[tex] \large\color{lime}\boxed{\colorbox{black}{Answer : - }}[/tex]
We know that, in ∆ABC,
∠A+∠B+∠C = 180°
But the triangle is right angled at C
ie., ∠C = 90°
Therefore, ∠A+∠B+ 90° = 180°
⇒ ∠A + ∠B = 90°
Therefore, cos(A + B) = cos 90º = 0
maths class 9
Multiply: 4√12 2√12
Answer:
[tex]4 \sqrt{122} \sqrt{12} \\ (4 \times 2) \times ( \sqrt{12} \times \sqrt{12} ) \\ (4 \times 2) \times 12 \\ 8 \times 12 \\ 96[/tex]
Calculus!
The volume of a substance, A, measured in cubic centimeters increases according to the exponential growth model dA/dt = 0.3A, where t is measured in hours. The volume of another substance, B, also measured in cubic centimeters increases at a constant rate of 1 cm^3 per hour according to the linear model dB/dt = 1. At t = 0, substance A has a volume A(0) = 3 and substance B has size B(0) = 5. At what time will both substances have the same volume?
Would it be correct to write the growth model of substance B as x + 5? And how could I write the growth model of substance A? Thank you in advance, and sorry for the poor formatting.
Answer:
The two substances will have the same volume after approximately 3.453 hours.
Step-by-step explanation:
The volume of substance A (measured in cubic centimeters) increases at a rate represented by the equation:
[tex]\displaystyle \frac{dA}{dt} = 0.3 A[/tex]
Where t is measured in hours.
And substance B is represented by the equation:
[tex]\displaystyle \frac{dB}{dt} = 1[/tex]
We are also given that at t = 0, A(0) = 3 and B(0) = 5.
And we want to find the time(s) t for which both A and B will have the same volume.
You are correct in that B(t) is indeed t + 5. The trick here is to multiply both sides by dt. This yields:
[tex]\displaystyle dB = 1 dt[/tex]
Now, we can take the integral of both sides:
[tex]\displaystyle \int 1 \, dB = \int 1 \, dt[/tex]
Integrate. Remember the constant of integration!
[tex]\displaystyle B(t) = t + C[/tex]
Since B(0) = 5:
[tex]\displaystyle B(0) = 5 = (0) + C \Rightarrow C = 5[/tex]
Hence:
[tex]B(t) = t + 5[/tex]
We can apply the same method to substance A. This yields:
[tex]\displaystyle dA = 0.3A \, dt[/tex]
We will have to divide both sides by A:
[tex]\displaystyle \frac{1}{A}\, dA = 0.3\, dt[/tex]
Now, we can take the integral of both sides:
[tex]\displaystyle \int \frac{1}{A} \, dA = \int 0.3\, dt[/tex]
Integrate:
[tex]\displaystyle \ln|A| = 0.3 t + C[/tex]
Raise both sides to e:
[tex]\displaystyle e^{\ln |A|} = e^{0.3t + C}[/tex]
Simplify:
[tex]\displaystyle |A| = e^{0.3t} \cdot e^C = Ce^{0.3t}[/tex]
Note that since C is an arbitrary constant, e raised to C will also be an arbitrary constant.
By definition:
[tex]\displaystyle A(t) = \pm C e^{0.3t} = Ce^{0.3t}[/tex]
Since A(0) = 3:
[tex]\displaystyle A(0) = 3 = Ce^{0.3(0)} \Rightarrow C = 3[/tex]
Therefore, the growth model of substance A is:
[tex]A(t) = 3e^{0.3t}[/tex]
To find the time(s) for which both substances will have the same volume, we can set the two functions equal to each other:
[tex]\displaystyle A(t) = B(t)[/tex]
Substitute:
[tex]\displaystyle 3e^{0.3t} = t + 5[/tex]
Using a graphing calculator, we can see that the intersect twice: at t ≈ -4.131 and again at t ≈ 3.453.
Since time cannot be negative, we can ignore the first solution.
In conclusion, the two substances will have the same volume after approximately 3.453 hours.
There were 642 students enrolled in a freshman-level chemistry class. By the end of the semester, the number of students who passed was 5 times the number of students who failed. Find the number of students who passed and the number who failed.
Answer:
535 students passed and 107 students failed
Step-by-step explanation:
Create a system of equations where p is the number of students who passed and f is the number of students who failed:
p + f = 642
p = 5f
Solve by substitution by plugging in 5f as p into the first equation, then solving for f:
p + f = 642
5f + f = 642
6f = 642
f = 107
So, 107 students failed.
Find how many students passed by multiplying this by 5:
107(5)
= 535
535 students passed and 107 students failed.
Find the values of the missing sides. You must use exact answers! PLEASE HURRY AND HELP
Answer:
x=4sqrt3 a=4 b=3 ,y=8sqrt3 c=8 d=3
Step-by-step explanation:
because this is a 30-60-90 triangle, it is easy to find the side lengths. the longer leg is sqrt(3) times the shorter leg so x= 12/sqrt(3) or 4sqrt(3). the hypotenuse is 2 times the shorter leg so y= 8sqrt(3)
pls help me asap !!!!
Answer:
9--7
Step-by-step explanation:
a random number generator is used to model the patters of animals in the wild. this type of study is called
Answer:
This type of study is called a simulation
Step-by-step explanation:
which exponential expression is equivalent to
Answer:
B
Step-by-step explanation:
(y^(4))^(1/5)=y^(4/5)
Which statement is true about the polynomial
–10m4n3 + 8m2n6 + 3m4n3 – 2m2n6 – 6m2n6 after it has been fully simplified?
It is a monomial with a degree of 4.
It is a monomial with a degree of 7.
It is a binomial with a degree of 6.
It is a binomial with a degree of 8.
Answer:
–10m4n3 + 8m2n6 + 3m4n3 – 2m2n6 – 6m2n6 = -7m4n3
⇒It is a monomial with a degree of 7 is correct
Step-by-step explanation:
help me with this two I don't understand
Step-by-step explanation:
5.
[tex](5 + 4 \sqrt{7} ){x}^{2} + (4 - 2 \sqrt{7} ) x- 1 = 0[/tex]
Simplify both radicals.
[tex](5 + \sqrt{112) {x}^{2} } + (4 - \sqrt{28} )x - 1 = 0[/tex]
Apply Quadratic Formula
First. find the discramnint.
[tex](4 - \sqrt{28} ) {}^{2} - 4(5 + \sqrt{112} )( - 1) = 64[/tex]
Now find the divisor 2a.
[tex]2(5 + \sqrt{112} ) = 10 + 8 \sqrt{7} [/tex]
Then,take the square root of the discrimant.
[tex] \sqrt{64} = 8[/tex]
Finally, add -b.
[tex] - (4 + 2 \sqrt{7} )[/tex]
So our possible root is
[tex] - (4 + 2 \sqrt{7} ) + \frac{8}{10 + 8 \sqrt{7} } [/tex]
Which simplified gives us
[tex] \frac{ 4 + 2 \sqrt{7} }{10 + 8 \sqrt{7} } [/tex]
Rationalize the denominator.
[tex] \frac{4 + 2 \sqrt{7} }{10 + 8 \sqrt{7} } \times \frac{10 - 8 \sqrt{7} }{10 - 8 \sqrt{7} } = \frac{ - 72 - 12 \sqrt{7} }{ - 348} [/tex]
Which simplified gives us
[tex] \frac{6 + \sqrt{7} }{29} [/tex].
6. The answer is 2.
9514 1404 393
Answer:
5. x = (6 +√7)/29; a=6, b=1, c=29
6. x = 2
Step-by-step explanation:
5.The quadratic formula can be used, where a=(5+4√7), b=(4-2√7), c=-1.
[tex]x=\dfrac{-b+\sqrt{b^2-4ac}}{2a}=\dfrac{-(4-2\sqrt{7})+\sqrt{(4-2\sqrt{7})^2-4(5+4\sqrt{7}})(-1)}{2(5+4\sqrt{7})}\\\\=\dfrac{-4+2\sqrt{7}+\sqrt{16-16\sqrt{7}+28+20+16\sqrt{7}}}{10+8\sqrt{7}}=\dfrac{4+2\sqrt{7}}{2(5+4\sqrt{7})}\\\\=\dfrac{(2+\sqrt{7})(5-4\sqrt{7})}{(5+4\sqrt{7})(5-4\sqrt{7})}=\dfrac{10-3\sqrt{7}-28}{25-112}=\boxed{\dfrac{6+\sqrt{7}}{29}}[/tex]
__
6.Use the substitution z=3^x to put the equation in the form ...
z² -3z -54 = 0
(z -9)(z +6) = 0 . . . . . factor
z = 9 or -6 . . . . . . . . value of z that make the factors zero
Only the positive solution is useful, since 3^x cannot be negative.
z = 9 = 3^2 = 3^x . . . . use the value of z to find x
x = 2
The side measurement of the wall of the Green House is 9m. Find the cost of the glass required for the walls of the Green House, if the cost of 1m2 glass is AED 12.
Answer:
AED 972
Step-by-step explanation:
Area of the wall = 9² = 81 m²
each m² costs AED 12
so 81 m² will cost 12×81 = AED 972
x and y are integers and 0 < x < y.
Write down two sets of values for x and y such that 6 = /3x+2y.
Answer:
x = 1
y=1.5
Step-by-step explanation:
3*1+2*1.5=6
The values of x and y in equation 6=3x+2y is for x is 1 and for y is 1.5.
We have given that,
x and y are integers and 0 < x < y.
6 = /3x+2y.
x=1 then
What is inequality?A statement of an order relationship greater than, greater than or equal to, less than, or less than or equal to between two numbers or algebraic expressions.
6=3+2y
6-3=2y
3/2=y
y=1.5
3*1+2*1.5=6
Therefore we get the values of x and y is for x is 1 and for y is 1.5.
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What is the measure of JK?
Find the sin P rounded to the nearest hundredth
Answer:
SOH-CAH-TOA
[tex]\sin \left(x\right)=\frac{6}{\sqrt{49+36}}[/tex] = 40.60°
SOH = SIN = OPP/HYP
SIN(Θ) = 6/[tex]\sqrt{49+36 }[/tex]
Step-by-step explanation:
what is -3/5 as a decimal
Answer:
-0.6
Step-by-step explanation:
Answer:
⅗ as a decimal is -0.6
Hope it's right if not then sorry, have a great day:)If 12(x - a)(x - b) = 12x² - 7x - 12 , then ab =
Answer choices :
1
-1
7
12
-12
Answer: -1
Step-by-step explanation:
12x^2-7x-12 = (4x+3)(3x-4)
4x+3=0. X = -3/4
3x-4=0. X = 4/3
(-3/4) (4/3) = -1
GIVING BRAINLIEST TO CORRECT ANSWERS
Answer:
b is the correct answer
Step-by-step explanation:
lowkey need help with this.
9514 1404 393
Answer:
c = 14
no extraneous solutions
Step-by-step explanation:
You can subtract the right-side expression, combine fractions, and set the numerator to zero.
[tex]\dfrac{c-4}{c-2}-\left(\dfrac{c-2}{c+2}-\dfrac{1}{2-c}\right)=0\\\\\dfrac{c-4}{c-2}-\dfrac{1}{c-2}-\dfrac{c-2}{c+2}=0\\\\\dfrac{(c-5)(c+2)-(c-2)^2}{(c-2)(c+2)}=0\\\\\dfrac{(c^2-3c-10)-(c^2-4c +4)}{(c-2)(c+2)}=0\\\\\dfrac{c-14}{(c-2)(c+2)}=0\\\\\boxed{c=14}[/tex]
__
Check
(14 -4)/(14 -2) = (14 -2)/(14 +2) -1/(2 -14) . . . . substitute for c
10/12 = 12/16 -1/-12
5/6 = 3/4 +1/12 . . . . true
There is one solution (c=14) and it is a solution to the original equation. There are no extraneous solutions.
M angle a=40° then m angle b=?
Answer:
not enough info
Step-by-step explanation:
5/√2+9/√8-2√50+√32 rationalise the denominator and simplify
The simplification of the expression is [tex]\frac{15\sqrt{2} }{4}[/tex]
How to rationalize the denominatorFirst, find the factors of the number that ahs square root
Given,
= [tex]\frac{5}{\sqrt{2} } + \frac{9}{\sqrt{6} } - \frac{2}{\sqrt{50} } + \sqrt{32}[/tex]
Multiply the numerators by the surd of the denominators
= [tex]\frac{5 *\sqrt{2} }{\sqrt{2}*\sqrt{2 } } + \frac{9 *\sqrt{8} }{\sqrt{8}* \sqrt{8} } - \frac{2 *\sqrt{50} }{\sqrt{50 * \sqrt{50} } } + \sqrt{32}[/tex]
Multiply through and find their square root
= [tex]\frac{5\sqrt{2} }{2} + \frac{18\sqrt{2} }{8 } - \frac{10\sqrt{2} }{50} + 16\sqrt{2}[/tex]
To simply, we have
= [tex]\frac{5\sqrt{2} }{2}+ \frac{9\sqrt{2} }{4} + \frac{1\sqrt{2} }{5} + 16\sqrt{2}[/tex]
Find the LCM
= [tex]\frac{10\sqrt{2} + 45\sqrt{2}+ 4\sqrt{2} + 16\sqrt{2} }{20}[/tex]
Add through
= [tex]\frac{75\sqrt{2} }{20}[/tex]
= [tex]\frac{15\sqrt{2} }{4}[/tex]
Thus, the simplification of the expression is [tex]\frac{15\sqrt{2} }{4}[/tex]
Learn more about surds here:
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I'm Timed
Which situation could this expression represent?
6 + 15 ÷ 3
Michael has 6 stamps in his collection. He adds 15 more stamps to the collection. He divides the collection into 3 piles. How many stamps are in each pile?
Walter has 6 stamps in his collection. He divides the stamps evenly into 3 piles and adds 15 new stamps to one of the piles. How many stamps are in this pile?
Andy has 15 stamps in his collection. He divides the stamps evenly into 3 piles and adds 6 stamps to one of the piles. How many stamps are in this pile?
Brycen has 15 stamps in his collection. He adds 6 more stamps to the collection. He divides the collection into 3 piles. How many stamps are in each pile?
Answer:
It's Micheal because he started with 6 and added 15 and he divided them into 3 piles
Question 9 (5 points)
3
6
9
--
What's the approximate measure of one interior angle of the regular polygon shown?
12
A) 1,620°
>
15
B) 220°
C) 2.7°
18
D) 147.3°
Answer:
147.3
Step-by-step explanation:
this is an hendecagon there is 11 sides the total interior measure is 1,620 if you divide that by each side which would be 11 you get 147.272727 which would ultimately round up to be 147.3
Help anyone can help me do this question,I will mark brainlest. The question is find the area of the shaded region.
Answer:
13. 10
14. 51
Step-by-step explanation:
Answer:
13. 10
14. 51
Step-by-step explanation:
A sociologist polled a random collection of people and asked them their
age and annual income. The two-way frequency table below shows the
results. Which of the following is true about the people polled?
A
People age 44 and under were more likely to earn at
least $50,000 than people age 45 and up.
B
People age 44 and under were less likely to earn at
least $50,000 than people age 45 and up.
C
People age 44 and under were equally likely to earn
at least $50,000 as people age 45 and up.
D
There is not enough information to determine if
people age 44 and under were more likely to earn at
least $50,000 than people age 45 and up.
Answer:
B
Step-by-step explanation:
The population, P, of six towns with time t in years are given by the following exponential equations:
(i) P = 1000 (1.08) Superscript t (ii) P = 600 (1.12) Superscript t
(iii) P = 2500 (0.9) Superscript t (iv) P = 1200 (1.185) Superscript t
(v) P = 800 (0.78) Superscript t (vi) 2000 (0.99) Superscript t
Which town decreasing the fastest?
a.
ii
c.
iii
b.
v
d.
vi
Please select the best answer from the choices provided
A
B
C
D
Given:
The population, P, of six towns with time t in years are given by the following exponential equations:
(i) [tex]P=1000(1.08)^t[/tex]
(ii) [tex]P = 600 (1.12)^2[/tex]
(iii) [tex]P =2500 (0.9)^t[/tex]
(iv) [tex]P=1200 (1.185)^t[/tex]
(v) [tex]P=800 (0.78)^t[/tex]
(vi) [tex]P=2000 (0.99)^t[/tex]
To find:
The town whose population is decreasing the fastest.
Solution:
The general form of an exponential function is:
[tex]P(t)=ab^t[/tex]
Where, a is the initial value, b is the growth or decay factor.
If b>1, then the function is increasing and if 0<b<1, then the function is decreasing.
The values of b for six towns are 1.08, 1.12, 0.9, 1.185, 0.78, 0.99 respectively. The minimum value of b is 0.78, so the population of (v) town [tex]P=800 (0.78)^t[/tex] is decreasing the fastest.
Therefore, the correct option is b.
A school bus has seating for 75 students. There are 13 buses at a school. What is the maximum number of students
the buses can seat
225 students
750 students
975 students
985 students
Help
Answer:
75 students and 13 buses are just 75 x 13
975 students
Step-by-step explanation:
75 x 13 = 975
A graph is shown.
How do you determine if this is a function or not? Is this a function. Help please
Answer:
Not a function
Step-by-step explanation:
we see on this graph,
(1,2) and (1,7)
we have two of the same x points, when put on a graph, that would be having 2 of the same inputs.
which always means it's not a function.
Simplify the following expression:
-3(x+6)+8x
3x-25
5x-22
-11+3x
5x-18
Answer:
5x -18
I hope this helped! have a nice day! :)Answer:
5x+18
Step-by-step explanation:
Given: x-5> -10.
I clicked it on accident so ignore the blue thing ! Help needed
Answer:
the first one
Step-by-step explanation:
[tex]x - 5 > - 10 \\ x > - 10 + 5 \\ x > - 5[/tex]
Which points are possible approximations for this system? Select two options.
Step-by-step explanation:
second: (2.2,-1.4)
third: (2.2,-1.35)
Step-by-step explanation:
hope it helps✨
G is a transformation of f. The graph below shows f as a solid blue line and g as a dotted red line. What is the formula of g in terms of f?
Answer: f(x-2) which is choice A.
The blue f(x) curve is shifted 2 units to the right to get the red g(x) dashed curve.
============================================================
Explanation:
For now, ignore the red dashed curve g(x). Imagine that the blue curve f(x) is fixed in place. If we shifted the xy axis to the left 2 units, then this gives the illusion the blue curve is moving even though the curve is fixed in place.
The operation "shift xy axis 2 units to the left" means each x input is 2 units smaller. So each x input is now x-2.
Therefore, going from f(x) to f(x-2) will shift the blue curve 2 units to the right to land perfectly on the red dashed g(x) curve.
