Given right triangle ABC with altitude BD drawn to hypotenuse AC. If BD = 3 and DC = 9, what is the length of AC?
Answers
Given right triangle ABC with altitude BD drawn to hypotenuse AC. If BD = 3 and DC = 9, the length of AC is: 4 units.
How to find the length?In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. Let's call the length of the hypotenuse AC as x, and the length of the segment containing point B as y. Then, the length of the other segment containing point C is x - y.
Using similar triangles, we can set up the following proportion:
BD/DC = y/(x - y)
Substituting the given values, we get:
3/9 = y/(x - y)
Simplifying this equation, we get:
x - y = 3y/9
x = 4y/3
We also know from the Pythagorean theorem that:
AC^2 = AB^2 + BC^2
Since triangle ABC is a right triangle, we have:
AB^2 + BC^2 = x^2
Substituting x = 4y/3, we get:
AB^2 + BC^2 = (4y/3)^2
But we also know that:
AB/BC = 3/4
So we can set up another proportion:
AB/BC = y/(x - y)
Substituting x = 4y/3, we get:
AB/BC = y/(4y/3 - y)
Simplifying this equation, we get:
AB/BC = y/((4/3)y - y)
AB/BC = y/((1/3)y)
AB/BC = 3
So we have:
AB = 3BC
Substituting this into AB^2 + BC^2 = (4y/3)^2, we get:
(3BC)^2 + BC^2 = (4y/3)^2
10BC^2 = 16y^2/9
But we also know that:
BC^2 + y^2 = x^2
Substituting x = 4y/3, we get:
BC^2 + y^2 = (4y/3)^2
5BC^2 = 7y^2/9
Combining this with 10BC^2 = 16y^2/9, we get:
15BC^2 = 21y^2/9
BC^2 = (7/3)y^2/3
Substituting this into BC^2 + y^2 = (4y/3)^2, we get:
(7/3)y^2/3 + y^2 = 16y^2/9
7y^2/9 + 9y^2/9 = 16y^2/9
16y^2/9 = 16y^2/9
So this equation is true for any value of y. Therefore, the length of AC is:
AC = x = 4y/3
Substituting y = BD = 3, we get:
AC = 4(3)/3 = 4
Therefore, the length of AC is 4 units.
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Related Questions
What is the equation of the line that passes through the point (-3,-1) and has a slope of 2
Answers
Answer:
y=2x-5
Step-by-step explanation:
We are going to use point slope form (shown below):
y-y1=m(x-x1)
Apply point slope:
y+1=2(x+3)
Distribute 2:
y+1=2x+6
Subtract 1 from both sides:
y=2x-5
‼️HELP PLEASE‼️ANSWER WITHIN 10 minutes ‼️‼️‼️‼️
Mmmm! I love cafe de olla this time of year, and so do
my neighbors. My recipe calls for two quarts of water,
three sticks of cinnamon, and one tablespoon of coffee.
This will make enough for eight people to share. In my
neighborhood, however, there are 36 people. How much
do I need of each ingredient to make enough for my
whole neighborhood to share?
Answers
Answer:
Step-by-step explanation:
you want to divide 36 by 8 because you have 36 people and the recipie only makes it for 8.
You know that you will need to make the recipe 4.5 times.
So, multiply all the ingredient numbers by 4.5
2 x 4.5 = 9 quarts of water
3 x 4.5 = 13.5 sticks of cinnamon
1 x 4.5 = 4.5 tablespoons of coffee
Answer: Im pretty sure you need 16 quartz of water, 24 sticks of cinnamon, and 8 tablespoons of coffee.
Step-by-step explanation:
Two bags, A and B, each contain only green marbles and red marbles.
There are 6 green marbles and 4 red marbles in bag A.
There are 8 green marbles and 2 red marbles in bag B.
One marble is going to be taken at random from bag A and placed in bag B.
A marble is then going to be taken at random from bag B.
Work out the probability that this marble will be a green marble.
Answers
Using it's concept, it is found that there is a 0.7818 = 78.18% probability that this marble will be a green marble.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
There are two ways to end up with a green marble selected.
