In right triangle ABC, altitude CD with length h is drawn to its
We also know AD=2 and DB=8. What is the length of
hypotenuse.
AC?
Answers
The length of the hypotenuse AC is √(h² + 4).
What is the Pythagorean theorem?Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We have,
Right triangle ACD.
AC² = CD² + AD²
AC² = h² + 2²
AC² = h² + 4
AC = √(h² + 4)
Thus,
AC is √(h² + 4).
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Related Questions
If two cubes have edges of 2 ft and 4 ft, what is the ratio of their surface areas?
Answers
Answer:
1/4
Step-by-step explanation:
2. A faucet for a 30-gallon bathtub fills at a rate of 3 gallons per minute.
If the drain lets water out at 1.5 gallons per minute, how long would it
take for the tub to overflow if both the faucet and drain were open at the
same time?
Answers
Answer:
20
Step-by-step explanation:
Knowing that it is a 30-gallon bathtub.
And it fills at a rate of 3 gallons per minute.
But also drains 1.5 gallons per minute.
So this is for the first minute.
3 - 1.5 = 1.5
So there will be 1.5 gallons of water in the tub after the first minute.
Now do,
30 ÷ 1.5 = 20
It will take 20 full minutes for the bathtub to fill up.
I want you to find the answer
Answers
The value of length BC is 18.9
What is cosine rule?Cosine Rule states that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.
Therefore,
c² = a² + b² - 2abcosC
To find the length BC we use cosine rule.
c² = 13² + 7² - 2(13)(7)cos140
c² = 218 - 182cos140
c² = 218-(-139.42)
c² = 218+139.2
c² = 357.2
c = √357.2
c = 18.9
Therefore, the length of BC is 18.9
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In the triangle, the value of the side BC is 18.9cm to 1 decimal place
How to determine BC?The side BC can be found using the cosine formula, Remember that Cosine Rule states that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.
The cosine formula states that
c² = a² + b² - 2abcosC
To find the length BC we use cosine rule.
c² = 13² + 7² - 2(13)(7)cos140
c² = 218 - 182cos140
c² = 218-(-139.42)
c² = 218+139.2
c² = 357.2
c = √357.2
c = 18.9
In conclusion, the value of the length of BC is 18.9cm
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10. Write an equation in slope-
intercept form for the line that
passes through (6, 5) and is parallel
to the line x + 3y = 9.
Answers
Answer:
y = -x + 11 or y + x = 11
Step-by-step explanation:
x + 3y = 9
3y = -x + 9 slope = -1 .
The slope of parallel lines have the same slope.
Now let m = -1 and use point (6, 5) into the slope intercept form and solve for "b".
y = mx + b
5 = -1(6) + b
5 = -6 + b
11 = b
Next write you equation using slope (m) = -1 and b = 11
y = -1x +11 or y = -x +11
In standard form the equation is y + x = 11
9514 1404 393
Answer:
y = -1/3x +7
Step-by-step explanation:
The standard form equation can be found by using the given point values in the given equation to find the new constant.
x +3y = (6) +3(5) = 21
Solving for y puts this equation into slope-intercept form.
3y = -x +21 . . . . . . . subtract x
y = -1/3x +7 . . . . . . divide by 3. This is slope-intercept form
Determine whether a triangle with the given side lengths is a right triangle.
Answers
Step-by-step explanation:
The first one is yes.
The second one is no.
The third one is yes.
The forth one is no.
solve the equation
-2x +8 = -10
x/-5 + -15 = -22
Answers
Answer to second one is X = 35
Question 2 of 10
If two triangles are congruent, which of the following statements must be
true? Check all that apply.
A. The corresponding sides of the triangles are congruent.
B. The corresponding angles of the triangles are congruent.
C. The triangles have the same size,
D. The triangles have the same shape.
Answers
The Countrywide building has a square base. It has 45 floors of offices, all of which have about the same number of windows.
If there are 8 windows on 1 side of the 23rd floor, what is a reasonable estimate for the number of windows in the entire building?
A. 8 windows
B. 45 windows
C. 360 windows
D. 1,440 windows
Answers
Answer:
Step-by-step explanation:
think it would be b
Carbon-11 has a half-life of 20 minutes. If a 50 gram sample of carbon-11 begins to decay, write a model for themount, A, that is still radioactiveafter m minutesThen, use your model to determine how much of the sample is still radioactive after 30 minutes. Round answer to nearesttenth of agram.
Answers
Answer:
\(A=50e^{-0.035t}\)There will be 17.5 grams of carbon-11 left after 30 minutes.
The exponential decay equation is noted by:
\(A=A_0e^{kt}\)Where:
A = amount present over time
A₀ = initial amount
k = rate of decay
t = time in minutes
Let us first find the value of k using the given that we have
From the problem, we have:
A = 1/2 gram
A₀ = 1 gram
k = ?
t = 20 minutes
Substituting these values and we will get:
\(\begin{gathered} A=A_0e^{kt} \\ \frac{1}{2}=1e^{k(20)} \\ \frac{1}{2}=1e^{k(20)} \\ k=-0.035 \end{gathered}\)Therefore, our model is going to be:
\(A=50e^{-0.035t}\)To find how much sample is still radioactive after 30 minutes, we just have to substitute t = 30 to the equation:
\(\begin{gathered} A=50e^{-0.035t} \\ A=50e^{-0.035(30)} \\ A=17.49688\approx17.5 \end{gathered}\)Therefore, there are 17.5 grams of carbon-11 left after 30 minutes.
Mark and a friend went out for dinner. The bill was $23.40. They will leave a 20% tip. How much of a tip will they leave
Answers
Answer: $4.68
Step-by-step explanation: $23.40 % 20% = $4.68.
I can’t find the answer for the application
Answers
Value of x is 16/91
How to Find value of x ?
In question
(8/7)/(13/9) = x / (2/9)
Divide the numbers 72/91 =x/(2/9)
Multiply all terms by the same value to eliminate fraction denominators182* (72/91) = 182* (x/(2/9))
Cancel multiplied terms that are in the denominator2 *72 = 819 * x
Multiply the numbers144 = 819 * x
Divide both sides by the same factor(144/819) = 819 *x / 819
SimplifyX = 16/91
The value of x is 16/91
Definition of Fraction :
A fraction represents a part of a whole or, more generally, any number of equal parts.In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator.There are in total six types of fractions such as:
Proper fractionImproper fractionMixed fractionLike fractionsUnlike fractionsEquivalent fractionsTo learn more about fractions refer :
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Find the errors and correct the following mathematical sentences.
Answers
Answer:
3(x-9) = 3x-3(9) = 3x-27
2x+3x = 5x
4p+3p+2p+p-9p = 7p+2p+p-9p = 10p-9p = p
Let me know if this helps!
Answer:
Here. These are the corrections
Shown below is a wooden six-sided (hexagon) frame. Which of
the following best approximates the slopes of the six line
segments?
O The slopes are approximately -1.4, 0, and 1.4.
O The slopes are approximately -1.7, 0, and 1.7.
O The slopes are approximately -1.8, 1, and 1.4.
O The slopes are approximately -1.7,0, and 1.4
Answers
The slopes are best approximated as: The slopes are approximately -1.7, 0, and 1.7.
How to find the slope between two coordinates?The formula to find the slope between two coordinates is expressed as:
Slope = (y₂ - y₁)/(x₂ - x₁)
The slope of each line above the x-axis are:
Slope 1 = (5 - 0)/(5 - 8)
Slope 1 = -1.7
Slope 2 = (5 - 5)/(5 - (-2))
Slope 2 = 0
Slope 3 = (5 - 0)/(-2 - (-5))
Slope 3 = 5/3 = 1.7
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6. Rosie went on a hiking trip. The first day she walked 18 kilometers. Each day since, she walked 90% of what she walked the day before. What is the total distance Rosie has traveled by the end of the 10th day? Round your final answer to the nearest kilometer.
Answers
Answer:
117
Step-by-step explanation:
math math math math math math math
Answers
The angle m∠JIX is 90 degrees.
How to find angles in line intersection?IX is perpendicular to IJ. Therefore, angle m∠JIX is 90 degrees.
IG bisect CIJ. Hence,
m∠CIG ≅ m∠GIJ
Therefore,
m∠CIX = 150 degrees
Hence, let's find m∠JIX.
Therefore, m∠JIX is 90 degrees because IX is perpendicular to IJ. Perpendicular lines forms a right angle.
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The measure of angle m∠JIX is estimated to be 90⁰.
How to find the angles?You should understand that an angle is a figure formed by two straight lines or rays that meet at a common endpoint, called the vertex.
IX is perpendicular to IJ. Therefore, angle m∠JIX is 90⁰.
Frim the given parameters,
IG⊥CIJ.
But; m∠CIG ≅ m∠GIJ
⇒ m∠CIX = 150⁰
Hence, let's find m∠JIX.
Therefore, m∠JIX is 90⁰ because IX is perpendicular to IJ. Perpendicular lines forms a right angle.
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what is the answer to 4n – 3?
Answers
Step-by-step explanation:
4n - 3 = 0
4n = 0 + 3
4n = 3
\(n \: = \frac{3}{4} \)
Consider the polynomial function q(x) = -2x^8 + 5x^6 -3x^5 + 50 What is the end behaviour of the graph of q?
Answers
The end behavior of the function q(x) is:
when x → ∞, q(x) → -∞when x → -∞, q(x) → -∞How to identify the end behavior?To know the end behavior we need to look at the degree and the sign of the leading coefficient.
If the degree is even, and the leading coefficient is negative, then in both ends the function will tend to negative infinity.
Here we can see that the function is:
q(x) = -2x⁸ + 5x⁶ - 3x⁵ + 50
So, the degree is 8, and the leading coefficient is -2, then the end behavior of the function is:
when x → ∞, q(x) → -∞
when x → -∞, q(x) → -∞
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A cone with a height of 8 inches and a radius of 6 inches was dilated using a scale factor of 2. Which
of the following statement is true?
Answers
Answer:
true yes sir
Step-by-step explanation:
A ratio station collects donations for a new board cast tower. The cost of construction is $25.50 per inch. How much does it cost to fund 4.5 inches of the construction?
Answers
Answer:
=$114.750
Step-by-step explanation:Length of new board cast tower=4.5 Inches
Cost of construction(per inch)=$25.50
To find cost=?
=25.50x4.5
=$114.750
...................................................................................
The required cost of the construction of a 4.5-inch tower is $114.75.
Given that,
A ratio station collects donations for a new board cast tower. The cost of construction is $25.50 per inch, how much it cost to fund 4.5 inches of the construction is to be determined.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
The cost of construction is $25.50 per inch.
The cost of 4.5 inches of construction = 25.50 × 4.5 = $114.75.
Thus, the required cost of the construction of a 4.5-inch tower is $114.75.
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erastdyfugihojlhgfdszerWestdyfughilj;hgufydtyrstzerxytcfyguhlij;lk
Answers
Answer:
36/27
Step-by-step explanation:
SOHCAHTOA, so tan is opposite over adjacent.
opposite = 36
adjacent = 27
So, tan C is 36/27
What is the sum of 9/12+4/12?
Answers
Answer:
13/12 = 1 1/12 = \(1\frac{1}{12}\)
Step-by-step explanation:
This is the answer because:
1) Since both fractions have a common denominator, all we have to do is add the numerators.
9/12 + 4/12 = 9 + 4 = 13/12 = 1 1/12
2) 13/12 converted into a mixed number fraction is 1 1/12 = \(1\frac{1}{12}\)
Hope this helps!
Enzo has fish in two aquariums. In one aquarium, the ratio of the number of guppies to the number of goldfish is 2:3. In the other, this ratio is 3:5. If Enzo has 20 guppies in total, the least number of goldfish that he could have is
A. 29
B. 30
c. 31
d. 32
Answers
cards and chips are being created for a board game by company the number of cards produced is proportional to the number of chips that are produced over a short period of time the company produced 32 cards and four chips what is the ratio of cars the chips produce State and simplest form as a unit rate in cards per chip (I NEED ANSWERS FAST)
Answers
Answer:
8 cards per chip
Step-by-step explanation:
So 32:4 is the ratio.
Divide by 4 to get 8 cards per chip.
2,239 ÷ 7
Division compatible numbers
Answers
Answer:the answer is 319.857 and round to 320
Step-by-step explanation:
7/8-square root of 6
Answers
Answer:
\( \frac{7}{8} - \sqrt{6} \\ \\ \frac{7}{8} - \frac{8 \sqrt{6} }{8} = \frac{7 - 8 \sqrt{6} }{8} \\ \\ \frac{7 - 8(2.449)}{8} = \frac{7 - 19.592}{8} \\ \\ = \frac{ - 12.592}{8} = - 1.574\)
I hope I helped you^_^
8. Ryan sells cars for a living. He gets paid $50 per day plus
a commission of 2% of the total cost of each car he sells. Ryan's daily
earnings (E) can be represented by the equation E = 0.02x + 50 where x
is the amount of his sales for the day.
a. What does the 0.02 represent in the equation?
b. How much did Ryan make on Monday if he only sold one car
for $4,400?
c. Ryan wants to make $1,000 in a day. What must his daily sales be
to reach this goal? Show all work necessary to justify your answer.
Answers
Answer:
a. the 2% commission he receives
b. $138
c. He must make $47,500 in sales
Step-by-step explanation:
a. No work needed
b. E= 0.02 (4,400) +50, which simplifies to E= 88+50 which continues to 138 dollars
c. To find this you already know E, so you can work backwards
1,000= 0.02 (x) + 50
then subtract 50 from each side
950 = 0.02 (x)
then divide both sides by the 0.02 to get X alone
47,500 = X
The stem-and-leaf plot below shows the number of pages each student in a class read the previous evening.
A stem and leaf plot showing the movie length in minutes shown. The stems from top to bottom are 0, 1, 2, 3, 4, 5. The first column of leaves is 0, 2, 2, 3, 2, 7. The second column of leaves is 0, 3, 4, 5, 4, blank. The third column of leaves is 5, 5, 6, 6, 6, blank, blank. The fourth column of leaves is 8, 8, 7, blank, blank, blank. The fifth column of leaves is blank, 8, 7, blank, blank, blank. The sixth column of leaves is blank, 9, 7, blank, blank, blank.
Which statement is true about the data set?
Its median is greater than its mode.
It has a range of 52 pages.
The value of the first quartile is 13.
The data is symmetric.
Answers
Answer:
The value of the first quartile is 13.
Step-by-step explanation:
0 0 0 5 8
1 2 3 5 8 8 9
2 2 4 6 7 7 7
3 3 5 6
4 2 4 6
5 7
Its median is greater than its mode.
median is 12th data point = 24 mode = 27 false
It has a range of 52 pages.
range is largest minus smallest = 57-0 = 57 false
The value of the first quartile is 13.
There are 11 data points 11/2 = 5.5 = 1st quartile is 6th data point = 13
The data is symmetric.
it is not symmetric
Answer:
C) The value of the first quartile is 13.
Step-by-step explanation:
OK for real this is a hard only verified experts can do this!!!!
Answers
The numeric value of the exponential expression in this problem is given by the following option:
A. 2^12.
How to obtain the numeric value of the exponential expression?The exponential expression for this problem is defined as follows:
8^x/2^y.
8 is the third power of 2, hence:
8 = 2^3.
When a term is elevated to two of it's powers, the powers are multiplied, hence:
(2^3)^x = 2^(3x).
Meaning that the exponential expression is then written as follows:
8^x/2^y = 2^(3x)/2^y.
When two terms of the same base and different exponents are divided, we keep the base and subtract the exponents, hence the expression is given as follows:
2^(3x)/2^y = 2^(3x - y).
As stated in the problem, the numeric value of the expression 3x - y is given as follows:
3x - y = 12.
Hence the entire expression is simplified as follows:
2^(3x - y) = 2^12.
Meaning that the correct option is given by option A.
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Answer:A. 2^12.
Step-by-step explanation:i did it and got it right
factor x-a in such a way that square root of x - square root of a is a factor
Answers
We want to factor the expression x - a, in such a way that we have one factor written as:
(√x - √a)
We will find that the factorized expression is:
(√x - √a)*(√x + √a)
Here we need to remember two things:
First, (√x)^2 = √(x^2) = x
also:
(x^2 - y^2) = (x + y)*(x - y)
Now, using the first property, we can rewrite our original expression as:
(x - a) = ( (√x)^2 - (√a)^2)
Now, using the second property, we can rewrite it as:
( (√x)^2 - (√a)^2) = (√x - √a)*(√x + √a)
Then we have:
(x - a) = (√x - √a)*(√x + √a)
Thus, we have factorized (x - a) in such a way that one of the factors is equal to (√x - √a)
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Two pence coins are used to make a square. If one millioncoins were used, what would be the length of the sides of the square?
How many square metres would these one million coins cover?
(The diameter of a 2p coin is 25mm to the nearest millimetre.
Answers
Answer:
i dont know the answer
Step-by-step explanation:
just put a random answer and hope for the best