Answers
Given:
A figure of a right triangle.
To find:
The value of x.
Solution:
According to the geometric mean attitude theorem, if an altitude is drawn from the right angle vertex to the hypotenuse, then the altitude is the geometric mean of segments of hypotenuse.
Using geometric mean attitude theorem, we get
[tex]\dfrac{3}{x}=\dfrac{x}{5}[/tex]
[tex]3\times 5=x\times x[/tex]
[tex]15=x^2[/tex]
[tex]\pm \sqrt{15}=x[/tex]
But side cannot be negative. So,
[tex]\sqrt{15}=x[/tex]
Therefore, the value of x is [tex]\sqrt{15}[/tex].
Related Questions
7. If it takes 2 gardeners 6 hours to landscape a garden, how long would
it take 3 gardeners?
Enter your answer
Question 7 is an example of...
Direct proportion
Inverse proportion
Answers
Answer:
it will take 12 hours
Step-by-step expl
Is 18.52 irrational or rational
Answers
:))))))))$$)))))
Nancy borrowed $150 from her parents to buy a video game system. She has agreed to pay them back $25 each week Which equation represents the amount of money
Nancy still owes her parents, P. after w weeks?
Answers
Answer:
P = 150 - 25w
Step-by-step explanation:
Amount borrowed = $150
Repayment amount = $25 each week
P = amount Nancy owes
w = number of weeks
Amount Nancy owes = amount borrowed - repayment plan per week
P = 150 - 25w
During the first week of repayment: when w = 1
P = 150 - 25w
P = 150 - 25(1)
= 150 - 25
= 125
P = $125
what slope equation is parallel to y=5x-10
Answers
Answer:
y = 5x + (anything except negative 10)
For example:
y = 5x + 5
Step-by-step explanation:
A parallel equation is any equation with the same slope, but a different y intercept. As long as your y intercept isn't - 10, your answer will be parallel.
A fish tank is initially filled with 400 liters of water containing 1 g/liter of dissolved oxygen. At noon, oxygenated water containing 10g/liter of oxygen flows in at a rate of 5 liters per minute and the well-mixed water is pumped out at a rate of 7 liters per minute.Let A(t) represent the amount of dissolved oxygen in the tank at time t. a) Write the differential equation that represents the problem.b) Solve the differential equation. c) At 1 p.m., what is the amount of dissolve oxygen in the fish tank
Answers
Answer:
a. [tex]dA(t)/dt = 50 - \frac{7A(t)}{400} where A(0) = 400[/tex]
b. [tex]A(t) = \frac{20000}{7} + \frac{17200}{7}e^{-7t/400}[/tex]
c. 3.717 kg
Step-by-step explanation:
a) Write the differential equation that represents the problem.
Let A(t) be the amount of dissolved oxygen in the tank at any time, t.
The net flow rate dA(t)/dt = mass flow in - mass flow out
Since 10 g/l of oxygen flows in at a rate of 5 l/min, the mass flow in is 10 g/l × 5 l/min = 50 g/min
Since A(t) is the amount of oxygen present in the tank at time, t, and the volume of the tank is 400 liters. The concentration of oxygen in the tank is thus A(t)/400 g/l.
