If G(x) = 1/x were shifted 4 units to the left and 4 units up , what would the new equation be?
Answers
Given: A function
\(G(x)=\frac{1}{x}\)Required: To determine the function's equation if G(x) is shifted 4 units to the left and 4 units up.
Explanation: The shifting of a function f(x) 'a' units to the left is f(x+c).
To shift a function f(x), 'b' units up is represented by adding 'b' to the function's value.
Hence, shifting the given function 4 units to the left and 4 units up is-
\(G(x)=\frac{1}{x+4}+4\)Final Answer: Option A is correct.
Related Questions
23. Kelvin travelled of his journey at 45 km/h and of the remaining journey at 90 km/h. The rest of his journey was completed in 1.2 h at an average speed of 100 km/h. What was the total time taken for the whole journey?
Answers
Answer:
4.6 hours
Step-by-step explanation:
we first need to calculate the total distance he covered and total time taken whole for the journey.
Distance= speed X time
time = Distance/speed
let the total distance be X. he covers 2/5 if the journey first.
2/5 = 0.4
Time = 0.4x/45 hours
the remaining journey is 3/5x
he covers 1/3 X 3/5= 0.2x
time taken = 0.2/90 X hours
the remaining distance = 100× 1.2 = 120km
we add 0.4x + 0.2x to get the fraction he had covered
0.6x.
the remaining distance was X - 0.6x = 0.4 X
thus 120 km represents 0.4x of the journey
we calculate now the value of X
0.4x = 120
X = 300km
Total time taken = 0.4x/45 + 0.2/90 + 1.2 hours
replace X to get time
2.7 hours + 0.7 hours + 1.2 hours
= 4.6 hours
Transform the given differential equation into an equivalent system of first-order differential equations.
X(4)-5x"-3x=5t3 sin (3t)
Let x1=x, x2=x', x3=x" and x4=x(3). Complete the system below
X1’=
X2’=
X3’=
X4’=
Answers
The system of first-order differential equations is as follows: \(x1'=x2, x2'=x3, x3'=5t^3sin(3t) - (x4-5x3+3x1)/5, x4'=x3.\)
X1’=x2
X2’=x3
\(X3’=5t^3sin(3t) - (X4-5x3+3x1)/5X4’= x3\)
The given equation is a third-order differential equation. To transform it into a system of first-order differential equations, we have to introduce three intermediate variables x2, x3 and x4. Thus, the new system of equations include the original equation, the equations of intermediate variables and the boundary conditions. The equations of the intermediate variables are \(x2'=x3, x3'=x4 and x4'=x3\). The equation of the original equation can be written as \(x1'=x2, x4-5x3+3x1=5t^3sin(3t)\). After substituting the equations of the intermediate variables, the equation of the original equation becomes \(x1'=x2, x3'=5t^3sin(3t) - (x4-5x3+3x1)/5.\) Therefore, the system of first-order differential equations is as follows: \(x1'=x2, x2'=x3, x3'=5t^3sin(3t) - (x4-5x3+3x1)/5, x4'=x3.\)
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Determine the measure of < 7
o 53
o 133
o 127
o 47
Answers
• 127
Explanation:
How to find 127,
The line is 180°, so you take 53 minus 180.
180-53=127
Hope this helps! Good luck :)
I think it’s 40%, am I correct?
Answers
my thought process is
There are 100 ticks (20 spaces with 5 marks)
the area it wants has 6 large spaces (6*5=30) and 3 marks
30+3 is 33
I need help with an online math class please. Thanks!
Answers
Answer:
turn off the WiFi. simple xD
The radius of the base of a cylinder is expanding at a constant rate of 3 mm/min. If the height of
the cylinder is a constant 20 mm, find the rate at which the VOLUME of the cylinder is changing at the
moment when the radius of the base of the cylinder is 10 mm. Also find the rate at which the SURFACE
AREA of the cylinder is changing at this same moment.
(V = r²h, SA=2лrh+2rr²)
I’m getting 1800pi mm^3/min for volume and 360pi mm^2/min for surface area but I’m not sure if it’s correct
Answers
The rate at which the volume of the cylinder is changing is 600 mm^3/min, and the rate at which the surface area is changing is 240π mm^2/min.
To find the rate at which the volume and surface area of the cylinder are changing, we can use the given formulas for volume and surface area and differentiate them with respect to time. Let's calculate the rates at the moment when the radius of the base is 10 mm.
Given:
Radius rate of change: dr/dt = 3 mm/min
Height: h = 20 mm
Radius: r = 10 mm
Volume of the cylinder (V) = \(r^2h\)
Differentiating with respect to time (t), we have:
dV/dt = 2rh(dr/dt) + \(r^2\)(dh/dt)
Since the height of the cylinder is constant, dh/dt = 0.
Substituting the given values:
dV/dt = 2(10)(20)(3) + (10^2)(0)
dV/dt = 600 + 0
dV/dt = 600 mm^3/min
Therefore, the rate at which the volume of the cylinder is changing at the given moment is 600 mm^3/min.
Surface area of the cylinder (SA) = 2πrh + 2π\(r^2\)
Differentiating with respect to time (t), we have:
dSA/dt = 2πr(dh/dt) + 2πh(dr/dt) + 4πr(dr/dt)
Again, since the height of the cylinder is constant, dh/dt = 0.
Substituting the given values:
dSA/dt = 2π(10)(0) + 2π(20)(3) + 4π(10)(3)
dSA/dt = 0 + 120π + 120π
dSA/dt = 240π mm^2/min
Therefore, the rate at which the surface area of the cylinder is changing at the given moment is 240π mm^2/min.
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Decompose 5/6
How can you solve this problem?
Answers
Answer:
3/6+2/6 or 1/6+1/6+1/6+1/6+1/6
Step-by-step explanation:
when you decompose a fraction ask yourself "what will add up to the numerator of the fraction?" when decomposing keep denominator the same.
3+2=5. answer 5/6
o
A toy rocket is shot vertically into the air from a launching pad 8 feet above the ground with an initial velocity of 72 feet per
second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function
h(t) = - 1612 + 72t + 8. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at second(s) after launch.
(Simplify your answer.)
The maximum height reached by the object is feet.
(Simplify your answer.)
Answers
Answer:
1845 totaly i help yo to up grade
Step-by-step explanation:
im help :)
perimiter question asap answer
Answers
The perimeter of the figure is 58 m.
To find the perimeter of the given figure we can divide the figure in three rectangles.
Rectangle 1:
Perimeter= 2 (l + w)
= 2(5 + 2)
= 2 x 7
= 14 m
Rectangle 2:
Perimeter= 2 (l + w)
= 2(5 + 1)
= 2 x 6
= 12 m
Rectangle 3:
Perimeter= 2 (l + w)
= 2(14 + 2)
= 2 x 16
= 32 m
So, the perimeter of the figure is
= 14 + 12 + 32
= 58 m
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2) Find the volume of the following cube:
511
5.ft
5.11
A.
B
O 25 ft.
15 ft.
O 5 ft.
125 ft.
C.
D
Answers
Answer:
A
Step-by-step explanation:
I think that is A.......
Here s a patter made from sticks
Answers
Answer:
Recursive formula of an arithmetic sequence is given by the expression,
Tn=a+(n−1)d
Where, Tn= nth term
a= First term of the sequence
n= Number of term
d= Common difference
Therefore, number of sticks in the 6th pattern are 32.
And number of sticks in the nth pattern are Tn=5n+2
From the picture attached,
Number of sticks in 1st pattern = 7
Number of sticks in 2nd pattern = 12
Number of sticks in 3rd pattern = 17
Sequence formed is 7, 12, 17..... nth term
This sequence has a common difference of 5 in each successive term so it will be an arithmetic sequence.
Therefore, nth term of the sequence will be,
Tn=a+(n−1)d
Tn=7+(n−1)5
Tn=5n+2
If n=6,
Tn=7+(6−1)5
Tn=7+25
Tn=32
Hope it helps !
Have a great day!
The interior angles formed by the sides of a quadrilateral have measures that sum to 360°.What is the value of x?
