Since the limit of f(x) is non-zero, the limit distributes over the quotient and
[tex]\displaystyle \lim_{x\to c} \frac{g(x)}{f(x)} = \frac{\displaystyle \lim_{x\to c}g(x)}{\displaystyle \lim_{x\to c}f(x)} = \frac{\dfrac15}{-4} = \boxed{-\frac1{20}}[/tex]
The count in a bacteria culture was 400 after 10 minutes and 1300 after 40 minutes. Asumming the count grows exponentially
-What was the initial size culture?
-Find the doubling period
-Find the population after 120 minutes
-When will the population reach 10000?
If the triangle on the grid below is translated by using the rule (x, y) right-arrow (x + 5, y minus 2), what will be the coordinates of B prime?
On a coordinate plane, triangle A B C has points (negative 1, 0), (negative 5, 0), (negative 1, 2).
(–2, 0)
(0, –2)
(5, –7)
Using translation concepts, it is found that the coordinates of the image of point B is given by: (0, –2).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the rule is given by:
(x,y) -> (x + 5, y - 2).
Hence, the image of point B, given by B', is:
(-5,0) -> (-5 + 5, 0 - 2) -> (0,-2).
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Find the Area (Need help ASAP)
Answer:
32
It wont always be easy, but always try to do what ' s right!
In a world of worriers, be the warrior!
When nothing goes right, go left.
Prove: ∠1 and ∠14 are supplementary angles.
Answer:
can you please send the images of figure of these angle
What is the formula for the nth term of the sequence 2,4,8,16,32
Answer:
Below in bold.
Step-by-step explanation:
4/2 = 2
8/4 = 2
Each term is obtained by multiplying the previous one by 2.
This is a geometric sequence with common ratio r = 2
the nth term
= a1r^(n-1) where a1 = the first term
= 2(2)^(n-1).
[tex] a_{n} = 2_{n}[/tex]
Step-by-step explanation:
[tex]a_{1} = 2[/tex]
[tex]d = a_{2} - a_{1}[/tex]
[tex] = 4 - 2 = > 2[/tex]
Getting the nth term
[tex]a_{n} = a_{1} + (n - 1)d[/tex]
[tex] a_{n} = 2 + (n - 1)2[/tex]
[tex] a_{n} = 2 + (2n - 2)[/tex]
[tex]a_{n} = 2 + 2n - 2[/tex]
[tex] a_{n} = 2n[/tex]
What values of c and d make the equation true? Assume x>0 and 20.
3
50x6y³ 5y √√2y
=
O c = 1, d = 3
O c = 1, d = 9
O c = 2, d = 8
O c = 2, d = 9
Answer:
c=1 and c=3
Step-by-step explanation:
If x>0 and y>0, then
\sqrt{\dfrac{50x^6y^3}{9x^8}}=\sqrt{\dfrac{25\cdot 2y^2\cdot y}{9x^2}}=\dfrac{5y\sqrt{2y}}{3x}.
9x
8
50x
6
y
3
=
9x
2
25⋅2y
2
⋅y
=
3x
5y
2y
.
If
\dfrac{5y\sqrt{2y}}{3x}
3x
5y
2y
is equal to
\dfrac{5y^c\sqrt{2y}}{dx},
dx
5y
c
2y
,
then
\begin{gathered}y=y^c\Rightarrow c=1,\\ \\3x=dx\Rightarrow d=3.\end{gathered}
y=y
c
⇒c=1,
3x=dx⇒d=3.
1. The area of a rectangular carpet is X² + X - 2. HINT: Area = length X breadth
a). if X is a whole number, use factorization to find the length and the breadth of the carpet in terms of X.
b). if X = 2 m, find the actual dimensions of the carpet.
c). it costs R50 per square metre to make such this carpet. how much will it cost to manufacture 5 carpets?
Answer:
look above
Step-by-step explanation:
hopeit hepls
rearrange the equation 12n + 3px = 7px
From factoring, the given equation can be rearranged as [tex]x=\frac{3n}{p}[/tex].
Factoring
In math, factoring or factorization is used to write an algebraic expression in factors. There are some rules for factorization. One of them is a factor out a common term for example: x²-x= x(x-1), where x is a common term.
For solving this question, the given equation should be rewritten using the variables n and p in different sides. After that, you should factor out a common term.
[tex]12n + 3px = 7px\\ \\ 12n=7px-3px\\ \\ 12n=4px\\ \\ x=\frac{12n}{4p} =\frac{4*3n}{4p}=\frac{3n}{p}\\ \\ x=\frac{3n}{p}[/tex]
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Given the graph, which coordinate point is NOT a solution?
Answer: (1, 2) (The third option)
Step-by-step explanation: A solution has to be on the line. (1, 2) is the only point that isn't on the line.
Help pls i will give 10 points
Answer:
1/4 for blue and 3/8 for green
Step-by-step explanation:
2 blue sections out of 8
2/8 simplified is 1/4
3 green sections out of 8
3/8 is the simplest form
Part 1 - Application
If the length of an arc of a circle of radius 7 is approximately 10.99 cm. What is the measure of the central
angle associated with the arc? Use 3.14 for It. Give your answer in degrees and radians (approximate to two
decimals and exact).
The measure of the central angle is 89.95 degree or 1.57 radians if the radius of the circle is 7 cm.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the centre of a circle)
We have a length of an arc of a circle of radius 7 is approximately 10.99 cm.
The radius r = 7 cm
The arc length l = 10.99 cm
We know,
l = rθ
θ is the central angle.
θ = l/r = 10.99/7 = 1.57 radians
To convert 1.57 radians into the degree multiply it by 180/π
θ = 89.95 degree
Thus, the measure of the central angle is 89.95 degree or 1.57 radians if the radius of the circle is 7 cm.
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A function and its inverse are shown on the same graph. Complete the sentences to compare the functions.
The y-intercept of f(x) has the same value as the ___
f(x)
The function(x) has a range including all values
greater than or equal to 0; therefore the, ____ does also.
The y-intercept of f(x) has the same value as the x-intercept. The function f⁻¹(x) has a range including all values greater than or equal to 0; function f(x) does also.
What is a function?Functions are found all across mathematics and are required for the creation of complex relationships.
A function and its inverse are shown on the same graph.
Complete the sentences to compare the functions.
The y-intercept of f(x) has the same value as the x-intercept.
The function f⁻¹(x) has a range including all values greater than or equal to 0; function f(x) does also.
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Use technology, what is the solution to this system? 4x+8y=30
Answer:
y=-1/2x+15/4
Step-by-step explanation:
transfer the equation into slope intercept form. subtract 4x from each side getting 8y=-4x+30 then divide by 8.
What is the distance between the following points?
Answer:
B
10
Step-by-step explanation:
go up 7 then over 3, add them together and you got 10
Please help me with this question
What is the value of x in the diagram
Answer:
51°
Step-by-step explanation:
the given angle of 102° is the arc angle between the 2 segment end points on the circle arc.
and this arc angle is always a seen from the center of the circle.
by moving the reference point back (to the other side of the circle) to the circle arc that angle is cut in half.
you could move that point to anywhere on the arc of the circle outside of the 2 endpoints, and the angle stays always the same.
FYI - now, if you move that point into the top half-circle between the 2 end points, the perspective flips around, and that angle becomes half of the 360-102 = 258° arc angle.
2x(2x-3)-3x(x-2) need help on this
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's evaluate ~
[tex]\qquad \sf \dashrightarrow \:2x(2x - 3) - 3x(x - 2)[/tex]
[tex]\qquad \sf \dashrightarrow \:(2x \sdot2x) - (2x \sdot3) - (3x \sdot x) - (3x \sdot - 2)[/tex]
[tex]\qquad \sf \dashrightarrow \: 4 {x}^{2} - 6x- 3 {x}^{2} - ( - 6x)[/tex]
[tex]\qquad \sf \dashrightarrow \:4 {x}^{2} - 3 {x}^{2} - 6x + 6x[/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} [/tex]
I hope the Step were clear to you ~
Answer:
x²
Step-by-step explanation:
Given: 2x(2x - 3) - 3x(x - 2)
Distributive Property: a(b + c) = ab + ac
1. Distribute
⇒ 2x(2x) + 2x(-3) + -3x(x) + -3x(-2)
⇒ 4x² - 6x - 3x² + 6x
2. Combine like terms
⇒ 4x² - 3x² - 6x + 6x
⇒ x²
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Which equation is represented by the graph below ?
The equation that represent the graph is y = (1/2)eˣ , Option B is the correct answer.
What is an Exponential Function ?An exponential function is what is denoted as y = eˣ
The graph has to be studied and the equation has to be determined.
To determine we will consider x = 0 for all the equation ,. which will give the y intercept , which is below 1 so Option C and D are stroked out.
Now we plot the graph for equation A and B
It can be easily understood from the graph that at x =0 , y = 0.5
Therefore , the equation that represent the graph is
y = (1/2)eˣ
Option B is the correct answer.
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Identify the type of function represented by f(x) = 2(1/2)^x
A. Exponential growth
B. Linear
C. Exponential decay
OD. Quadratic
Answer:
C) Exponential Decay
Step-by-step explanation:
Because the base inside of the parentheses is less than 1, the function will only get exponentially smaller over time.