Also, water is being pumped out at a rate of 7 l/min. So, the mass flow out is thus concentration × flow rate out = A(t)/400 g/l × 7 l/min = 7A(t)/400 g/min
So, dA(t)/dt = mass flow in - mass flow out
dA(t)/dt = 50 - 7A(t)/400 with A(0) = 400 l × 1 g/l = 400 g since the tank initially contains 1 g/l of dissolved oxygen and has a volume of 400 l
So, the differential equation is
dA(t)/dt = 50 - 7A(t)/400 where A(0) = 400 g
[tex]dA(t)/dt = 50 - \frac{7A(t)}{400} where A(0) = 400[/tex]
b) Solve the differential equation
To solve the equation, we use separation of variables, so
dA(t)/dt = 50 - 7A(t)/400 where A(0) = 400 g
dA(t)/(50 - 7A(t)/400) = dt
Integrating both sides, we have
∫dA(t)/(50 - 7A(t)/400) = ∫dt
-7/400 ÷ -7/400∫dA(t)/(50 - 7A(t)/400) = ∫dt
1/ (-7/400)∫-7/400dA(t)/(50 - 7A(t)/400) = ∫dt
(-400/7)㏑(50 - 7A(t)/400) = t + C
㏑(50 - 7A(t)/400) = -7t/400 + (-7/400)C
㏑(50 - 7A(t)/400) = -7t/400 + C' (C' = (-7/400)C)
taking exponents of both sides, we have
50 - 7A(t)/400 = exp[(-7t/400) + C']
50 - 7A(t)/400 = exp(-7t/400)expC'
[tex]50 - \frac{7A(t)}{400} = e^{-7t/400}e^{C'} \\50 - \frac{7A(t)}{400} = Ae^{-7t/400} A = e^{C'}\\ \frac{7A(t)}{400} = 50 - Ae^{-7t/400} \\A(t) = \frac{400}{7} X 50 - \frac{400}{7} Ae^{-7t/400} \\A(t) = \frac{20000}{7} - \frac{400}{7} Ae^{-7t/400}[/tex]
when t = 0 , A(0) = 400. So,
[tex]A(t) = \frac{20000}{7} - \frac{400}{7} Ae^{-7t/400} \\A(0) = \frac{20000}{7} - \frac{400}{7} Ae^{-7(0)/400}\\A(0) = \frac{20000}{7} - \frac{400}{7} Ae^{0/400}\\A(0) = \frac{20000}{7} - \frac{400}{7} Ae^{0}\\A(0) = \frac{20000}{7} - \frac{400}{7} A\\400 = \frac{20000}{7} - \frac{400}{7} A\\\frac{400}{7} A = 400 - \frac{20000}{7}\\\frac{400}{7} A = \frac{2800}{7} - \frac{20000}{7}\\\frac{400}{7} A = -\frac{17200}{7}\\\\A = -\frac{17200}{7} X \frac{7}{400} \\A = -43[/tex]
So,
[tex]A(t) = \frac{20000}{7} - \frac{400}{7} X -43e^{-7t/400} \\A(t) = \frac{20000}{7} + \frac{17200}{7}e^{-7t/400}[/tex]
c) At 1 p.m., what is the amount of dissolve oxygen in the fish tank.
At 1 p.m, t = 60 min
So, the amount of dissolved oxygen in the fish tank is A(60)
So,
[tex]A(t) = \frac{20000}{7} + \frac{17200}{7}e^{-7t/400}\\A(60) = \frac{20000}{7} + \frac{17200}{7}e^{-7X60/400}\\A(60) = \frac{20000}{7} + \frac{17200}{7}e^{-420/400}\\A(60) = \frac{20000}{7} + \frac{17200}{7}e^{-1.05}\\A(60) = \frac{20000}{7} + \frac{17200}{7} X 0.3499\\A(60) = \frac{20000}{7} + \frac{6018.93}{7} \\A(60) = \frac{26018.93}{7} \\A(60) = 3716.99 g[/tex]
A(60) ≅ 3717 g
A(60) ≅ 3.717 kg
find the component equation of the plane which is normal to the vector -2i+5j+k and which contains the point (-10;7;5).
Answers
Given:
A plane is normal to the vector = -2i+5j+k
It contains the point (-10,7,5).
To find:
The component equation of the plane.
Solution:
The equation of plane is
[tex]a(x-x_0)+b(y-y_0)+c(z-z_0)=0[/tex]
Where, [tex](x_0,y_0,z_0)[/tex] is the point on the plane and [tex]\left< a,b,c\right>[/tex] is normal vector.
Normal vector is -2i+5j+k and plane passes through (-10,7,5). So, the equation of the plane is
[tex]-2(x-(-10))+5(y-7)+1(z-5)=0[/tex]
[tex]-2(x+10)+5y-35+z-5=0[/tex]
[tex]-2x-20+5y-35+z-5=0[/tex]
[tex]-2x+5y+z-60=0[/tex]
[tex]-2x+5y+z=60[/tex]
Therefore, the equation of the plane is [tex]-2x+5y+z=60[/tex].
how to write 1/4z-1/3-1/7z^2 in az^2+bz
Answers
Answer:
huh?nani?
ksjn
lsjsmskkks
Help me pls! this is due tonite . I'm doing a ged practice test and I just have a few questions I haven't answered
When 36x⁴ + 12x⁸ is divided by 12x⁴ the result is:
A) 3+12x8
B)3+x⁴
C)3x+x²
Answers
Answer:
Step-by-step explanation:
36x⁴ /12x⁴ + 12x⁸ / 12x⁴
3x+x²
What is the slope of a line that passes through the following points (-2,-5) and (2, 5)?
a.-4/10
b.4/10
c.-10/4
d.10/4
Answers
n x 5 = I'm very Smart *wink wink* I could just search it up I'm not gonna though okay
Answers
Answer:
5n
Step-by-step explanation:
-4x-2y=-12
4x+8y=-24
solve it by elimation
Answers
Answer:
(x, y) = (6, -6)
Step-by-step explanation:
Find the missing number:
Answers
Answer:
20%
Step-by-step explanation:
Not sure if this is exactly correct, but let's say we start with 1 unit. If it increased by 25%, we get:
1 × 1.25 = 1.25 units.
Now, to get back to 1 unit, we need to find:
1.25 × ? = 1
? = [tex]\frac{1}{1.25}[/tex] = 0.80
So, 100% - 80 % = 20%
A 20% decrease.
Not completely sure though.
Which point is a solution to the following inequality? y<2x+2
Answers
Answer:
Y<2x
Step-by-step explanation:
Find the missing angle
Answers
Answer:
x=21
Step-by-step explanation:
69+90= 159
180-159=21
because to find missing angles you add together the known angles then subtract that from 180
69+11 = 80
180- 80 = 100
8x+5x^3-5 write polynomial in standard form, Then name the polynomial based on the degree and number of terms
Answers
Answer:
wag na baka imyday mo pa
Step-by-step explanation:
hahahahahahahahahahahahahahahahahaahhaahahahahahhahahahahahahahahahahahahahahahahahahahahahahahahhahahahah ahahahahahahaha ahahahahahahaha ahahahahahahaha hahahahahah ahahahahahahaha
Distribute. 8(x+30)+5
Answers
Answer:
8x + 245
Step-by-step explanation:
8(x + 30) + 5
8x + 240 +5
8x + 245
good luck, i hope this helps :)
Mary has two sisters. Her younger sister is 5 years younger Her older
sister is twice her age. Their ages add up to 47. How dd is Mary and each
of her sisters?
Answers
Explanation:
26 + 13 + 8 = 47
If the older sister is 26, then Mary is half that, meaning: 26/2 = 13
Mary is 13, and her younger sister is 5 years younger so: 13-5 = 8
Her younger sister is 8.
To double check, add up the ages and see if you get 47.
26 (older sister) + 13 (Mary) + 8 (younger sister) = 47
In ΔRST, the measure of ∠T=90°, the measure of ∠S=16°, and ST = 2.9 feet. Find the length of TR to the nearest tenth of a foot.
Answers
Answer:
0.8
Step-by-step explanation:
The measure of angle A in ABC is twice the measure of angle B and the measure of angle C is 20° less than the measure
of angle B. What are the measures of the angles in ABC?
Answers
Answer:
m∡A = 100°
m∡B = 50°
m∡C = 30°
Step-by-step explanation:
let 'x' = m∡B; 50°
let '2x' = m∡A; 100°
let 'x-20' = m∡C; 30°
x + 2x + x - 20 = 180
4x - 20 = 180
4x = 200
x = 50
Select all ratios equivalent to 4:3.
Answers
Answer:
8:6 and 16:12
Step-by-step explanation:
I am not usre what the answer could be
Answers
Answer:
[tex]x \le 5[/tex]
Step-by-step explanation:
Given
Shape: Cube
Dimensions: x, 3x and 2x
[tex]Volume < 900[/tex]
Required
Show that [tex]x \le 5[/tex]
First, calculate the volume
[tex]Volume = x * 3x * 2x[/tex]
[tex]Volume = 6x^3[/tex]
[tex]Volume < 900[/tex] becomes
[tex]6x^3 < 900[/tex]
Divide both sides by 9
[tex]x^3 < 150[/tex]
For [tex]x^3 < 150[/tex], the value of x as to be: 1, 2, 3, 4 or 5
Hence:
[tex]x \le 5[/tex]
Write this number in scientific notation 56,023,987
Answers
hope that helps
the Rangers played 40 games. They won 18 more games then they lost. How many games did they win?
Answers
9514 1404 393
Answer:
29
Step-by-step explanation:
Let w represent the number of wins. Then the number of losses is w-18. The total number of games played is ...
wins + losses = 40
w + (w-18) = 40
2w = 58
w = 29
The Rangers won 29 games.
What is the solution to the system of equations below?
s 2y = x + 6
1 3.x = y +7
(20, 13)
(13, 20)
(5, 4)
(4, 5)
Answers
Answer:
(4,5)
Step-by-step explanation:
If the complex number x = 3 + bi and |x|2 = 13, which is a possible value of b?
2
4
9
10
Answers
Answer:
A: 2
Step-by-step explanation:
EDGE 2021
Considering that the magnitude of the complex number x is of 13, a possible value of b is of 2.
What is a complex number?A complex number is modeled by:
z = a + bi.
In which:
a is the real part.b is the imaginary part.In this problem, the number is:
x = 3 + bi.
It's magnitude is given by:
[tex]|x| = \sqrt{3^2 + b^2}[/tex]
Then:
[tex]\sqrt{3^2 + b^2} = \sqrt{13}[/tex]
[tex]3^2 + b^2 = 13[/tex]
[tex]b = \pm \sqrt{4}[/tex]
[tex]b = \pm 2[/tex]
A possible value of b is of 2.
More can be learned about complex numbers at https://brainly.com/question/25572463
#SPJ2
I need to find the x of the triangle.
Answers
Elmer is purchasing 2 4/5 pounds of candy that cost $1.85 per pound.
If he pays with $10, how much will he get in change? HELP I WILL MARK BRAINIEST
Answers
Answer:
hi
Step-by-step explanation:
Daniel bought 1 pound of jelly beans and 2 pounds of chocolates for $2.00. ... for $1.50. How much would he have to pay on his next trip to the candy store if he bought 1 pound of each of the 4 kinds ... How many are there? Assign ... Multiply each equation by a factor, so that all equations will have the same total price: 3(1j +.
Hope this helps!
In one of ADNOC's onshore stations in the United Arab Emirates, oil is extracted and stored in large cylindrical tanks. If one of the tanks is 30
meters deep and 20 meters in diameter, find the Volume of the tank, use 3.14 for
(show your work)
Answers
Answer: 9420meters³
Step-by-step explanation:
The formula to calculate the volume of the cylindrical tank will be:
= πr²h.
where,
π = 3.14
r = radius = diameter/2 = 20/2 = 10
h = height = 30
Volume = πr²h
= 3.14 × 10² × 30
= 3.14 × 100 × 30
= 9420meters³
Which of the following properties is always true for a parallelogram?
A. Diagonals bisect each other
B. Diagonals are perpendicular
C. Diagonals are congruent
D. Diagonals bisect opposite angles
Answers
Answer:
c. is always true
Step-by-step explanation:
I am in need of help please.
Answers
Answer:
80 ft
Step-by-step explanation:
i dont really know if this is the right answer plz tell me if im wrong