Answer:
Step-by-step explanation:
Given that:
[tex]\mathsf{f(x) = x^2 -5 } \\ \\ \mathsf{x_1 = 2}[/tex]
The derivative of the first function of (x) is:
[tex]\mathsf{f'(x) =2x }[/tex]
According to Newton's Raphson method for function formula:
[tex]{\mathrm{x_{n+1} = x_n - \dfrac{f(x_n)}{f'(x_n)}}[/tex]
where;
[tex]\mathbf{x_1 =2}[/tex]
The first iteration is as follows:
[tex]\mathtt{f(x_1) = (2)^2 - 5} \\ \\ \mathbf{f(x_1) = -1}[/tex]
[tex]\mathtt{f'(x_1) = 2(2)} \\ \\ \mathbf{ = 4}[/tex]
[tex]\mathtt{\dfrac{f(x_1)}{f'(x_1)}} = \dfrac{-1}{4}}[/tex]
[tex]\mathbf{\dfrac{f(x_1)}{f'(x_1)} =-0.25}[/tex]
[tex]\mathtt{x_1 - \dfrac{f(x_1)}{f'(x_1)}} = \mathtt{2 - (-0.25)}}[/tex]
[tex]\mathbf{x_1 - \dfrac{f(x_1)}{f'(x_1)} = 2.25}[/tex]
Therefore;
[tex]\mathbf{x_2 = 2.25}[/tex]
For the second iteration;
[tex]\mathtt f(x_2) = (2.25)^2 -5}[/tex]
[tex]\mathtt f(x_2) = 5.0625-5}[/tex]
[tex]\mathbf{ f(x_2) =0.0625}[/tex]
[tex]\mathtt{f'(x_2)= 2(2.25)}[/tex]
[tex]\mathbf{f'(x_2)= 4.5}[/tex]
[tex]\mathtt{ \dfrac{f(x_2)}{f'(x_2)}} = \dfrac{0.0625}{4.5}}[/tex]
[tex]\mathbf{ \dfrac{f(x_2)}{f'(x_2)} = 0.01389}[/tex]
[tex]\mathtt{x_2 - \dfrac{f(x_2)}{f'(x_2)}} = \mathtt{2.25 -0.01389}}[/tex]
[tex]\mathbf{x_2 - \dfrac{f(x_2)}{f'(x_2)} = 2.2361}}[/tex]
Therefore, [tex]\mathbf{x_3 = 2.2361}[/tex]
S varies inversely as G. If S is 8 when G is 1.5, find S when G is 3. a) Write the variation. b) Find S when G is 3.
Step-by-step explanation:
a.
[tex]s \: = \frac{k}{g} [/tex]
[tex]8 = \frac{k}{1.5} [/tex]
[tex]k \: = 1.5 \times 8 = 12[/tex]
[tex]s = \frac{12}{g} [/tex]
b.
[tex]s = \frac{12}{3} [/tex]
s = 4
How are we supposed to find the Perimeter?
Find the particular solution to a differential equation whose general solution and initial condition are given. (C is the constant of integration.) x(t)
simplest form 2 3/4 x 4/5 *
Answer:
2 1/5
Step-by-step explanation:
2 3/4 * 4/5
Change the mixed number to an improper fraction
( 4*2+3)/4 * 4/5
11/4 * 4/5
The 4 in the numerator and denominator cancel
11/5
Changing back to a mixed number
5 goes into 11 2 times with 1 left over
2 1/5
Answer:
[tex]2\frac{1}{5}[/tex]
Step-by-step explanation:
[tex]2\frac{3}{4}*\frac{4}{5}\\\frac{11}{4}*\frac{4}{5}\\\frac{11}{5}\\ 2\frac{1}{5}[/tex]
Find the interquartile range of the following data set.
Number of Points Scored at Ten Basketball Games
57 63 44 29 36 62 48 50 42 34
A.21
B.28
C.6
D.34
Answer:
[tex]\huge\boxed{IQR = 21}[/tex]
Step-by-step explanation:
The data set given is:
57,63,44,29,36,62,48,50,42,34
Arrange in ascending order:
29,34,36,42,44,48,50,57,62,63
Place parenthesis around the number making two equal sets.
(29,34,36,42,44) | (48,50,57,62,63)
↑ ↑
Q1 Q3
Q1 = 36 , Q3 = 57
So, IQR = Q3-Q1
IQR = 57-36
IQR = 21
Answer:
[tex]\huge \boxed{\sf A. \ 21}[/tex]
Step-by-step explanation:
The data set is given,
[tex]\sf 57 \ 63 \ 44 \ 29 \ 36 \ 62 \ 48 \ 50 \ 42 \ 34[/tex]
Arrange the data set in ascending order.
[tex]\sf 29 \ 34 \ 36 \ 42 \ 44 \ 48 \ 50 \ 57 \ 62 \ 63[/tex]
Split the data set into two equal sets.
[tex]\sf 29 \ 34 \ 36 \ 42 \ 44 \ \ \ 48 \ 50 \ 57 \ 62 \ 63[/tex]
Find the median of the lower half and upper half.
[tex]\sf Median \ of \ lower \ half = 36[/tex]
[tex]\sf Median \ of \ upper \ half = 57[/tex]
Interquartile range = median of upper half - median of lower half
[tex]\sf IQR = 57 - 36[/tex]
[tex]\sf IQR = 21[/tex]
The interquartile range for the number of points scored at ten basketball games is 21.
I need all the steps
Answer:
ig
Step-by-step explanation:
[tex](9-\sqrt{-8} )- (5 + \sqrt{-32} ) \\(9-5) + (-\sqrt{-8}- \sqrt{-32} )\\4 - \sqrt{-8} -\sqrt{-32} \\4-2i\sqrt{2} -4i\sqrt{2} \\4-6i\sqrt{2}[/tex]
10) An amount of $1500.00 is invested for 3 years at rate of 2% for the first year and 5%, for
the 2nd year and 6% for the 3rd year.
a) Calculate the interest amount you will get if this is simple interest?
b) How much more or less you will get if this is compound interest?
Answer:
the interest is 195dollars
for the following questions, determine how many solutions each equation has. if one solution, state the value of x. x+6+8=2x-x+14? and is it a No solution, or a many solution or is it a one solution?
Answer:
infinite solutions
Step-by-step explanation:
x+6+8=2x-x+14
x+6+8=x+14
x+14=x+14
14=14
or
x=x
plug in any number
2+6+8=2(2)-2+14
16=16
another example
8+6+8=2(8)-8=14
22=22
3.24 (4 being repeated) to a fraction
Answer:
146/45
Step-by-step explanation:
Let x represent the value of the number of interest. Then we can do the following math to find its representation as a fraction.
[tex]x=3.2\overline{4}\\10x=32.4\overline{4}\\10x-x=9x=32.4\overline{4}-3.2\overline{4}=29.2\\\\x=\dfrac{29.2}{9}=\boxed{\dfrac{146}{45}}[/tex]
__
Comment on procedure
The power of 10 that we multiply by (10x) is the number of repeated digits. Here, there is a 1-digit repeat, so we multiply by 10^1. If there were a 2-digit repeat, we would compute 10^2x -x = 99x to rationalize the number.
Luke owns a trucking company. For every truck that goes out, Luke must pay the driver $17 per hour of driving and also has an expense of $1.75 per mile driven for gas and maintenance. On one particular day, the driver drove an average of 40 miles per hour and Luke's total expenses for the driver, gas and truck maintenance were $522. Write a system of equations that could be used to determine the number of hours the driver worked and the number of miles the truck drove. Define the variables that you use to write the system.
Answer:
17h+1.75m=522 m=40h
Step-by-step explanation:
Let h= {the number of hours the driver drove}
Let m= the number of miles driven
The driver makes $17 for each hour working, so if the driver worked for hh hours, Luke would have to pay him 17h17h dollars. The cost of gas and maintenance is $1.75 per mile, so for mm miles Luke's costs would be 1.75m1.75m dollars. The total cost of the route 17h+1.75m17h+1.75m equals \$522:$522:
17h+1.75m=522
17h+1.75m=522
Since the driver drove an avearge of 40 miles per hour, if the driver drove hour, he would have driven 40 miles, and if the driver drove hh hours, he would have driven 40h40h miles, therefore mm equals 40h:40h:
m=40h
m=40h
Write System of Equations:
17h+1.75m= 522
m=40h
The truck is going for a run for 6 hours and the system of the equation to solve a further problem related to this is [tex]\rm{Cost}=17x+1.75y[/tex]
The following are the different costs of the truck that Luke must be pay while running a truck:
Luke must pay the driver $17 per hour of driving.A truck has an expense of $1.75 per mile driven for gas and maintenance.Let ' x ' be the total time of driving a truck in hours.
and ' y ' be the total mile distance that is covered by the truck.
Therefore, the system of the equation for the overall running cost for a truck is given below.
[tex]\rm{Cost}=17x+1.75y[/tex]
Now, On one particular day, the driver drove an average of 40 miles per hour, and Luke's total expenses for the driver, gas and truck maintenance were $522.
Thus,
The total distance traveled by truck is 40x.
That is,
[tex]y=40x[/tex]
Substitute the values and solve them further.
[tex]522=17x+1.75y\\522=17x+1.75 \times 40x\\522=17x+70x\\522=87x\\x=6[/tex]
Thus, the truck is going for a run for 6 hours and the system of the equation to solve the further problems related to this is [tex]\rm{Cost}=17x+1.75y[/tex]
To know more about variables, please refer to the link:
https://brainly.com/question/14393109
Solve x/5 - 1/2 = x/6 (make sure to type the number only)
X/5 -1/2 = x/6
Find the least common denominator of the 3 denominators:5,2,6
The limited is 30
Multiply all 3 fractions by 30:
6x -15 = 5x
Subtract 6x from both sides:
-15 = -x
Multiply both sides by -1:
X = 15
The admission to a local carnival ride is $8.25 per person and $1.50 for each ride.
Answer:
You would multiply 8.25 by 3 which equals 24.75. Then multiply 1.50 by 8 which is 12.00.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Please tell me the answer ASAP Lynette's average score on five tests is 18. If she scores 24 points on her sixth test, what is her average score on all six tests? Show Your Work
Answer:
The average score of 6 tests is 19.
Step-by-step explanation:
Given that the average score of 5 tests is 18. So first, we have to find the total number of scores for 5 tests :
[tex]let \: x = total \: no. \: of \: scores[/tex]
[tex] \frac{x}{5} = 18[/tex]
[tex]x = 18 \times 5[/tex]
[tex]x = 90[/tex]
We have found out that the total scores for 5 tests is 90. So we have to find the average of 6 scores :
[tex] \frac{x + 24}{5 + 1} = \frac{90 + 24}{6} = \frac{114}{6} = 19[/tex]
[tex] \LARGE{ \boxed{ \rm{ \pink{Solution : )}}}}[/tex]
Given:Average score in 5 tests = 18He scored 24 points in 6th pointTo FinD:Find the average score in all six tests?How to find?We need to know how to find the average
☄ For this case, We are gonna find average score...!
[tex] \large{ \boxed{ \sf{Avg. \: score = \frac{Total \: score}{No. \: of \: tests} }}}[/tex]
So, Let's proceed further towards solution....
Solution:We have,
Avg. score = 18No. of tests = 5Finding total score in 5 tests,
⇛ Total score = Avg. score × No. of tests
⇛ Total score = 18 × 5
⇛ Total score = 90
According to question,
He scored 24 marks in 6th test⇛ Total score now = 90 + 24 = 114
No. of tests = 6Finding the average score of 6 tests,
⇛ Avg. score = 114 / 6
⇛ Avg. score = 19 points
☄ Avg. score of lynette in 6 tests = 19
━━━━━━━━━━━━━━━━━━━━
For the functions f(x)=4x+5 and g(x)=6x+4, find (f∘g)(0) and (g∘f)(0).
Answer:
Step-by-step explanation:
f(g(0))=
g(0)= 6(0) + 4 = 0 + 4 = 4
f(4)= 4(4)+5 = 16 + 5 = 21
g(f(0))=
f(0)= 4(0)+5 = 0+5 = 5
g(5)= 6(5)+4 = 30+4= 34
Write an equation showing the relationship between the lengths of the three sides of a right triangle.
Answer:
Below
Step-by-step explanation:
First triangle)
This triangle is a right one so we will apply the pythagorian theorem.
● 25 is the hypotenus
● 25^2 = b^2 + 24^2
■■■■■■■■■■■■■■■■■■■■■■■■■■
Seconde triangle)
Again it's a right triangle
x is the hypotenus.
● x^2 = 12^2 +5^2
● 12^2 = x^2-5^2
■■■■■■■■■■■■■■■■■■■■■■■■■■
This is a right triangle
AC is the hypotenus.
● AC^2 = BC^2 + BA^2
Notice that: BC = BE+EC and BA=BD+DA
● AC^2 = (BE+EC)^2 + (BD+DA)^2
Answer: 2) b = 7 3) x = [tex]\sqrt{119}[/tex]
Step-by-step explanation:
Use Pythagorean Theorem: (leg₁)² + (leg₂)² = hypotenuse²
2) b² + 24² = 25²
b² + 576 = 625
b² = 49
[tex]\sqrt{b^2}=\sqrt{49}[/tex]
b = 7
3) 5² + x² = 12²
25 + x² = 144
x² = 119
[tex]\sqrt{x^2}=\sqrt{119}[/tex]
[tex]x=\sqrt{119}[/tex]
PLEASE HELP !! (4/5) -50 POINTS-
Answer:
2 -7 6 7
1 3 -4 5
1 6 -15 -6
Step-by-step explanation:
An augmented matrix is the coefficients of the variables and then the solution in rows
Rewriting the equations
2x -7y +6x = 7
x +3y -4z = 5
x +6y -15z = -6
The matrix is
2 -7 6 7
1 3 -4 5
1 6 -15 -6
Simplify -12w + 7w - 3 - 6
Answer: Hi!
We can simplify this by combining like terms:
-12w + 7w - 3 - 6
-12w + 7w = -5w
-3 - 6 = -9
Out equation now looks like this:
-5w - 9
There's nothing left to simplify, so we're done!
Hope this helps!
graph the linear equation. Find three points that solve the equation, the plot them on the graph. -2y= 5x +11
Answer:
Three points are (0,-5.5), (-1,-3), (-2.2,0) and graph is shown below.
Step-by-step explanation:
The given equation is
[tex]-2y=5x+11[/tex]
We need to find three points that solve the equation.
Put x=0,
[tex]-2y=5(0)+11[/tex]
[tex]-2y=11[/tex]
[tex]y=-5.5[/tex]
Put x=-1,
[tex]-2y=5(-1)+11[/tex]
[tex]-2y=6[/tex]
[tex]y=-3[/tex]
Put y=0,
[tex]-2(0)=5x+11[/tex]
[tex]5x=-11[/tex]
[tex]x=-2.2[/tex]
So, three points (0,-5.5), (-1,-3) and (-2.2,0) are the solutions of the given equation.
Plot these points on a coordinate plane and connect them by a straight line as shown below.
Write as an equation: The sum of a number and 12 is 78.
Answer:
x+12=78
Step-by-step explanation:
like that? x because its an unknown number but if you actually want to know the number just subtract 78-12 equals 66.
Answer:
n + 12 = 78
Step-by-step explanation:
Let n = number.
n + 12 = 78
Suppose that you are standing 150 feet from a building and the angle of elevation to the top of the building is 42°. What is the building's height?
Answer:
135.06 feet
Step-by-step explanation:
Since the side of the building makes a right triangle with the ground and you know one side length and the degree angle between you and the top of the building we can use trigonometric function to find the height of the building. So since we know one side other than the hypotenuse we can use tangent to solve. Tangent is the opposite side over the adjacent side of the known angle.
opposite side = x
adjacent side = 150 feet
angle = 42°
tan(42°) = x/150 feet
150 feet * tan(42°) = x
x = 135.06 feet
The given line segment has a midpoint at (−1, −2). On a coordinate plane, a line goes through (negative 5, negative 3), (negative 1, negative 2), and (3, negative 1). What is the equation, in slope-intercept form, of the perpendicular bisector of the given line segment? y = −4x − 4 y = −4x − 6 y = One-fourthx – 4 y = One-fourthx – 6
Answer:
y = -4x - 6.
Step-by-step explanation:
We are given (-5, -3), (-1, -2), and (3, -1) for points of a line. First, we need to find the slope.
(-2 - -3) / (-1 - -5) = (-2 + 3) / (-1 + 5) = 1 / 4.
A perpendicular bisector would have a slope of -4, which is the negative reciprocal of 1/4.
Now that we have the slope, we can say that the equation is y = -4x + b. To find what is b, we can say that y = -2 and x = -1.
-2 = -4(-1) + b
-2 = 4 + b
b + 4 = -2
b = -6
So, the equation of the perpendicular bisector is y = -4x - 6.
Hope this helps!
Answer:
y = -4x - 6.
Step-by-step explanation:
Just took the test and got it right
Two trains are moving towards each other on the same railroad track. From this track there's an offshoot piece of railroad − the length of which is shorter than the length of the train but longer than the length of one train car. How can the trains pass each other?
Answer:
one car at a time
Step-by-step explanation:
For each car in the shorter train* (A) ...
train A leaves one of its cars on the offshootboth trains move until train B can move the car from the offshoot to the portion of track away from train Atrain B moves to allow the cycle to repeatWhen there are no more train A cars in front of train B, both trains can continue on their journey.
We assume cars can be decoupled at any point in the train, so that any required order of cars can be preserved. We further assume that train B can move any one of train A's cars in addition to all of its own.
_____
* The total number of car lengths that must pass the offshoot is (at least) the product of the number of cars in both trains, so it doesn't seem to matter which train makes use of the offshoot. We choose to decouple the cars of train A so that the minimum number of cycles is required--even though each cycle is longer.
Which represents a measure of volume?
O 5 cm
O 5 square cm
05 cm
05 cm
Answer:
a) 5[tex]cm^{3}[/tex]
Step-by-step explanation:
Bodies have three dimensions (width, height and depth). Measuring volume is calculating the number of cubic units that can fit inside.
When raising to 3, these dimensions are included and therefore 5[tex]cm^{3}[/tex] is a measure of volume.
Answer:
5cm^3
Step-by-step explanation:
Volume for a form will always be in cubic units.
Area of a shape will always be in squared units.
Length will not be in cubic or squared units.
Hence, the first option is a measure for volume.
The second option is equal to 5cm^2 which represents a measure for area, as does the fourth option.
The third option represents a measurement of length, for example the length of a line segment or the height of a figure.
Determine the equation of the exponantial function with a common ratio of 2, a horizontal asymptote at y=4 and passin through the point (2,10).
Answer:
Step-by-step explanation:
Find the largest integer which belongs to the following interval: (−∞, 8)
Answer:
7
Step-by-step explanation:
The following range includes numbers from negative infinity to 8. But, 8 isn't included, because there is a parentheses not a bracket. So, basically you can have 7.9999999. But, it asks for an integer, so it is 7.
The largest integer which belongs to the interval: (−∞, 8) is 7
To determine the largest integer, we will first ascertain what the use of parentheses and brackets denote.
The use of parentheses ( ) stands for open interval, that is, the extreme numbers of the set are not included.
If the brackets [ ] were used instead, that will be closed interval, that is, the extreme numbers of the set are included.
Since ( ) were used in the question, that means the extreme numbers −∞ and 8 are NOT included in the set.
Now, let us define an integer.
An integer is a positive or negative whole number or zero.
Hence, the integers in the set will include: −∞+1, −∞ + 2, ... 5, 6, and 7.
The largest integer here is 7
Hence, the largest integer which belongs to the interval: (−∞, 8) is 7
Learn more in the link below:
https://brainly.com/question/13324131
Greg is 10 years older than his brother gabe. He is also 3 times as old as gabe. How old is Greg?
Answer: 30 i think 10x3=30
Step-by-step explanation:
Answer using the graph
Answer:
8
Step-by-step explanation:
f(x)=x²+4 ( find quadratic equation: given vertex)
g(x)=x+2 ( find linear equation : given 2 points)
(f-g)(-2)
(x²+4-x-2)of (-2)
x²-x+2 now find (f-g)(-2)
-2²-(-2)+2=4+2+2=8
graph the linear equation using the slope and y-intercept y=1/9x+5
Answer:
Slope= 1/9
Y-Intercept= 5
round 1,965 to the nearest tenth
Step-by-step explanation:
1965 round to the nearest tenth is 1970
Answer:
1965.0
Step-by-step explanation:
Alonso brings $21 to the market to buy eggs and avocados. He gets eggs that cost $2.50. Then, he notices
that the store only sells avocados in bags of 3 for $5. He wants to buy as many avocados as he can with his
remaining money.
Let B represent the number of bags of avocados that Alonso buys.
1) Which inequality describes this scenario?
Answer:
Step-by-step explanation:
The money Alonso has is $21 which he wants to use to buy eggs and Avocados. The eggs he bought costs $2.50. Therefore the money remaining after the egg is bought is $18.50 (21 - 2.50)
Each bag of avocado cost $5, therefore the number of bags that can be bought with $18.50 is:
Bags of Avocado = $18.50 / $5 = 3.7 = 3 (to the previous whole number).
This means that the maximum number of bags of Avocado that can be bought is 3 bags. It can be represented by the inequality:
Bags ≤ 3
Answer:
2.50 + 5B ≤ 21;
Step-by-step explanation:
Cost of eggs = $2.50
Cost of avocado = $5 (bag of 3)
Total budgeted amount = $21
Bags of avocado = B
Therefore :
(Cost of eggs + cost of avocado) ≤ total budgeted amount
($2.50 + $5(B)) ≤ 21
2.50 + 5B ≤ 21
5B ≤ 21 - 2.50
5B ≤ 18.50
B ≤ 18.50 / 5
B ≤ 3.7
Therefore the maximum number of bags can purchase is 3(whole number without exceeding $21)
