The dimensions should be 6ft by 9ft.
Final answer:
The dimensions of the floor with an area of 54 square feet, where the width is 2/3 of the length, are 9 feet in length and 6 feet in width.
Explanation:
Pascal wants to find the dimensions of a floor where the area is 54 square feet and the width is 2/3 the length. To find the dimensions, we set up an equation where the length is L and the width is W, with W = (2/3)L. Since area is calculated by the formula Area = length times width, we get 54 = L times (2/3)L. Solving this equation by multiplying the length terms and then dividing both sides by 2/3, we get L² = 54 times (3/2), which simplifies to L² = 81. Taking the square root of both sides gives us L = 9 feet. Consequently, the width would be W = (2/3) times 9 = 6 feet. Therefore, the dimensions of the floor are 9 feet by 6 feet.
in a right circular cylinder of height 2 meters, if the volume is increasing at 10 m^3/min how fast is the radius of the cylinder increasing when the radius is 4in?
Given dimensions:
Height of the cylinder = 2 m
Volume is increasing at a rate of = 10 m³/min
Radius = 4 inches
Converting radius in meters.
1 inch = 0.0254 meters
4 inches = [tex]4\times0.0254=0.1016[/tex] meters
[tex]\frac{dv}{dt}=10[/tex]
we have to find, [tex]\frac{dr}{dt}=?[/tex]
Volume of the cylinder is given by [tex]\pi r^{2} h[/tex]
= [tex]\pi r^{2} *2 = 2\pi r^{2}[/tex]
Now differentiating with respect to 't'
[tex]\frac{dv}{dt} = \frac{d}{dt} (2\pi r^{2})[/tex]
[tex]\frac{dv}{dt} = 2\pi (2r)(\frac{dr}{dt})[/tex]
[tex]10=2\pi (2*0.1016)\frac{dr}{dt}[/tex]
[tex]10=2*3.14(0.2032)\frac{dr}{dt}[/tex]
[tex]\frac{dr}{dt}=\frac{10}{1.276}[/tex]
= 7.83 meter per minute.
Find the sum of the first 12 terms of the arithmetic series 32+27+22+...
Answer:77
32+27+22+17+12+7+2-3-8-13-15-18=77
Answer:
54
Step-by-step explanation:
The first twelve terms would be, in decreasing order, 32, 27, 22, 17, 12, 7,2, -3, -8,-13,-18,-23.
1. -23+22 = -1
2. -13+12 = -1
3. -18+17 = -1
4. -8+7 = -1
5. -3+2 = -1
Using these five facts, we can simplify this to 32+27 -5(1) = 32+27-5 = 54
What is an equivalent expression to (0.7g+0.6h-0.4)+(0.8-0.6h+0.5g)
Answer:
1.2g+0.4
Step-by-step explanation:
The equivalent expression should be 1.2g+0.4.
Given information:
The equation is (0.7g+0.6h-0.4)+(0.8-0.6h+0.5g)
Calculation of an expression:= (0.7g+0.6h-0.4)+(0.8-0.6h+0.5g)
= 0.7g + 0.6h - 0.4 + 0.8 - 0.6h + 0.5g
= 1.2g + 0.4
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Two cyclists, Alan and Brian, are racing around oval track of length 450m on the same direction simultaneously from the same point. Alan races around the track in 45 seconds before Brian does and overtakes him every 9 minutes. What are their rates, in meters per minute?
Answer:
Alan: 200 m/minBrian: 150 m/minStep-by-step explanation:
Let n represent the number of laps that Alan completes in 9 minutes. Then n-1 is the number of laps Brian completes, and the difference in their lap times in minutes per lap is ...
9/(n -1) - 9/n = 3/4 . . . . . minutes
Multiplying by (4/3)n(n -1), we get
12n -12(n -1) = n(n -1)
12 = n(n -1)
Solutions to this are n=4 and n=-3. We are only interested in the positive solution, n = 4. Then Alan's speed in m/min is ...
(4·450 m)/(9 min) = 200 m/min
Brian completes 3 laps in that 9-minute time, so his rate is ...
(3·450 m)/(9 min) = 150 m/min
Write the expression as a polynomial, using the corresponding formula for special product: (−a+b)(b–a)
Answer:
b² -2ab +a²
Step-by-step explanation:
The first factor can be rearranged to put the minus sign in the middle. Then you have
(b -a)(b -a) = (b -a)² = b² -2ab +a²
___
If you like, you can also write this as ...
a² -2ab + b² . . . . . . terms in lexicographical order
_____
The "special product" of interest here is the square of a binomial:
(p +q)² = p² +2pq +q²
You have p=b, q=-a, so the result is as shown above.
