The solution is (x, y, z) = (-1, 0, -2)
Given equations are:
2x−y+2z=−6 ---------------(1)
−3y+z=−2 ------------------(2)
2x−3z=4 -------------------(3)
From (2), z = -2+3y
Substitute this into (1) and (3)
(1)⇒ 2x-y+2(-2+3y) = -6
⇒ 2x+5y-4=-6
⇒2x+5y = -2
and
(3) ⇒ 2x-3(-2+3y)=4
⇒ 2x-9y+6 = 4
⇒ 2x-9y=-2
Now solve 2x+5y = -2 and 2x-9y=-2
Subtracting the equations above,
14y = 0
⇒y=0
Then from 2x-9y=-2, x = -1
From (2),z = -2+3y
⇒ z = -2
So the solution is (x, y, z) = (-1, 0, -2)
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2.
If a train travels between two cities in 3 hours at an average speed of 65 miles per hour, how long
would it take at an average speed of 80 miles per hour?
Answer:
At 65mph the car traveled 195 miles in 3hrs.
So divide 195 miles by 80mph to get 2.4375 hrs
The total attendance at a science museum is modeled by the function f(x)=17,371(1.041)x. If the initial total attendance (that is, the total attendance when x=0) was measured January 1, 2013, what was the initial total attendance?
The initial total attendance at a science museum is modeled by the function f(x)=17,371(1.041)x will be 17371.
How to calculate the value?It should be noted that from the information, the total attendance at a science museum is modeled by the function
In this case, the total attendance when x=0 will be:
f(x) = 17,371(1.041)x.
f(x) = 17,371(1.041^0)
= 17371 × 1
= 17371
Therefore, the total attendance when x = 0 will be 17371.
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ILL GIVE BRANNIEST TO THE CORRECT ANSWER Find the coordinates of the point
7/10 of the way from A to B.
Answer: X = 8.4 Y= 3.5
Step-by-step explanation:
These questions are about calculus, I would greatly appreciate your help on both questions!
asap, please!
For the function f(x) =(4 sin x)/(1+cosx) , then f'(x) = 4/(1+cosx) using quotient rule of differentiation and f'(2) = 2.00
What is quotient rule for differentiation?Quotient rule for differentiation states that the differentiation the division of two functions u, v is given as
(u/v)' = (u' v - u v')/v² , where ' represents first derivative with respect to independent variable
Given f(x) = (4sinx)/(1+cosx)
let u =4 sin x , v = 1+cos x , u'=4cos x , v' = -sin x
Then f(x) =u / v
Using quotient rule of differentiation:
f'(x) = ( u' v -u v' )/v² = (4cosx(1+cosx) +4sin²x )/(1+cos x)²
f'(x) = = 4(cos x +cos² x +sin² x)/(1+ cos x)² = 4(cos x +1)/(1+ cos x)²
f'(x) = 4/(1+ cos x)
To find value of f'(x) at x= 2
f'(5) = 4/(1+cos2) = 2.000609= 2.00(rounding off )
Therefore if f(x) = (4x² tan x)/sec x then f'(x) = 4/(1+cos x) and f'(2) =2.00
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edie earned a gross pay of $927.88 last week. determine the amount that edie contributed to both social security and medicare
Based on the gross pay to Edie of $927.88, the amount contributed by Edie Social Security was $57.53 and the amount to Medicare was $13.45
How to find contribution to social security?The current Social Security tax rate is 6.2% which means that to find the Social Security tax that Edie will contribute will be:
= Social security tax rate x Gross pay of Edie
= 927.88 x 6.2%
= $57.52856
= $57.53
The Medicare tax rate is 1.45%. The Medicare tax can therefore be found by multiplying the gross pay by the Medicare tax rate:
= 927.88 x 1.45%
= $13.45
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a contractor purchases 3 dozen pairs of padded work gloves for $44.28. she incorrectly calculates the unit price as $14.76 per pair of the expense report. what is the correct unit price? what is the error?
The unit price of the pairs of padded will be $1.23 per pair. The error is the price of the pairs of pads should have been divided by 12.
What is the value of the expression?When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.
For $44.28 a contractor buys 3 dozen pairs of cushioned work gloves.
The unit price of the pairs of padded will be given as,
⇒ $44.28 / (12 x 3)
⇒ $1.23 per pair
The unit price of the pairs of padded will be $1.23 per pair.
The error is the price of the pairs of pads should have been divided by 12.
