Karen runs 7 miles in 50 minutes. At the same rate, how many miles would she run in 75 minutes?

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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|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}

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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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.

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).

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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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

Answer:

the answer is 4gn Puig IT in

Answer:

false

Step-by-step explanation:

the answer is x=70

Answer: 180 degrees

Step-by-step explanation:

Angles on a line add to 180 degrees since they form a straight angle.

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.

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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Answer:

h(-7) = 44

Step-by-step explanation:

h(x) = h (-7) means x= -7

h(x) = (-7)² - 5

49 - 5

44

The flux is 9.

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]

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]

Answer:

Step-by-step explanation:

Answer:

etrf4f3dvef3rf3rfr2wrgwrf2rg3rf3rgerferferfef I'm

The minimum percentage of recently sold homes with prices between $197,650 and $242,350 is 88.9%.

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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Answer:

$0.90

Step-by-step explanation:

If each piece of chocolate is $1, then 8 pieces is $8. Wei Xun bought 8 pieces of chocolate and 10 lollipops, which came out to $17. The chocolate was $8 total, leaving $9 for the 10 lollipops. 9/10 = 0.9. So, each lollipop was $0.90, or 90 cents.

Answer:

a = 1

b = 2

c = 1

Factored form: (y + 1)^2 or (y + 1)(y + 1)

Step-by-step explanation:

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

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 $

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

Answer:

0.339

Step-by-step explanation:

Hope it helped!

Hii!

___________________________________________________________

Answer: 0.339

Explanation:

There are two rounding rules that will help us whenever we need to round a number! These are the rules.

---

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.

--

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]

Answer:

[tex]20a^3b^3[/tex]

Step-by-step explanation:

Binomial Series

[tex](a+b)^n=a^n+\dfrac{n!}{1!(n-1)!}a^{n-1}b+\dfrac{n!}{2!(n-2)!}a^{n-2}b^2+...+\dfrac{n!}{r!(n-r)!}a^{n-r}b^r+...+b^n[/tex]

Factorial is denoted by an exclamation mark "!" placed after the number. It means to multiply all whole numbers from the given number down to 1.

Example:  4! = 4 × 3 × 2 × 1

Therefore, the fourth term in the binomial expansion (a + b)⁶ is:

[tex]\implies \dfrac{n!}{3!(n-3)!}a^{n-3}b^3[/tex]

[tex]\implies \dfrac{6!}{3!(6-3)!}a^{6-3}b^3[/tex]

[tex]\implies \dfrac{6!}{3!3!}a^{3}b^3[/tex]

[tex]\implies \left(\dfrac{6 \times 5 \times 4 \times \diagup\!\!\!\!3 \times \diagup\!\!\!\!2 \times \diagup\!\!\!\!1}{3 \times 2 \times 1 \times \diagup\!\!\!\!3 \times \diagup\!\!\!\!2 \times \diagup\!\!\!\!1}\right)a^{3}b^3[/tex]

[tex]\implies \left(\dfrac{120}{6}\right)a^{3}b^3[/tex]

[tex]\implies 20a^3b^3[/tex]

Answer:

2+3+4 = 9

Add the three numbers of the three school districts that project to lose.

Answer:

First simply it as 2x²+3

(a) vertex (0,3)

(b)f(0)=3

(c) no x-intercept

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]

Th equation that can be used to find the umber of minutes Teri ran is m + 2 = 28 minutes.

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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