[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
Given:▪ [tex]\longrightarrow \sf{f(x) = |x + 4| + 2}[/tex]
You need to remember that the form of an Absolute Value Function is:
• For the vertex:
[tex]\small\longrightarrow \sf{H= \: \: x -coordinate}[/tex]
[tex]\small\longrightarrow \sf{K= y-coordinate}[/tex]
• For the definition:
If "a" is positive (+) , then the range of the function is:
[tex]\small\longrightarrow \sf{R:y \: \underline > \: k}[/tex]
If "a" is negative (-), the range of the function is:
[tex]\small\longrightarrow \sf{R: y \: \underline < \: k}[/tex]
In this case we can identify that:
[tex]\small\longrightarrow \sf{a = 1}[/tex]
[tex] \small\longrightarrow\sf{a = 2}[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
[tex] \large \bm{R: {f(x) \in ℝ | f(x) \underline > 2}}[/tex]
nvm no need liao
The curve y = ax^n, where a and n are constants, passes through the points (2.25, 27), (4, 64) and (6.25, p). Without using logarithms, calculate the value of a, of n and of p.
a. The value of n is 3/2
b. The value of a is 8.
c. The value of p is 125
The curve is an exponential function
What is an exponential function?An exponential function is a function of the form y = axⁿ where a and n are constants
a. How to find the value of n?
Since y = axⁿ where a and n are constants, passes through the points (2.25, 27), (4, 64) and (6.25, p), substituting these points into the equation, we have
y = axⁿ
27 = a(2.25)ⁿ (1)
64 = a(4)ⁿ (2)
P = a(6.25)ⁿ (3)
Dividing (2) by (1), we have
64/27 = a(4)ⁿ/a(2.25)ⁿ
4³/3³ = (4 ÷ 2¹/₄)ⁿ
4³/3³ = (4 ÷ ⁹/₄)ⁿ
4³/3³ = (4 × 4/9)ⁿ
4³/3³ = (16/9)ⁿ
4³/3³ = (4²/3²)ⁿ
(4/3)³ = (4/3)²ⁿ
Equating exponents, we have
2n = 3
n = 3/2
The value of n is 3/2
b. What is the value of a?Using equation (2)
64 = a(4)ⁿ
a = 64/(4)ⁿ
substituting n = 3/2 into the equation, we have
[tex]a = \frac{64}{4^{\frac{3}{2} } } \\= \frac{64}{(\sqrt{4 } )^{3} } \\= \frac{64}{2^{3} } \\= \frac{64}{8} \\= 8[/tex]
So, the value of a is 8.
c. What is the value of p.Using equation (3), we have
P = a(6.25)ⁿ (3)
substituting the values of a and n into the equation,we have
[tex]P = 8(6.25)^{\frac{3}{2} } \\= 8(\sqrt{6.25}) ^{3} \\= 8(2.5}) ^{3} \\= 8(15.625})\\= 125[/tex]
The value of p is 125
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The logarithmic function j(x) is defined as j(x)=log(x+5)−1. The graph below shows the logarithmic function k(x).
Which statement about the two functions is true?
A
Both functions have the same vertical asymptote.
B
Both functions have a domain of all real numbers.
C
The x-intercept of k(x) is greater than the x-intercept of j(x).
D
Function j(x) is greater than function k(x) for all values of x.
The correct statement regarding the logarithmic functions is:
C The x-intercept of k(x) is greater than the x-intercept of j(x).
What is the domain of a logarithmic function?A composite logarithmic function f(x) = log(g(x)) has the domain of g(x) > 0.
What are the vertical asymptotes of the logarithmic functions?For the function j(x), we have that it is at:
x + 5 = 0
x = -5.
For the function k(x), we have that it is at x = 5 from the graph.
What are the x-intercepts of the functions?For the function j(x), we have that:
log(x + 5) - 1 = 0
log(x + 5) = 1
10^[log(x + 5)] = 10^1
x + 5 = 1
x = -4.
For k(x), from the graph, it is at x = 6, hence option C is correct.
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The following are the ages of 13 history teachers in a school district. 24, 27, 29, 29, 35, 39, 43, 45, 46, 49, 51, 51, 56 Notice that the ages are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary
Minimum:
Lower quartile:
Median:
Upper quartile:
Maximum: Interquartile range:
The five-number summary and the interquartile range for the data set are given as follows:
Minimum: 24.Lower quartile: 29.Median: 43.Upper quartile: 50.Maximum: 56.Interquartile range: 50 - 29 = 21.What are the median and the quartiles of a data-set?The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.The first quartile is the median of the first half of the data-set.The third quartile is the median of the second half of the data-set.The interquartile range is the difference between the third quartile and the first quartile.In this problem, we have that:
The minimum value is the smallest value, of 24.The maximum value is the smallest value, of 56.Since the data-set has odd cardinality, the median is the middle element, that is, the 7th element, as (13 + 1)/2 = 7, hence the median is of 43.The first quartile is the median of the six elements of the first half, that is, the mean of the third and fourth elements, mean of 29 and 29, hence 29.The third quartile is the median of the six elements of the second half, that is, the mean of the third and fourth elements of the second half, mean of 49 and 51, hence 50.The interquartile range is of 50 - 29 = 21.More can be learned about five number summaries at https://brainly.com/question/17110151
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HELP FAST PLEASE!!
FIND THE SURFACE AREO OF EACH RECTANGULAR PRISM
The surface area of the rectangular prism is 3668.94 m²
Calculating Surface areaFrom the question, we are to determine the surface area of the rectangular prism
Surface area of a rectangular prism is given by the formula,
Surface area = 2(lw + lh + wh)
Where l is the length
w is the width
and h is the height
From the given diagram,
l = 35.7 m
w = 25.5 m
h = 15.1 m
Putting the parameters into the formula, we get
Surface area = 2(35.7×25.5 + 35.7×15.1 + 25.5×15.1)
Surface area = 2(910.35 + 539.07 + 385.05)
Surface area = 2(1834.47)
Surface area = 3668.94 m²
Hence, the surface area of the rectangular prism is 3668.94 m²
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You buy four boxes of fish sticks on sale at $1.99 per
box. The fish sticks regularly sell for $2.49 per box. Lemons are also
on sale at two for $1.00. How much money did you save by buying
the fish sticks on sale
The following are the ages of 13 history teachers in a school district. 24, 27, 29, 29, 35, 39, 43, 45, 46, 49, 51, 51, 56 Notice that the ages are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set.
Answer:
Below in bold.
Step-by-step explanation:
Minimum 24
Lower quartile 29
Median 43
Upper quartile = (49 + 51) / 2 = 50
Maximum = 56
Interquartile range = 50-29 = 21.
The graph of a quadratic function is represented by the table.
x f(x)
6 -2
7 4
8 6
9 4
10 -2
What is the equation of the function in vertex form?
Substitute numerical values for a, h, and k.
Big fraction
Parentheses
Vertical bars
Square root
Root
Superscript (Ctrl+Up)
Subscript (Ctrl+Down)
Plus sign
Minus sign
Middle dot
Multiplication sign
Equals sign
Less-than sign
Greater-than sign
Less-than or equal to
Greater-than or equal to
Pi
Alpha
Beta
Epsilon
Theta
Lambda
Mu
Rho
Phi
Sine
Cosine
Tangent
Arcsine
Arccosine
Arctangent
Cosecant
Secant
Cotangent
Logarithm
Logarithm to base n
Natural logarithm
Bar accent
Right left arrow with under script
Right arrow with under script
Angle
Triangle
Parallel to
Perpendicular
Approximately equal to
Tilde operator
Degree sign
Intersection
Union
Summation with under and over scripts
Matrix with square brackets
The equation of the function in vertex form exists f(x) = -2·(x - 8)² + 6.
What is the equation of the function in vertex form?The given values exist
x, f(x)
6, -2
7, 4
8, 6
9, 4
10, -2
The equation of the function in vertex form exists
f(x) = a(x - h)² + k
To estimate the values of a, h, and k,
When x = 6, f(x) = -2 then
-2 = a(6 - h)² + k
= (h²-12·h+36)·a + k.............(1)
When x = 7, f(x) = 4 then
4 = a( 7- h)² + k
= (h²-14·h+49)·a + k...........(2)
When x = 8, f(x) = 6
6 = a( 8- h)² + k ...........(3)
When x = 9, f(x) = 4.