Green in bag A(6/10 probability) and in bag B(9/11 probability).Red in bag A(4/10 probability) and green in bag B(8/11 probability).Hence, the probability that this marble will be a green marble is given by:
\(p = \frac{6}{10} \times \frac{9}{11} + \frac{4}{10} \times \frac{8}{11} = \frac{54 + 32}{110} = 0.7818 = 78.18\%\)
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On average yasmin drinks 3/4 of an 8 ounce glass of water in 1 1/4 hours how much can she drink per hour
Answers
Answer:
She drinks 4.8 ounces of water per hour
Step-by-step explanation:
We know
Yasmin drank 3/4 of an 8-ounce glass of water in 1 1/4 hours
3/4 of 8 ounce = 6 ounces
1 1/4 = 5/4 = 1.25 hours
How much can she drink per hour?
6 divided by 1.25 = 4.8 ounces of water per hour
So, she drinks 4.8 ounces of water per hour.
what is the value of y
Answers
Answer:
100°
Step-by-step explanation:
180 - 80 = 100
The line is 180 so you take away what you already know (80) and then you have 100.
Answer:
180 degree (exterior angle ) please follow and like me
The chart below shows conversion between yards and inches.
Conversion Chart
Yards
Inches
3
108
6
?
8
288
11
396
What is the missing value in the table?
144
180
198
216
Answers
step by step explanation :
to converting yard to inches you have to multiply whatever number u are given in yard by 36 to get your figure in inches
o multiply whatever number u are given in yard by 36 to get your figure in inches so we multiply 6 *36 to give us 216
o multiply whatever number u are given in yard by 36 to get your figure in inches so we multiply 6 *36 to give us 216answer:
216
Write the EXPLICT equation for the arithmetic sequence below: 12, 10, 8, 6
Answers
aₙ = 14- 2n is the EXPLICT equation for the arithmetic sequence below: 12, 10, 8, 6
What is Sequence?A sequence is an enumerated collection of objects in which repetitions are allowed and order matters
this is an arithmetic sequence whose n th term ( explicit formula) is
aₙ = a + (n - 1 )d
where d is the common difference and a the first term
The given sequence is 12,10,8,6
twelve comma ten comma eight comma six
d=10-12=-2
a=12
Apply in explicit formula
aₙ = 12+ (n - 1 )(-2)
aₙ = 12-2n +2
aₙ = 14- 2n
Hence aₙ = 14- 2n is the EXPLICT equation for the arithmetic sequence below: 12, 10, 8, 6
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I really need help on this please
Answers
Answer:
2 inches
Step-by-step explanation:
i think that this would be monday*3 + thursday*2 in order to find all five days
so (0.5*3)+(0.25*2)= 2inches.
hope this helps!
Plz help it is over due
Answers
Answer:
32/9
Step-by-step explanation:
(4/1) (9/8)=
32/9
Help please I will give you the brainliest
Answers
Answer:
well option D will be your answer
Step-by-step explanation:
hope it helps you
have a great day
18-
3. Your family is planning to take the Amtrak train from Hartford to New York City for a day trip. As a result
of some research you learn that your friend Jackie took the train with a group of 3 adults and 5 children and
it cost them $269.50. A cousin also took the train to the city with a group of 2 adults and 3 children and it
cost them $171.50. Find the price of an adult's ticket and the price of a child's ticket.
Answers
Answer: 67.37 for adult 45.91 for child
Step-by-step explanation:
how can I make the false equation true pls answer asap
Answers
Answer:
You can make it true by removing one of the factor's negative sign, such as -3 · 8 = -24.
Step-by-step explanation:
If we know that negative × negative = positive, then negative × positive = negative, so we have to remove the negative sign of one of the factors: -3 or -8.
Have a lovely rest of your day/night, and good luck with your assignments! ♡
Answer:
apply another negative to either -3, -8, or -24.
step by step explaination
you already have that
(-3) * (-8) is not -24
then what is it?
(-3) * (-8) = 24
the difference is that 24 is positive instead of negative
to reverse this, you can apply another negative in this equation (because its multiplication you can apply it anywhere)
if apply negative to 24
then (-3) * (-8) = -(-24)
(-3) * (-8) = 24
which is true!!
you can do this with -3 or -8 too
-(-3) * (-8) = -24
3* -8= -24 is true
(-3) * -(-8) = -24
-3* 8 =-24 is true
hope this helps !