What is the value of 5x+3 when x = 4?
09
O 12
23
O 60
Answer:
you do 5 multiplied by 4 and plus 3 I hope this helps
which system of equations shown below could be used to solve the following problem?
the sum of m and n is 32, and the value of m is three times the value of n. What is the value of n?
An equation is formed of two equal expressions. The correct option is C.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The given statement in the form of equations can be written as,
1. The sum of m and n is 32 ⇒ m + n = 32
2. The value of m is three times the value of n ⇒ m=3n
Hence, the correct option is C.
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You have just invested 1,500 into a stock compounded yearly at a rate of 9%. How much money will be in your account in 60 days? (Please explain)
Answer:
1522.584
Step-by-step explanation:
1500(1+.09/12)^2=1522.584
If f(x)=8-10x and g(x) =5x +4, what is the value of (fog)(-2)?
Answer:
68
Step-by-step explanation:
Any function is evaluated by putting the argument value where the variable is, then doing the arithmetic. When the argument is another function value, that function value is evaluated first.
__
f∘gThe "o" in (fog) is a stand-in for the "ring operator" (∘) which is the operator used to signify a composition. A composition is evaluated right-to-left. That means (f∘g)(x) ≡ f(g(x)). The value of g(x) is found first, and is operated on by the function f.
Writing the composition in the form f(g(x)) lets you identify the layers of parentheses. As with any expression evaluation, the Order of Operations applies. It tells you to evaluate the expression in the innermost parentheses and work your way out.
g(-2)To evaluate (f∘g)(-2) = f(g(-2)), we must first evaluate g(-2). That is ...
g(x) = 5x +4
g(-2) = 5(-2) +4 = -10 +4 = -6 . . . . . put -2 where x is, do the math
f(g(-2))Now that we know g(-2) = -6, we know this expression is ...
f(-6) = 8 -10(-6) = 8 +60 = 68 . . . . . substitute for x in 8-10x
Then the value we're looking for is ...
(f∘g)(-2) = 68
In the figure below, which term best describes point X?
B
OA. Centroid
OB. Incenter
O C. Circumcenter
OD. Orthocenter
Answer:
Centroid
Step-by-step explanation:
It is a centroid because x is the center of the triangle
may I get brainliest?
Hope this helps :)
The term best describes point X is option A. Centroid.
What is the centroid of a triangle and its coordinates?The point of intersection of a triangle's medians is its centroid (the lines joining each vertex with the midpoint of the opposite side).
here, we have,
If the surface is plane triangle approximately and mass is uniformly distributed, then its center of mass will lie on the centroid of that triangle.
we have,
If the triangle has its vertices as (x1, y1) (x2,y2) (x3,y3)
then the coordinates of the centroid of that triangle is given by:
(x, y ) = (x1+x2+x3/3 , y1+y2+y3/3 )
Hence, The term best describes point X is option A. Centroid.
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Maria orders t-shirts for her volleyball camp. Adult-sized T-Shirts cost $6.25 each and youth-sized T-Shirts cost $4.50. Maria has $550 to purchase both adult-sized and youth-sized T-Shirts. If she purchases 45 youth-sized T-Shirts, determine algebraically the maximum number of adult-sized T-Shirts she can purchase.
Answer:
55
Step-by-step explanation:
45 * 4.50 = 202.5
550 - 202.5 = 347.5
347.5/6.25 = 55.6 (55 full t shirts)
I also need help in this..
Answer:
(12x12)+(12x8)+(12x12)=
Step-by-step explanation:
add that up on ur calculator for the answer
what land is under muslim rule
Answer:
Under Islamic law, land ownership is classified into two main categories, frrstly, according to the mode of acquisition or how land came into the possession and ownership of the individual and secondly according to the type of taxation.
Answer:
Are you Muslim I think Pakistan or Saudi
the sum of the exterior angles of a pentagon equals what
Answer:
360 degrees
Step-by-step explanation:
The sum of the INTERior angles of a pentagon equal
(n-2)(180) = 540
each angle is then 540/5 = 108
each is a supplementary angle to the exterior angle
so EACH exterior angle is 180 - 108 = 72
there are 5 of these 5 * 72 = 360 degrees
Find the interest and the amount repaid.
Principal 500.00
Rate 12%
Time 18 months
what is the amount
Answer:
3844.98
Step-by-step explanation:
Use this formula: P(1+b)^x
500(1.12)^18 (put in calculator).
Hope this helps!
If not I am sorry.
What are the coordinates of the point where the line y = -x +5 intersects the x-axis?
O (0, -3)
O (0,3)
O (-3,0)
0 (3,0)
The answer is (3,0)
Sure hope this helps you