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Jill has 4 one-dollar bills, 3 quarters, 4 dimes, and 3 pennies. Mark has 3 one-dollar bills, 4 dimes, and 2 pennies. What is the difference between the amount of money Jill has and the amount of money Mark has? A B C $1.01 $1.76 $7.85 D $8.60.
Answer: Answer choice 'B'
Step-by-step explanation:
4.00 + 0.75 + 0.40 + 0.03 = $5.18. This is Jill's amount.
3.00 + 0.40 + 0.02 = $3.42. This is Mark's amount.
To find out how much more money Jill has in comparison to how much mark has, we need to subtract Jill's money by Mark's money ($5.18 - $3.42)
if done correctly, your answer should be $1.76 (answer 'B')
100 POINTS PLEASE ANSWER QUICK
Use the box plot below to answer the questions.
Part A: Estimate the IQR for the male data.
Part B: Estimate the difference between the median values of each data set.
Part C: Describe the distribution of the data and if the mean or median would be a better measure of center for each.
The median is a better measure of center for the male's data, while the mean is a better for the female's data.
What are quartiles?When we get data which can be compared relatively with each other, for finding quartiles, we arrange them in ascending or descending order.
Quartiles are then selected as 3 points such that they create four groups in the data, each groups approximately possessing 25% of the data.
(a) The IQR of the male's data
From the given male's boxplot, we have the following data elements;
Upper quartile (Q3) = 14
Lower quartile (Q1) = 2
Then the IQR is calculated as:
IQR = Q3 - Q1
So, we have:
IQR = 14 - 2
IQR = 12
Hence, the IQR for the given males' data is 12
(b) The difference between the median values can be calculated as;
Median of male's data = 14
Median of female's data = 9
The difference (d) between the median values is;
d = 14 - 9
d = 5
Hence, the difference between the median values of each data set is 5
(c) The distribution of data
It is found that the median is a better measure of center for the male's data, while the mean is a better measure of center for the female's data.
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The median is a better measure of center for the male's data, while the mean is a better for the female's data.
What are quartiles?
When we get data which can be compared relatively with each other, for finding quartiles, we arrange them in ascending or descending order.
Quartiles are then selected as 3 points such that they create four groups in the data, each groups approximately possessing 25% of the data.
(a) The IQR of the male's data
From the given male's boxplot, we have the following data elements;
Upper quartile (Q3) = 14
Lower quartile (Q1) = 2
Then the IQR is calculated as:
IQR = Q3 - Q1
So, we have:
IQR = 14 - 2
IQR = 12
Hence, the IQR for the given males' data is 12
(b) The difference between the median values can be calculated as;
Median of male's data = 14
Median of female's data = 9
The difference (d) between the median values is;
d = 14 - 9
d = 5
Hence, the difference between the median values of each data set is 5
(c) The distribution of data
It is found that the median is a better measure of center for the male's data, while the mean is a better measure of center for the female's data.
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HELP Trapezoid A'B'C'D' is the image of trapezoid ABCD under a rigid transformation.
The Image of the trapezoid under rigid transformation is given by A'B'C'D' attached below.
The unique process of changing an existing graph or graphed equation to create a completely different version of the given graph is known as graph transformation.
Without changing the figure, a transformation shifts it up, down, to the right, to the left, or diagonally.Rotation is the term used to describe the transformation of a figure around a specific point. A fixed point is used to rotate the figure either clockwise or counterclockwise.In the given figure we can see that the Trapezoid ABCD is rotated around a fixed point to get the image of the trapezoid A'B'C'D'.
So the figure gets a rotational transformation.
From the figure we can assume that the figure is rotated about 135° clockwise about a fixed point.
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Quantitative Reasoning :')
Answer:
Step-by-step explanation:
more taking a shower you use almost 3 gallons per a shower
Mathematics in the modern world
Answer:
Mathematics shaping the modern world.
The cost to rent a storage unit is different for two storage companies. Stack n’ Store charges $150 per month, plus a non refundable deposit of $175. Smart Storage charges $185 each month with no deposit. Complete the table showing the total cost for each company during the first six months and use it to answer the questions.
Lee plans to store clothes for four months. Which company offers the better deal?
After how many months is the total cost the same at both storage companies?
Month Cost at Stack n’ Store Cost at Smart Storage
1 $325 $185
2 $475 $370
3 $625 $555
4 $775 $740
5 $925 $925
6 $1075 $1100
The company that offers the better deal is Smart Storage.
After 5 months the cost would be the same at both storage companies.