: 4. (25 points) In planning a survival study to compare the survival of time between two treatment groups, we want to detect a 20% improvement in the median survival from 5 months to 6 months with 80% power at a = 0.05, and we plan on following patients for 1 year (12 months). Based on exponential assumption for survival distributions and 1 to 1 equal allocation of patient receiving either treatment A or treatment B, how many patients do we need to recruit for this study?
Answers
To detect a 20% improvement in median survival from 5 to 6 months with 80% power and a significance level of 0.05, following patients for 1 year, the required sample size can be calculated using power analysis formulas.
To determine the number of patients needed for the survival study, we can use power analysis calculations based on the specified parameters. In this case, we want to detect a 20% improvement in the median survival time from 5 months to 6 months, with 80% power at a significance level of 0.05. The study will follow patients for 1 year (12 months) assuming an exponential distribution for survival.
To calculate the required sample size, we can use statistical software or power analysis formulas. One common approach is to use the formula:
n = (2 * (Zα + Zβ)^2 * σ^2) / (δ^2)
where n is the required sample size, Zα is the Z-value for the chosen significance level (0.05), Zβ is the Z-value for the desired power (80%), σ is the standard deviation of the survival times (assumed to be equal for both treatment groups), and δ is the desired difference in survival times.
In conclusion, to detect a 20% improvement in median survival from 5 to 6 months with 80% power and a significance level of 0.05, following patients for 1 year, the required sample size can be calculated using power analysis formulas. By plugging in the appropriate values for Zα, Zβ, σ, and δ into the formula, the specific number of patients needed for the study can be determined.
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Compute the probability of event E if the odds in favor of E are 16 4 1911 (A) P(E) = (B) P(E) = (C) P(E) = (D) P(E) = (Type the probability as a fraction. Simplity your answer) (Type the probability as a fraction. Simplify your answer) (Type the probability as a fraction. Simplify your answer) (Type the probability as a fraction. Simplify your answer) 1
Answers
Given the odds in favor of event E as 16 to 4, the probability of event E is 4/5.The probability of event E is then the number of favorable outcomes divided by the total number of outcomes. So, P(E) = 16/20 = 4/5.
The odds in favor of event E are given as 16 to 4. To compute the probability of event E, we need to convert these odds into a fraction.
The odds in favor of E are 16 to 4, which means that for every 16 favorable outcomes, there are 4 unfavorable outcomes.
To find the probability, we add the number of favorable outcomes and the number of unfavorable outcomes together. In this case, 16 + 4 = 20.
The probability of event E is then the number of favorable outcomes divided by the total number of outcomes. So, P(E) = 16/20 = 4/5.
Therefore, the probability of event E is 4/5.In summary, given the odds in favor of event E as 16 to 4, the probability of event E is 4/5.
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Pls Help!!! Worth 99 Pts!!
Explain how to sketch a graph of the function f(x) = x3 + 2x2 – 8x. Be sure to include end-behavior, zeroes, and intervals where the function is positive and negative.
Answers
Answer:
First, for end behavior, the highest power of x is x^3 and it is positive. So towards infinity, the graph will be positive, and towards negative infinity the graph will be negative (because this is a cubic graph)
To find the zeros, you set the equation equal to 0 and solve for x
x^3+2x^2-8x=0
x(x^2+2x-8)=0
x(x+4)(x-2)=0
x=0 x=-4 x=2
So the zeros are at 0, -4, and 2. Therefore, you can plot the points (0,0), (-4,0) and (2,0)
And we can plug values into the original that are between each of the zeros to see which intervals are positive or negative.
Plugging in a -5 gets us -35
-1 gets us 9
1 gets us -5
3 gets us 21
So now you know end behavior, zeroes, and signs of intervals
Hope this helps
Answer:
The degree of the function is odd and the leading coefficient is positive – so the function goes to negative infinity as x goes to negative infinity and to positive infinity as x goes to positive infinity. The zeroes are –4, 0, and 2, all with multiplicity 1. The function is negative from negative infinity to –4 and from 0 to 2. The function is positive from –4 to 0 and from 2 to infinity.