Enter your answer in the box.
x =
Answers
x = 59
Because opposite angles are congruent, this is an isosceles trapezoid. Meaning x and 2x + 3 equal 180, half of the total interior angle. If you out that into equation form: x + 2x + 3 = 180. After combining like terms: 3x + 3 = 180. Then subtract 3 from both sides: 3x = 177. 177/3 = 59. x = 59.
if you invest $550.00 and your annual interest is 4%, what will be the interest
Answers
The annual interest is $22.
What is simple interest?Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.
Simple Interest = (Principal × Rate × Time) / 100
Given;
Amount invested= $550
Annual interest= 4%
SI= 550*4*1/100
=5.5*4
=22
Therefore, the simple interest will be $22.
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Four scenarios of statistical studies are given below. Decide which study uses a sample statistic.
Answers
A sample statistic is the specific group that you will collect data from.
What is a sample statistic?A sample statistic is any number derived from your sample data. The sample average, median, sample standard deviation, and percentiles are some examples. Because it is based on data obtained through random sampling, which is a random experiment, a statistic is a random variable. As a result, a statistic is both known and random.
A population is an entire group about which you want to draw conclusions. A sample is the specific group from which you will collect data. The sample size is always less than the total population size.
A sample is an analytic subset of a larger population in statistics. The use of samples enables researchers to conduct studies with more manageable data and more quickly. Randomly drawn samples have little bias if they are large enough, but obtaining such a sample can be costly and time-consuming.
Note that an overview of sample was given as the information is incomplete.
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Tom owns a landscaping business. He charges $40 for a yard cleanup, $50 to mow a lawn, and $75 to mulch a yard. On average, it takes Tom 25 minutes for a yard cleanup, 40 minutes to mow a lawn, and 2 hours to mulch a yard. Tom's clients are Mr. Hansen, Ms. Martinez, and Mrs. Johnson. . Mr. Hansen paid $125 for lawn services this week. . Tom spent more than an hour at Ms. Martinez' house this week. • Mrs. Johnson wrote Tom a check for $165 for the week. Tom made $405 from his three clients this week.
Answers
Answer:
Ms. Martinez = Tom received $115, $75 to mulch the yard and $40 for a yard cleanup.
Step-by-step explanation:
Tom made $405 for the week from his three clients
Mr. Hansen paid Tom $125
Mrs. Johnson paid Tom $165
405-165-125=115
Ms. Martinez paid Tom $115, which meant that he would have cleaned the yard ($40) and mulch the yard ($75)
The unit amount and time for each service offered by Tom can be represented as equations. The conclusion from the given parameters are:
Mr. Hansen paid $125 to mow a lawn and to mulch a yard.Mrs. Johnson paid $165 for the three servicesMs. Martinez paid $115 for a yard cleanup and to mulch a yard.Given that:
Cost
\(\$40 \to\) Yard cleanup
\(\$50 \to\) Mowing a lawn
\(\$75 \to\) Mulching a yard
Time
\(2\ hrs \to\) Yard cleanup
\(40\ mins \to\) Mow a lawn
\(2\ hrs \to\) Mulching a yard
\(Total\ Earnings = \$405\)
From the question, we understand that:
\(Mr.\ Hansen = \$125\)
Recall that:
\(\$50 \to\) Mowing a lawn
\(\$75 \to\) Mulching a yard
Add up:
\(\$50 + \$75 = 125\)
This means that Mr. Hansen paid $125 to mow a lawn and to mulch a yard.
\(Mrs.\ Johnson= \$165\)
Recall that:
\(\$40 \to\) Yard cleanup
\(\$50 \to\) Mowing a lawn
\(\$75 \to\) Mulching a yard
Add up:
\(\$40 + \$50 + \$75 =\$165\)
This means that Mrs. Johnson paid $165 for the three services
The amount paid by Ms. Martinez is calculated as follows:
\(Mr.\ Hansen + Mrs.\ Johnson + Ms.\ Martinez = Total\ Earnings\)
Substitute known values
\(\$125 + \$165 + Ms.\ Martinez = \$405\)
\(\$290 + Ms.\ Martinez = \$405\)
Collect like terms
\(Ms.\ Martinez = \$405 - \$290\)
\(Ms.\ Martinez = \$115\)
This means that Ms. Martinez paid $115
Recall that:
\(\$40 \to\) Yard cleanup
\(\$75 \to\) Mulching a yard
Add up
\(\$40 +\$75 = \$115\)
This means that Ms. Martinez paid $115 for a yard cleanup and to mulch a yard.
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A couple lives in Florida for 1/3 of the year. Each year has 12 months. What fraction of a year, in twelfths, does the couple not live in Florida?
Answers
Answer:
4/12
Step-by-step explanation:
plz give me a brainlies
The couple did not live for 2/3 part of the year.
What is fraction?Fractions are used to represent smaller pieces (or parts) of a whole.
Given that, A couple lives in Florida for 1/3 of the year,
12*1/3 = 4
Therefore, they lived for 4 months there,
And, They did not live for 12 - 4 = 8 months.
8 months in fraction = 8/12 = 2/3
Hence, The couple did not live for 2/3 part of the year.
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The coordinate grid shows points A through K. What point is a solution to the system of inequalities? y < −2x + 10 y < 1 over 2x − 2 coordinate grid with plotted ordered pairs, point A at negative 5, 4 point B at 4, 7 point C at negative 2, 7 point D at negative 7, 1 point E at 4, negative 2 point F at 1, negative 6 point G at negative 3, negative 10 point H at negative 4, negative 4 point I at 9, 3 point J at 7, negative 4 and point K at 2, 3 I B A F
Answers
Answer:
I think that it could be A, or the third choice.
We need to see which points are solutions for the given system of inequalities, thus the solutions are points B and L.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
Solving a system of inequalities we have the system here;
y <-2x + 10
y < 1/(2x - 2)
A point is a solution of the system if and only if it is a solution for both inequalities.
Now, Shade the region below the like for x = 5.
y = -2(5) + 10
= -10 + 10
= 0
For x= 0
y = -2(0) + 10
= 0 + 10
= (0, 10)
The diagram is attached below.
So, only B and L are solutions for the system.
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When a constant force is applied to an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object
with mass 4 kg, the acceleration of the object is 9 m/s². When the same force acts upon another object, its acceleration is 6 m/s². What is the mass of this
object?
Answers
Step-by-step explanation:
a = k/m or ma = k
using 4 and 9 4* 9 = k = 36
then the equation becomes:
ma = 36
using a = 6
6 * m = 36 shows m = 6 kg
given the qintic equation below, solve it to find the values of x. 2x^5_6x^3_4x^2_2x+4 =0
Answers
9514 1404 393
Answer:
x = {-0.5-√1.25, -0.5+√1.25, 2, -0.5+i√0.75, -0.5-i√0.75}
Step-by-step explanation:
I like to use a graphing calculator to find clues as to the roots of higher-degree polynomials. Here, we see that x=2 is the only real rational root. Dividing that out by synthetic division, we see the remaining quartic factor is ...
2x^5 -6x^3 -4x^2 -2x +4 = 0
2(x -2)(x^4 +2x^3 +x^2 -1) = 0
We can recognize that the quartic factor is actually the difference of two squares:
x^4 +2x^3 +x^2 -1 = (x^2 +x)^2 -1 = 0
So it resolves to two quadratic factors.
(x^2 +x +1)(x^2 +x -1) = 0
One will have real roots, as shown by the graph. The other will have complex roots.
x^2 +x + 1/4 = 1 +1/4 . . . . complete the square for the factor with real roots
(x +1/2)^2 = 5/4
x = -1/2 ± √(5/4) . . . . . . irrational real roots
__
x^2 +x = -1 . . . . . . . . . . the quadratic factor with complex roots
(x +1/2)^2 = -1 +1/4 . . . complete the square
x = -1/2 ± i√(3/4) . . . . irrational complex roots
__
In summary, the values of x that satisfy the equation are ...
x = 2
x = -1/2 ± √(5/4)
x = -1/2 ± i√(3/4)
Find the value of x that makes quadrilateral ABCD a rectangle if BE = 3x+1 and ED = 5x-3
Answers
The value of x that makes quadrilateral ABCD a rectangle if BE = 3x+1 and ED = 5x-3 is x = 2.
What is a rectangle?A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason.
Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.
There are four vertices and four sides.
Every vertex has an angle of 90 degrees.
