The terms through degree four of the Maclaurin series is [tex]f(x)=x+x^{2} +\frac{5x^{3} }{6} +\frac{5x^{4} }{6} +.....[/tex].
In this question,
The function is f(x) = [tex]\frac{sin(x)}{1-x}[/tex]
The general form of Maclaurin series is
[tex]\sum \limits^\infty_{k:0} \frac{f^{k}(0) }{k!}(x-0)^{k} = f(0)+\frac{f'(0)}{1!}x+\frac{f''(0)}{2!}x^{2} +\frac{f'''(0)}{3!}x^{3}+......[/tex]
To find the Maclaurin series, let us split the terms as
[tex]f(x)=sin(x)(\frac{1}{1-x} )[/tex] ------- (1)
Now, consider f(x) = sin(x)
Then, the derivatives of f(x) with respect to x, we get
f'(x) = cos(x), f'(0) = 1
f''(x) = -sin(x), f'(0) = 0
f'''(x) = -cos(x), f'(0) = -1
[tex]f^{iv}(x)[/tex] = cos(x), f'(0) = 0
Maclaurin series for sin(x) becomes,
[tex]f(x) = 0 +\frac{1}{1!}x +0+(-\frac{1}{3!} )x^{3} +....[/tex]
⇒ [tex]f(x)=x-\frac{x^{3} }{3!} +\frac{x^{5} }{5!}+.....[/tex]
Now, consider [tex]f(x) = (1-x)^{-1}[/tex]
Then, the derivatives of f(x) with respect to x, we get
[tex]f'(x) = (1-x)^{-2}, f'(0) = 1[/tex]
[tex]f''(x) = 2(1-x)^{-3}, f''(0) = 2[/tex]
[tex]f'''(x) = 6(1-x)^{-4}, f'''(0) = 6[/tex]
[tex]f^{iv} (x) = 24(1-x)^{-5}, f^{iv}(0) = 24[/tex]
Maclaurin series for (1-x)^-1 becomes,
[tex]f(x) = 1 +\frac{1}{1!}x +\frac{2}{2!}x^{2} +(\frac{6}{3!} )x^{3} +....[/tex]
⇒ [tex]f(x)=1+x+x^{2} +x^{3} +......[/tex]
Thus the Maclaurin series for [tex]f(x)=sin(x)(\frac{1}{1-x} )[/tex] is
⇒ [tex]f(x)=(x-\frac{x^{3} }{3!} +\frac{x^{5} }{5!}+..... )(1+x+x^{2} +x^{3} +......)[/tex]
⇒ [tex]f(x)=x+x^{2} +x^{3} - \frac{x^{3} }{6} +x^{4}-\frac{x^{4} }{6} +.....[/tex]
⇒ [tex]f(x)=x+x^{2} +\frac{5x^{3} }{6} +\frac{5x^{4} }{6} +.....[/tex]
Hence we can conclude that the terms through degree four of the Maclaurin series is [tex]f(x)=x+x^{2} +\frac{5x^{3} }{6} +\frac{5x^{4} }{6} +.....[/tex].
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A number line going from 0 to 1. the line is shaded from 0 to startfraction 7 over 12 endfraction. randy walks his dog each morning. he walks startfraction 7 over 12 endfraction of a mile in 7 minutes. how many miles does he walk in 1 minute? startfraction 7 over 12 endfraction divided by 7 =
Answer:
1/12 mile
Step-by-step explanation:
He walks 7/12 mile in 7 minutes.
In 1 minute, he walks 1/7 of the distance.
1/7 of 7/12 mile = 1/12 mile
(MID SCHOOL ALGEBRA)
can somebody explain to me from this image, why the -13x and +6 becomes +13x and -6?
Answer:
- (2x^2 - 13x + 6)
The above expression is in brackets and a negative sign is outside of the brackets. This means that when expanding the expression, we have to multiply each number with the negative sign (each number would switch their signs to the opposite one). Therefore, 2x^2 becomes -2x^2, -13x becomes 13x and 6 becomes -6.
2x-7>5
what value x represents?
please answer right or else I will report
Answer:
x > 6
Step-by-step explanation:
2x - 7 > 5
2x > 5 + 7
2x > 12
x > 6
Area of triangle in coordinate geometry
Ram sold to Shyam an article with 20% profit. Shyam sold same article for Rs. 504 with 5% profit to Ghanashyam. How much did it cost for Ram?
please do this with solutions quickly!!
Answer:
Rs 400 is the cost of an article for Ram.....
Step-by-step explanation:
X - cost of an article for Ram
120% = 1.2
1.2*X - Ram’s selling price
5% = 0.05
1.2*X*0.05 - Shyam selling price
1.2*X*0.05 = 504
X = Rs 400 is the cost of an article for Ram
Hope it Helps!!!!
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the properties to the regular polygons they describe.
A polygon is a figure that has a given number of sides.
What is a polygon?A polygon is an n - sided figure. The number of sides in a polygon is almost infinite. Let us now match the properties with the type of polygon.
a. 12.gon - An interior angle measures 150°
The polygon that has 12 sides is called the Dodecagon.
Given that the sum of the interior angles in a dodecagon is 1800, then each interior angle is; 1,800/12
= 150°
b. 15-gon - An exterior angle measures 24°
The polygon that contains 15 sides is called pentadecagon. Given that the sum of the exterior angles of polygon is 360 degrees and each exterior angle is 24° then;
360/ 24° = 15 sides
c. 16-gon - The sum of the interior angles is 2,520°
The polygon that contains 16 sides is called the hexadecagon. The sum of its interior angles is 2,520° hence each interior angle measures; 2,520°/16 = 157.5°
d. 18-gon - An interior angle measures 160°
A polygon that contains 18 sides is called an octadecagon .
We have;
160 = (n−2) × 180° / n
160n = 180n - 360
360 = 20n
n = 18
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Missing parts;
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the properties to the regular polygons they describe.
An interior angle measures 150".
An exterior angle measures 24.
The sum of the interior angles is 2520°.
An interior angle measures 160".
The sum of the exterior angles is 180º.
The sum of the interior angles is 2160°.
15-gon
16-gon
12.gon
18-gon
Answer:
15 gon = An exterior angle measure 2416 gon = The sum of the interior angles is 2,52012 = An interior angle measure 15018 = An interior angle measure 160Step-by-step explanation:
Complementary angles have measures (4x)° and (5x−27)°. find the measure of the larger angle.
Answer:
4x=90
X=90÷4
X=22.5
5x-27=90
5x=90+27
5x=117
X=117÷5
X=23.4
So 23.4 is a larger angle
What is the name of each of the two blue points in the hyperbola below?
A. Focus
B. Center
C. Vertex
D. Directrix
Ayudeme a resolver y poner signo positivo y negativo
Y no me borre la pregunta no es nada malo ;(
Debido a restricciones de extensión y la características del ejercicio, recomendamos leer la explicación de esta pregunta para mayores detalles sobre la adición de números enteros.
¿Cuáles son los resultados de cada suma?
En este ejercicio tenemos un grupo de sumas con números enteros positivos y negativos, en las cuales se prueba la capacidad del estudiante para realizar varias operaciones en serie (adición, sustracción) y comprender las diferencias entre números positivos, negativos y neutros. Ahora procedemos a determinar el resultado de cada una de las expresiones:
20 + 50 + 30 + 7 = 107
30 + 5 + 2 = 37
- 200 - 50 - 70 - 8 = - 328
- 500 + 100 - 20 + 50 = - 370
10 - 5 = 5
20 + 50 - 25 - 10 = 35
- 100 + 20 = - 80
- 30 + 5 + 4 - 20 + 8 = - 33
- 258 + 8 = - 250
- 10 + 20 + 520 - 100 + 8 = 438
- 20 - 5 - 42 + 3 = - 64
1000 - 200 + 50 + 30 - 45 + 75 - 87 + 90 + 50 - 100 + 50 - 10 = 903
- 400 + 500 - 200 - 50 + 48 + 8 - 47 - 50 = - 191
300 + 20 - 50 + 30 - 84 + 35 - 7 + 20 - 40 + 10 - 45 + 65 + 8 - 55 = 207
800 + 50 - 69 + 8 - 35 + 85 - 54 + 40 + 85 + 74 - 32 - 8 + 65 - 27 = 982
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Find the A.P whose second term is 12 and 7th term exceeds the 4th by 15
The 2nd term exists 12 and 7th term exceeds the 4th by 15 exists AP : 7,12,17,....
How to estimate the arithmetic progression?
Given : The second term exists 12th and the 7th term exceeds the 4th term by 15
The formula of the nth term :
[tex]$a_{n}=a+(n-1) d[/tex]
Where d exists a common difference
n be the number of terms
a be the first term
Substitute the value of n = 2
[tex]$a_{2}=a+(2-1) d=a+d[/tex]
Let, the second term exists 12
So, a + d = 12 ..........(1)
Substitute the value of n = 7
[tex]$a_{7}=a+(7-1) d=a+6 d[/tex]
Substitute n = 4
[tex]$a_{4}=a+(4-1) d=a+3 d[/tex]
We are given that the 7th term exceeds the 4th term by 15
So, a+6d-a-3d = 15
3d = 15
d = 5
Substitute the value of d in (1)
So, a+5 = 12
a = 12-5
a = 7
AP : a,a+d,a+2d,.... = 5, 7+5, 7+2(5),....=7,12,17,....
Therefore, AP : 7,12,17,....
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The volume of a spherical balloon is 20⅚πm³. Find the radius of the balloon.
Who can help me to answer this question? Please and thank you very much .
Answer: 2.5 meters
This value is exact without any rounding.
======================================================
Explanation:
The first task is to convert the mixed number 20⅚ into an improper fraction
I'll write 20⅚ as 20 & 5/6
The rule to use is a & b/c = (a*c + b)/c
So,
a & b/c = (a*c + b)/c
20 & 5/6 = (20*6+5)/6
20 & 5/6 = 125/6
This means the volume is exactly (125/6)pi cubic meters.
Plug this into the sphere volume formula and isolate the radius r like so
V = (4/3)*pi*r^3
(125/6)pi = (4/3)*pi*r^3
125/6 = (4/3)*r^3
(4/3)*r^3 = 125/6
4r^3 = 3*(125/6)
4r^3 = 125/2
r^3 = (125/2)*(1/4)
r^3 = 125/8
r = (125/8)^(1/3)
r = 5/2
r = 2.5
please please please
The amount of water in each mug is 2 / 5 litres
How to find the litres of water in each mug?The water bottle has 4/5 litres of water.
The litre of water is poured equally in 2 mugs.
Therefore, the amount of water in each mug can be calculated as follows;
amount of water in each mug = 4 / 5 ÷ 2
amount of water in each mug = 4 / 5 × 1 / 2
amount of water in each mug = 4 / 10
amount of water in each mug = 2 / 5 litres
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Help!!
why might you choose to write a recursive formula rather than an explicit formula to define a sequence
a. you need to know the 54th term in the sequence
b. the sequence is neither arithmetic or geometric
c. you need to know the value of three non-sequential terms in the sequence
d. the sequence is strictly geometric
We might choose to write a recursive formula rather than an explicit formula to define a sequence because (D) the sequence is strictly geometric.
What is a sequence?A sequence in mathematics is an enumerated collection of items in which repetitions are permitted and order is important. It, like a set, has members (also called elements, or terms). The length of the series is defined as the number of items (which could be infinite). Unlike a set, the same components can appear numerous times in a sequence at different points, and the order does important. Formally, a sequence can be defined as a function from natural numbers (the sequence's places) to the elements at each point. The concept of a sequence can be expanded to include an indexed family, which is defined as a function from an index set that may or may not contain integers to another set of elements.Recursive formulas are commonly used to compute the nth term of a sequence, where a(n) is the sum of all the preceding values.
Using its position, explicit formulas can compute a(n).
Therefore, we might choose to write a recursive formula rather than an explicit formula to define a sequence because (D) the sequence is strictly geometric.
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Answer: (D)
Step-by-step explanation:
took quiz
What is the sum?
A
B
C
D
Answer:
[tex]\displaystyle{\dfrac{5x-12}{(x+3)(x-3)} }[/tex]
Step-by-step explanation:
We are given the expression:
[tex]\displaystyle{\dfrac{3}{x^2-9} + \dfrac{5}{x+3}}[/tex]
First, factor the denominator [tex]\displaystyle{x^2-9}[/tex] to [tex]\displaystyle{(x+3)(x-3)}[/tex] via difference of two squares:
[tex]\displaystyle{\dfrac{3}{(x+3)(x-3)} + \dfrac{5}{x+3}}[/tex]
Next, multiply the expression 5/(x+3) by [tex]\displaystyle{x-3}[/tex] both denominator and numerator:
[tex]\displaystyle{\dfrac{3}{(x+3)(x-3)} + \dfrac{5(x-3)}{(x+3)(x-3)}}[/tex]
Add both together since they have same denominator now:
[tex]\displaystyle{\dfrac{3+5(x-3)}{(x+3)(x-3)} }[/tex]
Simplify the numerator:
[tex]\displaystyle{\dfrac{3+5x-15}{(x+3)(x-3)} }\\\\\displaystyle{\dfrac{5x-12}{(x+3)(x-3)} }[/tex]
Therefore, the sum is:
[tex]\displaystyle{\dfrac{5x-12}{(x+3)(x-3)} }[/tex]
Shandra drove 220 miles in 5 hours. if she continued at the same rate, how long would it take to travel 352 miles?
Answer:
8 Hours
Step-by-step explanation:
We know she travels 220 miles in 5 hours, so lets create an equation with a ratio which finds the miles she drives in a single hour, multiply that by x, and then set it equal to 352.
[tex]\frac{220}{5}x=352[/tex]
Multiply both sides by 5
[tex]220x=1760[/tex]
Divide both sides by 220
[tex]x=8[/tex]
Therefore it would take 8 hours.
8 Hours long would it take to travel 352 miles,
What is speed?The distance that an object travels in relation to the amount of time it takes to do so can be used to define speed. In other words, it is a measurement of an object's motion's speed without direction Velocities are what we get when speed and direction are combined. The SI unit system is most frequently used to express speed units. In that system, since distance is measured in metres and time is measured in seconds, speed is expressed in metres per second, or m/s. Three components make up the speed formula: distance, time, and speed.
We know she travels 220 miles in 5 hours, so lets create an equation with a ratio which finds the miles she drives in a single hour, multiply that by x, and then set it equal to 352.
Multiply both sides by 5
Divide both sides by 220
Hence, it would take 8 hours.
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Ask your teacher find the limit. use l'hospital's rule where appropriate. if there is a more elementary method, consider using it. lim x→1 [ln(x5 − 1) − ln(x3 − 1)]
Answer:
ln(5/3)
Step-by-step explanation:
The desired limit represents the logarithm of an indeterminate form, so L'Hopital's rule could be applied. However, the logarithm can be simplified to a form that is not indeterminate.
LimitWe can cancel factors of (x-1), which are what make the expression indeterminate at x=1. Then the limit can be evaluated directly by substituting x=1.
[tex]\diplaystyle \lim\limits_{x\to1}{(\ln(x^5-1)-\ln(x^3-1))}=\lim\limits_{x\to1}\ln{\left(\dfrac{x^5-1}{x^3-1}\right)}\\\\=\lim\limits_{x\to1}\ln\left(\dfrac{x^4+x^3+x^2+x+1}{x^2+x+1}\right)=\ln{\dfrac{5}{3}}[/tex]
If you use a 0. 025 level of significance in a (two-tail) hypothesis test, what is your decision rule for rejecting a null hypothesis that the population mean is 650 if you use the z test?
We have enough data to reject our null hypothesis if the value of our test statistics falls below critical values of z at a 1.25% level of significance (critical values are -1.645 and 1.645). This is because the test statistic value will not fall within this region.
Given that the population mean is 650, we do a two-tail hypothesis test with a level of significance of 0.025.
Let, μ = population mean
Thus, Null hypothesis, [tex]H_{0}[/tex]:μ= 650.
Alternate Hypothesis, [tex]H_{A}[/tex]:μ≠650
In this case, the population mean is equal to 650, according to the null hypothesis.
The alternative hypothesis, on the other hand, contends that the population mean is not 650.
First things first: the level of significance to be accepted for the two-tailed test is ([tex]\frac{\alpha }{2}[/tex]= [tex]\frac{0.025}{2}[/tex]) = 0.0125 or 1.25%.
Therefore, the following is the decision rule for rejecting a null hypothesis:
We have enough data to reject our null hypothesis if the value of our test statistics falls in the rejection region and is less than the critical values of z at a 1.25% level of significance (critical values are -1.645 and 1.645). This is because the test statistic value will not fall within this region.
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Find all values of x for which the series converges. (enter your answer using interval notation. ) [infinity] (4x)n n = 1
The series converges to 1/(1-9x) for -1/9<x<1/9
Given the series is ∑ [tex]9x^{n} x^{n}[/tex]
We have to find the values of x for which the series converges.
We know,
∑ [tex]ar^{n-1}[/tex] converges to (a) / (1-r) if r < 1
Otherwise the series will diverge.
Here, ∑ [tex](9x)^{n}[/tex] is a geometric series with |r| = | 9x |
And it converges for |9x| < 1
Hence, the given series gets converge for -1/9<x<1/9
And geometric series converges to a/(1-r)
Here, a = 1 and r = 9x
Therefore, a/(1-r) = 1/(1-9x)
Hence, the given series converges to 1/1-9x for -1/9<x<1/9
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A parabola has a vertex at (0,0). The equation for the directrix of the parabola is x = –4.
In which direction does the parabola open?
up
down
right
left
The direction does the parabola open is right. Option C
What is the equation of a parabola?
It is important to note that the general equation of a parabola is: y = a(x-h)² + k or x = a(y-k)² +h
where
⇒ (h , k) denotes the vertex.
Also, the standard equation of a regular parabola is y² = 4ax.
From the equation given , we have
The vertex of the parabola is at (0, 0)Directrix of the parabola is x = -4We know that when the vertex of the parabola is (0, 0) and the directrix is x = - a, the parabola will have the form;
y² = 4ax
It is important to note that ;
If the x - axis has a positive value, the parabola shifts to the leftif the x- axis has a negative value, the parabola shift to the rightFrom this, we can see that the parabola would open in the right direction
Thus, the direction does the parabola open is right. Option C
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Plsss helppp I’m dying!! —> Complete the square to determine if the equation is a circle, quadratic equation, or other
a) The equation represents an ellipse.
b) The equation represents a circle.
c) The equation represents a parabola.
How to infer the graphical form of a general equation
In this problem we have general equations of the form A · x² + B · y² + C · x + D · y + E = 0, which have to be modified into standard form to infer its graphical form. This procedure can be done by algebra properties:
16 · x² + 4 · y² + 96 · x - 8 · y + 84 = 0
[(4 · x)² + 2 · 12 · (4 · x)] + [(2 · y)² - 2 · 2 · (2 · y)] = - 84
[(4 · x)² + 2 · 12 · (4 · x) + 144] + [(2 · y)² - 2 · 2 · (2 · y) + 4] = 64
(4 · x + 12)² + (2 · y + 2)² = 64
4² · (x + 3)² + 2² · (y + 2)² = 64
(x + 3)² / 4 + (y + 2)² / 16 = 1 : Ellipse
x² + y² + 8 · x - 6 · y - 15 = 0
(x² + 8 · x) + (y² - 6 · y) = 15
(x² + 2 · 4 · x + 16) + (y² - 2 · 3 · y + 9) = 40
(x + 4)² + (y - 3)² = 40 : Circle
x² + 6 · x + 4 · y + 5 = 0
x² + 6 · x + 5 = - 4 · y
y = - (1 / 4) · x² - (3 / 2) · x - (5 / 4) : Parabola
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Evaluate each expression if x=2,y=-3 and z=1
Answer:
5) 26
6) 18
Step-by-step explanation:
Substitute the value of the variables in the expression and evaluate.
x = 2 ; y = -3 and z = 1
Absolute value: Absolute value of a real number is the non negative a value of x without regard its sign.
Example: I-3I = 3
I 3I = 3
5) 24 + Ix - 4I =24 + I 2 - 4I
= 24 + I-2I
= 24 + 2
= 26
6) 13 + I 8 +y I = 13 + I 8 + (-3)I
= 13 + I 5 I
= 13 + 5
= 18
Select the graph of the solution. Click until the correct graph appears. 3 x + 1 < 7
Answer:
Step-by-step explanation:
3x + 1 < 7...subtract 1 from both sides
3x < 7 - 1
3x < 6 ...divide both sides by 3
x < 6/3
x < 2
which means the second answer choice is correct!
Answer: Second Graph
Step-by-step explanation:
Given inequality
3x + 1 < 7
Subtract 1 on both sides
3x + 1 - 1 < 7 - 1
3x < 6
Divide 3 on both sides
3x / 3 < 6 / 3
x < 2
Apply the inequality to the graph
Since it is less than, the circle should be hollow
Since it is less than 2, the line should point to the left
Therefore, it should be the Second Graph
City community college plans to increase its enrollment capacity to keep up with an increasing number of student applicants. the college currently has an enrollment capacity of 2200 students and plans to increase its capacity by 70 students each year. what will the enrollment capacity be 3 years from now? a. 2480 b. 2410 c. 2340 d. 2240 please select the best answer from the choices provided a b c d
The correct option is B.
The enrollment capacity be 3 years from now is 2410
What is arithmetic sequence?A series of integers in which the difference between succeeding words is always the same is referred to as an arithmetic sequence or arithmetic progression. For instance, the difference in the arithmetic series 1, 5, 9, 13, 17,... is always 4. The common difference is what we refer to as.
How do you find arithmetic sequence?The formula for determining the nth term is used to locate a specific term in an arithmetic sequence. Step 1: An = a + (n - 1)d determines the nth term of an arithmetic series. Add the variables a = 2 and d = 3 to the formula in order to find the nth term.
According to the given information:At = a1 + (n - 1) x d is an equation that can be used to express the number of applications each year.
N equals 4 based on the information provided above. This corresponds to the term, which begins in three years.
At = 2200 + (4 - 1) x 70 = 2410
Thus, 2410 students could enroll at one time.
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Which of the following BEST defines an output? please help me, I've been stuck on this one for a while!
A statement which best defines an output is: B. an output is the result of a relation or the function rule, usually the y-values in a set of ordered pairs or on a table or graph.
What is a function?A function can be defined as a mathematical expression that defines and represents the relationship between two or more variable, which is typically modelled as input (x-values) and output (y-values).
The types of function.In Mathematics, there are different types of functions and these include the following;
Periodic functionInverse functionModulus functionSignum functionPiece-wise defined functionIn this context, we can infer and logically deduce that a statement which best defines an output is that it's the result of a relation or the function rule, which usually are the y-values in a set of ordered pairs, on a table or a graph.
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Complete Question:
Which of the following best defines an output?
A. An output is the value that determines another based on the relation or the function rule, usually the x-values in a set of ordered pairs or on a table or graph.
B. An output is the result of a relation or the function rule, usually the y-values in a set of ordered pairs or on a table or graph.
C. An output is a special type of relation for which there is a rule that pairs each input with exactly one output.
D. An output is a set of ordered pairs in which no y-value repeats.
. If (5, 7) and (-3, 0) lie on the line ax - by = -20.
i) Find the value of a & b. [IM]
ii) Write the equation of the line in standard form.
iii) Find the coordinate of the point of intersections of the given line with x-axis and y-axis respectively.
iv) Find two more solutions of the given line.
i) The coefficients of the equation of the line are a = 20 / 3 and b = 160 / 21.
ii) The equation of the line in standard form is (20 / 3) · x + (160 / 21) · y = - 20.
iii) The x-intercept and y-intercept of the line are (- 3, 0) and (0, - 21 / 8).
iv) Two alternative solutions of the equation of the line are 20 · x + (160 / 7) · y = - 60 and 140 · x + 160 = 420.
How to derive the equation of a line?
In this problem we know that form of an equation of the line and two points, on which the line pass through. i) We determine the values of the coefficients a and b by solving the following system of linear equations:
5 · a - 7 · b = - 20
- 3 · a = - 20
Whose solution is a = 20 / 3 and b = 160 / 21.
ii) The equation of the line in standard form is (20 / 3) · x + (160 / 21) · y = - 20.
iii) Now we find the coordinates of the intercepts of the line:
x-Intercept
(20 / 3) · x = - 20
x = - 3
y-Intercept
(160 / 21) · y = - 20
y = - 21 / 8
iv) We can find two alternative solutions by using multiples:
20 · x + (160 / 7) · y = - 60
140 · x + 160 = 420
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Which linear inequality is represented by the graph
Answer:[tex]\Large\boxed{First~choice.~y\leq \frac{1}{2}x+2 }[/tex]
Step-by-step explanation:
Determine the equation form of the inequalityGiven function form
Point-Slope form : y = mx + b
m = slopeb = y-interceptGiven the information from the graph
Since the graph crosses (0, 2), b = 2
Find the slope
Choose any two points from the graph
(x₁, y₁) = (0, 2)
(x₂, y₂) = (2, 3)
Slope = (y₂ - y₁) / (x₂ - x₁)
Slope = (3 - 2) / (2 - 0)
Slope = 1 / 2
m = 1 / 2
Therefore, the equation form of the inequality is y = (1/2)x + 2
Determine whether it is ≤ or ≥Since it is a solid line, the values on the line are also included. Thus, it must be either greater than or equal to, or less than or equal to.
The shaded region is below the solid line, therefore, it is ≤
Therefore, the inequality is [tex]\Large\boxed{y\leq \frac{1}{2}x+2 }[/tex]
To double-check the sign, we can substitute (0, 0) into the inequality to see whether it is true.
y ≤ (1/2) x + 2
0 ≤ (1/2) 0 + 2
0 ≤ 2 TRUE
Hope this helps!! :)
Please let me know if you have any questions
Evaluate each of the following
1: -21 ÷ 7
In order to solve a problem that begins with a negative number and is divided by a positive number, the answer must also be negative.
Divide 21 ÷ 7
we get = 3
Mark it as negative number = -3
Hope this helps :)
What type of number is -√/81?
Choose all answers that apply:
A. whole number
B. integer
C. rational
D. irrational
Answer:
Step-by-step explanation:
integer and rational
Figure 222 is a scaled copy of Figure 111.
PLEASE HELP
Identify the side in Figure 222 that corresponds to side \overline{CD}
CD
start overline, C, D, end overline in Figure 111.
Choose 1 answer:
Choose 1 answer:
25 Points please help me
ASAP and I will mark brainlyist
Answer:
(a)
1. 4.6... sample mean2. 4.6.. sample mean3. 4.8... sample mean4. 5.2... sample mean(b) range of sample means =0.6
(c)
FalseFalseFalseFalse