A hot iron ball of mass 200 g is cooled to a temperature of 22°C. 6.9 kJ of heat is lost to the surroundings during the process. What was the initial temperature of the ball? (ciron = 0.444 J/g°C)
Answer:
99.7 °C
Step-by-step explanation:
The units of ciron tell us that in order to have °C in the numerator, we need to divide the heat loss by the product of the mass and ciron:
∆T = (6900 J)/(0.444 j/g°C × 200 g) = 69/0.888 °C ≈ 77.7 °C
This is the change in temperature as the ball cooled, so its initial temperature was ...
22 °C +77.7 °C = 99.7 °C
in this right triangle the length of the hypotenuse, BC, is
Answer:
√13 units
Step-by-step explanation:
Find points B and C on the figure and locate the line between those points. The number next to the line is its length. Read the length from the diagram.
In a right triangle, the hypotenuse is the side across from the 90 degree angle. Without more information, we can't determine the length of the hypotenuse (BC), but if the lengths of the other two sides or the measurements of the other angles are known, the Pythagorean theorem or trigonometry can be used. It is expressed as BC^2 = AB^2 + AC^2.
Explanation:In a right triangle, the hypotenuse is the side that is opposite to the 90 degrees angle. In your right triangle, as you mentioned the sides as BC, I assume you have a triangle ABC where B and C are the two base angles and A is the right angle (90 degrees).
Without additional information such as the lengths of the other two sides (AB, AC), or the measurements of angles B or C, it is impossible to determine the length of the hypotenuse (BC). However, if you do have this information, you can use the Pythagorean theorem or trigonometric ratios to find the length. Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (BC) is equal to the sum of the squares of the lengths of the other two sides. It is expressed as BC^2 = AB^2 + AC^2.
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what is the sum of measurements of the interior angles of a 12-gon?
Answer:
1800
Step-by-step explanation:
Given in the question a polygon of 12 sides
Formula to calculate sum of interior angles of 12-gon is
(n – 2)180where n is the number of sides
which in this case = 12
plug values in the formula above
(12 - 2)180
12*180 - 180(2)
2160 - 360
1800
Sum of measurements of the interior angles of a 12sided polygon is 1800
Answer:
=1800°
Step-by-step explanation:
A 12 sided figure is called a do-decagon or a 12-gon. The general formula for calculating the sum of all interior angles of a regular polygon is=180(n-2)
n represents the number of sides of the polygon.
Therefore, the sum of all angles= 180(12-2)
=1800°
(-8/9) / (-2/3) * (-4 1/2) plz help urgent
Answer: (-6) is the answer for your question
Mr. Burnam decided to go hot air ballooning for his fortieth birthday. He launches from 6 feet above ground and then ascends 12 feet further. He didn't want to leave his wife behind, so he descends 20 feet to meet her. Where does mr. Burnam end up?
Answer:
2 feet below the ground level at the place where he started.
Step-by-step explanation:
After he adds 12 feet of elevation to the 6 feet above ground level where he launched, Mr Burnam is 6+12 = 18 feet above the ground level where he launched.
If he descends 20 feet, he will be 18 -20 = -2 feet above the ground level where he launched. That is, he is 2 feet below the ground level where he launched. We hope the ground slopes downward somewhat so Mr Burnam is not buried in the ground at that point.
Mr. Burnam ends up at 8 feet above ground.
To determine Mr. Burnam's final position, we need to consider each of his movements:
1. He starts from 6 feet above ground.
2. He ascends 12 feet further, so we add 12 feet to his initial height of 6 feet, which gives us (6 + 12 = 18) feet.
3. Then, he descends 20 feet to meet his wife. We subtract these 20 feet from his current height of 18 feet, which gives us (18 - 20 = -2) feet.
Since he can't be below ground, we adjust the calculation to reflect that he stops at ground level. Therefore, we take the absolute value of the result to find out how far above ground he is after the descent. The absolute value of -2 feet is 2 feet.
Now, we add this to the initial 6 feet from which he launched: (6 + 2 = 8) feet.
So, Mr. Burnam ends up at 8 feet above ground after all the ascending and descending.
Given circle assume that AB Is tangent to the circle and AD Passes through the center of the circle. If the circle has a radius of 5CM and AB is 6CM what is the length of the secant
Answer:
d. 2√34 cm
Step-by-step explanation:
Secant BD is the hypotenuse of right triangle ABD with legs given as AB = 6 cm and AD = 10 cm. Hence the Pythagorean theorem can be used to find BD:
BD = √(AB² +AD²) = √((6 cm)² +(10 cm)² = √136 cm = 2√34 cm
Last month Rachel power walked 2 1/5 miles per day on each of the 10 days. During the same week, she also joggged 8 1/4 Miles per days on 3 days. What was the total number of miles Rachel power walked and jogged last month?
she went a total of 46.75 miles
Which inequality represents the interval of tenths that the square root of 14 lies between?
Answer:
3.7 < √14 < 3.8
Step-by-step explanation:
First approximation
9 < 14 < 16, so
3 < √14 < 4
Second approximation
14 is closer to 16 than to 9.
Is √14 between 3.7 and 3.8? If so, then
3.7² < 14 < 3.8²
13.69 < 14 < 14.44. TRUE
The inequality is 3.7 < √14 < 3.8.
a similar figure compared to the original figure is ___ a translation. A.) sometimes B.) never C.) always D.) none of these choices will make a true statement
Answer:
A). Sometimes.
Step-by-step explanation:
Sometimes a translation because it might be a rotation or a reflection.
Translation in geometry always results in a similar figure. Hence, the correct answer is C.
A similar figure compared to the original figure is **always** a translation.
Translation in geometry involves moving a figure without rotating or flipping it. When a figure is translated, all the points move in the same direction by the same distance. This means that a translation produces a figure that is congruent to the original figure.
The 5th picture with the question I need help with.
Answer:
Step-by-step explanation:
27
How do I find The first figure is dilated to form the second figure.
Which statement is true?
A. The scale factor is 0.25.
B. The scale factor is 4.
C. The scale factor is 4.35.
D. The scale factor is 7.25.
Answer:
The marked choice is correct
Step-by-step explanation:
The scale factor is the ratio of the dimensions of the second figure to those of the first:
1.45/5.8 = 0.25
Answer:The scale factor is 0.25. Trust me, its right!
Please help!!!! ASAP I’ll mark you as brainliest
Answer:
Vel_jet_r = (464.645 mph) North + (35.35 mph) East
||Vel_jet_r|| = 465.993 mph
Step-by-step explanation:
We need to decompose the velocity of the wind into a component that can be added (or subtracted from the velocity of the jet)
The velocity of the jet
500 mph North
Velocity of the wind
50 mph SouthEast = 50 cos(45) East + 50 sin (45) South
South = - North
Vel_ wind = 50 cos(45) mph East - 50 sin (45) mph North
Vel _wind = 35.35 mph East - 35.35 mph North
This means that the resulting velocity of the jet is equal to
Vel_jet_r = (500 mph - 35.35 mph) North + 35.35 mph East
Vel_jet_r = (464.645 mph) North + (35.35 mph) East
An the jet has a magnitude velocity of
||Vel_jet_r|| = sqrt ((464.645 mph)^2 + (35.35 mph)^2)
||Vel_jet_r|| = 465.993 mph
Two friends live 27 miles apart. They left their houses at the same time and started to walk towards each other at 4 mph and 5 mph respectively. How soon did they meet?
Answer:
They meet in 3 hours
Step-by-step explanation:
Add 4 and 5, this gives you 9 miles an hour. Divide 27 by 9 and it results in 3 hours
In the equation kx^2 + 5x = 10k, find the other root if one root is -5.
Subtract 10k from both sides:
[tex] kx^2+5x-10k = 0 [/tex]
Assuming [tex]k\neq 0[/tex], divide both sides by k:
[tex] x^2+\dfrac{5}{k}x-10 = 0[/tex]
When you write a quadratic equation as [tex]x^2-sx+p [/tex], you know that the two solutions follow the properties
[tex]x_1+x_2=s,\quad x_1x_2=p [/tex]
So, in this case, we have
[tex]x_1+x_2=-\dfrac{5}{k},\quad x_1x_2=-10 [/tex]
Since we know that [tex]x_1=-5[/tex] we have:
[tex]\begin{cases}-5+x_2=-\dfrac{5}{k}\\ -5x_2=-10\end{cases}[/tex]
This system has solution [tex]k=\frac{5}{3},\ x=2[/tex]
Answer:
2
Step-by-step explanation:
One root = -5
We know ,
Product of roots = c/a-5 * x = -10k / k -5x = -10 x = 2Other root is 2 .
I have a stat class review and what would be the letter choice for this scatter plot?
A Scatterplot with the least squares regression line is shown.
estimate the value to the nearest half unit
what is the observed value for X=3
A 1.5
B -1.5
C 4.5
D 6
Please any explanation helps im offering 25 pts:)
The observed value when x = 3, estimated to the nearest half unit is y = 4.5.
What is known as observed value?The observed value is the actual value of the variable. The points on the regression line are called predicted values.
From the given image, we can observe that the value of y for which x is 3 is shown as somewhere between 4 and 5. The only value of y which lies between 4 and 5 in the given options is 4.5. It is the observed value.1.5, -1.5, and 6 do not lie between 4 and 5. Therefore, they are not the correct answers.Therefore, the observed value of y when x = 3, estimated to the nearest half unit is y = 4.5. The correct answer is option C.
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Any Help would be appreciated!!
Multiply.
(5 − 1)(6^2 + 3 + 7)
Answer:
184
Step-by-step explanation:
1st step
we simplify (5-1) which is just 4 and (3+7) which is 10
and we also simply 6^2 which is 36
now we plug the simplified terms back in
(4)(36+10)
(4)(46)
184
Answer:
184
Step-by-step explanation:
Subtract: 5 - 1 = 4
Power: 6 ^ 2 = 36
Add: 36 + 3 = 39
Add: 39 + 7 = 46
Multiple: 4 * 46 = 184
Please mark as brainiest
Betsy, a recent retiree, requires $5000 per year in extra income. She has $70000 to invest and can invest in B-rated bonds paying 15% per year or in a certificate of deposit (CD) paying 5% per year. How much money should be invested in each to realize exactly $5000 in interest per year?
Answer:
$15000 in bonds, $55000 in a CD
Step-by-step explanation:
Let x represent the amount Betsy invests in the B-rated bonds (in thousands). Then she will invest 70-x in a CD. Her interest (in thousands) will be ...
0.15x + .05(70 -x) = 5
0.10x + 3.5 = 5 . . . . . . . eliminate parentheses, collect terms
x + 35 = 50 . . . . . . . . . . multiply by 10
x = 15 . . . . . . . . . . . . . . . subtract 35
Then 70-x = 70-15 = 55
Betsy should invest $15000 in bonds, and $55000 in a CD.
To achieve $5000 in annual interest, Betsy should invest $15000 in B-rated bonds and $55000 in CDs.
Betsy, a recent retiree, requires $5000 per year in extra income. She has $70000 to invest and is considering two options: B-rated bonds paying 15% per year and certificates of deposit (CD) paying 5% per year. To find out how much she should invest in each to realize exactly $5000 in interest per year, we can set up a system of linear equations.
Let x be the amount invested in B-rated bonds and y be the amount invested in CDs. The equations based on the investment and the total interest required would be:
x + y = $700000.15x + 0.05y = $5000To solve this system, multiply the second equation by 100 to get rid of decimals:
15x + 5y = 500000Now, we can multiply the first equation by 5 to get:
5x + 5y = 350000Subtracting this from the modified second equation:
(15x + 5y) - (5x + 5y) = 500000 - 35000010x = 150000x = $15000Plug the value of x back into the first equation:
15000 + y = 70000y = $55000Betsy should invest $15000 in B-rated bonds and $55000 in a CD to achieve $5000 in annual interest.
a movie rental club charges a one time fee of $25 to join and $2 for every movie rented which equation could represent how much you would spend to join the club and rent movies for a year?
A c=12+25m
B c=25+2m
C c=12m+2
D c=25m+24
Answer:
The correct answer option is B. c = 25 + 2m.
Step-by-step explanation:
We are given that a movie rental club charges a one time fee of $25 to join and $2 for every movie rented.
We are to determine whether which of the given equations in the answer options represent how much you would spend to join the club and rent movies for a year.
The correct answer option is B. c = 25 + 2m.
One time charges = 25 plus $2 multiplied by the number of movies rented.
(8q+5)^2=64q^2+[]q+25
What is the missing value? []
Answer:
80
Step-by-step explanation:
The square of a binomial is ...
(a +b)^2 = a^2 + 2ab + b^2
You have a=8q, b=5, so the square is ...
(8q)^2 + 2(8q)(5) + (5)^2
= 64q^2 +80q +25
The coefficient missing from your given expression is 80.
A friend bought 2 boxes and 8 notebooks for school, it cost him $11 He went back to the store the same day to buy school supplies for his younger brother. He spent $11.25 on 3 boxes of pencils and 5 notebooks. How much would 7 notebooks cost?
Answer:
$5.25
Step-by-step explanation:
If the friend tripled the first purchase and subtracted twice the second purchase, he would have the cost of 3·8-2·5 = 14 notebooks. 7 notebooks would cost half that amount:
(3·$11 -2·11.25)/2 = $5.25 . . . . . cost of 7 notebooks
Which answer is the explicit rule for the sequence11,8.5,6,3.5,1
Answer: - 2.5n+13.5
Explanation:
[tex]11 - 8.5 = 2.5 \\ - 2.5n \times 1 = - 2.5 \\ it \: is \: negative \: as \: the \: sequence \: \\ decreases\\ 11 - - 2.5 = 13.5 \\ - 2.5n + 13.5[/tex]
The explicit rule for the sequence 11, 8.5, 6, 3.5, 1 is to subtract 2.5 from the previous term.
To find the explicit rule, we look for a pattern in the sequence. We can see that each term is decreasing by a constant amount. Let's calculate the difference between consecutive terms:
- The difference between the second term (8.5) and the first term (11) is 8.5 - 11 = -2.5.
- The difference between the third term (6) and the second term (8.5) is 6 - 8.5 = -2.5.
- The difference between the fourth term (3.5) and the third term (6) is 3.5 - 6 = -2.5.
- The difference between the fifth term (1) and the fourth term (3.5) is 1 - 3.5 = -2.5.
Since the difference is constant and equal to -2.5, we can express the nth term of the sequence, [tex]\( a_n \)[/tex], as:
[tex]\[ a_n = a_{n-1} - 2.5 \][/tex]
where [tex]\( a_{n-1} \)[/tex] is the previous term in the sequence. To express this in terms of n, we need to find the first term of the sequence and then apply the pattern. The first term, [tex]\( a_1 \)[/tex], is 11. Since we are subtracting 2.5 each time, the nth term can be written as:
[tex]\[ a_n = a_1 - (n - 1) \cdot d \][/tex]
where [tex]\( d \)[/tex] is the common difference, which is -2.5. Substituting [tex]\( a_1 = 11 \) and \( d = -2.5 \)[/tex], we get:
[tex]\[ a_n = 11 - (n - 1) \cdot (-2.5) \][/tex]
[tex]\[ a_n = 11 + 2.5n - 2.5 \][/tex]
[tex]\[ a_n = 8.5 + 2.5n \][/tex]
Therefore, the explicit rule for the nth term of the sequence is:
[tex]\[ a_n = 8.5 + 2.5n \][/tex]
This rule gives us the terms of the sequence when we substitute n = 1, 2, 3, 4, 5, etc. For example, for n = 1:
[tex]\[ a_1 = 8.5 + 2.5(1) = 8.5 + 2.5 = 11 \][/tex]
which matches the first term of the sequence.
Which of the following ordered pairs represents a solution to the linear inequality y>2x-3
Answer:
D. (2, 5)
Step-by-step explanation:
On a graph, (2, 5) is the only point in the solution space.
___
You can evaluate the inequality for each of the points to see which works.
A. 4 > 2·4 -3 . . . . false
B. 12 > 2·9 -3 . . . . false
C. 2 > 2·3 -3 . . . . false
D. 5 > 2·2 -3 . . . . TRUE
The sum of three positive numbers is 1. The difference between the first and second numbers is equal to the third number, while their sum is five times as large as the third number. What is the smallest of these numbers? pls answer quickly, 99 pts
Answer:
1/6
Step-by-step explanation:
The three numbers, a, b, c, satisfy the equations ...
a +b +c = 1a -b -c = 0a +b -5c = 0Subtracting the last equation from the first gives ...
(a +b +c) -(a +b -5c) = (1) -(0)
6c = 1
c = 1/6
Now, we know the sum of the first two numbers is 5/6 (five times the last), and the difference of the first two numbers is 1/6 (equal to the last). Then the least of the first two numbers is ...
(5/6 -1/6)/2 = 1/3
and the third number, 1/6, is shown to be the smallest.
The smallest of these numbers is 1/6.
____
In order, the numbers are 1/2, 1/3, 1/6.
____
Comment on finding the second-smallest number
For ...
a +b = 5/6 . . . . . sum of the two numbersa -b = 1/6 . . . . . . difference of the two numbersWe can find b by subtracting the second equation from the first:
(a +b) -(a -b) = (5/6) -(1/6)
2b = 4/6 = 2/3 . . . . . simplify
b = 1/3 . . . . . . . . . . . . divide by 2
Please note that half the difference of the sum and difference is the generic solution to finding the smallest in a "sum and difference" problem.
it is recommended that 13-year old girls get 45 milligrams of vitamin C each day . The table shows the vitamin C content of three foods . What precentage of the recommended amount will Ardis receive if she eats all of these foods in one day.
(Answers)
A 2.22
B 6.00
C 270
D 600
Need help on this please
Answer:
The answer is -3t(t^4 - 6t² - 1) ⇒ third answer
Step-by-step explanation:
∵ -3t^5 + 18t³ + 3t
∵ The common factor is -3t
∴ -3t(t^4 - 6t² - 1)