4 = a( 9- h)² + k ..........(4)
When x = 10, f(x) = -2
-2 = a(10- h)² + k ...........(5)
Subtract equation (1) from (2)
4 - 2 = a( 7- h)² + k - (a(6 - h)² + k )
= 13·a - 2·a·h........(6)
Subtract equation (4) from (2)
a (9 - h)² + k - a( 7- h)² + k
32a -4ah = 0
Simplifying the equation, we get
4h = 32
h = 32/4 = 8
From equation (6) we have;
13·a - 2·a·8 = 6
-3a = 6
a = -2
From equation (1), we have;
-2 = -2 × ( 10- 8)² + k
-2 = -8 + k
k = 6
The value of k = 6.
The equation of the function in vertex form exists f(x) = -2·(x - 8)² + 6.
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(50 POINTS!!!) find the total surface area and volume, then multiply by $0.004. please show your work!!
The Total surface area of the square pyramid = 115.2 in.²
The Volume of the square pyramid = 1,024 in.³.
What is the Total Surface Area of a Square Pyramid?The total surface are of a square pyramid is given as: TSA = SA = 1/2(P × l), where:
P = perimeter of the square base
l = slant height of the pyramid
What is the Volume of a Square Pyramid?The volume of a square pyramid = 1/3(a³ × h), where:
a = edge of the square base
h = height of the pyramid
Find the Total surface area of the Pyramid:
P = 4(a) = 4(8) = 32 in.
l = 7.2 in.
Total surface area of the square pyramid = 1/2(32 × 7.2)
Total surface area of the square pyramid = 115.2 in.²
Volume of the square pyramid:
a = 8 in.
h = 6 in.
Volume of the square pyramid = 1/3(8³ × 6)
Volume of the square pyramid = 1,024 in.³
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Garland has 9/10
of a pizza, the pizza needs to be equally divided between garland and her five friends. What fraction
of the pizza will each friend get?
Answer:
9/50
Step-by-step explanation:
We simply divide the pizza we have (9/10) by the number of friends (5):
9/10 : 5 = 9/50
evaluate 4 + 6 x 6 / 8
Answer:
8.5
Step-by-step explanation:
4 + (6)(6)/8=
17/2 = 8.5
Answer:
8.5
Step-by-step explanation:
6 x 6 = 36/8 = 4.5 + 4 = 8.5
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
(6, 1)
(1, 3)
(-7, 6)
Step-by-step explanation:
To have a function, each value used for x can appear only once.
The first set of points has as x: 1, -7, -3.
The only choice without 1, -7, or -3 for x is (6, 1)
The second set of points has as x: 2, 6, -7.
The only choice without 2, 6, or -7 for x is (1, 3)
The third set of points has as x: 1, -3, 6.
The only choice without 1, -3, or 6 for x is (-7, 6)
(6 1/7 divided by x + 3 5/9) / 4 1/6 = 1 1/3 what is x
let's firstly convert the mixed fractions to improper fractions and them proceed.
[tex]\stackrel{mixed}{6\frac{1}{7}}\implies \cfrac{6\cdot 7+1}{7}\implies \stackrel{improper}{\cfrac{43}{7}} ~\hfill \stackrel{mixed}{3\frac{5}{9}}\implies \cfrac{3\cdot 9+5}{9}\implies \stackrel{improper}{\cfrac{32}{9}} \\\\\\ \stackrel{mixed}{4\frac{1}{6}}\implies \cfrac{4\cdot 6+1}{6}\implies \stackrel{improper}{\cfrac{25}{6}} ~\hfill \stackrel{mixed}{1\frac{1}{3}}\implies \cfrac{1\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{4}{3}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{ ~~ \frac{6\frac{1}{7}}{x}+3\frac{5}{9} ~~ }{4\frac{1}{6}}~~ = ~~1\frac{1}{3}\implies \cfrac{ ~~ \frac{ ~~ \frac{43}{7} ~~ }{x}+\frac{32}{9} ~~ }{\frac{25}{6}}~~ = ~~\cfrac{4}{3}\implies \cfrac{ ~~ \frac{43}{7x}+\frac{32}{9} ~~ }{\frac{25}{6}}~~ = ~~\cfrac{4}{3}[/tex]
[tex]\cfrac{43}{7x}+\cfrac{32}{9}~~ = ~~\cfrac{25}{6}\cdot \cfrac{4}{3}\implies \cfrac{43}{7x}+\cfrac{32}{9}~~ = ~~\cfrac{50}{9}\implies \cfrac{43}{7x}~~ = ~~\cfrac{50}{9}-\cfrac{32}{9} \\\\\\ \cfrac{43}{7x}~~ = ~~\cfrac{18}{9}\implies \cfrac{43}{7x}=2\implies 43=14x\implies \cfrac{43}{14}=x\implies 3\frac{1}{14}=x[/tex]
PLEASE HELP IM STUCK
Answer:
y=1
Step-by-step explanation:
Since you already found x,
We will only be needing one equation to find y..
I will take equation two: 3(2)+2y=8
Step Two: 6+2y=8 (then you minus 6 on each side)
Step Three: 2y=2 (divide)
y=1
The volume occupied by 34 grams of brass is 4.0 cubic centimeters. the density of the brass is...
Answer:
8.5 g/cm^3
Step-by-step explanation:
Density = mass/volume
= 34 g / 4 cm^3 = 8.5 g/cm^3
Answer:
8.5 grams per cubic centimeter.
Step-by-step explanation:
Density = mass / volume
= 34 / 4
= 8.5 grams / cubic centimeter.
id love the help! (im not great at math)
Answer:
Area = 113.04 in^2
Step-by-step explanation:
you have the diameter which is twice the radius, the formula is in the question:
Area = πr^2
so
12: 2 = 6 (RADIUS)
Area = π6 ^ 2 =
Area = π 36 in^2
Area = 3.14 * 36
Area = 113.04 in^2
Drag each length to the correct location on the image. Each length can be used more than once, but not all lengths will be used.
What are the missing segment lengths shown in the image?
By applying Pythagoras theorem, the missing segment lengths of this triangles include:
CD = 10√2AC = 10√2BC = 10AB = 10How to find the missing segment lengths?Since triangle ACD is a right-angle triangle, we would use Pythagoras theorem to find the missing segment lengths of this triangles as follows:
c² = a² + b² ≡ AD² = CD² + AC²
Next, we would use cos trigonometric ratio to find side CD,
cos45 = adjacent/hypotenuse
cos 45 = CD/20
1/√2 = CD/20
CD = 1/√2 × 20
CD = (20√2)/2
CD = 10√2
For side AC, we have:
AD² = CD² + AC²
AC² = AD² - CD²
AC² = 20² - (10√2)²
AC² = 400 - 100(2)
AC = √200
AC = 10√2
From triangle ABC, we have:
cos45 = BC/10√2
BC = 10√2 × cos45
BC = 10√2 × 1/√2
BC = (10√2)/√2
BC = 10
For side AB, we have:
AB² = (10√2)² - 10²
AB² = 200 - 100
AB² = 100
AB = 10.
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Satia drives for 4 hours from a to b. angelique drives at half the speed of safia. find how many hours angelique takes to drive from a to b
Angelique takes 8 hours to drive from a to b.
What is the concept of speed, distance and time?How quickly something or someone is moving is indicated by their speed. If you know how far something travels and how long it takes, you can calculate their average speed. Speed equals distance x times time, according to the speed formula. Knowing the units for distance and time will help you determine what the units are for speed.
According to given Information:let us assume distance from a to b be x units.
let us assume speed of vehicle be y units/hour.
For case -1For Satia, speed=y units time=4 hours we know the formula of distance is:
distance=speed × time distance=(y× 4) units -------------------(1)
For case - 2Angelique :speed=y / 2 units time=?
We know the formula of distance is:
Distance=speed × time distance=(y/2)× time -------------------(2)
We can see that distance in both cases is equal,
So compare case (1) ad (2) ,
We get (y× 4)=(y/2)× time
On rearranging ,
Time= (4×2) hours=8 hours
hence,
Angelique takes 8 hours to cover the distance from a to b.
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The numbers of questions answered correctly by various students on a 1010-question quiz are an example of which type of data?
The numbers of questions answered correctly by various students on a 10 question quiz are an example of discrete data.
What is discrete data?Discrete data is the type of data that has clear spaces between values.
As a result, the test-scores are discrete data. Although most discrete data, refers to things we can count easily, it does not have to be numeric. Non-numeric categories could be described as discrete data.
Discrete data is a count that involves integers — only a limited number of values is possible. This type of data cannot be subdivided into different parts. Discrete data includes discrete variables that are finite, numeric, countable, and non-negative integers.
Discrete data is a type of quantitative data that includes figures and statistics of non divisible, single points of data that you can count. You typically write discrete data points as numbers that represent exact values, and discrete data usually represents single events that have already occurred. When reviewing discrete data, companies analyze exact figures like units that were sold on a given day or the hours that an employee worked during a certain week.
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Select the correct answer.
Consider function g.
9(z) = 3 sin (TZ)
Function g is horizontally stretched by a factor of 2 and then translated 2 units down to obtain function f. Which graph matches the described
transformation?
The y-intercept exists reduced by 2 units. Hence there exists a translation of 2 units down.
How to find the graph of the given function?
Let the function be g(z) = 3 sin (TZ).
A vertical stretch by a factor of k indicates that the point (x, y) on the graph of f (x) exists transformed to the point (x, ky) on the graph of g(x), where k < 1.
If k = 1, then the same graph we get, and if k > 1 we get a vertically shrink graph.
In our question, there exists a vertical stretch of 2. This means the new graph would have points as (x, y/2)
i.e. instead of f(x) = y, we have now f(x) = y/2
So transformation is g(x) = 3f(x)
The y-intercept exists reduced by 2 units. Hence there exists a translation of 2 units down.
Therefore, the correct answer is option C.
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Which graph shows the solution to this system of in
y>-1/3x+1
y> 2x-3
Answer:
Step-by-step explanation:
the graph is down below
What is the end behavior of the function f of x equals 3 times the cube root of x? as x → –[infinity], f(x) → –[infinity], and as x → [infinity], f(x) → [infinity]. as x → –[infinity], f(x) → [infinity], and as x → [infinity], f(x) → –[infinity]. as x → –[infinity], f(x) → 0, and as x → [infinity], f(x) → 0. as x → 0, f(x) → –[infinity], and as x → [infinity], f(x) → 0.
The function [tex]f(x)=4\sqrt[3]{x}[/tex] is a cube root function and the function end behavior is: [tex]x[/tex] → [tex]+[/tex] ∞, [tex]f(x)[/tex] → [tex]+[/tex] ∞, and as [tex]x[/tex] → - ∞, [tex]f(x)[/tex] → [tex]+[/tex] ∞
What is end behavior?The end behavior of a function f defines the behavior of the function's graph at the "ends" of the x-axis. In other words, the end behavior of a function explains the graph's trend when we look at the right end of the x-axis (as x approaches +) and the left end of the x-axis (as x approaches ).To determine the end behavior:
The equation of the function is given as: [tex]f(x)=4\sqrt[3]{x}[/tex]To determine the end behavior, we plot the graph of the function f(x).We can see from the accompanying graph of the function:As x approaches infinity, so does the function f(x), and vice versa.As a result, the function end behavior is:[tex]x[/tex] → [tex]+[/tex] ∞, [tex]f(x)[/tex] → [tex]+[/tex] ∞, and as [tex]x[/tex] → - ∞, [tex]f(x)[/tex] → [tex]+[/tex] ∞
Therefore, the function [tex]f(x)=4\sqrt[3]{x}[/tex] is a cube root function and the function end behavior is: [tex]x[/tex] → [tex]+[/tex] ∞, [tex]f(x)[/tex] → [tex]+[/tex] ∞, and as [tex]x[/tex] → - ∞, [tex]f(x)[/tex] → [tex]+[/tex] ∞
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The complete question is given below:
What is the end behavior of the function f of x equals negative 4 times the cube root of x?
As x → –∞, f(x) → –∞, and as x → ∞, f(x) → ∞.
As x → –∞, f(x) → ∞, and as x → ∞, f(x) → –∞.
As x → –∞, f(x) → 0, and as x → ∞, f(x) → 0.
As x → 0, f(x) → –∞, and as x → ∞, f(x) → 0.
Answer:
As x → –∞, f(x) → –∞, and as x → ∞, f(x) → ∞.
Step-by-step explanation:
I got it right on the test.
1/3 +1/6 in fraction form
[tex]\Large\texttt{Answer}[/tex]
[tex]\bf{\cfrac{1}{2}}[/tex]
[tex]\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}[/tex]
[tex]\Large\texttt{Process}[/tex]
Do you remember that we cannot add fractions when they have unlike denominators? We can onyl add fractions as long as they have the same denominator!
So here's the big idea: fractions must have the same denominator.
If we multiply the first fraction by 2, then both fractions will have the same denominator. *
* Why 2??
- Because:
We need to find the least common multiple of 3 and 6, which is 6. Next, what should 3 be multiplied by to result in 6? That's right, 2.
Also, we can only multiply the denominator by 2 as long as we multiply the numerator by 2!
So that's why we multiply the whole fraction by 2
[tex]\bf{\cfrac{1\times2}{3\times2}+\cfrac{1}{6}}[/tex]
Watch what happens
[tex]\bf{\cfrac{2}{6}+\cfrac{1}{6}}[/tex]
Add the numerators
[tex]\bf{\cfrac{2+1}{6}}[/tex]
[tex]\bf{\cfrac{3}{6}}[/tex]
Simplifying the fractions
[tex]\bf{\cfrac{3\div3}{6\div3}}[/tex]
[tex]\bf{\cfrac{1}{2}}[/tex]
Hope that helped
Answer: 1 / 2
Step-by-step explanation:
Given information
[tex]\frac{1}{3} ~+~\frac{1}{6}[/tex]
Convert the denominator (3, 6) into the same common denominator
Least Common Multiple (LCM) of 3 and 6 = 6
[tex]=\frac{1~*~2}{3~*~2} ~+~\frac{1}{6}[/tex]
[tex]=\frac{2}{6} ~+~\frac{1}{6}[/tex]
Combine two fractions
[tex]=\frac{2~+~1}{6}[/tex]
[tex]=\frac{3}{6}[/tex]
Simplify the fraction by dividing 3 on both numerator and denominator
[tex]=\frac{3~/~3}{6~/~3}[/tex]
[tex]=\Large\boxed{\frac{1}{2} }[/tex]
Hope this helps!! :)
Please let me know if you have any questions
f(x)
Which type of function describes f(x)?
•
Rational
Polynomial
O Logarithmic
• Exponential
Answer:
Exponential function
[tex]y=1.25(2)^x[/tex]
Step-by-step explanation:
Definitions
Asymptote: a line that the curve gets infinitely close to, but never touches.
Hole: a point on the graph where the function is not defined.
Polynomial Function[tex]f(x)=a_nx^n+a_{n-1}x^{n-1}+...+a_2x^2+a_1x+a_0[/tex]
An equation containing variables with non-negative integer powers and coefficients, that involves only the operations of addition, subtraction and multiplication.
A continuous function with no holes or asymptotes.
Rational Function[tex]f(x)=\dfrac{h(x)}{g(x)}[/tex]
An equation containing at least one fraction whose numerator and denominator are polynomials.
A rational function has holes and/or asymptotes.
A rational function has holes where any input value causes both the numerator and denominator of the function to be equal to zero.A rational function has vertical asymptotes where the denominator approaches zero.If the degree of the numerator is smaller than the degree of the denominator, there will be a horizontal asymptote at y = 0.If the degree of the numerator is the same as the degree of the denominator, there will be a horizontal asymptote at y = ratio of leading coefficients.If the degree of the numerator is exactly one more than the degree of the denominator, slant asymptotes will occur. Logarithmic Function[tex]f(x) =\log_ax[/tex]
A continuous function with a vertical asymptote.
A logarithmic function has a gradual growth or decay.
Exponential Function[tex]f(x)=ab^x[/tex]
The variable is the exponent.
A continuous function with a horizontal asymptote.
An exponential function has a fast growth or decay.
Answer: exponential
Step-by-step explanation:
PQRS is a cyclic quadrilateral.Chord RS is produced to T.K is a point on RS and W is a point on the circle such that QRKW is a parallelogram. PS and QW intersect at U. PST = 136° and Q₁ =100° Determine, with reasons, the size of: 8.1.1.R 8.1.2.P 8.1.3.PQW 8.1.4.U2
Answer:
Step-by-step explanation:
PS and QW intersect at U. PST = 136° and Q₁ =100°
Solve the system u=3x-4y, v=x+4y for x and y in terms of u and v. then find the value of the jacobian
Eliminate [tex]y[/tex].
[tex]u + v = (3x - 4y) + (x + 4y) = 4x \implies x = \dfrac{u+v}4[/tex]
Eliminate [tex]x[/tex].
[tex]u - 3v = (3x - 4y) - 3 (x + 4y) = -16y \implies y = \dfrac{3v-u}{16}[/tex]
The Jacobian for this change of coordinates is
[tex]J = \begin{bmatrix} x_u & x_v \\ y_u & y_v \end{bmatrix} = \begin{bmatrix} \dfrac14 & \dfrac14 \\\\ -\dfrac1{16} & \dfrac3{16} \end{bmatrix}[/tex]
with determinant
[tex]\det(J) = \dfrac14\cdot\dfrac3{16} - \dfrac14\cdot\left(-\dfrac1{16}\right) = \dfrac1{16}[/tex]
q=sqrt (c+d)/(c-d) solve for c
The equation for the variable 'c' is c = d(q² + 1)/(q² - 1). By using simple arithmetic operations on the original equation, the required equation can be obtained.
What is an equation?An equation is a relationship between two expressions given by a mathematical statement.
There are different types of equations. They are linear equations, quadratic, polynomial, etc.
Solving for c in the given equation:The given equation is
q = √((c + d)/(c - d))
Squaring on both, root gets canceled out
⇒ q² = (c + d)/(c - d)
⇒ q²(c - d) = (c + d)
⇒ cq² - dq² = c + d
Separating like terms aside,
cq² - c = d + dq²
⇒ c(q² - 1) = d(q² + 1)
⇒ c = d(q² + 1)/(q² - 1)
Therefore, the required equation is c = d(q² + 1)/(q² - 1).
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If the first two angles of a triangle measure 37° and 104°, what is the measurement of the third?
Answer:
67
Step-by-step explanation:
All triangles have three angles. The sum of the three angles should equal up to 180 degrees.
108-104-37= 67
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
[tex]y = mx + n[/tex]
[tex]m = \frac{y - y}{x - x} = \frac{5 - ( - 1)}{ - 5 - ( - 3)} = \frac{6}{ - 2} = - 3[/tex]
[tex]y = - 3x + n \\ [/tex]
Since both ( -3 , -1 ) and ( -5 , 5 ) pass through the line, they both satisfy its equation. Substitute any point in the new equation, I will choose ( -5 , 5 )[tex]5 = - 3( - 5) + n \\ n = 5 - 15 = - 10[/tex]
[tex]y = - 3x - 10[/tex]
Area of triangle in coordinate geometry
Practical Problem 2
Provide a practical problem below that you will use to represent inverse variation. The problem should be written in complete sentences.
Steps and Work:
List each step for solving the inverse variation practical problem and the work that corresponds with each step.
Answer
Give the correct answer that the app user is being asked to find.
The steps to solve the inverse variation will be:
Write the variation equation: y = k/x or k = xySubstitute in for the given values and find the value of kRewrite the variation equation: y = k/x with the known value of kSubstitute the remaining values and find the unknownHow to illustrate the variation example?The example will be y varies inversely with x and y = 2 when x = 5. Find y when x = 30
Step 1: Write the variation equation: y = k/x or k = xy:
k = xy
Step 2: Substitute in for the given values of x and y:
k = (2)(5) = 10
Step 3: Rewrite the variation equation: y = k/x with the known value of k (10):
y = 10/x
Step 4: Substitute the remaining values and find the unknown:
y = 10/30
y = 1/3
Therefore, y is 1/3 when x is 30.
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