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
Mansah earns a salary of GH¢ 10,000.00 per month, as a sales girl. In addition to the salary , she is given a commission of 15 percent of what ever sales that she makes in a month. In January this year, she made sales of GH¢ 1,500,00.00. What was the total Mansah earned at the end of January?
Answer:
66,000
Step-by-step explanation:
Answer:
GH¢32,500
Step-by-step explanation:
Monthly salary of Mensah=GH¢10,000.00
Commission=15%
15/100×GH¢ 1,500,00.00=GH¢22,500
Total amount earned=
Monthly salary+ Commission
GH¢10,000+GH¢22,500=GH¢32,500
Answer:
GH¢32,500
Step-by-step explanation:
Monthly salary of Mensah=GH¢10,000.00
Commission=15%
15/100×GH¢ 1,500,00.00=GH¢22,500
Total amount earned=
Monthly salary+ Commission
GH¢10,000+GH¢22,500=GH¢32,500
The average number of hours of sleep per night was 9.46 hours for a sample of 104 five to seven year-old children. The number 9.46 is a __________, because it is a number that can be computed from the sample of 104 children.
Answer:
Statistic
Step-by-step explanation:
-In statistics, a statistic is a characteristic or an attribute of a sample used to estimate or calculate the true values/characteristics of an entire population.
-The value 9.6 is only representative of the small sample size of 104 children.
-If the sample size is sufficient enough it can be used to calculate the population's mean, standard deviation and other Central Limit Theorem measures.
The number 9.46 is referred to as a statistic in this context. A statistic is a characteristic that can be computed from the data in a sample, like the average sleep time of 104 children in this case.
Explanation:The average number of hours of sleep per night was 9.46 hours for a sample of 104 five to seven year-old children. In this context, the number 9.46 is referred to as a statistic.
A statistic is a characteristic that can be computed from the data in a sample. For example, in this case, the data was collected from a group (or sample) of 104 children, and the average hours of sleep they got per night was calculated. The resultant number, 9.46 hours, serves as an estimation of the parameter we are interested in: the average sleep time of all 5 to 7 year-olds.
The term is frequently used in
statistics
, a branch of math that refers to the collection, analysis, interpretation, presentation, and organization of data.
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You want to construct an enclosed rectangular region using the side of a building as part of one side of the enclosed region. The building is 56 feet wide. You have 544 feet of fencing to use. Find the area of the largest region that you can enclose using these requirements
Answer:
13664 square feet
Step-by-step explanation:
Width of the Building=56 feet
Let the length of the building=L
Area of the building = LW=56L
A=56L
Available Perimeter for Fencing= 544 feet
Since we are using the side of the building as one part,
Perimeter = 2L+56=544
2L=544-56=488
L=244 feet
The area of the largest region that can be enclosed using theses requirements is given as:
Area = 244 X 56 =13664 square feet
To find the area of the largest region that can be enclosed with 544 feet of fencing alongside a 56-foot wide building, one sets up an equation for the fencing and solves for the width of the enclosure. The widest possible enclosure has a width of 244 feet, leading to a maximum area of 13,664 square feet.
To find the area of the largest rectangular region that can be constructed using the side of a building and a given amount of fencing, one must use the perimeter formula for a rectangle. Let's designate the widths of the rectangle that are not attached to the building as x, and the length that is attached to the building as 56 feet. Since two of the widths and one length will be enclosed by the fence, the total fencing used will be 2x + 56 feet.
Given that there are 544 feet of fencing available, we can set up the following equation:
2x + 56 = 544
Solving for x gives the width of the two sides not attached to the building:
2x = 488
x = 244 feet
The largest enclosed area will then be obtained by multiplying the length (alongside the building) by the width (the calculated x):
Area = 56 feet × 244 feet = 13664 square feet.
This calculation provides the largest possible rectangular area that can be enclosed with the given fencing, using the building as one side of the enclosure.
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
Purse A which contains $1,000 today. If you leave it alone, it will contain $1,200 tomorrow (by magic). The next day, it will have $1,400. This pattern of $200 additional dollars per day will continue. Purse B which contains 1 penny today. Leave that penny in there, because tomorrow it will (magically) turn into 2 pennies. The next day, there will be 4 pennies. The amount in the purse will continue to double each day. How much money will be in each purse after a week? After two weeks? The genie later added that he will let the money in each purse grow for three weeks. How much money will be in each purse then? Which purse contains more money after 30 days?
Answer:
Purse A will contain 2400 (by magic) and Purse B will have 64 pennies
Step-by-step explanation:
how this happened is, by magic Purse A went up by 200 every day for 7 days a week. 7*200 would be 1400 so you add that to the money from today and get 2400. Purse B somehow got from 1 penny to 64 in 7 days. The rule on this is to multiply by 2 every day. 1,2,4,8,16,32 and 64. have fun with your magic :3
What’s is 2+2 I really need help
Answer:
4
Step-by-step explanation:
Karinas science test scores for this quarter are 84,86,90 and 68. What score does she need on her fifth science test to get a test average of at least 84
Answer:
Karina must score atleast 92 on the fifth test to get a average of atleast 84.
Step-by-step explanation:
We are given the following in the question:
84, 86, 90, 68
We want the average score to be atleast 84.
Let x be the score on fifth test.
Formula:
[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]
Thus, we can write the equation:
[tex]\dfrac{84+86+90+68+x}{5}\geq 84\\\\\Rightarrow 84+86+90+68+x \geq 420\\\Rightarrow 328+x \geq 420\\\Rightarrow x \geq 92[/tex]
Thus, Karina must score atleast 92 on the fifth test to get a average of atleast 84.
On Martin's first stroke, his golf ball traveled 4/5 of the distance to the hole. On his second stroke, the ball traveled 79 meters and went into the hole. How many kilometers from the hole was Martin when he started?
Answer:
0.395 kilometre
Step-by-step explanation:
Given:
On Martin's first stroke, his golf ball traveled 4/5 of the distance to the hole.
On his second stroke, the ball traveled 79 meters and went into the hole.
Question asked:
How many kilometres from the hole was Martin when he started?
Solution:
Let distance from Martin starting point to the hole in meters = [tex]x[/tex]
On Martin's first stroke, ball traveled = [tex]\frac{4}{5} \ of \ total \ distance\ to\ the\ hole[/tex]
[tex]=\frac{4}{5} \times x=\frac{4x}{5}[/tex]
On his second stroke, the ball traveled and went to the hole = 79 meters
Total distance from starting point to the hole = Ball traveled from first stroke + Ball traveled from second stroke
[tex]x=\frac{4x}{5} +79\\ \\ Subtracting\ both\ sides\ by \ \frac{4x}{5}\\ \\ x- \frac{4x}{5}= \frac{4x}{5}- \frac{4x}{5}+79\\ \\ \frac{5x-4x}{5} =79\\ \\ By \ cross\ multiplication\\ \\ x=79\times5\\ \\ x=395\ meters[/tex]
Now, convert it into kilometre:
1000 meter = 1 km
1 meter = [tex]\frac{1}{1000}[/tex]
395 meters = [tex]\frac{1}{1000}\times395=0.395\ kilometre[/tex]
Thus, there are 0.395 kilometre distance from Martin starting point to the hole.
What can readers best infer about Blackfeet culture from
this excerpt?
O
O
O
O
how sickness was cured
what people gathered to eat
how people farmed the land
what religious beliefs people held
Answer:
b
Step-by-step explanation:
Answer:The answer is B
Step-by-step explanation:
If a = 4, Evaluate 35 - 3a
Answer:
23
Step-by-step explanation:
3 times 4 equals 12
then do
35 minus 12
Answer:
a=4
35-3a=
35-3(4)=
35- 12=23
Step-by-step explanation:
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.
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:
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:
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]
A local boys club sold 196 bags of mulch and made a total of $549. It sold two types of mulch: hardwood for $3.00 a bag and pine bark for $2.75 a bag. How many bags of each kind of mulch did it sell?
Have have a garden that is 9 feet by 12 feet and you want to buy a pathway around the garden that is x feet, write an expression for the area of the pathway
Answer:
An expression for the area of the pathway is [tex]4x^2+42x[/tex]
Step-by-step explanation:
Length of garden = 9 feet
Breadth of garden = 12 feet
Area of garden = [tex]Length \times Breadth = 9 \times 12 =108 ft^2[/tex]
We are given that you want to buy a pathway around the garden that is x feet
Width of pathway = x feet
Outer length = 9+x+x=9+2x
Outer breadth = 12+x+x=12+2x
Area of path including garden =[tex]Length \times Breadth = (9+2x)(12+2x)[/tex]
Area of path = Area of path including garden - Area of garden
Area of path =[tex](9+2x)(12+2x)-108[/tex]
Area of path =[tex]108+18x+24x+4x^2-108[/tex]
Area of path =[tex]4x^2+42x[/tex]
Hence an expression for the area of the pathway is [tex]4x^2+42x[/tex]
Which function has a constant rate of change -1/4?
A television network, Network A, is scheduling its fall lineup of shows. For the Tuesday night 8 p.m. slot, Network A has selected its top show. If its rival network, Network B, schedules its top show during the same time slot, Network A estimates that it will get 1.1 million viewers. However, if Network B schedules a different show during that time slot, Network A estimates that it will get 1.6 million viewers. Network A believes that the probability that Network B will air their top show is 0.4 and the probability that Network B will air another show is 0.6.
Determine the expected number of viewers (in millions) for Network A's top show.
Network A expects that how many million people will watch their show (type an integer or decimal).
Answer:
The number of viewers Network A expects will watch their show is 1.4 million viewers.
Step-by-step explanation:
The expected value is calculated by multiplying the possible outcomes by the probability of their occurrence and adding the results
Therefore, we have the expected value given by the following expression;
Estimated network A viewers where network B schedule top show = 1.1 million viewers
Estimated network A viewers where network B schedule a different show = 1.6 million viewers
Probability that Network B will air its top show = 0.4
Probability that Network B will air another show = 0.6
We therefore have;
Expected value, E of Network A viewers is therefore;
E = 1.1 × 0.4 + 1.6 × 0.6 = 0.44 + 0.96 = 1.4 million viewers.
Network A expects 1.4 million viewers will watch their show.
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
URGENT HELP!! You can work no more than 60 hours each week at your two jobs. Dog walking pays $7 per hour and your sales job at Computers & More, Inc. pays $12 per hour. You need to earn at least $450 each week to pay your bills. Your friend solves the system of inequalities x + y < 60 and 7x + 12y > 450 and tells you that a possible solution is (-3, 50). Is this a possible solution, why or why not?
Answer:
Is not a possible solution
Because the number of hours can not be negative
Step-by-step explanation:
Let
x------> the number of hours in the dog walking job
y-----> the number of hours in the sales job
we know that
-----> inequality A
------> inequality B
Remember that
If a ordered pair is a solution of the system of inequalities
then
the ordered pair must satisfy both inequalities
we have
------> Is not a possible solution
Because the number of hours can not be negative
Final answer:
Yes, (-3, 50) is a possible solution
Explanation:
The given system of inequalities is:
x + y < 60
7x + 12y > 450
To check if the solution (-3, 50) is possible, we substitute the values of x and y into the inequalities and check if the inequalities are true.
For the first inequality: (-3) + 50 < 60
47 < 60. This inequality is true.
For the second inequality: 7(-3) + 12(50) > 450
-21 + 600 > 450
579 > 450. This inequality is also true.
Since both inequalities are true when x = -3 and y = 50, we can conclude that (-3, 50) is a possible solution.
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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A forest ranger looking out from a ranger station can see a forest fire at a 35° angle of depression the Rangers position is 100 feet above the ground how far is the ranger station to the fire
To find the distance between the ranger station and the fire, we can use trigonometry and the angle of depression.
Explanation:To solve this problem, we can use trigonometry. Let's call the distance from the ranger station to the fire 'x'.
Using the angle of depression of 35°, we can set up the trigonometric equation:
tan(35°) = (height of the ranger station) / x
Plugging in the known values, we get:
tan(35°) = 100 / x
To find 'x', we can rearrange the equation:
x = 100 / tan(35°)
Using a calculator, we can find:
x ≈ 100 / 0.7002
x ≈ 142.811 feet
Therefore, the ranger station is approximately 142.811 feet away from the fire.
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Final Answer:
The ranger station is approximately 142.8 feet away from the fire horizontally.
Explanation:
To find how far the ranger station is from the fire, we can use trigonometry. The ranger is 100 feet above ground, and the angle of depression from the station to the fire is 35 degrees.
Here's how you solve the problem step by step:
1. Imagine a right triangle where the ranger station is at the top, the fire is at the right angle (on the ground), and the line of sight from the ranger makes the hypotenuse.
2. The angle of depression is measured from the horizontal down to the line of sight. However, because alternate interior angles formed by a transversal with two parallel lines are congruent, the angle of depression from the ranger's horizontal line of sight to the fire is equal to the angle of elevation from the ground up to the ranger's line of sight. Therefore, the angle at the bottom of the triangle (the fire's location) is also 35 degrees.
3. We are dealing with the opposite side (the height of the station, 100 feet) and the adjacent side (the distance from the base of the station to the fire, which we want to find). For such problems, we use the tangent function, which relates the opposite to the adjacent side in a right triangle:
[tex]\(\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}\)[/tex]
4. Plug in the known values:
[tex]\(\tan(35^\circ) = \frac{100 \text{ feet}}{\text{distance to fire}}\)[/tex]
5. We want to solve for the distance to the fire, so we rearrange the equation:
[tex]\(\text{distance to fire} = \frac{100 \text{ feet}}{\tan(35^\circ)}\)[/tex]
6. To find the distance to the fire, calculate [tex]\(\frac{100 \text{ feet}}{\tan(35^\circ)}\)[/tex]. You need to ensure you're working in degrees if using a calculator.
Let's do the math using an approximation for [tex]\(\tan(35^\circ)\)[/tex] (which is roughly 0.7002):
[tex]\(\text{distance to fire} = \frac{100 \text{ feet}}{0.7002}\\\\ \(\text{distance to fire} = 142.8 \text{ feet}\)[/tex]
Hence, the ranger station is approximately 142.8 feet away from the fire horizontally.
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 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.
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.
Mr. Tesoro drew this quadrilateral with two equal sides that meet at a right angle and a pair of equal opposite angles that are not right angles. What type of quadrilateral did he draw?
Answer:
The answer is kite.
Step-by-step explanation:
Well, just looking at the definition of a kite, we can see that it lines up with Mr. Tesoro's description and drawing of the quadrilateral. A kite has one right angle that meets up witht two equal lines. The opposite pair of lines, that are much longer, don't meet up to be a right angle. The definitions line up, so there's your match; the anser is kite.
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:
Jess made 3 different stacks of wooden blocks The first stack was 7 blocks high the second stack was 3 blocks higher than the first and the the final stack was 7 blocks higher than the second In the total how many blocks did Jess use for all 3 stacks
Answer:
Jess used 34 blocks
Step-by-step explanation:
the first stack =7
second stack =7+3=10
third stack =10+7=17
total: 7+10+17=34
Solve the equation: 3(x - 4) = -21 *
Answer:
x = -3
Step-by-step explanation:
simplify
3(x - 4) = -21
3x - 12 = -21
3x = = -9
x = -3