What are the total costs?The equation that represent the total cost of renting at Stack n’ Store is:
Total cost = non refundable deposit + charge per month
Total cost in the first month : $175 x ($150 x 1 ) = $325
Total cost in the second month : $175 x ($150 x 2 ) = $475
Total cost in the third month : $175 x ($150 x 3 ) = $625
Total cost in the fourth month : $175 x ($150 x 4) = $775
Total cost in the fifth month : $175 x ($150 x 5) = $925
Total cost in the sixth month : $175 x ($150 x 6) = $1075
The equation that represent the total cost of renting at Smart Storage is:
Total cost = cost per month x number of months
Total cost in the first month : $185 x 1 = $185
Total cost in the second month : $185 x 2 = $370
Total cost in the third month : $185 x 3 = $555
Total cost in the fourth month : $185 x 4 = $740
Total cost in the fifth month : $185 x 5 = $925
Total cost in the sixth month : $185 x 6 = $1,110
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Question 2 (1 point)
To find which number is one thousand times larger than 2.3 x 10^2, you would do the following steps.
O a
O b
O c
Od
Change 1,000 to Scientific notation and then add to (2.3 x 10^2)
Change 1,000 to Scientific notation and then multiply by (2.3 x 10^6)
Change 1,000 to Scientific notation and then divide by (2.3 x 10^6)
Change 1,000 to Scientific notation and then subtract from (2.3 x 10^6)
The correct answer choice as required in the task content is; Choice B; Change 1,000 to Scientific notation and then multiply by (2.3 x 10^6).
To find which number is one thousand times larger than 2.3 x 10², Change 1,000 to Scientific notation and then multiply by (2.3 x 10²).
Scientific notationThis is a method of writing or of displaying real numbers as a decimal number between 1 and 10 followed by an integer power of 10.
which number is one thousand times larger than 2.3 x 10²
Change 1,000 to Scientific notation and then multiply by (2.3 x 10²)1000 to scientific notation
= 10³
2.3 x 10² × 1000
= 2.3 x 10² × 10³
= 2.3 × 10^5
Furthermore, scientific notation helps us to express numbers in decimal number between 1 and 10 followed by an integer power of 10. It also help us to represent numbers in this pattern.
Therefore, to find which number is one thousand times larger than 2.3 x 10², Change 1,000 to Scientific notation and then multiply by (2.3 x 10²).
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change the subject. make x the subject
Answer:
X= 1/y
Step-by-step explanation:
[tex]y = 1 - \frac{1}{ \sqrt{1} - \frac{1}{1 - x} } \\ y = 1 - \frac{1}{1 - \frac{1}{1 - x} } \\ y - 1 = - \frac{1}{1 - \frac{1}{1 - x} } \\ y - 1 = - \frac{1}{ \frac{1 - x - 1}{1 - x} } \\ y - 1 = - \frac{1 - x}{ - x} \\ y - 1 = \frac{1 - x}{x} \\ yx - x = 1 - x \\ yx = 1 \\ x = \frac{1}{y} [/tex]
Solve these questions
1) x +2x + x = 68
2) x+y+3y= 45
3) x+y-4z= -32
4) x+y+z= ?
5) -x + 8x= 63
6) 4x+3x-x=42
Same questions as the pic
Answer:
here is the answers
Step-by-step explanation:
sample:
1. 4x = 68
x = 68/4
x = 17
Solution :
1) x + 2x + x = 68
>> 4x = 68
>> x = 68 / 4
>> x = 17
2) x + y + 3y = 45
>> x + 4y = 45
>> 17 + 4y = 45
>> 4y = 45 - 17
>> 4y = 28
>> y = 28 / 4
>> y = 7
3) x + y - 4z = -32
>> 17 + 7 - 4z = -32
>> 24 - 4z = -32
>> -4z = -32 - 24
>> -4z = -56
>> z = 56 / 4
>> z = 14
4) x + y + z = ?
>> 17 + 7 + 14
>> 24 + 14
>> 38
5) -x + 8x = 63
>> 7x = 63
>> x = 63 / 7
>> x = 9
6) 4x + 3x - x = 42
>> 7x - x = 42
>> 6x = 42
>> x = 42 / 6
>> x = 7
How much is 2 tablets 3 x per day for 14 days
Answer:
84 tablets with 6 per day
K
Convert the angle to a decimal in degrees.
16°43'27"
The value of the angle 16°43'27"is approximately 16.724167 degrees.
A plane angle is measured in degrees, with the letter ° typically used to indicate that one full rotation is equal to 360 degrees.
The radian is the SI unit for measuring angles.1 degree = [tex]\frac{\pi}{180}[/tex] radiansA complete rotation around a circle is 180°.A degree is a narrow enough angle for many practical tasks where full degrees are enough for precision. In those instances when this is not the case, such as in astronomy or for geographic coordinates (latitude and longitude), degree measurements may be expressed in decimal degrees.To convert a degree from minutes and seconds to decimal we must know the relation between degree and minutes and seconds.
1 degree=60 minutes.
1 minute = 60 seconds.
The given angle is 16°43'27"
27 seconds = 27 ÷ 60 minutes = 0.45 minutes = 0.45 ÷ 60 degree =0.0075 degree
43 minutes= 43 ÷ 60 degree = 0.71666666..
Total angle in decimal = 16+0.71666666+0.0075 =16.7241666...
Therefore required angle ≈ 16.7241667 degrees.
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FG is perpendicular to DM, if DF = 4R, FM = r + 21, and DF = FM, what is the value of R?
Answer:
(r+21 ) / 4
Step-by-step explanation:
as we can see DF = FM
and DF = 4R , FM =r+21
so,
4R = r+21
=> R= (r+21)/4
Help asap please!! I don’t understand
Answer: 2+[tex]\frac{6x-2}{x(x-3)}[/tex] ==> x[tex]\neq[/tex]0, x[tex]\neq[/tex]3
Step-by-step explanation:
f(x)=2x^2-2
g(x)=x^2-3x
(f/g)(x)=
[tex]\frac{2x^2-2}{x^2-3x}[/tex]=
[tex]\frac{2x^2-6x+6x-2}{x^2-3x}[/tex]=
[tex]\frac{2x^2-6x+6x-2}{x^2-3x}[/tex]=
2+[tex]\frac{6x-2}{x^2-3x}[/tex]=2+[tex]\frac{6x-2}{x(x-3)}[/tex] ==> x[tex]\neq[/tex]0, x[tex]\neq[/tex]3
3. Jerry purchased two cans of paint. He used 6/4 of it. How much did Jerry have
used in decimal?
A. 6.40
B. 4.60
C. 1.50
D. 0.67
The amount used in decimal is 1.50
How to determine the amount used?The given parameters are
Cans = 2
Amount used = 6/4
The amount used in decimal is calculated as:
Amount used = 6/4
Divide 6 by 4
So, we have
Amount used = 1.50
Hence, the amount used in decimal is 1.50
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using associative property
(y+12)+28
If f(1)=6f(1)=6 and f(n)=f(n-1)-2f(n)=f(n−1)−2 then find the value of f(6)
The value of function f(n) = f(n - 1) - 2, at n = 6 is f(6) = -4
In this question,
we have been given a function f(n) = f(n - 1) - 2
Also, we have been given the value of function f(n) for n = 1
i.e., f(1) = 6
We need to find the value of f(6).
For n = 2,
f(2) = f(2 - 1) - 2
f(2) = f(1) - 2
f(2) = 6 - 2
f(2) = 4
For n = 3,
f(3) = f(3 - 1) - 2
f(3) = f(2) - 2
f(3) = 4 - 2
f(3) = 2
For n = 4,
f(4) = f(4 - 1) - 2
f(4) = f(3) - 2
f(4) = 2 - 2
f(4) = 0
For n = 5,
f(5) = f(5 - 1) - 2
f(5) = f(4) - 2
f(5) = 0 - 2
f(5) = -2
For n = 6,
f(6) = f(6 - 1) - 2
f(6) = f(5) - 2
f(6) = -2 - 2
f(6) = -4
Therefore, the value of function f(n) = f(n - 1) - 2, at n = 6 is f(6) = -4
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Express the given function
Answer:
f(x) = [tex]{\displaystyle {\sqrt[8]{x}}}[/tex]
Step-by-step explanation:
If we let
[tex]g(x) = x^2 - 3\\\\\rm Then \;f(g(x) \;also \;written\; as\; (f\;\circ \rm \;g) \;is\; f(x^2 - 3)\\\\For\; this \;to \;be\; \sqrt[8]{x^2-3} , \\\\\rm f(x) \;has\;to\;be\;\sqrt[8]{x}[/tex]
Write equation in slope-intercept form (9,-5) slope -4/3
The equation of the line in slope intercept form is y = (-4/3)x + 7.
According to the slope intercept form, the equation of a line is given as-
y = mx + c
where m is the slope and c is the y intercept.
Here we are given that an equation passes through the point (9,-5) and has a slope of -4/3.
According to the point slope form, the equation of a line passing through (x1, y1) and slope m is given as-
(y - y1) = m(x - x1)
Here,
x1 = 9, y1 = -5 and m = -4/3
Thus,
(y + 5) = -4/3(x - 9)
3(y + 5) = -4(x - 9)
3y + 15 = -4x + 36
3y = -4x + 21
y = (-4/3)x + 21/3
y = (-4/3)x + 7
This is our equation in slope intercept format as m = -4/3 and c = 7
Thus, the equation of the line in slope intercept form is y = (-4/3)x + 7.
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please help with this! i am stuck
The required simplification of the given expression [tex]=\lim_{x \to \infty} \frac{x^2-4x +4}{x^2-4}[/tex] is 1.
Given that,
To determine the simplified value of the expression [tex]=\lim_{x \to \infty} \frac{x^2-4x +4}{x^2-4}[/tex].
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Given expression,
[tex]=\lim_{x \to \infty} \frac{x^2-4x +4}{x^2-4}[/tex]
[tex]=\lim_{x \to \infty} \frac{x^2(1-4/x +4/x^2)}{x^2(1-4/x^2)}[/tex]
Now put limits, so 1 / x², 1 / x becomes zero so,
= 1
Thus, the required simplification of the given expression is 1.
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PLEASE HELP FAST I ONLY HAVE ONE HOUR!!!!!!
Find all the solutions to the equation 4x3 + 16x2 + 28x = 0. 0, negative 4 + 2 i StartRoot 3 EndRoot, negative 4 negative 2 i StartRoot 3 EndRoot 0, 4 + 2 i StartRoot 3 EndRoot, 4 minus 2 i StartRoot 3 EndRoot 0, negative 2 + i StartRoot 3 EndRoot, negative 2 minus i StartRoot 3 EndRoot 0, 2 + StartRoot 3 EndRoot, 2 minus i StartRoot 3 EndRoot
The required solution to the equation 4x^3 + 16x^2 + 28x = 0 is 0, -2 + i√3, -2 - i√3
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .
Now the given equation is,
4x^3 + 16x^2 + 28x = 0
Taking x common we get,
x(4x^2 + 16x + 28) = 0
So, we get
x = 0
And 4x^2 + 16x + 28 = 0
or, x^2 + 4x + 7 = 0
Thus from the above equation is of the form
ax^2 + bx + c = 0
where, a = 1, b = 4 and c = 7
Therefore solution of the above equation is given as,
x = [-b ± √(b^2 - 4ac)] / 2a
Putting the values we get,
x = [-4 ± √(4^2 - 4*1*7)] / 2*1
so, x = [-4 ± √(16 - 28)] / 2
x = [-4 ± √(- 12)] / 2
x = [-4 ± 2√(- 3)] / 2
or, x = [-2 ± √(- 3)]
Since √-1 = i
∴ √(- 3) = i√3
Thus,
x = -2 ± i√3
So, the required values of x are 0, -2 + i√3, -2 - i√3.
Thus, the required solution to the equation 4x^3 + 16x^2 + 28x = 0 is 0, -2 + i√3, -2 - i√3.
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PLEASE HELP in the figure below, what is the value of x? Show all work
Answer:
x=19
Step-by-step explanation:
All of the angles add up to 180 degrees since it is a straight angle. So, the equation is:
3x+7+90+x+7=180
You combine like terms:
4x+104=180
Then you subtract on both sides:
4x=76
Then you divide by 4 on both sides:
x=19
Follow the guided instructions below to create the line of reflection that would map the pink figure onto the blue figure.
Answer:
Slope of one of the dotted lines:
[tex]y=x[/tex] or [tex]y=x+5[/tex]
Slope of the line of reflection:
[tex]y=-x[/tex]
Step-by-step explanation:
When seeing the dotted lines, both of them have a rise & run of 1, indicating that y = x. However, one of the lines has a y-intercept of 5, making it y = x + 5. So, the slopes for the dotted lines are [tex]y=x[/tex] or [tex]y=x+5[/tex].
The line of reflection has a rise & run of -1, and goes through the origin, indicating that the equation is y = -x.
Find the vertex of the quadratic function f(x)=(x+3)2−4
The vertex form of the quadratic equation is y + 4 = (x + 3)² and the vertex of the parabola is (h, k) = (- 3, - 4).
How to find the vertex of the parabola from the expression of a quadratic equation
Herein we find the expression of a quadratic equation in vertex form, whose definition is shown below:
4 · p · (y - k) = (x - h)² (1)
Where:
h, k - Coordinates of the vertex.
p - Distance from the vertex to the focus.
Then, the vertex form of the quadratic equation is y + 4 = (x + 3)² and the vertex of the parabola is (h, k) = (- 3, - 4).
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