For this case we have that by definition, the area of a rectangle is given by:
[tex]A = w * l[/tex]
Where:
w: Is the width of the rectangle
l: is the length of the rectangle
According to the data of the statement we have:
[tex]A = 81-x ^ 2\\w = 9-x[/tex]
So, the length is given by:
[tex]l = \frac {A} {w}\\l = \frac {81-x ^ 2} {9-x}[/tex]
We factor the numerator:
[tex]l = \frac {(9 + x) (9-x)} {9-x}[/tex]
We simplify:
[tex]l = 9 + x[/tex]
So, the length is [tex]9 + x[/tex]
Answer:
[tex]9 + x[/tex]
The area of the window is
What is the length of CD? round to the nearest tenth
Answer: it is c. 10.7 cm
Rounded to the nearest tenth, the length of CD is approximately 5.8 cm.
To find the length of CD in a right triangle ABC where:
BA = 10 cm (the side adjacent to angle B)
angle B = 30 degrees
angle C = 90 degrees (a right angle)
angle D = 25 degrees
We can use the trigonometric ratio for tangent (tan) since we know the measure of angle B and the length of side BA. The tangent of an angle in a right triangle is the ratio of the length of the side opposite to the angle to the length of the side adjacent to the angle.
In this case, we want to find CD, which is the side opposite to angle B. So, we can use the following relationship:
tan(B) = CD / BA
First, find the tangent of angle B (30 degrees):
tan(30 degrees) ≈ 0.5774 (rounded to four decimal places)
Now, we can solve for CD:
CD = tan(B) * BA
CD ≈ 0.5774 * 10 cm
CD ≈ 5.774 cm
Rounded to the nearest tenth, the length of CD is approximately 5.8 cm.
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An angle of -210 degree is in standard position. What are the coordinates of the point at which the terminal side intersects the unit circle?
Answer:
( -[tex]\sqrt{3}[/tex]/2 , -1/2)
Step-by-step explanation:
-210 degrees in standard position corresponds to an angle in the 3rd quadrant 30 degrees below the negative x-axis
The hypotenuse of the triangle here is 1, and we want the coordinates.
_______________________(0,0)
|(x = -root(3)/2)
|
| (y = -1/2)
The coordinates of the point at which the terminal side intersects the unit circle are (-√3/2, -1/2).
What is the cartesian plane?The cartesian plane is a two-dimensional coordinate plane that is formed when two parallel lines meet. The X-axis is the horizontal line, and the Y-axis is the vertical line. On the Cartesian plane, the coordinate point (x, y) indicates that the point is on the right of the origin if the sign of x is positive; otherwise, the point is on the left of the origin.
Given -210 degrees is in standard position,
-210° lies in the third quadrant,
which is 180° + 30° or π + 30°
the coordinate are x = cos(π + 30°)
and y = sin(π + 30°)
cos(π + Ф) = -cosФ and
sin(π + Ф) = -sinФ
x = cos(π + 30°) = -cos30° = -√3/2
y = sin(π + 30°) = -sin30° = -1/2
Hence the coordinates of points are (-√3/2, -1/2).
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Is (2,1) a solution of the system y=3x-5
Answer:
(2,1) is a solution
Step-by-step explanation:
y = 3x-5
Substitute the point into the equation and see if it is true
1 = 3(2)-5
1 = 6-5
1=1
This is true so the point is a solution
what type of graph does not have scale and aces defined on it?
Answer:
C
Step-by-step explanation:
If f(1) =7 and f(n)=-5f(n-1)-n
then find the value of
f(4)
Final answer:
Using the recursive relationship f(n) = -5f(n-1) - n, we calculated the values step by step to find that f(4) is -914.
Explanation:
The question asks us to find the value of f(4) given that f(1) = 7 and the recursive relationship f(n) = -5f(n-1) - n.
To find f(4), we need to compute it in a step-by-step manner by first finding f(2) and f(3), and using those results to finally compute f(4).
Starting with f(1) = 7, we calculate f(2):
f(2) = -5f(1) - 2 = -5*7 - 2 = -35 - 2 = -37.
Next, calculate f(3):
f(3) = -5f(2) - 3 = -5*(-37) - 3 = 185 - 3 = 182.
Finally, calculate f(4):
f(4) = -5f(3) - 4 = -5*182 - 4 = -910 - 4 = -914.
Therefore, the value of f(4) is -914.
Final answer:
Using the recursive function given, by computing step by step from f(1) up to f(4), we find that f(4) equals -914.
Explanation:
To find the value of f(4), we must use the given recursive relation f(n) = -5f(n-1) - n, starting with the base case f(1) = 7.
Find f(2):Therefore, f(4) = -914.
Find the volume of a cylinder with a base area of 25 pi in^2 And height equal to the radius. Give your answer both in terms of pi and rounded to the nearest tenth
Answer:
The answer to your question is Volume = 125 π in³
Step-by-step explanation:
Data
Volume = ?
Base area = 25π in²
height = radius
Process
1.- Find the radius
Area of the base = πr²
-Equal
πr² = 25π
-Solve for r
r² = 25π/π
-Simplify
r² = 25
-Result
r = 5 in
2.- Find the volume of the cylinder
Volume = πr²h
-Substitution
= (25π)(5)
-Simplification
Volume = 125 π in³
2x(x)=5
I need help
Step-by-step explanation:
X interprets (0,0), (-5, 0) all you must do is divide 5 by 2 so 5÷2=2.5 that is your answer
a data set includes the following test scores:75,82,62,78.The score on a retake is 96.it the retake score replaces the lowest test grade, how is the mean affected
Answer:
Increase by 8.75
Step-by-step explanation:
75+82+67+72=296
296/4= 74
74 = Original Mean
75+82+96+78=331
New mean 82.75
82.75-74=8.75
Answer:
The mean increased by 6.8
Step-by-step explanation:
Which function has a constant rate of change -1/4?
Madison and Franklin are 6 in apart on a
map that has a scale of 1 in: 7 mi. How
far apart are the real cities?
Final answer:
The actual distance between Madison and Franklin is 42 miles.
Explanation:
To find the actual distance between Madison and Franklin, we can use the given scale of 1 in: 7 mi. Since Madison and Franklin are 6 inches apart on the map, we can multiply the scale by the number of inches to find the distance in miles.
Distance in miles = Scale x Number of inches apart = 7 mi/in x 6 in = 42 miles
Therefore, the actual distance between Madison and Franklin is 42 miles.
Someone help please ?
Answer:
16
Step-by-step explanation:
(-3r ^-4) ^-4
(-3) ^-4 * (r^-4) ^-4
We know a^-b = 1/a^b and c^d^f = c^(d*f)
1/(-3)^4 * (r)^((-4*-4)
1/81 * r^16
The value of m is 16
What is the volume of a cone with a radius of 4 centimeters and a height of 10 centimeters?
Cone V= 3Bh
1. Rewrite the formula for the base area: = 1 / 22h
2. Substitute the values into the formula V= (42)(10)
3. Evaluate the power
V = ŽA(16)(10)
4. Simplify to find the volume of the cone to be
a cm
Answer:
160/3 got it on the ed thing
The volume of the cone is 167.5 cubic centimeters
How to determine the volume of the cone?The given parameters are:
Radius, r = 4 cm
Height, h = 10 cm
The volume is calculated using:
[tex]V = \frac 13 * \pi r^2h[/tex]
So, we have:
[tex]V = \frac 13 * 3.14 * 4^2 *10[/tex]
Evaluate
[tex]V = 167.5[/tex]
Hence, the volume of the cone is 167.5 cubic centimeters
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Max wants to rent a bicycle. The cost to rent a bike is a $5 insurance fee plus $3 per hour. Max has at most $20 to spend. Write an inequality to represent this scenario. Give a value that satisfies the inequality.
The inequality that represents Max's situation with renting a bicycle is 5 + 3h <= 20. Max can rent the bicycle for up to 5 hours with his $20 budget, and renting for 4 hours would satisfy the inequality.
Explanation:The inequality to represent Max's situation with renting a bicycle, considering his budget constraints, would be:
5 + 3h \<= 20
Where h represents the number of hours Max can rent the bike. To solve for h, you subtract 5 from both sides of the inequality (which represents the fixed insurance fee) and then divide by 3 (the hourly rate for renting the bike):
3h \<= 15
h \<= 5
Thus, Max can rent the bicycle for up to 5 hours to stay within his budget of $20. An example value that satisfies this inequality is 4 hours, which would cost Max $5 for insurance plus $12 for the rental time, totaling $17.
Dionne mails a package in the shape of a right rectangular prism the package was 3 inches high 14 inches wide and 20 inches long volume is ?
Answer:
840
Step-by-step explanation:
Answer:
Step-by-step explanation:
Zach use the steps to solve this equation when Zack check the solution, it didn’t work. What was his mistake
Answer:C
Step-by-step explanation:
A composite figure has a radius of 10 cm.
10 cm
What is the area of this composite figure? Use 3.14 for $.
23.55 cm
78.5 cm
© 235.5 cm?
314 cm?
Mark this and return
Save and Exit
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Next
Next
Answer: 314cm
Step-by-step explanation:
The area of a circle = πr^2
where π = 3.14
r = radius
From the question, we've been given the radius as 10cm. So, we plug the radius into the formula.
Area= πr^2
= 3.14 × (10 × 10)
= 3.14 × 100
= 314 cm
Answer:
Step-by-step explanation:
Given a composite figure,
A circle of radius r = 10cm
We want to find the area of the circle?
Area of a circle is calculated using
A = πr²
Where π is given to be 3.14
π = 3.14
And r is the radius of the circle
Then, area of the composite figure is
A = πr²
A = 3.14 × 10²
A = 3.14 × 100
A = 314 cm²
The last option is correct
A wheel completes 2.4 revolutions in 3 seconds.
What is the angular velocity of the wheel in radians per minute?
State your answer in exact form as a simplified fraction.
Answer:
The angular velocity of the wheel in radians per minute is 96·π·rad/min
Where π = 22/7 then the angular velocity is [tex]301\frac{5}{7} \ rad/min[/tex]
Step-by-step explanation:
The number of revolutions completed per 3 seconds = 2.4 revolutions
∴ The number of revolutions completed per second = 2.4/3 = 0.8 = 4/5 revolutions
The angle per revolution = 2π radians
∴ Angular velocity per second = 0.8×2×π rad/sec
The angular velocity of the wheel in radian per second = 1.6·π·rad/sec
1 minute = 60 Seconds
∴The angular velocity of the wheel in radians per minute = 96·π·rad/minute
Where π = 22/7 then the angular velocity = [tex]301\frac{5}{7} \ rad/min[/tex].
Answer:96pi
Step-by-step explanation:
A barrel contains 50 gallons of water water leaked out of the barrel at a rate of 5 gallons every 4 days at this rate how many days did it take for all 50 gallons of water to leak out of the barrel
Answer:
40 days
Step-by-step explanation:
A barrel contains 50 gallons of water leaked out of the barrel at a rate of 5 gallons every 4 days at this rate
5 gallons leaked out in 4 days
50 gallons will leak out in (50x4)/5 = 10 ×4 = 40 days
It will take 40 days for the 50 gallons(1 barrel) to leak out
A family went to a baseball game. They parked the car in a parking lot which charged $20. The cost per ticket was $27. Write an equation for the total cost of going to the baseball game, where y is the total cost and x is the total number of people. If the family spent $236, how many people went to the game?
Answer:
[tex]y=27x+20[/tex]
8 people went to the game.
Step-by-step explanation:
Let x represent number of tickets.
We have been given that the family parked the car in a parking lot which charged $20. The cost per ticket was $27.
The cost of x tickets would be [tex]27x[/tex].
The total cost of going to baseball game would be equal to cost x tickets plus parking cost that is [tex]27x+20[/tex].
Therefore, the equation [tex]y=27x+20[/tex] represents the total cost (y) of going to the baseball game.
To find the number of people who went to game, we will equate total cost with 236 as:
[tex]236=27x+20[/tex]
[tex]236-20=27x+20-20[/tex]
[tex]216=27x[/tex]
[tex]\frac{216}{27}=\frac{27x}{27}[/tex]
[tex]8=x[/tex]
Therefore, 8 people went to the game.
What equation is the gizmo using to find the y-coordinates?
a. y = r sin e
c. y=rtan 2
b. y = r cosa
d. none of the above
Answer:
Let play build royale together
Step-by-step explanation:
b. y = r cosa
Answer: A. y= r sin e
Step-by-step explanation: I just did it
A perfume company is coming out with a new perfume called "Nile" that has a bottle in the shape of a square pyramid the height of the bottle is 6 centimeters and each side is 8 centimeters long.What is the volume of the Perfume bottle in cubic cm?
Answer:
The volume of the Perfume bottle is 128 cubic cm.
Step-by-step explanation:
We are given the following in the question:
Height of bottle, h = 6 cm
Base edge of perfume bottle, a = 8 cm
The perfume bottle in the shape of square pyramid.
Volume of perfume bottle = Volume of square pyramid.
[tex]V = a^2\times \dfrac{h}{3}[/tex]
Putting values, we get,
[tex]V = (8)^2\times \dfrac{6}{3}\\\\V = 128\text{ cubic cm}[/tex]
Thus, the volume of the Perfume bottle is 128 cubic cm.
Line segment QP is tangent to the circle. A circle is shown. Secant M P and tangent Q P intersect at point P outside of the circle. Secant M P intersects the circle at point N. The length of Q P is n, the length of N P is 11.5, and the length of M N is 24. What is the length of line segment QP? Round to the nearest unit. 13 units 17 units 18 units 20 units
Answer:
The length of line segment QP is 20 units ⇒ 4th answer
Step-by-step explanation:
If a secant and a tangent are drawn from a point outside the circle, then the product of the lengths of the secant and its external segment equals the square of the length of the tangent segment
Look to the attached figure
∵ PQ is a tangent to the circle
∵ PM is a secant intersects the circle at points N and M
- That means the product of the lengths of PM and PN is
equal to the square of the length of PQ
∴ (PQ)² = (PN). (PM)
∵ The length of Q P is n units
∴ PQ = n
∵ The length of N P is 11.5 units
∴ NP 11.5
∵ The length of M N is 24 units
∴ MN = 24
- The length of the secant PM is the sum of the lengths of PN
and MN
∵ PM = PN+ NM
∴ PM = 11.5 + 24 = 35.5
Substitute the values of PQ, PN, and PM in the formula above
∵ n² = 11.5 × 35.5
∴ n² = 408.25
- Take √ for both sides
∴ n = 20.205197
- Round it to the nearest unit
∴ n = 20
∵ n is the length of PQ
∴ The length of line segment QP is 20 units
Answer:
D. 20 units
Step-by-step explanation:
Write each set of fractions with the lowest common denominator and then find which fraction is greater. 4/7 and 5/8 3/8 and 4/9 5/6 and 7/8 3/10 and 4/15
Answer:
[tex]\frac{32}{56}\ < \frac{35}{56}[/tex]
[tex]\frac{27}{72} \ < \frac{32}{72}[/tex]
[tex]\frac{20}{24}\ < \frac{21}{24}[/tex]
[tex]\frac{9}{30}\ >\frac{8}{30}[/tex]
Step-by-step explanation:
Given that,
First set of fraction is [tex]\frac{4}{7}\ and \ \frac{5}{8}[/tex].
Second set of fraction is [tex]\frac{3}{8}\ and \ \frac{4}{9}[/tex].
Third set of fraction is [tex]\frac{5}{6}\ and \ \frac{7}{8}[/tex].
Fourth set of fraction is [tex]\frac{3}{10}\ and \ \frac{4}{15}[/tex].
Now,
Considering the first set of fraction:
LCM of 7 and 8 is 56. Now, multiply by 8 to both numerator and denominator to [tex]\frac{4}{7}[/tex]. and multiply by 7 to both the numerator and denominator to [tex]\frac{5}{8}[/tex]. We get new set of fraction as [tex]\frac{32}{56}\ and\ \frac{35}{56}[/tex].
∴[tex]\frac{32}{56}\ < \frac{35}{56}[/tex]
Again considering the second set of fraction:
LCM of 8 and 9 is 72. Now, multiply by 9 to both the numerator and denominator to [tex]\frac{3}{8}[/tex]. and multiply by 8 to both the numerator and denominator to [tex]\frac{4}{9}[/tex]. We get new set of fraction as [tex]\frac{27}{72} \ and \ \frac{32}{72}[/tex].
∴[tex]\frac{27}{72} \ < \frac{32}{72}[/tex].
Again considering the third set of fraction:
LCM of 6 and 8 is 24. Now, multiply by 4 to both the numerator and denominator to [tex]\frac{5}{6}[/tex]. and multiply by 3 to both the numerator and denominator to [tex]\frac{7}{8}[/tex]. We get the new set of fraction as [tex]\frac{20}{24}\ and \ \frac{21}{24}[/tex].
∴[tex]\frac{20}{24}\ < \frac{21}{24}[/tex].
Again considering the fourth set of fraction:
LCM of 10 and 15 is 30.Now, multiply by 3 to both the numerator and denominator to [tex]\frac{3}{10}[/tex]. and multiply by 2 to both the numerator and denominator to [tex]\frac{4}{15}[/tex].We, get the new set of fraction as [tex]\frac{9}{30}\ and \ \frac{8}{30}[/tex].
∴ [tex]\frac{9}{30}\ >\frac{8}{30}[/tex]
In a sample of people at the school dance 11 out of 15 were in favor of having the photo booth. If all 300 students were surveyed about the photo booth how many are likely to be in favor of the photo booth?
Answer:
If all the 300 students were surveyed, 220 would have been in favor of the photo booth.
Step-by-step explanation:
Sample size = 15
People out of 15 in favor of photo booth = 11
Percentage of people in favor of school dance = [tex]\frac{11}{15} \times 100\% = 73\frac{1}{3} \%[/tex]
We have to find if all 300 students are surveyed how many will be in favor of photo booth. Remember that, the sample data is the best estimator of the population data. So, the sample data of 15 students will be the best estimator for the entire population of 300 students.
Since, in the sample of 15 students, [tex]73\frac{1}{3} \%[/tex] were in favor of photo booth, we would expect that if all the 300 students were surveyed, the same percentage will be in favor of photo booth. So we need to calculate [tex]73\frac{1}{3} \%[/tex] of 300.
[tex]73\frac{1}{3} \% \text{ of 300}\\\\ = 73\frac{1}{3} \% \times 300\\\\ =\frac{220}{3} \% \times 300\\\\ =\frac{220}{300} \times 300\\\\ = 220[/tex]
This means if all the 300 students were surveyed, 220 would have been in favor of the photo booth as per the sample data.
Approximately 220 out of 300 students are likely to be in favor of the photo booth.
To determine how many of the 300 students are likely to be in favor of the photo booth, we can use the proportion given by the sample.
1. Calculate the proportion of students in favor from the sample:
Proportion = Number in favor / Total surveyed = 11 / 15
Proportion = 0.7333 (rounded to four decimal places)
2. Apply this proportion to the entire school population:
Expected number in favor = Proportion × Total school population
Expected number in favor = 0.7333 × 300
Expected number in favor ≈ 220
Therefore, out of 300 students, approximately 220 students are likely to be in favor of the photo booth.
working together it takes two computers 10 minutes to send out a company's email. If it takes the slower computer 30 minutes to do the job on its own, how long will it take the faster computer to do the job on its own?
Answer: it will take the faster computer 15 minutes to do the job on its own.
Step-by-step explanation:
Let t represent the number of minutes it will take the faster computer to do the job on its own. It means that the rate at which it does the job per minute is 1/t
If it takes the slower computer 30 minutes to do the job on its own. It means that the rate at which it does the job on its own per minute is 1/30
By working together, they would work simultaneously and their individual rates are additive. Working together it takes two computers 10 minutes to send out a company's email. It means that the rate at which both computers work together per minute is 1/10 Therefore,
1/t + 1/30 = 1/10
Cross multiplying by 30x, it becomes
3x = x + 30
3x - x = 30
2x = 30
x = 30/2
x = 15 minutes
Two dozen unrelated students went to a party. Half of them brought their mother. Only 4 of them brought their father. How many people totally went to the party?
Answer:
34
Step-by-step explanation:
100 points!!! Simplify the bottom right so there are no radicals in the denominator.
Answer:
-
[tex] \frac{ - \sqrt{2} }{10} [/tex]
step by step:
[tex] \frac{ - 1}{5 \sqrt{2 } } \times \frac{ \sqrt{2} }{ \sqrt{2} } = \frac{ - \sqrt{2} }{5 \times 2} = \frac{ - \sqrt{2} }{10} [/tex]
multiply by the square root of 2 to get rid of the square root of 2 on the bottom, then simplify. hope this helped :)
[tex]\\ \sf{:}\longrightarrow \dfrac{-1}{5\sqrt{2}}[/tex]
Multiply 5√2 on both numerator and denominator[tex]\\ \sf{:}\longrightarrow \dfrac{-1(5√2)}{(5√2)^2}[/tex]
[tex]\\ \sf{:}\longrightarrow \dfrac{-5√2}{25(2)}[/tex]
[tex]\\ \sf{:}\longrightarrow \dfrac{-5√2}{50}[/tex]
[tex]\\ \sf{:}\longrightarrow \dfrac{-√2}{10}[/tex]
A line has the points (3,7) and (5,19) on it. What is the slope of that line?
A) 3
B) (8,26)
C) 6
D) -6
Answer:
C) 6
Step-by-step explanation:
19 - 7 = 12
5 - 3 = 2
12/2 = 6
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List the angles of the triangle in order from smallest to largest measure.
Answer:
G, I, H
Step-by-step explanation:
6 and 4 force H to be the largest and G to be the smallest.
For any right triangle, the 90 degree angle is always the largest. The longest side of a triangle is always opposite the largest angle. Similarly, the shortest side of a triangle is always opposite the smallest angle.
Angle G is opposite side HI = 4 which is the smallest side, so angle G is the smallest angle.
Angle H is the middle angle as this is the longer leg, but it is not longer than the hypotenuse. The hypotenuse is always the longest side.