3. consider all triangles formed by lines passing through the point ( 8 9 , 3) and both the x- and y-axes. find the dimensions of the triangle with the shortest hypotenuse.
Answers
The dimension of the triangle with the shortest hypotenuse is 2.98.
Here we have to find the dimensions of the triangle.
Given data:
the point given as (8/9, 3) and both passes through x and y-axis.
Let the slope of the line be m.
The line passing through (8/9,
Slope(m) = (y-3)/{x-(8/9)
y-3=m{x-(8/9)
y-mx=3–8m/9.
As this along with the coordinate axes make the right angled ∆, for the shortest hypotenuse
The x and y the intercepts for the line. So,
y/(3–8m/9)+x/{(3-8m/9)/(-m)}=1.
Where y intercept=(3–8m/9),
x intercept={(8m/9–3)/m.
So the length of hypotenuse;
Hypotenuse(h) = √[{(8m/9–3)/m}²+(3–8m/9)²]|
=|(8m/9–3)√(1+m²)/m
So the length of the hypotenuse is to be minimum for m, the hypotenuse is (19/9)×√2=2.98.
Therefore we get the hypotenuse as 2.98.
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Related Questions
4.33 is it heavier than 4.25
Answers
Answer:
Yes
Step-by-step explanation:
It is because 4.33 is more than 4.25.
4.33 > 4.25
If these cylinders and prisms were broken into two separate groups, what would be an equivalent ratio to 8/2? i dont have much longer and btw it doesn't have a picture.
100 points?
Answers
The Equivalent ratio to 8/2 is 4/1, 24/6, 32/8 and 48/12.
We have,
Cylinder and prism.
Here we have to find the equivalent ratio to 8/2.
First simplifying the given ratio as
8/2
= (4 x 2)/2
= 4 /1
Now, some more ratios equivalent to 8/2.
1. 8/2 x 3/3 = 24/ 6
2. 8/2 x 4/4 = 32/8
3. 8/2 x 6/6= 48/12
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What is 145% of 8000? Round to the nearest hundredth
Answers
Answer:
Step-by-step explanation:look it up
7990.00
a fair die is cast four times . calculate he probability of abtaining exactly two 6's
Answers
The probability of obtaining exactly two 6's in four rolls of a fair die is approximately 0.1608, or about 16.08%.
What is Probability theory ?
In probability theory, an outcome is the result of a random experiment, such as rolling a die, flipping a coin, or drawing a card from a deck. An outcome can be a single event, such as rolling a 3 on a die, or a combination of events, such as rolling a 1 and then a 4 on two consecutive rolls of a die.
The probability of an outcome is a number between 0 and 1 that measures the likelihood of that outcome occurring. A probability of 0 means that the outcome is impossible, while a probability of 1 means that the outcome is certain. For example, the probability of rolling a 7 on a single roll of a standard die is 0, because there is no face on the die with a 7. The probability of rolling a 1, 2, 3, 4, 5, or 6 is 1/6 each, because each face on the die has an equal chance of showing up.
The probability of obtaining a 6 on a single roll of a fair die is 1/6. The probability of not obtaining a 6 on a single roll is 5/6.
To obtain exactly two 6's in four rolls, we can use the following approach:
There are a total of 6^4 possible outcomes for four rolls of a die, as each roll can result in any of the six numbers.To obtain exactly two 6's, we need to choose two of the four rolls to be 6's, and the other two rolls to be non-6's. There are (4 choose 2) = 6 ways to choose which two rolls will be 6's.For each of these 6 ways, the probability of getting two 6's and two non-6's in that order is\((1/6)^2 * (5/6)^2.\)Therefore, the probability of obtaining exactly two 6's in four rolls is \(6* (1/6)^2 * (5/6)^2 = 0.1608\) (rounded to four decimal places).So the probability of obtaining exactly two 6's in four rolls of a fair die is approximately 0.1608, or about 16.08%.
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Evaluate the factorial expression.
14!/10!
Answers
Answer:
24024
Step-by-step explanation:
14! / 10!
14 × 13 × 12 × 11 × 10! / 10!
14 × 13 × 12 × 11
24024
Answer:
Step-by-step explanation 14! / 10!
14 × 13 × 12 × 11 × 10! / 10!
14 × 13 × 12 × 11
24024
Help fast if it’s correct I’ll make you the Brainly thing
) Which of the following expressions have a negative product?
