Considering it's horizontal asymptote, the statement describes a key feature of function g(x) = 2f(x) is given by:
Horizontal asymptote at y = 0.
What are the horizontal asymptotes of a function?They are the limits of the function as x goes to negative and positive infinity, as long as these values are not infinity.
Researching this problem on the internet, the functions are given as follows:
[tex]f(x) = 2^x[/tex].[tex]g(x) = 2f(x) = 2(2)^x[/tex]The limits are given as follows:
[tex]\lim_{x \rightarrow -\infty} g(x) = \lim_{x \rightarrow -\infty} 2(2)^x = \frac{2}{2^{\infty}} = 0[/tex]
[tex]\lim_{x \rightarrow \infty} g(x) = \lim_{x \rightarrow \infty} 2(2)^x = 2(2)^{\infty} = \infty[/tex]
Hence, the correct statement is:
Horizontal asymptote at y = 0.
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Is -7=7 an infinite solution or no solutions for a system of equations?
Answer:
no solutions
Step-by-step explanation:
-7 does not equal 7, so there are no solutions.
Infinite solutions would be if it was two equal values, for example, 7 = 7.
suppose a triangle has sides a, b, and c and the angle opposite the side of length a is acute what must be true?
A. b2+c2>a2
B. a2+b2
C. b2+c2
D. a2+b2=c2
The true statement about the triangle is (a) b^2 + c^2 > a^2
How to determine the true inequality?The sides are given as:
a, b and c
The angle opposite of side length a is an acute angle
The above means that:
The side a is the longest side of the triangle.
The Pythagoras theorem states that:
a^2 = b^2 + c^2
Since the triangle is not a right triangle, and the angle opposite a is acute.
Then it means that the square of a is less than the sum of squares of other sides.
This gives
a^2 < b^2 + c^2
Rewrite as:
b^2 + c^2 > a^2
Hence, the true statement about the triangle is (a) b^2 + c^2 > a^2
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What is the measure of the unknown angle?
image of a two hundred ninety seven degree angle and an unknown angle
60°
63°
64°
70°
Answer:
63
Step-by-step explanation:
A circle is 360 degrees
So, subtracting 297 from 360, we'd get 63 degrees
You are going on vacation with your family to the beach. You already spent $160 on
groceries for the week, and you know that each time you eat out you will spend another
$40. Does The relationship between the number of the Times eating out in the total budget represent a linear function?
Answer:$440, 9
Step-by-step explanation:
The relationship between the number of the times eating out in the total budget represent a linear function.
What is a linear function?"A linear functions are those whose graph is a straight line."
Given, I already spent $160 on groceries for the week.
Each time I eat out you will spend another $40.
Let, I eat 'x' times during vacation.
Therefore, the required function will be:
f(x) = 160 + 40x
Hence, the function is a linear function.
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What is the volume of the cone shown below?
A. 1344 cu. units
B. 504 cu. units
C. 4032 cu. units
D. 2016 cu. units
Work Shown:
r = 8 = radius
h = 63 = height
V = volume of the cone
[tex]V = \frac{1}{3}\pi*r^2*h\\\\V = \frac{1}{3}\pi*8^2*63\\\\V = \left(\frac{1}{3}*8^2*63\right)\pi\\\\V = \left(\frac{1}{3}*63*8^2\right)\pi\\\\V = \left(21*64\right)\pi\\\\V = 1344\pi\\\\[/tex]
Side note: You could write the symbol π as "pi" without quotes.
1. In the following diagram, PQRS is a square of side 8 cm. PQ, QR, RS and SP are semi-circular arcs with centres at the midpoint of the sides of the square. Find the area of theshaded region.
Answer:
Step-by-step explanation:
Why is it important to keep the two sides of an equation balanced when solving? what other properties do we use to rewrite expressions and equations?.
"Law of conservation of Mass and Energy", is the reason for which it is important to keep the two sides of an equation balanced when solving.
The other properties that we should consider while rewriting the expressions of an equation is that we should not multiply or divide the expressions by zero on both the sides.
According to the law of conservation of mass, mass is neither generated nor destroyed during a chemical process. For instance, when coal is burnt, the carbon atom in it transforms into carbon dioxide. The carbon atom transforms from a solid to a gas, yet its mass remains constant. Similar to this, according to the law of conservation of energy, energy cannot be generated or destroyed. For instance, kinetic energy is converted to potential energy when a toy vehicle is rolled down a ramp and collides with a wall.
While rewriting expressions of an equation, we should not multiply or divide them by zero, as multiplying or dividing by zero makes two non-equal expressions equal (0 and ∞ respectively.
This is the reason why is it important to keep the two sides of an equation balanced, and that the expressions should not be multiplied or divided by zero.
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Write the next 3 numbers in each sequence.
Answer:
The next 3 numbers will be 1 3/4, 2, and 2 1/4
Step-by-step explanation:
The numbers in the sequence are increase by 1/4. So to find the next number in the sequence and 1/4 to the previous number. Don't foget to simplify your answers. Ex.) Rather than saying 2 2/4 you would say 2 1/2.
Please give me more points so i can get help
Answer:
15°
Step-by-step explanation:
angle FGH = angle HGI ( since GH bisects angle FGI)
that means
(2x + 1) = (3x - 9)
= -x = -8
x = 8
angle HGI = (3x - 9)
= 3(8) - 9
24 - 9
= 15°
Answer:
21
Step-by-step explanation:
To find the measure of <HGI we first need to find the value of x
GH bisects angle <FI which means it divided the angle into two equal parts:
<FGH = <HGI
2x + 1 = 3x - 9 transfer like terms to the same side of the equation
1 + 9 = 3x - 2x
10 = x now replace x with 10
3*10 - 9 = 21
What is the slope of the line that contains the points (-2, 7) and (2, 3)?
Answer:
The slope of the line is -1.
Step-by-step explanation:
SLOPE OF A LINE FORMULA
SLOPE = Y2 - Y1/ x2 - x1
m = Y2 - Y1/ x2 - x1
m = 3 - 7 / 2- (-2)
m = -4/4
m = -1
The slope of the line is -1.
Calculate 50% of 684 m.
Give your answer in metres (m).
Answer:
342 mStep-by-step explanation:
Calculate 50% of 684 m.
Give your answer in metres (m).
50% = 1/2
so
684 : 2 = 342 m
Step-by-step explanation:
50% of 684
50/100 × 684
342m ans
whats the answer to this? I don't know how to do it but i need to factor it completely with whatever method gies with it.
Answer:
3x²y²(1 - 4xy²z)
Step-by-step explanation:
________________________________________
Factor 3 out of 12
Factor x² out of x³
Factor y² out of y⁴
you will get the GCF of 3x²y² and left with (1 - 4xy²z)
3x²y²(1 - 4xy²z)
________________________________________
Hoped this helped
Please help with this question thanks!!
Answer:
(-1,4)
Step-by-step explanation:
Step 1) Change both equations to slope intercept form
3x+y=1 ---> y=-3x+1
5x+y=-1 ---> y=-5x-1
Step 2) Plot lines accordingly on graph
Lines intersect at (-1,4)
On the unit circle centered at the origin [tex]\left(x^{2}+y^{2}=1 \right)[/tex], we pick three points at random. We cut the circle into three arcs at those points. What is the expected length of the arc containing the point (1,0)?
The expected length of the arc containing the point (1,0) is; π
How to solve Unit Circle Problems?First of all, it is pertinent to note that the lengths of the four arcs in which the circle is divided by the three points and (1, 0) have identical distributions.
The problem is same as dividing a circle of length 2π at four points chosen at random, and labelling one of them (1, 0). Now, let us make L₁, L₂, L₃, L₄ to be the lengths of the four arcs determined by those four points.
Thus, we have;
L₁ + L₂ + L₃ + L₄ = 2π
Whereas, the expected value of several random variables is additive as;
E[ L₁ + L₂ + L₃ + L₄] = [EL₁] + [EL₂] + [EL₃] + [EL₄]
By symmetry the lengths have the same probability distribution and as such; [EL₁] = [EL₂] = [EL₃] = [EL₄] and the sum must be 2π. Thus, we can say that each expected value is 2π/4 = π/4.
Finally, the expected value of the arc containing the point (1, 0) is the sum of the expected values of the two arcs that are adjacent to (1, 0), i.e.,
π/2 + π/2 = π
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Polygon C and polygon D are similar. The perimeter of polygon C is 60 inches,
and the perimeter of polygon Dis 12 inches. If one side of polygon C is 4
inches, what is the length of the corresponding side in polygon D?
A. 0.3 in
OB. 20 in
OC. 4 in
OD. 16 in
k
Answer:
Using the method of ratio and proportion, we find that the length of the side of Polygon D is 0.8in.
Step-by-step explanation:
Given that Polygon C and Polygon D are similar. This means that the ratio of the length of one side of Polygon C to the length of corresponding side of Polygon D will stay same even if we change the lengths.
Perimeter of polygon C = 60in
Perimeter of polygon D = 12in
Length of side of polygon C = 4in
Let us take the number of sides of both the polygons same. Let the length of the side of polygon D x inches. Let the number of sides be n.
First equation, 4n = 60
Second equation, xn = 12
Dividing second by first
(xn) / (4n) = 12 / 60
x / 4 = 1 / 5
x = 4 / 5 = 0.8in
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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Consider the equation.
please help me its math 10 points
Answer:
it should be 319
Step-by-step explanation:
Answer:
639 is the answers for the question
Step-by-step explanation:
please mark me as brainlest
Find the equation of the line which:
passes through (3, 4) and is perpendicular to y=x+2
Answer:
y = -x + 7.
Step-by-step explanation:
General form:-
y = mx + c where m = slope. So:
y = x + 2 has a slope of 1.
The line perpendicular to it has slope -1/1 = -1
To find the required line we use the point-slope form with m = -1, x1 = 3 and y1 = 4.
y - y1 = m(x - x1)
y - 4 = -1(x - 3)
y - 4 = -x + 3
y = -x + 7.
The graph shows two lines, A and B:
Based on the graph, which statement is correct about the solution to the tC system of equations for lines A and B?
O (3, 4) is the solution to both lines A and B.
© (3, 4) is the solution to line A but not to line B.
O (0, 2) is the solution to both lines A and B.
O (0, 2) is the solution to line A but not to line B.
Answer:
the answer is (3,4) is the solution to line A but not to line b
Which point is on the graph of f(x) = 3.4^x
O A. (1, 12)
OB. (0, 12)
O C. (12, 1)
O D. (0,0)
The point on the graph f(x) = 3.4ˣ is (0, 1)
None of the given options is correct.
What is a function?A function is a relationship between a number of inputs and outputs. A function is an association of inputs where each input is coupled with exactly one output. There is a range, co-domain, and domain for every function.
To determine which point is on the graph of f(x) = 3.4ˣ, we need to substitute the given x-coordinate into the function and see if we get the given y-coordinate.
Let's try each option:
A. (1, 12): f(1) = 3.4¹ = 3.4, so this point is not on the graph of f(x) = 3.4ˣ.
B. (0, 12): f(0) = 3.4⁰ = 1, so this point is not on the graph of f(x) = 3.4ˣ.
C. (12, 1): f(12) = 3.4¹² ≈ 108089.7, so this point is not on the graph of f(x) = 3.4ˣ.
D. (0, 1): f(0) = 3.4^0 = 1, so this point is on the graph of f(x) = 3.4ˣ.
Therefore, the point (0, 1) is on the graph of f(x) = 3.4ˣ. The answer is option D.
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In this triangle, what is the value of x?
Enter your answer, rounded to the nearest tenth, in the box.
The value of angle x is 67 degree.
What is a Right Angled Triangle ?A right angled Triangle is a triangle with one angle as 90 degree.
It is given that the for the angle x , the base of the triangle is 28 ft.
The hypotenuse = 72ft.
The trigonometric ratios can be used to find the value of x
cos x = 28 /72
x = cos⁻¹ (28/72)
x = 67 degree (Rounded off to nearest tenth)
Therefore the value of angle x is 67 degree.
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which exponential function has an initial value of 2?
Answer:
The function [tex]2(3^x)[/tex] has an initial value of [tex]2[/tex].
Step-by-step explanation:
An exponential function is a mathematical function of the following form: [tex]f(x)=a^x[/tex]where x is a variable, and a is a constant called the base of the function. The most commonly encountered exponential-function base is the transcendental number e, which is equal to approximately 2.71828. The exponential value can be found by solving the expression to proceed with a solution.
At the initial value, the exponential function is in the [tex]y[/tex] direction and [tex]x[/tex] is [tex]0[/tex] .
[tex]f(x)=2(3^x)\\f(x)=2(3^0)\\f(x)=2[/tex]
Therefore, the function that has an initial value of [tex]2[/tex] is [tex]2(3^x)[/tex].
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What function is represented below?
HELP ASAP!!
Answer:
C
Step-by-step explanation:
(1/4)^x-2 is the answer
Examine the equation.
-2(-x + 9) = 2(x - 9)
2x 18 = 2x - 18
This equation has
Infinite solutions
One solution
No solution
Answer:
No solution
Step-by-step explanation:
What is the factored form of 6n⁴ - 24n³ + 18n?
a.6n(n⁴+4n³+3n)
b.6n[n⁴ -4n³ +3n]
c.6n(n³-4n²+3)
d. 6n(n³ +4n²+3)
Answer:
answer is option C
Step-by-step explanation:
just take 6n as common and divine each value by it
The factored form of expression 6n⁴ - 24n³ + 18n is
6n (n² - 2n + 1) (n² - 2n + 3).
What is an expression?
An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example: so
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
First, we can factor out the greatest common factor of the expression, which is 6n:
6n(n³ - 4n² + 3n)
Next, we can factor the expression inside the parentheses by grouping:
n³ - 4n² + 3n = n²(n-4) + 3(n-4) = (n²+3)(n-4)
Substituting this back into the original expression.
6n (n² + 3) (n - 4)
However, we can further simplify by noticing that the expressions
(n² - 2n + 1) and (n² - 2n + 3) are both equivalent to (n - 1)² + 1 and (n - 1)² + 2, respectively.
Thus,
The factored form can also be written as 6n [ (n - 1)² + 1 ] [ (n - 1)² + 2 ]
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Need help with this ASAP if you could that would help!!
Answer:
the distance between DE is 2
The distance of EF is 5
The distance of FD is [tex]\sqrt{29}[/tex]
Perimeter is 7+[tex]\sqrt{29}[/tex]
Step-by-step explanation:
Distance of DE
[tex]\sqrt{(-3-(-3))^2+(3-1)^2}[/tex]
sqrt([tex](-3+3)^2+(2)^2[/tex])
sqrt([tex](0)^2+4[/tex])
[tex]\sqrt{4}[/tex]
=2
Distance of EF
[tex]\sqrt{(2-(-3))^2+(3-3)^2}[/tex]
Solve that like DE and it equals 5
Distance of FD
[tex]\sqrt{(2-(-3))^2+(3-1)^2}[/tex]
equals to [tex]\sqrt{29}[/tex]
P=DE+EF+FD
P=2+5+[tex]\sqrt{29}[/tex] = 7+[tex]\sqrt{29}[/tex]
I WILL GIVE BRAINIEST PLS HELP
∠2 and ∠8 are _____________ because they are _______________________.
supplementary/consecutive angles
congruent/consecutive angles
congruent/alternate interior angles
supplementary/alternate interior angles
Answer:
congruent/alternate interior angles
Step-by-step explanation:
just took the quiz
Please help!
What is the first step in solving the function below?
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow C.\:factor \:\: out \:\: 2x [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: 2 {x}^{3} - 18 {x}^{2} + 40x[/tex]
[tex]\qquad \tt \rightarrow \: 2x(x {}^{2} ) - 2x(9x) + 2x(20)[/tex]
[tex]\qquad \tt \rightarrow \: 2x( {x}^{2} - 9x + 20)[/tex]
Henceforth, The most efficient first step in factorising the given trinomial is to factor out 2x
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
The perimeter of a rectangle is 32 inches. The length is 1 foot, what is the width of the rectangle in inches?
Answer:
15
Step-by-step explanation:
divide the perimeter by two and minus 1
Answer: 15ft
Step-by-step explanation:
Start off by drawing a rectangle with the given information. Since it is a rectangle we know that the opposite side is also 1. So subtract 2 from 32 to get 30. Divide this by 2 and you will get your width of your rectangle. Hope this helps!
help this homework and it geometry
1) Given
2) Segment addition postulate
3) Substitution property
4) Segment addition postulate
5) Transitive property of equality