Step-by-step explanation:
sample response on edge 2022
I need help with this asap. I will mark brainliest to the correct answer
Answers
Answer:
I believe it's the second one
Will give brainliest
The ages of two groups of karate students are shown in the following dot plots:
A dot plot shows Age in years on the horizontal axis. For Group A, there are 2 dots on 4, 5 dots on 5, 3 dots on 7, 4 dots on 8, 2 dots on 9, 2 dots on 11, and 1 dot on 14. For Group B, there is 1 dot on 7, 2 dots on 8, 1 dot on 9, 1 dot on 11, 1 dot on 16, 2 dots on 19, 2 dots on 20, 2 dots on 21, and 1 dot on 26.
The mean absolute deviation (MAD) for group A is 2.07 and the MAD for group B is 5.51. Which of the following observations can be made using these data?
Group A has greater variability in the data.
Group A has less variability in the data.
Group B has a lower range.
Group B has a lower mean.
Answers
Answer:
Group A has greater variability in the data.
Step-by-step explanation:
We use elimination. Clearly, from the MAD, Group A has greater variability in the data.
So, choice 1.
The sides of a parallelogram are 40 feet and 70 feet long, and the smaller angle has a measure of 36º.
Find the length of the longer diagonal to the nearest whole number.
A.44ft
B.105 ft
C.69 ft
D.64 ft
Answers
Step-by-step explanation:
the longer diagonal is =
√(40²+70²+2(40)(70)cos 36°)
= √(1600+4900+5600(0.8))
= √ 6500 + 4530
= √11,030
= 105 ft
help me please for points
Answers
Answer:
B
Step-by-step explanation:
40-2n
when n=2
simply replace n with 2
therefore we have
=40-2(2)
=40-4
answer=36
Suppose you spin
the spinner twice.
What is the
probability of
spinning a red,
then green?
P (red, green) =
? show your answer as
a fraction in lowest
terms. Enter the
numerator.
Answers
The probability of spinning a red, then green is 1/4.
What is probability?Probability is a branch of mathematics that deals with the likelihood of an event occurring. It is the measure of the likelihood of an event occurring divided by the number of possible outcomes. Probability is used to determine the chances of a particular outcome occurring and can range from 0 to 1. Probability is applied in many areas, including finance, statistics, weather forecasting, and gambling.
The probability of spinning a red, then green is 1/4. This is because there are four equal parts on the spinner (red, blue, yellow, and green), and spinning red first and then green means that you have a 1 out of 4 chance of getting the desired result. Therefore, the numerator is 1 and the denominator is 4.
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Answer: It is 1/16
Step-by-step explanation: It said twice so you had to multiple 8 by 2 since there are 8 possible color panels.
a street light is at the top of a 14 ft tall pole. a woman 6 ft tall walks away from the pole with a speed of 4 ft/sec along a straight path. how fast is the tip of her shadow moving along the ground when she is 45 ft from the base of the pole? ft/sec how fast is the length of her shadow increasing? ft/sec
Answers
The speed of the tip of her shadow is 12.25 feet per second.
The rate at which the shadow grows is 12.25 - 7 = 5.25 ft/s.
When two variables are connected, we may also detect a relationship between their rates.
Assume y = f(x)
Then (dy ÷ dt) = f'(x)(dx ÷ dt)
Let y be the distance between the lady and the pole's base.
Let x be the distance between the tip of the shadow and the base of a pole.
Speed of woman = (dy ÷ dt) = 7
The speed of her shadow's tip = (dx ÷ dt)
The rate at which the shadow grows = (dx ÷ dt) - 7
Because triangles are alike,
((x - y) ÷ x) = 6 ÷ 14
1 - (y ÷ x) = 3 ÷ 7
(y ÷ x) = 4 ÷ 7
x = 7y ÷ 4
Now, differentiate the equation in terms of t and enter the known values:
dx ÷ dt = (7 ÷ 4) × (dy ÷ dt)
dx ÷ dt = (7 ÷ 4) × 7
dx ÷ dt = 12.25
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help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Answer: 19.6 feet
Step-by-step explanation:
Using the Pythagorean theorem,
\(x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6\)
Six times the sum of a number and 8 equals 5.
Into an equation
Answers
Answer:
6*(x+8) = 5
Step-by-step explanation:
let x be the unknown number
We multiply 6 times the sum of a number and 8
That is equal to 5
6*(x+8) = 5
y= x-8
y= 8 +x
What is the solution
Answers
Answer:
x-8=8-x
x=8
y=8-8
y=0
Step-by-step explanation:
y=0
x=8
Answer:
x=8,y=0
Step-by-step explanation:
y=x-8
y=8-x
So,
x-8=8-x
x+x=8+8
2x=16
x=8
Now,
y=x-8
y=8-8
y=0
hellllllllllllllllllp...
Answers
Given:
The expression is:
\(\dfrac{15m^2-3}{3m-1}\)
To find:
The simplified value of the given expression.
Solution:
We have,
\(\dfrac{15m^2-3}{3m-1}\)
On dividing, we get
\((3m-1)|\overline{15m^2+0m-3}|5m+\dfrac{5}{3}\)
\(-(15m^2-5m)\)
\(\overline{\quad \quad -5m-3}\)
\(-(5m-\dfrac{5}{3})\)
\(\overline{\quad \quad -\dfrac{4}{3}}\)
Here, quotient is \(5m+\dfrac{5}{3}\) and the remainder is \(-\dfrac{4}{3}\).
Therefore, \(\dfrac{15m^2-3}{3m-1}=5m+\dfrac{5}{3}-\dfrac{4}{3(3m-1)}\).
Over the course of 3 days, Calvin spent 10 hours delivering newspapers. He spent the same amount of time each day delivering newspapers. Which of the following equations represents the amount of time Calvin spent delivering papers each day?
A: 3 ÷ 10
B: 10 ÷ 3 =
C:10 ÷ 7 =
D: 7 ÷ 10 =
Answers
Which of the following segments is a radius of 0?
Answers
Answer:
D. RO
Step-by-step explanation:
In which quadrants do solutions for the inequality y is less than or equal to two sevenths times x plus 1 exist? i, iii, and iv i, ii, and iii i and iv all four quadrants
Answers
The solutions for the inequality y ≤ 2/7x + 1 exist in quadrants I, III, and IV.
What is the quadrants?
The quadrants are the four regions that result from dividing a Cartesian coordinate plane into four parts using two perpendicular lines, the x-axis and y-axis.
The inequality y ≤ 2/7x + 1 represents a line on the x-y plane. The solutions for the inequality are the points on the plane that lie below or on the line. In a standard Cartesian coordinate system with x-axis and y-axis, the x-axis separates the plane into two parts: the upper half-plane (quadrant I) and the lower half-plane (quadrants III and IV). The y-axis separates the plane into two more parts: the right half-plane (quadrants I and IV) and the left half-plane (quadrants II and III).
So the solutions for the inequality y ≤ 2/7x + 1 lie in the region of the x-y plane that is in the lower half-plane (quadrants III and IV) and the right half-plane (quadrant I). Therefore, the solutions exist in quadrants I, III, and IV.
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Answer:
AS: I, III, and IV
Step-by-step explanation:
Q's; In which quadrants do solutions for the inequality y is less than or equal to two thirds times x minus 4 exist?
AS: I, III, and IV
Look at the graph for a better understanding :P
please help! will mark brainliest
Answers
Answer:
I think b sorry if im wrong
Express the location of the point on the number line as both a fraction and a decimal. A number line that has moving left to right, a starting mark at 0, nine unlabeled tick marks, a tick mark labeled one-tenth, nine unlabeled tick marks, a tick mark labeled two-tenths, nine unlabeled tick marks, and an ending tick mark at three-tenths. There is a dot at the ninth tick mark to the right of one-tenth.
Answers
Answer:
9 / 100 ; 0.09
Step-by-step explanation:
From the line plot given :
The number of unlabeled ticks marks between any two labeled tick marks can be obtained by :
(Difference between any two successive labeled tick marks / number of tick marks)
Picking the labeled tick marks, 0 and 1/10
(1/10 - 0) / 10
1 / 10 ÷ 10
1/ 10 * 1 / 10 = 1 / 100
To find the marked point : (this is tick mark 9 from 0) ;
Number of ticks * distance between ticks
Location of marked tick = 1 / 100 * 9 = 9 / 100
Decimal equivalent = 9/100 = 0.09
