}\text{ ( Left Hand Side)}[/tex]Next,
[tex]3\text{ ( 2 a - 6 ) = 3 \lbrack{}2(}\frac{-3}{13})\text{ - 6 }\rbrack\text{ = 3 \lbrack}\frac{-6}{13}\text{ - 6\rbrack= 3\lbrack}\frac{-6}{13}\text{ - }\frac{78}{13}\rbrack[/tex][tex]=\text{ 3 \lbrack }\frac{-84}{13}\text{ \rbrack = }\frac{-252}{13}\text{ ( Right Hand Side)}[/tex]CONCLUSION:
From the solution and from the verification of the answers, we can see that the correct answer is:
[tex]a\text{ = }\frac{-\text{ 3}}{13}[/tex]There are 27 students in Mr. Mello's class. Find the total number of pages the students
read by the end of November.
WILL GET 100 POINTS AND BRAINLIST.
Answer:
No solution.
Step-by-step explanation:
Why I say this problem has no solution is due to the fact that the amount of pages is unclassified. This leads you to guessing how many pages there might be for each chapter of the students' individual books, and guessing would not be an effective method as it could lead you to thinking of any random number between 1 - 60 at the most. Therefore, this problem has no solution. If you have further concerns about this problem, I recommend addressing them to your teacher. Otherwise, have a great day. :)
I know this is easy and i should know but im actually stumped on this one
For the given triangles:
There are 3 pairs of congruent angles
the triangles can not be proved using the congruent angles
the congruent angles used to prove the similarity of the triangles
So, the answer will be:
For the given triangle, we can not prove they are congruent.
What is the surface area of the solid that this net can form?8 mm25 mm8 mm5 mm5 mm8 mm8 mm5 mm5 mm8 mm8 mm25 mmO 730 square millimetersO 875 square millimeters0 1,000 square millimetersO 1,444 square millimeters
The solid is formed by 6 rectangles.
Calculate the area of each one and then add them to obtain the surface area (SA),
Area of a rectangle: Length x width
A1 = 8 x 5 = 40 mm2
A2= 25x5 = 125 mm2
A3 = 8 x 5= 40 mm2
A4 = 25 x 8 = 200 mm2
A5 = 25x5 = 125 mm2
A6 = 25 x 8 = 200mm2
SA = A1+A2+A3+A4+A5+A6 = 40 + 125 +40 +200 +125+ 200 = 730 mm2
Take away 5 from p????????????????
Answer:
p - 5
Step-by-step explanation:
5 - p = p - 5
3. Square SQRE has coordinates S(2, 2) Q (5,2)R (5. – 1). Find the coordinates of E. I gotta turn it in tomorrow
Given:
Square SQRE has coordinates S(2, 2) Q (5,2), and R (5. – 1).
To find:
The coordinates of E.
Explanation:
Let (x, y) be the coordinates of E.
Using the midpoint formula,
[tex]p=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]As we know,
The diagonals of the square are intersected by its midpoint.
So, the Midpoint of SR and QE is the same in a given square SQRE.
[tex]\begin{gathered} Midpoint\text{ of SR = Midpoint of QE} \\ (\frac{2+5}{2},\frac{2-1}{2})=(\frac{5+x}{2},\frac{2+y}{2}) \\ (\frac{7}{2},\frac{1}{2})=(\frac{5+x}{2},\frac{2+y}{2}) \end{gathered}[/tex]Equating the coordinates we get,
[tex]\begin{gathered} \frac{7}{2}=\frac{5+x}{2} \\ 7=5+x \\ x=2 \\ \frac{1}{2}=\frac{2+y}{2} \\ 1=2+y \\ y=-1 \end{gathered}[/tex]Therefore, the coordinate of E is (2, -1).
Final answer:
The coordinate of E is (2, -1).
I need help. I think I left out a step. I need to find the volume of the rectangle prism.
Given a rectangular prism with the following dimensions:
H = Height = 26
L = Length = 20
W = Width = 12
To be able to determine its volume, we will be using the following formula:
[tex]\text{ Volume = L x W x H}[/tex]We get,
[tex]\text{ Volume = L x W x H}[/tex][tex]\text{ = 20 x 12 x 26}[/tex][tex]\text{ Volume = }6240[/tex]Therefore, the volume of the rectangular prism is 6,240.