Answer: This equation is not a function.
Step-by-step explanation:
Ok, a function is something like a "machine".
It takes an input value, x, and transforms it into an output value, y.
Such that for every input x, the function can transform it into only one value of y.
for example, if we have a "function" f(x)
such that f(2) = 3 and f(2) = 4
(for the same input, x = 2, we have two different outputs)
Then this is not a function.
Now, the given equation is:
x^2 + y^2 = 5
This is actually the equation for a circle, centered at the point (0, 0) and with a radius equal to √5.
Then, if we want to transform it into y(x), we can see a problem
If x = 0, we have:
0^2 + y^2 = 5
y^2 = 5
then we have two possible values for y:
y = +√5
y = -√5
Then for one value of x, we have two values of y.
This means that this is not a function.
Answer:
No. The vertical line touches the graph at more than one point at once.
Step-by-step explanation:
I just did it
You work for a roofing company and must order the correct number of tiles to complete the final side of the roof. It is in the shape of a trapezoid. The numbers of tiles in each row form a sequence. We know we will have 20 rows to complete the job. The first row has ten tiles. Each row has two more tiles than the previous row. Is this sequence arithmetic or geometric?
Answer:
ljj
Step-by-step explanation:
llk
Yes , the series is an arithmetic sequence of common difference 2
What is Arithmetic Progression?
An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"
The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁
Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]
Given data ,
Let the number of terms n = 20
The number of tiles in the first row = 10 tiles
The number of tiles in the second row = 2 more than first row
The number of tiles in the second row = 12 tiles
The number of tiles in the third row = 14 tiles
So , the sequence will be , 10 , 12 , 14 , 16 ...
The number of terms n = 20
The first term a = 10
The common difference d = second term - first term
The common difference d = 12 - 10 = 2
The series is an arithmetic sequence and the 20th term of the sequence will be
a₂₀ = a + ( n - 1 )d
a₂₀ = 10 + ( 19 ) 2
a₂₀ = 10 + 38
a₂₀ = 48 tiles
Hence , the series is an arithmetic sequence
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Simplify: (-2)(-3)+(4)(-8)
Simplify: (3)(-6)-18
Answer:
4
Step-by-step explanation:
Answer:
-26, and -36
Step-by-step explanation:
(-2) (-3) + (4) (-8)
6 + -32 = -26
(3) (-6) - 18
-18 + -18 = -36
Which statement best describes the function h(t) = 210 - 15t?
Oh is the function name; h(t) is the input, or independent variable; and t is the output, or dependent variable.
O h is the function name; t is the input, or independent variable; and h(t) is the output, or dependent variable.
O t is the function name; h(t) is the input, or independent variable; and h is the output, or dependent variable.
Ot is the function name; h is the input, or independent variable; and h(t) is the output, or dependent variable.
Answer:
h is the function name; t is the input, or independent variable; and h(t) is the output, or dependent variable.
Step-by-step explanation:
The explanation is in the answer.
h is the function name; h(t) is the input, or independent variable; and t is the output, or dependent variable is correct statement.
The given function is h(t) = 210 - 15t
The function is named h, and it takes an input value t (the independent variable) and produces an output value 15t (the dependent variable).
The function is often written as h(t) = 15t to make it clear that h is a function of t.
Hence, h is the function name; h(t) is the input, or independent variable; and t is the output, or dependent variable is correct statement.
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Create a scatterplot for the following population data, using t = 0 to stand for 1950. Then
estimate the population of Namibia in the years 1940, 1997, and 2005. Note: Population
values are in thousands. (Hint: Begin by determining which row is the x-value and which row
is the y-value)
Answer:
The population of Namibia in the years 1940, 1997, and 2005 was 371.2 , 1671.64 and 2064.74 respectively.
Step-by-step explanation:
Refer the attached figure
We will use equation calculator to find the equation of given plot
[tex]y = 483.36 \times e^0.0264x[/tex]
We are supposed to find the population of Namibia in the years 1940, 1997, and 2005.
x values are years
y values are population
For 1940, [tex]x = -10, y = y = 483.36 \times e^{0.0264(-10)} = 371.2[/tex]
For 1997, [tex]x = 47, y = y = 483.36 \times e^{0.0264 \times 47} = 1671.64[/tex]
For 2005,[tex]x = 55, y = y = 483.36 \times e^{0.0264 \times 55} = 2064.74[/tex]
Hence The population of Namibia in the years 1940, 1997, and 2005 was 371.2 , 1671.64 and 2064.74 respectively.
(x-y)²-(x+y)² a)0 b)2y² c)-2y² d)-4xy e)-2(x+y)²
Answer:
D
Step-by-step explanation:
-4xy
will be your answer after factoring
Answer:
d
Step-by-step explanation:
Given
(x - y)² - (x + y)² ← expand both factors using FOIL
= x² - 2xy + y² - (x² + 2xy + y²) ← distribute by - 1
= x² - 2xy + y² - x² - 2xy - y² ← collect like terms
= - 4xy → d
The citizens of a certain community were asked to choose their favorite pet. The pie chart below shows the distribution of the citizens' answers. If there are 140,000 citizens in the community, how many chose Fish or Cats?
Incomplete Question:
The content of the pie chart is as follows:
Hamsters = 9% ; Snakes = 10% ; Cats = 23%
Birds = 21% ; Dogs = 26% ; Fish = 11%
Answer:
The number of citizens who chose cat or fish is 47,600
Step-by-step explanation:
Given
Number of citizens = 140,000
Required
Determine the number of those that chose fish or cats
First, we need to calculate the percentage of those whose pets are either cats or fish
[tex]Percentage = Cat + Fish[/tex]
Substitute 23% for cat and 11% for fish
[tex]Percentage = 23\% + 11\%[/tex]
[tex]Percentage = 34\%[/tex]
Next, is to multiply the calculated percentage by the number of citizens
[tex]Cat\ or\ Fish = Percentage * Number\ of\ Citizens[/tex]
[tex]Cat\ or\ Fish = 34\% * 140000[/tex]
[tex]Cat\ or\ fish = 47600[/tex]
Hence, the number of citizens who chose cat or fish is 47,600
the number of citizens who chose cat or fish is 47,600
The calculation is as follows;= Number of citizens × total percentage
[tex]= 140,000 \times (23\% + 11\%)\\\\= 140,000 \times 34\%[/tex]
= 47,600
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Expand the following using the Binomial Theorem and Pascal’s triangle. Show your work. (x + 2)6 (x − 4)4 (2x + 3)5 (2x − 3y)4 In the expansion of (3a + 4b)8, which of the following are possible variable terms? Explain your reasoning. a2b3; a5b3; ab8; b8; a4b4; a8; ab7; a6b5
Answer:
The answer is below
Step-by-step explanation:
Expansion using pascal triangle:
a) (x + 2)⁶ = x⁶2⁰ + 6(x⁵)(2)¹ + 15(x⁴)(2²) + 20(x³)(2³) + 15(x²)(2⁴) + 6(x)(2⁵) + 1(2⁶)
= x⁶ + 12x⁵ + 60x⁴ + 160x³ + 240x² + 192x + 64
b) (x-4)⁴ = x⁴ + 4(x³)(-4) + 6(x²)(-4)² + 4(x)(-4)³ + 1(x⁰)(-4)⁴
=x⁴-16x³+96x²-256x+256
c) (2x + 3)⁵ = (2x)⁵ + 5(2x)⁴(3) + 10(2x)³(3)² + 10(2x)²(3)³ + 5(2x)(3)⁴ + 1(2x)⁰(3)⁵ =
= 32x⁵ + 240x⁴ + 720x³ + 1080x² + 810x + 243
d) (2x-3y)⁴ = 1(2x)⁴(-3y)⁰ + 4(2x)³(-3y) + 6(2x)²(-3y)² + 4(2x)(-3y)³ + 1(2x)⁰(-3y)⁴
= 16x⁴- 96x³ + 216x² - 216x + 81
Expansion using binomial where [tex]C(n,r)=\frac{n!}{(n-r)!r!}[/tex]
a) (x + 2)⁶ = C(6,0)[x⁶2⁰] + C(6,1)[(x⁵)(2)¹] + C(6,2)[(x⁴)(2²)] + C(6,3)[(x³)(2³)] + C(6,4)[(x²)(2⁴)] + C(6,5)[(x)(2⁵)] + C(6,6)[(2⁶)]
= x⁶2⁰ + 6(x⁵)(2)¹ + 15(x⁴)(2²) + 20(x³)(2³) + 15(x²)(2⁴) + 6(x)(2⁵) + 1(2⁶)
= x⁶ + 12x⁵ + 60x⁴ + 160x³ + 240x² + 192x + 64
b) (x-4)⁴ = C(4,0)[x⁴] + C(4,1)[(x³)(-4)] + C(4,2)[(x²)(-4)²] + C(4,3)[(x)(-4)³] + C(4,4)[(x⁰)(-4)⁴]
= x⁴ + 4(x³)(-4) + 6(x²)(-4)² + 4(x)(-4)³ + 1(x⁰)(-4)⁴
=x⁴-16x³+96x²-256x+256
c) (2x + 3)⁵ = C(5,0)[(2x)⁵] + C(5,1)[(2x)⁴(3)] + C(5,2)[(2x)³(3)²] + C(5,3)[(2x)²(3)³] + C(5,4)[(2x)(3)⁴] + C(5,5)[(2x)⁰(3)⁵]
= (2x)⁵ + 5(2x)⁴(3) + 10(2x)³(3)² + 10(2x)²(3)³ + 5(2x)(3)⁴ + 1(2x)⁰(3)⁵
= 32x⁵ + 240x⁴ + 720x³ + 1080x² + 810x + 243
d) (2x-3y)⁴ = C(4,0){(2x)⁴(-3y)⁰} + C(4,1)[(2x)³(-3y)] + C(4,2)[(2x)²(-3y)²] + C(4,3)[(2x)(-3y)³] + C(4,4)[(2x)⁰(-3y)⁴]
= 1(2x)⁴(-3y)⁰ + 4(2x)³(-3y) + 6(2x)²(-3y)² + 4(2x)(-3y)³ + 1(2x)⁰(-3y)⁴
= 16x⁴- 96x³ + 216x² - 216x + 81
In the expansion of (3a + 4b)⁸, the only possible variable terms are a⁵b³, b⁸, a⁴b⁴, a⁸, ab⁷ because for each of them, the sum of there powers is eight. If the sum of the powers is not 8 then it is not correct.
For a²b³, the sum of the power is 5, for ab⁸ the sum of power is 9 and for a⁶b⁵ the sum of the power is 11 therefore thy are not correct.
As per the question expand the bimonoidal theorem and the pascal triangle. Showing the (x+2)6 (x-4)4 (2x+3)5 (2x-3y)4.
Expansion using pascal triangle:a) (x + 2)⁶ = x⁶2⁰ + 6(x⁵)(2)¹ + 15(x⁴)(2²) + 20(x³)(2³) + 15(x²)(2⁴) + 6(x)(2⁵) + 1(2⁶) = x⁶ + 12x⁵ + 60x⁴ + 160x³ + 240x² + 192x + 64b) (x-4)⁴ = x⁴ + 4(x³)(-4) + 6(x²)(-4)² + 4(x)(-4)³ + 1(x⁰)(-4) =x⁴-16x³+96x²-256x+256c) (2x + 3)⁵ = (2x)⁵ + 5(2x)⁴(3) + 10(2x)³(3)² + 10(2x)²(3)³ + 5(2x)(3)⁴ + 1(2x)⁰(3)⁵ = 32x⁵ + 240x⁴ + 720x³ + 1080x² + 810x + 243d) (2x-3y)⁴ = 1(2x)⁴(-3y)⁰ + 4(2x)³(-3y) + 6(2x)²(-3y)² + 4(2x)(-3y)³ + 1(2x)⁰(-3y)⁴ = 16x⁴- 96x³ + 216x² - 216x + 81.Learn more about the use the binomial theorem.
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classify what type of number is 8/2
Answer:
unsimplified improper fraction
Step-by-step explanation:
8/2 could be simplified into 4 and its an improper fraction bc proper fraction form is 4/1 or just 4
sam leases a car for 24 months. the car will cost him $7,000 if he decides to buy it at the end of the lease. What term describes the $7,000
Answer:
Residual value
[tex]integrate \: ln(x) [/tex]
Answer:
ln(x) = 1/x... It's a basic rule of Calculus.
find the third term of the geometric sequence when a1 = 1/4 and r=-2
Answer:
1
Step-by-step explanation:
(-2)(1/4)=-1/2
(-2)(-1/2)
=1
the third term of the geometric sequence with first term = 1/4 and common ratio r = -2 is 1
We have a geometric sequence in which the first term is [tex]\frac{1}{4}[/tex] and the common ratio is -2.
We have to find the third term of this geometric sequence.
What is the formula to find the [tex]n^{th}[/tex] term of a geometric sequence?The formula to find the [tex]n^{th}[/tex] term of a geometric sequence with first term [tex]a_{1}[/tex] and common ratio r is -
[tex]a_{n} =a_{1} r^{n-1}[/tex]
In our question, [tex]a_{1}[/tex] = [tex]\frac{1}{4}[/tex] and r = -2 and n =3.
Substituting the values, we get -
[tex]a_{3} =\frac{1}{4}(-2)^{3-1} = \frac{1}{4} (-2)^{2} =\frac{1}{4}\times4=1[/tex]
Hence, the third term of the geometric sequence with first term = 1/4 and common ratio r = -2 is 1.
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The solutions to \[2x^2 - 10x + 13 = 0\]are $a+bi$ and $a-bi,$ where $a$ and $b$ are positive. What is $a\cdot b?$[tex]The solutions to\[2x^2 - 10x + 13 = 0\]are $a+bi$ and $a-bi,$ where $a$ and $b$ are positive. What is $a\cdot b?$[/tex]
Answer:
5/8
Step-by-step explanation:
(10 +/- √100-104)/4
(10 +/- 2i)/4
5/4 +/- 1/2i
5/4 * 1/2 = 5/8
Determine the standard deviation of the data below. (1, 2, 3, 4, 5)
Answer:
[tex]\sqrt{2}[/tex] or 1.414
Step-by-step explanation:
1) Find the mean. 1+2+3+4+5 = 15. 15/5= 3
2) For each data point, find the square of its distance to the mean. (4, 1, 0, 1, 4)
3) Sum the values from Step 2. 10
4) Divide by the number of data points. 10/5= 2
5) Take the square root. [tex]\sqrt{2}[/tex]
Answer:
the answer square root of 2! just did the test and got it right :)
Step-by-step explanation:
another question what's the formula for an open end of a cylinder??
Answer:
Formula for an opened end of a cylinder =
[tex]\pi r^2 +2\pi rh\\[/tex]
Closed at both end =
[tex]2\pi r^2 +2\pi r h[/tex]
Opened at both end =
[tex]2\pi rh[/tex]
Step-by-step explanation:
Write this expression as a complex number in standard form
Answer:
[tex]81+144i[/tex]
Step-by-step explanation:
We want to simplify:
[tex]\displaystyle (-3\sqrt{-81})(-5+\sqrt{-9}) + 9i[/tex]
Recall that:
[tex]\displaystyle \sqrt{-a} = i\sqrt{a}[/tex]
Therefore:
[tex]\displaystyle \begin{aligned} (-3\sqrt{-81})(-5+\sqrt{-9}) + 9i & = (-3i\sqrt{81})(-5+i\sqrt{9})+9i \\ \\ &= -(3i(9))(-5+i(3))+9i \\ \\ & = -27i(-5+3i)+9i \\ \\ & = 135i -81i^2 + 9i \\ \\ & = 144i - 81i^2 \\ \\ & = 81+144i\end{aligned}[/tex]
Note that i² = -1.
In conclusion:
[tex]\displaystyle (-3\sqrt{-81})(-5+\sqrt{-9})+9i = 81 + 144i[/tex]
Find the inverse. (SHOW WORK)
Let f(x) = y
y = log3(x+1) - 1
Plug x in y and y in x
x = log3(y+1) - 1
x + 1 = log3(y+1)
3^(x+1) - 1 = y
[tex]y = 3^{x+1}[/tex] - 1
This is the inverse function.
Hope it helps! xxxx
Answer:
y = [tex]3^{(x+1)}[/tex] -1
Step-by-step explanation:
x = [tex]log_{3}[/tex](y + 1) - 1
x + 1 = log₃(y + 1)
[tex]3^{(x+1)}[/tex] = y + 1
[tex]3^{(x+1)}[/tex] -1 = y
PLEASE HELP!!! What is factoring? Why is it useful to try to factor out the GCF first when factoring? Explain the relationship between factoring and multiplying polynomials. Give an example to help explain. Factor x^2-25, 3x^2-12x-15, and x^3+2x^2+3x+6 . What are the key features needed to graph a polynomial function? Explain how to find these key features to sketch a rough graph of a polynomial function. Why would someone want to factor a polynomial? Provide real world examples of different questions we can answer or facts we can determine from factoring a polynomial.
Answer:
What is factoring?Factoring is finding what to multiply to find an expression. It is like splitting expression into a multiplication of simplified expression.
Why is it useful to try to factor out the GCF first when factoring?Greatest common factor or GCF of two numbers is the largest number that divides evenly in both numbers, GCF works the same in polynomials, which divide the expression evenly .
Explain the relationship between factoring and multiplying polynomials. Give an example to help explainFactoring take away the multiplication, to factorize a polynomial it means take apart what is multiplied. the best example is a²+b²+2ab ( multiplied)
factorize :(a+b)(a+b) take apart what is multiplied
Factor x^2-25, 3x^2-12x-15, and x^3+2x^2+3x+6x²-25 =(x+5)(x-5)
3x²-12x-15 = 3(x²-4x-5) GCF=3
3(x-5)(x+1)
x³+2x²+3x+6 (x+2) common factor
(x+2)(x²+3)
What are the key features needed to graph a polynomial function?the key features are the vertex, axis of symmetry, x and y intercept
Explain how to find these key features to sketch a rough graph of a polynomial functionparabola : y=ax²+bx+c
ex: 3x²-12x-15
find vertex (h,k)
h=-b/2a =-(-12)/2(3)=2
k=f(h)=f(2)=3(2)²-12(2)-15
k=12-24-15=-27
vertex=(2,-27)
x intercept is when the graph =0 (y=0)
y intercept when x=0 then y= the constant c and where the graph cross the y axis
axis of symmetry is the x of the vertex: is a line about which a parabola is symmetrical and vertical when the axis of symmetric is vertical.
Why would someone want to factor a polynomial? Provide real world examples of different questions we can answer or facts we can determine from factoring a polynomial.factor a polynomial helps us understand more about equations,factoring helps us rewrite the polynomial into simpler expression.
example from real life:
A homeowner has a back yard and wants to turn it to garden beds so he can plant his vegetables, he wants to fill it with dirt he needs 240 cubic feet to fill it the length is 4 feet than the width , and the height is 4
solve:
length=W+4
height=1/3 w
V=length* width* height
240=(w+4)(w)(4)
351= 4w²+16w
4w²+16w-240=0
take 4 as common factor
4(w²+4w-60)
now factorize:
4(w-6)(w+10)=0
The parentheses are around 270-54, the value is _______. When the parentheses are around 54÷9, the value is _______.
What is the answer? I'm having trouble with GoMath! I can't seem to figure it out.
Answer:
Im pretty sure they stay the same. But that might just be me
Someone plzzzz help I don’t get this at all
Answer:
Option B
Step-by-step explanation:
The slope of the line BC is,
[tex] \frac{ - 2 - 8}{7 - 3} [/tex]
[tex] = \frac{ - 10}{4} = - \frac{5}{2} [/tex]
Since AD is altitude to BC, we can say AD is perpendicular to BC, so the slope of the line AD which is perpendicular line to BC will be,
[tex] \frac{2}{5} [/tex]
Helpppppppppppppppppppppppp im not smart pls don't just say some bull i need help ill just get it deleted
Answer:
a. 6m
b. m-2
c. 5(m-2)
d. 6m +5m -10= 56
E. 11m=66
divide by 6: m=6
Maple Granola= 6$
Apple Granola= 4$
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
ITS REALLY IMPORTANT
can somebody please explain how to find the surface and lateral area please and thank you!!
Answer:
The lateral area of the figure = 480 m²
The surface area = 720 m²
Step-by-step explanation:
By definition, we have;
The lateral area is the area of the vertically facing sides of or the area of the triangular faces of a pyramid
The surface area is the area of the entire surface = Lateral area + The other surface areas of the object
For a pyramid, the surface area = Lateral area + Area of base
The figure in the question is a pentagon based pyramid with five triangles on the sides
The lateral area of the figure = 5 × area of the 5 triangles = 5 × Base × Height
The lateral area of the figure = 5 × 12 × 8 = 480 m²
The lateral area of the figure = 480 m²
The surface area = Area of the base + Lateral surface area
Area of the regular pentagon base = 1/2 × Perimeter of the pentagon × Apothem
Perimeter of the pentagon = 5 × 12 = 60 m
Apothem = Perpendicular distance from the pentagon's side to the center = 8.3 m
∴ Area of the regular pentagon base = 1/2 × 60 × 8 = 240 m²
∴ The surface area = 240 +480 =720 m²
The surface area = 720 m²
-14 = x - 12 pls answer this if I can and check answer
Answer:
x = -2
Step-by-step explanation:
-14 = x - 12
-14 + 12 = x
-2 = x
check:
-14 = -2 - 12
SOMEONE PLZ HELP ASAP !!!!!!
Answer:
a = 53.13
b = 42.76
c= 0
Step-by-step explanation:
as the question said i was supposed to use a calculator which i did
Enter the values for the variables that give the correct simplified expressions, x=>=0; sqrt(50x ^ 2) = sqrt(25 - 2x ^ 2) = 5x * sqrt(b); b =; sqrt(32x) = sqrt(16.2x) = e * sqrt(2x); c =; sqrt(38n) = sqrt(8 * 2 * pi) = e * sqrt(2n); e =; sqrt(72x ^ 2) = sqrt(36 * 2 * x ^ 2) = gx * sqrt(2); g =
Answer:
b=2
c=4
e=3
g=6
Step-by-step explanation:
You need to prepare 30mL solution of a 1:8 syrup solution. You have on hand 50% syrup solution and a 1:20 soda solution. How many mL of each solution do you need to create the final solution?
Answer:
5 ml of 50% syrup solution will be used to create the final solution
Step by step Explanation:
Let the amount of 50% solution that was used = b
Which means ( 30 - b ) is the amount of 1/200 solution used then we can derive an equation as follows,
set up will then be,
0.5b +0.05(30 -b) = 1/8 (30)
We can simplifiy this as
0.5b+ 1.5 -0.05b = 3.75
Then make b the subject of the formula we have
0.45b = 2.25
b= 2.25/0.45
b = 5 ml
Therefore, 5ml of 50% syrup solution will be used to create the final solution
in the circle below, ...
Answer:
angle FEG = 66⁰
angle GFH = 90⁰
what is 1680 mm in feet
5.51181102 feet (5 feet 6 9⁄64 inches)
IT IS FOR NOW IM GIVING BRAINLIEST HRRY UP AND 10 POINTS Simplify the expression. What classification describes the resulting polynomial? (8x2 + 3x) − (12x2 − 1) A. linear binomial B. quadratic binomial C. quadratic trinomial D. linear monomial
Answer:
The equation would be a quadratic trinomial
Step-by-step explanation:
Step 1: Expand the equation to remove the brackets
0 = 8x² + 3x - 12x² + 1
Step 2: Collect like terms
0 = -4x² + 3x + 1
Step 3: Count number of terms
0 = -4x² + 3x + 1
1 2 3
Therefore there are 3 terms and this is a quadratic equation making the answer B, a quadratic trinomial
is {3,…} a defined set
Answer:
is infinite set... because dots meaning non stop