Choose ALL the correct expressions.
9. 10
- 8.8
11. (-2)
- 6.7
-3. (-4)
-5. (-5)
Answers
-8.8
11(-2)
-6.7
Suppose the given confidence level is 85%, what is the corresponding z critical value?
Answers
A local orchestra is holding a charity concert concert at the community center. Each adult ticket $12, and child ticket costs $8. The organizers of the event hope to raise no less than $2,500, and the community center can seat up to 280 people. This graph and system in inequalities represent this situation, where x represents the number of adult tickets and y represents the number of child tickets. 12x + 8y> 2,500. X + y < 280
Answers
The answer is (180,80)
To solve this problem, we have to plot the graph, using a tool. This question relates to an inequality and graphical method is a reliable approach to solve inequality problem.
InequalityThe given question is an inequality situation where we are asked to use graph to solve.
The data given are
adult ticket = $12child ticket = $8Total amount raised = $2500Total number of people = 280The inequality for this problem is given is as
\(12x + 8y > 2500\\x + y < 280\)
Kindly find the attached image as the graph and solution to this problem.
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What is the area of parallelogram ABCD
Answers
Explanation: the formula for finding the area of a parallelogram is A=bh (Area=Base x Height). The base is 3cm and the height is 3cm.
4. Mary bought 12 pounds of blueberries to make 5 pies. She divided the blueberries
many pounds of blueberries were in each pie?
2.4 pounds
5. Write each quotient as a fraction or mixed number.
Quot
Problem
4:5
5:4
12:20
Answers
Answer:
Step-by-step explanation:
12/5=2.4 lb of blueberry in each pie
4/5=4/5 not a mixed number
5/4=1 1/4
12/20=3/5
tell whether the ordered pair is a solution of the equation! please help i will mark you brainliest
Answers
Answer:
the answer is
yes to 7 and no to 10
Step-by-step explanation:
7. y = 3x---------> 2*3 = 6
10. y = 7x+2--------------> 2*7=14--> 14+2 = 16
16 does not equal 0
How do we solve this?
Answers
Answer:
f(x)=11+7√x
f'(x)=7/(2x^(1/2))
putting x=1
f'(1) = 7/(2×1^(1/2))
= 7/2 = 3.5
putting x=2
f'(2) = 7/(2×2^(1/2))
= 7/(2×√2)
= 7√2/4
= 2.47 (rounded to the nearest hundredth)
f'(3) = 7/(2×3^(1/2))
= 7/(2×√3)
= 7√3/6
= 2.02 (rounded to the nearest hundredth)
PLEASE SHOW YOUR WORK ON HOW TO SOLVE THIS PROBLEM!! BEST ANSWER ILL GET MARKED BRAINIEST!
4x+5/x+7
Answers
Answer:
x = 2.4
Step-by-step explanation:
4x + 5 / x + 7
combine like terms
X + 4x = 5x
5 + 7= 12
12/ 5x
Divide
12 /5= 2.4
X= 2.4
Brett and Andy applied for the same credit card from the same bank. Brett was given a card with an APR of 12.6%. What was his monthly percentage rate? Andy was given a card with an APR of 16.2% what was his monthly percentage rate? if each of them had an average daily balance of $7,980, and had to pay a finance charge, how much more would. Andy pay than Brett?
Answers
Andy would pay $23.94 more in finance charges compared to Brett, given their respective APRs, average daily balances, and monthly percentage rates.
To calculate the monthly percentage rate (MPR) from the given annual percentage rate (APR), we divide the APR by 12.
For Brett:
APR = 12.6%
MPR = 12.6% / 12 = 1.05%
For Andy:
APR = 16.2%
MPR = 16.2% / 12 = 1.35%
Next, we can calculate the finance charge for each individual using the formula: finance charge = average daily balance * MPR.
For Brett:
Finance charge = $7,980 * 1.05% = $83.79
For Andy:
Finance charge = $7,980 * 1.35% = $107.73
To find the difference in the finance charges between Andy and Brett, we subtract Brett's finance charge from Andy's finance charge:
Difference = $107.73 - $83.79 = $23.94
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What is one fifth of twenty more than half
of 80?
(A) 8
(B) 10
(C) 12
(D) 13
Answers
Answer:
(C) 12
Step-by-step explanation:
To solve this problem, we can use the following steps:
Find half of 80: 80/2 = 40
Add 20 to half of 80: 40 + 20 = 60
Find one fifth of the result: 60/5 = 12
Therefore, one fifth of twenty more than half of 80 is equal to 12. The correct answer is (C) 12.
Answer:
(C) 12
Step-by-step explanation:
What is one fifth of twenty more than half of 80
0.5 × 80 = 40
What is one fifth of twenty more than half of 80
40 + 20 = 60
What is one fifth of twenty more than half of 80
1/5 × 60 = 60/5 = 12
Mackenzie has a 30 ounce soft drink. She drinks 28 ounces. Enter the percentage of ounces Mackenzie has left of her soft drink. Round your answer to the nearest hundredth.
Answers
Answer:
100
Step-by-step explanation:
30-28=100 if u round it to thr nearest hundreth because
30 2-2=0
- 18-8=10
-28
10 rounded to tye nearest hunderth is 100
Please someone explain how to solve for x.
Answers
Answer:
x =30
Step-by-step explanation:
We can use ratios to solve
18 20
--------- = ----------
18+27 20+x
Simplify
18 20
--------- = ----------
45 20+x
Using cross products
18 *(20+x) = 20*45
18 ( 20+x) = 900
Divide each side by 18
18 /18*(20+x) = 900/18
20+x =50
Subtract 20 from each side
20+x-20 = 50-20
x=30
Answer:
30
Step-by-step explanation:
to solve this type of problem you need to cross multiply.So you get the pairs which are 18 and 20 and 27 and x so the equation looks like 18/20=27/x so 18 times x is 18x and 20 times 27 is 540 so the equation is now 18c=540 then you divide both sides by 18 so x will be isolated which means x will be by itself so 18x divided by 18 is x and 540 divided by 18 is 30 so the equation is now x=30
A triangle can have at most
right angle.
04
01
OO
2
Answers
The answer would be number 1.
Have a great day/night!
A bowl has 8 green grapes and 15 red grapes. Henry randomly chooses a grape, eats it, and then chooses another grape. (a) What is the probability that both grapes are green? (b) What is the probability that Henry eats a red grape then a green grape?
Answers
Answer:
A. 28/253
B. 60/253
Step-by-step explanation
A. first step is to add all the grapes up which = 23
then you would put the
green grapes/ the total which would be 8/23
since henry ate one grape you would subtract 8-1 and then 23-1 and you would get 7 and 22
then you would put 7/22 and multiply 8/23 which gets you 28/253
B. first you put red grapes over total grapes which are 15/23
then,
you would do the green grapes which are 8/22
you would multiply 15/23 and 8/22 which = 60/253
If you can get this before I do I'll give brainliest
Answers
Answer:
The answer is B
Step-by-step explanation:
hope this helps,
please give brainliest if you like my answer,
have a great day
So the actual equation that I put into this piece would be 4/5+6.9y-8
Now you have to rewrite this from only trying the (+) sign which comes as
4/5+6.9y+(-8)
So in this first number it’s 4/5 not -4/5 and the other number is -8 not 8.
Therefore Maggie differentiated the signs from these following numbers. Since Maggie did the communitive incorrectly.
HELP ME PLEASEEE!!!!Jordan spent 5 hours over the weekend studying for 3 tests. He spent an equal amount of time studying for each test. How long did Jordan spend studying for each test? Answers:
1 3/4 hours. 3/5 hours. 1/5 hours. or 1 2/3
Answers
Answer:
oh god I wanna feel dead oh god i wanna feel dead
please help !! i’m struggling
Answers
¿Aún necesitas ayuda? Podría intentar ayudar
.In a different biology lab, a population of single-cell parasites also reproduces hourly. An equation which gives the number of parasites, , after hours is Explain what the numbers 100 and 3 mean in this situation.
Answers
Answer: p=50 h=2
Step-by-step explanation:
so its 50 x 2=100 is the answer then u add 3
Select the correct answer.
Solve the following equation for x.
x2 - 36 = 0
A.
x = 1; x = -36
B.
x = -1; x = 36
C.
x = -6; x = 6
D.
x = -18; x = 18
Answers
Answer: D
Step-by-step explanation:
2x-36=0
+36 +36
___________
2x=36
x=18
Even if one equation, -18 was not solved, you can easily cross out the ones without 18 and get the answer.
need help with math
Answers
Answer:
its c im pretty sure lmk if im wrong
Step-by-step explanation:
Solve by graphing. x2 + 2x – 3 = 0
Answers
By graphing or visualizing the parabolic shape, we can observe where the graph intersects the x-axis, which represents the solutions to the equation. In this case, the solutions are x = -3 and x = 1.
