Answers
Given:
In right triangle ABC, BD is the altitude drawn to hypotenuse AC.
[tex]AD=20, DC=45[/tex]
To find:
The length of BD.
Solution:
According to geometric mean theorem of triangles, if an altitude is drawn to the hypotenuse of a triangle, then the altitude is the geometric mean of the segments of the hypotenuse.
Using geometric mean theorem of triangles, we get
[tex]BD^2=AD\times DC[/tex]
[tex]x^2=20\times 45[/tex]
[tex]x^2=900[/tex]
Taking square root on both sides, we get
[tex]x=\dfrac{900}[/tex]
[tex]x=30[/tex]
Therefore, the length of BD is 30 units and the correct option is C.
Related Questions
If you deposit ₱10,000 into an account that earns 5% annual interest compounded semiannually, how long will it take until there is ₱12,000 in the bank account
Answers
Answer:
t = 3.69 ≈ 3. 7 years
Step-by-step explanation:
Given :
P = 10,000
r = 5%= 0.05
A = 12,000
n = 2 ( because it is compounded semi - annually )
[tex]A = P (1 + \frac{r}{n})^{nt}\\[/tex]
[tex]12000 = 10000(1 + \frac{0.05}{2})^{2 t}\\\\1.2 = ( 1 + \frac{0.05}{2})^{2t}\\\\1.2 = (1.025)^{2t}\\\\log \ 1.2 = 2t \ log \ 1.025\\\\2t = \frac{log 1.2 }{log 1.025} \\\\2t = \frac{0.1823}{0.0247}\\\\2t = 7.3805\\\\t = 3.69[/tex]
Find the value of the missing angles in the following figures
Answers
Answer:
ans: ii) 87° and iii) 60°
Step-by-step explanation:
ii)
y° = 180° - ( 56° + 37°)
missing angle on triangle is alternate angle of y° so are equal and sum of angles of triangle is 180°
iii)
x° + 2x° = 180°
sum of co interior angles is 180°
A survey found that one out of five Americans says he or she has visited a doctor in any given month. If 10 people are selected at random, find the probability that at least 3 will
have visited a doctor last month.
Answers
I took the test
On
Ed
Gen
Unity
Multiply the following complex numbers (7 + 2i)(2+3i) O A. 20-25i B. 8-25i O C. 8+ 25i O D. 20-25i
Answers
Đáp án là C: 8+25i nhé
8+ 25i
Answer:
C. 8+25i
Just took it, it's correct :)
if 4,1,2 in middle is 21
if 2,1,4 in middle is 16
then 1,4,2 what is number in middle?
Answers
Answer:
5
Step-by-step explanation:
21-16=5
hope it helps!!
is this an Olympiad qn?
A table is made using the following two patterns.
Pattern 3: Starting number: 5, Rule: add 1
Pattern y: Starting number: 10, Rule: add 2
Complete the table for the given patterns.
Answers
Answer:
x = 6, y = 12
x = 7 y = 14
Step-by-step explanation:
im pretty sure that right, hope this helps!
If these two triangles are similar, find the vale of x.
Answers
Answer:
24
Step-by-step explanation:
just use sss theorem and get the answer
12x = 16 x 18
12x = 288
x = 288/12
x = 24
Find the radius of a circle in which the central angle, a, intercepts an arc of the given length s.
a = 60°, s = 44 ft
The radius is ft.
(Round to the nearest hundredth as needed.)
Answers
Answer:
42.02 ft
Step-by-step explanation:
60 : 360 = 44 : x
x = 264 ft (length of the circumference)
C = 2 * radius * pi
radius = C / 2 * pi
Radius = 264 / 2 * pi = 42,016905 ft
Find the volume of a sphere with a diameter of 4 inches. Use 3.14 for π
.
Round your answer to the nearest hundredth.
The volume of the sphere is cubic inches.
Answers
Answer:
33.51 cubic inches
Step-by-step explanation:
Formula for volume of a sphere is V= 4 /3 · π · r3
We know the diameter is 4, and the radius is half the diameter, so the radius is 2.
V = 4 /3 · π · [tex]2^{3}[/tex]
≈ 33. 51032
Rounded to the nearest hundreth is 33.51.
pls help me i will mark brainliest if you are right !
Answers
Answer:
second option
Step-by-step explanation:
diameter= 22 cm
radius = diameter/2
=22/2
11 cm
volume of a sphere = [tex]\frac{4}{3}*pie* r^3[/tex]
=[tex]\frac{4}{3} * 3.14 *11^3[/tex]
=4.186666 * 1331
=5572 . 5 cubic centimeters (cm^3)
.
Given g(x)=-x+4, find g(-4)
Answers
Answer:
g(-4) = 8
Step-by-step explanation:
g(-4) = - ( - 4 ) + 4
= 8
If this helps you, please give brainliest!
Payment types vary at the grocery store. Here are the proportions of the leading three payment methods: Payment Method Cash Credit Cards Debit Cards Proportion 0.11 0.43 0.21 If a transaction is selected at random, the probability that the customer did not pay with a Debit Card is .
Answers
Answer:
0.79
Step-by-step explanation:
Given the probability distribution :
Payment Methd: Cash Credit Cards Debit Cards Proportion : ____0.11 ____ 0.43 _____0.21
The probability that a customer did not pay with debit card can be obtained as :
If customer did not pay with debit card, then he would have paid with any of the other payment methods
This Can best be obtained using the complement method
P(not debit card) = 1 - P(debit card)
P(debit card) = 0.21
P(not debit card) = 1 - 0.21
P(not debit card) = 0.79
What is the range of f(x) = 3X?
O A. All real numbers greater than 3
O B. All real numbers greater than or equal to 3
O C. All positive real numbers
O D. All real numbers
Answers
a)Loss is denoted by a negative integer and profit is denoted by a positive integer. A
cement company earns a profit of ₹ 10 per bag of white cement and a loss of ₹ 5 per
bag of grey cement. The company sells 325 bags of white cement and 500 bags of
grey cement. What is its profit or loss?
Answers
Answer:
There was a profit of ₹750.
Step-by-step explanation:
325 bags of white cement
Profit of 10 for each bag of white cement. So
[tex]P = 325*10 = 3250[/tex]
500 bags of grey cement.
Loss of 5 for each bag of grey cement. So
[tex]L = 5*500 = 2500[/tex]
What is its profit or loss?
3250 - 2500 = 750
Positive, so profit. There was a profit of ₹750.
Select the correct answer.
The function g(x) = x is transformed to obtain function :
Rx) = g(x) + 1.
Which statement describes how the graph of his different from the graph of g?
ОА
The graph of his the graph of gvertically shifted up 1 unit.
OB.
The graph of his the graph of g horizontally shifted right 1 unit.
OC. The graph of his the graph of g horizontally shifted left 1 unit
D. The graph of his the graph of g vertically shifted down 1 unit.
Answers
Answer: A
Step-by-step explanation:
help whats the answer??
Answers
Answer:
2 7/12
Step-by-step explanation:
You have to get all the fractions to a common denominator. Smallest common denominator would be 12.
5 and 3/4 turns to 5 and 9/12
2/3 turns to 8/12
2 and 1/2 turns to 2 and 6/12
8/12 + 2 6/12 = 3 2/12
5 9/12 - 3 2/12 = 2 7/12
2 7/12 being the remaining amount
a housewife spent 3/7 of her money to buy yams and 1/2 of the remainder to buy rice what is the fraction of her money left
Answers
Answer:
Fraction of money spent on calculator = 2/5
Find the fraction of money left:
1 - 2/5 = 3/5
Find the fraction of money spent on a book:
4/7 x 3/5 = 12/35
Answer: She spent 12/35 of the money on a book
------------------------------------------------------------------------------------------------
To find the fraction of saving:
Fraction of money saved = 1 - calculator - book
Fraction of money saved = 1 - 2/5 - 12/35 = 9/35
Fraction of the money saved = 9/35
Step-by-step explanation:
Starting at a train station, Train A goes toward its destination to the right by 600
miles, and Train B goes to the left by 500 miles. Which of the following signed
numbers best represents Train A's direction and distance toward its destination?
A.-600
B.-500
C.500
D.600
Answers
9514 1404 393
Answer:
D. 600
Step-by-step explanation:
On a number line, positive numbers increase to the right. 600 to the right would be considered to be +600, choice D.
A fish tank initially contains 15 liters of pure water. Brine of constant, but unknown, concentration of salt is flowing in at 4 liters per minute. The solution is mixed well and drained at 4 liters per minute. Let xx be the amount of salt, in grams, in the fish tank after tt minutes have elapsed. Find a formula for the rate of change in the amount of salt, dx/dtdx/dt, in terms of the amount of salt in the solution xx and the unknown concentration of incoming brine cc. dxdt
Answers
Answer:
dx/dt = 4c - 4x/15
Step-by-step explanation:
a. Find a formula for the rate of change in the amount of salt, dx/dtdx/dt, in terms of the amount of salt in the solution
Let c be the concentration of the incoming brine in grams per liter. Since it flows in at a rate of 4 liters per minute, the mass flow in is thus 4m.
Let x be the mass of salt present at time, t. The concentration of salt present at time, t is thus mass of salt/volume of tank = x/15. Since the well mixed solution is drained at 4 liters per minute, the mass flow out is thus 4x/15.
The net rate of change of amount of salt dx/dt = mass flow in - mass flow out
dx/dt = 4c - 4x/15
if a line with an angle of inclination 120⁰ and passes trough (√3,1),then what is the equation of a line
Answers
Answer:
The equation of a line, having inclination 120° with positive direction of x-axis, .of x-axis, which is at a distance of 3 units from the origin is. 1. See answer ... where α is the angle with the positive X-axis, made by the perpendicular line drawn Now, from equation the equation of the straight line will be.
Step-by-step explanation:
Given the functions below, find (g•h) (1).
g(x) = х^2 +4+ 2х
h(x) = — 3х + 2
-7
-30
35
7
Answers
Answer:
-7
Step-by-step explanation:
We are given the following functions:
[tex]g(x) = x^2 + 4 + 2x[/tex]
[tex]h(x) = -3x + 2[/tex]
(g•h) (1)
The multiplication is:
[tex](g \times h)(1) = g(1) \times h(1)[/tex]
So
[tex]g(x) = 1^2 + 4 + 2(1) = 7[/tex]
[tex]h(1) = -3(1) + 2 = -3 + 2 = -1[/tex]
Then
[tex]g(1) \times h(1) = 7(-1) = -7[/tex]
So -7 is the answer.
Find the inverse of \(\Large h(x) = \frac {3}{2}x + 1 \)
Answers
Answer:
[tex]h(x) = \frac {3}{2}x + 1 \\ { \tt{let \: the \: inverse \: be \: { \bold{m}}}} \\ { \tt{m = \frac{1}{ \frac{3}{2}x + 1 } }} \\ \\ { \tt{m = \frac{2}{3x + 2} }} \\ \\ { \tt{m(3x + 2) = 2}} \\ \\ { \tt{3x + 2 = \frac{2}{m} }} \\ \\ { \tt{x = \frac{2 - 2m}{3m} }} \\ \\ { \tt{x = \frac{2}{3m}(1 - m) }} \\ \\ { \bf{h {}^{ - 1} (x) = \frac{2}{3x}(1 - x) }}[/tex]
The diameter of a pipe is normally distributed, with a mean of 0.8 inch and a variance of 0.0025. What is the probability that the diameter of a randomly selected pipe will exceed 0.9 inch?
Answers
Answer:
0.02275
Step-by-step explanation:
Standard deviation is the square root of variance
Standard deviation= Square(0.0025)= 0.05
Because of the normally distributed, the z- score for 0.9 inches is:
(0.9-0.8)/0.05= 2
-> P(x<= 0.9)= P(2) = 0.97725
-> P (x>= 0.9)= 1-0.97725 = 0.02275
I need help with this
Answers
sorry if i’m wrong
Select all the expressions that are equivalent to 4x + 2.
A. 8x +4
B. 1/2(8x + 4)
C. 1/2(2x +1)
D. 2 (2x + 1)
E. 2x + 2x +1 + 1
Answers
Answer the following and round to one decimal place.
Answers
Step-by-step explanation:
5 1/2% = 5.5% = 5.5/100 = 0.055
0.055 * 68 = 3.74
Answer:
3.74
Step-by-step explanation:
[tex]5\frac{1}{2}%[/tex] of 68
In order to do this you need to convert 5 1/2 into a decimal!
Answer: 5.5
Explanation: 5 is a whole number and half of one unit will be 0.5
5 + 0.5 = 5.5
Then multiply 5.5 and convert 68 into "0.68"
5.5 × 0.68 = 3.74
Answer: 3.74
How many one-to-one correspondences are there between two sets with
6 elements each?
Answers
Answer:
6 * 5 * 4 * 3 * 2 * 1, i.e. 6! or 720. Of course, since both sets have the same number of elements, you can't have one-to-one without being onto, aka a surjection, so “one to one correspondence” is the right term (or bijection—merci, M.
Step-by-step explanation:
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follow me
carry on learning
100%sure
someone can help me with this?
Answers
Answer:
3q + 2p =
Step-by-step explanation:
Perimeter refers to the outside lines only so hence, 3q + 2p =
A Little League baseball coach wants to know if his team is representative of other teams in scoring runs. Nationally, the average number of runs scored by a Little League team in a game is 5.7. He chooses five games at random and finds the mean number of runs scored is 7.4 with a sample standard deviation of 2.88.
Required:
Is it likely that his team's scores is different than the national average?
Answers
Answer:
That result implies that t(s) is in the acceptance region for H₀ then we accept H₀, there is not statistics difference between the LL team and the national average
Step-by-step explanation:
The National average number of runs scored by a LL team is
μ = 5.7
Sample Information:
size sample n = 5
sample average x = 7.4
sample standard deviation s = 2.88
Is required to investigate if that sample average is statistically different from the National average
We will do a test with 95 % of confidence Interval that means
significance level α = 5 % or α = 0.05.
The sample size is 5 then even when we assume normal distribution the sample size indicates that we need to use t-student distribution. Furthermore, as the question is if the sample average is different from the national the test will be a two-tail test.
Then α = 0.05 α/2 = 0.025
df = n - 1 df = 5 - 1 df = 4
Then from t-student table we get t(c) = 2.132
Hypothesis test:
Null Hypothesis H₀ x = μ
Alternative Hypothesis Hₐ x ≠ μ
To calculate t (s)
t(s) = ( x - μ ) / s/√n
t(s) = ( 7.4 - 5.7 )* 2.24 / 2.88
t(s) = 1.7* 2.24 / 2.88
t(s) = 1.32
Comparing t(s) and t(c)
1.32 < 2.132
That result implies that t(s) is in the acceptance region for H₀ then we accept H₀, there is not statistics difference between the LL team and the national average
attendance drop at 7% this year to 1050 what was the attendance before the drop
Answers
Answer:
7% divided by 1050 is basically 73.5 but the fraction of that is 147/2 hope u find my answer reasonable have a great day.
Step-by-step explanation: