Translate to an equation. Then solve the equation.
Seven times the difference of some number and 2 amounts to the quotient of 112 and 8.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. The centre of circle x2+y2+4x-6y+4=0 is (-2,3) and radius is 3.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

The given equation is x2+y2+4x-6y+4=0.

The standard form of circle is (x-h)^2+(y-k)^2=r^2

where (h,k) is centre and r is the radius of the circle.

We need to convert x2+y2+4x-6y+4=0 to standard form.

x2+4x+y2-6y=-4.

Add +4 and +9 on both sides

(x2+4x+4)+(y2-6y+9)=-4+4+9

(x2+4x+4)+(y2-6y+9)=9

(x+2)^2+(y-3)^2=3^2

When we compare the above equation with standard form we get

centre (-2,3) and radius is 3.

Therefore the center and radius of the circle x2+y2+4x-6y+4=0 is (-2, 3) and 3.

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Answer:

50

Step-by-step explanation:

So, put 2 hours into minutes. You get 120. Now, seeing how you have 20 song requests, and each one takes 3.5 minutes, multiply those two values. Now you have 70. After doing that, just subtract 70 from 120 and get 50.

The height of each story is 20 feet.

The value of x is 3 feet.

The score on the third quiz is 10

The number of action figures that would be produced on Friday is 182.

The equation that can be used to determine the height of each story is:

46 = x + x + 6

46 = 2x + 6

46 - 6 = 2x

40 = 2x

x = 40 / 2

x = 20 feet

The equation that can be used to solve for x is:

35 = 5x + 5x + 5

35 - 5 = 5x + 5x

30 = 10x

x = 30 / 10

x = 3 feet

Total quiz score = score on first quiz + score on second quiz + score on third quiz

(15 x 3) = 24 + 11 + score on third quiz

45 = 35 + score on third quiz

score on third quiz = 45 - 35

score on third quiz = 10

x = total amount of figures produced in a week - sum of figures produced from Monday to Thursday

(50 x 5) - (12 + 12 + 16 + 28)

250 - 68

X = 182

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Based on the miles that each car can travel on, the unit rate of miles per gallon for each car is:

The car that can therefore travel the greater distance on 1 gallon of gasoline is the Blue car.

The blue car can travel 38.5 miles on 1.25 gallons of gasoline. The unit rate is:
= 38.5 / 1.25

= 30.8 miles per gallon

The red car can travel 22/5 miles on 0.80 gallons of gasoline so the unit rate is:

= 22/5 ÷ 0.80

= 5.5 miles per gallon

The blue car can therefore travel the greater distance on 1 gallon of gasoline.

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Answer:

x =[tex] \frac{45}{7} [/tex]

Step-by-step explanation:

7x + y = 48

substitute y with 3 as given so,

7x + 3 = 48

7x = 48 - 3

7x = 45

x = 45 ÷ 7

x = [tex] \frac{45}{7} [/tex]

hope this helps

The amount that would be added to Beginning Retained Earnings balance to determine Ending Retained Earnings Balance is net income of $14,640

The  amount would be  subtracted from Beginning Retained Earnings balance to determine Ending Retained Earnings Balance is the cash dividends of $1,000

What is net income?

The net income is the excess of fees earned by Adventure Travel  in the year ended  over its total expenses, in essence, we need to determine its total expenses first and foremost, which comprises of salaries expense, rent expense, depreciation expense, advertising expense and office supplies expense

total expenses=32,800+16,800+3960+4000+2800

total expenses=60,360

fees earned=75,000

net income =fees earned-total expenses

net income=75,000-60,360

net income=$14,640

Now the closing retained earnings comprises of beginning retained earnings plus the net income minus the cash dividends paid

Retained earnings=$14,640+$ 10,260-$1,000

Retained earnings=$23,900

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Answer:

No

Step-by-step explanation:

An example:

Look where two walls meet. They meet at a vertical line. Let's call that line A.

Now look at where the ceiling and another wall meet (this wall is not the same as the previous two walls mentioned). The ceiling and this new wall meet at line B

Lines A and B are skew lines since they'll never cross even if you extend them out forever. They aren't parallel lines either because they don't point in the same 3D direction.

Check out the diagram below.

The value of x is for the given equation is 7/2.

An algebraic expression (or variable expression) is a term that has been combined with addition, subtraction, multiplication, and division operations.

To simplify an algebraic expression, we simply combine similar terms. As a result, variables with similar characteristics will be combined. The same abilities will now be created by combining similar variables.

The given equation is 4x-(10-x) =15/2.

4x - 10 + x + 15/2

5x - 10 = 15/2

Dividing both sides by 5 to obtain:

x - 2 = 3/2

Multiply both sides by 2 to get:

2x - 4 = 3

2x = 3 + 4
x = 7/2

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The mean score of all of these students together, rounded to 1 decimal place is 84.3

What is the mean score in each case?

The mean score in each test taken is the total scores of all students that took the test divided by the number of students, in essence, the total score is determined as the mean score multiplied by number of students

total score for 57 students=87.1*57

total score for 57 students= 4,964.7

total score for 10 students=68.6*10

total score for 10 students=686.0

mean score of all of these students together=(4,964.7+686.0)/(57+10)

mean score of all of these students together= 84.3

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Answer:

324309

 doctors were registered that year.

Step-by-step explanation:

The questions says, "18.1% of all registered doctors are females"

(Consider, total number of registered doctors as [tex]x[/tex])

that's, 18.1 % of [tex]x[/tex] are female.

and 18.1% of [tex]x[/tex] is 58,700

.

Answer:

175,

Step-by-step explanation:

perfect cube needs an extra 7 and two 5s.When u put these numbers you will see

Answer:

I LOVE GREAT BRITINNNNNNN

Step-by-step explanation:

Answer:

It will take 2.2 hours for the trains to meet.

Step-by-step explanation:

Given,

Distance between two trains = 396 miles

Speed of one train = 95 mph

Speed of other train = 85 mph

Combined speed of trains = 95+85 = 180 mph

Distance = Speed * Time

Time =

Time =

Time = 2.2 hours

It will take 2.2 hours for the trains to meet.

Keywords: speed, distance

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Step-by-step explanation:

The value of x is 6 for the data having the median as 9.

We are given some data:

x - 4, x, 2 x and 2 x + 12

We are also given that the median of these terms = 9

M = 9

Now, we have to find the value of x

Now, we know that the median of some data having even values will be:

M = 2nd term + 3rd term / 2

M = x + 2 x / 2

9 = 3 x / 2

3 x = 18

x = 18 / 3

x = 6

Therefore, we get that, the value of x is 6 for the data having the median as 9.

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Answer:

Step-by-step explanation:

f(x) = x^2 + 4x is specified as a function. When the x is replaced in "f(x)" is replaced with a number, you treat it as a variable.

In this case, f(-3) is almost exactly like saying x = -3.

Everywhere x is in the function is replaced with -3, because you are plugging it in to find a value. Here is a demonstration:

f(-3) = (-3)^2 + 4(-3)

f(-3) = 9 - 12

f(-3) = -3

The answer to your question is -3. Don't be afraid to ask anymore questions regarding this if you are confused.

Answer:

(0,3) (3,5)

Step-by-step explanation:

You already have a point of (0,3) so graph that point and then using the slope go up 2 and right 3 so the other point you'll have is (3,5).

Equation: y = 2/3x + 3

Perpendicular slope is opposite sign reciprocal i.e. -3/2

Equation: y = -3/2x + 3

points on graph (0,3) (2,0)

Answer: [tex]-\frac{43}{6}d - \frac{1}{8}[/tex]

Step-by-step explanation:

Convert everything to improper fractions:

[tex](-\frac{10}{3}d+\frac{3}{4}) - (\frac{23}{6}d-\frac{7}{8}) \\[/tex]

Multiply right side by two to get common denominator and distribute negative sign on to both terms in the second set of parenthesis:

 [tex]-\frac{20}{6}d+\frac{6}{8}-\frac{23}{6}d-\frac{7}{8}[/tex]

Combine like terms:

[tex]= -\frac{43}{6}d-\frac{1}{8}[/tex]

===========================================================

Explanation:

M is at 2 and J is at 18

This is a gap of 18-2 = 16

The ratio 2:3 has 2+3 = 5 parts total. Divide the gap of 16 into 5 equal parts to get 16/5 = 3.2 units

Each part is 3.2 units wide

Double this to get 2*3.2 = 6.4; the doubling is because of the "2" in "2:3"

Now add 6.4 to M = 2 to get 2+6.4 = 8.4 which is the location of point X

-----------------------

Check:

Segment MX is 8.4 - 2 = 6.4 units long

Segment XJ is 18-8.4 = 9.6 units long

The ratio 6.4:9.6 is the same as 64:96 and it fully reduces to 2:3 to confirm the answer. Or you could notice that (6.4)/(9.6) = 64/96 = 2/3

Answer:

No, it is not the solution.

Step-by-step explanation:

-4(15)-6=54

-60-6=54

-66=54

nope

First substitute [tex]x=\tan^{-1}(y)[/tex] to rewrite the integral as

[tex]\displaystyle \int_0^{\pi/4} \sqrt{\tan(x) - \tan^2(x)} \, dx = \int_0^1 \frac{\sqrt{y-y^2}}{1+y^2} \, dy[/tex]

Now use an Euler substitution, [tex]z=\frac{\sqrt{y-y^2}}y[/tex] to rewrite it again as

[tex]\displaystyle \int_0^{\pi/4} \sqrt{\tan(x) - \tan^2(x)} \, dx = 2 \int_0^\infty \frac{t^2}{(t^2+1)^2 + 1) (t^2 + 1)} \, dt[/tex]

where we take

[tex]\sqrt{y - y^2} = \sqrt{-y(y-1)} = yt \implies y = \dfrac1{1+t^2} \text{ and } dy = -\dfrac{2t}{(1+t^2)^2} \, dt[/tex]

Partial fractions:

[tex]\displaystyle \frac{t^2}{((t^2+1)^2+1) (t^2 + 1)} = \dfrac{t^2+2}{t^4+2t^2+2} - \dfrac1{t^2+1}[/tex]

so that

[tex]\displaystyle \int_0^{\pi/4} \sqrt{\tan(x) - \tan^2(x)} \, dx = 2 \left(\int_0^\infty \frac{t^2+2}{t^4+2t^2+2} \, dt - \int_0^\infty \frac{dt}{t^2+1}\right)[/tex]

The second integral is trivial,

[tex]\displaystyle \int_0^\infty \frac{dt}{t^2+1} = \lim_{t\to\infty}\tan^{-1}(t) - \tan^{-1}(0) = \frac\pi2[/tex]

For the other, I'm compelled to use the residue theorem, though real methods are doable too (e.g. trig substitution). Consider the contour integral

[tex]\displaystyle \int_\Gamma f(z) \, dz = \int_\Gamma \frac{z^2+2}{z^4+2z^2+2} \, dz[/tex]

where [tex]\Gamma[/tex] is a semicircle in the upper half of the complex plane, and its diameter lies on the real axis connecting [tex]-R[/tex] to [tex]R[/tex]. The value of this integral is 2πi times the sum of the residues in the upper half-plane. It's fairly straightforward to convince ourselves that the integral along the circular arc vanishes as [tex]R\to\infty[/tex], so the contour integral converges to the integral over the entire real line. Note that

[tex]\displaystyle 2 \int_0^\infty \frac{t^2+2}{t^4+2t^2+2} \, dt = \int_{-\infty}^\infty \frac{t^2+2}{t^4+2t^2+2} \, dt[/tex]

since the integrand is even.

Find the poles of [tex]f(z)[/tex].

[tex]z^4 + 2z^2 + 2 = 0 \\\\ ~~~~ \implies (z^2+1)^2 = -1 \\\\ ~~~~ \implies z^2 = -1 \pm i \\\\ ~~~~ \implies z = \pm \sqrt{-1 \pm i} = \sqrt[4]{2}\, e^{\pm i(3\pi/8 + \pi k)}[/tex]

where [tex]k\in\{0,1\}[/tex].

The two poles we care about are at [tex]z_1=\sqrt[4]{2}\,e^{i\,3\pi/8}[/tex] and [tex]z_2=\sqrt[4]{2}\,e^{-i\,11\pi/8}[/tex]. Compute the residues at each one.

[tex]\displaystyle \mathrm{Res}\left\{f(z),z=z_1\right\} = \lim_{z\to z_1} \frac{f(z)}{z-z_1} = -\frac1{2^{7/4}}\,ie^{-i\,\pi/8} \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~= -\frac1{2^{7/4}} \left(\sin\left(\frac\pi8\right) + i \cos\left(\frac\pi8\right)\right)[/tex]

[tex]\displaystyle \mathrm{Res}\left\{f(z),z=z_2\right\} = \lim_{z\to z_2} \frac{f(z)}{z-z_2} = -\frac1{2^{7/4}}\,ie^{i\,\pi/8} \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~= \frac1{2^{7/4}} \left(\sin\left(\frac\pi8\right) - i \cos\left(\frac\pi8\right)\right)[/tex]

By the residue theorem,

[tex]\displaystyle \int f(z) \, dz = 2\pi i \sum_{\rm poles} \mathrm{Res}\{f(z)\} = \frac{4\pi}{2^{7/4}} \cos\left(\frac\pi8\right)[/tex]

We also have

[tex]\displaystyle \cos^2\left(\dfrac\pi8\right) = \dfrac{1 + \cos\left(\frac\pi4\right)}2 = \dfrac{2 + \sqrt2}4 \implies \cos\left(\frac\pi8\right) = \dfrac{\sqrt{2+\sqrt2}}2[/tex]

Then the remaining integral is

[tex]\displaystyle \int_0^\infty \frac{t^2+2}{t^4+2t^2+2} \, dt = \frac{4\pi}{2^{7/4}} \cos\left(\frac\pi8\right) = \sqrt{\frac12 + \frac1{\sqrt2}} \, \pi[/tex]

It follows that

[tex]\displaystyle \int_0^{\pi/4} \sqrt{\tan(x) - \tan^2(x)} \, dx = \boxed{\left(\sqrt{\frac12 + \frac1{\sqrt2}} - 1\right) \pi}[/tex]

Tim's weight is 280 pounds.

Let t, j and r represent Tim's, Jim's and George's weight respectively.

The following equations can be determined giving the information in the question:

t = 2j equation 1

j = g - 50 equation 2

r = 10 + g equation 3

r = 200

Substitute for r in equation 3 : 200 = 10 + g

g = 200 - 10

g = 190

Substitute for g in equation 2 : j = 190 - 50 = 140

Substitute for g in equation 3: t = 2(140)

140 x 2 = 280

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Question 1

Opposite sides of a trapezoid are parallel. So, by the same-side interior angles theorem,

[tex]-16x+10x+86=180 \\ \\ 10x+70=180 \\ \\ 10x=110 \\ \\ x=11[/tex]

Question 2

Opposite sides of a trapezoid are parallel. So, by the same-side interior angles theorem,

[tex]9x+30+7x-10=180 \\ \\ 16x+20=180 \\ \\ 16x=160 \\ \\ x=10[/tex]

Answer:

Step-by-step explanation:

Dont really understand what your asking, is it fx=x+1? If so this should be it:

Q and R are collinear because they lie in the same straight line.

Check whether Q and R are collinear from the given figure.

Collinear points are the points that lie on the same straight line or in a single line. If two or more two points lie on a line close to or far from each other, then they are said to be collinear, in Euclidean geometry.

Here, Q and R are collinear because they lie in the same straight line.

A set of points in space are coplanar if there exists a geometric plane that contains them all.

Point S is outside the planes, so point S is non-coplanar with either plane.

The intersection of two planes is always a line.

The intersection between the two planes creates a line.

Line l intersects two planes V and W.

Therefore, Q and R are collinear because they lie in the same straight line.

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Answer:

i dont understand what is this

Answer:

Step-by-step explanation: per means divide and capita means person

so you would divide

$53143 by 1.3333333  to get your answer $ 39857 since you are rounding to the nearest dollar