Answer:
18 inches by 80 inches
Step-by-step explanation:
The given relations can be used in conjunction with the Pythagorean theorem to find the rectangle dimensions.
__
setupLet x and y represent the width and length of the rectangle, respectively. One of the relations is that between length and width:
y = 2x +44 . . . . . length is 44 more than twice the width
The other relation is described by the Pythagorean theorem. The square of the diagonal is the sum of the squares of the length and width:
x² +y² = (y +2)²
__
solutionExpanding the second equation, and subtracting y², we find ...
x² +y² = y² +4y +4
x² = 4y +4
Substituting for y using the first equation gives the quadratic ...
x² = 4(2x +44) +4
x² = 8x +180 . . . . . . . eliminate parentheses
x² -8x +16 = 196 . . . . add 16 -8x to make perfect squares
(x -4)² = 14²
We're only interested in the positive solution, so ...
x = 4 +14 = 18 . . . . . . . . square root, add 4
y = 2(18) +44 = 80
The dimensions of the rectangle are 18 inches wide by 80 inches long.
_____
Check
The diagonal is √(18² +80²) = √6724 = 82.
The value of x for the function f(x) = 100+ 0.3x is 210, when
f(x) = 121. True Or False
Answer:
false
Step-by-step explanation:
the answer is x=70
graph x=4y , x+y=7.0
Answer:
First find the x and y intercepts. Recall that intercepts intersect the x and y axis of a graph, therefore either the x or y value of a coordinate point must be 0 in order for it to be an intercept.
After you find the intercept, plot the them on the cartesian coordinate system and draw a straight line (it’s a linear equation) going through the two intercepts.
Side note: Not sure how credentials work on Quora yet. I meant to say I am a student
The equation of the lines can be plotted on the graph after calculating the coordinates on each line.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have two linear equation:
x = 4y
x + y = 7.0
To plot the linear equation first we will find the few coordinates to plot on the coordinate plane.
For the equation of line:
x = 4y
x 0 1 2 3 -1 -2 -3
y 0 4 8 12 -4 -8 -12
For the equation of line:
x + y = 7.0
x 0 1 2 3 -1 -2 -3
y 7 6 5 4 8 9 10
Thus, the equation of the lines can be plotted on the graph after calculating the coordinates on each line.
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Need help with number 2 please!!!
Answer:
Function g(x) is function f(x) vertically stretched by a factor of 6, reflected in the x-axis, and translated 2 units up.
Step-by-step explanation:
The graph of function f(x) is the parent function.
(Parent functions are the simplest form of a given family of functions).
The graph of g(x) is related to the graph of f(x) by a series of transformations. To determine the series of transformations, work out the steps of how to go from f(x) to g(x).
Transformations
For a > 0
[tex]\begin{aligned} y =a\:f(x) \implies & f(x) \: \textsf{stretched/compressed vertically by a factor of }\:a \\& \textsf{If }a > 1 \textsf{ it is stretched by a factor of}\: a\\& \textsf{If }0 < a < 1 \textsf{ it is compressed by a factor of}\: a \end{aligned}[/tex]
[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]
[tex]y=f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
Parent function:
[tex]f(x)=x^3[/tex]
Step 1
Multiply the parent function by 6:
[tex]\implies 6f(x)=6x^3[/tex]
Therefore, this is a vertical stretch by a factor of 6.
Step 2
Now make the function negative:
[tex]\implies -6f(x)=-6x^3[/tex]
Therefore, this is a reflection in the x-axis.
Step 3
Finally, add 2 to the function:
[tex]\implies -6f(x)+2=-6x^3+2[/tex]
Therefore, the function has been translated 2 units up.
Conclusion
Function g(x) is function f(x) vertically stretched by a factor of 6, reflected in the x-axis, and translated 2 units up.
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(1 point)Let S be the part of the plane 2x+2y+z= 1 which lies in the first octant, oriented upward. Find the flux of the vector field
F = 2i+2j + 2k across the surface S.
The flux is 9.
What is Flux?Flux is the presence of a force field in a specified physical medium, or the flow of energy through a surface.
Given:
2x+2y+z= 1
F = 2i+2j + 2k
Now,
r = xi + yj + z( 1-2x-2y) K
dr/dx= i - 2k
dr/dy = j-2k
dr/dx* dr/dy
= ( i - 2k) * (j-2k)
= 2i + 2j + k
F(x)= 2i+2j + 2k
F(x). da = 4 +4 +2 = 10 dxdy
Hence, flux
= [tex]\int\limits^1_0 {\int\limits^{1-2y}_0 {10 } \, dx dy } \,[/tex]
= [tex]\int\limits^1_0[/tex] 10(1-2y) dx
= [tex]\int\limits^1_0[/tex] 10-2y
= 10(1) - (1)²
=9
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The plane has intercepts (1/2, 0, 0), (0, 1/2, 0), and (0, 0, 1). Parameterize [tex]S[/tex] by the vector function
[tex]\vec s(u,v) = \dfrac{(1-u)(1-v)}2 \, \vec\imath + \dfrac{u(1-v)}2 \, \vec\jmath + v \,\vec k[/tex]
with [tex]0\le u\le1[/tex] and [tex]0\le v\le1[/tex]. (More explicitly, we have the parameterization
[tex]\vec s(u,v) = (1-v)((1-u) p_1 + u p_2) + v p_3[/tex]
where [tex]p_i[/tex] denote the given points.)
The normal vector to [tex]S[/tex] is
[tex]\vec n = \dfrac{\partial\vec s}{\partial u} \times \dfrac{\partial\vec s}{\partial v} = \dfrac{1-v}2\,\vec\imath + \dfrac{1-v}2\,\vec\jmath + \dfrac{1-v}4\,\vec k[/tex]
Then the flux of [tex]\vec F = 2\,\vec\imath+2\,\vec\jmath+2\,\vec k[/tex] across [tex]S[/tex] is given by the surface integral,
[tex]\displaystyle \iint_S \vec F \cdot d\vec\sigma = \iint_S \vec F \cdot \vec n \, dA[/tex]
[tex]\displaystyle = \int_0^1 \int_0^1 \left(2\,\vec\imath+2\,\vec\jmath+2\,\vec k) \cdot \left(\frac{1-v}2\,\vec\imath + \frac{1-v}2\,\vec\jmath + \frac{1-v}4\,\vec k\right) \, du \, dv[/tex]
[tex]\displaystyle = \frac52 \int_0^1 \int_0^1 (1-v) \, du \, dv[/tex]
[tex]\displaystyle = \frac52 \int_0^1 (1-v) \, dv = \boxed{\frac54}[/tex]
evaluate question 3 only
Step-by-step explanation:
(4²-x²)³/²
or,(4+X) (4-X)
Substitute [tex]x = 4 \sin(y)[/tex], so that [tex]dx = 4\cos(y)\,dy[/tex]. Part of the integrand reduces to
[tex]16 - x^2 = 16 - (4\sin(y))^2 = 16 - 16 \sin^2(y) = 16 (1 - \sin^2(y)) = 16 \cos^2(y)[/tex]
Note that we want this substitution to be reversible, so we tacitly assume [tex]-\frac\pi2\le y\le \frac\pi2[/tex]. Then [tex]\cos(y)\ge0[/tex], and
[tex](16-x^2)^{3/2} = 16^{3/2} \left(\cos^2(y)\right)^{3/2} = 64 |\cos(y)|^3 = 64 \cos^3(y)[/tex]
(since [tex]\sqrt{x^2} = |x|[/tex] for all real [tex]x[/tex])
So, the integral we want transforms to
[tex]\displaystyle \int (16 - x^2)^{3/2} \, dx = 64 \int \cos^3(y) \times 4\cos(y) \, dy = 256 \int \cos^4(y) \, dy[/tex]
Expand the integrand using the identity
[tex]\cos^2(x) = \dfrac{1+\cos(2x)}2[/tex]
to write
[tex]\displaystyle \int (16 - x^2)^{3/2} \, dx = 256 \int \left(\frac{1 + \cos(2y)}2\right)^2 \, dy \\\\ = 64 \int (1 + 2 \cos(2y) + \cos^2(2y)) \, dy \\\\ = 64 \int (1 + 2 \cos(2y) + \frac{1 + \cos(4y)}2\right) \, dy \\\\ = 32 \int (3 + 4 \cos(2y) + \cos(4y)) \, dy[/tex]
Now integrate to get
[tex]\displaystyle 32 \int (3 + 4 \cos(2y) + \cos(4y)) \, dy = 32 \left(3y + 2 \sin(2y) + \frac14 \sin(4y)\right) + C \\\\ = 96 y + 64 \sin(2y) + 8 \sin(4y) + C[/tex]
Recall the double angle identity,
[tex]\sin(2y) = 2 \sin(y) \cos(y)[/tex]
[tex]\implies \sin(4y) = 2 \sin(2y) \cos(2y) = 4 \sin(y) \cos(y) (\cos^2(y) - \sin^2(y))[/tex]
By the Pythagorean identity,
[tex]\cos(y) = \sqrt{1 - \sin^2(y)} = \sqrt{1 - \dfrac{x^2}{16}} = \dfrac{\sqrt{16-x^2}}4[/tex]
Finally, put the result back in terms of [tex]x[/tex].
[tex]\displaystyle \int (16 - x^2)^{3/2} \, dx \\\\ = 96 \sin^{-1}\left(\frac x4\right) + 128 \frac x4 \frac{\sqrt{16-x^2}}4 + 32 \frac x4 \frac{\sqrt{16-x^2}}4 \left(\frac{16-x^2}{16} - \frac{x^2}{16}\right) + C \\\\ = 96 \sin^{-1}\left(\frac x4\right) + 8 x \sqrt{16 - x^2} + \frac14 x \sqrt{16 - x^2} (8 - x^2) + C \\\\ = \boxed{96 \sin^{-1}\left(\frac x4\right) + \frac14 x \sqrt{16 - x^2} \left(40 - x^2\right) + C}[/tex]
When treated with an antibiotic, 92% of all the dolphins are cured of an ear infection. If 7 dolphins are treated, find the probability that exactly 4 are cured.
The probability is
(Round your answer to 4 decimal places.)
The probability that exactly 4 are cured from 7 dolphins is 0.0128
What is Probability ?Probability is the likeliness of an event to occur and it has a range of 0 to 1, where 0 means unlikely and 1 indicates certainty of the event to happen.
It is given that the 92% of all the dolphins are cured of an ear infection ,When treated with an antibiotic
If there are total dolphins given as 7
On the basis of given data
The dolphin that cannot be cured is given by
1 - p = 1 - (92/100) = 0.08 = 8/100
q = (8/100)
n= 7
r = 4
Therefore by Binomial Distribution
[tex]P = ^nC_r p^r q^{n-r}[/tex]
Putting the values
[tex]P = ^7C_4 (\dfrac{92}{100})^4 (\dfrac{8}{100})^{7-4}[/tex]
[tex]P = \dfrac{7!}{4! \;3!} (\dfrac{92}{100})^4 (\dfrac{8}{100})^{7-4}[/tex]
P = 0.0128
Therefore the probability is 0.0128.
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Steve bought a new car for $22,000 but paid 93% of the list price. How much was the list price
Answer:
approximately $23,655.91 (rounded to the nearest hundredths place)
Step-by-step explanation:
[tex]22,000=0.93x\\x=23,655.91[/tex]
Answer:
Step-by-step explanation:
let the list price=x
93% of x=22,000
x=22,000 ×100/93
≈23,655.91 $
The function G is defined by g (X) =X^2+2
Find g(4n)
Answer:
the answer is 4gn Puig IT in
Write and solve an inequality that means a number plus six is less than or equal to twenty-four.
Answer:
Inequality: x + 6 ≤ 24
Solution: x ≤ 18
Step-by-step explanation:
Plus: "+" → to add something to something else
Less than or equal to: "≤" → the expression on the left side of the inequality sign is smaller than the expression on the right side of the sign.
Let x be the unknown number.
A number plus 6 is less than or equal to twenty-four:
x + 6 ≤ 24
To solve the found inequality, subtract 6 from both sides:
⇒ x + 6 - 6 ≤ 24 - 6
⇒ x ≤ 18
Therefore, the solution to the inequality is x ≤ 18. The unknown number x can be any real number equal to or less than 18.
No be n
n+6≤24Solve
n≤24-6n≤18Solution set
(-oo,18]Solve for x in the inequality |2x + 5| ≤ 11. (If this is an "and" inequality, give your answer as a single compound inequality. If this is an "or" inequality, separate your answers using a comma.) Solve for x in the inequality | 2x + 5 | ≤ 11. ( If this is an " and " inequality , give your answer as a single compound inequality . If this is an " or " inequality , separate your answers using a comma . )
|2x + 5| ≤ 11
x = 3
2(3) + 5
6 + 5
11 ≤ 11
The solution for the x in the inequality |2x + 5| ≤ 11 is {-8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3}
What is inequality?Inequality shows relation between two expression which are not equal to each others.
The given inequality is,
|2x + 5| ≤ 11
To find the solution for the x, solve the inequality,
|2x + 5| ≤ 11
-11 ≤ 2x + 5 ≤ 11
Subtract 5 from whole the expression,
-11 - 5 ≤ 2x + 5 - 5 ≤ 11 - 5
-16 ≤ 2x ≤ 6
-8 ≤ x ≤ 3
The value of x for the given inequality varies from -8 to 3.
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Select the correct answer from each drop-down menu. Consider this system of equations: (equation A) (equation B) The solution for the system of equations is .
The solution for the system of equations is: (99/13, 150/13)
Given the two expression 2/3x+3/5y=12 and 5/2y-3x=6
We have to find solution of two given expression.
To find the value of x, we have to eliminate y by making y the subject of formula in any of the equations.
Multiply equation A by 5/3 t.o get,
5/3(2/3x) + 5/3(3/5y) = 5/3(12)
10/9x + y = 20
y = 20 - 10/9x
substituting for y into equation b, we have:
5/2(20 - 10/9x) - 3x = 6
50 - 25/9x - 3x = 6
52/9x = 44
52x = 396
The expression that gives the value of x is: 52x = 396
Hence, x = 396/52 = 99/13
y = 20 - 10/9(99/13) = 20 - 110/13 = 150/13
Hence The solution for the system of equations is: (99/13, 150/13)
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Can someone help me? I’ll give brainliest to whoever gets it right first
Answer:
the measure of line AD is 8
Step-by-step explanation:
lines AD and BC are equal, due to the markings on the lines
this means that if line BC is 8, than line AD is also 8
round 0.3391 to the nearest thousandth
Answer:
0.339
Step-by-step explanation:
Hope it helped!
Hii!
___________________________________________________________
Answer: 0.339
Explanation:
Rounding Rules
There are two rounding rules that will help us whenever we need to round a number! These are the rules.
If the number that you need to round is followed by a digit that is less than 5, you round down.If the number that you need to round is followed by a digit that is either greater than or equal to 5, you round up.---
Now that we know the rules, let's get down to solving our problem! ^^
The nearest thousandth is 3 decimal places.
_._ _ _ <==== Nearest thousandth
The third number after the decimal point is 9. After it is a digit that is less than 5. According to the rounding rules, we should round down.
[tex]\boldsymbol{0.3391=== > 0.339}[/tex]
--
Hope that this helped! Best wishes.
--
Based on local population projections for 2010, school district 31 will lose 5 teaching positions, district 222 will lose 5 teachers, and district 225 will lose 2. Write a
signed number that represents the total number of teachers that these three school districts are projected to lose.
What is the signed number that represents the total number of positions that these three districts are projected to lose?
Answer:
2+3+4 = 9
Add the three numbers of the three school districts that project to lose.
Mountain Climbing Gym has a gym registration fee of $30 and then charges $55 per month for all access climbing.
Susie wanted to model what she has spent in total on the climbing gym at any given month in the future.
Fill in the blanks for the equation if C = total Cost and m = number of months.
Answer:
C=55m + 30
Step-by-step explanation:
You would multiply 55 by the number of months so you'd get 55m, and since 30 is a one time fee you would just add 30 to your monthly payment.
Suppose that prices of recently sold homes in one neighborhood have a mean of $220,000 with a standard deviation of $7450. Using Chebyshev's Theorem, what is the minimum percentage of recently sold homes with prices between $197,650 and $242,350? Round your answer to one decimal place.
The minimum percentage of recently sold homes with prices between $197,650 and $242,350 is 88.9%.
What is Mean ?Mean is the ratio of the sum of all the data points to the number of data points.
It is given that
mean of $220,000 with a standard deviation of $7450.
The range is given , let the range is represented by x - --y
It is given that x = 197650 and y = 242350
Let the number of homes sold is k
To determine the value of k
upper level = (y-mean)/standard deviation = (242350-220000)/7450 = 3
lower level = (mean-x)/standard deviation = (220000-197650)/7450 = 3
probability = 1-(1/k²)
k= 3
= 1 - (1/3^2)
= 1 - 1/9
= 0.889 or 88.9%
So, the minimum percentage of recently sold homes with prices between $197,650 and $242,350 is 88.9%.
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Find the midpoint of the line segment whose endpoints are given. (9,3), (10,- 10)
Answer:
Step-by-step explanation:
(xm , ym ) = x1 + x2 / 2 and y1 + y2 / 2
= 9 +3 / 2 = 10 -10 / 2
= 12/2 = 0/2
= 6 = 0
So midpoints are (6 , 0)
Answer:
midpoint = [tex](9\frac{1}{2} , -3\frac{1}{2} )[/tex]
Step-by-step explanation:
To find the midpoint of a line segment, you have to find the average of the x and y-values of the end-points, i.e., add the x-coordinate values and divide the answer by 2, and do the same for the y-coordinate values.
• midpoint = [tex](\frac{x_{2} + x_1}{2}, \frac{y_2 + y_1}{2} )[/tex]
= [tex](\frac{9 + 10}{2}, \frac{3 + (-10)}{2} )[/tex]
= [tex](\frac{19}{2}, \frac{-7}{2} )[/tex]
= [tex](9\frac{1}{2} , -3\frac{1}{2} )[/tex]
Two buses leave a station at the same time and travel in opposite directions. One bus travels12m/hrslower than the other. If the two buses are 765 miles apart after 6 hours, what is the rate of each bus?
distance = speed * time
the first bus speed = x
second bus = x - 12
the sum of distance = 765 miles
first distance = 6x
second distance = 6 (x -12)
6x + 6(x-12) = 765
x + x -12 = 127.5
2x = 139.5
x = 69.75 mi/h which is the faster bus
the second bus speed = 57.75 mi/h
Find the inverse of the function.
y=x+9
Answer: [tex]y=x-9[/tex]
Step-by-step explanation:
To find the inverse of a function you must first swap the places of x and y
[tex]x=y+9[/tex]
Now solve for y
Step 1: Flip the equation.
[tex]y+9=x[/tex]
Step 2: Subtract 9 from both sides.
[tex]y+9-9=x-9\\y=x-9[/tex]
julie ran a race 2 minutes faster than teri did. if teri ran the race in 28 minutes, what equation would be used to find the number of minutes teri took to run the race
Th equation that can be used to find the umber of minutes Teri ran is m + 2 = 28 minutes.
How many minutes did it take Teri to run the race?Addition is a mathematical operation that is used to determine the sum of two or more numbers.
The total minutes run by Julie = minutes ran by Teri + 2
28 = m + 2
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what is the domain of the ordered pair shown in the graph?
Answer:
D.
Step-by-step explanation:
It is the only one that contains all the x-values of the points. (Domain is the set of x-values).
Find the perimeter of the following shape, given its curves are made from parts of circles.
Give your answers in terms of .
4cm
4cm
4cm
The diagram is not drawn to scale.
Using the diagram, if angle 3 + angle 4 is a straight line then what is the total
measure?
Answer: 180 degrees
Step-by-step explanation:
Angles on a line add to 180 degrees since they form a straight angle.
Match each fraction to a reasonable estimate.
(-6/11)
(-7/9)
(-3/13)
(-1/4)
(-3/4)
(-1/2)
Which one goes with each?
Answer:
-6/11 goes with -1/2
-7/9 goes with -3/4
-3/13 goes with -1/4
Step-by-step explanation:
6/11 is close to 6/12 which is the same as 1/2, so -6/11 goes with -1/2
7/9 is close to 6.75/9 which is 3/4, so -7/9 is close to -3/4
3/13 is close to 3/12 which is the same as 1/4, so -3/13 goes with -1/4
When we're solving minimum or maximum problems, are we h or the constant k? looking for the constant
In solving minimum and maximum problems, result we are looking for would be the constant, k.
What is being solved for in minimum and maximum problems?When looking for the minimum functional value, we are looking for the constant, k because it can be thought of as the absolute minimum value.
An open parabola would then have k as the maximum functional value which means that the constant k is the value being sought.
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How many solutions exist for the given equation?
3(x - 2) = 22 -x
Answer:
One solution
Step-by-step explanation:
The equation can be rewrite as 3x - 6 = 22 - x
so we try to get all the x on one side so we add x and 6 to both sides so we get 4x = 28 then we divide by 4 both side and get x=7
help! asap! algebra 2
We can subtract the function that represents the cost in 2000 from the function that represents the cost in 1990.
Doing this gives us [tex](-20t^{2}+1000)-(-10t^{2}+1500)=\boxed{-10t^{2}-500}[/tex]
A consultant needs to make at least $600 this week. She earns $120 for each
new written piece and $60 for each review. Which of the following inequalities
represents the possible combinations of reviews and new written pieces that
she must complete?
OA. 120x+60 y ≤ 600
OB. 120x+60y < 600
O C. 120x+60y 2 600
OD. 120x+60y > 600
SUBMIT
consider the parabola given by the equation:
f(x)=2x^2+12-9
find the following for this parabola:
a) the vertex
b) the vertical intercept is the point
c) find the coordinates of the two x-intercept of the parabola and write them as a list, separated by commas
Answer:
First simply it as 2x²+3
(a) vertex (0,3)
(b)f(0)=3
(c) no x-intercept
Which graph represents the function f(x)=−3x−2?
Answer:
Step-by-step explanation:
