Answer:
18x-3
Step-by-step explanation:
f(x)= 3x + 10x
g(x)=5x - 3
f(x)+g(x) = 3x + 10x + 5x - 3
Combine like terms
= 18x -3
Answer:
3^x+15x-3
Step-by-step explanation:
this is the right answer i just did it
\
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.
Pls help Which of the following exponential equations is equivalent to the logarithmic equation below ? In x = 7
Answer:
Step-by-step explanation:
Let's write that out completely:
[tex]ln_e(x)=7[/tex] The rule for going from log to exponential is what I call the "circular rule" in my classes and the kids never forget it. Take the base of the log, raise it to the power of the number on the other side of the equals sign, and then circle back to set it equal to the argument.
e is the base. Raise e to the 7th and circle back to set the whole thing equal to x (x is called the argument):
[tex]e^7=x[/tex] choice C.
Find the slope of the line passing through (6.-1) and (7,3). Let (x1, y1) = (6.-1) and (x2.72) =
(7,3). List the coordinates, fill in the slope formula, and then simplify.
1 =
X2=
J1 =
12=
slope =
Answer:
X1=6
X2=7
y1= -1
y2= 3
now,
slope = y2-y1/x2-x1
= 3+1/7-6
=4/1
=1
hence slope= 1
hlpppppppppppppppppppppppppppppppp
Answer:
c
Step-by-step explanation:
-7.5 is less than 6.5
Determine the period
Answer:
16 units
Step-by-step explanation:
period = length of an interval that contains exactly one copy of the repeating pattern, so from one peak to another peak.
in this graph its the peaks are 1 and 17, hence the period is 16
Please help solve for x
Answer:
8.49
Step-by-step explanation:
there is a little formula related to the famous formula of Pythagoras.
it says that the height of a triangle is the square root of the product of both segments of the baseline (the segments the height splits the baseline into).
so, x is actuality the height of the triangle.
x = sqrt(3×24) = sqrt(72) = 8.49
what is the answer to this
3x-y=7
2x-2y=2
Answer:
x = 3
y = 2
Step-by-step explanation:
3x - y = 7 ------------(i)
2x - 2y = 2 ---------(ii)
Multiply equation (i) by (-2)
(i)*(-2) - 6x + 2y = -14
(ii) 2x - 2y =2 {Add both equation. now y will be eliminated}
-4x = -12 {Divide both sides by -4}
x = -12/-4
x = 3
Plug in x = 3 in equation (i)
2*3 - 2y = 2
6 - 2y = 2
Subtract 6 from both sides
-2y = 2 - 6
-2y = -4
Divide both sides by 2
y = -4/-2
y = 2
Answer:
x = 3, y = 2
Step-by-step explanation:
Given the 2 equations
3x - y = 7 → (1)
2x - 2y = 2 → (2)
Multiplying (1) by - 2 and adding to (2) will eliminate the y- term
- 6x + 2y = - 14 → (3)
Add (2) and (3) term by term to eliminate y
- 4x + 0 = - 12
- 4x = - 12 ( divide both sides by - 4 )
x = 3
Substitute x = 3 into either of the 2 equations and solve for y
Substituting into (1)
3(3) - y = 7
9 - y = 7 ( subtract 9 from both sides )
- y = - 2 ( multiply both sides by - 1 )
y = 2
solution is (3, 2 )
Deion is saving up to buy a new phone. He already has $95 and can save an additional $7 per week using money from his after school job. How much total money would Deion have after 6 weeks of saving? Also, write an expression that represents the amount of money Deion would have saved in w weeks.
The expression that represents the amount of money Deion would have saved in w weeks is 95 + 7w and the total savings after 6 weeks will be $137.
What is an expression?A statement expressing the equality of two mathematical expressions is known as an equation.
A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
An expression is a mathematical proof of the equality of two mathematical expressions.
As per the given,
Initial fixed money = $95
Per week saving $7/week
Total money = fixed money + money in w weeks.
⇒ 95 + 7w
For 6 weeks, w = 6
⇒ 95 + 7× 6 = $137.
Hence "The expression that represents the amount of money Deion would have saved in w weeks is 95 + 7w and the total savings after 6 weeks will be $137".
To learn more about expression,
https://brainly.com/question/14083225
#SPJ3
Which polynomial is a binomial?
Condition for increasing decreasing and concavity of function
Answer:
If the concavity of f changes at a point (c,f(c)), then f′ is changing from increasing to decreasing (or, decreasing to increasing) at x=c. That means that the sign of f″ is changing from positive to negative (or, negative to positive) at x=c. This leads to the following theorem
Step-by-step explanation:
The previous section showed how the first derivative of a function, f′ , can relay important information about f . We now apply the same technique to f′ itself, and learn what this tells us about f . The key to studying f′ is to consider its derivative, namely f′′ , which is the second derivative of f . When f′′>0 , f′ is increasing. When f′′<0 , f′ is decreasing. f′ has relative maxima and minima where f′′=0 or is undefined. This section explores how knowing information about f′′
Let f be differentiable on an interval I . The graph of f is concave up on I if f′ is increasing. The graph of f is concave down on I if f′ is decreasing. If f′ is constant then the graph of f is said to have no concavity.
Note: We often state that " f is concave up" instead of "the graph of f is concave up" for simplicity.
The graph of a function f is concave up when f′ is increasing. That means as one looks at a concave up graph from left to right, the slopes of the tangent lines will be increasing. Consider Figure 3.4.1 , where a concave up graph is shown along with some tangent lines. Notice how the tangent line on the left is steep, downward, corresponding to a small value of f′ . On the right, the tangent line is steep, upward, corresponding to a large value of f′ .
pls help me asap !!!!
Answer:
9--7
Step-by-step explanation:
which exponential expression is equivalent to
Answer:
B
Step-by-step explanation:
(y^(4))^(1/5)=y^(4/5)
the sum of numerator and denominator of the fraction is 12 and the denominator is 2 more than numerator.find the fraction
Let numerator be x
Denominator=x+2ATQ
[tex]\\ \sf\longmapsto x+x+2=12[/tex]
[tex]\\ \sf\longmapsto 2x+2=12[/tex]
[tex]\\ \sf\longmapsto 2x=12-2[/tex]
[tex]\\ \sf\longmapsto 2x=10[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{10}{2}[/tex]
[tex]\\ \sf\longmapsto x=5[/tex]
Now the fraction is
[tex]\\ \sf\longmapsto \dfrac{x}{x+2}[/tex]
[tex]\\ \sf\longmapsto \dfrac{5}{5+2}[/tex]
[tex]\\ \sf\longmapsto \dfrac{5}{7}[/tex]
-- Their sum is 12.
-- If they were equal, each would be 6.
-- To make them differ by 2 without changing their sum, move 1 from the numerator (make it 5), to the denominator (make it 7).
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.
To learn more about the values visit:
https://brainly.com/question/25770607
#SPJ2
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)
What is the measure of JK?
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:
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
Will Mark Brainnlest Please help me
Answer:
l = 2, m = - 1, n = - 6
Step-by-step explanation:
A scalar matrix has its diagonal elements equal and all other elements zero, so
2l - 4 = 0 ( add 4 to both sides )
2l = 4 ( divide both sides by 2 )
l = 2
---------------------------------------
3l + n = 0
3(2) + n = 0
6 + n = 0 ( subtract 6 from both sides )
n = - 6
--------------------------------------
3m - n = 3
3m - (- 6) = 3
3m + 6 = 3 ( subtract 6 from both sides )
3m = - 3 ( divide both sides by m )
m = - 1
a call centre aims to deal with calls in less than 5 minutes
calls come in randomly
Answer:
1/8
Step-by-step explanation:
Let "A" = the next call of a customer's complaint
Let "B" = the next call completed under 5 minutes
P(A) = 1/4
P(B) = 1/2
So ----> P(AB) = P(A) times P(B) P(AB)
= 1/4 times 1/2 = 1/8
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.
what is the answer to x if 2x = 7
Geometry I need help someone help me
Answer:
fohohcoufohohcouvhop
Step-by-step explanation:
typing mistake sorry
[tex]\\ \sf\longmapsto x+73=90[/tex]
[tex]\\ \sf\longmapsto x=90-73[/tex]
[tex]\\ \sf\longmapsto x=17[/tex]
Why?
Sum of two complementary angles is 90°
Solve the equation by completing the square.
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:
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
Given the a center (-1, -2) and a radius r = 2. Identify the circle.
Answer:
1st option
1st graph has the centre on (-1,-2) and the distance of the circumference from the centre is 2
Answered by GAUTHMATH
Determine the domain of the function.
a All real number except 11
b x > 11
c All real numbers
d x < 11
Answer:
i think its all real numbers
Step-by-step explanation:
i think!! im not so sure
Please help me solve this question!
Classify the polygon as regular or irregular, and concave or convex.
Answer:
This would be a regular polygon.
Step-by-step explanation:
A regular polygon has congruent sides and interior angles.
An irregular polygon does not have congruent sides and all interior angles.
A convex polygon does not have a interior angle greater than 180°.
Lastly, a concave polygon has only one interior angle greater than 180°.
Using the process of elimination, it would not be a convex or concave polygon. Now we have either a regular or irregular polygon. This polygon can not be a irregular polygon because all the sides are congruent. This means that this polygon is a regular polygon!
The given polygon is a regular convex polygon.
What is a polygon ?In geometry, a polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain (or polygonal circuit). The bounded plane region, the bounding circuit, or the two together, may be called a polygon.
The segments of a polygonal circuit are called its edges or sides. The points where two edges meet are the polygon's vertices or corners. The interior of a solid polygon is sometimes called its body.
Given,
Polygon has 8 edges and 8 vertices.
1. Regular or Irregular:
A regular polygon has congruent sides and interior angles.
In the figure all sides are of equal length and the angle are same so, It is a regular polygon.
2. Convex or concave:
Convex polygon has all interior angles less than 180° while in concave polygon at least one interior angle should be greater than 180°.
In the given polygon all angles are less than 180°, so it is a convex polygon.
Hence, by the above explanation, the given polygon is regular convex polygon.
Learn more about polygons here:
https://brainly.com/question/24464711
#SPJ2