Answer:
The speed of the river is 3 miles per hour.Step-by-step explanation:
In downstream, the speed of the boat will be (9 + r) miles per hour and in upstream the speed of the boat will be (9 - r) miles per hour.
Ratio of the speed in downstream to the speed in upstream is (9 + r):(9 - r).
Hence, the ratio of the time taken by the boat to cover the distance in downstream to upstream is (9 - r):(9 + r).
[tex]\frac{9 - r}{9 + r} = \frac{2}{4} \\18 - 2r = 9 + r\\3r = 9\\r = 3[/tex]
All 203 students at Polk School eat lunch at the same time. One
day 19 students were absent. If 8 students sit at each table in
the lunchroom, how many tables were used that day at lunch?
Answer:
The number of tables were used that day at lunch is 23 tables.
Step-by-step explanation:
Given as :
The total number of students in the Polk school = 203
On one day the number of students absent = 19
So, The number of student present on that day = Total student - absent students
I.e The number of student present on that day = 203 - 19 = 184
The number of students sit on each table = 8
Let The number of tables were used that day at lunch = n
So, According to question
The number of tables were used that day at lunch = [tex]\dfrac{\textrm The number of student present on that day}{\textrm Total number of students sit on each table}[/tex]
I.e n = [tex]\frac{184}{8}[/tex]
∴ n = 23 tables
So, The number of tables were used that day at lunch = n = 23 tables
Hence, The number of tables were used that day at lunch is 23 tables. Answer
which of the following are true statements? Check all that apply logM^(p)=p*logM log ((M)/((N)))=logM-logN log ((M)/((N)))=(logM)/(logN) (logM)^(p)=p*logM
The expressions logM^(p)=p*logM and log ((M)/((N)))=logM-logN both correctly apply rules of logarithm, while log ((M)/((N)))=(logM)/(logN) and (logM)^(p)=p*logM don't.
Explanation:The subject matter involves logarithmic identities in Mathematics, specifically, rules of logarithms. Logarithms have certain properties that allow us to simplify complex expressions.
Let's go through each expression:
logM^(p)=p*logM: This is a correct identity. It's known as the power rule of logarithms, which states that the log of a number raised to an exponent is equal to the exponent multiplied by the log of the number. log ((M)/((N)))=logM-logN: This is also a correct identity. It's known as the quotient rule of logarithms, which states that the log of a quotient is the difference of the logs. log ((M)/((N)))=(logM)/(logN): This statement is false. It's an incorrect assumption about the rules of logarithms. (logM)^(p)=p*logM: This statement is also false. The power in this case refers to the exponent on the entire log term, which is different from the power rule. Learn more about Rules of Logarithms here:https://brainly.com/question/30287525
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An old house has a basement stairway that has steps with 7.25 inch vertical risers and 7 inch horizontal treads. What is the slope of the stairway? Round to two decimal places.
Answer:
1.04 inch
Step-by-step explanation:
Given: Old house has a basement stairways with 7.25 inch vertical riser and 7 inch horizontal treads.
Remember; horizontal treads is known as run in steps.
Now, calculating the slope of the stairways.
Formula: [tex]Slope= \frac{Rise}{Run}[/tex]
Rise= 7.25 inch
Run= 7 inch.
Subtituting the value in the formula
Slope= [tex]\frac{7.25}{7}= 1.0357 \approx 1.04[/tex] (∵ Round to two decimal)
∴ Slope of stairways is 1.04.
Semicircles
whose centers A
are the midpoints .
of the sides of
square ABCD are .
drawn. If the
measure of each
side of the square
is 4 cm, what is the area, nearest to
the tenth of a sq cm, of the shaded
portion of the figure?
Answer:
The area of the shaded portion of the figure is [tex]9.1\ cm^2[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
The shaded area is equal to the area of the square less the area not shaded.
There are 4 "not shaded" regions.
step 1
Find the area of square ABCD
The area of square is equal to
[tex]A=b^2[/tex]
where
b is the length side of the square
we have
[tex]b=4\ cm[/tex]
substitute
[tex]A=4^2=16\ cm^2[/tex]
step 2
We can find the area of 2 "not shaded" regions by calculating the area of the square less two semi-circles (one circle):
The area of circle is equal to
[tex]A=\pi r^{2}[/tex]
The diameter of the circle is equal to the length side of the square
so
[tex]r=\frac{b}{2}=\frac{4}{2}=2\ cm[/tex] ---> radius is half the diameter
substitute
[tex]A=\pi (2)^{2}[/tex]
[tex]A=4\pi\ cm^2[/tex]
Therefore, the area of 2 "not-shaded" regions is:
[tex]A=(16-4\pi) \ cm^2[/tex]
and the area of 4 "not-shaded" regions is:
[tex]A=2(16-4\pi)=(32-8\pi)\ cm^2[/tex]
step 3
Find the area of the shaded region
Remember that the area of the shaded region is the area of the square less 4 "not shaded" regions:
so
[tex]A=16-(32-8\pi)=(8\pi-16)\ cm^2[/tex]
---> exact value
assume
[tex]\pi =3.14[/tex]
substitute
[tex]A=(8(3.14)-16)=9.1\ cm^2[/tex]
A circle is divided into 6 equal parts. what is the total angle measure of 1 part?
Answer:
[tex]dis \: is \: easy \\ angle \: in \: a \: circle = 360 \\ the \: angle \: is \: divided \: into \: six \: part \\ divide \: the \: 360 \: by \: 6 \\ \frac{360}{6} = 60 \\ therefore \: the \: angle \: of \: one \: part \: \\ = 60 \: degree[/tex]
Write a linear function f with the values f(2)=4 and f(−7)=9. A function is f(x)=
Answer:
f(x) = -5/9 x + 5 1/9
Step-by-step explanation:
f(2)=4 and f(−7)=9 means the line pass through (2,4) and (- 7,9)
f(x) = mx + b
m = (y-y') / (x-x') = (9 - 4) / (- 7 - 2) = - 5/9
for (2,4) : b = f(x) - mx = y - mx = 4 - (- 5/9) x 2 = 4 + 10/9 = 46/9 = 5 1/9
f(x) = -5/9 x + 5 1/9
check for (-7, 9) f(-7) = (-5/9) * (-7) + 5 1/9 = 35/9 + 46/9 = 81/9 = 9
Final answer:
The linear function that satisfies the given points f(2)=4 and f(-7)=9 is f(x) = (-5/9)x + (46/9).
Explanation:
To write a linear function f(x) that satisfies f(2)=4 and f(-7)=9, one must determine the slope and y-intercept of the line. A linear function has the form y = mx + b, where m is the slope and b is the y-intercept.
First, let's find the slope using the two points (2, 4) and (-7, 9):
Slope (m) = (y2 - y1) / (x2 - x1) = (9 - 4) / (-7 - 2) = 5 / -9.
Now we have the slope which is -5/9. We can use one of the points and the slope to find the y-intercept (b). Let's use the point (2, 4):
4 = (-5/9)(2) + b
b = 4 + (10/9) = 46/9
Therefore, the linear equation of the function is:
f(x) = (-5/9)x + (46/9).
Brook states that the distance on the line is 4 units. Caleb states that the whole line does not have a distance because it continues on forever. Vivian states that the line is 6 units long.
Answer:
kaleb is correct
Step-by-step explanation:
The awsner is Brook did the distance between L and M, Vivian however did the distance between M and N. Hope this helps you
67+46
Find the solution and model how you found your answer
113
Step-by-step explanation:
7 plus 6 is 14 carry the one over to the 6 of the 67 then add the one the six and the four that equals 11
that gets you
113
What is 0.21666667 as a rounded percent
Answer:
23%
Step-by-step explanation: ???
409 divided by 2 = a 24 R1 B 25 r1 C 204 R1 d 205 r1
Answer:
answer c-204 r1
Step-by-step explanation:
409 divided by 2 is 204.5 or 204 r1
which way is the closest estimate of this product 518 * 5
518x5=2,590, So your estimate is about 2,600, Because we want to round up, So we look in the tens place and we see a nine, so that means we go up on, Also 5 and up means we gonna round up and 5 and below means we gonna round down.
The answer to 518*5 is 2590 or rounded, 3000, or 2600.
You can get your answer my multiplying 518 by 5 and rounding it to the nearest thousands place, hundreds place or tens place.
Hope this helped!
Calculate the average rate of change of f(x) =x^2/4 - 5 for 3 ≤ x ≤ 5
Answer:
2
Step-by-step explanation:
Average rate of change of a function between x=a and x=b is:
[ f(b) − f(a) ] / (b − a)
On the interval 3 ≤ x ≤ 5:
[ f(5) − f(3) ] / (5 − 3)
[ (5²/4 − 5) − (3²/4 − 5) ] / (5 − 3)
(25/4 − 5 − 9/4 + 5) / (5 − 3)
(25/4 − 9/4) / (5 − 3)
(16/4) / 2
2
Determine the type and number of solutions of x^2 + 10x − 25 = 0. A two real solutions B one real solution C two imaginary solutions
Answer:
two real solution
Step-by-step explanation:
x^2 + 10x − 25 = 0
we can solve this by finding out the value of x
lets assume the equation is a\times x^{2}+b\times x+c=0
x=-b\pm \sqrt{(b^{2}-4ac)}\div 2a
x=-10\pm\sqrt{100+4*25}\div2
x=-5\pm5\sqrt2
then we get both real value of x
so two real solution
one half the cost of a dress decreased by $12 is the same as 2/5 the cost of a dress. What is the cost of the dress?
Answer:
$120
Step-by-step explanation:
Let the cost of the dress be "c"
ONE HALF the cost DECREASED by 12, can be written as:
[tex]\frac{1}{2}c-12[/tex]
2/5th the cost of dress, can be written as:
[tex]\frac{2}{5}c[/tex]
Now, we equate both parts and solve for c to get cost of dress. Shown below:
[tex]\frac{1}{2}c-12=\frac{2}{5}c\\\frac{1}{2}c-\frac{2}{5}c=12\\\frac{5-4}{10}c=12\\\frac{1}{10}c=12\\c=\frac{12}{\frac{1}{10}}\\c=12*10\\c=120[/tex]
Thus,
The ccost of the dress is $120
What is the approximate circumference of the circle shown below?
A. 37.8 cm
B. 92.9 cm
C. 46.5 cm
D. 23.2 cm
Answer:c
Step-by-step explanation:
Answer:
Step-by-step explanation:
C
omplete the paragraph proof.
Given: M is the midpoint of
Prove: ΔPKB is isosceles
Triangle P B K is cut by perpendicular bisector B M. Point M is the midpoint of side P K.
It is given that M is the midpoint of and . Midpoints divide a segment into two congruent segments, so . Since and perpendicular lines intersect at right angles, and are right angles. Right angles are congruent, so . The triangles share , and the reflexive property justifies that . Therefore, by the SAS congruence theorem. Thus, because _____________. Finally, ΔPKB is isosceles because it has two congruent sides.
corresponding parts of congruent triangles are congruent
base angles of isosceles triangles are congruent
of the definition of congruent segments
of the definition of a right triangle
Answer:
Complete paragraph proof withe Diagram is below.
Δ PMB ≅ Δ KMB ...........SAS congruence theorem
∴ PB ≅ KG ......corresponding parts of congruent triangles are congruent
Step-by-step explanation:
Complete the paragraph proof.
Given: M is the midpoint of
Prove: ΔPKB is isosceles
Triangle P B K is cut by perpendicular bisector B M. Point M is the midpoint of side P K.
It is given that M is the midpoint of and . Midpoints divide a segment into two congruent segments, so . Since and perpendicular lines intersect at right angles, and are right angles. Right angles are congruent, so . The triangles share , and the reflexive property justifies that . Therefore, by the SAS congruence theorem. Thus, because __corresponding parts of congruent triangles are congruent _.
Finally, ΔPKB is isosceles because it has two congruent sides.
Δ PMB ≅ Δ KMB ...........SAS congruence theorem
∴ PB ≅ KG ......corresponding parts of congruent triangles are congruent
Answer: A
Step-by-step explanation:
Separate the number 41 and the two parts so that the first number is eight more than twice the second number what are the two numbers
The two numbers are 30 and 11
Solution:
Given that we have to separate the number 41 into two parts
Let the second number be "x"
Given that first number is eight more than twice the second number
first number = eight more than twice the second number
first number = 8 + twice the "x"
first number = 8 + 2x
So we can say first number added with second number ends up in 41
first number + second number = 41
8 + 2x + x = 41
8 + 3x = 41
3x = 41 - 8
3x = 33
x = 11
first number = 8 + 2x = 8 + 2(11) = 8 + 22 = 30
Thus the two numbers are 30 and 11
Brainliest!!!
Draw a tree diagram to show the sample space for each event.
a shirt with style choices crew-neck and v-neck and colors blue, yellow, or green
Answer:
3rd option
Step-by-step explanation:
We have two kind of necks and three different colours so the andswer would be 3rd option
Crew-neck :CB,CY,CG
V-neck : VB,VY,VG
Answer:
The 3rd one is correct.
Step-by-step explanation:
Select the best answer for the question
17. A local supermarket sells shrimp for $4.50 per pound and lobster for $7.25 per pound.
You have a total budget of $95.75. If you buy 7 pounds of lobster, how many pounds of shrimp
can you purchase?
Answer:
10
Step-by-step explanation:
Multiply 7.25 and 7
that gets you 50.75
Then subtract 50.75 from 95.75
thats get you 45
Last divide 45 from 4.50
that gets you 10
10.) A soccer team plays 104 tournaments in two
years, playing the same number of tournaments each
year. In each tournament they play 3 games. If they
won a total of 55 games in first year and 103 games
in the second year,A. how many games did they lose in
both years? B.Is the number of games won greater than
The number of games lost? Show your work below to
justify your anwser.
.
Answer:
A. The Number of Lost games = 154 Games
B. Number of games won is greater than the number of games lost.
Step-by-step explanation:
A. how many games did they lose in both years?
Total Number of games = 104 tournaments x 3 Games in each tournament
Total Number of games = 312 Games
The No. of Lost games= Total Games in 2 years - Games won in 1st year - Games won in 2nd year
The No. of Lost games = 312 - 55 - 103
The No. of Lost games = 154 Games
B. Is the number of games won greater than the number of games lost?
Total Number of Games won = 158 Games
Total Number of Games lost = 154 Games
Hence, Total Number of Games won is greater than the Total Number of Games lost.
Complete this sequence: 88511, 16351, ?, 10251
Answer:
73155
Step-by-step explanation:
To complete the sequence, we need to know the pattern.
88511= [tex]8+8, 8-5, 5\times 1, \frac{1}{1} = 16351[/tex]
16351= [tex]1+6, 6-3, 3\times 5, \frac{5}{1} = 73155[/tex]
73155= [tex]7+3, 3-1, 1\times 5, \frac{5}{5} = 10251[/tex]
10251
∴ The missing number is 73155 and complete sequence is 88511,16351,73155, 10251
A bookstore costs $105 a day to keep open, and it spends $12 for each book
that it sells. If each book sells for $15, what is the break-even point for this
bookstore?
After selling 35 books, the store will break-even.
Step-by-step explanation:
Given,
Cost required per day to keep store open = $105
Amount spent on each book = $12
Let,
n be the number of books.
Total costs = 12n + 105
Selling price of each book = $15
Total revenue = 15n
For braking even;
Costs = Revenue
[tex]12n+105=15n\\105=15n-12n\\105=3n\\3n=105[/tex]
Dividing both sides by 3
[tex]\frac{3n}{3}=\frac{105}{3}\\n=35[/tex]
After selling 35 books, the store will break-even.
Keywords: revenue, cost, division
Learn more about division at:
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the smith family is driving to a vacation spot the number of miles they have left is 540-60x where x represents the number of driving hours what does 60x represent
Answer:
The number of miles traveled for x hours
Step-by-step explanation:
Need help on 5
Is it function and explain why.
Answer:
#5
It is not a function because the some x-values can have more than one possible y-value. The x-values can have the positive and negative y-value.
Step-by-step explanation:
The equation is the equation for a circle. When you graph a circle, it does not pass the vertical line test.
Example: if x is 6
6² + y² = 100
36 + y² = 100
y² = 100 - 36
y² = 64
y = ± √64 This is true because: (-8)² = 64 AND 8² = 64
y = -8 OR 8
By the way, for #4 it is not a function.
The points (13, 4) and (13, -4) mean that x will have more than one y value. The x-value 13 will have y-values 4 and -4.
of the 20 basketball games so far this year,tracy has attended 14.what percent of basketball games has tracy attended
Answer: Tracey attended 70% of the basketball games.
Step-by-step explanation:
you would multiply 14 by 100then you would multiply 20 by xthat equals 1400=20xthen you divide both sides of the equal sign by 20and get 70%Answer:
70%
Step-by-step explanation:
As a fraction, 14 / 20.
If you multiply the 2 Terms by 5, you would get 70 / 100 which equals 70%.
Best of Luck!
What is the standard form of the equation 6, -3 with a slope of two over three
Answer:
The equation of line is y= [tex]\dfrac{2}{3}[/tex] x - 7
Step-by-step explanation:
Given as :
The points as [tex]x_1[/tex] = 6
And [tex]y_1[/tex] = - 3
The slope of the line = m = [tex]\dfrac{2}{3}[/tex]
Now, The equation of line in slope-point form
y - [tex]y_1[/tex] = m × (x - [tex]x_1[/tex])
Or, y - (-3) = [tex]\dfrac{2}{3}[/tex] × (x - 6)
Or, y + 3 = [tex]\dfrac{2}{3}[/tex] × (x - 6)
Or, 3 × (y + 3) = 2 × (x - 6)
Or, 3 y + 9 = 2 x - 12
Or, 3 y = 2 x - 12 - 9
Or, 3 y = 2 x - 21
∴ y = [tex]\dfrac{2}{3}[/tex] x - [tex]\dfrac{21}{3}[/tex]
i.e y = [tex]\dfrac{2}{3}[/tex] x - 7
So, The equation of line = y = [tex]\dfrac{2}{3}[/tex] x - 7
Hence, The equation of line is y= [tex]\dfrac{2}{3}[/tex] x - 7 Answer
paolo read 40 books in one year 35% of the books paolo read were non fiction. how many nonfiction and fiction books did he read?
Answer:
Paolo reads in total 26 fiction and 14 non- fiction books.
Step-by-step explanation:
Here, the total number of books read by Paolo = 40 books
The percentage of non-fiction books read = 35%
Now, 35% of total books read = 35% of 40
⇒ [tex]\frac{35}{100} \times 40 = 14[/tex]
So, the number of non -fiction books read by Paolo = 14
Now, the number of fiction booosk read
= Total books read - Non- Fiction books read
= 40 - 14 = 26
So, the number of fiction books read by Paolo = 26
Hence, Paolo reads in total 26 fiction and 14 non- fiction books.
1/3 the weight of a bar of gold plus 30 pounds equals the weight of that bar of gold. How much does the bar of gold weigh?
Answer:
Step-by-step explanation:
Final answer:
To find the weight of the bar of gold, solve the equation (1/3)x + 30 = x, where x represents the weight of the bar. After simplifying, the weight of the bar is found to be 45 pounds.
Explanation:
To solve this problem, let's assume the weight of the bar of gold is x pounds. According to the given information, one-third of the weight of the bar of gold plus 30 pounds equals the weight of the bar of gold. This can be written as:
(1/3)x + 30 = x
To solve for x, we can start by subtracting (1/3)x from both sides of the equation:
(1/3)x + 30 - (1/3)x = x - (1/3)x
This simplifies to:
30 = (2/3)x
To isolate x, we can multiply both sides of the equation by 3/2:
(3/2)(30) = (3/2)(2/3)x
45 = x
Therefore, the bar of gold weighs 45 pounds.
If 10 minutes is how long it took Lisa to walk 1/4 of the way home, how long does it take to walk 2/3 of the way home?
Answer:
[tex]26\frac{2}{3}[/tex] minutes (or 26 minutes 40 seconds)
Step-by-step explanation:
This problem can be very easily solved with ratios and proportions.
We can create two ratios and equate them. Then we cross multiply and find the unknown.
Let the time it takes to walk 2/3rd of the way be "t".
We will keep minutes on top (numerator) and the fractional way on the bottom (denominator) when creating our ratios.
Simply put, 10 mins = 1/4th of the way, so "t" mins means 2/3rd of the way. Thus we can write:
[tex]\frac{10}{\frac{1}{4}}=\frac{t}{\frac{2}{3}}\\\frac{1}{4}t=10*\frac{2}{3}\\\frac{1}{4}t=\frac{20}{3}\\t=\frac{\frac{20}{3}}{\frac{1}{4}}\\t=\frac{20}{3}*\frac{4}{1}\\t=\frac{80}{3}\\t=26\frac{2}{3}[/tex]
sO, IT IS GOING to take [tex]26\frac{2}{3}[/tex] minutes to go 2/3rdof the way.
Or, 26 minutes and 40 seconds
Final answer:
To find out how long it takes to walk 2/3 of the way home, set up a proportion using the information given. so 26.7 minutes take to walk.
Explanation:
To find out how long it takes to walk 2/3 of the way home, we can set up a proportion using the information given. If 10 minutes is how long it took Lisa to walk 1/4 of the way, we can say that:
10 minutes = 1/4 of the way
To find out how long it takes to walk 2/3 of the way, we can set up another proportion:
x minutes = 2/3 of the way
We can cross multiply the proportions to solve for x:
10 * (2/3) = x * (1/4)
20/3 = x/4
To solve for x, we can multiply both sides of the equation by 4:
80/3 = x
So, it takes approximately 26.7 minutes to walk 2/3 of the way home.
complete the equcomplete the equation of the line whose slope is -2 and y intercept is (0,3)ation of the line whose slope is -2 and y intercept is (0,3)
Complete the equation of the line whose slope is -2 and y intercept is (0,3)
Answer:The equation of the line whose slope is -2 and y intercept is (0,3) is y = -2x + 3
Solution:Given that line has slope of -2 and y - intercept of (0, 3)
We have to find the equation of line
The equation of line can be found by using the slope intercept form
The slope intercept form is given as:
y = mx + c
Where "m" is the slope of line and "c" is the y-intercept
Here given that slope = m = -2
y - intercept is the y-coordinate of a point where a line intersects the y-axis.
So here y intercept is (0, 3) and we get c = 3
Substituting the values in slope intercept form we get,
y = -2x + 3
Thus the equation of line is found