To solve the quadratic equation x^2 + 2x - 3 = 0 by graphing, we can plot the graph of the equation and find the x-values where the graph intersects the x-axis.
First, let's rearrange the equation to the standard form: x^2 + 2x - 3 = 0.
We can create a graph by plotting points for different values of x and then connecting them. However, I can describe the process and the key points on the graph.
1. Find the x-intercepts: These are the points where the graph intersects the x-axis. To find them, set y (the equation) equal to zero and solve for x:
0 = x^2 + 2x - 3.
This quadratic equation can be factored as (x + 3)(x - 1) = 0.
Therefore, x = -3 or x = 1.
2. Plot the points: Plot the points (-3, 0) and (1, 0) on the graph. These are the x-intercepts.
3. Draw the graph: The graph of the equation x^2 + 2x - 3 = 0 is a parabola that opens upward. It will pass through the x-intercepts (-3, 0) and (1, 0).
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A zip wire runs between two posts, 25m apart. The zip wire is at an angle of 10∘ to the horizontal. Calculate the length of the zip wire.
Answers
The length of the zip wire is approximately 25.42 meters.
To calculate the length of the zip wire, we can use trigonometry and the given information about the angle and the distance between the two posts.
Given:
Distance between the two posts: 25m
Angle of the zip wire to the horizontal: 10°
We can use the trigonometric function cosine (cos) to find the length of the zip wire. Cosine relates the adjacent side to the hypotenuse of a right triangle.
In this case, the adjacent side is the distance between the two posts (25m) and the hypotenuse is the length of the zip wire that we want to calculate.
Using the cosine function:
cos(angle) = adjacent/hypotenuse
cos(10°) = 25m/hypotenuse
To find the hypotenuse (length of the zip wire), we can rearrange the equation:
hypotenuse = 25m / cos(10°)
Using a calculator or trigonometric tables, we can find the value of cos(10°) to be approximately 0.9848.
Therefore, the length of the zip wire is:
hypotenuse = 25m / 0.9848 ≈ 25.42m
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If
f(x) = -2x
and
g(x) =x2+3
Find
f(g(x)) = [? ]x2 +
![Iff(x) = -2xandg(x) =x2+3Findf(g(x)) = [? ]x2 +](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/Hh0VcJS7U4EW7Z7doEU5D92a1K0P2l53.png)
Answers
The composite function f(g(x)) has a value of -2x^2 - 6.
Calculating the composite functionFrom the question, we have the following parameters that can be used in our computation:
Fuctions f(x) and g(x)
To find f(g(x)), we first need to evaluate g(x) and then use the result as the input for f(x).
So we have:
g(x) = x^2 + 3
Now we substitute this expression into f(x) and simplify:
f(g(x)) = f(x^2 + 3) = -2(x^2 + 3) = -2x^2 - 6
Therefore, f(g(x)) = -2x^2 - 6.
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Termites reproduce at a rate of about 2.4% each day.
Your house has 1,200 termites in it’s foundation.
• Determine an equation that models the reproductive rate of the termites in the house.
•How long will it take for the number of termites to double?
Answers
Answer:
29 days
Step-by-step explanation:
1200(1.024)^n = 2400
(1.024)^n = 2
n log 1.024 = log 2
n = (log 2) / log1.024 = 29 days
Answer this Fraction based Question I will provide you 50point + make you as brainliest.
Answers
It is given that 2/5 of all patients admitted to ward 17.
Remining fraction is:
1 - 2/5 = 5/5 - 2/5 = 3/5So 3/5 of patients admitted to ward 18.
Since 1/6 of all patients moved to another ward, and the reminder assigned as before, the initial fraction becomes:
1 - 1/6 = 6/6 - 1/6 =5/6Now, 3/5 of the new fraction, 5/6 is admitted to ward 18.
That is:
3/5*5/6 = 3/6 = 1/2This is half of the patients.
The difference of the number of the patients admitted to ward 17 is the same fraction of the number of infected:
10*2/5 = 4So the difference of patients is 4.