Equal and parallel opposed sides are bisected by a diagonal.
We know that the diagonals of a rectangle bisect each other.
Thus, for the quadrilateral to be a rectangle we have:
BE = ED
3x + 1 = 5x - 3
1 + 3 = 5x - 3x
4 = 2x
x = 2
Hence, the value of x that makes quadrilateral ABCD a rectangle if BE = 3x+1 and ED = 5x-3 is x = 2.
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Describe a situation that can be represented by the expression –15 + 8.
Answers
Answer:
-7
Step-by-step explanation:
Tiger Woods was 15 under par after the third round of a golf tournament, but was 8 over par for the fourth round. So, his score for the entire tournament was -15 + 8 = -7 (That is, 7 under par).
Calculate the Scale Factor given the points A( 12, 4) and A' (9, 3).
Answers
The Scale Factor is 0.75, or 3/4
What is scale Factor?Scale factor is a ratio of two related lengths, areas, volumes, or other quantities. It is used to describe how a figure is enlarged or reduced in size. For example, when a figure is enlarged, the scale factor is greater than one, and when a figure is reduced, the scale factor is less than one. Scale factors can be used to calculate the lengths of sides and areas of figures when one side or area is known.
The Scale Factor is calculated by dividing the coordinates of point A' (9, 3) by the coordinates of point A (12, 4). Therefore, the Scale Factor is 0.75, or 3/4.
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Which of the following represents the LCM of 98 ab^ 3 and 231 a^ 3 ?
Answers
The Least Common Multiple (LCM) for 98 and 231, notation LCM (98, 231), is 3234.
Solution by using the division method:
This method consists of grouping by separating the numbers that will be decomposed on the right side by commas while on the left side we put the prime numbers that divide any of the numbers on the right side. We starting with the lowest prime numbers, divide all the row of numbers by a prime number that is evenly divisible into 'at least one' of the numbers. We stop when it is no longer possible to divide (the the last row of results is all 1's). See below how it works step-by-step.
2 | 98, 231
3 | 49, 231
7 | 49, 77
7 | 7, 11
11 | 1, 11
1 | 1, 1
The LCM is the product of the prime numbers in the first column, so:
LCM = 2 . 3 . 7 . 7 . 11 = 3234
Solution by listing multiples:
This method consists of listing the multiples of all the numbers that we want to find the LCM. Multiples of a number are calculated by multiplying that number by the natural numbers 2, 3, 4, ..., etc. See below:
* The multiples of 98 are 98, 196, 294, 392, 490, 588, ..., 3234
* The multiples of 231 are 231, 462, 693, 924, 1155, ..., 3234
Because 3234 is the first number to appear on both lists of multiples, 3234 is the LCM of 98 and 231.
Hence the answer is The Least Common Multiple (LCM) for 98 and 231, notation LCM (98, 231), is 3234.
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Need help finding the length
Answers
Answer:
27
Step-by-step explanation:
First, we need to find x. We are given the perimeter, which is 2l + 2w, so from there, we have an equation of 2(4x-1) + 2(3x+2) = 100. By working through it, we get that x = 7. We're asked to find WX, so plug 7 into 4x - 1 and get 27.
Answer:
27 unitsStep-by-step explanation:
Perimeter of rectangle is 2(l) + 2(w).
The perimeter is given 100 units.
2(4x-1) + 2(3x+2) = 100
Solve for x.
8x-2+6x+4=100
14x+2=100
14x=98
x=7
Plug x as 7 for the side WX.
4(7) - 1
28-1
= 27
An insurance company claims that in the population of homeowners, the mean annual loss from fire is u-$5000 with a standard deviation of o-$250
distribution of loss is strongly right-skewed: Many policies have $0 loss, but a few have large losses.
If we create a sampling distribution with a sample of 64 homeowners, what is the z-score that corresponds to a sample average of $5100?
Round to four decimals
Type your answer.
1 point
Answers
Answer:
To find the z-score, we use the formula:
z = (x - mu) / (sigma / sqrt(n))
where:
x = sample mean = $5100
mu = population mean = $5000
sigma = population standard deviation = $250
n = sample size = 64
Substituting the values, we get:
z = (5100 - 5000) / (250 / sqrt(64))
z = 2.56
Therefore, the z-score that corresponds to a sample average of $5100 is 2.56 (rounded to four decimals).
Step-by-step explanation:
I clicked on the black picture. thought is was the box to enter the answer.
Graph the line. pllzzzzzzzz
Answers
Answer:
Step-by-step explanation:
X: -2, -1, 0, 1, 2,...
Y: -2, -1, 0, 1, 2,...
(y=x)
PLEASE HELP! I ONLY HAVE 8 MINUTES LEFT!
Answers
Mean, Median, Mode, Appropriate Measures, Standard
Deviation
Use this data set to answer all questions on this page.
513, 490, 496, 380, 490, 513, 503, 513, 500, 492
Question 1 Which of the following would be APPROPRIATE measure(s) of center. (1)Mean (2)Median (3) Mode. Question 2 Find the standard deviation. Round your answer to the tenths place(one decimal place)
Answers
Answer:
Question 1: The appropriate measures of center for this data set would be (1) Mean and (2) Median. There is no mode in this data set as there are no repeating values.
Question 2: To find the standard deviation, we first need to find the mean:
Mean = (513 + 490 + 496 + 380 + 490 + 513 + 503 + 513 + 500 + 492) / 10 = 494.0
Next, we find the difference between each data point and the mean:
(513 - 494.0), (490 - 494.0), (496 - 494.0), (380 - 494.0), (490 - 494.0), (513 - 494.0), (503 - 494.0), (513 - 494.0), (500 - 494.0), (492 - 494.0)
19, -4, 2, -114, -4, 19, 9, 19, 6, -2
Then we square each difference:
361, 16, 4, 12996, 16, 361, 81, 361, 36, 4
The sum of these squared differences is:
361 + 16 + 4 + 12996 + 16 + 361 + 81 + 361 + 36 + 4 = 14136
To find the variance, we divide the sum of squared differences by the number of data points minus one:
Variance = 14136 / 9 = 1570.7
Finally, we find the standard deviation by taking the square root of the variance:
Standard deviation = √1570.7 ≈ 39.6 (rounded to the tenths place)
Step-by-step explanation:
Can I get help with this, I’m so confused
Answers
The linear and exponential equations for the amount of money in the banks indicates;
TCF Bank Equation
y = 100·x + 1000
Well Fargo Bank Equation
y = (1.06)ˣ
The number of years it will take for both accounts to have the same amount of money is about 17 years
What is an exponential equation?An exponential equation is an equation of the form; y = a·bˣ, where the input variable, x is an exponent.
The equation for calculating the amount in each bank, based on the details are;
TCF Bank;
Amount invested = $1,000
Amount added each year = 100·x
The TCF Bank Equation is; y = 100·x + 1000Well Fargo Bank Equation
The percentage of the amount earned as interest each year = 6% = 0.06
The exponential equation for compound interest amount is; y = 1000·(1 + 0.06)ˣ
Therefore; y = 1000·(1.06)ˣ
The Well Fargo Bank Equation is; y = 1000·(1.06)ˣWhen the amount in the two accounts have the same amount of money, we get;
1000·(1.06)ˣ = 100·x + 1000
Therefore; (1.06)ˣ = (100·x + 1000)/1000 = 0.1·x + 1
(1.06)ˣ = 0.1·x + 1
Solving the above equation using the substitution method and graphing indicates that we get;
x = 0, and x ≈ 17.125732
Therefore, it takes about 17 years for the two accounts to have the same amount of money
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I have a question..
find the length of arc RS. Use 3.14 for Pi. Round to the nearest tenth
Answers
Answer:
See Explanation
Step-by-step explanation:
Your question seem incomplete; however, I'll give a general guideline you can follow when solving for length of an arc.
The length of an arc is calculated as follows;
Length = θ/360 * 2πr
Where θ is the central angle and r is the radius
Take for instance, θ = 60 and r = 6cm
The solution will be;
Length = 60/360 * 2 * 3.14 * 6cm
Length = ⅙ * 2 * 3.14 * 6cm
Length = 6.28cm
So, for any values of θ and π, you'll get your results when you apply the above formula.
Answer:
try 16.96?
Step-by-step explanation: