the printed matter on a 14 by 18 centimeter page of a book must covor 140 square centimeters. if all margins are to be the same width, how wide should they be?
Answers
x----------------> width of the margin
we know that
[Area printed matter]=140
[Area printed matter]=[(14-2x)*(18-2x)]
then
[(14-2x)*(18-2x)]=140--------> (252-28x-36x+4x²)=140
(252-64x+4x²)=140----------> 4x²-64x+112=0
using a graph tool---------> I solve the quadratic equation
see the attached figure
x1=2
x2=14----------> is not solution
the answer is
the margin should be 2 cm
Related Questions
Which statement below completes Anastasia's proof?
Answers
In triangle ADC and BCD, AB = DC (opposite sides of a rectangle are congruent)
In triangle ADC and BCD, AB = DC (opposite sides of a rectangle are parallel)
In triangle ADC and BCD, AD = BC (opposite sides of a rectangle are congruent)
In triangle ADC and BCD, AD = BC (opposite sides of a rectangle are parallel)
are the statments
Which of the following will typically offer the lowest interest rate?
A. Basic savings
B. Certificate of deposit
C. Savings bond
D. Money market savings
@countonme123 @sara17,
Answers
the distance between between two distinct points on number line is always greater than zero?
true or flase,
Answers
Great Dish believes that it will need new equipment in 8 years. The equipment will cost $26,000. What lump sum should be invested today at 12%, compounded semiannually, to yield $26,000? a. $20,186.02 c. $16,388.00 b. $16,145.82 d. $10,234.80
Answers
Answer:
d. $10,234.80
Step-by-step explanation:
we are given
The equipment will cost $26,000
so, Amount is $26000
A=26000
should be invested today at 12%
r=12%=0.12
It is compounded semiannually
so, n=2
t=8
now, we can use formula
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
now, we can plug values
[tex]26000=P(1+\frac{0.12}{2})^{2\times 8}[/tex]
now, we can solve for P
[tex]P=10234.80338[/tex]
what is the inverse and then graph the function and its inverse f(×)=-5n-14
Answers
The inverse is x = -5y - 14 Now solve for y
x + 14 = - 5y
y = (x + 14)/-5 I have included a graph to show these two relationships.
Red Line: y = -5x - 14
Blue Line: y = (x + 14)/-5
Glamour runs 2/3 mile each day she wants to know how many days she has to run before she has run a whole number of miles
Answers
2/3 × 1 = 2/3
2/3 × 2 = 4/3 (or 1 1/3)
2/3 × 3 = 2
You can also convert 2/3 to a decimal by dividing the numerator by the denominator and then multiply that to get a whole number.
ANSWER:
Glamour will have to run for 3 days to run a whole number of miles. The whole number is 2.
If mike drank more than half the juice inhis glass.what fraction of the juice could mike have drunk.
Answers
3. A prop for the theater club’s play is constructed as a cone topped with a half-sphere. What is the volume of the prop? Round your answer to the nearest tenth of a cubic inch. Use 3.14 to approximate pi.
14ich long 9inch wide half of shape with dotted line
Answers
Vt=Vc+Vh
Vt is the volumen of the prop.
Vc is the volumen of the cone.
Vh is the volume of the hemisphere.
2. The volume of the cone (Vc) is:
Vc=1/3(πr²h)
r=9 in
h=14 in
π=3.14
4. Then, you have:
Vc=(3.14)(9 in)²(14 in)/3
Vc=3560.76 in³/3
Vc=1186.92
5. The volume of the hemisphere (Vh) is:
Vh=2/3(πr³)
π=3.14
r=9 in
6. Then, you have:
Vh=(2)(3.14)(9 in)³/3
Vh=4578.12 in³/3
Vh=1526.04 in³
7. Finally, the volumen of the prop (Vt) is:
Vt=Vc+Vh
Vt=1186.92 in³+1526.04 in³
Vt=2713.0 in³
What is the volume of the prop?
The volume of the prop is 2713.0 in³
Help please, explain each step or no points.
Answers
pop/500 = 5/7
pop = 500*5/7 ≈ 357
357 of the next 500 songs downloaded are expected to be pop songs.
On each of 3 days Derrick rode 6.45 km to school 150 meters to the library and then 500 m back home how many km did he ride for the three days all together
Answers
You can find this by adding the 3 distances together and multiplying by 3. Also remember to watch the units as 500m = .5km.
Find the volume of a cylinder with a diameter of 8 inches and a height that is three times the radius. Use 3.14 for pi and round your answer to the nearest hundredth. (Hint: You may only enter numerals, decimal points, and negative signs in the answer blank) (4 points)
Answers
area of a circle =
diameter/2 = radius
so 4^2 = 16 16*3.14 = 50.24
50.24*(4*3) = 50.24*12 = 602.88
mafaaaaaaaaaaaaaaaaaaaaa
Answers
Add [tex]2[/tex] each of your sides
Like:
[tex]-5 + 2 \leq n - 2 + 2 \leq 2 +2 \\ \\ -3 \leq n \leq 4 \\ \\ Answer: C. \\ \\ \\ Good \\luck \\ on \\ your \\ assignment \\ and \\ enjoy \\ your \\ day\\ \\ \\ \\ LoveYourselfFirst:)[/tex]
-5 ≤ n - 2 AND n - 2 ≤ 2
-5 + 2 ≤ n
-3 ≤ n
n ≥ -3
n - 2 ≤ 2
n ≤ 2 + 2
n ≤ 4
So -3 ≤ n ≤ 4 (Third one)
1. Let f(x)=8/1+3e^−0.7x. What is the value of f (−3)?
2. Let f(x)=20/1+9e^3x. What is the y-intercept of the graph of f(x)?
3. Let f(x)=24/1+3e^−1.3x. What are the asymptotes of the graph of f(x)?
4. Let f(x)=15/1+4e^−0.2x. What is the point of maximum growth rate for the logistic function f(x)?
5. Let f(x)=24/1+3e^−1.3x. Over what interval is the growth rate of the function decreasing?
Answers
This detailed answer covers evaluating functions at specified values, identifying the y-intercept of a function's graph, determining asymptotes, identifying points of maximum growth rate in logistic functions, and intervals where the function's growth rate is decreasing, all critical concepts in understanding mathematical functions in high school.
Explanation:The questions provided are focused on evaluating specific values of functions, understanding the y-intercept of a graph, determining asymptotes, identifying points of maximum growth rate, and assessing intervals of decreasing growth rate for various exponential and logistic functions. Each of these concepts plays a crucial role in understanding the behaviors and characteristics of different types of mathematical functions, which are fundamental in high school mathematics.
To find f(-3) for the function f(x)=8/(1+3e^{-0.7x}), substitute x=-3 and evaluate.The y-intercept of a graph is found by evaluating the function at x=0.Asymptotes can be determined by evaluating the limits of the function as x approaches infinity or negative infinity.The point of maximum growth rate for a logistic function occurs at the point where the function's second derivative changes sign.The growth rate is decreasing over intervals where the second derivative of the function is negative.
Answer ASAP
Find the area
Answers
In this problem, you are asked to find the area of the trapezoid. The formula in finding the area of the trapezoid is:
A = [(a + b)/2] x h
Where a = base 1
b = base 2
h = height
Substituting the given measurements to the formula:
A = [(1.7 m + 6.7 m) / 2] x 5 m
A = (8.4 m / 2) x 5 m
A = 4.2 m x 5 m
A = 21 m^2
Therefore, the area of the trapezoid is 21 square meters.
solving the whole thing
Answers
x---------------> distance from people living to the city center
we Know that
Zone 1 covers people living within three miles of the city center
Zone 1 ------------> [x < 3 miles]
Zone 2 covers those between three and seven miles from the center
Zone 2 ------------> [ 3 <= x < = 7 miles]
Zone 3 covers those over seven miles from the center
Zone 3 ------------> [ x > 7 miles]
calculate the distance between two points to find the value of x
case A) point (0,0) point (3,4)
x=√[(y2-y1)² +(x2-x1)²]----------> √[(4-0)² +(3-0)²]------> √[16+9]
x=√25-------------> x=5 miles
the answer Part A)
people living in (3,4)
x=5 miles -------------> covers Zone 2 [ 3 < =x <= 7 miles]
case B) point (0,0) point (6,5)
x=√[(y2-y1)² +(x2-x1)²]----------> √[(5-0)² +(6-0)²]------> √[25+36]
x=√61-------------> x=7.81 miles
the answer Part B)
people living in (6,5)
x=7.81 miles -------------> covers Zone 3 [ x > 7 miles]
case C) point (0,0) point (1,2)
x=√[(y2-y1)² +(x2-x1)²]----------> √[(2-0)² +(1-0)²]------> √[4+1]
x=√5-------------> x=2.23 miles
the answer Part C)
people living in (1,2)
x=2.23 miles -------------> covers Zone 1 [ x < 3 miles]
case D) point (0,0) point (0,3)
x=√[(y2-y1)² +(x2-x1)²]----------> √[(3-0)² +(0-0)²]------> √[9]
x=√9-------------> x=3 miles
the answer Part D)
people living in (0,3)
x=3 miles -------------> covers Zone 2 [ 3 < =x <= 7 miles]
case E) point (0,0) point (1,6)
x=√[(y2-y1)² +(x2-x1)²]----------> √[(6-0)² +(1-0)²]------> √[36+1]
x=√37-------------> x=6.08 miles
the answer Part E)
people living in (1,6)
x=6.08 miles -------------> covers Zone 2 [ 3 < = x <= 7 miles]
solve for X
This is 10th grade Geometery (USA)
Answers
[tex] \frac{55}{35} = \frac{x}{42} [/tex]
Now you can cross multiply:
[tex]55(42) = 35x[/tex]
Solve for x:
[tex]x = \frac{55(42)}{35} = 66 [/tex]
So, x = 66.
A 3 lb bag of one brand of cat food costs $3.52. A 6 lb bag of another brand costs $6.80. Which brand is cheaper per pound?
Answers
We have then:
Mark 1:
3 lb costs $ 3.52
P = (3.52) / (3) = 1.17 $ / lb
Mark 2:
6 lb costs $ 6.80
P = (6.80) / (6) = 1.13 $ / lb
Answer:
Mark 2 is cheaper per pound:
1.13 $ / lb
Tropical forests are being lost at the rate of 5 million hectares per year. how many hectares per day is that? how many hectares per minute?
Answers
365 days in a year
1440 minutes in a day (24hrs)
1. _____is when an asset increases in value.
~depreciation
~appreciation
~inflation
~purchasing power
2. when money loses some of its value over time, it is caused by_____
-inflation
-FICA
-purchasing power
-recalculating worth
ive tried i need help @bibby @phi someone :( @SolomonZelman,
Answers
1) Appreciation is when an asset increases in value.
2) When money loses some of its value over time, it is caused by inflation
The appreciating assets is any asset which value is increasing it is a an increased demand.
Therefore,
When value of assets increases in value?
Appreciation
1) Appreciation is when an asset increases in value.
Next,
The impact inflation has on the time value of money is that decrease the value of dollar over time.
Therefore,
2) When money loses some of its value over time, it is caused by inflation
Therefore,
1) Appreciation is when an asset increases in value.
2) When money loses some of its value over time, it is caused by inflation
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what is 62% of 25 ?
im horrible at this plz help
Answers
Convert 62% into a decimal: 0.62. Then multiply them: 0.62 · 25, which equals 15.5 !
'of' means multiplication.
[tex]\sf 62\%\times 25[/tex]
Convert 62% to a decimal, divide it by 100(since percentages are parts of 100):
62/100 = 0.62
[tex]\sf 0.62\times 25[/tex]
Multiply:
[tex]\sf\boxed{\sf 15.5}[/tex]
help!!!!!!! please !!!!!!!
Answers
If 1 inch represents 75 miles on a map, then how many inches will represent 1500 miles? a. 10 c. 12 b. 20 d. 14
Answers
Here is your answer:
The proper answer to your question is option B "20".
Here is how:
Just use this equation:
1500/75=20
Which means its 12!
If you need anymore help feel free to ask me!
Hope this helps!
20 inches
Explanation:
We are given that:
1 inch represents 75 miles
Therefore,
To solve this question, we will simply use cross multiplication as follows:
1 inch ..................> 75 miles
?? inches ............> 1500 miles
Number of inches = (1500*1) / (75) = 20 inches
Hope this helps :)
What is the inverse of f(x) = 8x - 7
Answers
Work:
Y=8x-7 —> x=8y-7
Solve for y
x+7=8y
y=(x+7)/8
The inverse of the function f(x) = 8x - 7 can be found by switching the x and y, then solving for y. This gives the inverse function as f^-1(x) = (x + 7) / 8.
Explanation:The inverse of a function is calculated by switching the input and output variables. Given your question, we are to find the inverse of the function f(x) = 8x - 7. To do this, we first rename f(x) as y, giving us y = 8x - 7.
Next, we switch the positions of x and y, leading to x = 8y - 7. Then, to isolate y which represents the inverse function, we should solve the equation for y: x + 7 = 8y and y = (x + 7) / 8. So, the inverse of the function f(x) = 8x - 7 is f^-1(x) = (x + 7) / 8.
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What is the graph of the function f(x) = the quantity of x plus 4, all over x plus 6?
Answers
1. The denominator gives a discontinuity point at (x = - 6). You can tell that is happening just by looking at the graph at x = - 6. The range at that point is - infinity to plus infinity. Other critical points are much better behaved. The y intercept is when x = 0 or 4/6 = 2/3. So the point is (0,2/3)
There is one x intercept at y = 0. When that happens
x + 4 = 0
x = - 4
Point (-4,0)
Notice the whole denominator gets multiplied out. 0 * (x + 6) = 0
A system of inequalities is graphed below. The variable x represents the number of cans someone is buying, and y represents the number of bottles. Conditions on the maximum amount of total weight and volume lead to two of the inequalities.
Which descriptions correspond to solutions of this system?
7 cans and 140 bottles
12 cans and 40 bottles
8 cans and 120 bottles
9 cans and 70 bottles
Answers
We will analyze each case to verify the answer
see the attached figure
Point A) 7 cans and 140 bottles------------> (x,y)=(7,140)----> is not solution
Point B) 12 cans and 40 bottles------------> (x,y)=(12,40)----> is not solution
Point C) 8 cans and 120 bottles------------> (x,y)=(8,120)----> is a solution
Point D) 9 cans and 70 bottles------------> (x,y)=(9,70)-------> is a solution
the answer is
the solutions are
8 cans and 120 bottles
9 cans and 70 bottles
An explosion causes debris to rise vertically with an initial velocity of 160 feet per second. What is the speed of debris when the height is 300 feet?
I am using the formula: -16t^2 + vot + h0 because the question is referring to feet.
Answers
We know there will be a constant downward acceleration of 32.15 ft/s^2.
Use the following equation:
v_final^2 = v_initial^2 + 2ah
v_final^2 = (160 ft/s)^2 + 2(-32.15 ft/s^2)(300 ft) = 6310 ft^2/s^2
v_final = (6310 ft^2/s^2)^1/2 = 79.4 ft/s.
The speed of the debris is 79.4 ft/s
Calculation of the speed:Since there is an initial velocity of 160 feet per second, height is 300feet
So, we applied the below formula
[tex]v_({final})^2 = v_({initial})^2 + 2ah\\\\ v_({fina})l^2 = (160 ft/s)^2 + 2(-32.15 ft/s^2)(300 ft)\\\\ = 6310 ft^2/s^2\\\\ = (6310 ft^2/s^2)^{1/2}\\\\ = 79.4 ft/s.[/tex]
Therefore, The speed of the debris is 79.4 ft/s
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Select the ratios whose simplest form is 8/7
Answers
16:14
56:49
I hope this helps.
Answer:
48:42
16:14
56:49
Step-by-step explanation:
I hope I made your day
Your sock drawer has 3 pairs of black socks, 4 pairs of brown socks, 1 pair of yellow socks and 5 pairs of blue socks. you reach into the drawer in the dark and randomly pick out 2 pairs for your business trip. what is the probability your pick out in this order. 2 black pairs?
Answers
Black socks: 3
Probability to pick out black socks: 3/13
After one pick out (You picked out a pair of black socks):
Probability to pick out black socks: 2/12
Multiply them:
2/12 * 3/13 = 1/26 ≈ 0,038
The probability your pick out in this order 2 black pairs 1/26.
What is the probability?
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Mathematics to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory.
According to the question,
The sock drawer has 3 pairs of black socks, 4 pairs of brown socks, 1 pair of yellow socks and 5 pairs of blue socks.
All socks together = 3+4+5 = 13
Black socks = 3
Probability to pick out black socks: 3/13
After one pick out (You picked out a pair of black socks),
Probability to pick out black socks: 2/12
Then, the probability = 2/12 × 3/13 = 1/26.
Hence the required probability = 2/12 × 3/13 = 1/26.
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HELP WITH THESE SERIES OF QUESTIONS!!
1. Factor the polynomial. 3x^3 − 27x^2 + 19
2. Factor the polynomial. 15z^3 + 25z^2
3. Factor the polynomial. 9x^7 + 33x^3
Answers
2. 5x^2 x (3x+5)
3. 3x^3 x (3x^4 +11)
Will give Metal! From 1948 to 1994, South Africa existed under a system of apartheid. Under this system, white South Africans- about 18% of the population- controlled all of the instruments of government: the Parliament, the Executive Branch, and the courts. Black and non-white South Africans had few legal rights and could not vote in elections. Voting was limited to white South African citizens. . This passage is describing what type of government? A) autocratic B) democratic C) dictatorship D) oligarchic,